[
    {
        "q_id": "9772_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            4,
            6,
            7,
            8,
            9,
            11,
            14,
            15,
            16,
            20,
            22,
            24,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            38,
            39,
            40,
            43,
            44,
            45,
            49,
            50,
            51,
            52,
            53,
            54,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            66,
            68,
            70,
            71,
            74,
            75,
            77,
            79,
            80,
            81,
            82,
            83,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            99,
            100,
            103,
            104,
            108,
            109,
            111,
            112,
            113,
            114,
            116,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            98,
            107,
            115
        ],
        "rewards": [
            [
                9.422444815765128e-07,
                1.0677026154806063e-06,
                9.422448185435711e-07,
                1.5534977545886537e-06,
                1.209865539295696e-06,
                5.043474081993875e-07,
                1.5534975693979422e-06,
                6.475949526020042e-07,
                1.5534973841895917e-06,
                8.315279285351409e-07
            ],
            [
                3.288748281295496e-06,
                2.2603251062270446e-06,
                NaN,
                1.209866260432471e-06,
                1.2098655392921197e-06,
                1.5534983101602148e-06,
                8.315277302857965e-07,
                1.7603434231777837e-06,
                7.338210680021253e-07,
                NaN
            ],
            [
                8.315278294114555e-07,
                3.726638839878908e-06,
                3.288748281329893e-06,
                2.902313023130843e-06,
                1.5534971990126997e-06,
                6.475950298011458e-07,
                8.315281267861397e-07,
                1.209865539295696e-06,
                7.338213304363436e-07,
                1.760342793638743e-06
            ],
            [
                0.0,
                3.288750633518874e-06,
                5.422217677078203e-06,
                6.144173137126169e-06,
                2.2603237589542675e-06,
                1.0129989772532511e-05,
                4.785095065171522e-06,
                2.9023126771227976e-06,
                1.7603430034867993e-06,
                4.222832941142044e-06
            ],
            [
                1.760343633031919e-06,
                8.315278294072958e-07,
                2.5612828213934817e-06,
                3.2887506336235617e-06,
                1.5534971990126997e-06,
                1.5534983101602148e-06,
                5.715003789017068e-07,
                1.3709573702822306e-06,
                1.994729008145876e-06,
                5.043474081993875e-07
            ],
            [
                0.0001398221240496514,
                3.288750241561788e-06,
                0.9999546021265855,
                4.2228334445370225e-06,
                4.2228324377164004e-06,
                1.0129993395088066e-05,
                1.7603438428800754e-06,
                1.9947297215043796e-06,
                2.7535700949523498e-05,
                1.0129995809247506e-05
            ],
            [
                3.288749065423109e-06,
                1.7603434231833873e-06,
                7.338210680021253e-07,
                1.8925141472773765e-05,
                3.288750633488963e-06,
                5.043473480766399e-07,
                1.0677033791583005e-06,
                2.7535694382378416e-05,
                7.338212429562581e-07,
                1.0129988564578197e-05
            ],
            [
                4.785095065204162e-06,
                NaN,
                0.9999724643025077,
                1.9947292459347367e-06,
                0.9999417087284312,
                6.144172404693786e-06,
                5.422219616140078e-06,
                6.475945666063607e-07,
                NaN,
                3.12019039369228e-05
            ],
            [
                4.4508515805735777e-07,
                NaN,
                7.338207180864763e-07,
                NaN,
                5.715004470334646e-07,
                9.422445939054222e-07,
                2.260325375664839e-06,
                2.9023109472494878e-06,
                1.0677032518814388e-06,
                2.561281294760143e-06
            ],
            [
                3.4663249714325014e-07,
                3.46632497145457e-07,
                3.466325797888292e-07,
                3.927860597945825e-07,
                1.2098652508287273e-06,
                1.6373764721072816e-07,
                2.3823702359290413e-07,
                3.059021904571643e-07,
                5.04347348075149e-07,
                4.450849988758202e-07
            ],
            [
                2.2603234895372223e-06,
                3.288747889284851e-06,
                2.5612828213934817e-06,
                1.7603432133296774e-06,
                1.0129992187400498e-05,
                1.4738987243478167e-05,
                1.7603440527286572e-06,
                6.962257079832313e-06,
                3.288748281329893e-06,
                5.144222592963322e-05
            ],
            [
                0.00012339454558103757,
                5.422217030747413e-06,
                4.0063711294555596e-05,
                6.9622595696935874e-06,
                2.9023112931873767e-06,
                0.00012339460437519212,
                1.30071315662049e-05,
                2.26032402841657e-06,
                6.144175334468545e-06,
                6.605215256765022e-05
            ],
            [
                9.610238067382736e-05,
                NaN,
                2.144495097113319e-05,
                5.422219615898437e-06,
                2.561282516042282e-06,
                2.2603251061664e-06,
                1.3007123813193233e-05,
                4.222835457526079e-06,
                1.2098658277082653e-06,
                3.726639284125553e-06
            ],
            [
                4.222835458175145e-06,
                0.9999986290429587,
                2.260325106237323e-06,
                3.288749065423109e-06,
                8.939700566801578e-06,
                2.260325106237323e-06,
                1.9947301970972664e-06,
                2.5612831267086116e-06,
                2.5612825160562587e-06,
                NaN
            ],
            [
                3.7266406168624155e-06,
                1.0677029973114952e-06,
                2.5612831267202583e-06,
                1.2098656835224664e-06,
                1.209866260432471e-06,
                4.222833444590791e-06,
                1.0677032518578904e-06,
                1.0677032518785256e-06,
                1.5534981249697903e-06,
                2.90231094723893e-06
            ],
            [
                1.0677027427525368e-06,
                5.715003789017068e-07,
                2.3823702359290413e-07,
                1.5534973841895917e-06,
                3.46632497145457e-07,
                4.450848927621807e-07,
                3.927860597935108e-07,
                9.422445939054222e-07,
                4.4508510499849186e-07,
                5.04347528440776e-07
            ],
            [
                1.670141786295194e-05,
                2.561281905390075e-06,
                4.222833947960866e-06,
                6.962257909785973e-06,
                2.2603240284371276e-06,
                2.7535691100960147e-05,
                6.962255419868303e-06,
                1.6701417862648148e-05,
                7.48462005189952e-05,
                4.222834451382849e-06
            ],
            [
                1.3709578605617394e-06,
                1.0677028700320085e-06,
                4.222831934052698e-06,
                1.9947304348595095e-06,
                NaN,
                1.9947306726594253e-06,
                3.2887486731252264e-06,
                7.338207180864763e-07,
                1.0677032518700286e-06,
                3.2887482810382622e-06
            ],
            [
                1.8925148241872038e-05,
                6.144175334468545e-06,
                NaN,
                1.370957860576702e-06,
                7.889260704732132e-06,
                5.422219616265831e-06,
                7.889261645090304e-06,
                1.0129993395336818e-05,
                1.8925143729575624e-05,
                8.939694172957213e-06
            ],
            [
                6.1441724046434924e-06,
                5.422218323487975e-06,
                8.315281267861397e-07,
                2.7535697667202906e-05,
                0.9999938558268755,
                7.338208055536515e-07,
                1.7603425837855082e-06,
                3.7266388398585725e-06,
                6.962255419931625e-06,
                3.288748673265808e-06
            ],
            [
                NaN,
                5.829126555256903e-05,
                NaN,
                1.0129993395217047e-05,
                8.939694172867777e-06,
                1.4738983729053029e-05,
                2.902312331170226e-06,
                0.00010889693530623988,
                5.422217677078203e-06,
                1.3709575337078829e-06
            ],
            [
                1.994730672675753e-06,
                1.7603438428800754e-06,
                5.715003789046955e-07,
                3.9278634073625165e-07,
                6.475947210031623e-07,
                NaN,
                1.0677028700363782e-06,
                6.144177531811707e-06,
                4.222832437798974e-06,
                1.2098659719757836e-06
            ],
            [
                3.1201900218617364e-05,
                3.535624650150453e-05,
                1.7603438428800754e-06,
                7.889260704818233e-06,
                4.0063682641226247e-05,
                0.0003353500710872051,
                5.1442195268327955e-05,
                4.785095635624897e-06,
                9.422447062294175e-07,
                4.450852111148132e-07
            ],
            [
                6.962257909785973e-06,
                2.5612828213934817e-06,
                6.144177531811707e-06,
                1.5534983101644536e-06,
                3.726638395634011e-06,
                1.209865539295696e-06,
                7.338208055664991e-07,
                6.475950298021765e-07,
                8.939695238634211e-06,
                1.8925143729954285e-05
            ],
            [
                1.2098652508424818e-06,
                2.90231094723893e-06,
                9.422445939032799e-07,
                7.338208055664991e-07,
                1.760343003481596e-06,
                1.3709576971425944e-06,
                5.715005151606823e-07,
                7.889259764517575e-06,
                1.5534981249697903e-06,
                1.5534981249697903e-06
            ],
            [
                1.7603434231833873e-06,
                1.3709568799919866e-06,
                4.222833444590791e-06,
                2.902310947190096e-06,
                7.338209805200689e-07,
                1.3709575337016483e-06,
                5.71500719545698e-07,
                3.2887490653647836e-06,
                8.939698435657833e-06,
                1.1478766757049986e-05
            ],
            [
                2.561281600086738e-06,
                6.962258739796719e-06,
                1.209866260432471e-06,
                3.2887494574832472e-06,
                1.994729008145876e-06,
                1.0677033791612137e-06,
                1.994730672675753e-06,
                2.2603251062450327e-06,
                2.2603245673443566e-06,
                1.0677027427624903e-06
            ],
            [
                1.99472900813862e-06,
                1.0677029973192638e-06,
                1.3007125363719486e-05,
                3.2887498495150166e-06,
                8.315277302819205e-07,
                8.315284241650899e-07,
                9.422448185534261e-07,
                5.422219616228845e-06,
                1.760343633031919e-06,
                1.2098658277489788e-06
            ],
            [
                6.475948754012522e-07,
                1.9947299593014888e-06,
                1.2098659719788098e-06,
                NaN,
                7.338208055664991e-07,
                3.2887506336235617e-06,
                2.9023112932296107e-06,
                8.315278294072958e-07,
                6.962259569750576e-06,
                6.962254589978262e-06
            ],
            [
                8.939699501229642e-06,
                1.012999460278499e-05,
                2.2603234895176927e-06,
                4.222833947932061e-06,
                2.9023112932045342e-06,
                6.962254589914941e-06,
                1.0129993395217047e-05,
                1.3709570434219446e-06,
                2.260324836776948e-06,
                1.6701421845057263e-05
            ],
            [
                2.902311639126627e-06,
                2.5612828213934817e-06,
                1.3709567165617364e-06,
                2.2603237589676295e-06,
                NaN,
                4.222834954753043e-06,
                1.760343003481596e-06,
                1.209865539274514e-06,
                2.9023119851781017e-06,
                1.5534983101602148e-06
            ],
            [
                5.043475284430694e-07,
                1.5534971990126997e-06,
                3.288748673265808e-06,
                6.962257079465052e-06,
                1.6701425825857226e-05,
                NaN,
                1.3007123812554424e-05,
                3.726638839806038e-06,
                5.422220262636381e-06,
                3.120191881321371e-05
            ],
            [
                7.338208055664991e-07,
                2.5612831267202583e-06,
                6.475947982022763e-07,
                1.3709570434219446e-06,
                1.994729008145876e-06,
                2.902311639183378e-06,
                1.1478764021029928e-05,
                6.475950298011458e-07,
                5.4222209089700225e-06,
                1.2098659719757836e-06
            ],
            [
                5.422220909009474e-06,
                1.9947299593078385e-06,
                1.760343213335281e-06,
                4.785094494750855e-06,
                3.12019225345861e-05,
                1.7603432133296774e-06,
                2.561281600076256e-06,
                5.8291286393273546e-05,
                3.7266410611296085e-06,
                3.2887506336086064e-06
            ],
            [
                4.222833444506298e-06,
                2.5612822107167428e-06,
                1.0677032518814388e-06,
                3.726639284017094e-06,
                9.422442569315887e-07,
                1.2098658277451275e-06,
                8.315281267834927e-07,
                1.9947301970972664e-06,
                6.144173869558639e-06,
                5.043474683156057e-07
            ],
            [
                1.7603425837855082e-06,
                4.785096776468749e-06,
                7.338208055664991e-07,
                1.994730672668496e-06,
                1.3007126914612648e-05,
                2.2603237589779086e-06,
                1.9947292459347367e-06,
                6.144176799334096e-06,
                2.9023133690980155e-06,
                8.939696304311336e-06
            ],
            [
                2.5612825160562587e-06,
                6.962257909722651e-06,
                0.00012339454553615247,
                3.7266383955882547e-06,
                2.561282516066741e-06,
                3.120190021339598e-05,
                4.222834451327159e-06,
                6.144175334418252e-06,
                4.006369219233375e-05,
                2.75356812556058e-05
            ],
            [
                2.9023119851635836e-06,
                1.6701419853518415e-05,
                1.4738983729535602e-05,
                7.484622715666203e-05,
                1.8925141472773765e-05,
                0.00013982210728420155,
                6.144172404587612e-06,
                3.72664061671159e-06,
                6.144177531767002e-06,
                6.962254589781966e-06
            ],
            [
                3.466325797896173e-07,
                2.7535704231844484e-05,
                1.5534984953453635e-06,
                1.7603440527286572e-06,
                1.012999098021058e-05,
                3.288748673360027e-06,
                9.422450431989127e-07,
                1.209865827752005e-06,
                3.2887478892683997e-06,
                8.939700567094277e-06
            ],
            [
                2.902313369111213e-06,
                4.785096206013061e-06,
                7.889262585541864e-06,
                NaN,
                2.144494330062167e-05,
                7.889266347356409e-06,
                1.0129992186202796e-05,
                6.144177531459659e-06,
                1.4738985483504099e-05,
                5.4222202624563834e-06
            ],
            [
                6.475947210046347e-07,
                3.9278610661822475e-07,
                4.4508505193932864e-07,
                1.760343213335281e-06,
                8.315283250394546e-07,
                7.338207180864763e-07,
                5.715003789046955e-07,
                1.0677026154806063e-06,
                1.553497754577351e-06,
                6.475947210046347e-07
            ],
            [
                1.9947304348862686e-06,
                4.785093924362895e-06,
                1.9947292459347367e-06,
                9.422443692574719e-07,
                6.475951069985296e-07,
                8.315277302841894e-07,
                4.450849458218309e-07,
                1.5534979397790343e-06,
                3.288748673376478e-06,
                4.450848927650143e-07
            ],
            [
                4.450852111155216e-07,
                5.71500719545698e-07,
                1.5534975693979422e-06,
                NaN,
                3.05902336324494e-07,
                9.422447062294175e-07,
                1.209866260432471e-06,
                1.7603434231833873e-06,
                1.5534971990169383e-06,
                1.2098661162056318e-06
            ],
            [
                8.939697369980456e-06,
                1.6373766672994222e-07,
                7.338209805240734e-07,
                1.3709568799879344e-06,
                1.5534977545886537e-06,
                1.1478772231086046e-05,
                3.466327450765785e-07,
                3.059021175261338e-07,
                2.2603237589779086e-06,
                1.3709568799879344e-06
            ],
            [
                1.7603432132784448e-06,
                1.9947290081177566e-06,
                4.2228339479858295e-06,
                1.994730197071414e-06,
                2.2603248367512505e-06,
                1.5534975693933505e-06,
                5.04347468318358e-07,
                1.5534971989427613e-06,
                NaN,
                9.422443692489024e-07
            ],
            [
                2.9023119851781017e-06,
                2.4300243631890864e-05,
                1.3007134667259441e-05,
                2.4300252321904572e-05,
                1.3007130015488633e-05,
                6.144172404738491e-06,
                9.422444815814404e-07,
                1.370957860576702e-06,
                2.9023112932177327e-06,
                7.338207180864763e-07
            ],
            [
                2.1024341622426268e-07,
                1.6373762769138607e-07,
                1.3709568799919866e-06,
                1.4449795205429202e-07,
                8.764249540862797e-08,
                5.715005832886879e-07,
                1.2098652508424818e-06,
                2.699577774560111e-07,
                NaN,
                3.927863407379485e-07
            ],
            [
                7.338212429537553e-07,
                NaN,
                1.3709575337078829e-06,
                1.3709572068478697e-06,
                2.902312677104321e-06,
                1.3007125363719486e-05,
                1.8925150497848527e-05,
                1.3007125363908762e-05,
                4.222831934352267e-06,
                2.260325106237323e-06
            ],
            [
                1.553498124964492e-06,
                6.962255419279419e-06,
                2.5612819054028872e-06,
                4.222831934156396e-06,
                2.2603237589779086e-06,
                5.715003789046955e-07,
                1.994729721518893e-06,
                2.26032402841657e-06,
                3.288748673295719e-06,
                4.222831934321543e-06
            ],
            [
                1.0677024881829577e-06,
                1.0677024881829577e-06,
                1.370956716529941e-06,
                1.0677026154619133e-06,
                1.7603434231705793e-06,
                6.475947981975644e-07,
                1.2098653950480359e-06,
                8.315280276456036e-07,
                1.2098652508287273e-06,
                1.209865683500459e-06
            ],
            [
                2.7535687811228037e-05,
                6.144173869558639e-06,
                4.450848927650143e-07,
                NaN,
                2.9023112932045342e-06,
                1.892515500808112e-05,
                3.2887494574518405e-06,
                1.3709576971425944e-06,
                3.120191881525687e-05,
                2.561282210729555e-06
            ],
            [
                1.9947297215043796e-06,
                4.785092783454444e-06,
                1.3709576971242028e-06,
                3.927863875616689e-07,
                6.962255419931625e-06,
                1.994730197090463e-06,
                1.5534977545886537e-06,
                4.785093353874907e-06,
                5.422218969818919e-06,
                3.288747889284851e-06
            ],
            [
                2.2603242978871282e-06,
                4.222834451403972e-06,
                1.7603438428800754e-06,
                2.902312677137316e-06,
                1.4738989000181669e-05,
                NaN,
                3.9278634073732336e-07,
                1.3709578605729614e-06,
                3.288749849477628e-06,
                1.5534975693979422e-06
            ],
            [
                1.0677027427624903e-06,
                2.9023123311583482e-06,
                5.04347528446051e-07,
                7.338212429582604e-07,
                1.9947292459347367e-06,
                NaN,
                8.315281267882195e-07,
                1.0677029973219343e-06,
                2.9023112932296107e-06,
                2.902312677150514e-06
            ],
            [
                NaN,
                4.222834451382849e-06,
                1.209865827752005e-06,
                4.785094494783494e-06,
                1.994729008151319e-06,
                1.994730672675753e-06,
                8.315279285370317e-07,
                7.88926446679691e-06,
                5.715003789046955e-07,
                1.4738976701411704e-05
            ],
            [
                1.7603430034867993e-06,
                8.315281267834927e-07,
                3.7266379513162962e-06,
                2.9023116392097746e-06,
                3.288749065423109e-06,
                2.902311639183378e-06,
                NaN,
                6.962255419931625e-06,
                8.939697369980456e-06,
                6.475945666063607e-07
            ],
            [
                1.4738978457872657e-05,
                1.3007125362323574e-05,
                1.7603427935518875e-06,
                3.12019262448351e-05,
                3.5356242267696286e-05,
                1.4738980215111302e-05,
                3.120192624733229e-05,
                0.00010889692226829425,
                1.6701425824307884e-05,
                1.3007131565376817e-05
            ],
            [
                8.93969950132721e-06,
                2.7535681254804434e-05,
                3.1201922533564516e-05,
                7.889261645355786e-06,
                1.012999218752948e-05,
                3.2887486733420804e-06,
                8.939697369785323e-06,
                4.785093353909723e-06,
                4.222832941142044e-06,
                1.4738983729053029e-05
            ],
            [
                2.2603242978871282e-06,
                3.927862939126708e-07,
                2.9023116391675407e-06,
                1.2098656835224664e-06,
                6.144175334468545e-06,
                3.288750241374845e-06,
                1.3709570434178922e-06,
                2.2603242978665707e-06,
                2.2603245673155757e-06,
                9.422447062202052e-07
            ],
            [
                1.994730434879465e-06,
                4.222832941193893e-06,
                1.3709568799823232e-06,
                2.9023112932045342e-06,
                3.726641061109272e-06,
                6.144176066795103e-06,
                2.1444958640087166e-05,
                9.4224425692559e-07,
                1.9947304348703948e-06,
                1.9947304348703948e-06
            ],
            [
                3.7266383956509585e-06,
                9.422442569334097e-07,
                2.2603234895372223e-06,
                NaN,
                9.422442569290178e-07,
                1.7603440527334603e-06,
                9.422450432030903e-07,
                NaN,
                1.994729008151319e-06,
                0.0009110511391935638
            ],
            [
                2.6995790618469934e-07,
                5.715003789033962e-07,
                4.222833947897496e-06,
                7.338208055664991e-07,
                8.315278294097538e-07,
                1.5534983101549167e-06,
                8.315284241650899e-07,
                1.994729483723626e-06,
                1.994729721518893e-06,
                5.043473480777865e-07
            ],
            [
                3.726638395527247e-06,
                1.2098655392871682e-06,
                7.889259764079887e-06,
                1.5534979397740895e-06,
                4.2228349546493465e-06,
                5.422217030707961e-06,
                3.7266379512857925e-06,
                2.5612812947508257e-06,
                1.9947292459265734e-06,
                6.962257079465052e-06
            ],
            [
                3.7266397283908927e-06,
                4.222834954801051e-06,
                1.2098653950692178e-06,
                1.0677026154806063e-06,
                2.382368815916736e-07,
                1.209865539295696e-06,
                1.3709573702822306e-06,
                1.209866260432471e-06,
                5.422217677152175e-06,
                6.475951069985296e-07
            ],
            [
                1.7603440527286572e-06,
                1.1478765389065974e-05,
                5.715003789033962e-07,
                1.209865539295696e-06,
                4.222833444590791e-06,
                6.962255419653012e-06,
                2.753569110256289e-05,
                4.785096205882502e-06,
                4.222833444590791e-06,
                1.012999218776902e-05
            ],
            [
                5.4222176771176554e-06,
                5.144223206152219e-05,
                3.7266406168624155e-06,
                NaN,
                2.2603248367656408e-06,
                1.0129987357287368e-05,
                8.939698435657833e-06,
                NaN,
                6.144172404693786e-06,
                NaN
            ],
            [
                1.7603430034439723e-06,
                1.2098652508287273e-06,
                1.9947294837154625e-06,
                1.994729483705484e-06,
                1.3709572068272963e-06,
                6.475947210031623e-07,
                1.553497384196656e-06,
                2.902312331170226e-06,
                1.5534979397740895e-06,
                8.315277302819205e-07
            ],
            [
                3.2887490653647836e-06,
                1.2098652508424818e-06,
                8.315283250394546e-07,
                8.315280276626197e-07,
                7.889263526345123e-06,
                8.315277302841894e-07,
                NaN,
                1.370957860576702e-06,
                1.5534975693979422e-06,
                4.4508515805735777e-07
            ],
            [
                2.430024073523505e-05,
                9.422444815814404e-07,
                9.422445939054222e-07,
                1.0677027427600627e-06,
                2.9023109471689794e-06,
                2.5612834320563895e-06,
                6.962254589978262e-06,
                1.2098656835252174e-06,
                1.3709572068553509e-06,
                1.2098659719788098e-06
            ],
            [
                1.670141786231398e-05,
                1.7603438428740716e-06,
                1.2098662604247682e-06,
                1.5534979397740895e-06,
                2.9023126769050284e-06,
                1.3007126914245925e-05,
                2.2603234895053587e-06,
                1.5534971989809095e-06,
                1.012999097997104e-05,
                1.3709575337016483e-06
            ],
            [
                4.7850933539684755e-06,
                0.0008040860564734336,
                1.370957860576702e-06,
                9.422450431954847e-07,
                NaN,
                5.71500651413193e-07,
                3.059022998581767e-07,
                5.715002426460124e-07,
                1.0677024882029858e-06,
                6.475950297993789e-07
            ],
            [
                8.315277302857965e-07,
                1.7603430034867993e-06,
                2.902312677150514e-06,
                1.2098661162056318e-06,
                2.2603253756874524e-06,
                1.9947304348595095e-06,
                7.338210680021253e-07,
                NaN,
                1.994729721518893e-06,
                1.994730672675753e-06
            ],
            [
                1.2098661162056318e-06,
                1.209865827740176e-06,
                0.9998766054265111,
                6.47595107001401e-07,
                4.78509278348926e-06,
                5.043475885688201e-07,
                4.222833947932061e-06,
                3.466326211113502e-07,
                8.315281267800897e-07,
                3.726639284144195e-06
            ],
            [
                1.2098652508347793e-06,
                4.222833947960866e-06,
                2.9023126771227976e-06,
                2.561283432035425e-06,
                1.8925152753790864e-05,
                5.422221555296344e-06,
                2.902312677137316e-06,
                1.7603434231777837e-06,
                2.2603234895289998e-06,
                1.7603425837702984e-06
            ],
            [
                4.222833947932061e-06,
                2.9023133690637e-06,
                3.7266383955882547e-06,
                2.9023119851635836e-06,
                1.4738985486265496e-05,
                5.422221555340727e-06,
                6.144174601991196e-06,
                3.12019039369228e-05,
                3.726638395634011e-06,
                8.93969310662177e-06
            ],
            [
                6.475949525919915e-07,
                NaN,
                6.475951069961737e-07,
                2.5612828213934817e-06,
                1.0129988565084915e-05,
                1.5534971989907999e-06,
                8.315282259051341e-07,
                5.043476486902204e-07,
                1.994729721518893e-06,
                3.7266410611296085e-06
            ],
            [
                1.5534981249697903e-06,
                5.422217030707961e-06,
                3.288749065406658e-06,
                1.5534975693933505e-06,
                1.5534979397740895e-06,
                1.3709576971425944e-06,
                3.726637951387472e-06,
                5.829127250060064e-05,
                3.288749065423109e-06,
                5.422220262636381e-06
            ],
            [
                2.9023119850527192e-06,
                NaN,
                4.78509392429544e-06,
                1.209865683518615e-06,
                2.7535700949523498e-05,
                4.785094494672519e-06,
                6.962259569313662e-06,
                2.1444943294263477e-05,
                8.481103127419174e-05,
                3.726639728348526e-06
            ],
            [
                1.760343213335281e-06,
                1.5534983101478522e-06,
                5.715007195431641e-07,
                2.5612819054133693e-06,
                2.90231094723893e-06,
                6.475947210012481e-07,
                1.2098661161982042e-06,
                9.422445939002803e-07,
                3.2887486732358968e-06,
                1.994729483694599e-06
            ],
            [
                4.4508526417298334e-07,
                4.450849988811838e-07,
                1.3709575337078829e-06,
                8.315281267861397e-07,
                1.3709576971425944e-06,
                4.222832437677995e-06,
                6.475948754012522e-07,
                1.760344052693435e-06,
                2.260324836787226e-06,
                1.9947292459347367e-06
            ],
            [
                3.120190393794438e-05,
                2.2603242978778778e-06,
                4.222834954778007e-06,
                5.422218969858371e-06,
                7.889259764359722e-06,
                1.2098652508391807e-06,
                5.422221555380179e-06,
                7.889260704818233e-06,
                1.8925141473186853e-05,
                1.892514598469098e-05
            ],
            [
                1.7603438428564603e-06,
                4.2228319344021954e-06,
                NaN,
                4.785092783371756e-06,
                3.2887506336086064e-06,
                1.1478765389368729e-05,
                4.785094494672519e-06,
                NaN,
                9.422448185534261e-07,
                8.939696304311336e-06
            ],
            [
                2.56128282131428e-06,
                1.3709572068478697e-06,
                1.5534977545243671e-06,
                0.0002305067706362583,
                6.962253759670401e-06,
                0.9999379495309465,
                1.4738989000181669e-05,
                6.475948754012522e-07,
                4.78509563550957e-06,
                4.006369696446335e-05
            ],
            [
                NaN,
                1.9947292459347367e-06,
                4.785095635655362e-06,
                6.962257909785973e-06,
                2.3823682479181176e-07,
                2.561281600086738e-06,
                1.444980209564556e-07,
                3.288749065423109e-06,
                5.043476486915964e-07,
                NaN
            ],
            [
                4.78509278348926e-06,
                NaN,
                2.902311639183378e-06,
                NaN,
                NaN,
                1.3007134667259441e-05,
                NaN,
                1.2098659719788098e-06,
                5.422217030707961e-06,
                1.2098655392871682e-06
            ],
            [
                1.99472900813862e-06,
                4.785093353940187e-06,
                1.5534979397790343e-06,
                1.0677024881980089e-06,
                1.8925141473978602e-05,
                1.0129988564974359e-05,
                9.610239212762526e-05,
                3.927860597945825e-07,
                1.1478766757718129e-05,
                1.3709572068522336e-06
            ],
            [
                3.4663274507713016e-07,
                9.422447062294175e-07,
                4.222835458044565e-06,
                5.715003107767143e-07,
                7.338209805240734e-07,
                9.422443692574719e-07,
                7.338207180898968e-07,
                1.1253509497883659e-07,
                4.785093353940187e-06,
                5.043472278322555e-07
            ],
            [
                1.2098656835224664e-06,
                3.2887506336086064e-06,
                1.0677032518578904e-06,
                2.9023119851899796e-06,
                3.466325797888292e-07,
                1.5534975693979422e-06,
                3.466325797888292e-07,
                1.9947304348862686e-06,
                7.338213304363436e-07,
                9.422445939032799e-07
            ],
            [
                7.338209805224048e-07,
                4.222832437798974e-06,
                4.785096206013061e-06,
                1.7603440527286572e-06,
                8.939693106873817e-06,
                2.902312677150514e-06,
                1.7603440527286572e-06,
                1.2098656835224664e-06,
                4.785094494750855e-06,
                2.2603234895289998e-06
            ],
            [
                6.962254589914941e-06,
                2.9023116392097746e-06,
                6.144176066943187e-06,
                1.2098658277489788e-06,
                5.422217677152175e-06,
                1.5534983101644536e-06,
                1.147877359872636e-05,
                2.5612816000646084e-06,
                1.5534971990169383e-06,
                4.785096776394765e-06
            ],
            [
                2.902310947208574e-06,
                1.2098659719601033e-06,
                NaN,
                1.1478770862255766e-05,
                1.5534973842030142e-06,
                7.889266347715168e-06,
                1.2098662604291696e-06,
                8.315280276546789e-07,
                5.043473480730849e-07,
                6.962255419931625e-06
            ]
        ]
    },
    {
        "q_id": "9936_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                6.47595107001401e-07,
                1.3709575336860625e-06,
                1.8553905760024476e-07,
                2.5612819054028872e-06,
                7.338211554688417e-07,
                1.2098659719788098e-06,
                2.3823690999160957e-07,
                1.2098659719716573e-06,
                1.444980726324838e-07,
                2.902313023063532e-06
            ],
            [
                1.8553919030776337e-07,
                4.691164920214251e-08,
                8.7642516304188e-08,
                5.315787506598473e-08,
                1.1253524254615121e-07,
                1.637377057673536e-07,
                1.4449798650476187e-07,
                2.1024326584582131e-07,
                1.2751910369275402e-07,
                1.637377057673536e-07
            ],
            [
                2.382369667929001e-07,
                1.4449800373065699e-07,
                3.466327450756327e-07,
                4.450849988811838e-07,
                4.450849988798682e-07,
                1.0129994602057158e-05,
                2.6995768091310296e-07,
                5.715003789033962e-07,
                2.1024334103505245e-07,
                1.6373764721072816e-07
            ],
            [
                2.3823690999160957e-07,
                1.637377057673536e-07,
                4.450849458200093e-07,
                1.637377643243723e-07,
                5.043475284430694e-07,
                2.3823690999160957e-07,
                2.902312331170226e-06,
                7.338207180898968e-07,
                8.764245361752286e-08,
                2.1024344128660572e-07
            ],
            [
                5.315786239218605e-08,
                1.855391239539711e-07,
                9.931195693628605e-08,
                2.1024341622426268e-07,
                1.5534983101478522e-06,
                6.023574911170301e-08,
                1.444980381819277e-07,
                6.023574911170301e-08,
                1.2751899728286965e-07,
                1.6373762769138607e-07
            ],
            [
                1.4449800373065699e-07,
                2.102433410343832e-07,
                2.6995771309523475e-07,
                2.382368815916736e-07,
                5.315789407666425e-08,
                4.6911638017556955e-08,
                1.444980726324838e-07,
                2.1024341622297196e-07,
                5.315787506598473e-08,
                8.764255809528314e-08
            ],
            [
                7.734415776805048e-08,
                3.059021904571643e-07,
                7.734424996967756e-08,
                9.422444815792981e-07,
                7.338207180864763e-07,
                2.6995790618252024e-07,
                1.1253518888464745e-07,
                9.422445939002803e-07,
                1.6373774480535133e-07,
                1.4449798650476187e-07
            ],
            [
                1.1253506814842375e-07,
                1.8553903548231313e-07,
                1.0129995810463632e-05,
                5.715004470295662e-07,
                7.338210680021253e-07,
                6.475947982037486e-07,
                1.9947306726594253e-06,
                8.315278294114555e-07,
                5.04347528440776e-07,
                6.144176066901277e-06
            ],
            [
                6.475945666051092e-07,
                5.715002426486762e-07,
                5.71500719545698e-07,
                2.1024339116134898e-07,
                7.338212429582604e-07,
                2.1024331597262577e-07,
                6.475945666051092e-07,
                1.7603434231777837e-06,
                3.0590237279085045e-07,
                9.422448185534261e-07
            ],
            [
                1.8553910183674878e-07,
                1.6373772528704005e-07,
                8.764241182641775e-08,
                5.715003107767143e-07,
                1.8553910183674878e-07,
                6.47595107001401e-07,
                2.6995784182183607e-07,
                3.927863407379485e-07,
                1.1253524254650944e-07,
                2.3823682479317953e-07
            ],
            [
                4.691164920214251e-08,
                5.043473480777865e-07,
                1.6373766672973748e-07,
                7.73441946488886e-08,
                2.3823682479181176e-07,
                1.6373764721072816e-07,
                7.734421308914719e-08,
                1.8553916819032217e-07,
                1.2751899728286965e-07,
                1.855391681891831e-07
            ],
            [
                3.0590226339061185e-07,
                2.699578418172324e-07,
                2.3823699519225038e-07,
                2.1024336609724313e-07,
                3.9278610661366994e-07,
                3.4663253846316044e-07,
                5.715004470243685e-07,
                3.05902226922147e-07,
                2.1024341622368903e-07,
                2.382369667914917e-07
            ],
            [
                0.9998766054549163,
                1.8553907971682908e-07,
                1.8925145985895816e-05,
                2.38237023590304e-07,
                1.444980209564556e-07,
                2.1024334103581732e-07,
                9.422444815814404e-07,
                1.0677028700422047e-06,
                5.04347528446051e-07,
                0.9999810748585525
            ],
            [
                7.338209805200689e-07,
                8.764242227418718e-08,
                1.2098662604291696e-06,
                6.023569884718319e-08,
                3.059022998576899e-07,
                5.043472879504592e-07,
                5.043475284430694e-07,
                3.4663249714451116e-07,
                1.4449795205429202e-07,
                4.691162683297406e-08
            ],
            [
                6.475949525981759e-07,
                3.927862939126708e-07,
                2.1024341622368903e-07,
                6.475950297942253e-07,
                5.715005832853093e-07,
                1.1253525596134564e-07,
                3.466325384661554e-07,
                2.6995777745711594e-07,
                3.0590226339061185e-07,
                1.855391239539711e-07
            ],
            [
                5.715007195384861e-07,
                5.715003107655392e-07,
                3.9278624708775595e-07,
                5.04347528440776e-07,
                8.315283250260307e-07,
                2.3823682479181176e-07,
                1.855391681891831e-07,
                4.450849458200093e-07,
                3.9278610661366994e-07,
                5.04347528440776e-07
            ],
            [
                0.9999993106387906,
                0.9999960330145606,
                9.422443692489024e-07,
                0.9999983463108096,
                0.9999974387187065,
                0.9999962733589406,
                2.699577452746696e-07,
                8.315283250371857e-07,
                0.9999960330136145,
                0.9999981261243943
            ],
            [
                2.3823688159237777e-07,
                2.3823685319244518e-07,
                1.8553903548231313e-07,
                9.931193325852072e-08,
                1.4449798650551755e-07,
                8.764249540862797e-08,
                1.6373766672973748e-07,
                5.043472879540142e-07,
                2.1024336609843824e-07,
                2.6995784182140636e-07
            ],
            [
                0.9999724642991594,
                0.9999992188514838,
                0.9999997761971849,
                0.9999995262092729,
                3.927862939126708e-07,
                0.9999910603005069,
                0.9999934595635582,
                0.9999980052693287,
                0.9999885212264247,
                1.0677027427471959e-06
            ],
            [
                2.6995784182073116e-07,
                1.1253510839355284e-07,
                3.0590237279032884e-07,
                5.043476486902204e-07,
                3.466327450756327e-07,
                9.422449308716635e-07,
                8.764249540862797e-08,
                2.102433159721477e-07,
                5.043474683220276e-07,
                1.5534975693979422e-06
            ],
            [
                9.931188590255539e-08,
                1.6373762769138607e-07,
                1.4449800373065699e-07,
                8.764249540862797e-08,
                1.637377448057981e-07,
                2.3823688159237777e-07,
                1.6373774480479287e-07,
                1.1253526937656726e-07,
                2.1024339116082313e-07,
                1.4449805540740185e-07
            ],
            [
                4.4508505193932864e-07,
                1.444980726324838e-07,
                1.637377057673536e-07,
                5.315784971839039e-08,
                3.4663249714325014e-07,
                1.4449802095609418e-07,
                8.764252675194995e-08,
                3.466325384661554e-07,
                1.444980726324838e-07,
                9.422443692489024e-07
            ],
            [
                4.785096776499213e-06,
                5.043472879504592e-07,
                1.7603438428460541e-06,
                5.04347287945184e-07,
                5.043475885576967e-07,
                3.059023727894942e-07,
                2.6995768091310296e-07,
                2.699577774560111e-07,
                1.855391239544352e-07,
                7.338213304283347e-07
            ],
            [
                8.315278294114555e-07,
                1.3709575337159875e-06,
                8.764252675194995e-08,
                1.209865827752005e-06,
                1.7603430034867993e-06,
                2.102433410343832e-07,
                0.99998107485629,
                1.637377448057981e-07,
                1.1253524254615121e-07,
                3.288748281329893e-06
            ],
            [
                0.9999993524049706,
                0.9999981261252877,
                0.9999960330136158,
                0.9999993524052794,
                0.9999995549148952,
                0.9999970976887079,
                0.9999994631250604,
                0.9999991148426479,
                0.9999993106391191,
                0.9999996533673791
            ],
            [
                4.785096206076165e-06,
                3.4663274507098256e-07,
                2.382369383923073e-07,
                1.6373766672888118e-07,
                3.0590226339061185e-07,
                6.475951069985296e-07,
                3.059023727894942e-07,
                4.450852111135988e-07,
                1.2751904288710323e-07,
                3.9278615344178325e-07
            ],
            [
                0.9999992188516698,
                0.9999995818811275,
                0.9999990577554065,
                0.999998126125064,
                0.9999996940978826,
                0.9999981261241704,
                0.9999994631251882,
                0.9999955048200329,
                0.9999960330140877,
                0.9999981261248407
            ],
            [
                0.9999898700078256,
                0.9999945777810364,
                0.9999898700054085,
                0.9999038975512872,
                0.9999885212332588,
                0.999984310448438,
                0.9999898700126594,
                0.9999925887183729,
                0.9999916019269751,
                0.9999843104446947
            ],
            [
                1.0677029973192638e-06,
                1.4449807263312446e-07,
                3.059021175261338e-07,
                3.927863875616689e-07,
                3.05902336324494e-07,
                8.315278294114555e-07,
                6.475945666063607e-07,
                3.927862002663297e-07,
                3.927862470899887e-07,
                4.450852641737424e-07
            ],
            [
                4.691168275589384e-08,
                2.6995768091383957e-07,
                9.422445939054222e-07,
                5.043473480777865e-07,
                9.422444815814404e-07,
                1.2098659719788098e-06,
                1.7603425837903113e-06,
                5.043472278322555e-07,
                6.47594952603035e-07,
                4.4508494582405734e-07
            ],
            [
                2.2603234895372223e-06,
                6.475950297942253e-07,
                2.561281294760143e-06,
                1.1478764021029928e-05,
                3.927860597945825e-07,
                1.2098659719757836e-06,
                2.1024336609843824e-07,
                1.3709570434178922e-06,
                1.9947292459347367e-06,
                2.69957906184239e-07
            ],
            [
                3.466325384661554e-07,
                2.1024341622368903e-07,
                3.4663262110945863e-07,
                1.275190884913241e-07,
                3.05902117523595e-07,
                5.04347348075149e-07,
                3.4663249714325014e-07,
                1.8553910183548312e-07,
                2.382369667914917e-07,
                1.994729721518893e-06
            ],
            [
                7.734418542875216e-08,
                6.023572038912295e-08,
                1.1253510839355284e-07,
                2.3823688159237777e-07,
                3.059022998569248e-07,
                2.69957906184239e-07,
                2.3823696679230424e-07,
                1.2751904288710323e-07,
                1.6373762769138607e-07,
                1.2751910369275402e-07
            ],
            [
                6.475948754012522e-07,
                1.855391239539711e-07,
                1.8553903548231313e-07,
                1.6373770576776313e-07,
                1.855391681898159e-07,
                6.023569884692295e-08,
                1.855391239539711e-07,
                3.9278634073625165e-07,
                2.6995768091310296e-07,
                8.7642516304188e-08
            ],
            [
                3.0590237278838124e-07,
                1.6373774480479287e-07,
                2.3823702359138736e-07,
                2.382368815916736e-07,
                9.422443692446175e-07,
                2.382370235922541e-07,
                2.699577774560111e-07,
                3.059023727894942e-07,
                1.0677031245905116e-06,
                2.3823690999160957e-07
            ],
            [
                4.691160446380562e-08,
                1.6373762769138607e-07,
                2.3823690999160957e-07,
                2.382369667929001e-07,
                5.04347287955046e-07,
                2.3823688159237777e-07,
                2.1024331597152624e-07,
                1.4449798650569826e-07,
                2.1024329090929374e-07,
                8.764254764780641e-08
            ],
            [
                2.102434412871794e-07,
                3.0590219045914655e-07,
                1.3007133116732079e-05,
                2.69957906184239e-07,
                0.9999999317439627,
                1.275190580884987e-07,
                4.785096206076165e-06,
                7.33821330437595e-07,
                2.2603248367949354e-06,
                1.3709576971463352e-06
            ],
            [
                0.9999785550465441,
                0.9999687980886947,
                0.9999955048189639,
                0.9999949062956088,
                0.9999969105059241,
                1.444980209564556e-07,
                0.9999921107383667,
                0.999987780922541,
                0.9999930377445931,
                0.9999921107402463
            ],
            [
                1.4449795205429202e-07,
                3.466327037539638e-07,
                9.42244930862237e-07,
                3.466325797888292e-07,
                2.699578096393206e-07,
                1.994729008145876e-06,
                2.1024334103505245e-07,
                3.9278634073625165e-07,
                2.6995790618350237e-07,
                6.475945666063607e-07
            ],
            [
                0.9997388096007964,
                0.999990483751723,
                0.9999938558268698,
                0.999993037744588,
                0.9998911030406151,
                0.9999925887227852,
                0.9999904837505912,
                0.9999916019269832,
                0.9999877809269213,
                0.9999952149032294
            ],
            [
                0.9999938558261346,
                0.9999832985781708,
                0.9999984465018756,
                0.9999904837483158,
                0.9999995818811275,
                0.9999964991455875,
                0.999996910504449,
                0.9999964991464227,
                0.999999607213753,
                0.9999970976887083
            ],
            [
                3.05902117523595e-07,
                5.043475885674441e-07,
                1.8553907971758842e-07,
                1.6373766672888118e-07,
                8.764245361752286e-08,
                1.4449798650551755e-07,
                2.102433410343832e-07,
                1.1253518888464745e-07,
                7.734415776805048e-08,
                2.1024326584582131e-07
            ],
            [
                2.699577774585891e-07,
                2.699578096393206e-07,
                3.466327863983311e-07,
                9.422449308716635e-07,
                8.764254764749753e-08,
                1.6373766672888118e-07,
                2.382368247924618e-07,
                6.023578501491997e-08,
                7.734424996967756e-08,
                1.8553919030776337e-07
            ],
            [
                2.3823702359138736e-07,
                0.9999984465024312,
                6.475946437928669e-07,
                0.9999756997622029,
                0.9999989322973851,
                0.9999974387168747,
                0.9999877809239969,
                0.9999955048178898,
                0.9999967112521128,
                0.9999987121041707
            ],
            [
                2.2603251062450327e-06,
                6.475949526020042e-07,
                1.7603430034867993e-06,
                1.2098659719788098e-06,
                1.760343213335281e-06,
                4.785096206076165e-06,
                1.067703124601679e-06,
                1.994729721518893e-06,
                4.22283545819819e-06,
                6.47595107001401e-07
            ],
            [
                5.3157837044597743e-08,
                1.275190580884987e-07,
                1.2751904288710323e-07,
                1.3709575337078829e-06,
                3.927860597935108e-07,
                2.6995784182073116e-07,
                4.691162683297406e-08,
                1.444980726324838e-07,
                1.637377057673536e-07,
                8.764252675194995e-08
            ],
            [
                1.1253506814797596e-07,
                3.0590237279032884e-07,
                1.1253506814797596e-07,
                2.3823696679230424e-07,
                1.6373770576776313e-07,
                1.2751907329024393e-07,
                3.4663266243111764e-07,
                6.023569884692295e-08,
                2.3823685319244518e-07,
                2.6995784182073116e-07
            ],
            [
                1.760342793638743e-06,
                1.855391681906175e-07,
                3.05902226922147e-07,
                7.73442776300517e-08,
                1.275190276853036e-07,
                3.4663253846718004e-07,
                3.4663249714612693e-07,
                2.6995774527577444e-07,
                8.764245361708445e-08,
                2.6995774527577444e-07
            ],
            [
                4.691167716359673e-08,
                9.931190958026426e-08,
                3.927861534406222e-07,
                1.444980726324838e-07,
                2.430023493865361e-05,
                3.059021539909339e-07,
                1.2751908849088918e-07,
                1.2751908849167202e-07,
                3.466327450756327e-07,
                2.1024329090929374e-07
            ],
            [
                2.382369383923073e-07,
                6.825604537781398e-08,
                9.422449308774482e-07,
                8.764249540862797e-08,
                1.2751899728286965e-07,
                1.275190884913241e-07,
                1.2751910369310194e-07,
                1.444980726324838e-07,
                3.4663278639892215e-07,
                8.7642516304188e-08
            ],
            [
                2.3823690999160957e-07,
                2.102433410343832e-07,
                5.04347348070562e-07,
                3.927861066170637e-07,
                1.1253509497835043e-07,
                1.275190276853036e-07,
                3.4663249714451116e-07,
                5.715003788993679e-07,
                1.4449800373065699e-07,
                3.05902263389638e-07
            ],
            [
                8.315281267834927e-07,
                1.2098661161927025e-06,
                3.05902226922147e-07,
                1.2098655392871682e-06,
                3.0590226339061185e-07,
                3.927863875584984e-07,
                4.4508505193791187e-07,
                3.9278605979208185e-07,
                8.315284241560147e-07,
                5.043472879504592e-07
            ],
            [
                1.2751904288739315e-07,
                2.6995784182140636e-07,
                1.8553919030858602e-07,
                3.466327450765785e-07,
                1.855391239539711e-07,
                3.0590215399183813e-07,
                3.059022269250683e-07,
                3.927862470899887e-07,
                1.4449807263312446e-07,
                2.3823702359290413e-07
            ],
            [
                1.8553903548231313e-07,
                2.1024326584639497e-07,
                6.475949526003845e-07,
                3.059021175247079e-07,
                5.043474081993875e-07,
                2.3823682479181176e-07,
                3.9278605979208185e-07,
                3.05902226923399e-07,
                1.855391239544352e-07,
                6.825603724068787e-08
            ],
            [
                4.450849458218309e-07,
                5.043474081993875e-07,
                1.8553919030858602e-07,
                3.927862939126708e-07,
                1.3709568799919866e-06,
                5.715006514176113e-07,
                8.31528424162821e-07,
                3.224185864592658e-08,
                9.422447062240614e-07,
                5.043474081993875e-07
            ],
            [
                0.9999724643089434,
                2.1024341622426268e-07,
                2.69957906184239e-07,
                1.855391239539711e-07,
                3.9278634073732336e-07,
                2.1024341622368903e-07,
                1.8553905760062447e-07,
                2.10243290909724e-07,
                5.04347348075149e-07,
                1.637376862489725e-07
            ],
            [
                3.9278605979208185e-07,
                5.043475885696228e-07,
                1.6373764720990908e-07,
                1.275190884913241e-07,
                1.2098652508424818e-06,
                6.023578501491997e-08,
                3.05902336324494e-07,
                1.855391681906175e-07,
                2.382368815916736e-07,
                1.6373766672821107e-07
            ],
            [
                1.275190276859705e-07,
                2.3823688159291947e-07,
                1.275190580890061e-07,
                7.734421308914719e-08,
                1.8553919030858602e-07,
                2.1024334103581732e-07,
                1.1253513522447425e-07,
                1.2751899728311609e-07,
                1.444979692800516e-07,
                7.734424996967756e-08
            ],
            [
                8.315281267800897e-07,
                4.4508526417014975e-07,
                2.699578096393206e-07,
                1.370957860576702e-06,
                6.825605351455307e-08,
                2.6995790618252024e-07,
                1.8553907971855875e-07,
                5.715006514105942e-07,
                1.4449805540740185e-07,
                9.422449308716635e-07
            ],
            [
                3.0590215399183813e-07,
                3.05902263389638e-07,
                6.825604537781398e-08,
                2.102433410343832e-07,
                1.8553907971758842e-07,
                2.1024334103505245e-07,
                1.2751899728286965e-07,
                1.8553910183607374e-07,
                1.8553916819032217e-07,
                2.6995790618252024e-07
            ],
            [
                2.6995768091310296e-07,
                2.6995774527657245e-07,
                5.043475284430694e-07,
                2.1024329090929374e-07,
                4.450849458200093e-07,
                8.764255809528314e-08,
                3.466327450756327e-07,
                4.139939521459479e-08,
                6.825601283086733e-08,
                3.059021175247079e-07
            ],
            [
                1.6373768624837685e-07,
                1.370957860576702e-06,
                5.043474683220276e-07,
                4.2228324377740105e-06,
                1.444980381819277e-07,
                2.6995784182140636e-07,
                1.637377057673536e-07,
                3.288748673360027e-06,
                7.734421308914719e-08,
                6.47595107001401e-07
            ],
            [
                1.067703124601679e-06,
                1.8553916819032217e-07,
                2.10243290909724e-07,
                4.691161005609407e-08,
                1.1253518888531272e-07,
                1.5534983101644536e-06,
                1.1253509497883659e-07,
                2.699576809143613e-07,
                2.6995777745711594e-07,
                2.3823696679230424e-07
            ],
            [
                4.4508526417014975e-07,
                1.1253508156317518e-07,
                3.466326624322211e-07,
                2.699578740011634e-07,
                1.3709567165461505e-06,
                2.382369383923073e-07,
                6.825598028364134e-08,
                4.450852111155216e-07,
                6.825606165129312e-08,
                1.1253508156317518e-07
            ],
            [
                3.05902226923399e-07,
                2.3823690999160957e-07,
                1.6373768624837685e-07,
                1.1253518888531272e-07,
                7.734423152941018e-08,
                1.8553903548231313e-07,
                3.9278605979208185e-07,
                6.825601283086733e-08,
                1.8553916819032217e-07,
                2.3823688159237777e-07
            ],
            [
                1.9555699355175906e-08,
                1.637377448057981e-07,
                2.699578740011634e-07,
                2.3823685319244518e-07,
                1.8553916819032217e-07,
                2.3823690999160957e-07,
                1.4449800373065699e-07,
                1.855391239539711e-07,
                2.3823690999160957e-07,
                5.315787506598473e-08
            ],
            [
                1.6373764721072816e-07,
                1.275189972825217e-07,
                1.8553905759969634e-07,
                5.715006514151423e-07,
                6.475950297868629e-07,
                1.2751899728286965e-07,
                1.8553914607128047e-07,
                2.699578096393206e-07,
                2.6995777745711594e-07,
                6.475948754012522e-07
            ],
            [
                1.209866260432471e-06,
                8.315281267882195e-07,
                2.3823690999323465e-07,
                8.315280276626197e-07,
                6.475945666063607e-07,
                8.315280276626197e-07,
                1.637376862489725e-07,
                2.699578740032504e-07,
                4.450848927658745e-07,
                9.422442569315887e-07
            ],
            [
                0.9999930377437537,
                0.9999989969859121,
                0.9999964991451697,
                2.6995790618350237e-07,
                7.734415776836702e-08,
                4.4508494582314646e-07,
                1.0677027427600627e-06,
                0.9999987901341727,
                0.9999967112501518,
                0.9999910603068987
            ],
            [
                1.7603427935518875e-06,
                3.4663253846316044e-07,
                1.2751901248391176e-07,
                2.382369383878655e-07,
                2.3823690999063455e-07,
                1.3709575336947905e-06,
                1.6373774480479287e-07,
                1.7603432132784448e-06,
                7.338210679979539e-07,
                3.059023363207381e-07
            ],
            [
                3.288749065423109e-06,
                5.04347528440776e-07,
                3.0590229985101266e-07,
                1.9947299593078385e-06,
                9.931189774140912e-08,
                7.338210680021253e-07,
                6.144173137170873e-06,
                3.0590237278838124e-07,
                2.5612831267202583e-06,
                2.6995790618252024e-07
            ],
            [
                3.653482080235082e-08,
                3.927862002654366e-07,
                2.1024341622426268e-07,
                1.637377057673536e-07,
                9.422442569290178e-07,
                3.9278624708775595e-07,
                2.6995771309523475e-07,
                1.8553919030776337e-07,
                1.6373764721039308e-07,
                2.699576809107705e-07
            ],
            [
                2.1024344128660572e-07,
                1.275190580884987e-07,
                6.023574911170301e-08,
                1.637377643243723e-07,
                3.05902117523595e-07,
                0.0005527785509648304,
                3.059021904580685e-07,
                1.4449805540740185e-07,
                1.4449798650476187e-07,
                1.5534971990169383e-06
            ],
            [
                9.931195693628605e-08,
                1.6373764721039308e-07,
                1.8553903548231313e-07,
                3.9278605979208185e-07,
                1.6373762769138607e-07,
                6.82560128305259e-08,
                3.726637951387472e-06,
                8.764241182605906e-08,
                2.102434162245973e-07,
                2.6995777745711594e-07
            ],
            [
                1.5534971990169383e-06,
                6.475946438055299e-07,
                2.2603248367949354e-06,
                1.5534973842076057e-06,
                3.05902263391829e-07,
                0.4687906266262437,
                9.422449308774482e-07,
                8.315278294114555e-07,
                8.315280276626197e-07,
                3.059022998576899e-07
            ],
            [
                3.059023727869902e-07,
                2.3823685319244518e-07,
                1.0677026154730804e-06,
                1.9947304348595095e-06,
                3.927862470861484e-07,
                3.9278605979208185e-07,
                2.1024344128660572e-07,
                1.2751904288710323e-07,
                3.059023363221292e-07,
                3.059021904571643e-07
            ],
            [
                3.7266392839425286e-06,
                1.7603432132912532e-06,
                3.9278615344178325e-07,
                9.931198061405701e-08,
                2.3823688159237777e-07,
                3.466325384661554e-07,
                2.1024341622368903e-07,
                2.9023130230846496e-06,
                7.338211554531576e-07,
                1.2098656835076114e-06
            ],
            [
                7.889259764517575e-06,
                5.715003107767143e-07,
                2.561282516066741e-06,
                1.3709567165617364e-06,
                3.9278610661902853e-07,
                5.715003789046955e-07,
                1.0677032518814388e-06,
                2.561281294760143e-06,
                5.043476486924565e-07,
                4.450852111148132e-07
            ],
            [
                0.9999964991460044,
                0.9999724643122128,
                0.999994906294394,
                0.9999987901338843,
                0.999986992873094,
                0.9999921107355387,
                0.9999983463098232,
                0.9999964991455869,
                0.9999989322972577,
                0.9999970976880164
            ],
            [
                1.1253516205489029e-07,
                2.3823682479181176e-07,
                5.043474683204221e-07,
                1.2751904288710323e-07,
                2.1024334103505245e-07,
                1.6373774480535133e-07,
                1.4449807263287805e-07,
                1.8553907971758842e-07,
                2.3823688159291947e-07,
                1.4449805540651476e-07
            ],
            [
                1.855391681906175e-07,
                1.0677029973219343e-06,
                1.994729008145876e-06,
                2.3823690999323465e-07,
                2.6995784182183607e-07,
                1.27519088491875e-07,
                0.9999964991464233,
                2.6995774527577444e-07,
                1.4449802095666915e-07,
                0.9999982396572077
            ],
            [
                9.931190958026426e-08,
                6.825601283086733e-08,
                1.637377448057981e-07,
                1.637377448057981e-07,
                8.764247451307293e-08,
                1.2751910369275402e-07,
                1.6373768624837685e-07,
                1.2751910369310194e-07,
                1.637377057673536e-07,
                2.3823685319244518e-07
            ],
            [
                3.059021175247079e-07,
                3.927861066170637e-07,
                1.6373774480479287e-07,
                5.043475885674441e-07,
                2.1024331597152624e-07,
                2.1024344128660572e-07,
                1.637377448057981e-07,
                3.9278605979208185e-07,
                3.4663266242969896e-07,
                2.102433660979124e-07
            ],
            [
                1.8553914607267268e-07,
                3.288747889284851e-06,
                1.275190124842887e-07,
                7.338212429582604e-07,
                8.764252675194995e-08,
                2.2603234895372223e-06,
                0.9999969105044486,
                3.059021904580685e-07,
                3.059021904580685e-07,
                2.9023109472494878e-06
            ],
            [
                5.043472278322555e-07,
                8.315281267882195e-07,
                6.023569166654288e-08,
                5.043475284468537e-07,
                6.475945666063607e-07,
                2.3823690999323465e-07,
                6.47594952603035e-07,
                3.726637951387472e-06,
                6.475945666063607e-07,
                1.7603425837903113e-06
            ],
            [
                1.8553905759969634e-07,
                1.6373762769138607e-07,
                1.3709576971463352e-06,
                4.222833444590791e-06,
                1.370957860576702e-06,
                3.9278629391427843e-07,
                1.760342793638743e-06,
                2.6995777745711594e-07,
                4.450851049991497e-07,
                2.6995784182183607e-07
            ],
            [
                1.1253506814797596e-07,
                1.6373764721039308e-07,
                1.6373764721091427e-07,
                3.6534807736504303e-08,
                1.444979692797559e-07,
                1.1253520230052635e-07,
                1.6373770576776313e-07,
                4.691164920214251e-08,
                2.3823702359138736e-07,
                1.3709575337159875e-06
            ],
            [
                5.715004470243685e-07,
                7.338208055680009e-07,
                1.209865250822125e-06,
                2.699577774560111e-07,
                3.0590215398829087e-07,
                2.2603234895372223e-06,
                3.05902263391829e-07,
                6.47594798194325e-07,
                9.422444815814404e-07,
                8.315280276456036e-07
            ],
            [
                3.466327037548308e-07,
                3.927861066170637e-07,
                2.6995784182140636e-07,
                4.450852641717689e-07,
                3.059022998569248e-07,
                3.4663253846718004e-07,
                1.3709570434122812e-06,
                4.450848927650143e-07,
                5.715002426460124e-07,
                5.715004470313855e-07
            ],
            [
                2.3823690999160957e-07,
                2.382369667914917e-07,
                2.6995771309523475e-07,
                4.4508505193791187e-07,
                1.1253525596134564e-07,
                6.475947210012481e-07,
                3.927860597935108e-07,
                2.260325106237323e-06,
                3.4663266242969896e-07,
                2.1024336609724313e-07
            ],
            [
                2.6995771309523475e-07,
                9.931195693628605e-08,
                1.6701425827133152e-05,
                2.6995784182073116e-07,
                6.475947982002148e-07,
                2.3823702359290413e-07,
                2.3823690999160957e-07,
                4.4508510499737865e-07,
                1.637377643243723e-07,
                8.7642516304188e-08
            ],
            [
                5.715006514105942e-07,
                9.422445939002803e-07,
                5.043472879504592e-07,
                2.1024334103505245e-07,
                5.715003788993679e-07,
                3.7266392840781026e-06,
                3.927862470861484e-07,
                1.2098656835136636e-06,
                1.3709575337016483e-06,
                6.475950297942253e-07
            ],
            [
                5.715002426486762e-07,
                0.9999980052709935,
                0.9999957771665615,
                2.3823688159291947e-07,
                5.04347528446051e-07,
                9.422448185534261e-07,
                6.475947982037486e-07,
                1.8553907971855875e-07,
                2.6995784182183607e-07,
                4.450850519403407e-07
            ],
            [
                1.760343003481596e-06,
                2.699578096393206e-07,
                2.1024326584639497e-07,
                3.927862002641863e-07,
                5.715002426439334e-07,
                2.3823699519143784e-07,
                2.5612831267202583e-06,
                1.1253518888464745e-07,
                6.47594952595231e-07,
                5.715005832886879e-07
            ],
            [
                1.2098659719524008e-06,
                5.715003107738556e-07,
                1.7603436329978976e-06,
                2.3823699519143784e-07,
                2.9023119851899796e-06,
                3.7266410611296085e-06,
                1.0677033791437343e-06,
                3.4663249714612693e-07,
                3.0590237279032884e-07,
                4.4508521110762794e-07
            ],
            [
                8.764241182605906e-08,
                1.275190580884987e-07,
                3.059021175247079e-07,
                4.1399375473868e-08,
                3.4663262110945863e-07,
                3.059021175247079e-07,
                3.05902226923399e-07,
                4.6911638017556955e-08,
                1.4449805540651476e-07,
                1.637377643243723e-07
            ],
            [
                2.3823688159291947e-07,
                2.699577774560111e-07,
                6.47595107001401e-07,
                2.6995784182183607e-07,
                9.422449308774482e-07,
                1.6373766672994222e-07,
                5.04347348070562e-07,
                3.05902226922147e-07,
                3.2887506336235617e-06,
                5.043474683240344e-07
            ],
            [
                1.4449802095609418e-07,
                5.043472278312808e-07,
                2.6995784182073116e-07,
                7.734428685019034e-08,
                3.466327450756327e-07,
                2.1024341622426268e-07,
                2.6995784182073116e-07,
                1.4449795205429202e-07,
                2.3823688159237777e-07,
                1.8553907971758842e-07
            ],
            [
                4.785096206047877e-06,
                3.927862470905692e-07,
                3.466325384661554e-07,
                1.0677027427624903e-06,
                3.059022998569248e-07,
                1.3709575337159875e-06,
                1.5534981249736758e-06,
                4.222834451403972e-06,
                4.4508499888275247e-07,
                1.9947292459406333e-06
            ],
            [
                0.9999930377445865,
                0.9999975938973754,
                0.9999938558276008,
                0.9999962733602737,
                3.9278624708775595e-07,
                0.9999970976873246,
                0.9999987901347498,
                0.9999967112517222,
                0.9999962733602741,
                0.9999984465020606
            ],
            [
                1.3709572068553509e-06,
                1.3709576971463352e-06,
                1.9947299593078385e-06,
                4.1399365603508136e-08,
                1.7603440527334603e-06,
                4.2228339479858295e-06,
                6.475946438055299e-07,
                1.209865827752005e-06,
                4.450851049991497e-07,
                2.561282210740037e-06
            ],
            [
                9.931193325852072e-08,
                1.4449798650476187e-07,
                2.382369383923073e-07,
                1.1253521571574156e-07,
                3.4663266243111764e-07,
                1.4449800373065699e-07,
                9.931188590255539e-08,
                1.1253521571574156e-07,
                2.3823702359290413e-07,
                1.444980209564556e-07
            ],
            [
                1.8553910183607374e-07,
                4.450848927637999e-07,
                2.1024341622426268e-07,
                5.715003788993679e-07,
                2.699577774530648e-07,
                3.927862939126708e-07,
                9.931202796957073e-08,
                2.1024329090867228e-07,
                1.4449800373065699e-07,
                3.92786340734912e-07
            ],
            [
                1.5534975693979422e-06,
                2.3823682479181176e-07,
                2.102433410343832e-07,
                1.855391239539711e-07,
                3.4663253846718004e-07,
                2.1024336609843824e-07,
                2.1024341622368903e-07,
                7.734423152941018e-08,
                1.4449805540740185e-07,
                1.1253520230052635e-07
            ],
            [
                5.715003107738556e-07,
                0.9999995818813269,
                0.999999495652532,
                0.9999967112521135,
                0.9999992661786699,
                0.9999952149060803,
                0.9999991684722701,
                7.734424996967756e-08,
                0.9999998461826588,
                3.927862470899887e-07
            ],
            [
                6.023574911170301e-08,
                1.4449795205429202e-07,
                1.4449805540740185e-07,
                3.0590226339061185e-07,
                2.6995771309523475e-07,
                2.1024344128660572e-07,
                7.73441946488886e-08,
                9.931195693628605e-08,
                5.04347348075149e-07,
                2.6995768091310296e-07
            ],
            [
                0.9999991148429644,
                2.1024334103505245e-07,
                1.1253517547010071e-07,
                0.9999687980739015,
                9.931198061405701e-08,
                9.931187406410953e-08,
                2.382370235922541e-07,
                3.9278634073732336e-07,
                1.4449795205429202e-07,
                1.760343633031919e-06
            ],
            [
                0.9999904837471807,
                0.9999991684721707,
                0.9999967112493678,
                0.9999994284997575,
                0.9999921107374169,
                0.9999993106391191,
                0.9999980052702793,
                0.9999977396751641,
                0.9999972735290805,
                0.9999981261239468
            ],
            [
                3.72663883989755e-06,
                2.1024336609638268e-07,
                1.8553919030624466e-07,
                3.0590237279085045e-07,
                1.4449802095666915e-07,
                2.699578096403948e-07,
                2.6995790618252024e-07,
                4.450851580540182e-07,
                4.450851049959619e-07,
                1.8553907971879076e-07
            ],
            [
                3.4663266243111764e-07,
                2.3823682479181176e-07,
                3.05902226922147e-07,
                1.6373766672888118e-07,
                2.382368815916736e-07,
                9.931186222482958e-08,
                1.444980726324838e-07,
                4.450848927650143e-07,
                3.0590226338838606e-07,
                2.699578096393206e-07
            ],
            [
                5.04347348070562e-07,
                3.059022998569248e-07,
                1.275190884913241e-07,
                6.023572038882162e-08,
                2.102433410343832e-07,
                1.0677032518700286e-06,
                5.04347287945184e-07,
                2.1024334103505245e-07,
                2.1024344128660572e-07,
                9.931195693628605e-08
            ],
            [
                8.7642516304188e-08,
                2.3823690999160957e-07,
                8.315277302788957e-07,
                2.6995777745711594e-07,
                1.8553910183607374e-07,
                1.855391681891831e-07,
                2.3823690999160957e-07,
                1.2751910369275402e-07,
                2.382368247924618e-07,
                1.6373766672888118e-07
            ],
            [
                3.927863875616689e-07,
                6.47595107001401e-07,
                1.3709573702856596e-06,
                9.610238067382736e-05,
                3.9278629391427843e-07,
                1.0677032518814388e-06,
                4.4508515805735777e-07,
                9.422444815814404e-07,
                4.450848927658745e-07,
                6.475947982037486e-07
            ],
            [
                5.715004470243685e-07,
                0.9999990577550694,
                1.444979692797559e-07,
                1.9947292459347367e-06,
                3.9278634073098236e-07,
                4.4508505193932864e-07,
                1.3709575337159875e-06,
                4.450851580540182e-07,
                3.059021904580685e-07,
                2.3823688159291947e-07
            ],
            [
                3.466324971415162e-07,
                4.450848927637999e-07,
                5.715003107738556e-07,
                8.31528126775552e-07,
                5.715006514105942e-07,
                4.450851580555361e-07,
                1.8553905759969634e-07,
                1.3709575337159875e-06,
                2.1024334103505245e-07,
                5.043472879504592e-07
            ],
            [
                3.466325384661554e-07,
                1.6373762769138607e-07,
                1.8553910183607374e-07,
                9.931193325852072e-08,
                2.1024326584639497e-07,
                3.4663266243111764e-07,
                2.1024326584639497e-07,
                1.2751908849167202e-07,
                1.4449805540740185e-07,
                2.6995784182140636e-07
            ],
            [
                1.1253521571574156e-07,
                5.3157811697009444e-08,
                1.2751910369275402e-07,
                6.023576347299818e-08,
                9.931200429212718e-08,
                3.4663274507713016e-07,
                8.764254764749753e-08,
                1.1253516205489029e-07,
                1.8553919030776337e-07,
                2.382369383923073e-07
            ],
            [
                5.715006514151423e-07,
                3.0590215399183813e-07,
                4.450851580555361e-07,
                6.475945666033422e-07,
                2.561282210729555e-06,
                7.338209805224048e-07,
                6.475945666009864e-07,
                3.9278605979208185e-07,
                1.855391239539711e-07,
                1.7603432133296774e-06
            ],
            [
                5.422221555380179e-06,
                9.422445939002803e-07,
                1.209865539298447e-06,
                1.2098652508287273e-06,
                3.927861066170637e-07,
                7.338209805133949e-07,
                2.430024073523505e-05,
                2.3823702359138736e-07,
                1.994729721518893e-06,
                1.7603425837903113e-06
            ],
            [
                1.8553919030776337e-07,
                6.475947209985977e-07,
                3.9278634073625165e-07,
                1.2751908849088918e-07,
                1.6373774480479287e-07,
                8.764242227380856e-08,
                3.059021175247079e-07,
                2.3823696679230424e-07,
                1.444980726324838e-07,
                1.4449805540700758e-07
            ],
            [
                1.5534977545886537e-06,
                2.1024339116168358e-07,
                3.059022998581767e-07,
                7.338209805240734e-07,
                3.4663278639892215e-07,
                7.338208930460318e-07,
                2.102434162245973e-07,
                7.338209805240734e-07,
                2.260323758987159e-06,
                3.72663883989755e-06
            ],
            [
                4.450851580555361e-07,
                3.466327863983311e-07,
                0.9999980052693282,
                0.9999989322967484,
                0.9999987901341728,
                0.9999949062968222,
                0.9999972735307054,
                0.999999168471576,
                0.9999921107336572,
                2.102433911580983e-07
            ],
            [
                9.931198061405701e-08,
                1.6373766672888118e-07,
                1.637377643243723e-07,
                9.931198061405701e-08,
                1.444980726324838e-07,
                1.2751908849167202e-07,
                2.3823688159237777e-07,
                6.825600469380719e-08,
                1.4449795205429202e-07,
                1.4449796927932878e-07
            ],
            [
                3.927862002641863e-07,
                3.059021904571643e-07,
                2.699577452775239e-07,
                2.1024336609843824e-07,
                2.1024336609874897e-07,
                5.715005151574337e-07,
                5.715005151574337e-07,
                1.5229968619423794e-08,
                1.8553907971758842e-07,
                1.4449795205429202e-07
            ],
            [
                4.450852641737424e-07,
                7.338210680021253e-07,
                1.9947299593078385e-06,
                1.5534984953552536e-06,
                3.05902336324494e-07,
                2.699577774589574e-07,
                1.6373774480605869e-07,
                1.4449802095666915e-07,
                3.4663249714612693e-07,
                3.05902336324494e-07
            ],
            [
                6.475947982037486e-07,
                3.466326624336003e-07,
                9.422442569315887e-07,
                3.2887498495150166e-06,
                2.2603253756874524e-06,
                5.715003788993679e-07,
                3.4663249714612693e-07,
                1.4449805540700758e-07,
                1.8553910183607374e-07,
                1.209865827752005e-06
            ],
            [
                1.6373774480535133e-07,
                2.6995784182073116e-07,
                3.4663249714325014e-07,
                2.3823690999236795e-07,
                2.3823690999063455e-07,
                2.1024331597152624e-07,
                2.382369383923073e-07,
                2.3823690999160957e-07,
                1.4449803818156628e-07,
                1.1253514863909295e-07
            ],
            [
                2.3823699519290042e-07,
                8.764245361708445e-08,
                1.2751904288710323e-07,
                2.1024331597262577e-07,
                1.6373766672888118e-07,
                1.2751901248454963e-07,
                1.6373774480479287e-07,
                1.8553903548231313e-07,
                3.927862939126708e-07,
                1.4449798650476187e-07
            ]
        ]
    },
    {
        "q_id": "9700_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            11,
            16,
            17,
            19,
            21,
            22,
            24,
            25,
            29,
            32,
            33,
            34,
            35,
            38,
            42,
            43,
            45,
            46,
            47,
            48,
            49,
            52,
            53,
            54,
            55,
            56,
            57,
            60,
            61,
            67,
            68,
            69,
            72,
            73,
            78,
            83,
            84,
            87,
            89,
            91,
            95,
            102,
            106,
            108,
            111,
            113,
            114,
            116,
            118,
            122,
            124,
            127
        ],
        "rewards": [
            [
                9.931202796993203e-08,
                1.4449805540740185e-07,
                1.2751901248454963e-07,
                9.422449308748773e-07,
                9.931190958076104e-08,
                1.637377448057981e-07,
                2.10243290909724e-07,
                1.1253516205489029e-07,
                2.1024336609843824e-07,
                5.315781803390236e-08
            ],
            [
                2.2603251062270446e-06,
                3.05902226922147e-07,
                4.2228334445658276e-06,
                1.209865539295696e-06,
                1.3709575337078829e-06,
                7.338212429582604e-07,
                2.3823699519143784e-07,
                4.450851580555361e-07,
                3.059023727894942e-07,
                1.2098652508424818e-06
            ],
            [
                1.8553907971682908e-07,
                6.475947210031623e-07,
                3.927861534370498e-07,
                3.466327450756327e-07,
                4.450851580555361e-07,
                3.466325384661554e-07,
                1.8553903548231313e-07,
                3.927861534370498e-07,
                9.422448185478557e-07,
                4.450848927650143e-07
            ],
            [
                1.855391239544352e-07,
                2.3823690999323465e-07,
                6.475949526020042e-07,
                3.466326211113502e-07,
                8.93969950132721e-06,
                6.962257909785973e-06,
                6.144173869502757e-06,
                2.260325106237323e-06,
                2.4300249423965898e-05,
                1.670141786325573e-05
            ],
            [
                2.9023133690821773e-06,
                4.450850519360903e-07,
                2.2603248367656408e-06,
                2.902310946944611e-06,
                3.726641061027928e-06,
                8.315281267800897e-07,
                9.422444815792981e-07,
                1.3709572068422585e-06,
                3.2887502415438413e-06,
                1.7603434231705793e-06
            ],
            [
                6.9622587397397306e-06,
                8.939696304116203e-06,
                1.7603434231777837e-06,
                5.4222183234485234e-06,
                4.2228324377740105e-06,
                1.7603427936263351e-06,
                2.902311639183378e-06,
                2.561281600049467e-06,
                2.7535697667202906e-05,
                3.726638395611981e-06
            ],
            [
                2.902312677104321e-06,
                1.1478769494250387e-05,
                2.260324567268294e-06,
                3.288749065077638e-06,
                1.8925155009767892e-05,
                8.939697369785323e-06,
                6.962255419868303e-06,
                4.0063682639477306e-05,
                8.939700566801578e-06,
                6.14417533430649e-06
            ],
            [
                4.450848927621807e-07,
                4.450851049959619e-07,
                3.0590215399183813e-07,
                2.382369667914917e-07,
                2.3823685319244518e-07,
                5.043474683204221e-07,
                4.450849458218309e-07,
                3.0590215399183813e-07,
                8.315283249522945e-07,
                1.0677024881980089e-06
            ],
            [
                4.4508510499849186e-07,
                1.4449800373065699e-07,
                3.927862002641863e-07,
                2.1024334103505245e-07,
                5.043474081993875e-07,
                1.6373762769138607e-07,
                6.475951069855719e-07,
                2.5612825160562587e-06,
                3.9278610661902853e-07,
                NaN
            ],
            [
                2.6995774527718623e-07,
                8.315279285370317e-07,
                4.450848927650143e-07,
                3.466325797896173e-07,
                4.450850519403407e-07,
                4.450849988811838e-07,
                5.715005832886879e-07,
                1.855391239544352e-07,
                3.4663278639892215e-07,
                3.466327037548308e-07
            ],
            [
                7.338209805240734e-07,
                1.209865539295696e-06,
                7.338213304363436e-07,
                1.0677033791612137e-06,
                5.715002426486762e-07,
                1.2098656835224664e-06,
                3.9278605979534166e-07,
                5.715003107767143e-07,
                8.315277302857965e-07,
                5.715003107767143e-07
            ],
            [
                1.5534975693792215e-06,
                2.9023116391477434e-06,
                2.2603242978007868e-06,
                2.5612812947508257e-06,
                9.422443692489024e-07,
                1.3709570434178922e-06,
                7.338207180864763e-07,
                1.0677028700203557e-06,
                1.5534975693869924e-06,
                1.7603438428800754e-06
            ],
            [
                8.764247451307293e-08,
                7.734418542875216e-08,
                6.023573475041126e-08,
                3.927860597945825e-07,
                6.825602910433871e-08,
                2.102433410343832e-07,
                5.315784971839039e-08,
                5.315784971839039e-08,
                9.931187406410953e-08,
                3.05902263389638e-07
            ],
            [
                1.1478768126057254e-05,
                4.785095065132354e-06,
                3.288750241561788e-06,
                2.902312331081799e-06,
                4.2228324377740105e-06,
                1.0677033791437343e-06,
                2.9023133690980155e-06,
                7.338209805200689e-07,
                3.7266406168624155e-06,
                4.785094494750855e-06
            ],
            [
                1.067702870039777e-06,
                2.382369951932796e-07,
                1.2098656835224664e-06,
                9.931200429212718e-08,
                1.9947304348862686e-06,
                3.466325797888292e-07,
                3.466326211113502e-07,
                2.6995790618469934e-07,
                3.927860597945825e-07,
                NaN
            ],
            [
                5.043476486915964e-07,
                3.059022998576899e-07,
                2.6995768091310296e-07,
                5.043475885657239e-07,
                3.0590215399183813e-07,
                2.6995784182140636e-07,
                1.2098659719232413e-06,
                3.059021175255426e-07,
                5.043475885634304e-07,
                5.043472278227948e-07
            ],
            [
                4.785092783454444e-06,
                2.5612828211442287e-06,
                1.1478773599102191e-05,
                5.715004470295662e-07,
                3.288748673295719e-06,
                8.939697369882888e-06,
                1.3709572068422585e-06,
                6.962257079376403e-06,
                4.785096775389454e-06,
                1.3709567165530083e-06
            ],
            [
                5.043473480730849e-07,
                2.1024331597262577e-07,
                2.1024334103505245e-07,
                6.475945666051092e-07,
                1.6373766672973748e-07,
                1.8553903548231313e-07,
                2.1024326584639497e-07,
                3.0590215399183813e-07,
                1.4449798650551755e-07,
                3.927863875584984e-07
            ],
            [
                1.6373770576776313e-07,
                4.691162124067829e-08,
                3.9278605979534166e-07,
                1.275190276859705e-07,
                1.2751905808881762e-07,
                1.1253518888531272e-07,
                6.475946438022905e-07,
                1.0677026154774503e-06,
                1.0677032518209896e-06,
                9.931190958076104e-08
            ],
            [
                1.0677027427600627e-06,
                1.6373770576776313e-07,
                2.699577452746696e-07,
                2.699578740011634e-07,
                2.3823690999236795e-07,
                3.059021904559123e-07,
                2.699577452746696e-07,
                1.2751905808809277e-07,
                5.043472879525233e-07,
                6.475946437966953e-07
            ],
            [
                1.4449796927932878e-07,
                3.0590226339061185e-07,
                2.69957906184239e-07,
                1.8553905759893702e-07,
                1.275190884903093e-07,
                1.6373766672973748e-07,
                1.6373768624837685e-07,
                8.7642516304188e-08,
                2.10243290909724e-07,
                1.2751899728286965e-07
            ],
            [
                3.726639728370556e-06,
                6.962256249821764e-06,
                3.059023727894942e-07,
                3.059023727894942e-07,
                1.8925157265710765e-05,
                1.4738981972323349e-05,
                2.3823699519225038e-07,
                7.338213304196583e-07,
                1.0677033791583005e-06,
                3.059023363207381e-07
            ],
            [
                2.382370235933104e-07,
                1.2751908849167202e-07,
                1.2751908849167202e-07,
                3.059022998576899e-07,
                9.931198061405701e-08,
                3.927862470899887e-07,
                3.059022998576899e-07,
                2.382369951932796e-07,
                1.2751901248454963e-07,
                2.1024326584639497e-07
            ],
            [
                1.3709568799760888e-06,
                9.422445939002803e-07,
                9.422444815679433e-07,
                1.0677033791583005e-06,
                3.726638395611981e-06,
                2.561282210729555e-06,
                9.422449308716635e-07,
                8.315277302788957e-07,
                9.422448185478557e-07,
                1.2098653950692178e-06
            ],
            [
                9.93120161306789e-08,
                2.3823693839290317e-07,
                5.715007195447234e-07,
                4.4508494582405734e-07,
                5.043472879525233e-07,
                3.059022269250683e-07,
                2.3823682479292225e-07,
                1.8553919030858602e-07,
                5.043472879540142e-07,
                1.6373764720990908e-07
            ],
            [
                1.1253513522391131e-07,
                5.315784971839039e-08,
                1.1253513522447425e-07,
                8.764244316973974e-08,
                6.023574911170301e-08,
                1.2751899728311609e-07,
                9.931190958076104e-08,
                6.023572038912295e-08,
                6.825609419848033e-08,
                1.8553903548231313e-07
            ],
            [
                2.2603251062270446e-06,
                1.3709576971425944e-06,
                1.2098659719716573e-06,
                8.315282259009745e-07,
                1.2098655392921197e-06,
                7.338208930391909e-07,
                8.315277302788957e-07,
                6.475946437996402e-07,
                8.315281267861397e-07,
                7.338211554783522e-07
            ],
            [
                2.1024341622426268e-07,
                2.1024339116168358e-07,
                NaN,
                2.102434412875379e-07,
                1.0677026154806063e-06,
                1.8553910183607374e-07,
                1.0677033791612137e-06,
                4.450848927658745e-07,
                6.475948754012522e-07,
                5.043474081993875e-07
            ],
            [
                2.1024341622426268e-07,
                2.3823688159291947e-07,
                5.043472278255469e-07,
                2.382368815916736e-07,
                3.0590226339061185e-07,
                2.902312331081799e-06,
                5.715003107715166e-07,
                1.855391239544352e-07,
                1.444980209564556e-07,
                3.9278634073732336e-07
            ],
            [
                3.9278615344178325e-07,
                5.04347528440776e-07,
                4.450851049959619e-07,
                3.0590211752206485e-07,
                3.9278638755671223e-07,
                1.6373772528581146e-07,
                3.4663262110945863e-07,
                4.4508515805199415e-07,
                4.450851049890802e-07,
                3.927862002625787e-07
            ],
            [
                1.8553903548231313e-07,
                1.209865827752005e-06,
                7.338208055664991e-07,
                3.927860597945825e-07,
                1.6373768624837685e-07,
                2.1024331597066579e-07,
                1.6373770576776313e-07,
                5.043476486915964e-07,
                8.764240137829087e-08,
                3.05902190458764e-07
            ],
            [
                3.059023363221292e-07,
                9.422448185534261e-07,
                1.7603436330179102e-06,
                1.8553916819032217e-07,
                3.927862002641863e-07,
                1.8553910183607374e-07,
                2.382370235922541e-07,
                5.043474081993875e-07,
                1.7603427936263351e-06,
                3.0590215399183813e-07
            ],
            [
                8.315279285351409e-07,
                1.2098658277451275e-06,
                2.902313023130843e-06,
                5.04347468318358e-07,
                3.059022269250683e-07,
                2.260324567337161e-06,
                1.0129989772532511e-05,
                1.7603425837702984e-06,
                9.422448185435711e-07,
                1.2098653950656417e-06
            ],
            [
                8.315281267800897e-07,
                3.466327037539638e-07,
                1.209865250822125e-06,
                7.338209805170655e-07,
                4.450848927650143e-07,
                8.315281267800897e-07,
                5.71500651413193e-07,
                7.338212429537553e-07,
                1.3709573702722555e-06,
                7.338209805200689e-07
            ],
            [
                5.715005151606823e-07,
                1.2098658277264215e-06,
                2.699577774585891e-07,
                1.3709576971425944e-06,
                6.9622554185195676e-06,
                6.475948754012522e-07,
                1.2098658277451275e-06,
                7.3382080556433e-07,
                4.450852641656969e-07,
                5.043474081931949e-07
            ],
            [
                9.422447062202052e-07,
                2.3823699519290042e-07,
                6.475947210012481e-07,
                7.338208930391909e-07,
                5.043472879525233e-07,
                3.927862939075802e-07,
                1.0677026154730804e-06,
                7.338212429582604e-07,
                8.315279285351409e-07,
                1.0677028700363782e-06
            ],
            [
                2.3823688159291947e-07,
                9.931193325852072e-08,
                7.734418542839164e-08,
                2.6995790618469934e-07,
                2.3823693839325527e-07,
                5.043473480777865e-07,
                1.1253516205427619e-07,
                1.637377448057981e-07,
                6.825606165129312e-08,
                3.9278610661902853e-07
            ],
            [
                3.4663278639892215e-07,
                7.338207180898968e-07,
                1.5534981249697903e-06,
                1.994729483723626e-06,
                6.475946438022905e-07,
                1.0677028700266676e-06,
                6.475947982037486e-07,
                9.422447062294175e-07,
                5.715006514176113e-07,
                6.475950298011458e-07
            ],
            [
                5.715002426475718e-07,
                2.260324028427877e-06,
                6.475947210031623e-07,
                6.475946437966953e-07,
                8.315281267882195e-07,
                7.338210680021253e-07,
                2.6995790618350237e-07,
                3.466325797896173e-07,
                2.1024334103505245e-07,
                5.715005832886879e-07
            ],
            [
                2.2603253755476615e-06,
                3.9278605979011705e-07,
                1.0677027427471959e-06,
                5.04347348070562e-07,
                1.3709578605455302e-06,
                3.9278605979011705e-07,
                1.3709578605455302e-06,
                6.475950297821511e-07,
                8.315280276546789e-07,
                3.2887478890769702e-06
            ],
            [
                3.05902226922147e-07,
                5.043474683204221e-07,
                5.715007195353674e-07,
                3.92786340734912e-07,
                9.422448185478557e-07,
                2.3823690999063455e-07,
                3.4663257978638593e-07,
                6.475947210012481e-07,
                3.059023727894942e-07,
                3.0590237278838124e-07
            ],
            [
                1.760343003481596e-06,
                7.338207180864763e-07,
                8.315277302788957e-07,
                8.315283250371857e-07,
                2.2603242978871282e-06,
                4.4508505193791187e-07,
                1.3709572068522336e-06,
                7.338213304283347e-07,
                3.927860597935108e-07,
                1.3709576971425944e-06
            ],
            [
                1.553498495308628e-06,
                3.4663262110945863e-07,
                9.931195693628605e-08,
                1.4449796927932878e-07,
                2.69957906184239e-07,
                1.8553905759969634e-07,
                1.855391681898159e-07,
                9.931190958076104e-08,
                3.4663249714451116e-07,
                2.102433660979124e-07
            ],
            [
                2.1024334103505245e-07,
                1.6373770576776313e-07,
                3.46632497145457e-07,
                3.466327863983311e-07,
                3.927862002663297e-07,
                5.043472879540142e-07,
                2.6995790618350237e-07,
                2.382368815916736e-07,
                3.927863875616689e-07,
                2.3823699519143784e-07
            ],
            [
                8.939699501229642e-06,
                6.144176799283803e-06,
                1.7603432133136672e-06,
                4.785095635592258e-06,
                2.4300232043987867e-05,
                1.3709570434178922e-06,
                1.670141786231398e-05,
                6.9622579096593295e-06,
                5.422219616228845e-06,
                1.3709567165530083e-06
            ],
            [
                2.1024326584582131e-07,
                8.315279285351409e-07,
                4.4508526416286326e-07,
                3.059021539909339e-07,
                6.475951069985296e-07,
                6.475947210046347e-07,
                5.043474081993875e-07,
                1.0677033791583005e-06,
                5.71500651413193e-07,
                4.4508505193932864e-07
            ],
            [
                2.902312677137316e-06,
                5.715005151606823e-07,
                1.5534975693792215e-06,
                1.1253518888531272e-07,
                4.785092783454444e-06,
                1.1253525596134564e-07,
                7.338209805224048e-07,
                1.0677026154730804e-06,
                9.422447062294175e-07,
                5.715003107755449e-07
            ],
            [
                2.9023126771227976e-06,
                1.994729483723626e-06,
                3.2887498495150166e-06,
                9.422444815726566e-07,
                2.2603234895289998e-06,
                1.553497199007048e-06,
                6.144176799227922e-06,
                6.144176066795103e-06,
                7.889266347636241e-06,
                0.9988304894678607
            ],
            [
                4.450850519403407e-07,
                2.1024331597262577e-07,
                3.466327037548308e-07,
                4.450848927650143e-07,
                1.9947292459347367e-06,
                6.475950298011458e-07,
                2.10243290909724e-07,
                3.059022269250683e-07,
                1.5534975693869924e-06,
                1.6373766672973748e-07
            ],
            [
                2.3823699519290042e-07,
                7.734415776836702e-08,
                2.1024339116168358e-07,
                1.4449800373118268e-07,
                1.6373766672973748e-07,
                1.4449805540763184e-07,
                7.734421308914719e-08,
                1.6373774480605869e-07,
                1.6373764721072816e-07,
                2.382370235933104e-07
            ],
            [
                1.067703251864202e-06,
                2.260325375664839e-06,
                4.222834451355964e-06,
                1.994729483694599e-06,
                2.561282821352716e-06,
                2.5612816000646084e-06,
                2.260325375664839e-06,
                1.5534975693869924e-06,
                1.5534981249496567e-06,
                2.9023116391477434e-06
            ],
            [
                9.931186222523604e-08,
                1.637377448057981e-07,
                4.691162124067829e-08,
                9.931185038635267e-08,
                3.653481209178873e-08,
                9.931186222523604e-08,
                5.315786239218605e-08,
                9.931193325852072e-08,
                6.023569884718319e-08,
                1.6373776432509826e-07
            ],
            [
                7.338207180864763e-07,
                6.475945666051092e-07,
                8.315277302788957e-07,
                1.994730197090463e-06,
                1.2098653950656417e-06,
                8.315278294072958e-07,
                1.5534983101602148e-06,
                5.043476486915964e-07,
                2.260324567337161e-06,
                1.2098659719757836e-06
            ],
            [
                1.7603430034743913e-06,
                9.931193325852072e-08,
                2.102434412875379e-07,
                7.338213304363436e-07,
                2.382369667929001e-07,
                7.338212429504183e-07,
                5.422220262555012e-06,
                1.0677031245953668e-06,
                1.147876812620341e-05,
                6.475947210046347e-07
            ],
            [
                1.2098662604126641e-06,
                1.2098652508347793e-06,
                6.475949525981759e-07,
                6.47594798194325e-07,
                1.0677026154730804e-06,
                5.715006514151423e-07,
                8.315281267861397e-07,
                8.31528424162821e-07,
                5.715003107738556e-07,
                9.422450431989127e-07
            ]
        ]
    },
    {
        "q_id": "9237_mmlu_physics",
        "cot_ids": [
            0,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            13,
            15,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            45,
            47,
            48,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            90,
            91,
            92,
            93,
            95,
            96,
            98,
            99,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.450849988811838e-07,
                6.475945666063607e-07,
                4.4508510499849186e-07,
                1.0677027427624903e-06,
                1.209866260432471e-06,
                1.9947299592933255e-06,
                5.04347468323289e-07,
                8.315281267882195e-07,
                2.3823690999323465e-07,
                3.927862002663297e-07
            ],
            [
                1.370957860576702e-06,
                1.444979692800516e-07,
                1.5534983101644536e-06,
                2.260323758987159e-06,
                2.102434162245973e-07,
                3.466326624336003e-07,
                1.7603438428660665e-06,
                1.553498124964492e-06,
                7.338208930460318e-07,
                9.422450432014836e-07
            ],
            [
                4.450852641737424e-07,
                1.6373772528704005e-07,
                5.043473480777865e-07,
                1.4449798650551755e-07,
                3.927862470899887e-07,
                1.8553919030858602e-07,
                1.8553905760062447e-07,
                2.1024341622426268e-07,
                1.637377448057981e-07,
                9.931195693628605e-08
            ],
            [
                0.9999992661790198,
                1.0129987357517693e-05,
                0.9999955048200326,
                1.1253525596174225e-07,
                0.9999993524054337,
                0.999999114843281,
                0.9999984465018757,
                0.9999988634362896,
                9.93120161310289e-08,
                0.999998239657417
            ],
            [
                2.10243290909724e-07,
                1.6373766672973748e-07,
                1.3709573702822306e-06,
                3.4663266243308805e-07,
                6.47595107001401e-07,
                1.2098652508424818e-06,
                2.699576809143613e-07,
                1.2098652508391807e-06,
                1.012999098021058e-05,
                1.8553919030858602e-07
            ],
            [
                4.450851580555361e-07,
                8.315283250394546e-07,
                3.927862002663297e-07,
                1.5534983101478522e-06,
                5.043475284430694e-07,
                7.338211554801876e-07,
                2.2603234895289998e-06,
                3.9278615344178325e-07,
                1.0677028700363782e-06,
                3.466327037553825e-07
            ],
            [
                3.0590215398968196e-07,
                3.059022998569248e-07,
                4.450852111148132e-07,
                6.475949526020042e-07,
                2.3823696679230424e-07,
                6.475950297971703e-07,
                3.927861066170637e-07,
                5.715004470313855e-07,
                3.466327450756327e-07,
                4.450851049959619e-07
            ],
            [
                0.9999995262092163,
                1.7603434231833873e-06,
                0.999999631011372,
                0.9999996310116358,
                0.9999985406237801,
                1.9947299593078385e-06,
                0.9999990577557436,
                2.430024073461624e-05,
                0.9998766054698486,
                2.5612828213934817e-06
            ],
            [
                3.059021904580685e-07,
                1.9947299593078385e-06,
                2.102434412875379e-07,
                4.450852641737424e-07,
                8.315284241665078e-07,
                5.1442207537151994e-05,
                3.0590237279085045e-07,
                3.4663249714612693e-07,
                1.8553907971855875e-07,
                5.71500651413193e-07
            ],
            [
                2.699578739999358e-07,
                8.315284241560147e-07,
                8.315279285370317e-07,
                8.315280276505193e-07,
                4.450851049941403e-07,
                8.939695238634211e-06,
                9.422448185478557e-07,
                3.927862939126708e-07,
                5.715003789017068e-07,
                9.422443692489024e-07
            ],
            [
                4.450851580540182e-07,
                5.043475885657239e-07,
                NaN,
                NaN,
                0.0003353502312141809,
                9.422444815814404e-07,
                8.315278294114555e-07,
                3.466326624336003e-07,
                3.4663266243111764e-07,
                1.5534975693979422e-06
            ],
            [
                0.9999992188519494,
                0.9999997761970781,
                0.9999991148428592,
                0.9999995549149483,
                0.9999996072138937,
                0.9999983463110071,
                0.9999983463098239,
                0.9999999006880431,
                0.9999995549151075,
                7.338208930460318e-07
            ],
            [
                6.475950298021765e-07,
                1.275190732904469e-07,
                1.1253506814842375e-07,
                2.699577774585891e-07,
                1.994729008151319e-06,
                4.450852111155216e-07,
                6.475946438055299e-07,
                3.05902336324494e-07,
                2.6995774527718623e-07,
                3.927862002663297e-07
            ],
            [
                4.450848927658745e-07,
                1.209866260432471e-06,
                2.902312331170226e-06,
                2.2603248367949354e-06,
                3.05902263391829e-07,
                NaN,
                1.5534984953552536e-06,
                3.927862002663297e-07,
                7.338208055680009e-07,
                7.338208055680009e-07
            ],
            [
                3.9278615344178325e-07,
                4.4508505193932864e-07,
                2.90231094723893e-06,
                2.6995784182140636e-07,
                1.3709568799919866e-06,
                7.889260704968913e-06,
                4.785093924389007e-06,
                9.422443692555439e-07,
                3.288747889284851e-06,
                1.5534983101602148e-06
            ],
            [
                0.9999988634360197,
                0.9999992661786702,
                0.9999984465024322,
                3.726638395634011e-06,
                0.9999938558239557,
                0.9999980052705186,
                0.9999985406241287,
                0.9999852610111153,
                0.9999989322971308,
                0.9999955048173607
            ],
            [
                1.5534977545886537e-06,
                NaN,
                2.3823688159291947e-07,
                3.9278605979534166e-07,
                NaN,
                9.422448185510695e-07,
                9.422448185534261e-07,
                4.222832941193893e-06,
                7.889260704968913e-06,
                NaN
            ],
            [
                6.475947982037486e-07,
                5.04347468323289e-07,
                2.699576809143613e-07,
                2.699578740032504e-07,
                7.338208055664991e-07,
                8.315277302788957e-07,
                8.315284241650899e-07,
                5.043472278322555e-07,
                3.2887498495150166e-06,
                6.475948754012522e-07
            ],
            [
                NaN,
                3.927863407379485e-07,
                9.422443692574719e-07,
                7.338209805240734e-07,
                1.3709568799919866e-06,
                2.382368247924618e-07,
                2.3823702359290413e-07,
                NaN,
                NaN,
                7.338208930460318e-07
            ],
            [
                NaN,
                2.5612831267202583e-06,
                1.7603427936335396e-06,
                1.1478768125911099e-05,
                1.0677026154774503e-06,
                1.1478764021029928e-05,
                3.726638839878908e-06,
                3.2887482813149375e-06,
                6.475947210031623e-07,
                1.5534977545886537e-06
            ],
            [
                2.260324028443809e-06,
                1.5534971990169383e-06,
                4.222834954753043e-06,
                2.6995790618469934e-07,
                NaN,
                7.338211554813555e-07,
                1.3709573702856596e-06,
                5.715002426486762e-07,
                NaN,
                5.715005832895975e-07
            ],
            [
                0.999998712104171,
                0.999964643732559,
                0.9999986290431211,
                1.5534984953453635e-06,
                1.3709575337078829e-06,
                3.2887502415438413e-06,
                2.144494841482881e-05,
                0.0004878571793783068,
                7.88926164518358e-06,
                7.338212429464139e-07
            ],
            [
                6.475950298021765e-07,
                1.2098659719788098e-06,
                2.1024334103553052e-07,
                9.931186222523604e-08,
                8.764244316973974e-08,
                7.338212429582604e-07,
                5.715006514176113e-07,
                1.2098659719788098e-06,
                8.764242227418718e-08,
                8.315278294114555e-07
            ],
            [
                NaN,
                1.0129993395336818e-05,
                1.0677027427624903e-06,
                1.0677026154827912e-06,
                8.315277302857965e-07,
                6.47594952603035e-07,
                2.561283126728994e-06,
                8.31528325040778e-07,
                1.994729008151319e-06,
                4.450851049959619e-07
            ],
            [
                1.994730197071414e-06,
                3.72664061671159e-06,
                3.7266406168403854e-06,
                NaN,
                1.3709567165579959e-06,
                2.9023126771227976e-06,
                3.288749065406658e-06,
                2.1444940744864302e-05,
                2.260324836776948e-06,
                1.9947304348703948e-06
            ],
            [
                2.3823702359290413e-07,
                5.04347468323289e-07,
                3.4663274507713016e-07,
                2.102434412875379e-07,
                1.4449798650551755e-07,
                9.422443692574719e-07,
                5.043476486924565e-07,
                3.4663274507713016e-07,
                1.4449800373118268e-07,
                2.382369951932796e-07
            ],
            [
                5.715003789046955e-07,
                NaN,
                1.2098652508424818e-06,
                3.9278634073732336e-07,
                6.475948754012522e-07,
                5.715005832886879e-07,
                NaN,
                2.382368531929327e-07,
                4.450849988811838e-07,
                5.715005832886879e-07
            ],
            [
                2.382368531929327e-07,
                1.444979692800516e-07,
                NaN,
                1.637377057680051e-07,
                1.6373764721039308e-07,
                3.059022998576899e-07,
                2.382369667929001e-07,
                2.6995774527718623e-07,
                2.6995790618469934e-07,
                NaN
            ],
            [
                3.05902263391829e-07,
                NaN,
                NaN,
                1.994730672668496e-06,
                1.4449803818215767e-07,
                NaN,
                1.0677029973219343e-06,
                8.764254764780641e-08,
                2.699577774589574e-07,
                4.450851049991497e-07
            ],
            [
                1.994729959224386e-06,
                1.3709567165617364e-06,
                1.1253516205489029e-07,
                2.699578740032504e-07,
                8.315280276626197e-07,
                5.715003107767143e-07,
                3.4663274507713016e-07,
                2.699577774589574e-07,
                1.637377057680051e-07,
                1.1253508156363576e-07
            ],
            [
                2.1024331597262577e-07,
                1.5534975693979422e-06,
                3.466327863983311e-07,
                5.043475885674441e-07,
                2.699577774585891e-07,
                2.1024341622368903e-07,
                5.043474081993875e-07,
                1.637377448057981e-07,
                5.043475885674441e-07,
                7.338213304363436e-07
            ],
            [
                7.338208055680009e-07,
                2.6995784182183607e-07,
                1.4449802095666915e-07,
                4.4508515805735777e-07,
                3.927863407379485e-07,
                1.2751908849167202e-07,
                1.4449798650569826e-07,
                1.1253520230052635e-07,
                1.8553910183674878e-07,
                5.3157830707696514e-08
            ],
            [
                7.338210679979539e-07,
                2.561283432035425e-06,
                9.422449308748773e-07,
                6.962256249758443e-06,
                1.994729008145876e-06,
                8.315282259089153e-07,
                9.422444815765128e-07,
                2.561283432035425e-06,
                5.715004470295662e-07,
                4.785096206047877e-06
            ],
            [
                2.102434412875379e-07,
                4.4508515805735777e-07,
                1.370957860576702e-06,
                5.715007195447234e-07,
                9.422442569334097e-07,
                2.2603251062450327e-06,
                7.338212429594283e-07,
                3.4663278639892215e-07,
                NaN,
                1.209865827752005e-06
            ],
            [
                3.288747889284851e-06,
                4.785093924389007e-06,
                3.9278634073625165e-07,
                5.043472879481655e-07,
                9.422448185534261e-07,
                3.927862470861484e-07,
                5.144221366885164e-05,
                2.561281294760143e-06,
                3.466325384678894e-07,
                4.4508494582314646e-07
            ],
            [
                0.9999996072137062,
                0.9999995818813268,
                2.699576809143613e-07,
                0.9999982396563679,
                0.9999999317439953,
                1.3007126914612648e-05,
                0.9999910603026418,
                0.9999987901338849,
                0.9999999273417923,
                0.9999741325721768
            ],
            [
                1.5534979397829198e-06,
                2.699576809143613e-07,
                1.275190124846946e-07,
                1.0677029973219343e-06,
                0.00010889689638175376,
                1.3709572068553509e-06,
                8.315278294114555e-07,
                8.315279285370317e-07,
                2.9023112932296107e-06,
                NaN
            ],
            [
                2.90231094723893e-06,
                3.466325384661554e-07,
                5.71500719545698e-07,
                6.962257079889302e-06,
                1.0677029973219343e-06,
                3.9278620026686556e-07,
                1.994729721518893e-06,
                3.466326211113502e-07,
                2.69957906184239e-07,
                NaN
            ],
            [
                6.825600469412533e-08,
                2.69957906184239e-07,
                1.855391239544352e-07,
                2.382368531929327e-07,
                2.1024341622368903e-07,
                1.5534979397790343e-06,
                1.4449807263312446e-07,
                1.2751899728286965e-07,
                5.043475284468537e-07,
                7.734421308914719e-08
            ],
            [
                1.855391681898159e-07,
                2.6995774527577444e-07,
                2.382368815916736e-07,
                2.1024339116082313e-07,
                2.6995771309523475e-07,
                1.8553910183607374e-07,
                3.466324971415162e-07,
                2.1024334103505245e-07,
                1.4449805540740185e-07,
                1.2098662604192665e-06
            ],
            [
                8.481104140395962e-05,
                1.3709576971463352e-06,
                9.422443692574719e-07,
                8.315277302857965e-07,
                1.994729483729522e-06,
                NaN,
                3.288748281329893e-06,
                1.760342793638743e-06,
                1.0677026154806063e-06,
                2.2603234895372223e-06
            ],
            [
                1.2098652508424818e-06,
                1.4449796928021588e-07,
                NaN,
                1.8553910183674878e-07,
                3.65348425788669e-08,
                0.8175744761936437,
                NaN,
                1.275190124846946e-07,
                3.05902190458764e-07,
                0.00026119021642442364
            ],
            [
                9.93118503859575e-08,
                4.4508515805735777e-07,
                7.338207180898968e-07,
                1.1253525596174225e-07,
                1.8553910183674878e-07,
                1.5534984953552536e-06,
                9.422447062294175e-07,
                1.637377448057981e-07,
                4.450852111155216e-07,
                1.0677024882029858e-06
            ],
            [
                2.260324028427877e-06,
                NaN,
                1.3709576971425944e-06,
                2.9023112932177327e-06,
                1.7603432133296774e-06,
                7.338211554783522e-07,
                2.9023112932045342e-06,
                8.315281267834927e-07,
                3.7266410611296085e-06,
                5.422218969895357e-06
            ],
            [
                7.338209805240734e-07,
                1.9947301970972664e-06,
                3.466325797896173e-07,
                2.699577774585891e-07,
                8.315277302857965e-07,
                1.760343213335281e-06,
                7.338208055664991e-07,
                1.2751905808881762e-07,
                1.5534971990126997e-06,
                4.22283545819819e-06
            ],
            [
                9.422449308774482e-07,
                3.05902190458764e-07,
                3.059022269250683e-07,
                3.9278634073732336e-07,
                1.3709567165617364e-06,
                8.315278294114555e-07,
                1.8553907971855875e-07,
                NaN,
                4.4508515805735777e-07,
                1.7603430034867993e-06
            ],
            [
                3.059022269250683e-07,
                1.1253513522447425e-07,
                1.1253512180925583e-07,
                5.71500719545698e-07,
                9.931193325852072e-08,
                1.1253525596134564e-07,
                6.475949526003845e-07,
                1.1253521571574156e-07,
                1.2098659719788098e-06,
                1.6373766672973748e-07
            ],
            [
                3.927862470899887e-07,
                1.5534984953453635e-06,
                8.315284241597959e-07,
                3.288750633569722e-06,
                1.3709567165530083e-06,
                1.7603432133136672e-06,
                7.338208930355202e-07,
                7.338212429504183e-07,
                0.9999910602994533,
                8.315278294072958e-07
            ],
            [
                4.450852111148132e-07,
                0.999998346310612,
                0.9999998024947272,
                0.9999952149055104,
                0.9999987901343176,
                1.4449802095666915e-07,
                0.9999925887166103,
                NaN,
                0.9999916019299783,
                1.6373774480605869e-07
            ],
            [
                1.2751904288710323e-07,
                6.825600469412533e-08,
                9.422442569315887e-07,
                9.931188590255539e-08,
                2.6995784182183607e-07,
                9.931189774187203e-08,
                9.931202796993203e-08,
                8.764245361752286e-08,
                4.6911677163762064e-08,
                8.764254764780641e-08
            ],
            [
                1.370957860576702e-06,
                3.4663266242969896e-07,
                3.7266397283908927e-06,
                5.422220262636381e-06,
                3.0590219045914655e-07,
                9.422445939032799e-07,
                1.3007133116353526e-05,
                2.2603253756956754e-06,
                7.338207180601138e-07,
                2.5612828213934817e-06
            ],
            [
                1.4449805540700758e-07,
                1.8553910183607374e-07,
                2.699577774585891e-07,
                3.7266406168624155e-06,
                3.927862470899887e-07,
                2.6995774527577444e-07,
                3.466326624322211e-07,
                3.466326624322211e-07,
                3.4663262110945863e-07,
                1.4449795205429202e-07
            ],
            [
                4.450848927637999e-07,
                4.2228319344021954e-06,
                3.7266401726359486e-06,
                5.715007195447234e-07,
                8.315281267882195e-07,
                8.315284241650899e-07,
                1.3709567165617364e-06,
                6.475945666051092e-07,
                2.561281294760143e-06,
                4.4508494582314646e-07
            ],
            [
                0.9999998257021837,
                0.9998204720146521,
                0.9999998724809419,
                0.9999989322975131,
                0.9999942280799784,
                0.9999999067050943,
                0.9999997463981335,
                0.9999987121052458,
                0.9999960330140913,
                0.9999996940977732
            ],
            [
                1.4738985486506781e-05,
                2.260323758987159e-06,
                3.927862470899887e-07,
                3.059022998576899e-07,
                1.7603425837855082e-06,
                NaN,
                6.962253760024999e-06,
                2.5612812947508257e-06,
                7.338212429582604e-07,
                6.475945666051092e-07
            ],
            [
                5.715005832886879e-07,
                2.10243290909724e-07,
                0.9999945777784548,
                5.043476486924565e-07,
                NaN,
                5.043474683240344e-07,
                0.9999969105055562,
                3.927861534406222e-07,
                3.4663278639892215e-07,
                5.043472278322555e-07
            ],
            [
                4.222834451327159e-06,
                1.553498495338299e-06,
                3.4663249714612693e-07,
                3.288748673295719e-06,
                6.144173869446876e-06,
                NaN,
                4.4508510499849186e-07,
                NaN,
                3.726638839878908e-06,
                3.0590226339061185e-07
            ],
            [
                0.9999997463981032,
                0.9999998802069017,
                0.9999985406239533,
                0.9999998362622552,
                0.9999987901347495,
                0.9999987121044782,
                0.9999990577551827,
                0.9999997617631753,
                0.999999674368742,
                0.9999997761971315
            ],
            [
                0.9999997761970782,
                0.9999983463096266,
                0.9999980052707561,
                0.9999960330136171,
                3.927863407379485e-07,
                0.9999993524052793,
                0.9999997126314811,
                3.9278634073732336e-07,
                2.6995774527718623e-07,
                0.9999991148433868
            ],
            [
                0.9999994631249323,
                3.726639284125553e-06,
                0.99999926617867,
                2.5612822107167428e-06,
                4.4508494582405734e-07,
                0.9999974387184023,
                2.3823682479292225e-07,
                3.927862002663297e-07,
                0.9999991684720717,
                1.275190276859705e-07
            ],
            [
                3.4663253846473677e-07,
                3.4663249714325014e-07,
                5.04347468323289e-07,
                5.04347528440776e-07,
                1.5534984953552536e-06,
                1.760342793638743e-06,
                1.7603430034655858e-06,
                2.9023109472494878e-06,
                3.0590237279032884e-07,
                2.3823685319244518e-07
            ],
            [
                1.855391239544352e-07,
                1.4449800373118268e-07,
                1.8553910183674878e-07,
                3.466327450765785e-07,
                9.931189774187203e-08,
                1.2751901248454963e-07,
                5.3157811697009444e-08,
                NaN,
                1.1253522913127183e-07,
                1.1253514863968147e-07
            ],
            [
                4.4508515805735777e-07,
                1.209865827752005e-06,
                3.288748673376478e-06,
                2.382369951932796e-07,
                8.315281267882195e-07,
                2.1024334103581732e-07,
                5.715006514176113e-07,
                2.699578740032504e-07,
                5.043475885696228e-07,
                6.475950298021765e-07
            ],
            [
                1.2751899728311609e-07,
                8.315283250394546e-07,
                2.3823690999323465e-07,
                8.764244316973974e-08,
                9.422445939054222e-07,
                1.6373774480605869e-07,
                4.139941495546278e-08,
                0.9999798543140412,
                2.1024341622426268e-07,
                1.855391681906175e-07
            ],
            [
                2.6995771309523475e-07,
                2.1024341622368903e-07,
                2.69957906184239e-07,
                3.466325797888292e-07,
                2.6995777745711594e-07,
                1.444980209564556e-07,
                2.3823693839290317e-07,
                2.69957906184239e-07,
                2.3823693839290317e-07,
                8.315281267800897e-07
            ],
            [
                5.043475885674441e-07,
                2.1444950971601277e-05,
                5.715005832886879e-07,
                1.3709573702822306e-06,
                6.47594952595231e-07,
                2.2603234895289998e-06,
                1.7603434231705793e-06,
                2.9023119851781017e-06,
                1.2098653950656417e-06,
                1.3709576971425944e-06
            ],
            [
                1.0677029973219343e-06,
                1.3709576971425944e-06,
                5.043475284468537e-07,
                2.5612819054133693e-06,
                NaN,
                3.72663883989755e-06,
                1.8553907971855875e-07,
                1.0677027427600627e-06,
                NaN,
                4.4508494582405734e-07
            ],
            [
                7.734416698849138e-08,
                1.8553910183674878e-07,
                1.4449798650551755e-07,
                1.2751905808881762e-07,
                1.8553905760062447e-07,
                9.931193325852072e-08,
                2.382369951932796e-07,
                2.3823690999290963e-07,
                5.3157830707696514e-08,
                7.73441946488886e-08
            ],
            [
                3.927862002654366e-07,
                3.72663883989755e-06,
                1.855391239547094e-07,
                NaN,
                2.90231094723893e-06,
                4.450852111155216e-07,
                7.338213304316717e-07,
                1.0677027427624903e-06,
                1.9947299593078385e-06,
                NaN
            ],
            [
                5.144220139740624e-05,
                0.9999969105044496,
                0.9999945777823296,
                0.9999996743687035,
                0.9999546021152791,
                0.9999989322967487,
                0.999999631011592,
                2.75356845363217e-05,
                0.9999989322967487,
                0.999954602147754
            ],
            [
                1.370957860576702e-06,
                1.760342793638743e-06,
                3.466327037553825e-07,
                1.994729721518893e-06,
                5.715007195431641e-07,
                1.0677027427624903e-06,
                6.475947982037486e-07,
                6.475947210046347e-07,
                4.450852111148132e-07,
                6.475945666051092e-07
            ],
            [
                5.715007195353674e-07,
                7.338212429537553e-07,
                8.315282259089153e-07,
                1.2098662604247682e-06,
                8.315280276546789e-07,
                7.338209805200689e-07,
                2.699578740011634e-07,
                7.338210679909462e-07,
                7.338207180761315e-07,
                1.2098655392811161e-06
            ],
            [
                1.5534973842076057e-06,
                6.144177531811707e-06,
                6.475945666051092e-07,
                1.8553910183674878e-07,
                5.043474683240344e-07,
                2.2603248367949354e-06,
                5.715005832895975e-07,
                8.315284241665078e-07,
                6.144173136952939e-06,
                5.71500515161527e-07
            ],
            [
                2.1024344128660572e-07,
                4.450851049991497e-07,
                6.475947210046347e-07,
                NaN,
                NaN,
                4.785096776468749e-06,
                3.726638839878908e-06,
                4.222833444590791e-06,
                8.315283250394546e-07,
                1.7603427936335396e-06
            ],
            [
                NaN,
                7.88926446679691e-06,
                3.2887482813149375e-06,
                NaN,
                1.5534981249697903e-06,
                3.2887502415438413e-06,
                1.5534975693933505e-06,
                9.422443692555439e-07,
                4.785093353940187e-06,
                2.561281600086738e-06
            ],
            [
                0.9999996310116359,
                6.475945666063607e-07,
                0.9999955048178878,
                0.9999869928653583,
                0.9999996310113719,
                0.9999986290424668,
                2.699578740032504e-07,
                6.962253760024999e-06,
                0.9999916019310056,
                3.05902336324494e-07
            ],
            [
                9.931189774187203e-08,
                3.0590219045914655e-07,
                3.4663274507713016e-07,
                6.475945666063607e-07,
                1.2751905808881762e-07,
                2.10243290909724e-07,
                1.1253508156363576e-07,
                2.1024336609874897e-07,
                2.102434412875379e-07,
                1.8553905760062447e-07
            ],
            [
                1.637377448057981e-07,
                4.450851580555361e-07,
                6.475948754012522e-07,
                1.6373774480479287e-07,
                2.6995784182140636e-07,
                5.71500719545698e-07,
                3.9278634073732336e-07,
                3.059023727894942e-07,
                4.450849988798682e-07,
                1.2751902768478173e-07
            ],
            [
                1.8553914607267268e-07,
                3.466326624336003e-07,
                1.8553907971879076e-07,
                1.275190428875671e-07,
                3.927862470899887e-07,
                6.825606165129312e-08,
                4.450852111155216e-07,
                NaN,
                5.043475885696228e-07,
                8.315279285370317e-07
            ],
            [
                4.691162124067829e-08,
                6.825602910433871e-08,
                7.734425919002834e-08,
                1.1253525596174225e-07,
                4.4508515805735777e-07,
                1.275190428875671e-07,
                1.1253509497883659e-07,
                1.4449796928021588e-07,
                8.76424013786396e-08,
                2.1024334103581732e-07
            ],
            [
                3.4663266243308805e-07,
                5.715002426486762e-07,
                2.2603253756956754e-06,
                3.9278615344178325e-07,
                3.059022269250683e-07,
                5.043472278322555e-07,
                3.9278634073732336e-07,
                5.043473480777865e-07,
                3.4663249714612693e-07,
                7.338208930460318e-07
            ],
            [
                0.9999942280792904,
                0.999998540623084,
                0.9999999317440197,
                0.9999999226558515,
                0.9999898700114476,
                0.9999785550439698,
                0.9999991684721713,
                3.466326624336003e-07,
                0.9999949062956114,
                NaN
            ],
            [
                2.6995774527718623e-07,
                1.637377057680051e-07,
                2.3823685319244518e-07,
                3.059021175261338e-07,
                7.33821330437595e-07,
                3.927862470905692e-07,
                3.466325797888292e-07,
                3.927863875616689e-07,
                4.450851580555361e-07,
                5.715005832886879e-07
            ],
            [
                0.9999904837449173,
                2.260324567337161e-06,
                0.9999843104521859,
                0.9999756997680205,
                0.9999910603058464,
                0.99998431044844,
                5.715002426486762e-07,
                0.9999969105066626,
                1.3709567165617364e-06,
                0.9999967112521128
            ],
            [
                3.726641061109272e-06,
                1.994729483723626e-06,
                NaN,
                5.043474683204221e-07,
                4.785094494716039e-06,
                6.962256249885085e-06,
                1.9947299593078385e-06,
                6.962257909785973e-06,
                6.144176799283803e-06,
                1.7603434231833873e-06
            ],
            [
                1.0677026154806063e-06,
                6.144176799334096e-06,
                8.93969950132721e-06,
                1.0129993395336818e-05,
                1.7603440527286572e-06,
                2.2603242978778778e-06,
                NaN,
                6.605216044933028e-05,
                2.5612825160562587e-06,
                6.475949526020042e-07
            ],
            [
                0.9999996310115042,
                NaN,
                0.9999987121047857,
                0.9999810748451025,
                1.7603434231833873e-06,
                NaN,
                0.9999984465024324,
                6.144176066901277e-06,
                8.315284241650899e-07,
                4.4508494582314646e-07
            ],
            [
                5.315781803390236e-08,
                6.475950298021765e-07,
                1.3709575337159875e-06,
                2.6995774527718623e-07,
                5.043475885696228e-07,
                2.699577452775239e-07,
                NaN,
                NaN,
                1.637377057680051e-07,
                2.9023112932296107e-06
            ],
            [
                NaN,
                NaN,
                4.785095065232451e-06,
                4.785095635655362e-06,
                2.1024331597262577e-07,
                1.0677032518814388e-06,
                7.338210680021253e-07,
                4.450849988811838e-07,
                2.902312677150514e-06,
                3.059022998576899e-07
            ],
            [
                1.444979692800516e-07,
                2.3823696679327928e-07,
                3.466327863983311e-07,
                2.382368531929327e-07,
                2.102434162245973e-07,
                3.05902263391829e-07,
                2.3823690999323465e-07,
                1.4449798650551755e-07,
                1.2751899728311609e-07,
                4.450852111155216e-07
            ],
            [
                NaN,
                1.0677026154827912e-06,
                NaN,
                5.715005832895975e-07,
                5.043475885696228e-07,
                5.043474081993875e-07,
                3.9278620026686556e-07,
                6.962254589978262e-06,
                8.315277302841894e-07,
                2.5612834320563895e-06
            ],
            [
                1.0677031245905116e-06,
                3.927862939126708e-07,
                5.715007195431641e-07,
                4.4508526417298334e-07,
                4.450849458200093e-07,
                6.475947982002148e-07,
                6.475951069985296e-07,
                1.8553903548231313e-07,
                1.5534971990126997e-06,
                5.715007195447234e-07
            ],
            [
                1.1253513522447425e-07,
                8.76424013786396e-08,
                1.8553919030826963e-07,
                4.450851049991497e-07,
                1.1253520230052635e-07,
                1.1253506814842375e-07,
                9.931200429212718e-08,
                3.466325797900508e-07,
                3.05902263391829e-07,
                2.1024339116168358e-07
            ],
            [
                4.4508505193932864e-07,
                1.0129992187658463e-05,
                3.9278615344178325e-07,
                7.338212429582604e-07,
                8.315283250371857e-07,
                7.338208055489796e-07,
                8.315278294072958e-07,
                1.6373766672973748e-07,
                5.043476486915964e-07,
                1.2098659719441482e-06
            ],
            [
                1.5534981249697903e-06,
                NaN,
                NaN,
                2.2603242978871282e-06,
                1.0677024882009222e-06,
                3.466325384661554e-07,
                6.144172404738491e-06,
                9.422450432014836e-07,
                1.0677024881980089e-06,
                1.3709567165579959e-06
            ],
            [
                NaN,
                4.222834954687752e-06,
                7.338209805240734e-07,
                3.2887478892683997e-06,
                2.1024326584639497e-07,
                5.04347528446051e-07,
                1.9947304348862686e-06,
                3.288748673376478e-06,
                1.9947301970972664e-06,
                6.144176066943187e-06
            ],
            [
                9.931189774187203e-08,
                6.023579219579052e-08,
                1.4449805540763184e-07,
                2.699577774585891e-07,
                NaN,
                3.05902263391829e-07,
                2.1024336609874897e-07,
                1.275190276859705e-07,
                9.931195693628605e-08,
                9.931202796993203e-08
            ],
            [
                0.9999989969861516,
                0.9999982396559483,
                NaN,
                1.7603440527222532e-06,
                1.760343003481596e-06,
                4.2228329411708495e-06,
                0.9999970976873263,
                0.9999985406243017,
                0.999994577779752,
                5.043472879540142e-07
            ],
            [
                0.9999934595604404,
                1.2098656835224664e-06,
                0.9999898700054063,
                0.9999978766217927,
                0.9999646437577976,
                0.9999898700102455,
                0.9999990577551822,
                0.9999949062950001,
                0.9999993106387906,
                0.9999998802069587
            ],
            [
                NaN,
                1.275190428875671e-07,
                7.338208055680009e-07,
                NaN,
                1.6373766672994222e-07,
                5.043472278322555e-07,
                2.90231233114251e-06,
                1.7603438428188364e-06,
                3.7266379512857925e-06,
                3.288749065423109e-06
            ],
            [
                0.999999712631481,
                0.9999995549151075,
                0.9999995262093858,
                0.9999991148431757,
                0.9999991684717743,
                0.9999989969854339,
                0.9999985406236054,
                0.9999984465018762,
                0.9999687980961468,
                0.9999994956523515
            ],
            [
                4.4508515805735777e-07,
                7.338207180898968e-07,
                4.450848927658745e-07,
                1.275190276859705e-07,
                4.450851049991497e-07,
                8.764249540862797e-08,
                1.6373764721072816e-07,
                1.855391681906175e-07,
                8.315280276626197e-07,
                3.466327037553825e-07
            ],
            [
                7.338208930460318e-07,
                4.4508515805735777e-07,
                1.994729721518893e-06,
                2.2603242978871282e-06,
                4.4508515805735777e-07,
                8.315284241665078e-07,
                1.370957860576702e-06,
                3.2887494574832472e-06,
                1.5534975693979422e-06,
                1.0677024882029858e-06
            ],
            [
                2.699578096403948e-07,
                8.7642558095602e-08,
                8.764241182641775e-08,
                3.059022269254856e-07,
                1.275191036933194e-07,
                6.47595107001401e-07,
                8.315279285370317e-07,
                5.3157811697009444e-08,
                1.4449802095666915e-07,
                3.653479467066246e-08
            ],
            [
                6.475945666051092e-07,
                2.1024336609843824e-07,
                1.9947292459347367e-06,
                9.422442569315887e-07,
                2.5612831267202583e-06,
                2.69957906184239e-07,
                3.288748673376478e-06,
                2.2603251062450327e-06,
                2.1024341622426268e-07,
                3.4663249714451116e-07
            ],
            [
                2.5612812947508257e-06,
                3.7266401726173067e-06,
                6.144173137170873e-06,
                9.422450432030903e-07,
                3.9278634073732336e-07,
                5.043474081993875e-07,
                2.382369667929001e-07,
                NaN,
                NaN,
                2.753568453712307e-05
            ],
            [
                1.0129993394959082e-05,
                0.9999985406243016,
                1.300712846477255e-05,
                0.9999993524053565,
                0.9999992661788447,
                5.715003789046955e-07,
                NaN,
                0.9999885212359904,
                0.9999992661787573,
                0.9999980052700416
            ]
        ]
    },
    {
        "q_id": "10256_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999994956525319,
                8.764245361752286e-08,
                3.653485564473625e-08,
                0.9999994631251882,
                5.3157837044597743e-08,
                4.691165479443628e-08,
                3.2241839428313264e-08,
                1.4449798650551755e-07,
                4.139936066832438e-08,
                6.023572038912295e-08
            ],
            [
                0.9999999226557778,
                0.9999999656787243,
                0.9999999434137974,
                0.9999999123575046,
                0.9999999397642725,
                0.999999943413784,
                0.9999999656786996,
                0.9999999468421883,
                0.9999999634651661,
                0.9999999397642796
            ],
            [
                0.9999910603036981,
                0.9999957771650476,
                0.9999998024947037,
                0.999999057754957,
                0.9999995262093292,
                7.338208930443633e-07,
                0.9999986290423032,
                0.9999989322975121,
                0.9999998802069731,
                0.9999810748562873
            ],
            [
                0.9999999176675044,
                0.9999999123575778,
                0.9999999697115768,
                0.9999999273418788,
                0.999999946842182,
                0.9999999226557316,
                0.9999999358793714,
                0.9999999434137166,
                0.9999998724810026,
                0.9999996940977002
            ],
            [
                1.7603436330179102e-06,
                2.1024344128584085e-07,
                1.8553916819032217e-07,
                5.715002426460124e-07,
                5.043472879504592e-07,
                8.315277302841894e-07,
                1.0677029973158649e-06,
                2.1024336609843824e-07,
                2.1024336609843824e-07,
                0.9999990577551817
            ],
            [
                0.9999999006880312,
                0.9999999715466493,
                0.9999999468421122,
                0.9999999697115696,
                0.9999999226557409,
                0.9999998642566542,
                1.0,
                0.9999999611088533,
                0.9999999067051276,
                0.9999999715466731
            ],
            [
                0.9999984465016905,
                4.139934092760465e-08,
                0.9999997300421583,
                8.764245361752286e-08,
                0.9999993524049703,
                1.9947294837154625e-06,
                0.9999995262094422,
                0.9999999611088812,
                0.9999994631247402,
                0.9999994284993488
            ],
            [
                1.0,
                0.9999990577555188,
                0.9999999067049832,
                0.9999999559305522,
                0.9999985406232574,
                0.9999998362622943,
                0.9999996310113279,
                0.999999391641036,
                0.9999999067050053,
                0.9999999397642508
            ],
            [
                0.9999991148430699,
                0.9999998942829099,
                0.9999999500628214,
                0.9999998024946801,
                0.9999999176674357,
                0.9999997617630616,
                0.9999999697115696,
                0.9999999317439954,
                1.2751905808881762e-07,
                0.9999999778404896
            ],
            [
                0.9999999317439221,
                0.9999996743686257,
                0.9999999226558146,
                0.9999967112521123,
                1.125352291309328e-07,
                0.9999998802069016,
                0.9999998024947037,
                0.9999980052705171,
                0.9999984465020607,
                0.9999994284994169
            ],
            [
                0.9999999358793791,
                0.9999999732705698,
                0.9999998724809875,
                0.9999999468421503,
                0.9999999530884012,
                0.9999999468421756,
                0.9999998802069016,
                0.9999999226557317,
                0.9999999273417922,
                0.9999992188517627
            ],
            [
                0.9999991684717743,
                0.9999992188516696,
                4.691159887151251e-08,
                7.73442776303243e-08,
                6.023572038912295e-08,
                1.6373776432509826e-07,
                0.9999995549151073,
                0.9999996940978826,
                1.27519088491875e-07,
                0.9999998144609424
            ],
            [
                2.9023133690821773e-06,
                0.9999962733602749,
                8.315280276580819e-07,
                8.315284241597959e-07,
                2.699578096403948e-07,
                1.2098655392871682e-06,
                1.209865683518615e-06,
                1.2098652508391807e-06,
                0.9999997617630616,
                2.382368815932174e-07
            ],
            [
                0.999999855501979,
                0.999999391641036,
                0.9999995262096116,
                0.9999877809181776,
                0.9999994631247402,
                0.9999957771675655,
                3.4663278639892215e-07,
                0.9999997617629764,
                9.931190958076104e-08,
                0.9999832985722168
            ],
            [
                1.2098653950606901e-06,
                2.5612828213818346e-06,
                9.422449308774482e-07,
                5.043472879540142e-07,
                2.3823693839325527e-07,
                5.043472278322555e-07,
                2.260323758923431e-06,
                9.422447062270609e-07,
                1.370957860567974e-06,
                5.043475284447896e-07
            ],
            [
                0.9999999226557501,
                0.9999998144608983,
                0.9999999006879838,
                0.9999998874647977,
                0.999999974890018,
                0.9999999804443147,
                0.9999999468421312,
                0.9999999358794021,
                0.9999998724809723,
                0.9999999656787243
            ],
            [
                0.9999977396765126,
                5.3157900413760374e-08,
                6.825597214718257e-08,
                3.65348425788669e-08,
                0.9999930377445915,
                1.0129995810463632e-05,
                0.9999992661786699,
                0.9999997617630617,
                0.9999960330145606,
                0.9999989322967483
            ],
            [
                0.999999653367503,
                1.6373776432481905e-07,
                1.8553907971855875e-07,
                0.9999994284994169,
                0.9999991684716754,
                0.9999986290424671,
                0.9999989969861512,
                0.9999987901340284,
                0.9999996072137062,
                0.9999921107383599
            ],
            [
                4.450851580540182e-07,
                0.9999994631249963,
                6.144177531767002e-06,
                1.2098655392921197e-06,
                1.275190124842887e-07,
                0.9999994631249962,
                0.9999992661791073,
                0.999999789756634,
                3.927863875616689e-07,
                1.4449805540740185e-07
            ],
            [
                0.9999992188513902,
                0.9999999273418096,
                0.9999998642567189,
                0.9999999123575046,
                0.9999999656787121,
                0.9999999778405239,
                0.9999999500627798,
                0.9999999586005999,
                0.9999999656787243,
                0.9999999764113436
            ],
            [
                0.9999921107402411,
                0.9999999397642653,
                0.9999970976887078,
                0.9999995549150013,
                2.1024334103553052e-07,
                0.9999980052705173,
                8.764245361752286e-08,
                1.2751907329024393e-07,
                0.9999967112497599,
                2.1024339116134898e-07
            ],
            [
                0.9999999586006096,
                0.9999997126315153,
                0.9999999434137098,
                0.9999997463981939,
                0.9999999273417663,
                0.9999999123575778,
                0.9999998724809267,
                0.9999999715466256,
                0.9999999434137368,
                0.9999999559305522
            ],
            [
                0.999999310638626,
                0.9999982396569971,
                1.4449805540740185e-07,
                0.9999999067050943,
                2.510998494020641e-08,
                0.9999996533673376,
                0.9999994631251882,
                0.9999999067049831,
                0.9999999500628274,
                0.9999485577741677
            ],
            [
                6.023572038912295e-08,
                0.9999955048168161,
                1.2751899728286965e-07,
                0.999988521235993,
                0.9999997463980729,
                0.9999994284996212,
                1.370957860567974e-06,
                0.9999987121044778,
                1.8553907971879076e-07,
                0.9999998362622357
            ],
            [
                0.9999994284997575,
                0.999999802494633,
                0.9999999434137368,
                0.9999993524050477,
                0.9999999006880905,
                0.9999997761971849,
                0.9999998724810027,
                0.9999998555020307,
                0.999999814460876,
                0.999999391641036
            ],
            [
                1.4449800373118268e-07,
                0.9999996310115039,
                5.04347528446051e-07,
                1.0677027427600627e-06,
                0.9999995818812272,
                0.9999999226557316,
                9.931202796993203e-08,
                7.338207180884785e-07,
                0.9999996940976638,
                0.9999999123575046
            ],
            [
                0.9999995818811274,
                0.9999981261243943,
                0.9999999273418355,
                0.9999989322966213,
                0.9999999791830738,
                0.9999999559305732,
                0.9999999273417836,
                0.9999962733589419,
                0.999999965678712,
                0.999999974890009
            ],
            [
                0.999999057754957,
                1.2098652508347793e-06,
                0.9999986290431203,
                8.315282259089153e-07,
                0.9999993524053563,
                1.0677027427525368e-06,
                0.9999998362622747,
                5.715004470295662e-07,
                0.9999996533674615,
                0.9999991148426477
            ],
            [
                0.9999997761971315,
                0.999999922655787,
                0.999998712104324,
                1.0,
                0.9999998461826405,
                0.9999999358793409,
                0.9999984465026165,
                0.9999999273418443,
                0.999999802494633,
                0.9999998874647709
            ],
            [
                0.9999987121049382,
                0.9999942280779083,
                0.9999990577556309,
                0.9999978766210319,
                0.9999999468421503,
                0.9999998802069731,
                0.999999746398224,
                0.9999988634362896,
                0.9999998874647977,
                0.9999999273418356
            ],
            [
                0.9999999468421502,
                0.9999999317439872,
                9.93120161310289e-08,
                0.999999900688043,
                0.9999998642566704,
                0.9999969105055531,
                0.9999999226557224,
                5.3157811697009444e-08,
                0.9999993916411811,
                3.4663249714612693e-07
            ],
            [
                1.4449802095666915e-07,
                1.2751902768612997e-07,
                0.9999999559305943,
                0.999999939764258,
                0.9999999611089183,
                0.999999814460854,
                0.999999953088334,
                0.9999997761971049,
                9.93120161310289e-08,
                0.9999999559306153
            ],
            [
                7.88926352599354e-06,
                2.6995777745711594e-07,
                7.889264466639056e-06,
                1.8553910183548312e-07,
                2.5612828213690224e-06,
                8.31527928532683e-07,
                3.059022998569248e-07,
                1.0677027427525368e-06,
                7.338208055664991e-07,
                1.4449798650476187e-07
            ],
            [
                0.9999999358793485,
                0.9999999397642868,
                3.4663266243308805e-07,
                1.0,
                0.999999943413757,
                7.734415776836702e-08,
                0.9999999530884012,
                0.9999981261250639,
                0.9999999006879721,
                0.9999999006879957
            ],
            [
                2.510997296685283e-08,
                3.653479902594117e-08,
                2.845334728018925e-08,
                6.825598842065202e-08,
                6.825605351455307e-08,
                4.691161005609407e-08,
                4.139935079796334e-08,
                5.3157811697009444e-08,
                7.734416698849138e-08,
                6.825608606172863e-08
            ],
            [
                1.7257837976594428e-08,
                0.9999999123574836,
                0.9999997463981032,
                0.9999999611088951,
                1.0,
                0.9999999397642222,
                0.9999999697115479,
                1.9947292459347367e-06,
                0.9999998942829854,
                0.9999999397643154
            ],
            [
                0.9999999123575568,
                0.9999991684716751,
                0.9999996072139403,
                0.9999997897565838,
                0.9999999397643011,
                2.1024329090929374e-07,
                0.9999998257021837,
                0.9999998555020135,
                0.9999999123575987,
                0.9999999067050832
            ],
            [
                0.9999994284997575,
                0.9999995262095551,
                7.889264466725156e-06,
                1.4738978458140753e-05,
                1.7603427936263351e-06,
                0.9999985406234314,
                6.144173137014406e-06,
                3.288749849477628e-06,
                1.5534983101301911e-06,
                2.561283432035425e-06
            ],
            [
                0.9999985406234316,
                0.9999984465018755,
                0.9999994284995531,
                1.4449805540763184e-07,
                0.9999989322966211,
                0.9999969105048165,
                0.9999986290431205,
                0.9999990577554064,
                0.9999962733607172,
                9.931200429212718e-08
            ],
            [
                0.9999998942829602,
                0.9999916019269727,
                0.999999825702163,
                0.999620015521309,
                6.825597214718257e-08,
                1.275190580890061e-07,
                0.9999999358794174,
                0.999903897597087,
                0.9999998555019963,
                1.6373774480605869e-07
            ],
            [
                0.9999930377462458,
                0.9999996940976636,
                0.9999999468421376,
                0.9999994956525318,
                0.9999998555019274,
                0.9999999273418875,
                0.9999999530883229,
                0.9999925887219021,
                0.9999999732705411,
                0.999999927341853
            ],
            [
                0.9999999317439383,
                0.999999789756684,
                0.9999999123575046,
                0.9999993916409634,
                0.9999998362622747,
                0.9999986290431205,
                0.9999999226557592,
                0.9999998942830233,
                0.9999994284995531,
                0.9999996072138466
            ],
            [
                0.999999931743914,
                0.9999999468421439,
                0.9999999500628036,
                0.9999998724809116,
                0.9999999865595807,
                0.999999935879402,
                0.9999999530883564,
                0.9999999732705698,
                0.9999998642566542,
                0.9999999586006492
            ],
            [
                0.9999994284994168,
                9.422449308716635e-07,
                0.9999998942829854,
                0.9999999273417749,
                2.69957906184239e-07,
                8.315282259117513e-07,
                0.9999999006879957,
                0.9999999226558238,
                9.422447062270609e-07,
                0.9999991684717742
            ],
            [
                0.9999996533674204,
                0.005220124593313314,
                0.9999992188518558,
                0.999999391640891,
                0.9999998257021422,
                0.9999993106389548,
                0.9999995262093857,
                0.9999996533674617,
                0.999999746398224,
                0.9999981261241704
            ],
            [
                0.9999969105044496,
                1.275190276859705e-07,
                0.9999952149049393,
                0.9999998555019791,
                0.9999993916411085,
                0.9999998362622943,
                0.9999969105040807,
                5.3157811697009444e-08,
                0.9999998257022045,
                0.9999938558232044
            ],
            [
                0.9999997897565838,
                0.9999999634651444,
                0.9999999226557776,
                0.9999999176675731,
                0.9999999067050943,
                0.9999999434137704,
                0.9999999697115912,
                0.9999998144609645,
                1.5534984953453635e-06,
                0.9999999358793714
            ],
            [
                2.3823682479181176e-07,
                0.9999910603026382,
                0.9999910603068982,
                8.315280276607289e-07,
                2.382369383923073e-07,
                9.931198061405701e-08,
                7.338209805170655e-07,
                1.0677029973158649e-06,
                3.7266401726359486e-06,
                7.338211554783522e-07
            ],
            [
                2.2603237589676295e-06,
                1.6373772528677946e-07,
                0.9999995262096116,
                0.9999991148433864,
                0.9999996940978825,
                0.9999998874649318,
                2.382368247924618e-07,
                5.315789407685159e-08,
                8.939700566907275e-06,
                1.8553916819032217e-07
            ],
            [
                0.999999974889997,
                0.9999999434137232,
                0.9999997617630049,
                0.9999998257020798,
                0.9999999530883564,
                0.9999994956525318,
                0.999998346311006,
                0.9999999006880668,
                0.999999825702163,
                3.466325384678894e-07
            ],
            [
                0.9999978766210321,
                2.5109990926882483e-08,
                0.9999992188519489,
                1.5229988590535506e-08,
                9.931189774187203e-08,
                6.825597214718257e-08,
                0.9999996072137529,
                0.9999981261237235,
                4.691160446380562e-08,
                0.9999997761970781
            ],
            [
                0.999997593897375,
                0.9999993106387082,
                1.0677024881980089e-06,
                6.825601283086733e-08,
                0.9999999715466323,
                1.2098653950692178e-06,
                0.99999995860059,
                1.7603434231777837e-06,
                0.9999949062943945,
                0.9999997463980124
            ],
            [
                0.9999997617631184,
                0.9999999226557778,
                0.9999998555019274,
                0.9999999006880549,
                0.999999581881277,
                0.9999994284992806,
                0.9999999226557408,
                0.9999996940978461,
                0.9999993524048931,
                0.999999855501979
            ],
            [
                0.9999998802069302,
                0.9999997126314468,
                3.9278615344178325e-07,
                0.9999998362623334,
                0.9999996533674204,
                0.9999997300420939,
                8.764241182641775e-08,
                0.9999996743686257,
                0.9999998942830485,
                0.9999997761971314
            ],
            [
                0.9999991684715762,
                0.9999995262094423,
                0.999999310638626,
                0.9999997463981939,
                0.999999310639037,
                0.9999991148431756,
                0.9999995818811275,
                0.9999975938976617,
                0.9999990577557435,
                0.999999631011592
            ],
            [
                0.9999989969860318,
                2.2603240283888175e-06,
                0.999994577781037,
                0.9999998942829855,
                0.9999998724809268,
                0.9999997126314811,
                0.9999997126314126,
                5.422220908925639e-06,
                0.9999994631251881,
                5.043475885688201e-07
            ],
            [
                8.7642558095602e-08,
                0.9999997300421904,
                1.275190428875671e-07,
                0.9999999434138109,
                0.999999931743979,
                0.9999969105044493,
                0.9999998642566866,
                3.9278629391427843e-07,
                0.9999999634651836,
                6.825597214718257e-08
            ],
            [
                0.9999998642567028,
                0.999999917667573,
                6.825606978801862e-08,
                3.6534807736504303e-08,
                0.9999910603069027,
                1.9555694692738946e-08,
                0.9999999634651443,
                3.0590237279085045e-07,
                7.338207180864763e-07,
                3.466325797896173e-07
            ],
            [
                0.9999999176675436,
                0.9999999697115877,
                0.9999990577556311,
                0.9999994956524716,
                0.9999898700102381,
                4.691162683297406e-08,
                0.9999904837494502,
                2.8453367631661124e-08,
                9.931189774187203e-08,
                0.9999970976883625
            ],
            [
                3.726637951367137e-06,
                0.9999998874647977,
                0.9999785550516269,
                0.9999995262093856,
                0.9999930377404357,
                0.9999978766217925,
                0.9999998942830485,
                0.9999992188514834,
                0.999998790134461,
                4.450852111148132e-07
            ],
            [
                6.023573475041126e-08,
                2.1024331597262577e-07,
                1.2751910369310194e-07,
                4.691160446380562e-08,
                4.691162683297406e-08,
                4.4508505193932864e-07,
                3.224184327183648e-08,
                9.931187406410953e-08,
                0.9999945777803863,
                5.043472879540142e-07
            ],
            [
                0.9999986290429571,
                0.9999996940977366,
                0.9999998874647575,
                0.9999995262092163,
                0.9999983463102177,
                0.9999967112505453,
                0.9999955048168164,
                8.764254764780641e-08,
                0.9999982396572071,
                0.999998239655948
            ],
            [
                0.999999825702163,
                0.9999999123575255,
                0.9999998874647307,
                0.9999996940976638,
                1.6373774480605869e-07,
                0.9999999732705761,
                0.9999998802068873,
                0.9999995262093292,
                4.139934586278605e-08,
                1.637376862489725e-07
            ],
            [
                0.999999894283061,
                0.9999995818811275,
                0.9999999123574629,
                0.9999999559305576,
                0.9999990577550694,
                0.9999994631251242,
                0.9999998362622748,
                0.9999957771645439,
                1.27519088491875e-07,
                0.9999999434137165
            ],
            [
                5.04347468323289e-07,
                5.315784971839039e-08,
                2.3823688159237777e-07,
                3.72664061681327e-06,
                2.3823702359290413e-07,
                4.2228329411708495e-06,
                1.8553903548231313e-07,
                1.1253518888531272e-07,
                1.855391460719133e-07,
                2.3823690999160957e-07
            ],
            [
                0.999999946842163,
                0.9999999468421377,
                0.9999999500628571,
                0.9999964991455871,
                0.9999994631249961,
                0.9999996310115479,
                0.9999998257022045,
                0.9999999434137098,
                0.9999998362622943,
                5.715004470295662e-07
            ],
            [
                0.9999989969862709,
                0.9999991684720717,
                0.9999996743687033,
                0.9999994284996894,
                0.9999996072138467,
                0.999999927341801,
                0.9999999273418095,
                0.9999996533672137,
                0.9999994284996212,
                0.9999934595619987
            ],
            [
                0.9999996072138466,
                0.9999999634651923,
                0.9999998874647307,
                0.9999999468421186,
                0.9999998874649184,
                0.9999998555019274,
                0.9999998724809874,
                0.9999999176674651,
                0.9999999123574523,
                0.999999730042287
            ],
            [
                1.7257815346360178e-08,
                5.3157837044597743e-08,
                3.466325384678894e-07,
                0.9999998802069444,
                1.6373774480605869e-07,
                0.999997273529731,
                7.734414854823498e-08,
                0.9999996310115038,
                0.9999994631248682,
                0.9999975938973746
            ],
            [
                0.9999999611088904,
                0.9999998874647977,
                0.999999894283061,
                0.9999999273418442,
                0.9999999656787365,
                0.9999999634651792,
                0.9999999358794479,
                0.9999999468421565,
                0.9999999468421693,
                0.9999997300422547
            ],
            [
                0.9999978766212849,
                0.9999996310115039,
                0.9999978766210321,
                1.1253509497883659e-07,
                2.6995784182140636e-07,
                9.931186222523604e-08,
                0.9999997897567341,
                0.9999998874649318,
                6.825597214718257e-08,
                8.76424013786396e-08
            ],
            [
                0.9999998874647977,
                0.9999998024946095,
                0.9999990577555186,
                0.9999999748900151,
                0.9999999434137368,
                0.9999998461826405,
                0.9999998555020135,
                0.9999996940978095,
                0.9999999656787365,
                6.023568448589658e-08
            ],
            [
                4.6911638017556955e-08,
                1.8553919030858602e-07,
                4.139938534423022e-08,
                0.9999980052695663,
                5.3157837044597743e-08,
                1.6373776432509826e-07,
                4.691162124067829e-08,
                7.734416698849138e-08,
                9.931187406410953e-08,
                5.3157811697009444e-08
            ],
            [
                1.0,
                1.0,
                0.9999998555019618,
                0.9999998942829855,
                0.9999999123574836,
                0.9999999397642653,
                0.9999999176674945,
                0.9999999677581568,
                0.9999999677581568,
                0.9999999748900181
            ],
            [
                7.338211554801876e-07,
                3.059022269254856e-07,
                0.9999999006880194,
                0.9999996533674615,
                0.9999993106387903,
                0.9999999123575464,
                0.9999996940977003,
                3.9278605979534166e-07,
                0.9999999434138109,
                5.715006514167015e-07
            ],
            [
                3.9278629391427843e-07,
                0.9999999123574419,
                0.9999997761971849,
                0.9999998461826038,
                0.9999999500628511,
                0.9999997300421904,
                0.9999995549150542,
                0.9999997617629764,
                0.9999999226558515,
                8.7642516304188e-08
            ],
            [
                8.764249540862797e-08,
                0.9999996743686644,
                7.73442776303243e-08,
                0.9999980052693285,
                0.9999982396565773,
                0.9999985406234315,
                1.6373766672973748e-07,
                0.9999994631247402,
                0.9999990577549571,
                0.9999994956524115
            ],
            [
                0.9999999006881022,
                0.9999999123574732,
                0.9999998802069016,
                0.9999999123575046,
                0.9999999397642294,
                0.9999999067050387,
                0.9999945777803854,
                0.9999999358794174,
                0.999999967758122,
                0.9999999273418096
            ],
            [
                0.9999990577555188,
                2.511001487368099e-08,
                0.9999967112517204,
                5.715003789046955e-07,
                0.9999999006880904,
                0.9999967112521141,
                0.9999987121046312,
                0.9999991148432811,
                0.9999995818810775,
                0.9999998257021007
            ],
            [
                0.9999994284992806,
                0.9999996743688586,
                0.9999996533674204,
                9.931187406410953e-08,
                0.9999991684716752,
                0.9999978766212855,
                0.999999057755294,
                0.9999997300420939,
                0.9999996072137062,
                0.9999994284994169
            ],
            [
                0.9999930377445874,
                0.9999998802069444,
                4.139934586278605e-08,
                0.9999974387177908,
                0.999999057755631,
                0.999997739676242,
                0.9999993916406733,
                0.9999997617630617,
                0.9999999611089043,
                0.9999987121052454
            ],
            [
                0.9999822214502913,
                0.9999991684716751,
                0.9999996940977732,
                6.475945666051092e-07,
                0.9999957771675637,
                0.9999993524050476,
                0.999998346310612,
                0.9999999067049832,
                0.9999970976876701,
                9.422450432014836e-07
            ],
            [
                0.9999997617630333,
                0.9999995549150013,
                0.9999999176674651,
                0.9999992661787572,
                0.9999998144609202,
                0.9999996940977731,
                0.9999952149060801,
                0.9999960330155062,
                0.9999996533674617,
                0.9999984465024311
            ],
            [
                3.059023363231725e-07,
                5.315785605528784e-08,
                4.4508526417298334e-07,
                8.764248496084983e-08,
                6.825608606172863e-08,
                3.9278610661902853e-07,
                1.444979692800516e-07,
                3.653479467066246e-08,
                4.691162124067829e-08,
                6.475951069985296e-07
            ],
            [
                5.3157811697009444e-08,
                0.9999975938968014,
                5.3157837044597743e-08,
                2.8453354063983556e-08,
                1.2751910369310194e-07,
                1.1253508156363576e-07,
                3.9278634073732336e-07,
                1.6373766672973748e-07,
                3.927862470899887e-07,
                9.931196877517082e-08
            ],
            [
                0.9999999500628513,
                0.9999999317439872,
                0.9999998144609203,
                0.9999992661787573,
                5.043474683220276e-07,
                0.999998239657417,
                0.9999992188514834,
                0.9999987901338844,
                0.9999998555019618,
                0.9999993106392012
            ],
            [
                1.0,
                1.0,
                7.73442776303243e-08,
                0.999999917667573,
                0.9999999530883956,
                0.9999999586006245,
                0.9999999656787039,
                1.0,
                0.9999999273418096,
                0.9999993524054336
            ],
            [
                0.9999999358793332,
                0.9999999006880075,
                0.999999939764294,
                0.999999955930568,
                0.9999999559306101,
                0.9999999123574838,
                0.9999998942829855,
                0.9999999273417836,
                0.9999999434137098,
                0.9999999530883341
            ],
            [
                0.9999999732705379,
                0.9999999358793791,
                0.9999999226557501,
                0.9999997617629764,
                0.9999999500627916,
                0.9999997617629764,
                0.9999999530883509,
                0.9999999273418702,
                0.9999999176675142,
                0.9999999697115803
            ],
            [
                0.9999997126314811,
                1.8553919030708836e-07,
                3.466327450756327e-07,
                3.466326211105621e-07,
                6.825598028392069e-08,
                1.8553905760024476e-07,
                6.475945666033422e-07,
                2.6995768091383957e-07,
                5.715002426460124e-07,
                7.338210680002898e-07
            ],
            [
                0.9999999226558146,
                0.9999999067051165,
                0.9999999847700224,
                0.9999999273418183,
                0.9999999358793562,
                0.9999998802069159,
                0.9999999468421883,
                0.9999999006881378,
                0.9999999634651661,
                0.9999999715466527
            ],
            [
                0.9999994284994169,
                0.9999999434137637,
                0.9999981261252874,
                0.9999994631247403,
                1.2751908849167202e-07,
                6.023569166654288e-08,
                5.315781803390236e-08,
                0.9999998555019791,
                0.9999996310115479,
                0.9999989969859121
            ],
            [
                4.4508510499849186e-07,
                7.734414854823498e-08,
                0.9999993524053563,
                0.9999934595596603,
                1.9947292459265734e-06,
                2.3823699519290042e-07,
                0.9999991684721709,
                7.338207180884785e-07,
                1.994730672675753e-06,
                1.8553914607237736e-07
            ],
            [
                0.9999996072136593,
                0.9999955048189612,
                1.4449807263312446e-07,
                0.9999995262092728,
                1.6373770576776313e-07,
                0.9999995818813766,
                0.9999986290431204,
                1.27519088491875e-07,
                6.825606978822427e-08,
                0.9999994956525919
            ],
            [
                0.99999976176309,
                0.9999999317439465,
                0.9999995549150011,
                0.9999998642567028,
                0.9999998362623529,
                0.9999999358793485,
                0.9999999611089089,
                0.9999987121044775,
                0.9999998802068873,
                0.9999996533672549
            ],
            [
                0.9999995262092163,
                0.9999999530883732,
                0.9999999317439546,
                0.9999998874648514,
                0.9999999468421946,
                0.9999998724809419,
                0.9999996310115039,
                0.999999653367379,
                0.9999999006879721,
                0.9999999226557593
            ],
            [
                1.300713311614059e-05,
                0.9999994631251242,
                0.9999999273418356,
                4.78509392429544e-06,
                0.9999999804443287,
                6.47595107001401e-07,
                0.9999988634365607,
                8.315281267861397e-07,
                3.7266410611296085e-06,
                2.8453371023563735e-08
            ],
            [
                0.9999993916407458,
                1.275190732904469e-07,
                8.939694172770212e-06,
                8.764251630441717e-08,
                5.043472879540142e-07,
                0.9999981261243934,
                2.3823693839290317e-07,
                3.2887478892683997e-06,
                0.9999938558246677,
                1.0677033791583005e-06
            ],
            [
                0.9999997300421261,
                0.9999996940976272,
                0.9999996310115039,
                0.9999997761971049,
                0.9999999530883789,
                0.9999998874648782,
                0.9999998724809116,
                0.9999999611088719,
                1.0,
                0.999999931743979
            ],
            [
                0.9999999006880075,
                0.9999985406239535,
                6.023571320847322e-08,
                0.9999993106387903,
                2.5109975960189263e-08,
                NaN,
                0.9999992188518558,
                0.9999988634366965,
                4.139934092760465e-08,
                0.9999986290423036
            ],
            [
                0.9999960330150323,
                5.715006514167015e-07,
                0.9999998555019618,
                0.9999994631249961,
                0.9999989322968758,
                0.9999983463098232,
                0.9999992661789322,
                0.9999998362622747,
                0.999994228081351,
                1.4738978458140753e-05
            ],
            [
                7.734423152941018e-08,
                9.931189774187203e-08,
                0.9999999273418615,
                9.931193325852072e-08,
                0.9999990577549572,
                1.637377057680051e-07,
                3.224185864592658e-08,
                1.1253513522447425e-07,
                6.023569166654288e-08,
                7.73441946488886e-08
            ],
            [
                3.927862470899887e-07,
                3.466326211113502e-07,
                0.9999997126315496,
                0.9999999358794096,
                0.9999869928684492,
                3.059021175255426e-07,
                0.9999983463096259,
                0.999999931743979,
                0.9999999067050498,
                7.734423152941018e-08
            ],
            [
                0.9999998942830106,
                0.9999999067051276,
                0.9999999468421377,
                0.9999999358794174,
                1.0,
                0.9999998942829099,
                0.9999999697115443,
                0.9999999611088858,
                0.9999998555020135,
                1.0
            ],
            [
                0.9999999656786915,
                0.9999998942830358,
                0.9999999434137907,
                0.9999999434137502,
                0.9999999530883174,
                0.9999998461826222,
                0.9999999500628513,
                0.9999999176674454,
                0.9999999273418528,
                0.9999999067050721
            ],
            [
                0.9999996072136594,
                0.9999995262093292,
                0.9999999176675632,
                0.9999960330140881,
                0.999998346309626,
                7.338210680021253e-07,
                0.9999993524053563,
                0.9999930377404364,
                0.999999352405202,
                0.9999938558224734
            ],
            [
                0.9999998642566542,
                0.9999999067051499,
                0.9999998362623332,
                0.9999997300422547,
                0.999999953088362,
                0.999998932297512,
                0.999999965678708,
                0.9999999634652097,
                0.9999994956527122,
                0.9999999006879838
            ],
            [
                0.9999998874648112,
                3.4663274507713016e-07,
                5.422217030707961e-06,
                0.9999991684718734,
                0.9999999500628511,
                5.043476486924565e-07,
                5.715003789046955e-07,
                0.9999995818812769,
                0.9999832985741968,
                0.9999997617630049
            ],
            [
                0.9999996533672137,
                0.9999989969854337,
                8.315282259117513e-07,
                0.9999978766212855,
                4.450848927650143e-07,
                3.2887482812506295e-06,
                0.9999989969860317,
                6.144172404587612e-06,
                0.9999996533674615,
                7.889266347786918e-06
            ],
            [
                0.9999998642566704,
                1.0677026154806063e-06,
                3.9278634073732336e-07,
                0.9999995549150013,
                0.9999994631249962,
                0.9999997463980729,
                0.999998629043284,
                0.9999832985821591,
                0.9999992188514832,
                1.1478768126057254e-05
            ],
            [
                0.9999999226557501,
                0.9999999067050276,
                0.9999999434137232,
                0.9999993106388724,
                0.9999999317439627,
                0.9999999500628155,
                2.3823688159291947e-07,
                0.9999996940978095,
                0.9999999358793562,
                0.9999999656787324
            ],
            [
                1.4449807263312446e-07,
                0.9999990577550694,
                1.855391239544352e-07,
                2.1024334103553052e-07,
                5.3157837044597743e-08,
                7.734421308914719e-08,
                4.1399375473868e-08,
                1.2751905808881762e-07,
                1.444980209564556e-07,
                5.3157811697009444e-08
            ],
            [
                0.9999991684719726,
                0.9999996743686644,
                0.9999995818810776,
                1.444979692800516e-07,
                4.222832437798974e-06,
                0.9999957771645435,
                0.9999993524053563,
                6.475946438042047e-07,
                5.043472879540142e-07,
                2.382369951932796e-07
            ],
            [
                0.9999996072137062,
                0.9999999500628631,
                0.9999986290424668,
                9.931189774187203e-08,
                1.275191036933194e-07,
                6.023568448589658e-08,
                4.691162124067829e-08,
                7.734416698849138e-08,
                0.9999999434137232,
                0.9999996533674617
            ],
            [
                8.764254764780641e-08,
                0.9999999468421122,
                0.9999999358794402,
                0.9999999176674553,
                0.9999998555019274,
                5.3157830707696514e-08,
                0.9999998461826405,
                0.9999977396746252,
                0.9999998362623138,
                0.9999999273418095
            ],
            [
                0.9999945777797417,
                0.999998790134317,
                1.0677026154806063e-06,
                1.0677033791583005e-06,
                0.9999987121044779,
                1.1253525596174225e-07,
                0.9999987121050917,
                0.9999987121046314,
                0.9999985406236057,
                0.9999992661788447
            ],
            [
                0.9999998461827138,
                0.9999998461826405,
                1.6373774480605869e-07,
                0.999999922655833,
                0.9999999358793638,
                0.9999999500628453,
                0.999999955930589,
                0.9999999530884012,
                0.9999999397642437,
                0.9999999559305628
            ],
            [
                0.9999999123574523,
                0.9999991148427533,
                0.9999960330126682,
                0.999999391641181,
                0.9999999697115587,
                0.9999999500628155,
                0.9999999226558238,
                3.05902336324494e-07,
                0.9999997463981636,
                4.222832941142044e-06
            ],
            [
                1.8553919030826963e-07,
                0.9999989322967487,
                7.734423152941018e-08,
                0.9999988634357478,
                0.9999985406232575,
                3.927862002663297e-07,
                4.450852111148132e-07,
                1.275190276859705e-07,
                0.9999996743686257,
                9.931186222523604e-08
            ],
            [
                0.999999674368781,
                0.9999983463100203,
                0.9999999067049831,
                0.999999391641181,
                0.9999997761971582,
                0.9999998362622943,
                0.9999993916406733,
                0.9999993916410359,
                0.9999822214439369,
                0.9999999634651486
            ],
            [
                0.9999981261250639,
                0.9999991148429642,
                0.9999991684720717,
                6.475950298011458e-07,
                0.0004878572366839336,
                9.422442569315887e-07,
                0.9999998024945624,
                0.9999996310115479,
                5.715003789046955e-07,
                0.999999746398073
            ],
            [
                0.9999960330145614,
                0.9999978766212855,
                0.9999974387177906,
                0.9999832985841509,
                4.450850519403407e-07,
                0.9999960330140881,
                0.999999855501979,
                3.22418970812682e-08,
                2.845334728018925e-08,
                0.9999957771670617
            ],
            [
                0.9999992661788447,
                0.9999993106388727,
                0.9999998362622358,
                0.9999995262092728,
                0.999998346311006,
                0.9999998642566704,
                0.9999997761970248,
                5.715003789046955e-07,
                0.9999986290424667,
                0.9999992188513902
            ],
            [
                0.9999995818810776,
                0.9999994956525919,
                0.9999998724809419,
                0.9999991684720717,
                0.9999991684719727,
                0.9999998642566381,
                0.9999987901338843,
                0.9999998461826405,
                0.9999993916408184,
                0.9999996533673378
            ],
            [
                0.9999999697115876,
                0.9999999434137502,
                0.9999989969862708,
                0.9999999176675829,
                0.9999995262092728,
                1.0,
                0.9999970976880161,
                0.9999998942830485,
                0.9999999500628511,
                0.9999921107336581
            ],
            [
                0.9999998362622943,
                0.9999998461827138,
                0.9999999273418096,
                3.4663278639892215e-07,
                6.825600469412533e-08,
                9.931202796993203e-08,
                0.9999832985761816,
                8.764241182641775e-08,
                0.9999989969861512,
                0.9999998874648648
            ],
            [
                0.9999996940978825,
                0.9999992188516695,
                0.9999998024947037,
                0.9999998724809875,
                0.9999999123575987,
                0.9999997897566089,
                0.9999999176674651,
                0.9999999006881141,
                0.9999999468421059,
                0.999999931743979
            ],
            [
                2.699577774585891e-07,
                0.9999993106390369,
                0.9999999226558329,
                9.931190958076104e-08,
                0.9999972735300566,
                0.9999998942829855,
                6.023579219579052e-08,
                1.4449807263312446e-07,
                0.9999999530883956,
                0.9999999586006344
            ]
        ]
    },
    {
        "q_id": "10100_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.2603234895289998e-06,
                2.6995784182140636e-07,
                2.1024341622297196e-07,
                7.338209805170655e-07,
                3.9278615344178325e-07,
                3.466326624322211e-07,
                6.14417753171671e-06,
                5.043475885688201e-07,
                9.422450432014836e-07,
                5.715003789033962e-07
            ],
            [
                1.0677033791612137e-06,
                0.9999832985821582,
                2.5612831267202583e-06,
                4.222833444590791e-06,
                1.444979692797559e-07,
                0.9999485577866174,
                8.315279285370317e-07,
                3.927862002654366e-07,
                4.785095635655362e-06,
                9.422449308774482e-07
            ],
            [
                2.90231094723893e-06,
                7.88926446679691e-06,
                1.8925152754169532e-05,
                5.715005832886879e-07,
                7.338212429582604e-07,
                9.422448185478557e-07,
                2.1024331597262577e-07,
                3.466325797896173e-07,
                0.9999485577988745,
                6.475945666051092e-07
            ],
            [
                0.9999955048168303,
                0.99999106030481,
                0.9999977396759767,
                0.9999986290426334,
                0.9999967112501615,
                0.9999955048173664,
                0.9999957771645561,
                0.9999960330131492,
                0.9999921107336698,
                0.9999967112509431
            ],
            [
                0.9999832985821718,
                8.7642516304188e-08,
                5.715003107755449e-07,
                2.902311639183378e-06,
                3.2887506336086064e-06,
                1.0677032518814388e-06,
                0.9999952149072203,
                2.6995784182140636e-07,
                1.6701429808632785e-05,
                0.999989216690366
            ],
            [
                0.9990889489983473,
                3.120191509592808e-05,
                5.043474081993875e-07,
                0.999996273361608,
                2.382368247909451e-07,
                3.0590229985449037e-07,
                2.3823702359138736e-07,
                3.927862939113312e-07,
                5.715007195384861e-07,
                0.9999756997506362
            ],
            [
                1.99473067264854e-06,
                1.2098659719757836e-06,
                2.9023109472244114e-06,
                5.715005832872586e-07,
                3.05902263389638e-07,
                5.043475885657239e-07,
                1.0677029973158649e-06,
                7.3382080556433e-07,
                2.3823685319244518e-07,
                2.3823685319244518e-07
            ],
            [
                0.9999910603047731,
                0.9999904837437787,
                0.9999898700078182,
                0.9999339478556374,
                2.5612828213934817e-06,
                0.9999964991439192,
                6.144175334468545e-06,
                0.9999930377454169,
                6.144174601991196e-06,
                0.9999877809269088
            ],
            [
                0.9999996072137999,
                0.999999939764294,
                1.0,
                0.9999999067050276,
                0.9999998362623332,
                1.0677028700363782e-06,
                1.0,
                0.9999998802069873,
                0.9999998144608319,
                0.9999996940977732
            ],
            [
                3.466325384661554e-07,
                9.422443692555439e-07,
                1.6373764721039308e-07,
                1.637377643243723e-07,
                3.927862470899887e-07,
                2.9023133690980155e-06,
                2.699577774585891e-07,
                1.637377448057981e-07,
                1.8553905760024476e-07,
                2.1024336609638268e-07
            ],
            [
                0.999997739675974,
                0.9999985406239538,
                0.999999674368781,
                0.9999997897565588,
                0.9999999006881497,
                0.9999980052707553,
                0.9999981261237241,
                0.9999993106392014,
                0.9999942280806676,
                0.9999997761971315
            ],
            [
                0.9999992188512974,
                0.999998996985434,
                0.9999997300421585,
                0.9999999273418009,
                0.999998629042794,
                0.999999927341775,
                0.9999999273418962,
                0.9999999358794021,
                0.9999997897567343,
                1.4449805540740185e-07
            ],
            [
                5.04347468323289e-07,
                3.288750241561788e-06,
                1.7603427936335396e-06,
                1.5534984953510149e-06,
                7.889261645355786e-06,
                2.9023123311583482e-06,
                4.785093353940187e-06,
                5.422219616228845e-06,
                4.785096206047877e-06,
                2.5612834320470717e-06
            ],
            [
                3.059022998569248e-07,
                0.999998346310809,
                0.9999970976876715,
                9.422445939032799e-07,
                0.9999992661788448,
                0.9999998802069302,
                1.2098659719716573e-06,
                1.6373770576776313e-07,
                0.9999981261243939,
                0.9999810748450204
            ],
            [
                1.6373776432509826e-07,
                1.6373774480479287e-07,
                0.9999952149043689,
                3.466327863983311e-07,
                1.855391460719133e-07,
                1.9947299592933255e-06,
                2.3823693839290317e-07,
                1.0,
                2.1024329090929374e-07,
                1.6373776432481905e-07
            ],
            [
                0.9999999358794479,
                0.9999992188513905,
                0.9999995549148953,
                0.9999969105062917,
                0.9999987901346061,
                0.9999960330145626,
                0.9999969105062911,
                0.9999993106387086,
                0.999998446502062,
                0.9999987901337405
            ],
            [
                1.2098659719757836e-06,
                0.9999724643122256,
                0.9998911030392968,
                0.9999599362984023,
                1.9947304348862686e-06,
                1.7603434231833873e-06,
                0.9999949062962167,
                6.144172404738491e-06,
                3.726638839878908e-06,
                0.9998911030785114
            ],
            [
                1.855390354818069e-07,
                0.9999990577549573,
                0.9999989969854339,
                0.9999994284994851,
                0.9999997300421584,
                1.4449805540740185e-07,
                0.9999997126314812,
                1.0677032518785256e-06,
                0.9999998461826588,
                0.9999988634362901
            ],
            [
                0.9996200155649312,
                0.9999952149072175,
                4.785095635624897e-06,
                1.2098661161982042e-06,
                0.9999822214481979,
                1.994730434879465e-06,
                0.9999955048162821,
                0.9999785550414579,
                2.902311639183378e-06,
                5.043476486915964e-07
            ],
            [
                0.9999991684715762,
                1.1253513522447425e-07,
                1.8553907971855875e-07,
                4.139935079796334e-08,
                0.99996464373252,
                0.9999984465022462,
                0.999997876621539,
                9.93118503859575e-08,
                2.3823699519290042e-07,
                3.9278634073625165e-07
            ],
            [
                0.999997438717791,
                4.4508526417298334e-07,
                0.9999960330155077,
                2.3823682479181176e-07,
                2.102434162245973e-07,
                0.9999994631249323,
                3.9278634073732336e-07,
                0.999999746398073,
                4.450850519403407e-07,
                4.450849458200093e-07
            ],
            [
                2.260324836787226e-06,
                1.3709576971425944e-06,
                2.6995768091383957e-07,
                2.3823690999290963e-07,
                6.475948754012522e-07,
                3.059022269250683e-07,
                1.0677029973219343e-06,
                1.2098652508347793e-06,
                6.023573475041126e-08,
                2.6995774527657245e-07
            ],
            [
                0.9999646437536365,
                0.9999994631251885,
                1.5534983101602148e-06,
                0.9999978766220463,
                0.9999974387168755,
                2.5612831267202583e-06,
                1.760344052714248e-06,
                0.999996499143921,
                0.9999706884580853,
                0.9999985406232583
            ],
            [
                1.637377643243723e-07,
                0.9999988634365607,
                0.9999994284997576,
                9.931196877456114e-08,
                5.043476486833397e-07,
                0.999989870012655,
                8.764252675194995e-08,
                1.8553919030776337e-07,
                7.734428685019034e-08,
                0.9999952149037977
            ],
            [
                1.994729483705484e-06,
                0.9999998724810027,
                1.0,
                2.902310947208574e-06,
                0.9999998642566543,
                0.9999998874648648,
                0.9999955048189634,
                0.9999987121044781,
                1.2098661162023305e-06,
                8.315279285351409e-07
            ],
            [
                3.0590215399183813e-07,
                1.9947304348862686e-06,
                2.5612819054133693e-06,
                1.3709568799919866e-06,
                2.561281600086738e-06,
                3.2887506336235617e-06,
                2.1024326584639497e-07,
                5.043474683156057e-07,
                4.785093353940187e-06,
                7.734419464850171e-08
            ],
            [
                3.1201922533564516e-05,
                0.00020342699786118494,
                0.9988304896632779,
                0.9999852610198042,
                0.9999756997564054,
                6.962254589978262e-06,
                0.0011695100137466014,
                6.144173869603344e-06,
                0.9999546021260426,
                0.999983298578184
            ],
            [
                0.9999810748450114,
                1.553497199007048e-06,
                0.9999485577620151,
                6.962259569750576e-06,
                4.785092783519724e-06,
                1.444979692797559e-07,
                0.9999885212346241,
                2.1024339116134898e-07,
                8.764250585640737e-08,
                1.8553903548231313e-07
            ],
            [
                1.6373772528636992e-07,
                1.1253514863909295e-07,
                1.6373776432481905e-07,
                1.1253517547010071e-07,
                0.9999974387180971,
                1.6373774480479287e-07,
                2.1024339116082313e-07,
                6.825598842035714e-08,
                1.444980726324838e-07,
                6.144175334239434e-06
            ],
            [
                1.0677033791583005e-06,
                7.889266347715168e-06,
                0.9999925887227897,
                0.9999974387171802,
                0.9999993106392013,
                0.999999789756634,
                0.9999964991443364,
                0.9999998642566704,
                0.9999986290421403,
                8.315279285351409e-07
            ],
            [
                1.8553905760024476e-07,
                0.9999996940978098,
                1.6373774480479287e-07,
                5.715007195384861e-07,
                0.9999910603047677,
                3.466324971396247e-07,
                0.9999974387171799,
                3.9278610661545617e-07,
                0.9999995818813269,
                4.139935079796334e-08
            ],
            [
                0.9999969105055547,
                6.144177531767002e-06,
                2.561282516042282e-06,
                8.315282259117513e-07,
                3.9278610661902853e-07,
                1.0677026154806063e-06,
                3.9278624708775595e-07,
                0.9999741325567009,
                6.475946438055299e-07,
                0.9999756997535224
            ],
            [
                3.2887506336235617e-06,
                2.7535704231844484e-05,
                0.9999724642958409,
                5.144221366361183e-05,
                0.9997694932313523,
                0.9999832985801692,
                0.9999969105048166,
                0.9999832985781686,
                0.99998987000661,
                4.785095065232451e-06
            ],
            [
                0.9999997617631469,
                0.9999989322966213,
                1.0,
                0.9999969105044496,
                0.9999980052702796,
                0.999999730042094,
                0.9999993524052021,
                0.9999993106387904,
                0.9999991684715762,
                0.9999997761971317
            ],
            [
                0.9999972735290809,
                5.043474683220276e-07,
                2.382368247924618e-07,
                0.999999526209499,
                0.9999992661791074,
                0.9999962733620522,
                0.9999995262093858,
                1.2751905808881762e-07,
                0.9999997463981334,
                0.9999999176675437
            ],
            [
                0.99984156376652,
                2.9023112932177327e-06,
                0.9999724643089616,
                5.715002426475718e-07,
                0.9999892166852206,
                8.764247451307293e-08,
                4.785092783519724e-06,
                8.315279285351409e-07,
                0.9999975938973747,
                3.2887478892683997e-06
            ],
            [
                2.9023119851781017e-06,
                0.999996033014092,
                0.9999921107402484,
                0.9999756997680338,
                1.209865539295696e-06,
                0.9999984465016905,
                1.5534977545886537e-06,
                0.9999822214418349,
                0.999996711249371,
                0.9999904837449124
            ],
            [
                4.4508494582314646e-07,
                1.8553914607267268e-07,
                3.466326211105621e-07,
                3.466327037553825e-07,
                6.475948754012522e-07,
                1.3709576971316842e-06,
                1.1253510839355284e-07,
                5.04347468323289e-07,
                1.637377057673536e-07,
                2.3823702359290413e-07
            ],
            [
                2.3823682479181176e-07,
                6.475950298011458e-07,
                1.2098662604049616e-06,
                0.9999998024946566,
                9.422448185534261e-07,
                1.2751910369275402e-07,
                6.825608606148807e-08,
                0.9999957771680689,
                4.450852111148132e-07,
                7.73442776300517e-08
            ],
            [
                0.9999981261237242,
                0.99999691050666,
                0.9999980052709944,
                0.9999974387171836,
                0.9999998362623334,
                0.9999998642566866,
                0.999999825702059,
                0.9999981261252882,
                0.9999904837505891,
                0.9999987121046318
            ],
            [
                1.1253514863968147e-07,
                1.3709575336860625e-06,
                9.931195693628605e-08,
                1.9947301970587145e-06,
                9.931200429181105e-08,
                1.2751908849167202e-07,
                0.9999981261252878,
                4.22283394786293e-06,
                1.637377643243723e-07,
                0.9999995818810776
            ],
            [
                0.00010889689635877873,
                0.9999984465016906,
                0.9998766053820318,
                0.9997040428005498,
                1.3007126914612648e-05,
                1.9947301970813926e-06,
                0.999995777167063,
                3.2887498495150166e-06,
                0.9999724642991056,
                0.9999930377454203
            ],
            [
                3.288748673360027e-06,
                1.0677032518814388e-06,
                3.4663266242969896e-07,
                4.450849988798682e-07,
                9.422449308716635e-07,
                4.450851580540182e-07,
                0.9999869928653538,
                5.043472879525233e-07,
                0.9999724643089485,
                0.9999869928668941
            ],
            [
                0.9999892166890838,
                5.715006514105942e-07,
                0.9999986290427939,
                0.9999977396754349,
                0.9999980052707552,
                4.4508515805199415e-07,
                0.9999974387180973,
                0.9999977396751654,
                0.9999934595627793,
                0.9999969105055564
            ],
            [
                1.0,
                8.31528424162821e-07,
                0.999999310639037,
                0.9999999123574524,
                1.0,
                0.9999992188514834,
                0.9999997897565588,
                0.9999996743688975,
                1.209865250822125e-06,
                0.9999978766222988
            ],
            [
                8.764245361752286e-08,
                5.715003788993679e-07,
                5.043473480777865e-07,
                6.475947982037486e-07,
                1.2098658277335738e-06,
                1.2751901248454963e-07,
                0.9999646437622716,
                1.1478768126057254e-05,
                6.475947210046347e-07,
                2.6995790618350237e-07
            ],
            [
                6.475947210031623e-07,
                8.315277302841894e-07,
                0.9999962733602753,
                3.0590237279032884e-07,
                4.785092783519724e-06,
                0.9999987121043244,
                5.715003789046955e-07,
                2.382369667929001e-07,
                4.450848927658745e-07,
                0.9999978766215388
            ],
            [
                1.3709575337078829e-06,
                1.0677033791583005e-06,
                0.9999999123575464,
                1.760343423160973e-06,
                8.315279285351409e-07,
                0.9999832985761902,
                1.3709575337078829e-06,
                1.0,
                2.699577774585891e-07,
                7.338211554801876e-07
            ],
            [
                8.764245361752286e-08,
                4.691162683297406e-08,
                2.699578096399958e-07,
                0.9999910603058323,
                8.764254764749753e-08,
                2.260325375650449e-06,
                0.9999989969861516,
                6.023573475041126e-08,
                1.6373766672973748e-07,
                1.4449798650551755e-07
            ],
            [
                0.9999869928746538,
                0.9999964991443366,
                0.9999898700042068,
                0.9999945777803889,
                0.9999930377404351,
                0.9999978766222987,
                0.9999785550567721,
                0.9999977396765131,
                6.475950297993789e-07,
                3.53562549305363e-05
            ],
            [
                3.05902263391829e-07,
                2.3823696679230424e-07,
                0.9999898700066219,
                0.9999964991455893,
                1.5534983101602148e-06,
                0.9999988634357478,
                0.9999960330121961,
                0.9999996940977731,
                0.9999945777829724,
                0.9999756997506108
            ],
            [
                2.699577774560111e-07,
                7.338209805200689e-07,
                1.7603425837606927e-06,
                9.422450431989127e-07,
                1.7603432133296774e-06,
                1.5534984953453635e-06,
                8.315281267861397e-07,
                6.962257909785973e-06,
                1.3709576970949014e-06,
                2.1024341622297196e-07
            ],
            [
                9.422445938861406e-07,
                5.04347528440776e-07,
                8.315277302747361e-07,
                1.6373766672888118e-07,
                1.3709575336947905e-06,
                2.102433660979124e-07,
                8.315277302788957e-07,
                1.2098656835076114e-06,
                2.6995784182140636e-07,
                1.3709575336947905e-06
            ],
            [
                0.9953904287415024,
                0.9999417087137051,
                1.4738976701411704e-05,
                0.9999798543164268,
                0.9998601779263891,
                0.9999251537908795,
                2.4300243631272052e-05,
                0.9999546021206861,
                0.9999885212277776,
                0.9999646437325314
            ],
            [
                1.2098652508424818e-06,
                6.475945666033422e-07,
                1.0677026154774503e-06,
                3.927861066170637e-07,
                3.4663266243111764e-07,
                3.927862002654366e-07,
                2.1024326584582131e-07,
                8.315280276607289e-07,
                6.475947210031623e-07,
                3.4663266242969896e-07
            ],
            [
                7.338210679979539e-07,
                5.043476486902204e-07,
                2.5612825160562587e-06,
                1.7603427936335396e-06,
                3.05902190458764e-07,
                4.450849988798682e-07,
                1.3709572068478697e-06,
                1.7603438428800754e-06,
                1.0677029973158649e-06,
                0.9999852610110236
            ],
            [
                8.764244316973974e-08,
                9.931187406410953e-08,
                2.6995768091383957e-07,
                9.931200429181105e-08,
                3.466327450756327e-07,
                0.9999970976866338,
                2.3823682479181176e-07,
                2.6995777745711594e-07,
                8.764249540862797e-08,
                3.059021539909339e-07
            ],
            [
                2.5612819054028872e-06,
                3.2887494572514376e-06,
                3.2887490652451393e-06,
                1.4449798650476187e-07,
                3.2887490653408545e-06,
                3.2887494573232236e-06,
                1.9947301970813926e-06,
                5.043472278322555e-07,
                1.7603436329978976e-06,
                2.2603245672867952e-06
            ],
            [
                0.9999998257021214,
                0.999997438717181,
                1.444980209564556e-07,
                0.999999927341827,
                0.9999989969854339,
                0.9999995818811276,
                0.9999997126314469,
                0.9999991684719727,
                0.9999997897566592,
                0.9999995818814266
            ],
            [
                1.444980726324838e-07,
                1.8553919030826963e-07,
                3.0590233632400716e-07,
                8.764244316973974e-08,
                0.9999993106388726,
                0.9999970976880164,
                3.059021539909339e-07,
                2.3823688159237777e-07,
                0.9999980052698042,
                0.9999989322975126
            ],
            [
                0.9999599362935554,
                0.9999938558239362,
                0.99995993630786,
                0.9999983463110063,
                0.9999960330150331,
                0.9999832985761912,
                4.222835458148261e-06,
                1.2098653950606901e-06,
                0.9999885212264104,
                1.1478769494396542e-05
            ],
            [
                8.315281267861397e-07,
                2.1024336609638268e-07,
                2.102433159721477e-07,
                0.9998415638223355,
                1.0,
                8.315282259117513e-07,
                0.9999706884685335,
                3.0590229985449037e-07,
                0.9999998642566219,
                1.4449798650476187e-07
            ],
            [
                6.02357491113469e-08,
                8.764250585586932e-08,
                0.9999989322967486,
                3.4663266243308805e-07,
                1.0677026154619133e-06,
                4.4508510499737865e-07,
                3.927862002654366e-07,
                2.3823688159291947e-07,
                1.8553905760024476e-07,
                0.9999998802069017
            ],
            [
                4.450850519403407e-07,
                1.6373766672888118e-07,
                3.9278634073625165e-07,
                1.1253514863909295e-07,
                1.6373770576776313e-07,
                1.4449802095609418e-07,
                3.9278634073625165e-07,
                3.927862470899887e-07,
                1.1253518888464745e-07,
                1.6373776432481905e-07
            ],
            [
                4.222833947960866e-06,
                1.3007133116732079e-05,
                0.9999485577986323,
                0.9999706884580937,
                0.9999151889287973,
                0.9998204720566296,
                7.484623620251482e-05,
                0.9999832985722189,
                2.144495608424996e-05,
                0.00026119021636362646
            ],
            [
                0.9999949062956113,
                1.0677027427600627e-06,
                2.10243290909724e-07,
                0.9999970976890561,
                8.764242227418718e-08,
                5.315784971839039e-08,
                0.9999938558254082,
                0.9999960330131454,
                0.9999949062968241,
                6.825598842065202e-08
            ],
            [
                3.4663266242969896e-07,
                1.0677031245990084e-06,
                4.4508510499849186e-07,
                2.6995777745711594e-07,
                1.370957697068717e-06,
                1.2098659719757836e-06,
                0.999999607213753,
                0.9999978766217918,
                3.4663266243111764e-07,
                4.450848927658745e-07
            ],
            [
                3.466327863983311e-07,
                2.9023119851781017e-06,
                1.7603440527286572e-06,
                1.0677027427471959e-06,
                1.209865539295696e-06,
                5.715006514105942e-07,
                0.9999687980961398,
                1.2098656835224664e-06,
                1.0677032518700286e-06,
                2.1024329090929374e-07
            ],
            [
                0.18242552602881168,
                4.006370174184034e-05,
                0.9997965730284856,
                0.9999987121049385,
                1.275190124842887e-07,
                0.9999975938985224,
                1.0677027427600627e-06,
                0.9999798543044061,
                1.2751901248454963e-07,
                0.9999955048184245
            ],
            [
                1.553498124964492e-06,
                1.4449807263287805e-07,
                0.9999999123574523,
                2.1024331597262577e-07,
                3.9278634073625165e-07,
                5.715007195384861e-07,
                9.422445939032799e-07,
                2.6995768091383957e-07,
                1.444979692797559e-07,
                3.0590229985449037e-07
            ],
            [
                6.962257909785973e-06,
                2.260324567337161e-06,
                0.00010889693530623988,
                9.422448185510695e-07,
                0.9999646437451394,
                0.9999999358794402,
                0.9999724643089335,
                1.5534973842030142e-06,
                2.561281600076256e-06,
                7.889261645427538e-06
            ],
            [
                1.0677033791583005e-06,
                0.9997694932625872,
                0.999986153992162,
                2.5612828213818346e-06,
                0.0001795279449140676,
                0.9999038975399355,
                1.5534971990126997e-06,
                1.0677031245905116e-06,
                0.9999952149060785,
                2.1444958640087166e-05
            ],
            [
                1.5534983101478522e-06,
                4.222832941111319e-06,
                4.4508494582314646e-07,
                0.999933947847812,
                8.315277302788957e-07,
                5.422218323399208e-06,
                3.927862939113312e-07,
                1.3709568799879344e-06,
                1.300713311614059e-05,
                9.422448185510695e-07
            ],
            [
                5.422217677152175e-06,
                1.0129989772412744e-05,
                1.2098652508424818e-06,
                1.2098652508391807e-06,
                0.9999955048200324,
                0.9999646437409403,
                0.9149009596336303,
                0.9997388097890473,
                0.9999904837460543,
                0.9999599362888304
            ],
            [
                0.9999869928746594,
                0.9999997300421261,
                0.999993855822474,
                0.999987780926914,
                0.9999985406230838,
                0.9999785550592865,
                0.9999724643155298,
                0.9999810748495156,
                0.9999869928669182,
                0.9999991684718736
            ],
            [
                2.6995768091310296e-07,
                5.043475284430694e-07,
                7.338210679979539e-07,
                3.05902263389638e-07,
                1.4449805540651476e-07,
                6.475948753991907e-07,
                3.466327450756327e-07,
                3.9278605979208185e-07,
                6.475948753991907e-07,
                5.04347408197782e-07
            ],
            [
                0.9999910603015745,
                0.9999972735290806,
                1.6373772528704005e-07,
                1.1253513522447425e-07,
                6.475947982037486e-07,
                0.9999869928653436,
                3.9278605979534166e-07,
                1.6373764721039308e-07,
                0.9999898700054105,
                3.9278605979534166e-07
            ],
            [
                0.9999785550491073,
                0.9999986290423036,
                0.9999986290426303,
                0.999997273528431,
                8.315282259089153e-07,
                3.46632497145457e-07,
                0.9999957771675669,
                6.144173869558639e-06,
                0.9999990577552943,
                0.9999945777823307
            ],
            [
                1.994730672668496e-06,
                2.430024073333442e-05,
                8.315282259089153e-07,
                7.338213304316717e-07,
                1.3709570434122812e-06,
                3.059021175255426e-07,
                7.338210680002898e-07,
                7.338210679979539e-07,
                7.338210679979539e-07,
                2.902310947208574e-06
            ],
            [
                5.71500651413193e-07,
                4.4508510499849186e-07,
                1.7603436330179102e-06,
                5.043474081957179e-07,
                2.1024329090929374e-07,
                2.102433410343832e-07,
                2.3823682479181176e-07,
                1.8553907971855875e-07,
                1.444979692797559e-07,
                1.2751905808881762e-07
            ],
            [
                0.9999646437325226,
                0.9999832985821656,
                0.9999646437324844,
                0.9999741325752028,
                0.9999251537728575,
                5.14422197953122e-05,
                0.9999910603058371,
                2.4300237837960777e-05,
                9.931192141912081e-08,
                0.00010889693529435623
            ],
            [
                3.726638839878908e-06,
                0.9999646437578114,
                0.9999910603058366,
                1.994729483723626e-06,
                2.1444945858485726e-05,
                0.9999983463104151,
                0.9999546021261274,
                0.9999646437577848,
                0.9999949062943951,
                0.9999852610233092
            ],
            [
                1.8553919030826963e-07,
                0.9999969105051858,
                1.1478769493916314e-05,
                0.9999975938982361,
                0.9999994284994169,
                0.9999989322967487,
                0.9999970976869796,
                8.764254764749753e-08,
                0.9999997617630901,
                0.9999993916406735
            ],
            [
                3.927860597945825e-07,
                9.931188590255539e-08,
                9.931190958076104e-08,
                1.1253524254615121e-07,
                2.102433159721477e-07,
                0.9999955048162842,
                1.6373766672888118e-07,
                0.9999982396563678,
                1.7603440527222532e-06,
                2.3823688159237777e-07
            ],
            [
                0.9999957771665567,
                0.0003353501511018999,
                0.999997273529406,
                0.9999974387168744,
                0.999991601925971,
                0.00048785717971890487,
                0.9999852610197972,
                1.6701425827133152e-05,
                0.9999646437324751,
                0.9996646499726131
            ],
            [
                2.102433159721477e-07,
                0.9999998642567189,
                5.422219616228845e-06,
                5.715002426460124e-07,
                0.9999998461826588,
                0.9999832985821525,
                1.4738983729535602e-05,
                0.9999251537462258,
                4.4508515805735777e-07,
                1.760343003481596e-06
            ],
            [
                5.422217677078203e-06,
                1.2098659719716573e-06,
                1.2098653950656417e-06,
                9.422449308716635e-07,
                5.043474081993875e-07,
                1.6373770576776313e-07,
                1.7603438428800754e-06,
                1.3709576971425944e-06,
                5.715004470313855e-07,
                1.994730434879465e-06
            ],
            [
                0.9999546021098639,
                0.9999945777790995,
                0.9999949062931794,
                0.9999981261237237,
                0.9999996072138936,
                0.9999972735294054,
                0.9999892166865246,
                0.99999649914684,
                0.9999885212359991,
                0.9999724643057024
            ],
            [
                2.6995774527657245e-07,
                1.370957860576702e-06,
                3.05902190458764e-07,
                6.144176799334096e-06,
                1.4449805540740185e-07,
                1.0129993395217047e-05,
                1.4738981972564636e-05,
                1.2098652508391807e-06,
                8.764245361752286e-08,
                4.450848927650143e-07
            ],
            [
                0.9999687980775371,
                3.4663249714612693e-07,
                8.315282259117513e-07,
                0.999977172000163,
                0.9999996940978096,
                1.3709567165617364e-06,
                3.9278610661902853e-07,
                4.4508510499849186e-07,
                0.9999952149037977,
                7.338210680021253e-07
            ],
            [
                0.9999975938979493,
                0.9999949062925791,
                0.9999921107374254,
                0.9999978766217915,
                0.9999945777790987,
                0.9999983463100209,
                0.9999986290424671,
                0.999999581881277,
                0.9999952149032287,
                0.999997593896515
            ],
            [
                1.444980381819277e-07,
                0.999997876621792,
                3.288750633545794e-06,
                1.2098659719661556e-06,
                5.3157830707696514e-08,
                1.1253516205489029e-07,
                1.6373772528677946e-07,
                0.9999930377445863,
                0.999999802494586,
                9.931189774187203e-08
            ],
            [
                0.999999391640746,
                1.637377057673536e-07,
                1.2751899728311609e-07,
                1.6373764721039308e-07,
                0.9999998802068873,
                0.9999832985741924,
                0.9999983463100209,
                0.9999972735300571,
                6.825608606148807e-08,
                3.9278624708775595e-07
            ],
            [
                0.9999995818811773,
                3.927863875616689e-07,
                0.9999898700114471,
                0.9999974387171812,
                1.5534983101478522e-06,
                0.9999938558268702,
                0.9999994284994171,
                0.9999955048178913,
                0.9999997761972116,
                0.9999989969859128
            ],
            [
                0.9999988634358837,
                0.9999998724809419,
                1.2098661162023305e-06,
                1.0677027427600627e-06,
                0.9999985406234319,
                0.9999999176675239,
                0.999998932297385,
                0.9999998802069302,
                0.9999998461826037,
                0.9999996743688976
            ],
            [
                2.260323758987159e-06,
                0.9999964991439197,
                0.999997739675973,
                0.999998932296749,
                2.260324836787226e-06,
                4.450852111120808e-07,
                1.637377643243723e-07,
                0.9999996533675031,
                3.7266401726173067e-06,
                1.2098661162023305e-06
            ],
            [
                8.315279285351409e-07,
                5.715007195431641e-07,
                0.9999687980924327,
                0.9997388096341436,
                1.3709575337078829e-06,
                1.209865683518615e-06,
                5.71500515159253e-07,
                9.422442569290178e-07,
                1.067702870039777e-06,
                5.71500515159253e-07
            ],
            [
                2.6995774527657245e-07,
                1.0677031245990084e-06,
                4.450852111148132e-07,
                1.855391239544352e-07,
                1.1253510839355284e-07,
                1.855391239539711e-07,
                3.9278634073732336e-07,
                6.1441746020359e-06,
                2.3823688159237777e-07,
                0.9999964991443374
            ],
            [
                0.9999995818810776,
                0.9999756997651154,
                7.338208055664991e-07,
                4.450848927650143e-07,
                0.9997694933434612,
                2.9023119851781017e-06,
                5.04347468323289e-07,
                1.0677033791583005e-06,
                3.288748673360027e-06,
                4.2228324377740105e-06
            ],
            [
                1.9947304348862686e-06,
                0.9999910603026364,
                7.889265407327733e-06,
                6.475947982037486e-07,
                0.9999852610145298,
                0.9999952149072189,
                3.535623807260338e-05,
                0.9999724643089597,
                0.999997876620526,
                2.1444943302650045e-05
            ],
            [
                0.9999962733607193,
                0.9999988634358837,
                3.466327863983311e-07,
                1.1253514863909295e-07,
                2.3823685319244518e-07,
                0.9999997617630333,
                1.275190276853036e-07,
                2.102433410343832e-07,
                0.9999995549151074,
                0.9999987121046315
            ],
            [
                1.3709572068354007e-06,
                4.785095635624897e-06,
                2.9023133690425823e-06,
                0.9999999530883172,
                0.9999969105066602,
                1.2098658277451275e-06,
                5.715002426475718e-07,
                0.9999996533673791,
                3.9278615343901467e-07,
                1.0677028700363782e-06
            ],
            [
                4.450852111148132e-07,
                5.71500515159253e-07,
                0.9999999397643083,
                2.382368247924618e-07,
                1.7603425837855082e-06,
                2.699578096399958e-07,
                0.9999970976890551,
                3.9278610661822475e-07,
                1.2098661162023305e-06,
                0.9999969105055547
            ],
            [
                0.9999998874648917,
                0.9999999468421122,
                0.9999998144609645,
                0.9999998024947037,
                0.9999987901341734,
                2.6995784182073116e-07,
                0.9999993916410361,
                0.9999998874647441,
                0.9999978766217923,
                0.9999984465022463
            ],
            [
                2.6995777745711594e-07,
                3.466325384661554e-07,
                2.382368247924618e-07,
                1.444980209542543e-07,
                1.855391681883394e-07,
                3.9278634073625165e-07,
                3.4663266242969896e-07,
                1.6373774480404828e-07,
                3.466325384661554e-07,
                1.6373766672649848e-07
            ],
            [
                1.209865539295696e-06,
                1.209865827740176e-06,
                5.04347287955046e-07,
                0.9999983463108091,
                0.9999977396762431,
                9.422445939002803e-07,
                1.2098662604192665e-06,
                0.9999978766205266,
                1.0677033791612137e-06,
                8.764245361752286e-08
            ],
            [
                1.444979692797559e-07,
                4.450852111120808e-07,
                1.444979692797559e-07,
                7.338208055579897e-07,
                6.144172404738491e-06,
                1.637377057673536e-07,
                2.3823696679230424e-07,
                8.939700567004841e-06,
                1.1253520230052635e-07,
                1.8553907971855875e-07
            ],
            [
                0.9999962733598304,
                0.9999798543020191,
                0.9999964991439201,
                0.9999916019249775,
                1.3709570434178922e-06,
                5.715003788993679e-07,
                0.9999987121043248,
                2.6995771309523475e-07,
                0.9999724643188062,
                3.0590215399183813e-07
            ],
            [
                1.9947297215125433e-06,
                6.475947982002148e-07,
                1.0677026154774503e-06,
                1.2098661162023305e-06,
                1.994730672668496e-06,
                1.7603427936335396e-06,
                1.2098662604291696e-06,
                2.902312331170226e-06,
                3.288750241561788e-06,
                3.2887498495150166e-06
            ],
            [
                4.139934586278605e-08,
                2.1024331597262577e-07,
                4.450852111148132e-07,
                1.1253516205489029e-07,
                0.9999885212332518,
                3.9278610661822475e-07,
                1.637377448057981e-07,
                1.2751905808881762e-07,
                2.382369667929001e-07,
                1.4449798650551755e-07
            ],
            [
                0.999999946842163,
                0.999996711250938,
                0.9999785550516415,
                0.999999825702163,
                0.9999969105044494,
                0.9999983463102178,
                0.999966785817139,
                0.999968798081304,
                0.9999957771655524,
                0.9999999067050276
            ],
            [
                0.9999910603005089,
                0.9999972735284304,
                0.9999646437325255,
                0.9999417087276253,
                0.999981074856318,
                0.9999957771655532,
                0.9999852610215635,
                0.9999921107402446,
                0.9999832985762038,
                0.9999960330131431
            ],
            [
                1.0129993393319151e-05,
                1.3007130014636887e-05,
                2.6995790618252024e-07,
                2.3823688159237777e-07,
                3.4663278639265633e-07,
                4.222833444429485e-06,
                1.9947301970587145e-06,
                5.422217030209884e-06,
                1.0677026154774503e-06,
                5.422220907909759e-06
            ],
            [
                0.9999999317439954,
                0.9999930377454167,
                0.9999960330131437,
                0.9999977396748958,
                0.9999998024945624,
                0.9999975938973766,
                0.999999631011592,
                0.9999998024947273,
                0.999998540623258,
                0.9999997463981334
            ],
            [
                0.999997097686978,
                0.9999952149055077,
                8.233247603685483e-08,
                0.9999967112517207,
                0.9999992188512971,
                0.9999599363126715,
                0.99999649914684,
                0.9999151889691621,
                0.9999910603015723,
                0.999995777168069
            ],
            [
                2.9023119851781017e-06,
                9.931188590255539e-08,
                1.0129987357407137e-05,
                1.637377448057981e-07,
                2.902312331170226e-06,
                1.9947297215125433e-06,
                1.760343003481596e-06,
                2.753568453792444e-05,
                0.9999898700078189,
                1.892514598551715e-05
            ],
            [
                2.561281905390075e-06,
                1.994730434879465e-06,
                0.9999898700126536,
                0.9999810748450226,
                3.7266406168624155e-06,
                1.5534981249697903e-06,
                0.9999038976084988,
                0.9999599362936233,
                1.7603434231833873e-06,
                1.7603440527286572e-06
            ],
            [
                1.0677029973158649e-06,
                0.9999861540004193,
                5.71500651413193e-07,
                1.275190580884987e-07,
                5.043476486902204e-07,
                4.4508510499849186e-07,
                1.2098659719716573e-06,
                6.475947210031623e-07,
                1.8553910183548312e-07,
                2.102433159721477e-07
            ],
            [
                0.9998911031174278,
                0.0001584361981391736,
                0.9997040429406584,
                0.9999885212359925,
                5.422217030663578e-06,
                0.9996646497373984,
                0.9999151889287293,
                0.9998911031172123,
                0.9999038975741514,
                0.9998601779106551
            ],
            [
                0.9999892166878099,
                2.6995774527657245e-07,
                3.466326211105621e-07,
                2.382368247924618e-07,
                2.1024339116134898e-07,
                7.338208930443633e-07,
                2.6995784182073116e-07,
                1.7603432133296774e-06,
                7.338208055664991e-07,
                0.9999981261246177
            ],
            [
                2.1024331597262577e-07,
                3.46632497145457e-07,
                2.3823688159237777e-07,
                4.450852641737424e-07,
                1.1253514863909295e-07,
                1.8553907971855875e-07,
                1.3709573702778664e-06,
                1.27519088491875e-07,
                9.422442569315887e-07,
                3.927862002663297e-07
            ],
            [
                5.043474082005342e-07,
                7.338207180838067e-07,
                2.382368247924618e-07,
                9.422450431912e-07,
                1.209865250822125e-06,
                3.059022998576899e-07,
                7.338212429582604e-07,
                4.450849988811838e-07,
                5.715003788993679e-07,
                8.315282259009745e-07
            ],
            [
                0.9999989969855536,
                0.9999997761971315,
                0.9999992661791073,
                0.9999999397642294,
                0.999999746398073,
                0.9999999176675436,
                0.9999998802069587,
                1.9947294837154625e-06,
                0.999999789756659,
                9.422450431989127e-07
            ],
            [
                6.023573475041126e-08,
                5.715004470313855e-07,
                1.6373776432509826e-07,
                2.1024339116082313e-07,
                1.444979692800516e-07,
                1.855390354818069e-07,
                2.6995768091383957e-07,
                0.9999962733598301,
                2.10243290909724e-07,
                2.1024339116082313e-07
            ],
            [
                2.6995771309523475e-07,
                2.6995784182140636e-07,
                4.450852641717689e-07,
                0.9999952149049374,
                3.0590237279032884e-07,
                1.6373766672888118e-07,
                6.475949526020042e-07,
                5.043474081993875e-07,
                4.4508510499849186e-07,
                3.9278638755992735e-07
            ],
            [
                0.999999218851856,
                0.9999945777790971,
                0.9999999006880904,
                0.9999975938985229,
                0.9999998144608983,
                1.0677028700363782e-06,
                0.9999987901338845,
                0.9999987121043244,
                0.9999998461827139,
                0.9999999067050165
            ],
            [
                5.715004470313855e-07,
                0.9999945777823281,
                6.475947982022763e-07,
                1.8553905760062447e-07,
                6.475946438022905e-07,
                5.04347468323289e-07,
                0.9999986290427939,
                0.9999964991455884,
                1.2098652508391807e-06,
                0.9999989969855534
            ],
            [
                1.1253521571574156e-07,
                1.0677032518700286e-06,
                1.7603436330179102e-06,
                7.3382080556433e-07,
                8.315277302841894e-07,
                1.2751908849167202e-07,
                1.5534975693979422e-06,
                1.275190276859705e-07,
                2.3823685319244518e-07,
                0.014063624796284271
            ]
        ]
    },
    {
        "q_id": "9643_mmlu_physics",
        "cot_ids": [
            1,
            2,
            6,
            7,
            10,
            12,
            13,
            14,
            16,
            17,
            18,
            19,
            20,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            40,
            41,
            42,
            44,
            46,
            47,
            48,
            49,
            50,
            52,
            55,
            56,
            57,
            58,
            59,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            72,
            73,
            74,
            75,
            76,
            79,
            80,
            81,
            83,
            86,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            113,
            114,
            117,
            118,
            119,
            120,
            121,
            124,
            125,
            127
        ],
        "rewards": [
            [
                3.726637951028202e-06,
                3.726639728370556e-06,
                1.2098655392921197e-06,
                1.76034258364702e-06,
                1.7603440527286572e-06,
                1.3709567165461505e-06,
                6.475950297971703e-07,
                1.0677032518748838e-06,
                1.5534975693933505e-06,
                2.9023119851781017e-06
            ],
            [
                2.3823690999323465e-07,
                1.8553907971855875e-07,
                5.043472278312808e-07,
                1.3709575337125585e-06,
                2.3823690999290963e-07,
                5.043472278322555e-07,
                3.059022269250683e-07,
                1.6373764720923895e-07,
                8.315279285351409e-07,
                1.6373770576683237e-07
            ],
            [
                1.0677026154730804e-06,
                7.338207180761315e-07,
                1.855391681898159e-07,
                1.2098662604291696e-06,
                9.422444815409489e-07,
                6.47594952595231e-07,
                5.04347468318358e-07,
                7.889263526345123e-06,
                1.0677032518785256e-06,
                7.338208055536515e-07
            ],
            [
                9.422449308716635e-07,
                2.9023133690821773e-06,
                1.994729483729522e-06,
                9.931195693628605e-08,
                6.475950298021765e-07,
                5.715006514176113e-07,
                1.6373768624837685e-07,
                3.466327037553825e-07,
                1.370957860576702e-06,
                1.9947297214944016e-06
            ],
            [
                2.260324836776948e-06,
                5.422218323399208e-06,
                9.422448185388577e-07,
                2.5612812947240366e-06,
                1.0129987356706945e-05,
                NaN,
                4.2228324377164004e-06,
                8.31527928532683e-07,
                5.422217677078203e-06,
                1.3709578605455302e-06
            ],
            [
                1.3709573702722555e-06,
                1.994729483630195e-06,
                8.315278294072958e-07,
                9.422448185510695e-07,
                1.3709570434178922e-06,
                4.222835458148261e-06,
                9.422448185435711e-07,
                3.288748281220719e-06,
                7.338212429537553e-07,
                8.315278294072958e-07
            ],
            [
                9.422444815765128e-07,
                6.475949526020042e-07,
                2.902313369111213e-06,
                5.043472879540142e-07,
                3.466326211113502e-07,
                6.475947981975644e-07,
                1.0677032518785256e-06,
                1.012998977264307e-05,
                8.31528424162821e-07,
                7.3382080556433e-07
            ],
            [
                6.475949526020042e-07,
                3.466326211113502e-07,
                2.102434412875379e-07,
                7.338207180864763e-07,
                3.9278615344178325e-07,
                3.927860597935108e-07,
                1.8553903548231313e-07,
                7.338208055664991e-07,
                2.3823682479292225e-07,
                6.475947982037486e-07
            ],
            [
                2.3823690999323465e-07,
                1.8553910183674878e-07,
                3.9278605979534166e-07,
                9.422448185510695e-07,
                1.7603432133296774e-06,
                7.338207180898968e-07,
                9.422450432030903e-07,
                9.422442569290178e-07,
                4.450851049991497e-07,
                3.288750241561788e-06
            ],
            [
                4.4508494582314646e-07,
                7.338209805090567e-07,
                3.9278610661902853e-07,
                9.422442569315887e-07,
                2.6995790618350237e-07,
                2.6995771309523475e-07,
                3.05902190458764e-07,
                1.6373774480535133e-07,
                3.927860597945825e-07,
                6.475947982037486e-07
            ],
            [
                1.2751908849167202e-07,
                2.1024336609874897e-07,
                1.444979692800516e-07,
                8.764254764749753e-08,
                3.927862470899887e-07,
                1.6373766672973748e-07,
                5.04347287955046e-07,
                2.1024341622426268e-07,
                3.466325384678894e-07,
                1.6373770576776313e-07
            ],
            [
                1.5534981249574276e-06,
                6.475949525981759e-07,
                7.338209805200689e-07,
                5.043473480777865e-07,
                1.6701423836262173e-05,
                2.2603234895289998e-06,
                2.5612816000646084e-06,
                2.90231094723893e-06,
                6.475951069985296e-07,
                1.5534981249574276e-06
            ],
            [
                5.043472879525233e-07,
                7.338211554783522e-07,
                1.0677029973158649e-06,
                4.785094494750855e-06,
                NaN,
                6.962254589978262e-06,
                5.422218323487975e-06,
                3.927862470861484e-07,
                4.450848927658745e-07,
                2.382368815916736e-07
            ],
            [
                1.444980209564556e-07,
                2.382368247924618e-07,
                1.1253513522391131e-07,
                3.0590215399183813e-07,
                1.1253506814842375e-07,
                6.475949526020042e-07,
                2.699577774530648e-07,
                9.931186222523604e-08,
                5.043475885674441e-07,
                1.8553910183548312e-07
            ],
            [
                8.31527928532683e-07,
                9.422442569315887e-07,
                3.9278615344178325e-07,
                3.4663262110945863e-07,
                6.475950297942253e-07,
                8.315283250394546e-07,
                1.2098662604291696e-06,
                6.475945665900901e-07,
                1.9947292459347367e-06,
                2.260325106237323e-06
            ],
            [
                1.275190884913241e-07,
                1.994730672675753e-06,
                3.927862470899887e-07,
                1.067703124601679e-06,
                1.209865539295696e-06,
                2.1024334103352274e-07,
                1.2751904288710323e-07,
                2.6995790618469934e-07,
                1.994729483723626e-06,
                1.760342793638743e-06
            ],
            [
                8.315279285351409e-07,
                3.9278610661902853e-07,
                5.043474081993875e-07,
                5.043475885674441e-07,
                9.422448185534261e-07,
                3.0590237279032884e-07,
                1.8553916819032217e-07,
                3.927860597945825e-07,
                4.4508510499849186e-07,
                4.450852111148132e-07
            ],
            [
                5.715005151606823e-07,
                1.6373772528704005e-07,
                3.4663278639892215e-07,
                3.927862002663297e-07,
                1.4449805540740185e-07,
                2.699577774585891e-07,
                3.9278615344178325e-07,
                2.6995774527718623e-07,
                2.382369951932796e-07,
                5.043476486924565e-07
            ],
            [
                3.927862470905692e-07,
                1.1253509497883659e-07,
                1.1253512180925583e-07,
                9.931202796993203e-08,
                3.288749457469787e-06,
                1.1253508156363576e-07,
                2.6995774527718623e-07,
                2.5612819054133693e-06,
                2.102434412875379e-07,
                0.9999832985742799
            ],
            [
                0.9999969105044512,
                2.3823699519143784e-07,
                1.9947297215125433e-06,
                0.9999916019239913,
                NaN,
                0.9999599363128039,
                0.9999898700042273,
                0.9999916019240217,
                0.9999986290429589,
                3.2887502415767434e-06
            ],
            [
                9.422442569097361e-07,
                4.222832437747125e-06,
                1.1478768119563723e-05,
                8.315279285205827e-07,
                5.715005832853093e-07,
                2.5612822106421996e-06,
                1.3709573702566696e-06,
                8.315284241560147e-07,
                1.760343213335281e-06,
                5.715003789017068e-07
            ],
            [
                9.931195693628605e-08,
                8.764245361752286e-08,
                6.023569884718319e-08,
                5.715006514176113e-07,
                1.8553919030858602e-07,
                6.475950298021765e-07,
                1.4449807263312446e-07,
                1.6373764721072816e-07,
                1.275190732904469e-07,
                2.3823693839325527e-07
            ],
            [
                4.222834954753043e-06,
                4.450849458179853e-07,
                2.902312677150514e-06,
                7.338208055664991e-07,
                8.315280276546789e-07,
                7.338208055664991e-07,
                3.288750241561788e-06,
                3.2887478892683997e-06,
                1.760342583722268e-06,
                1.2098656834922064e-06
            ],
            [
                3.927860597945825e-07,
                1.27519073289925e-07,
                2.382370235922541e-07,
                2.382368815916736e-07,
                2.260325106237323e-06,
                1.3709576971425944e-06,
                3.9278634073732336e-07,
                1.637377448057981e-07,
                1.2751901248454963e-07,
                9.422448185510695e-07
            ],
            [
                5.043472278227948e-07,
                0.9982992778810917,
                4.4508489275752546e-07,
                3.7266410611296085e-06,
                3.726637951387472e-06,
                5.422218969858371e-06,
                1.2098662604291696e-06,
                0.9999877809269355,
                4.222834954778007e-06,
                9.422445939054222e-07
            ],
            [
                3.927862470861484e-07,
                1.8553907971682908e-07,
                3.466327037512053e-07,
                1.6373762769138607e-07,
                4.450852111135988e-07,
                2.382368815916736e-07,
                4.4508505193386385e-07,
                3.927862470816829e-07,
                1.8553910183548312e-07,
                5.71500651413193e-07
            ],
            [
                1.670142582682936e-05,
                6.475948754012522e-07,
                1.3709570434219446e-06,
                3.726639728370556e-06,
                4.222831934379152e-06,
                1.1478764020727177e-05,
                4.7850933538313875e-06,
                4.785095635592258e-06,
                3.2887490653408545e-06,
                4.785092783519724e-06
            ],
            [
                2.3823688159069855e-07,
                3.9278624708775595e-07,
                8.764244316933122e-08,
                3.059021175261338e-07,
                3.9278615344178325e-07,
                2.382368815916736e-07,
                3.0590237279032884e-07,
                3.4663249714451116e-07,
                2.3823696679230424e-07,
                2.699578740011634e-07
            ],
            [
                1.7603427936183298e-06,
                8.31528424162821e-07,
                1.3709572068422585e-06,
                1.3709567165530083e-06,
                4.2228334445658276e-06,
                1.0677024881941248e-06,
                8.93969950132721e-06,
                2.9023116391978967e-06,
                2.9023133690980155e-06,
                4.2228319344021954e-06
            ],
            [
                2.6995774527718623e-07,
                2.382369667929001e-07,
                2.3823690999290963e-07,
                1.2751899728311609e-07,
                3.059022998576899e-07,
                1.5534973842076057e-06,
                4.4508510499849186e-07,
                3.9278634073732336e-07,
                3.059022269250683e-07,
                4.450851580566494e-07
            ],
            [
                2.260324836787226e-06,
                2.26032402841657e-06,
                1.4738976701411704e-05,
                1.0129989772532511e-05,
                8.939697369882888e-06,
                2.4300232043987867e-05,
                2.2603248367512505e-06,
                0.00020342702218063233,
                0.02033235289743556,
                8.939696304311336e-06
            ],
            [
                1.6373776432509826e-07,
                1.1253508156363576e-07,
                4.450848927658745e-07,
                3.059022998581767e-07,
                2.699576809143613e-07,
                5.71500719545698e-07,
                4.450852111155216e-07,
                3.059022998581767e-07,
                7.338208055680009e-07,
                5.715003107767143e-07
            ],
            [
                6.475946438055299e-07,
                5.422218969858371e-06,
                2.6995784182183607e-07,
                1.0677033791612137e-06,
                1.275190580890061e-07,
                1.209865539295696e-06,
                3.9278629391427843e-07,
                1.3709573702822306e-06,
                3.466325384678894e-07,
                2.1024344128660572e-07
            ],
            [
                5.715005832886879e-07,
                3.466325797888292e-07,
                3.05902190458764e-07,
                5.043476486915964e-07,
                3.059021175261338e-07,
                3.4663253846718004e-07,
                1.2098662604291696e-06,
                8.315281267882195e-07,
                4.4508510499849186e-07,
                3.4663253846718004e-07
            ],
            [
                6.47594952595231e-07,
                5.043472278280699e-07,
                4.450848927637999e-07,
                2.69957906184239e-07,
                3.05902226923399e-07,
                3.4663278639738526e-07,
                9.422442569208767e-07,
                2.6995784182140636e-07,
                2.1024329090929374e-07,
                6.475947210012481e-07
            ],
            [
                1.6373762769138607e-07,
                1.8553905760062447e-07,
                5.315784971839039e-08,
                2.260324028372372e-06,
                3.466327037553825e-07,
                8.7642558095602e-08,
                1.1253509497835043e-07,
                2.102434162245973e-07,
                5.315787506598473e-08,
                2.3823690999323465e-07
            ],
            [
                1.2098659719757836e-06,
                5.715003107715166e-07,
                1.0677029973192638e-06,
                6.475951069696694e-07,
                4.222834954778007e-06,
                6.47594566594213e-07,
                4.450848927637999e-07,
                1.5534981249574276e-06,
                4.785092783519724e-06,
                4.4508510499849186e-07
            ],
            [
                5.715006514167015e-07,
                7.338209805133949e-07,
                1.3709575337159875e-06,
                3.927862939126708e-07,
                6.475946437996402e-07,
                9.422448185478557e-07,
                2.382368247924618e-07,
                3.2887478892683997e-06,
                9.422447062202052e-07,
                4.450851580555361e-07
            ],
            [
                1.1253512180925583e-07,
                3.05902336324494e-07,
                2.102434412875379e-07,
                9.931202796993203e-08,
                9.931190958076104e-08,
                1.8553919030858602e-07,
                1.855391681906175e-07,
                2.10243290909724e-07,
                7.734416698849138e-08,
                2.102434412875379e-07
            ],
            [
                2.1024339116168358e-07,
                1.5534983101602148e-06,
                1.6373776432509826e-07,
                2.3823690999323465e-07,
                2.6995784182140636e-07,
                9.93120161306789e-08,
                1.6373764721072816e-07,
                1.994730434879465e-06,
                2.3823693839325527e-07,
                5.715005151606823e-07
            ],
            [
                2.699576809143613e-07,
                2.102434412875379e-07,
                3.927862470899887e-07,
                3.466327037548308e-07,
                1.4449805540740185e-07,
                6.475945665900901e-07,
                2.382368815916736e-07,
                2.1024336609843824e-07,
                3.466325797888292e-07,
                3.4663249714451116e-07
            ],
            [
                8.315278294072958e-07,
                7.338209805200689e-07,
                1.0677027427624903e-06,
                7.338209805224048e-07,
                1.0677028700363782e-06,
                1.994729721436347e-06,
                1.3709578605729614e-06,
                1.2098662604291696e-06,
                1.3709570434178922e-06,
                1.7603427936263351e-06
            ],
            [
                1.5534979397740895e-06,
                1.2098655392811161e-06,
                1.2098662604291696e-06,
                1.0677032518748838e-06,
                9.422449308138184e-07,
                3.2887498494551953e-06,
                1.760344052714248e-06,
                1.3709568799679844e-06,
                1.0677033791437343e-06,
                8.315284241597959e-07
            ],
            [
                1.3709570434178922e-06,
                5.043472879525233e-07,
                6.475949525981759e-07,
                1.7603440527046419e-06,
                6.475949526020042e-07,
                1.5534984953453635e-06,
                0.0002034269491749444,
                4.785092783519724e-06,
                5.4222176771176554e-06,
                3.726638839878908e-06
            ],
            [
                1.7603438428460541e-06,
                6.475948753991907e-07,
                3.0590233632400716e-07,
                5.043476486915964e-07,
                6.475949525981759e-07,
                1.1253512180925583e-07,
                3.9278605979534166e-07,
                2.69957906184239e-07,
                3.05902190458764e-07,
                6.9622587397397306e-06
            ],
            [
                2.3823685319244518e-07,
                2.561281294760143e-06,
                1.067703124601679e-06,
                2.2603251062450327e-06,
                5.422217677152175e-06,
                1.2098653950692178e-06,
                5.715006514105942e-07,
                6.475949525981759e-07,
                3.059021175261338e-07,
                4.450850519403407e-07
            ],
            [
                1.3709567165617364e-06,
                6.475947982037486e-07,
                2.3823696679327928e-07,
                4.4508494582405734e-07,
                2.699576809143613e-07,
                7.889266347786918e-06,
                4.450850519403407e-07,
                8.764242227418718e-08,
                1.0677027427624903e-06,
                1.9947304348862686e-06
            ],
            [
                6.962259569630266e-06,
                1.5534981249574276e-06,
                6.475947210031623e-07,
                5.422217677078203e-06,
                4.450851049941403e-07,
                1.300712846477255e-05,
                4.539785781961294e-05,
                1.7603425837855082e-06,
                6.1441724046434924e-06,
                4.78509278348926e-06
            ],
            [
                3.4663262110945863e-07,
                4.450852111148132e-07,
                9.422444815765128e-07,
                3.7266401726359486e-06,
                5.715003789033962e-07,
                5.043475885674441e-07,
                7.338211554783522e-07,
                4.450851580555361e-07,
                1.7603434231777837e-06,
                6.475947982037486e-07
            ],
            [
                1.3709570434122812e-06,
                7.338213304283347e-07,
                3.726641061058432e-06,
                6.475948753991907e-07,
                1.2098661161927025e-06,
                7.338208055536515e-07,
                6.144175334172377e-06,
                9.422443692489024e-07,
                7.338211554758494e-07,
                1.0677027427525368e-06
            ],
            [
                4.450852111148132e-07,
                8.315283250371857e-07,
                6.475945666063607e-07,
                2.5612819054133693e-06,
                2.1024339116168358e-07,
                6.475947210012481e-07,
                1.8553916819032217e-07,
                5.715007195431641e-07,
                1.6373762769138607e-07,
                1.9947297215125433e-06
            ],
            [
                1.8553916819032217e-07,
                1.6373768624837685e-07,
                1.2751904288710323e-07,
                2.6995790618350237e-07,
                1.8553905759893702e-07,
                1.8553910183607374e-07,
                2.382369667929001e-07,
                9.931189774140912e-08,
                4.450851049959619e-07,
                2.102433660979124e-07
            ],
            [
                1.2098661162056318e-06,
                3.059022269250683e-07,
                3.9278610661902853e-07,
                2.3823699519290042e-07,
                2.2603240284371276e-06,
                2.3823685319244518e-07,
                5.715006514167015e-07,
                3.059021175255426e-07,
                3.9278634073732336e-07,
                3.05902190458764e-07
            ],
            [
                8.315284241650899e-07,
                6.962256249821764e-06,
                6.475947210012481e-07,
                1.209865827752005e-06,
                8.315284241560147e-07,
                1.3709576971463352e-06,
                1.2098652508424818e-06,
                3.9278605979208185e-07,
                3.9278610661902853e-07,
                5.04347468323289e-07
            ],
            [
                4.4508494582405734e-07,
                2.1024326584639497e-07,
                3.0590237279085045e-07,
                1.0677029973219343e-06,
                3.4663274507713016e-07,
                5.715003789046955e-07,
                1.0677026154827912e-06,
                1.855391239544352e-07,
                2.1024341622426268e-07,
                2.6995774527718623e-07
            ],
            [
                8.939695238536645e-06,
                2.2603242978778778e-06,
                1.2098655392871682e-06,
                1.3709575337016483e-06,
                1.5534981249697903e-06,
                1.2098662604247682e-06,
                3.466325797888292e-07,
                1.2098661161789477e-06,
                8.31528424162821e-07,
                1.067703379154416e-06
            ],
            [
                3.05902336324494e-07,
                4.4508510499849186e-07,
                2.1024334103505245e-07,
                3.9278638755671223e-07,
                3.927862002663297e-07,
                1.5534984953453635e-06,
                1.275190276859705e-07,
                1.3709568799879344e-06,
                1.3709567165579959e-06,
                3.466324971415162e-07
            ],
            [
                1.5534973842076057e-06,
                3.4663257978780455e-07,
                6.475947210046347e-07,
                4.4508515805735777e-07,
                1.9947292459406333e-06,
                6.962256249517824e-06,
                2.7535691095550887e-05,
                1.637377448057981e-07,
                1.2751902768612997e-07,
                3.120190020862863e-05
            ],
            [
                8.315281267882195e-07,
                2.6995790618469934e-07,
                5.715007195447234e-07,
                3.059021175261338e-07,
                9.422448185510695e-07,
                3.288749065423109e-06,
                1.7603432133136672e-06,
                2.2603237589676295e-06,
                1.7603432132464244e-06,
                5.715005151606823e-07
            ],
            [
                1.9947294836483373e-06,
                1.0129995810343862e-05,
                1.3709575336654889e-06,
                7.889259764273619e-06,
                1.4738985486265496e-05,
                1.994729483694599e-06,
                1.2098655392811161e-06,
                2.260324028427877e-06,
                1.7603427936263351e-06,
                6.14417533430649e-06
            ],
            [
                1.4449805540740185e-07,
                6.825600469412533e-08,
                4.450848927658745e-07,
                2.1024334103505245e-07,
                1.2751899728311609e-07,
                1.6373776432509826e-07,
                3.9278634073732336e-07,
                1.1253509497883659e-07,
                1.637377448057981e-07,
                7.338208055664991e-07
            ],
            [
                1.067703251864202e-06,
                3.288749849368453e-06,
                1.994730434847717e-06,
                1.2098661161927025e-06,
                1.9947297214544894e-06,
                1.067703251864202e-06,
                1.3709575336947905e-06,
                4.450848927637999e-07,
                4.222834954461155e-06,
                6.475945665900901e-07
            ],
            [
                5.715003789017068e-07,
                2.6995771309523475e-07,
                2.1024326584639497e-07,
                5.715005832853093e-07,
                2.382369667929001e-07,
                4.450852111120808e-07,
                1.6373774480535133e-07,
                1.2098653950656417e-06,
                4.4508510499849186e-07,
                9.422442569208767e-07
            ],
            [
                0.00010889694829665246,
                0.9999969105044583,
                0.9999251537737832,
                8.315278294114555e-07,
                1.892514598551715e-05,
                0.9999724643123662,
                0.9999756997564868,
                0.9998204720385467,
                0.999996033015047,
                8.481104140395962e-05
            ],
            [
                2.699578096403948e-07,
                7.338207180898968e-07,
                2.699578740032504e-07,
                3.466327037553825e-07,
                4.450852111155216e-07,
                3.059022269250683e-07,
                1.6373766672973748e-07,
                5.715003789046955e-07,
                1.275190732904469e-07,
                1.2751901248454963e-07
            ],
            [
                8.315280276546789e-07,
                1.5534984953453635e-06,
                2.5612819053399912e-06,
                1.209865539274514e-06,
                1.7603434231705793e-06,
                1.7603438428460541e-06,
                1.0677027427471959e-06,
                1.3709572068272963e-06,
                1.0677033791495609e-06,
                1.5534971989696065e-06
            ],
            [
                2.260323489490968e-06,
                0.9999296881251298,
                0.9995121428362608,
                8.939695236593446e-06,
                3.288749849477628e-06,
                2.2603253755949437e-06,
                1.1478768126057254e-05,
                5.422217030747413e-06,
                1.9947297214944016e-06,
                8.315279285149107e-07
            ],
            [
                6.962254589851619e-06,
                1.2098655392871682e-06,
                1.0677024881980089e-06,
                NaN,
                3.059021904571643e-07,
                7.338210679909462e-07,
                3.0590226339061185e-07,
                8.315279285351409e-07,
                5.043472879504592e-07,
                6.475947209985977e-07
            ],
            [
                5.715003788993679e-07,
                3.0590237279085045e-07,
                2.699577774585891e-07,
                2.1024331597262577e-07,
                1.4449800373065699e-07,
                6.475945666051092e-07,
                6.9622570780973205e-06,
                1.209865539295696e-06,
                1.3709567165579959e-06,
                8.315281267882195e-07
            ],
            [
                1.855391239539711e-07,
                1.6373766672821107e-07,
                0.9999885212333747,
                6.60521761905875e-05,
                2.699578739999358e-07,
                2.1024341622297196e-07,
                3.0590215399183813e-07,
                3.927860597935108e-07,
                0.9999379494828645,
                7.338208055664991e-07
            ],
            [
                3.927862939126708e-07,
                0.9999892166839539,
                0.9999993916408915,
                0.9999986290424677,
                0.9999991684722711,
                0.9999930377429334,
                0.9999987901344631,
                0.9999984465020632,
                0.999998996986032,
                0.9999972735303839
            ],
            [
                2.5612834320563895e-06,
                1.9947297215125433e-06,
                2.902312331170226e-06,
                1.9947299593078385e-06,
                1.994730672675753e-06,
                5.043472879540142e-07,
                3.05902336324494e-07,
                3.288748673376478e-06,
                7.338209805224048e-07,
                7.338209805240734e-07
            ],
            [
                1.209865827752005e-06,
                3.059022998581767e-07,
                3.927860597945825e-07,
                4.450850519403407e-07,
                3.4663249714612693e-07,
                2.5612819054133693e-06,
                5.043475885674441e-07,
                3.466327863983311e-07,
                3.9278605979534166e-07,
                2.6995774527718623e-07
            ],
            [
                7.338213304363436e-07,
                6.475951069985296e-07,
                1.4449805540763184e-07,
                NaN,
                3.927863875616689e-07,
                3.927862002641863e-07,
                5.315788140303327e-08,
                1.3709578605617394e-06,
                9.931187406410953e-08,
                NaN
            ],
            [
                NaN,
                5.043475885606781e-07,
                1.0677032518785256e-06,
                2.2603242978665707e-06,
                2.5612831267202583e-06,
                2.6995774527577444e-07,
                7.338213304283347e-07,
                2.6995774527577444e-07,
                3.9278610661366994e-07,
                4.450848927637999e-07
            ],
            [
                3.4663253846718004e-07,
                2.6995784182140636e-07,
                3.4663253846718004e-07,
                1.994730672675753e-06,
                3.927860597945825e-07,
                2.1024341622297196e-07,
                2.6995784182183607e-07,
                1.1253512180873128e-07,
                1.4449805540740185e-07,
                4.450851049959619e-07
            ],
            [
                3.059021175261338e-07,
                1.4449805540740185e-07,
                1.553498124964492e-06,
                2.9023133690637e-06,
                1.9947299593078385e-06,
                1.8553907971855875e-07,
                2.6995774527718623e-07,
                1.1253516205489029e-07,
                1.855391239544352e-07,
                2.6995771309523475e-07
            ],
            [
                2.1024341622426268e-07,
                8.315282259117513e-07,
                5.715005832853093e-07,
                9.422448185435711e-07,
                3.05902190458764e-07,
                3.4663266242969896e-07,
                2.6995774527577444e-07,
                9.422444815679433e-07,
                1.0677029973192638e-06,
                2.3823699519290042e-07
            ],
            [
                6.023571320847322e-08,
                5.043472278322555e-07,
                8.76424013786396e-08,
                1.1253514863909295e-07,
                9.931185038635267e-08,
                2.102434162245973e-07,
                2.1024334103505245e-07,
                1.6701427812931038e-05,
                2.1024331597262577e-07,
                1.067703124601679e-06
            ],
            [
                8.764245361752286e-08,
                1.370957860576702e-06,
                3.9278634073732336e-07,
                2.6995774527718623e-07,
                4.450852641737424e-07,
                9.93120161306789e-08,
                4.4508510499849186e-07,
                6.475947210031623e-07,
                1.0677026154806063e-06,
                1.76034300345598e-06
            ],
            [
                1.3709576971425944e-06,
                1.0129992187658463e-05,
                1.9947306726213275e-06,
                8.315277302841894e-07,
                5.715005832886879e-07,
                1.067703379154416e-06,
                9.422448185435711e-07,
                3.726638395611981e-06,
                3.726638839833152e-06,
                2.260324836787226e-06
            ],
            [
                1.0677027427624903e-06,
                NaN,
                1.0677027427600627e-06,
                1.760344052714248e-06,
                1.2098659719524008e-06,
                3.288749065423109e-06,
                1.9947304348862686e-06,
                4.450852111148132e-07,
                7.338208930391909e-07,
                4.222833947960866e-06
            ],
            [
                1.5534979397267575e-06,
                6.475950298011458e-07,
                2.902312331125353e-06,
                8.315280276626197e-07,
                NaN,
                1.0677026154730804e-06,
                1.760343213335281e-06,
                7.338212429582604e-07,
                1.9947301970972664e-06,
                2.902313369111213e-06
            ],
            [
                7.88926164518358e-06,
                3.466325797896173e-07,
                1.3709575336947905e-06,
                3.059022269250683e-07,
                2.1024336609843824e-07,
                7.338210679979539e-07,
                3.4663266243308805e-07,
                9.422444815679433e-07,
                4.450848927650143e-07,
                9.422445939032799e-07
            ],
            [
                4.450851580555361e-07,
                3.726639284144195e-06,
                1.994730197071414e-06,
                5.715003789033962e-07,
                5.043475885696228e-07,
                3.288750633569722e-06,
                1.3709572068522336e-06,
                6.475948754028718e-07,
                1.0677032518748838e-06,
                5.04347528446051e-07
            ],
            [
                7.338212429504183e-07,
                1.067703251864202e-06,
                8.31528126775552e-07,
                1.1478773599425825e-05,
                1.3709572068354007e-06,
                1.0677031245905116e-06,
                1.067703251864202e-06,
                7.338208055536515e-07,
                1.2098662604126641e-06,
                1.994729245878497e-06
            ],
            [
                1.6373764720923895e-07,
                5.71500515159253e-07,
                6.475951069985296e-07,
                1.6373774480535133e-07,
                1.275190732904469e-07,
                9.931190958076104e-08,
                9.931198061405701e-08,
                1.6373772528581146e-07,
                1.4449805540651476e-07,
                2.3823690999160957e-07
            ],
            [
                2.902312331125353e-06,
                1.7603434231777837e-06,
                1.7603427936263351e-06,
                1.3709578605617394e-06,
                1.0677032518785256e-06,
                7.338209805200689e-07,
                3.2887486733420804e-06,
                1.3709570434178922e-06,
                2.561283432035425e-06,
                7.889263526180094e-06
            ],
            [
                6.475951069985296e-07,
                2.3823693839290317e-07,
                2.699578740011634e-07,
                4.450852111135988e-07,
                7.338213304283347e-07,
                8.315284241597959e-07,
                3.466327037539638e-07,
                8.315284241597959e-07,
                3.927862002625787e-07,
                3.288750633488963e-06
            ],
            [
                3.466327450765785e-07,
                3.9278634073732336e-07,
                2.699577774585891e-07,
                4.450848927637999e-07,
                7.338211554783522e-07,
                3.9278605979534166e-07,
                3.05902190458764e-07,
                3.466327037548308e-07,
                3.0590226338490835e-07,
                3.9278634073732336e-07
            ],
            [
                2.144495608378187e-05,
                1.3709567165461505e-06,
                7.338212429582604e-07,
                8.315280276580819e-07,
                6.475948754012522e-07,
                2.382369383923073e-07,
                1.2098655392662613e-06,
                3.059023363221292e-07,
                1.4449805540700758e-07,
                1.9947304348703948e-06
            ],
            [
                5.715006514040971e-07,
                2.5612825160096693e-06,
                3.059023363221292e-07,
                1.2098662604192665e-06,
                5.715003107738556e-07,
                3.466327863945479e-07,
                5.043475284430694e-07,
                2.2603248367173307e-06,
                5.043472879525233e-07,
                8.315284241597959e-07
            ]
        ]
    },
    {
        "q_id": "9886_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            19,
            20,
            21,
            23,
            25,
            26,
            27,
            29,
            31,
            32,
            34,
            35,
            36,
            39,
            40,
            41,
            42,
            44,
            45,
            46,
            48,
            49,
            50,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            66,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            77,
            78,
            79,
            80,
            81,
            82,
            85,
            87,
            91,
            92,
            94,
            95,
            97,
            98,
            99,
            101,
            104,
            106,
            108,
            109,
            110,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            125,
            127,
            28,
            33,
            84,
            88,
            100,
            102
        ],
        "rewards": [
            [
                1.9947306726594253e-06,
                8.939695238536645e-06,
                2.4300246527309398e-05,
                1.3709575336654889e-06,
                1.892514598551715e-05,
                8.315277302788957e-07,
                1.760344052714248e-06,
                1.9947297215043796e-06,
                3.2887502415243994e-06,
                3.927862939126708e-07
            ],
            [
                6.475951069985296e-07,
                3.7266401726173067e-06,
                1.994730197090463e-06,
                1.3709575337078829e-06,
                1.8925155009767892e-05,
                6.1441767987808774e-06,
                1.067702870039777e-06,
                1.7603438428800754e-06,
                7.338207180864763e-07,
                1.7603427936263351e-06
            ],
            [
                7.338212429537553e-07,
                2.902312677137316e-06,
                6.475950297942253e-07,
                NaN,
                1.760344052714248e-06,
                7.338209805133949e-07,
                3.288749457469787e-06,
                1.5534971990126997e-06,
                1.5534979397740895e-06,
                2.260325106237323e-06
            ],
            [
                9.422445939002803e-07,
                1.0677024882009222e-06,
                5.043474081993875e-07,
                6.475950298011458e-07,
                2.902313023130843e-06,
                5.71500242637956e-07,
                7.338210680021253e-07,
                5.043476486833397e-07,
                1.209865539295696e-06,
                1.7603438428800754e-06
            ],
            [
                1.0677024881980089e-06,
                7.338209805224048e-07,
                NaN,
                6.475951069985296e-07,
                9.422450431989127e-07,
                1.5534971989809095e-06,
                1.0677028700363782e-06,
                1.3709567165579959e-06,
                6.962253759828703e-06,
                5.043474081993875e-07
            ],
            [
                2.6995790618469934e-07,
                6.962258739271155e-06,
                5.715004470313855e-07,
                1.0677027427624903e-06,
                7.338209805200689e-07,
                5.715004470313855e-07,
                3.05902190458764e-07,
                3.059021904571643e-07,
                5.715005832853093e-07,
                9.422447062270609e-07
            ],
            [
                8.939700567004841e-06,
                1.2098658277451275e-06,
                9.422443692330485e-07,
                2.9023119851055122e-06,
                1.760343003481596e-06,
                6.475946437928669e-07,
                1.6373774480535133e-07,
                NaN,
                2.2603234895289998e-06,
                4.4508510499849186e-07
            ],
            [
                6.47594952595231e-07,
                5.715005832886879e-07,
                5.04347468323289e-07,
                3.927862002641863e-07,
                4.4508515805199415e-07,
                1.9947297214182054e-06,
                4.450848927599543e-07,
                9.422443692555439e-07,
                6.475947210031623e-07,
                4.785095064601411e-06
            ],
            [
                5.715007195431641e-07,
                5.043472879540142e-07,
                3.288749457409966e-06,
                1.0,
                5.715003107715166e-07,
                1.2098658277264215e-06,
                2.5612834320214477e-06,
                2.430024362999023e-05,
                1.3709575337078829e-06,
                2.902310947190096e-06
            ],
            [
                1.3709575336654889e-06,
                1.3709575336654889e-06,
                6.475946437928669e-07,
                8.315278293951957e-07,
                8.31528424146183e-07,
                8.315279285205827e-07,
                5.043472879481655e-07,
                5.715007195353674e-07,
                2.902312677084523e-06,
                1.370957370247318e-06
            ],
            [
                3.059021175261338e-07,
                5.04347287955046e-07,
                2.260324567337161e-06,
                6.475947210031623e-07,
                1.0677032518785256e-06,
                3.4663274507713016e-07,
                5.715002426486762e-07,
                6.962256249682458e-06,
                6.144177531767002e-06,
                9.422449308774482e-07
            ],
            [
                3.9278605979011705e-07,
                3.9278615344178325e-07,
                1.8553910183607374e-07,
                6.475946437966953e-07,
                5.04347528446051e-07,
                3.059021904571643e-07,
                3.0590215399183813e-07,
                1.2098659719524008e-06,
                2.1024334103505245e-07,
                2.1024341622368903e-07
            ],
            [
                1.9947306726358406e-06,
                2.561283126639892e-06,
                4.785094494628999e-06,
                2.260323489490968e-06,
                2.9023133689924295e-06,
                5.715005832762133e-07,
                3.2887490652810324e-06,
                1.5534981248330927e-06,
                2.9023116390104826e-06,
                6.9622579095833456e-06
            ],
            [
                1.2098659719716573e-06,
                1.99472924590571e-06,
                7.889266347636241e-06,
                2.902310947208574e-06,
                2.9023126771227976e-06,
                1.2098662604247682e-06,
                3.726641061085547e-06,
                6.144176799283803e-06,
                1.7603434231705793e-06,
                8.315284241597959e-07
            ],
            [
                1.2098655392871682e-06,
                9.4224425692559e-07,
                5.422217030555087e-06,
                7.338212429537553e-07,
                1.2098655392811161e-06,
                4.22283545795623e-06,
                2.5612822106841303e-06,
                1.2098655392871682e-06,
                2.2603242978665707e-06,
                1.7603427935518875e-06
            ],
            [
                6.475950298011458e-07,
                4.4508510499849186e-07,
                1.5534975692866768e-06,
                5.043476486915964e-07,
                5.04347528446051e-07,
                3.059021175261338e-07,
                8.315283250371857e-07,
                3.927860597935108e-07,
                3.05902263389638e-07,
                3.927862002625787e-07
            ],
            [
                8.764245361752286e-08,
                2.6995784182140636e-07,
                2.382369667929001e-07,
                3.059022998576899e-07,
                3.466325797896173e-07,
                2.1024336609843824e-07,
                1.4449796927932878e-07,
                8.315283250371857e-07,
                5.715005832886879e-07,
                2.382370235933104e-07
            ],
            [
                5.04347287955046e-07,
                4.450848927650143e-07,
                1.067702615468225e-06,
                9.422448185478557e-07,
                1.5534981249697903e-06,
                9.422444815765128e-07,
                3.0590215399183813e-07,
                3.0590237279032884e-07,
                6.475948753930064e-07,
                4.450852111148132e-07
            ],
            [
                NaN,
                NaN,
                8.315281267861397e-07,
                3.9278615344178325e-07,
                1.5534977545886537e-06,
                5.043475885674441e-07,
                NaN,
                8.31527928532683e-07,
                2.699578096393206e-07,
                7.338208055664991e-07
            ],
            [
                7.338208930391909e-07,
                2.102434412875379e-07,
                3.466327037548308e-07,
                3.927862002663297e-07,
                1.5534979397740895e-06,
                8.315278294072958e-07,
                3.288750633518874e-06,
                2.2603240284371276e-06,
                8.315278294072958e-07,
                2.1444943290362748e-05
            ],
            [
                3.288749457409966e-06,
                2.9023112932045342e-06,
                1.5534975693933505e-06,
                1.5534973841895917e-06,
                1.2098662604126641e-06,
                1.9947290081286418e-06,
                2.260324836776948e-06,
                1.553498495338299e-06,
                1.9947301970813926e-06,
                1.7603425837606927e-06
            ],
            [
                2.3823693839290317e-07,
                2.1024326584639497e-07,
                4.450849988811838e-07,
                1.3709567165579959e-06,
                5.715003789046955e-07,
                7.338207180864763e-07,
                3.4663249714612693e-07,
                3.9278610661902853e-07,
                4.450848927637999e-07,
                4.450852111135988e-07
            ],
            [
                2.902313369111213e-06,
                2.260325106237323e-06,
                1.0129990980100021e-05,
                4.785096776468749e-06,
                NaN,
                NaN,
                3.7266406168624155e-06,
                4.450851580555361e-07,
                NaN,
                1.7603432133296774e-06
            ],
            [
                1.1253509497883659e-07,
                1.8925157264919016e-05,
                4.222834451355964e-06,
                8.315280276456036e-07,
                3.2887498494282754e-06,
                NaN,
                3.288748673360027e-06,
                NaN,
                NaN,
                1.0129987357407137e-05
            ],
            [
                1.7603432133296774e-06,
                9.422448185510695e-07,
                1.0677027427600627e-06,
                4.450851049959619e-07,
                1.6373764721072816e-07,
                5.715002426486762e-07,
                1.3709576971425944e-06,
                2.382370235933104e-07,
                2.1024331597262577e-07,
                2.382368531929327e-07
            ],
            [
                8.315283250371857e-07,
                5.715007195353674e-07,
                1.0677026154730804e-06,
                8.31528126775552e-07,
                9.4224425692559e-07,
                9.422442569208767e-07,
                5.043474683204221e-07,
                3.059022998576899e-07,
                8.315284241597959e-07,
                8.315277302588544e-07
            ],
            [
                1.5534975693869924e-06,
                6.475947210012481e-07,
                2.2603234895176927e-06,
                1.0677026154730804e-06,
                1.7603430034743913e-06,
                7.338211554783522e-07,
                1.7603440527046419e-06,
                1.7603438428740716e-06,
                1.3709567165579959e-06,
                NaN
            ],
            [
                8.315283250371857e-07,
                1.0677026154551157e-06,
                1.3709575337016483e-06,
                9.4224425692559e-07,
                3.726638395611981e-06,
                1.553497754577351e-06,
                1.2098658277451275e-06,
                2.9023112931688987e-06,
                1.2098655392871682e-06,
                4.450849988811838e-07
            ],
            [
                6.144176799166453e-06,
                1.1478765388898939e-05,
                4.0063692188981614e-05,
                4.0063696966212295e-05,
                1.3007130014376633e-05,
                2.1444956082767684e-05,
                4.222831934321543e-06,
                1.1478766757404937e-05,
                1.4738985485461206e-05,
                3.2887502414436403e-06
            ],
            [
                2.2603242978871282e-06,
                2.9023112932177327e-06,
                1.0677029972993568e-06,
                8.315284241401329e-07,
                5.715003107738556e-07,
                8.315280276546789e-07,
                1.0677031245905116e-06,
                5.715005832853093e-07,
                6.475949525834513e-07,
                5.715006514151423e-07
            ],
            [
                1.275190732904469e-07,
                9.931199245322124e-08,
                5.04347287955046e-07,
                1.0677027427600627e-06,
                0.99999457777974,
                5.043476486915964e-07,
                7.338208930460318e-07,
                0.9999921107374258,
                8.764242227418718e-08,
                7.338210680021253e-07
            ],
            [
                5.043475885674441e-07,
                6.475948754012522e-07,
                1.637377448057981e-07,
                8.315279285351409e-07,
                7.338207180864763e-07,
                5.715007195447234e-07,
                2.6995790618469934e-07,
                5.715007195431641e-07,
                3.0590237278838124e-07,
                6.475948754012522e-07
            ],
            [
                1.0677031245905116e-06,
                1.5534981249574276e-06,
                1.553498310118888e-06,
                1.3709576971160984e-06,
                1.3709567164663505e-06,
                2.561283431942246e-06,
                NaN,
                9.422450431732037e-07,
                3.2887494573232236e-06,
                3.0590211752206485e-07
            ],
            [
                5.04347528446051e-07,
                3.726639728348526e-06,
                1.5534977545886537e-06,
                1.5534973841309562e-06,
                1.2098653950656417e-06,
                9.422444815792981e-07,
                3.726641061085547e-06,
                6.144173869558639e-06,
                2.260324567337161e-06,
                9.422443692489024e-07
            ],
            [
                1.7603430034743913e-06,
                8.315278294097538e-07,
                7.338209805200689e-07,
                2.5612812947380135e-06,
                3.7266406168827523e-06,
                NaN,
                1.7603425837855082e-06,
                5.043472278280699e-07,
                1.9947297215043796e-06,
                3.927862939126708e-07
            ],
            [
                1.2098658277451275e-06,
                1.5534979397740895e-06,
                1.3709567165530083e-06,
                8.315281267861397e-07,
                4.450849988811838e-07,
                2.902310947208574e-06,
                1.2098659719524008e-06,
                1.5534983101602148e-06,
                1.760344052714248e-06,
                3.726639728370556e-06
            ],
            [
                3.2887490653109436e-06,
                2.561281600049467e-06,
                4.2228334438149845e-06,
                4.785093353874907e-06,
                2.9023119851055122e-06,
                7.338208930391909e-07,
                1.0677028700203557e-06,
                6.962254589914941e-06,
                3.2887498493983645e-06,
                4.785094494576774e-06
            ],
            [
                1.7603436329978976e-06,
                2.5612825160096693e-06,
                1.7603430033799313e-06,
                2.5612834320214477e-06,
                1.0677027427525368e-06,
                4.785092783454444e-06,
                2.260325375664839e-06,
                1.3709572068422585e-06,
                NaN,
                1.7603425837702984e-06
            ],
            [
                7.889266347786918e-06,
                NaN,
                9.422444815792981e-07,
                1.7603427936335396e-06,
                8.315283250371857e-07,
                9.422444815792981e-07,
                4.222834954778007e-06,
                3.4663278639892215e-07,
                1.5534981249697903e-06,
                3.7266397283908927e-06
            ],
            [
                4.450852111120808e-07,
                4.785095065204162e-06,
                2.902313369111213e-06,
                2.2603251062270446e-06,
                2.382370235933104e-07,
                1.3709567165530083e-06,
                NaN,
                1.2098653950656417e-06,
                7.338209805224048e-07,
                1.2098662604247682e-06
            ],
            [
                8.315281267882195e-07,
                1.5534981249574276e-06,
                4.2228329411708495e-06,
                2.5612825160562587e-06,
                2.2603253756874524e-06,
                8.315278294072958e-07,
                7.338208930391909e-07,
                6.144176799334096e-06,
                1.0677028700363782e-06,
                3.288749849477628e-06
            ],
            [
                4.450852111148132e-07,
                2.2603245673155757e-06,
                1.209865539295696e-06,
                1.370957860576702e-06,
                1.7603430034867993e-06,
                6.475948754012522e-07,
                1.0677033790883835e-06,
                3.7266401726359486e-06,
                1.8925145983795953e-05,
                1.0677028700422047e-06
            ],
            [
                1.7603440527046419e-06,
                5.04347468318358e-07,
                1.2098662604247682e-06,
                5.715006514040971e-07,
                2.5612812947508257e-06,
                3.7266401726173067e-06,
                9.422450431989127e-07,
                1.5534975693869924e-06,
                1.0677026154730804e-06,
                1.0129995810343862e-05
            ],
            [
                NaN,
                2.144495097113319e-05,
                2.5612828213934817e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                0.0024726234971822122,
                2.5612828213818346e-06,
                NaN
            ],
            [
                1.0129992186202796e-05,
                8.315278293951957e-07,
                4.222835457906302e-06,
                5.422217030032353e-06,
                7.338208930391909e-07,
                1.5534975692866768e-06,
                2.260324836776948e-06,
                1.0677029973192638e-06,
                7.338210679909462e-07,
                1.0677028700363782e-06
            ],
            [
                3.9278605979534166e-07,
                2.90231094723893e-06,
                5.043472278322555e-07,
                5.04347287955046e-07,
                6.47595107001401e-07,
                1.0677026154806063e-06,
                1.209866260432471e-06,
                3.927862002663297e-07,
                1.2098652508424818e-06,
                3.46632497145457e-07
            ],
            [
                2.561283431942246e-06,
                1.5534975693601474e-06,
                6.9622537599680095e-06,
                1.4738985486265496e-05,
                9.422445939002803e-07,
                1.3709568799919866e-06,
                1.99472924590571e-06,
                4.222833444590791e-06,
                1.7603434231705793e-06,
                2.5612828213934817e-06
            ],
            [
                1.2098659719788098e-06,
                NaN,
                7.338209805240734e-07,
                2.1444950971601277e-05,
                1.7603430034743913e-06,
                NaN,
                2.1444950970626095e-05,
                8.315279285351409e-07,
                4.450848927658745e-07,
                1.9947301970451086e-06
            ],
            [
                9.422445939054222e-07,
                3.1201922535494165e-05,
                0.001501181982076743,
                1.994729483729522e-06,
                7.338210680021253e-07,
                NaN,
                2.4300252321904572e-05,
                4.450848927658745e-07,
                4.006367786720367e-05,
                0.012431650132847308
            ],
            [
                4.2228339479858295e-06,
                1.0129988565084915e-05,
                1.6701421845361053e-05,
                4.222832941193893e-06,
                2.902313369111213e-06,
                NaN,
                2.9023116391978967e-06,
                8.939694172957213e-06,
                1.4449800373065699e-07,
                1.9947299593014888e-06
            ],
            [
                1.7603438428660665e-06,
                1.5534981249574276e-06,
                2.561283126679493e-06,
                1.99472924590571e-06,
                1.8925141461620395e-05,
                1.99472924590571e-06,
                2.2603251061664e-06,
                6.962259569560613e-06,
                3.726639283901856e-06,
                1.0677033791437343e-06
            ],
            [
                4.450851580555361e-07,
                8.315283250371857e-07,
                3.0590226339061185e-07,
                5.715006514151423e-07,
                3.9278615344178325e-07,
                4.450848927637999e-07,
                9.422444815765128e-07,
                4.785093924047376e-06,
                7.338209805133949e-07,
                3.466327863961242e-07
            ],
            [
                6.825608606148807e-08,
                1.6373764721072816e-07,
                1.8553903548231313e-07,
                1.1253512180925583e-07,
                1.6373768624837685e-07,
                1.855391681906175e-07,
                3.927862002641863e-07,
                9.931195693628605e-08,
                1.2751899728286965e-07,
                3.4663249714451116e-07
            ],
            [
                1.1253526937656726e-07,
                3.4663262110945863e-07,
                1.2098658277451275e-06,
                3.466325797888292e-07,
                1.6373774480535133e-07,
                3.927862470861484e-07,
                3.0590215399183813e-07,
                3.927863875584984e-07,
                2.6995774527577444e-07,
                3.9278615344178325e-07
            ],
            [
                6.962256249885085e-06,
                3.927863875616689e-07,
                3.288750241561788e-06,
                5.4222183235249605e-06,
                3.9278605979534166e-07,
                1.7603425837791042e-06,
                2.6995790618469934e-07,
                NaN,
                1.4449795205429202e-07,
                2.5612819054028872e-06
            ],
            [
                1.2098658277451275e-06,
                8.315280276546789e-07,
                1.0677032518748838e-06,
                2.2603248367358324e-06,
                2.5612812947380135e-06,
                8.315281267834927e-07,
                1.3709567165386693e-06,
                1.2098656834922064e-06,
                8.315284241560147e-07,
                1.3709575336947905e-06
            ],
            [
                8.315278293951957e-07,
                6.475947210031623e-07,
                7.338208930391909e-07,
                1.0677031245905116e-06,
                1.2098653950656417e-06,
                7.338211554783522e-07,
                1.7603427936263351e-06,
                1.2098658277451275e-06,
                4.2228339479858295e-06,
                2.9023123310580418e-06
            ],
            [
                3.9278615344178325e-07,
                6.144175334468545e-06,
                1.0677032518785256e-06,
                1.067703124601679e-06,
                6.962256249885085e-06,
                5.043472879540142e-07,
                8.315280276607289e-07,
                5.043476486915964e-07,
                2.5612819054133693e-06,
                3.535625071859258e-05
            ],
            [
                9.422442569208767e-07,
                2.260324028351814e-06,
                1.7603436330179102e-06,
                1.9947292458603553e-06,
                2.561281905390075e-06,
                6.1441731370702875e-06,
                1.0677027427525368e-06,
                2.561283431942246e-06,
                8.93969736955767e-06,
                1.9947306726358406e-06
            ],
            [
                5.71500515159253e-07,
                2.902310947208574e-06,
                1.0677032518700286e-06,
                5.715005832886879e-07,
                4.450851580555361e-07,
                1.2098662604247682e-06,
                NaN,
                2.382370235922541e-07,
                5.715004470313855e-07,
                5.715003107767143e-07
            ],
            [
                9.422449308748773e-07,
                8.315277302649045e-07,
                1.2098662604126641e-06,
                1.7603436329978976e-06,
                1.9947297215043796e-06,
                5.422218969661113e-06,
                3.7266379513434106e-06,
                2.9023126769050284e-06,
                5.715005832853093e-07,
                3.7266406168403854e-06
            ],
            [
                4.4508494582405734e-07,
                1.553498495308628e-06,
                6.475951069855719e-07,
                5.715007195431641e-07,
                3.288747889284851e-06,
                2.5612828213934817e-06,
                1.5534975692259223e-06,
                6.962258739796719e-06,
                2.260324836776948e-06,
                3.4663257978039603e-07
            ],
            [
                3.4663249714451116e-07,
                6.962255419653012e-06,
                6.9622595696935874e-06,
                1.5534975693707442e-06,
                2.9023112931873767e-06,
                1.760344052714248e-06,
                NaN,
                6.475950297942253e-07,
                1.01299946023704e-05,
                6.144176066850984e-06
            ],
            [
                2.902311639183378e-06,
                NaN,
                2.260324836776948e-06,
                1.0677028700363782e-06,
                3.2887490653408545e-06,
                2.5612831266946347e-06,
                NaN,
                9.4224425692559e-07,
                4.785095065232451e-06,
                NaN
            ],
            [
                1.5534983101602148e-06,
                6.475947210031623e-07,
                6.475951069985296e-07,
                1.3709567165579959e-06,
                5.043472879525233e-07,
                7.338212429537553e-07,
                2.5612831267202583e-06,
                5.715005832886879e-07,
                1.3709567165530083e-06,
                6.475948754012522e-07
            ],
            [
                5.043474081993875e-07,
                1.6701417859519093e-05,
                1.3709572068522336e-06,
                2.2603234895176927e-06,
                5.043472879540142e-07,
                2.9023133690980155e-06,
                4.450849988811838e-07,
                1.0677026154730804e-06,
                3.2887486733420804e-06,
                6.962254589781966e-06
            ],
            [
                2.6995774527718623e-07,
                3.927862002663297e-07,
                9.422450431989127e-07,
                6.475950298011458e-07,
                3.927860597945825e-07,
                5.715005832886879e-07,
                8.315280276546789e-07,
                3.466325797888292e-07,
                1.3709575337159875e-06,
                1.8553914607128047e-07
            ],
            [
                1.2098655392871682e-06,
                5.043472879525233e-07,
                1.3709575337016483e-06,
                5.715004470313855e-07,
                6.475945666051092e-07,
                5.043472879525233e-07,
                7.338208930355202e-07,
                1.0677032518700286e-06,
                9.422450431989127e-07,
                7.338212429504183e-07
            ],
            [
                1.9947306726594253e-06,
                5.715002426439334e-07,
                4.222832437677995e-06,
                7.338209805224048e-07,
                3.72664061671159e-06,
                8.315278294072958e-07,
                4.222834451355964e-06,
                1.3709578605617394e-06,
                1.2098655392811161e-06,
                4.450849988811838e-07
            ],
            [
                4.450851580555361e-07,
                9.422443692527585e-07,
                2.561282516042282e-06,
                1.4738987243478167e-05,
                NaN,
                1.0677031245905116e-06,
                NaN,
                6.475951069985296e-07,
                1.2098655392921197e-06,
                2.2603234895289998e-06
            ],
            [
                1.067702742726318e-06,
                1.9947304348332037e-06,
                8.31528126775552e-07,
                1.7603434231777837e-06,
                2.260324567337161e-06,
                5.04347348070562e-07,
                1.2098655391947376e-06,
                2.2603245673279107e-06,
                1.012999460278499e-05,
                4.222831934202483e-06
            ],
            [
                NaN,
                9.422447062202052e-07,
                NaN,
                NaN,
                NaN,
                2.5612828213934817e-06,
                7.338207180761315e-07,
                5.043472879525233e-07,
                1.9947292459347367e-06,
                1.6701419854156377e-05
            ],
            [
                1.0677032518700286e-06,
                3.7266397283908927e-06,
                1.7603434231833873e-06,
                3.927862002641863e-07,
                3.466327037539638e-07,
                4.4508515805199415e-07,
                7.338213304316717e-07,
                3.4663249714325014e-07,
                9.422444815814404e-07,
                4.785092783519724e-06
            ],
            [
                NaN,
                5.043475885674441e-07,
                1.7603438428740716e-06,
                9.422449308748773e-07,
                3.0590237279032884e-07,
                3.927863875584984e-07,
                4.785095635624897e-06,
                7.338211554783522e-07,
                1.3709570434178922e-06,
                1.994729483705484e-06
            ],
            [
                0.9995121428979942,
                1.0677032518700286e-06,
                1.994729008145876e-06,
                1.0677026154774503e-06,
                6.475947981975644e-07,
                1.2098661162023305e-06,
                1.5534981249574276e-06,
                1.0677033791583005e-06,
                2.2603242978213447e-06,
                6.475947210031623e-07
            ],
            [
                9.422442569290178e-07,
                0.999978555051631,
                2.5612828213934817e-06,
                2.1024336609874897e-07,
                3.05902190458764e-07,
                8.315278294114555e-07,
                1.760343213335281e-06,
                NaN,
                NaN,
                3.466327450756327e-07
            ],
            [
                0.9999852610198116,
                3.927860597945825e-07,
                4.4508510499849186e-07,
                1.6373774480535133e-07,
                3.05902263389638e-07,
                3.059021175261338e-07,
                3.46632497145457e-07,
                3.0590237279085045e-07,
                3.059022269250683e-07,
                2.382369383923073e-07
            ],
            [
                3.927861534406222e-07,
                8.764251630441717e-08,
                5.715007195447234e-07,
                0.9978172839897415,
                8.315284241650899e-07,
                NaN,
                1.0677031245905116e-06,
                1.7603432133136672e-06,
                0.9998766054406608,
                5.04347348075149e-07
            ],
            [
                NaN,
                3.7266410611296085e-06,
                7.338209805240734e-07,
                1.3709568799919866e-06,
                NaN,
                1.0677026154806063e-06,
                NaN,
                3.288750241561788e-06,
                1.3709572068422585e-06,
                NaN
            ],
            [
                1.0677028700203557e-06,
                4.222833444590791e-06,
                1.0677028700363782e-06,
                3.9278615344178325e-07,
                8.315283250371857e-07,
                2.5612825160562587e-06,
                3.9278634073732336e-07,
                1.2098659719757836e-06,
                1.855391681906175e-07,
                4.785095635624897e-06
            ],
            [
                1.994729721469003e-06,
                3.2887502415438413e-06,
                3.7266383955882547e-06,
                2.5612831266165976e-06,
                5.422217030614265e-06,
                4.222835458044565e-06,
                2.902310947208574e-06,
                2.260324297853209e-06,
                2.9023112931688987e-06,
                3.7266397282926013e-06
            ],
            [
                2.3823685319244518e-07,
                1.8553916819032217e-07,
                2.6995774527718623e-07,
                3.0590226339061185e-07,
                4.450851580555361e-07,
                5.715007195447234e-07,
                2.699577774585891e-07,
                6.475947209953583e-07,
                3.466326624322211e-07,
                2.382368815916736e-07
            ],
            [
                2.2603248367358324e-06,
                3.2887490652451393e-06,
                2.2603245672497918e-06,
                4.222833947897496e-06,
                4.222832437677995e-06,
                2.260324567268294e-06,
                1.994729721469003e-06,
                1.9947294836483373e-06,
                1.7603434231505666e-06,
                2.5612812946681295e-06
            ],
            [
                3.466327450765785e-07,
                1.7603434231833873e-06,
                1.760342793638743e-06,
                NaN,
                9.422444815628016e-07,
                1.5534979397740895e-06,
                1.147877359957198e-05,
                NaN,
                1.5534973842076057e-06,
                3.4663278639892215e-07
            ],
            [
                3.726637951387472e-06,
                2.2603242978665707e-06,
                3.7266406168624155e-06,
                2.5612812946890944e-06,
                2.90231094723893e-06,
                1.3709567165530083e-06,
                2.5612828213690224e-06,
                NaN,
                1.994730197071414e-06,
                3.726639728370556e-06
            ],
            [
                2.561283431986506e-06,
                3.288750633545794e-06,
                1.7603440527046419e-06,
                2.9023119851266288e-06,
                2.9023123311055552e-06,
                3.726640172537657e-06,
                6.962255419051463e-06,
                1.01299946023704e-05,
                2.2603245673155757e-06,
                1.7603427935967163e-06
            ],
            [
                6.475951069932288e-07,
                4.222834954514924e-06,
                8.315284241560147e-07,
                2.2603248366762157e-06,
                1.9947304348703948e-06,
                5.422220908703723e-06,
                2.561282210530385e-06,
                1.2098662604126641e-06,
                1.994729721396435e-06,
                1.5534973841895917e-06
            ],
            [
                5.043474683220276e-07,
                4.450852641717689e-07,
                3.4663278639892215e-07,
                5.043474081957179e-07,
                1.5534981249496567e-06,
                9.422448185510695e-07,
                1.0677031245851707e-06,
                9.4224425692559e-07,
                6.475947210031623e-07,
                1.5534975693488444e-06
            ],
            [
                2.260323758939877e-06,
                4.785096776468749e-06,
                1.3709572068422585e-06,
                NaN,
                3.7266383955611403e-06,
                1.994730197071414e-06,
                1.7603425837791042e-06,
                1.9947297215125433e-06,
                3.726641061085547e-06,
                7.338213304363436e-07
            ],
            [
                1.2098662604049616e-06,
                1.855391239547094e-07,
                2.561281905390075e-06,
                1.3709576971379186e-06,
                1.0677032518748838e-06,
                7.338209805224048e-07,
                3.4663249714451116e-07,
                1.5534979397740895e-06,
                3.288749849477628e-06,
                3.726637951387472e-06
            ],
            [
                2.561281600049467e-06,
                1.1478764020372226e-05,
                4.222833444467892e-06,
                NaN,
                1.1478766756653273e-05,
                NaN,
                6.1441731370702875e-06,
                5.422217030707961e-06,
                4.222831934352267e-06,
                3.535624228441698e-05
            ],
            [
                2.561283126679493e-06,
                7.338207180864763e-07,
                9.422447062094932e-07,
                1.994729008105057e-06,
                3.726641061109272e-06,
                6.144176066795103e-06,
                1.209865539274514e-06,
                2.260325375664839e-06,
                3.726639728370556e-06,
                4.785092783415276e-06
            ],
            [
                NaN,
                2.430024942462891e-05,
                4.222833444590791e-06,
                4.785092783519724e-06,
                5.715007195447234e-07,
                4.2228329411708495e-06,
                NaN,
                7.338209805224048e-07,
                6.962256249821764e-06,
                1.2098655392921197e-06
            ],
            [
                1.7603440527046419e-06,
                2.5612819054028872e-06,
                5.1442207537151994e-05,
                2.260324567302214e-06,
                1.3709576971061233e-06,
                4.785093923768848e-06,
                3.7266392839425286e-06,
                1.760344052714248e-06,
                9.422442569290178e-07,
                1.5534979397740895e-06
            ],
            [
                1.55349775456958e-06,
                1.473898197154587e-05,
                5.422217677028889e-06,
                4.785095635592258e-06,
                2.2603242978007868e-06,
                1.1478770862067849e-05,
                1.994729721482609e-06,
                3.726640172503764e-06,
                NaN,
                6.9622595696935874e-06
            ],
            [
                4.450851049941403e-07,
                5.715005832886879e-07,
                2.1024329090867228e-07,
                2.6995771309523475e-07,
                5.043472879540142e-07,
                4.450850519403407e-07,
                5.715004470295662e-07,
                2.1024326584639497e-07,
                9.422443692446175e-07,
                6.47594952595231e-07
            ],
            [
                1.3709575337078829e-06,
                7.889265407255982e-06,
                2.260325106237323e-06,
                1.0677024881980089e-06,
                1.7603432133296774e-06,
                1.0677031245905116e-06,
                1.1478765389368729e-05,
                1.012999098021058e-05,
                3.2887494574518405e-06,
                1.5534971990126997e-06
            ],
            [
                5.715007195431641e-07,
                4.450851580555361e-07,
                7.88926446679691e-06,
                1.0677024881980089e-06,
                5.043474081993875e-07,
                7.338211554783522e-07,
                3.05902190458764e-07,
                3.0590215399183813e-07,
                2.2603242978665707e-06,
                3.927862002641863e-07
            ]
        ]
    },
    {
        "q_id": "9133_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            9,
            11,
            12,
            13,
            14,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            24,
            25,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            49,
            50,
            52,
            53,
            54,
            55,
            57,
            58,
            59,
            60,
            61,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            78,
            79,
            80,
            81,
            83,
            85,
            86,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            98,
            101,
            102,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            119,
            120,
            122,
            124,
            127
        ],
        "rewards": [
            [
                6.475946438022905e-07,
                5.04347408197782e-07,
                7.338209805224048e-07,
                5.043475885674441e-07,
                5.71500651413193e-07,
                4.450852111120808e-07,
                3.927862002606139e-07,
                5.715007195431641e-07,
                4.450852111135988e-07,
                3.9278638755992735e-07
            ],
            [
                2.90231094723893e-06,
                1.2098662604291696e-06,
                3.0590226339061185e-07,
                2.5612825160562587e-06,
                5.043474081993875e-07,
                3.059022269250683e-07,
                1.3709567165579959e-06,
                1.5534975693933505e-06,
                5.043472879540142e-07,
                1.994730672668496e-06
            ],
            [
                1.3709572068553509e-06,
                NaN,
                5.043475284468537e-07,
                1.0677033791630344e-06,
                NaN,
                8.315282259151545e-07,
                4.4508515805735777e-07,
                9.422449308789479e-07,
                2.3823682479317953e-07,
                NaN
            ],
            [
                7.484621836619826e-05,
                6.144176066943187e-06,
                8.481108183851022e-05,
                5.8291265555961825e-05,
                1.3007126914612648e-05,
                1.5534984953552536e-06,
                2.7535694384882703e-05,
                4.785096776468749e-06,
                1.147877359957198e-05,
                7.889264466868659e-06
            ],
            [
                1.2098659719757836e-06,
                1.8553903548231313e-07,
                5.715005832886879e-07,
                3.7266397283908927e-06,
                2.382369667929001e-07,
                3.466326211113502e-07,
                2.561282210740037e-06,
                1.1253517547010071e-07,
                3.466326211113502e-07,
                9.422445939054222e-07
            ],
            [
                1.5534981249697903e-06,
                2.5612828213934817e-06,
                9.422450431989127e-07,
                1.5534979397790343e-06,
                1.6701415872385704e-05,
                2.9023119851781017e-06,
                5.422220909009474e-06,
                0.0001584362170463008,
                2.90231094723893e-06,
                6.144174601991196e-06
            ],
            [
                1.7603425837903113e-06,
                2.5612819054133693e-06,
                6.962258739796719e-06,
                1.1478772231232203e-05,
                4.222832437798974e-06,
                2.2603245673443566e-06,
                4.222834954801051e-06,
                6.1441767993788005e-06,
                4.785096206076165e-06,
                2.561282210740037e-06
            ],
            [
                4.222831934379152e-06,
                3.7266410611296085e-06,
                8.31527928532683e-07,
                1.3709573702822306e-06,
                1.5534975693933505e-06,
                1.2098652508424818e-06,
                8.315281267882195e-07,
                8.315282259138311e-07,
                NaN,
                1.067703124601679e-06
            ],
            [
                7.889263526345123e-06,
                3.726637951387472e-06,
                4.785093353940187e-06,
                5.144220140264605e-05,
                8.315277302819205e-07,
                4.222833444590791e-06,
                1.7603434231833873e-06,
                2.9023112932177327e-06,
                3.726639284125553e-06,
                1.9947292459347367e-06
            ],
            [
                4.4508494582405734e-07,
                1.2098652508424818e-06,
                1.760343213335281e-06,
                6.475945666063607e-07,
                9.422450432014836e-07,
                6.475948754028718e-07,
                2.1024326584639497e-07,
                1.209866260432471e-06,
                5.043473480777865e-07,
                3.9278605979534166e-07
            ],
            [
                6.144176066901277e-06,
                2.561281600086738e-06,
                8.939694172957213e-06,
                2.902312677150514e-06,
                2.4300234941880266e-05,
                7.889266347786918e-06,
                1.0129993395336818e-05,
                3.726639284144195e-06,
                6.144176066943187e-06,
                3.288749065423109e-06
            ],
            [
                1.0677028700422047e-06,
                3.7266401726359486e-06,
                1.9947301970972664e-06,
                1.2098659719788098e-06,
                1.5534975693979422e-06,
                5.043475885696228e-07,
                3.9278629391427843e-07,
                2.699577774585891e-07,
                1.994729721518893e-06,
                3.2887502415767434e-06
            ],
            [
                5.71500515161527e-07,
                2.6995790618469934e-07,
                1.0677027427624903e-06,
                5.043473480777865e-07,
                8.315277302857965e-07,
                5.043475284468537e-07,
                3.9278629391427843e-07,
                1.0677028700422047e-06,
                1.2098656835252174e-06,
                1.0677027427624903e-06
            ],
            [
                1.7603430034867993e-06,
                9.422448185534261e-07,
                5.043476486924565e-07,
                4.2228339479858295e-06,
                3.9278634073732336e-07,
                2.56128282131428e-06,
                1.2098661161982042e-06,
                1.5534973841895917e-06,
                5.422220909041528e-06,
                4.2228319344021954e-06
            ],
            [
                7.338209805240734e-07,
                1.3709567165617364e-06,
                4.222834954801051e-06,
                1.5534984953552536e-06,
                6.962253760024999e-06,
                1.1478766757853845e-05,
                7.889261645427538e-06,
                NaN,
                1.3709576971463352e-06,
                NaN
            ],
            [
                1.9947299593078385e-06,
                8.939700567094277e-06,
                0.9999904837449227,
                0.9999938558276095,
                1.0677024882029858e-06,
                2.9023116392097746e-06,
                0.9999938558232199,
                2.2603253756956754e-06,
                NaN,
                6.962257909842961e-06
            ],
            [
                2.2603253756956754e-06,
                NaN,
                4.450848927658745e-07,
                1.7603430034867993e-06,
                4.450852641737424e-07,
                6.144173869603344e-06,
                8.315277302841894e-07,
                2.561281294760143e-06,
                1.3709567165617364e-06,
                7.338207180898968e-07
            ],
            [
                NaN,
                6.47594952603035e-07,
                9.422447062294175e-07,
                2.3823690999323465e-07,
                1.5534983101644536e-06,
                6.825601283086733e-08,
                7.734414854823498e-08,
                2.699578096403948e-07,
                8.764245361752286e-08,
                4.450851049991497e-07
            ],
            [
                3.05902190458764e-07,
                2.699578096403948e-07,
                1.7603440527286572e-06,
                4.006370652227855e-05,
                1.994729721518893e-06,
                7.338210680021253e-07,
                3.4663274507713016e-07,
                2.2603253756956754e-06,
                3.2887506336235617e-06,
                2.260323758987159e-06
            ],
            [
                5.715003789046955e-07,
                1.5534971990169383e-06,
                4.222834954801051e-06,
                1.0677024882029858e-06,
                1.9947304348862686e-06,
                1.994729483729522e-06,
                1.1478772231232203e-05,
                3.288747889284851e-06,
                8.315277302857965e-07,
                1.0129988565084915e-05
            ],
            [
                3.059022998581767e-07,
                3.466325797896173e-07,
                1.27519088491875e-07,
                1.2098662604291696e-06,
                1.7603430034867993e-06,
                5.04347287955046e-07,
                2.2603253756956754e-06,
                4.785092783519724e-06,
                7.338208930460318e-07,
                1.0677028700363782e-06
            ],
            [
                2.6995771309523475e-07,
                2.2603234895289998e-06,
                1.3709567165530083e-06,
                3.72664061681327e-06,
                NaN,
                1.2098653950656417e-06,
                6.1441724046434924e-06,
                9.422444815765128e-07,
                6.475947210012481e-07,
                8.315278294072958e-07
            ],
            [
                1.3709576971463352e-06,
                4.5397857828200684e-05,
                2.5612834320563895e-06,
                1.3709573702856596e-06,
                2.5612834320563895e-06,
                1.0677029973219343e-06,
                1.7603430034867993e-06,
                1.5534971990169383e-06,
                NaN,
                1.0677027427624903e-06
            ],
            [
                3.7266410611296085e-06,
                1.0677026154806063e-06,
                2.561282210740037e-06,
                1.0677026154774503e-06,
                5.715005151606823e-07,
                9.422442569290178e-07,
                5.422220262636381e-06,
                3.466327450765785e-07,
                9.422449308774482e-07,
                1.5534975693979422e-06
            ],
            [
                0.9999995818813768,
                0.99999905775552,
                0.999986153998788,
                1.4738976701652988e-05,
                0.9999957771650588,
                0.9999988634365629,
                0.9999546021099659,
                0.9999485577683489,
                0.9999724642959317,
                7.889266347786918e-06
            ],
            [
                1.760342793638743e-06,
                1.3709573702822306e-06,
                2.5612834320563895e-06,
                5.715003789046955e-07,
                5.715002426475718e-07,
                2.5612834320563895e-06,
                3.466327037539638e-07,
                5.715003789033962e-07,
                1.9947297215125433e-06,
                1.3709568799919866e-06
            ],
            [
                9.422450432030903e-07,
                2.9023119851899796e-06,
                1.0677026154827912e-06,
                0.999993855823207,
                0.9999962733607176,
                3.7266410611465547e-06,
                1.5534981249736758e-06,
                8.315278294114555e-07,
                3.927862470905692e-07,
                1.209865827752005e-06
            ],
            [
                4.785092783519724e-06,
                0.999964643732562,
                1.994729721518893e-06,
                1.3007134667436886e-05,
                1.994729721518893e-06,
                1.670142980920999e-05,
                1.9947299593078385e-06,
                1.1478772231086046e-05,
                8.939693107288474e-06,
                NaN
            ],
            [
                7.338211554813555e-07,
                1.370957860576702e-06,
                1.994729721518893e-06,
                2.260323758987159e-06,
                1.209866260432471e-06,
                1.2098661162056318e-06,
                7.338208055680009e-07,
                1.370957860576702e-06,
                8.315284241665078e-07,
                5.422218969895357e-06
            ],
            [
                4.4508515805735777e-07,
                3.7266383956509585e-06,
                0.999999352405125,
                1.3709573702856596e-06,
                2.561281294760143e-06,
                7.338211554813555e-07,
                2.2603251062450327e-06,
                1.209866260432471e-06,
                1.7603440527334603e-06,
                NaN
            ],
            [
                1.9947301970972664e-06,
                1.3709576971463352e-06,
                2.561283126728994e-06,
                3.288747889284851e-06,
                3.2887506336235617e-06,
                5.043475284468537e-07,
                1.5534973842076057e-06,
                6.475947210046347e-07,
                3.288747889284851e-06,
                1.2098659719788098e-06
            ],
            [
                1.2751905808881762e-07,
                1.4449796927932878e-07,
                1.2751905808881762e-07,
                4.450848927650143e-07,
                2.1024331597262577e-07,
                2.3823690999290963e-07,
                1.6373774480479287e-07,
                1.855391239539711e-07,
                1.2751907328949007e-07,
                2.1024331597152624e-07
            ],
            [
                3.466326624336003e-07,
                0.9999485578051369,
                1.6701421845361053e-05,
                1.994729483729522e-06,
                4.222834451403972e-06,
                1.0677032518814388e-06,
                0.999999218851949,
                0.9999986290429573,
                2.561283126728994e-06,
                3.927861534431675e-07
            ],
            [
                4.222834954778007e-06,
                1.5534973842076057e-06,
                1.2098656835224664e-06,
                4.450851580566494e-07,
                6.475950298011458e-07,
                4.222833444590791e-06,
                1.2098652508424818e-06,
                6.475947210031623e-07,
                3.72663883989755e-06,
                1.9947299593014888e-06
            ],
            [
                7.33821330437595e-07,
                NaN,
                4.450848927658745e-07,
                8.315284241665078e-07,
                1.5534981249736758e-06,
                3.9278620026686556e-07,
                NaN,
                1.209865827752005e-06,
                3.059022998581767e-07,
                6.475946438055299e-07
            ],
            [
                4.222832941193893e-06,
                4.222834954778007e-06,
                8.315277302857965e-07,
                3.059021175261338e-07,
                2.9023133690980155e-06,
                2.5612819054133693e-06,
                1.0677032518814388e-06,
                1.4449807263312446e-07,
                1.275190580890061e-07,
                1.3709567165617364e-06
            ],
            [
                2.699577774585891e-07,
                3.0590219045914655e-07,
                3.4663266243308805e-07,
                1.209865539298447e-06,
                2.9023116392097746e-06,
                1.1253520230052635e-07,
                2.3823696679327928e-07,
                2.102434412871794e-07,
                3.466327037553825e-07,
                2.1024326584702836e-07
            ],
            [
                NaN,
                0.9999843104430419,
                0.9999916019250144,
                2.90231094723893e-06,
                1.209865827752005e-06,
                2.5612819054133693e-06,
                3.53562422882756e-05,
                0.9999977396749007,
                3.7266406168827523e-06,
                0.9999984465028054
            ],
            [
                4.4508510499849186e-07,
                2.561281294760143e-06,
                6.475945666051092e-07,
                9.422448185534261e-07,
                4.4508494582405734e-07,
                5.043476486915964e-07,
                3.4663278639892215e-07,
                7.338210680021253e-07,
                1.0677026154806063e-06,
                5.04347528446051e-07
            ],
            [
                2.2603253756956754e-06,
                1.2098656835252174e-06,
                7.338209805240734e-07,
                1.7603430034867993e-06,
                7.338207180898968e-07,
                1.1478770862882149e-05,
                0.9999898700126952,
                0.999994577781687,
                1.3709573702856596e-06,
                2.5612834320563895e-06
            ],
            [
                3.466326624336003e-07,
                7.33821330437595e-07,
                2.561281600086738e-06,
                7.338209805240734e-07,
                5.71500719545698e-07,
                3.726637951387472e-06,
                1.8553910183674878e-07,
                2.102434162245973e-07,
                5.043475885696228e-07,
                7.338208930460318e-07
            ],
            [
                1.6373766672973748e-07,
                1.8553903548231313e-07,
                3.059022998576899e-07,
                1.1253516205489029e-07,
                2.1024331597262577e-07,
                1.2751905808881762e-07,
                4.785095635655362e-06,
                1.4449805540740185e-07,
                2.1024341622426268e-07,
                3.4663249714612693e-07
            ],
            [
                1.6373776432481905e-07,
                9.422448185534261e-07,
                1.8553903548231313e-07,
                2.3823702359290413e-07,
                6.475950298011458e-07,
                1.6373762769138607e-07,
                4.450849988811838e-07,
                9.422449308774482e-07,
                4.450849988811838e-07,
                1.275190124842887e-07
            ],
            [
                0.9999997300422871,
                1.0129994602895546e-05,
                0.9999997761970248,
                0.9999997126314811,
                0.9999996533674617,
                0.9999994631251246,
                0.00012339454559719625,
                0.9999997300421261,
                0.9999995549148422,
                0.9999994284994852
            ],
            [
                6.9622587397397306e-06,
                1.7603440527286572e-06,
                4.222834954778007e-06,
                2.4300252321904572e-05,
                4.785092783519724e-06,
                2.144495608378187e-05,
                2.144494585801764e-05,
                2.4300243631272052e-05,
                1.4738985486506781e-05,
                1.0677032518748838e-06
            ],
            [
                1.994729483729522e-06,
                4.450848927658745e-07,
                3.4663278639892215e-07,
                3.4663274507713016e-07,
                3.05902336324494e-07,
                7.338208930460318e-07,
                3.059022269250683e-07,
                1.2751901248454963e-07,
                4.450848927658745e-07,
                4.450850519403407e-07
            ],
            [
                1.6373770576776313e-07,
                9.422442569315887e-07,
                2.6995784182140636e-07,
                1.6373770576776313e-07,
                3.9278610661902853e-07,
                1.5534973842076057e-06,
                5.043472879540142e-07,
                1.5534983101644536e-06,
                4.450852641737424e-07,
                1.2751908849167202e-07
            ],
            [
                1.147877359957198e-05,
                8.939698435657833e-06,
                2.561282210740037e-06,
                2.5612828213934817e-06,
                2.902312331170226e-06,
                3.1201900218617364e-05,
                6.9622595696935874e-06,
                3.726639284144195e-06,
                6.962256249885085e-06,
                1.994730672675753e-06
            ],
            [
                6.023572038912295e-08,
                1.6373774480605869e-07,
                1.275190276859705e-07,
                2.102434162245973e-07,
                3.4663249714612693e-07,
                2.3823693839325527e-07,
                6.023569884718319e-08,
                9.931202796993203e-08,
                9.931187406410953e-08,
                1.1253506814842375e-07
            ],
            [
                4.4508515805735777e-07,
                3.9278629391427843e-07,
                1.5534971990169383e-06,
                9.422450432030903e-07,
                3.05902263391829e-07,
                4.450851049991497e-07,
                9.422443692574719e-07,
                6.47594952603035e-07,
                1.7603438428848787e-06,
                5.71500515161527e-07
            ],
            [
                2.2603237589779086e-06,
                1.370957860567974e-06,
                7.338210680002898e-07,
                4.450849458218309e-07,
                3.7266406168624155e-06,
                5.715002426460124e-07,
                4.450849458200093e-07,
                5.715005832886879e-07,
                1.0677028700363782e-06,
                1.5534979397677313e-06
            ],
            [
                1.7603425837903113e-06,
                5.715006514176113e-07,
                8.315277302857965e-07,
                3.288749849529972e-06,
                5.043475284468537e-07,
                1.994729008151319e-06,
                2.9023119851899796e-06,
                1.5534975693979422e-06,
                5.043472278322555e-07,
                1.7603425837903113e-06
            ],
            [
                0.9999955048168234,
                1.892515501014656e-05,
                3.535624228698939e-05,
                4.785092783519724e-06,
                7.889259764517575e-06,
                1.4738980215593877e-05,
                0.9999339478566389,
                7.88926446679691e-06,
                0.9999955048162958,
                5.4222183235249605e-06
            ],
            [
                1.5534971990126997e-06,
                6.475947210012481e-07,
                2.2603251062450327e-06,
                3.7266401726359486e-06,
                7.889265407327733e-06,
                7.889265407255982e-06,
                3.1201907657271834e-05,
                2.2603253756956754e-06,
                2.3823690999290963e-07,
                5.422218323487975e-06
            ],
            [
                5.04347528446051e-07,
                4.785093924389007e-06,
                4.450852111155216e-07,
                7.338207180864763e-07,
                5.422220262636381e-06,
                1.994729483729522e-06,
                1.3709567165617364e-06,
                1.8553919030858602e-07,
                6.475945666063607e-07,
                9.422444815814404e-07
            ],
            [
                3.9278620026686556e-07,
                2.1024336609874897e-07,
                5.043475284468537e-07,
                4.4508499888275247e-07,
                2.3823682479317953e-07,
                6.82560779249779e-08,
                4.450850519409479e-07,
                1.2751902768612997e-07,
                1.1253524254650944e-07,
                2.699577774589574e-07
            ],
            [
                1.0677024882029858e-06,
                2.902313023130843e-06,
                1.0677024882029858e-06,
                1.3709576971463352e-06,
                4.450851049991497e-07,
                NaN,
                5.043474081957179e-07,
                2.9023112932296107e-06,
                6.47594875403829e-07,
                4.450852111155216e-07
            ],
            [
                3.288747889284851e-06,
                6.144173137170873e-06,
                3.72663883989755e-06,
                3.288749849529972e-06,
                2.2603251062450327e-06,
                2.260323758987159e-06,
                8.939697370069891e-06,
                2.902312331170226e-06,
                1.2098659719788098e-06,
                1.7603427936335396e-06
            ],
            [
                1.2098652508424818e-06,
                0.9999984465018776,
                0.9999972735287593,
                1.209865827752005e-06,
                6.475945666063607e-07,
                8.315279285370317e-07,
                2.2603248367949354e-06,
                3.2887502415767434e-06,
                9.422442569334097e-07,
                2.2603242978943238e-06
            ],
            [
                3.9278629391427843e-07,
                6.475945666063607e-07,
                3.05902336324494e-07,
                2.9023119851899796e-06,
                9.422444815814404e-07,
                1.3709575337159875e-06,
                2.2603248367949354e-06,
                5.043474683240344e-07,
                5.043475284468537e-07,
                1.5534983101644536e-06
            ],
            [
                0.9999916019280048,
                0.9998911030535255,
                0.9999981261250666,
                0.999998629042958,
                0.9999995262094423,
                0.999997438717794,
                0.0009110512479652931,
                0.9999930377446,
                3.7266397283908927e-06,
                6.144175334468545e-06
            ],
            [
                2.10243290909724e-07,
                5.715006514176113e-07,
                4.4508494582405734e-07,
                5.715005151606823e-07,
                8.315278294114555e-07,
                1.2098659719788098e-06,
                2.2603251062450327e-06,
                7.338207180898968e-07,
                2.2603253756956754e-06,
                1.2098653950692178e-06
            ],
            [
                2.1024341622426268e-07,
                1.275190884913241e-07,
                1.6373770576776313e-07,
                2.1024331597262577e-07,
                1.275190884913241e-07,
                1.1253514863968147e-07,
                9.931189774187203e-08,
                1.4449800373065699e-07,
                1.1253517547010071e-07,
                1.4449805540740185e-07
            ],
            [
                NaN,
                0.9999925887210608,
                2.9023112932296107e-06,
                6.144176799334096e-06,
                4.222834954801051e-06,
                3.2887502415767434e-06,
                0.999991601927007,
                1.3709567165617364e-06,
                0.9999967112513449,
                5.715002426486762e-07
            ],
            [
                1.8925150497435443e-05,
                5.422221555296344e-06,
                5.144221980055201e-05,
                3.726637951367137e-06,
                3.1201926253802263e-05,
                5.715005832886879e-07,
                0.9999516743622557,
                8.939695238536645e-06,
                1.6701419854156377e-05,
                7.889266347636241e-06
            ],
            [
                5.422219616265831e-06,
                0.9999964991468467,
                0.9999986290431226,
                0.9999687980925226,
                0.9999984465024336,
                NaN,
                9.610239210944684e-05,
                NaN,
                8.481106162154104e-05,
                0.9999974387180995
            ],
            [
                1.0677029973219343e-06,
                5.04347287955046e-07,
                1.5534973842076057e-06,
                3.4663266243308805e-07,
                8.315280276626197e-07,
                2.260323758987159e-06,
                4.2228339479858295e-06,
                4.2228339479858295e-06,
                1.3709573702856596e-06,
                6.475945666063607e-07
            ],
            [
                1.2751902768612997e-07,
                1.1253524254650944e-07,
                1.6373768624837685e-07,
                1.4449795205429202e-07,
                3.466326624336003e-07,
                9.931198061405701e-08,
                1.6373770576776313e-07,
                1.2751905808881762e-07,
                5.04347528446051e-07,
                2.6995774527718623e-07
            ],
            [
                3.466326624336003e-07,
                5.043474683240344e-07,
                1.5534973842076057e-06,
                5.71500515161527e-07,
                7.338207180898968e-07,
                4.4508515805735777e-07,
                1.209865827752005e-06,
                2.699577452775239e-07,
                4.450852111155216e-07,
                4.785094494811783e-06
            ],
            [
                1.5534975693979422e-06,
                3.7266379514061143e-06,
                4.222834451403972e-06,
                4.222833948008874e-06,
                2.9023119851899796e-06,
                1.5534979397829198e-06,
                7.889264466868659e-06,
                9.422445939054222e-07,
                2.2603245673443566e-06,
                1.7603440527334603e-06
            ],
            [
                1.5534975693979422e-06,
                1.2098653950692178e-06,
                1.0677029973219343e-06,
                5.422217677152175e-06,
                7.338209805240734e-07,
                4.450848927658745e-07,
                3.288747889284851e-06,
                9.422442569315887e-07,
                6.475945666063607e-07,
                4.4508515805735777e-07
            ],
            [
                2.2603234895372223e-06,
                1.9947292459406333e-06,
                7.338210680032098e-07,
                5.715005832895975e-07,
                5.043474683240344e-07,
                8.315279285370317e-07,
                2.5612819054133693e-06,
                1.9947299593078385e-06,
                7.338209805240734e-07,
                1.760342793638743e-06
            ],
            [
                1.2751908849167202e-07,
                6.962258739796719e-06,
                3.059022998576899e-07,
                3.05902263391829e-07,
                8.315284241665078e-07,
                3.927863407379485e-07,
                1.4449805540740185e-07,
                1.2098661162056318e-06,
                6.475946438055299e-07,
                1.3709570434250617e-06
            ],
            [
                3.466325384678894e-07,
                1.994729483729522e-06,
                3.7266383956509585e-06,
                7.889259764517575e-06,
                2.561283126728994e-06,
                7.338212429594283e-07,
                6.1441767993788005e-06,
                9.422443692574719e-07,
                8.939699501416646e-06,
                1.5534977545886537e-06
            ],
            [
                1.1253525596174225e-07,
                2.382369667929001e-07,
                8.764245361752286e-08,
                9.931189774187203e-08,
                1.1253513522447425e-07,
                4.4508499888275247e-07,
                1.6373776432509826e-07,
                1.1253509497883659e-07,
                6.825602910433871e-08,
                1.1253525596174225e-07
            ],
            [
                5.043475885696228e-07,
                3.9278605979534166e-07,
                6.47595107001401e-07,
                5.715002426486762e-07,
                3.9278629391427843e-07,
                2.699577774589574e-07,
                5.422217030781934e-06,
                6.475947210046347e-07,
                5.715002426486762e-07,
                1.067703124601679e-06
            ],
            [
                3.7266379514061143e-06,
                1.7603425837903113e-06,
                7.338207180898968e-07,
                1.5534977545886537e-06,
                2.1024339116168358e-07,
                5.043475885696228e-07,
                7.338209805240734e-07,
                1.0677027427624903e-06,
                7.338209805240734e-07,
                1.0677027427624903e-06
            ],
            [
                2.2603245673443566e-06,
                2.561283126728994e-06,
                3.927862939126708e-07,
                1.5534984953552536e-06,
                1.209865539298447e-06,
                1.994729483729522e-06,
                2.9023112932296107e-06,
                3.2887494574832472e-06,
                1.0677026154827912e-06,
                2.2603248367949354e-06
            ],
            [
                1.2098661162056318e-06,
                6.475947210046347e-07,
                3.9278610661902853e-07,
                2.5612834320470717e-06,
                1.855391239544352e-07,
                3.4663249714612693e-07,
                1.5534979397790343e-06,
                2.382369667929001e-07,
                7.338213304363436e-07,
                6.475947210031623e-07
            ],
            [
                5.422217677152175e-06,
                3.4663249714612693e-07,
                1.760343213335281e-06,
                4.450852641737424e-07,
                1.5534973842076057e-06,
                3.927863875616689e-07,
                1.7603425837903113e-06,
                9.422443692574719e-07,
                6.475947982037486e-07,
                3.927863875616689e-07
            ],
            [
                6.47594952603035e-07,
                6.825600469412533e-08,
                5.3157837044597743e-08,
                1.4449795205472734e-07,
                6.825602910433871e-08,
                5.043475885696228e-07,
                4.691162683297406e-08,
                2.8453354063983556e-08,
                1.4449796928021588e-07,
                1.4449807263312446e-07
            ],
            [
                3.288749849529972e-06,
                1.7603425837903113e-06,
                NaN,
                1.5534975693979422e-06,
                5.715002426486762e-07,
                1.0677027427624903e-06,
                6.475945666063607e-07,
                NaN,
                1.5534981249736758e-06,
                6.47594952603035e-07
            ],
            [
                3.466326624336003e-07,
                6.47595107001401e-07,
                NaN,
                4.4508499888275247e-07,
                1.5534981249736758e-06,
                NaN,
                NaN,
                5.715005832895975e-07,
                5.043475885696228e-07,
                7.338212429594283e-07
            ],
            [
                0.9999980052695705,
                0.9999934595612343,
                0.9999985406232637,
                0.99999926617867,
                0.9999986290431208,
                0.9999981261241744,
                0.9999981261241758,
                0.9999485578051915,
                0.9999989969856747,
                0.9999981261250686
            ],
            [
                1.0677026154806063e-06,
                7.484626297687326e-05,
                7.338210680021253e-07,
                7.338210680021253e-07,
                4.222833444590791e-06,
                1.0129989772532511e-05,
                2.90231094723893e-06,
                6.475949526020042e-07,
                1.0677029973192638e-06,
                1.0677027427600627e-06
            ],
            [
                1.2098659719788098e-06,
                1.0129988565084915e-05,
                8.939698435657833e-06,
                2.5612819054028872e-06,
                6.144173137126169e-06,
                5.422218323487975e-06,
                1.209866260432471e-06,
                3.7266401726173067e-06,
                4.53978632394714e-05,
                2.2603237589676295e-06
            ],
            [
                1.067703124601679e-06,
                1.209865539295696e-06,
                4.4508526417298334e-07,
                8.315277302857965e-07,
                1.209866260432471e-06,
                3.4663253846718004e-07,
                4.785092783519724e-06,
                1.0677026154806063e-06,
                3.9278610661902853e-07,
                6.475950298011458e-07
            ],
            [
                0.9999992188515768,
                0.9999861539888709,
                0.9999945777797462,
                0.9999892166890899,
                0.9999996072136126,
                0.9999987901341734,
                1.4449803818215767e-07,
                0.9999861539888636,
                2.1444945858485726e-05,
                4.222834954801051e-06
            ],
            [
                7.33821330437595e-07,
                4.4508515805735777e-07,
                7.338212429594283e-07,
                NaN,
                1.760342793638743e-06,
                1.994729483729522e-06,
                7.33821330437595e-07,
                5.043472278322555e-07,
                6.47595107001401e-07,
                3.288749849529972e-06
            ],
            [
                0.9999997761970247,
                0.9999832985761973,
                1.147877359957198e-05,
                0.9996646497383156,
                0.9999975938965165,
                9.422443692574719e-07,
                0.999999057755182,
                6.475950298021765e-07,
                6.144176066943187e-06,
                2.9023116392097746e-06
            ],
            [
                1.994729483729522e-06,
                3.2887502415767434e-06,
                6.962259569750576e-06,
                5.422220909041528e-06,
                0.00010889690936027806,
                2.2603245673443566e-06,
                1.0677032518814388e-06,
                4.22283545819819e-06,
                3.288747889284851e-06,
                6.144173137170873e-06
            ],
            [
                3.288748281329893e-06,
                3.059022998581767e-07,
                1.7603440527286572e-06,
                8.315283250394546e-07,
                8.315282259138311e-07,
                8.939698435657833e-06,
                7.338210680021253e-07,
                1.067702870039777e-06,
                3.288748281329893e-06,
                5.04347528446051e-07
            ],
            [
                5.043475885696228e-07,
                2.1024334103581732e-07,
                5.043475885696228e-07,
                2.2603242978943238e-06,
                5.043472278322555e-07,
                3.9278620026686556e-07,
                2.3823690999290963e-07,
                1.4449800373118268e-07,
                1.1253514863968147e-07,
                6.47595107001401e-07
            ],
            [
                0.9999988634361555,
                1.994729483729522e-06,
                1.012998977264307e-05,
                2.9023116392097746e-06,
                1.994729483729522e-06,
                1.994729483729522e-06,
                2.902312331170226e-06,
                0.999891103091973,
                2.5612834320563895e-06,
                7.338207180898968e-07
            ],
            [
                1.0677027427624903e-06,
                2.382370235933104e-07,
                3.726639284144195e-06,
                5.043475885696228e-07,
                8.315280276626197e-07,
                1.8553907971855875e-07,
                8.315282259138311e-07,
                8.315277302857965e-07,
                5.715006514176113e-07,
                3.05902190458764e-07
            ],
            [
                2.3823682479292225e-07,
                NaN,
                5.715005832895975e-07,
                9.422450432030903e-07,
                4.222834954801051e-06,
                1.9947299593078385e-06,
                3.466325384682834e-07,
                1.5534975693979422e-06,
                9.422445939054222e-07,
                5.715006514176113e-07
            ],
            [
                6.475947982037486e-07,
                4.222833444590791e-06,
                1.3709570434219446e-06,
                1.370957860576702e-06,
                3.5356238069902345e-05,
                1.012999097997104e-05,
                1.2098656835224664e-06,
                2.699577774585891e-07,
                6.475949526020042e-07,
                7.338210680021253e-07
            ]
        ]
    },
    {
        "q_id": "10118_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            41,
            44,
            45,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            77,
            79,
            80,
            81,
            83,
            84,
            86,
            87,
            88,
            89,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3709573702822306e-06,
                3.466327450765785e-07,
                2.1024341622426268e-07,
                2.699576809143613e-07,
                6.475945666051092e-07,
                1.5534973842076057e-06,
                5.04347468323289e-07,
                1.6373772528704005e-07,
                1.444980209564556e-07,
                6.475950298011458e-07
            ],
            [
                2.6995790618350237e-07,
                1.8553910183607374e-07,
                2.382369951932796e-07,
                2.1024334103581732e-07,
                3.927862002663297e-07,
                5.043472879525233e-07,
                4.4508494582314646e-07,
                3.05902263391829e-07,
                3.466325797896173e-07,
                2.3823696679327928e-07
            ],
            [
                NaN,
                5.422218969895357e-06,
                NaN,
                NaN,
                9.422444815814404e-07,
                1.3709573702856596e-06,
                4.450852641737424e-07,
                NaN,
                1.5534973842076057e-06,
                1.5534979397829198e-06
            ],
            [
                1.8925157265710765e-05,
                5.043476486915964e-07,
                5.422219616228845e-06,
                4.450852111155216e-07,
                9.422448185478557e-07,
                6.475947210031623e-07,
                1.7603438428800754e-06,
                9.422442569315887e-07,
                2.3823688159291947e-07,
                1.9947297215125433e-06
            ],
            [
                5.422219616265831e-06,
                2.9023112932177327e-06,
                5.715007195447234e-07,
                1.7603440527286572e-06,
                2.3823688159291947e-07,
                1.5534983101602148e-06,
                8.939700567094277e-06,
                1.067703124601679e-06,
                1.5534984953552536e-06,
                5.715003107755449e-07
            ],
            [
                9.422444815814404e-07,
                4.4508515805735777e-07,
                3.4663266243308805e-07,
                7.338212429582604e-07,
                8.315279285351409e-07,
                5.715005832886879e-07,
                1.209865539298447e-06,
                5.715004470326849e-07,
                2.561283126728994e-06,
                NaN
            ],
            [
                0.9999984465015058,
                3.9278634073732336e-07,
                4.785096206076165e-06,
                3.4663249714451116e-07,
                5.715003789046955e-07,
                3.466327037539638e-07,
                2.1024336609843824e-07,
                1.994729721518893e-06,
                3.7266397283908927e-06,
                1.5534975693979422e-06
            ],
            [
                9.422445939002803e-07,
                1.9947301970972664e-06,
                2.561281600086738e-06,
                1.0677027427569065e-06,
                1.3709575337159875e-06,
                3.927860597945825e-07,
                8.939693107288474e-06,
                5.043472879540142e-07,
                2.1024344128584085e-07,
                4.4508494582405734e-07
            ],
            [
                8.315284241650899e-07,
                1.5534973842076057e-06,
                6.475949526020042e-07,
                1.994729008145876e-06,
                9.422447062294175e-07,
                2.90231094723893e-06,
                5.715005832895975e-07,
                9.422450432014836e-07,
                2.699578740032504e-07,
                1.9947292459347367e-06
            ],
            [
                8.939693107288474e-06,
                6.475950298021765e-07,
                1.7603427936335396e-06,
                8.315282259138311e-07,
                3.05902336324494e-07,
                NaN,
                5.043476486915964e-07,
                1.3709573702822306e-06,
                5.043472879540142e-07,
                8.315283250394546e-07
            ],
            [
                1.0677028700422047e-06,
                1.7603434231833873e-06,
                2.902312331170226e-06,
                1.7603425837903113e-06,
                NaN,
                1.012998977264307e-05,
                4.450852111148132e-07,
                1.3709575337159875e-06,
                1.209865539295696e-06,
                7.338207180898968e-07
            ],
            [
                1.9947292459347367e-06,
                8.315281267834927e-07,
                1.3709576971425944e-06,
                1.5534981249697903e-06,
                4.5397874057886045e-05,
                0.9999962733598354,
                8.481103129578775e-05,
                1.2098656835224664e-06,
                9.422448185534261e-07,
                4.222834954778007e-06
            ],
            [
                9.422450431989127e-07,
                5.043475885696228e-07,
                1.4738983729535602e-05,
                2.9023116392097746e-06,
                2.902313023130843e-06,
                3.9278605979534166e-07,
                1.3709575337159875e-06,
                3.535624228030111e-05,
                1.3709575337016483e-06,
                2.9023119851781017e-06
            ],
            [
                2.5612828213934817e-06,
                5.422220909009474e-06,
                7.338209805240734e-07,
                5.715004470313855e-07,
                8.93969950132721e-06,
                1.7603440527286572e-06,
                5.04347468323289e-07,
                2.5612828213818346e-06,
                1.9947297215125433e-06,
                1.3709576971425944e-06
            ],
            [
                3.466326624336003e-07,
                4.4508515805735777e-07,
                2.561281294760143e-06,
                3.4663262111182307e-07,
                7.338209805240734e-07,
                1.3709575337159875e-06,
                7.338207180898968e-07,
                4.785095065232451e-06,
                4.785096776499213e-06,
                1.5534973842076057e-06
            ],
            [
                2.9023119851899796e-06,
                6.962255419931625e-06,
                5.715007195431641e-07,
                3.466327037539638e-07,
                2.902313369111213e-06,
                3.726639284144195e-06,
                8.939695238634211e-06,
                7.338207180898968e-07,
                1.9947297215043796e-06,
                1.209865827752005e-06
            ],
            [
                3.535625071730638e-05,
                0.9998601779781217,
                NaN,
                5.71500515159253e-07,
                0.9999967112521171,
                0.9999962733620538,
                1.3709575337159875e-06,
                1.3709575337078829e-06,
                1.2098659719757836e-06,
                0.999999581881327
            ],
            [
                0.999999352405048,
                2.7535694385633984e-05,
                4.2228319344021954e-06,
                2.75356812556058e-05,
                6.962256249885085e-06,
                8.939695238634211e-06,
                1.012999581057419e-05,
                0.9999967112501555,
                6.962253760024999e-06,
                4.006370174664993e-05
            ],
            [
                7.338207180864763e-07,
                3.466325797888292e-07,
                8.315279285351409e-07,
                9.422445939032799e-07,
                9.422448185510695e-07,
                7.338211554783522e-07,
                1.5534971990126997e-06,
                2.382369383923073e-07,
                1.3709575337159875e-06,
                3.9278634073732336e-07
            ],
            [
                1.3709570434250617e-06,
                NaN,
                1.5534975693979422e-06,
                2.561283126728994e-06,
                3.7266410611465547e-06,
                NaN,
                NaN,
                1.994729483729522e-06,
                2.1444943302650045e-05,
                1.3709575337159875e-06
            ],
            [
                1.067703124601679e-06,
                2.2603245673443566e-06,
                2.69957906184239e-07,
                6.9622537599680095e-06,
                1.9947292459347367e-06,
                2.902312331170226e-06,
                8.315280276626197e-07,
                4.450852111148132e-07,
                1.5534975693979422e-06,
                3.927862002663297e-07
            ],
            [
                1.7603438428848787e-06,
                NaN,
                1.209865827752005e-06,
                4.7850933539684755e-06,
                2.9023112932296107e-06,
                2.561283126728994e-06,
                8.315277302857965e-07,
                1.2098653950716937e-06,
                1.2098659719788098e-06,
                2.5612834320563895e-06
            ],
            [
                1.5534971990169383e-06,
                9.422450432014836e-07,
                9.422450432014836e-07,
                5.715006514176113e-07,
                7.338208055680009e-07,
                2.2603251062450327e-06,
                8.315281267834927e-07,
                6.475947210031623e-07,
                6.475945666063607e-07,
                NaN
            ],
            [
                NaN,
                7.338209805200689e-07,
                3.9278629391427843e-07,
                1.2098653950656417e-06,
                1.7603430034867993e-06,
                3.059022998558814e-07,
                1.7603438428800754e-06,
                1.5534983101602148e-06,
                4.450852111148132e-07,
                4.450849458218309e-07
            ],
            [
                3.05902263391829e-07,
                2.102434162245973e-07,
                1.012998977264307e-05,
                1.6373762769138607e-07,
                9.422442569334097e-07,
                2.2603245673443566e-06,
                2.10243290909724e-07,
                4.4508499888219586e-07,
                1.1253513522447425e-07,
                2.3823702359290413e-07
            ],
            [
                2.5612834320470717e-06,
                2.2603240284371276e-06,
                2.5612828213934817e-06,
                5.043476486915964e-07,
                7.338212429582604e-07,
                2.260324836776948e-06,
                1.5534983101602148e-06,
                1.760343003481596e-06,
                9.422442569315887e-07,
                3.7266397283908927e-06
            ],
            [
                5.043475284468537e-07,
                9.422450432030903e-07,
                0.9999972735307054,
                4.4508515805735777e-07,
                8.315278294072958e-07,
                3.059022998581767e-07,
                1.5534984953552536e-06,
                5.043472278322555e-07,
                4.450852111155216e-07,
                8.315284241665078e-07
            ],
            [
                3.059022269250683e-07,
                2.382369951932796e-07,
                NaN,
                NaN,
                3.4663262111182307e-07,
                2.102434162245973e-07,
                1.760342793638743e-06,
                2.382368531929327e-07,
                3.9278615344178325e-07,
                3.466327037553825e-07
            ],
            [
                2.561281294760143e-06,
                0.9999995818812273,
                0.9999997617629766,
                1.4449805540700758e-07,
                0.9999995549147361,
                1.8553903548231313e-07,
                NaN,
                1.5534979397829198e-06,
                6.962257079889302e-06,
                0.9999991148429646
            ],
            [
                8.315281267882195e-07,
                NaN,
                0.9999985406230839,
                NaN,
                NaN,
                NaN,
                NaN,
                6.475945666063607e-07,
                6.962257909842961e-06,
                1.3709572068553509e-06
            ],
            [
                5.043476486915964e-07,
                5.715005151606823e-07,
                2.6995774527718623e-07,
                6.475945666051092e-07,
                8.315279285370317e-07,
                8.315284241560147e-07,
                3.927863875616689e-07,
                5.715005832886879e-07,
                4.450848927650143e-07,
                3.927862002663297e-07
            ],
            [
                3.4663249714612693e-07,
                1.760343213335281e-06,
                6.475947982037486e-07,
                1.9947301970972664e-06,
                8.315282259138311e-07,
                2.5612828213934817e-06,
                9.422447062294175e-07,
                3.2887506336086064e-06,
                4.785095635655362e-06,
                1.7603438428800754e-06
            ],
            [
                4.450849988811838e-07,
                6.47595107001401e-07,
                1.6373762769138607e-07,
                2.1024341622426268e-07,
                5.715003789046955e-07,
                1.2751899728286965e-07,
                3.4663249714612693e-07,
                5.715003107767143e-07,
                4.4508510499849186e-07,
                5.043473480777865e-07
            ],
            [
                9.422450432014836e-07,
                1.8553905760062447e-07,
                1.370957860576702e-06,
                4.785094494811783e-06,
                1.5534983101602148e-06,
                8.315284241650899e-07,
                3.9278605979534166e-07,
                1.7603430034867993e-06,
                5.715005832886879e-07,
                4.4508494582405734e-07
            ],
            [
                8.315277302857965e-07,
                2.902312331170226e-06,
                1.0677032518814388e-06,
                2.6995771309523475e-07,
                3.72663883989755e-06,
                9.422450432014836e-07,
                3.059022998576899e-07,
                2.561281294760143e-06,
                1.9947292459347367e-06,
                2.3823702359290413e-07
            ],
            [
                1.3709576971463352e-06,
                4.785093924389007e-06,
                4.785094494811783e-06,
                3.466326624336003e-07,
                6.962257079889302e-06,
                1.5534971990169383e-06,
                NaN,
                4.222834451403972e-06,
                NaN,
                4.2228319344021954e-06
            ],
            [
                2.2603240284371276e-06,
                1.2098653950656417e-06,
                6.475951069985296e-07,
                4.450851580555361e-07,
                5.043475885674441e-07,
                NaN,
                2.6995771309523475e-07,
                7.338212429594283e-07,
                5.715006514151423e-07,
                9.422442569315887e-07
            ],
            [
                7.338212429582604e-07,
                NaN,
                6.475951069985296e-07,
                1.3709572068522336e-06,
                8.315284241650899e-07,
                9.422442569315887e-07,
                7.338210680021253e-07,
                1.3709567165579959e-06,
                1.7603425837903113e-06,
                1.5534984953510149e-06
            ],
            [
                1.4449802095609418e-07,
                5.04347348075149e-07,
                1.8553905760024476e-07,
                3.466325797896173e-07,
                1.444979692797559e-07,
                3.059021539909339e-07,
                7.338213304316717e-07,
                8.764249540862797e-08,
                2.382369667929001e-07,
                1.637377448057981e-07
            ],
            [
                3.927862002663297e-07,
                3.927862002663297e-07,
                1.5534984953552536e-06,
                8.315277302857965e-07,
                7.338208055664991e-07,
                3.059022998576899e-07,
                1.5534971990169383e-06,
                1.760342793638743e-06,
                2.902312331170226e-06,
                NaN
            ],
            [
                8.315279285370317e-07,
                4.222833948008874e-06,
                1.892514373029853e-05,
                2.2603253756956754e-06,
                4.006370652227855e-05,
                8.93969843573914e-06,
                6.1441767993788005e-06,
                1.1478766757853845e-05,
                3.7266379514061143e-06,
                5.422220909041528e-06
            ],
            [
                4.785096776468749e-06,
                4.450852111148132e-07,
                2.561281294760143e-06,
                2.6995774527718623e-07,
                2.382370235933104e-07,
                3.059022998576899e-07,
                5.043474081993875e-07,
                2.6995790618350237e-07,
                1.5534975693869924e-06,
                1.9947304348703948e-06
            ],
            [
                0.9999993524053566,
                0.9999967112493686,
                0.9999994956527124,
                0.9999995262092728,
                0.9999955048200323,
                0.9999996072136127,
                5.043472879540142e-07,
                0.9999995549148951,
                0.9999995262094422,
                0.9999996533672139
            ],
            [
                7.889264466868659e-06,
                0.9999992661786699,
                5.715003107767143e-07,
                3.0590219045914655e-07,
                5.422217677152175e-06,
                1.0677032518814388e-06,
                6.475947210046347e-07,
                5.4222183235249605e-06,
                3.05902263391829e-07,
                4.4508510499849186e-07
            ],
            [
                0.9999989322970035,
                0.9999983463108111,
                0.9999995818814267,
                7.889266347786918e-06,
                0.9999988634357492,
                0.9999646437411454,
                0.9999985406241286,
                2.1444948415296896e-05,
                0.9999975938982374,
                0.9999988634358837
            ],
            [
                4.4508510499849186e-07,
                1.5534973842076057e-06,
                9.422443692574719e-07,
                8.315278294114555e-07,
                2.5612819054133693e-06,
                NaN,
                1.0677027427600627e-06,
                6.1441746020359e-06,
                5.04347287955046e-07,
                3.535624650279074e-05
            ],
            [
                1.473898900066424e-05,
                3.059021904571643e-07,
                4.785093924389007e-06,
                2.3823690999160957e-07,
                5.715002426486762e-07,
                2.2603245673443566e-06,
                0.999996910505186,
                3.05902336324494e-07,
                0.9999995262092163,
                1.0677032518785256e-06
            ],
            [
                5.422218323487975e-06,
                3.1201922535494165e-05,
                6.962259569630266e-06,
                3.120192625482384e-05,
                5.715006514151423e-07,
                7.889266347636241e-06,
                7.889265407327733e-06,
                1.370957860576702e-06,
                1.9947299593014888e-06,
                1.1478765389368729e-05
            ],
            [
                2.561282516066741e-06,
                9.422448185510695e-07,
                8.315278294072958e-07,
                1.7603427936263351e-06,
                1.7603430034867993e-06,
                6.1441767993788005e-06,
                1.209865539274514e-06,
                5.043472879540142e-07,
                5.422217030747413e-06,
                3.927863875584984e-07
            ],
            [
                6.144177531767002e-06,
                6.475945666051092e-07,
                2.2603248367949354e-06,
                4.450848927658745e-07,
                7.889265407327733e-06,
                7.338208930460318e-07,
                1.5534975693979422e-06,
                2.4300243631890864e-05,
                4.785094494811783e-06,
                1.3007130015677909e-05
            ],
            [
                0.9999988634362905,
                2.4300249425247723e-05,
                0.9999942280792926,
                0.9999974387180995,
                0.9999993524050478,
                0.9999981261241728,
                0.9999934595627888,
                2.9023109472244114e-06,
                0.9999960330136195,
                0.9999987901343178
            ],
            [
                1.5534981249697903e-06,
                1.7603425837855082e-06,
                1.3709573702822306e-06,
                9.422449308774482e-07,
                1.209866260432471e-06,
                1.3709576971379186e-06,
                NaN,
                NaN,
                5.422219616228845e-06,
                1.9947294837154625e-06
            ],
            [
                1.300713156582635e-05,
                4.222833947932061e-06,
                4.222834954778007e-06,
                NaN,
                6.962256249885085e-06,
                3.288748281329893e-06,
                1.7603425837606927e-06,
                1.2098655392871682e-06,
                2.9023119850527192e-06,
                7.889260704531226e-06
            ],
            [
                3.2887502415767434e-06,
                3.288747889284851e-06,
                3.535625493182252e-05,
                2.902312331170226e-06,
                3.4663249714451116e-07,
                1.5534975693979422e-06,
                1.5534981249574276e-06,
                1.994729483723626e-06,
                2.2603245673443566e-06,
                4.785096776468749e-06
            ],
            [
                3.288748281329893e-06,
                9.422448185534261e-07,
                1.3709572068522336e-06,
                8.315284241650899e-07,
                1.3709567165617364e-06,
                5.715004470326849e-07,
                3.726637951387472e-06,
                8.315277302841894e-07,
                3.288750241561788e-06,
                5.04347468323289e-07
            ],
            [
                2.5612819054133693e-06,
                1.553498495338299e-06,
                1.5534975693979422e-06,
                7.889265407327733e-06,
                3.7266401726359486e-06,
                7.338213304363436e-07,
                2.5612819054028872e-06,
                2.5612828213934817e-06,
                1.5534971990126997e-06,
                NaN
            ],
            [
                1.9947297215125433e-06,
                4.222833444590791e-06,
                7.889265407255982e-06,
                4.2228339479858295e-06,
                3.72663883989755e-06,
                1.0677027427600627e-06,
                3.7266410611296085e-06,
                8.315281267882195e-07,
                4.2228339479858295e-06,
                1.7603430034655858e-06
            ],
            [
                4.22283545819819e-06,
                8.939696304311336e-06,
                3.535626757653154e-05,
                6.144177531811707e-06,
                5.422217030747413e-06,
                2.4300249425247723e-05,
                7.889260704968913e-06,
                0.00013982210754460409,
                4.222833444590791e-06,
                1.5534975693979422e-06
            ],
            [
                1.0677026154774503e-06,
                1.3709567165530083e-06,
                1.2098659719716573e-06,
                4.2228324377740105e-06,
                4.222835458175145e-06,
                7.338209805224048e-07,
                2.1024334103505245e-07,
                7.338209805200689e-07,
                8.315278294072958e-07,
                4.222834954778007e-06
            ],
            [
                5.043473480766399e-07,
                4.222831934379152e-06,
                2.69957906184239e-07,
                6.475947982002148e-07,
                9.422450431989127e-07,
                7.338209805240734e-07,
                1.3709570434178922e-06,
                8.31528424162821e-07,
                3.927860597945825e-07,
                1.0677027427525368e-06
            ],
            [
                0.9999972735300576,
                0.99999759389795,
                0.9999982396569985,
                0.9999977396754366,
                0.9999967112497639,
                0.9999861540004431,
                0.9999982396569999,
                0.9999984465028027,
                0.9999822214482692,
                0.9999990577550704
            ],
            [
                2.1444940746307572e-05,
                1.994729721518893e-06,
                4.4508510499849186e-07,
                2.9023119851899796e-06,
                9.422442569334097e-07,
                NaN,
                NaN,
                NaN,
                6.962257079889302e-06,
                3.72663883989755e-06
            ],
            [
                7.338207180801359e-07,
                3.059021904559123e-07,
                3.4663262110803996e-07,
                9.422450431860582e-07,
                8.315284241560147e-07,
                2.69957906184239e-07,
                1.7603438428740716e-06,
                3.059023363221292e-07,
                5.715003788993679e-07,
                3.2887482813149375e-06
            ],
            [
                0.9999990577550696,
                1.2098659719788098e-06,
                2.9023116392097746e-06,
                0.999999607213753,
                2.2603242978871282e-06,
                9.422443692555439e-07,
                0.9999997300421262,
                0.9999982396569974,
                3.9278605979534166e-07,
                9.422443692555439e-07
            ],
            [
                3.2887502415767434e-06,
                4.785096776499213e-06,
                NaN,
                4.22283545819819e-06,
                1.0677027427624903e-06,
                6.475949525981759e-07,
                4.785095635624897e-06,
                5.715007195447234e-07,
                6.475950298011458e-07,
                1.5534975693933505e-06
            ],
            [
                2.699578096393206e-07,
                4.450851580555361e-07,
                8.315281267882195e-07,
                1.3709576971425944e-06,
                1.0677027427600627e-06,
                NaN,
                3.927862002663297e-07,
                2.902312331170226e-06,
                1.3709567165579959e-06,
                7.338212429537553e-07
            ],
            [
                1.760344052714248e-06,
                5.422218969818919e-06,
                4.222831934321543e-06,
                2.561283432035425e-06,
                1.7603438428740716e-06,
                4.78509278348926e-06,
                4.785095635624897e-06,
                1.99472900813862e-06,
                1.5534984953453635e-06,
                1.7603434231705793e-06
            ],
            [
                1.2098652508424818e-06,
                1.0677032518814388e-06,
                1.2098662604291696e-06,
                1.3709568799919866e-06,
                4.006370174664993e-05,
                9.422448185510695e-07,
                1.0677032518814388e-06,
                1.2098652508424818e-06,
                1.994730672675753e-06,
                1.209865539295696e-06
            ],
            [
                0.9999997300421906,
                0.9999991684718741,
                3.7266410611296085e-06,
                1.2098659719757836e-06,
                2.561281600086738e-06,
                3.535625493182252e-05,
                NaN,
                6.475947210031623e-07,
                3.9278610661902853e-07,
                0.999998712104939
            ],
            [
                2.699576809143613e-07,
                4.4508510499849186e-07,
                3.927862002641863e-07,
                5.04347468323289e-07,
                4.450848927658745e-07,
                3.059021175261338e-07,
                8.315281267882195e-07,
                4.4508494582314646e-07,
                NaN,
                7.338208055664991e-07
            ],
            [
                3.0590215399183813e-07,
                7.338211554813555e-07,
                3.0590219045914655e-07,
                5.043474081993875e-07,
                8.315283250371857e-07,
                3.927860597945825e-07,
                3.927863407379485e-07,
                4.450848927637999e-07,
                1.209865827752005e-06,
                6.475946438042047e-07
            ],
            [
                4.22283545819819e-06,
                5.043473480777865e-07,
                NaN,
                9.422444815814404e-07,
                3.9278629391427843e-07,
                4.785095635655362e-06,
                1.209866260432471e-06,
                2.2603242978871282e-06,
                1.2098661162056318e-06,
                9.422449308774482e-07
            ],
            [
                6.47595107001401e-07,
                3.059022998581767e-07,
                3.9278629391427843e-07,
                3.9278620026686556e-07,
                3.4663274507713016e-07,
                NaN,
                2.902312677150514e-06,
                5.043475885696228e-07,
                2.2603245673443566e-06,
                6.144176066943187e-06
            ],
            [
                3.46632497145457e-07,
                1.0677024881980089e-06,
                4.4508515805735777e-07,
                2.902312677137316e-06,
                8.315284241650899e-07,
                3.2887506336086064e-06,
                6.47595107001401e-07,
                1.760343213335281e-06,
                1.994730672675753e-06,
                1.7603434231833873e-06
            ],
            [
                2.2603245673443566e-06,
                9.422449308748773e-07,
                3.7266410611296085e-06,
                5.715002426475718e-07,
                1.2098656835224664e-06,
                NaN,
                1.994729721518893e-06,
                1.209865539295696e-06,
                5.043472278322555e-07,
                1.2098656835224664e-06
            ],
            [
                7.889261645269683e-06,
                9.422442569290178e-07,
                5.422220262599396e-06,
                3.726639728348526e-06,
                6.144173137126169e-06,
                2.902313023101807e-06,
                3.7266379513434106e-06,
                2.902312677137316e-06,
                3.2887486733420804e-06,
                2.430025232128576e-05
            ],
            [
                7.338210680021253e-07,
                1.6373774480605869e-07,
                3.059021175261338e-07,
                1.5534971990169383e-06,
                5.715005832886879e-07,
                8.315281267882195e-07,
                7.338208930460318e-07,
                1.012998977264307e-05,
                1.209866260432471e-06,
                5.715005151606823e-07
            ],
            [
                NaN,
                NaN,
                2.2603253756956754e-06,
                1.0129988565084915e-05,
                NaN,
                0.9999989969859123,
                4.539786324145319e-05,
                0.9999986290431205,
                9.422447062294175e-07,
                6.144176066943187e-06
            ],
            [
                5.829126555256903e-05,
                NaN,
                1.3709567165617364e-06,
                2.6995768091310296e-07,
                5.71500515161527e-07,
                9.422450432014836e-07,
                NaN,
                7.338208055680009e-07,
                9.422445939054222e-07,
                3.535626336201389e-05
            ],
            [
                3.120191137762131e-05,
                6.144173137170873e-06,
                NaN,
                1.2098661162056318e-06,
                1.012999218776902e-05,
                4.785095065232451e-06,
                2.9023116392097746e-06,
                2.902312677150514e-06,
                1.760342793638743e-06,
                NaN
            ],
            [
                1.994729483729522e-06,
                0.9999974387171836,
                1.2098656835252174e-06,
                2.561281600086738e-06,
                0.9998415638432204,
                9.422443692574719e-07,
                8.315277302857965e-07,
                7.3382080556433e-07,
                2.2603242978871282e-06,
                0.9999992661791077
            ],
            [
                8.315284241597959e-07,
                2.902313023101807e-06,
                1.9947304348703948e-06,
                1.0677027427600627e-06,
                1.2098652508424818e-06,
                3.2887478892683997e-06,
                1.3709567165617364e-06,
                1.2098653950656417e-06,
                1.994729008145876e-06,
                2.260325106237323e-06
            ],
            [
                2.2603253756956754e-06,
                7.88926446679691e-06,
                0.0001233945603033627,
                2.7535694385633984e-05,
                NaN,
                NaN,
                2.9023133690637e-06,
                8.939700567094277e-06,
                7.889259764517575e-06,
                1.473898900066424e-05
            ],
            [
                9.931193325852072e-08,
                9.931193325852072e-08,
                8.315284241650899e-07,
                1.4449803818215767e-07,
                2.10243290909724e-07,
                2.1024331597288867e-07,
                1.637376862489725e-07,
                2.1024334103581732e-07,
                3.927862939126708e-07,
                1.6373766672973748e-07
            ],
            [
                9.422444815792981e-07,
                8.315281267834927e-07,
                1.8925143729575624e-05,
                6.9622587397397306e-06,
                2.902312677137316e-06,
                3.288748673360027e-06,
                1.994730197090463e-06,
                4.222834954778007e-06,
                1.3007123813382511e-05,
                5.043475885674441e-07
            ],
            [
                3.7266397283908927e-06,
                4.006367786720367e-05,
                1.7603434231777837e-06,
                8.939694172957213e-06,
                2.902312677150514e-06,
                7.889263526345123e-06,
                3.120190393794438e-05,
                NaN,
                9.422445939032799e-07,
                4.785095065232451e-06
            ],
            [
                1.3007123813382511e-05,
                NaN,
                1.0677032518814388e-06,
                5.715003107767143e-07,
                1.7603427936263351e-06,
                2.5612819054028872e-06,
                NaN,
                3.2887506335906595e-06,
                NaN,
                3.288749849529972e-06
            ],
            [
                3.0590219045914655e-07,
                7.338210680021253e-07,
                4.4508510499849186e-07,
                1.892514598627448e-05,
                6.475950298021765e-07,
                NaN,
                4.539787947559951e-05,
                5.043472278322555e-07,
                9.422448185534261e-07,
                3.1201915096836145e-05
            ],
            [
                5.043474683204221e-07,
                3.927862470899887e-07,
                3.4663262111182307e-07,
                1.3709575337159875e-06,
                8.31528325040778e-07,
                5.04347528446051e-07,
                NaN,
                3.2887502415767434e-06,
                0.9999993524052794,
                3.466327037553825e-07
            ],
            [
                1.855391018347238e-07,
                1.3709572068478697e-06,
                8.315279285351409e-07,
                5.043474081993875e-07,
                6.475945666033422e-07,
                1.2098656835136636e-06,
                1.0677028700363782e-06,
                3.4663266243111764e-07,
                6.475950297942253e-07,
                3.059021175247079e-07
            ],
            [
                9.422443692555439e-07,
                1.2098661162056318e-06,
                1.3709578605729614e-06,
                1.5534971989992774e-06,
                1.994729008105057e-06,
                1.760343633031919e-06,
                2.2603242978871282e-06,
                5.043472879540142e-07,
                3.288749065423109e-06,
                1.3709573702822306e-06
            ],
            [
                9.93120161306789e-08,
                1.6373764720990908e-07,
                1.6373762769138607e-07,
                2.699577774585891e-07,
                1.2751905808881762e-07,
                2.382370235922541e-07,
                1.1253524254650944e-07,
                9.93120161310289e-08,
                1.6373776432509826e-07,
                1.125352291309328e-07
            ],
            [
                5.043472879540142e-07,
                0.9999994631251884,
                NaN,
                0.9999995818814268,
                0.9999978766217927,
                0.9999993106386266,
                0.9999992188518564,
                0.9999993916408912,
                1.0677028700363782e-06,
                0.9999988634362903
            ],
            [
                1.370957860576702e-06,
                1.1478765389368729e-05,
                5.04347287955046e-07,
                6.144176066943187e-06,
                5.715002426486762e-07,
                0.9999996072139404,
                0.999998540623084,
                5.715006514176113e-07,
                2.753568453792444e-05,
                NaN
            ],
            [
                1.994730197090463e-06,
                2.2603234895372223e-06,
                1.5534973841895917e-06,
                NaN,
                3.2887506336086064e-06,
                3.7266397283908927e-06,
                8.939700567094277e-06,
                7.889260704968913e-06,
                6.962258739796719e-06,
                9.422450432014836e-07
            ],
            [
                3.7266383956509585e-06,
                2.382368815932174e-07,
                3.535625914749675e-05,
                2.2603251062450327e-06,
                1.3709573702822306e-06,
                2.3823696679327928e-07,
                4.22283545819819e-06,
                2.2603248367949354e-06,
                2.561281294760143e-06,
                4.4508494582405734e-07
            ],
            [
                3.927862002663297e-07,
                3.466326624336003e-07,
                2.699578740032504e-07,
                1.8553919030858602e-07,
                1.7603440527286572e-06,
                6.475946438022905e-07,
                2.1024326584702836e-07,
                3.4663274507713016e-07,
                3.466325797900508e-07,
                NaN
            ],
            [
                1.7603425837791042e-06,
                2.902310947208574e-06,
                6.144173869603344e-06,
                3.53562549305363e-05,
                1.0129994602895546e-05,
                NaN,
                1.9947297215125433e-06,
                4.785093924330255e-06,
                4.222832437798974e-06,
                7.338211554783522e-07
            ],
            [
                NaN,
                1.209865539298447e-06,
                1.5534979397829198e-06,
                3.466325797900508e-07,
                1.4449807263312446e-07,
                NaN,
                2.9023116392097746e-06,
                9.422444815814404e-07,
                5.043475885696228e-07,
                6.47595107001401e-07
            ],
            [
                7.338207180864763e-07,
                1.2098653950656417e-06,
                6.475945666051092e-07,
                5.043472879540142e-07,
                1.7603440527286572e-06,
                3.7266406168827523e-06,
                3.7266397283908927e-06,
                7.338207180864763e-07,
                1.3709576971425944e-06,
                6.475947210031623e-07
            ],
            [
                1.209865827752005e-06,
                4.450852641737424e-07,
                2.2603242978871282e-06,
                1.2098652508424818e-06,
                5.04347528446051e-07,
                2.902312677150514e-06,
                2.6995784182183607e-07,
                1.2098659719788098e-06,
                2.561282516066741e-06,
                1.3709567165617364e-06
            ],
            [
                1.0677024881980089e-06,
                1.9947304348703948e-06,
                5.422217030707961e-06,
                3.535625071730638e-05,
                8.315281267861397e-07,
                1.6701429808632785e-05,
                4.222835458175145e-06,
                1.5534979397740895e-06,
                2.260324567337161e-06,
                1.5534975693933505e-06
            ],
            [
                6.475950298021765e-07,
                3.535626336201389e-05,
                9.422442569315887e-07,
                2.902312331170226e-06,
                1.7603425837855082e-06,
                8.315283250394546e-07,
                1.2098652508424818e-06,
                6.962258739796719e-06,
                1.9947304348862686e-06,
                1.9947299593078385e-06
            ],
            [
                1.6701423836262173e-05,
                6.475946438055299e-07,
                4.22283545819819e-06,
                2.902312677150514e-06,
                5.715005832853093e-07,
                5.715003107767143e-07,
                5.715004470313855e-07,
                NaN,
                2.2603240284371276e-06,
                3.466327450765785e-07
            ],
            [
                3.9278610661902853e-07,
                NaN,
                1.209865539298447e-06,
                6.47595107001401e-07,
                3.4663262111182307e-07,
                2.382368815932174e-07,
                2.7535694385633984e-05,
                NaN,
                NaN,
                9.422443692574719e-07
            ],
            [
                0.999998446502803,
                0.9999993106391194,
                0.999999114843176,
                0.9999988634366976,
                0.9999982396561593,
                5.043476486924565e-07,
                1.6701421845361053e-05,
                0.9999981261250661,
                9.422449308748773e-07,
                4.222834954778007e-06
            ],
            [
                2.699578096393206e-07,
                2.6995771309523475e-07,
                1.6373776432509826e-07,
                1.6373764721072816e-07,
                1.5534971990169383e-06,
                2.382369667929001e-07,
                2.6995774527577444e-07,
                2.699576809143613e-07,
                3.05902190458764e-07,
                2.10243290909724e-07
            ],
            [
                1.5534975693933505e-06,
                1.5534981249697903e-06,
                2.260325106237323e-06,
                1.2098653950656417e-06,
                1.0677029973219343e-06,
                1.3709573702822306e-06,
                3.726639284144195e-06,
                5.4222183235249605e-06,
                5.422219616265831e-06,
                1.7603438428800754e-06
            ],
            [
                8.939693107288474e-06,
                4.222834451403972e-06,
                1.6701421845361053e-05,
                1.9947299593078385e-06,
                2.561283126728994e-06,
                8.315277302841894e-07,
                4.450850519403407e-07,
                6.144177531811707e-06,
                1.0129988565084915e-05,
                1.370957860576702e-06
            ],
            [
                1.994729008145876e-06,
                1.5534973842030142e-06,
                1.0129993395336818e-05,
                5.422217030747413e-06,
                3.535625914621054e-05,
                3.7266401725935817e-06,
                1.2098652508424818e-06,
                NaN,
                8.939696304311336e-06,
                2.5612812947380135e-06
            ],
            [
                1.0677033791583005e-06,
                1.2098661161982042e-06,
                2.260324567337161e-06,
                8.315281267861397e-07,
                2.9023130231176453e-06,
                5.04347348075149e-07,
                9.422449308748773e-07,
                NaN,
                1.2098652508347793e-06,
                6.475951069961737e-07
            ],
            [
                7.88926446679691e-06,
                1.7603427936335396e-06,
                1.994729483729522e-06,
                9.422443692574719e-07,
                8.315279285370317e-07,
                3.2887506336235617e-06,
                4.4508494582405734e-07,
                4.222834954801051e-06,
                4.785093924330255e-06,
                3.9278615344178325e-07
            ]
        ]
    },
    {
        "q_id": "9091_mmlu_physics",
        "cot_ids": [
            1,
            2,
            6,
            7,
            8,
            9,
            10,
            11,
            13,
            15,
            16,
            17,
            18,
            19,
            22,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            38,
            39,
            40,
            41,
            42,
            43,
            45,
            49,
            51,
            52,
            53,
            56,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            71,
            72,
            73,
            74,
            76,
            78,
            80,
            81,
            83,
            85,
            87,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            105,
            108,
            109,
            111,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                NaN,
                2.10243290909724e-07,
                5.422220262636381e-06,
                4.222833444590791e-06,
                2.699577774585891e-07,
                2.699577774585891e-07,
                1.0677032518814388e-06,
                7.338210680021253e-07,
                9.422448185534261e-07,
                2.6995774527718623e-07
            ],
            [
                3.726638839878908e-06,
                2.902311639183378e-06,
                1.1478772230929451e-05,
                1.0677032518785256e-06,
                NaN,
                1.5534973841895917e-06,
                NaN,
                4.785093353940187e-06,
                3.726641061109272e-06,
                6.144176799334096e-06
            ],
            [
                1.3007133116542802e-05,
                1.0677024881980089e-06,
                6.475950298011458e-07,
                9.422444815765128e-07,
                NaN,
                1.0677032518785256e-06,
                NaN,
                1.994729483723626e-06,
                8.315278294097538e-07,
                8.315277302788957e-07
            ],
            [
                1.7603425837702984e-06,
                1.5534981249697903e-06,
                4.222832941072913e-06,
                2.2603240283888175e-06,
                1.0677027427600627e-06,
                7.338212429582604e-07,
                1.5534984953453635e-06,
                1.5534975693979422e-06,
                1.3709567165579959e-06,
                9.422448185534261e-07
            ],
            [
                6.475945666051092e-07,
                3.9278610661366994e-07,
                4.4508510499849186e-07,
                1.3709572068522336e-06,
                1.3709570434122812e-06,
                2.6995790618252024e-07,
                7.338209805200689e-07,
                6.475945666051092e-07,
                4.4508494582405734e-07,
                4.450848927650143e-07
            ],
            [
                2.102433660979124e-07,
                2.1024341622426268e-07,
                3.9278610661902853e-07,
                6.475947210046347e-07,
                8.315280276626197e-07,
                3.466327450756327e-07,
                1.2098662604291696e-06,
                1.9947304348862686e-06,
                5.043476486915964e-07,
                1.0677026154806063e-06
            ],
            [
                1.4449795205429202e-07,
                2.5612828213818346e-06,
                1.3709576971379186e-06,
                9.422447062202052e-07,
                1.3709576971425944e-06,
                7.338210680021253e-07,
                1.6373768624837685e-07,
                2.1024331597152624e-07,
                1.444979692800516e-07,
                2.69957906184239e-07
            ],
            [
                7.338209805224048e-07,
                6.475951069985296e-07,
                4.4508510499849186e-07,
                3.466325797896173e-07,
                5.043472879540142e-07,
                2.260324567337161e-06,
                NaN,
                8.315277302788957e-07,
                7.338210680021253e-07,
                1.3709576971425944e-06
            ],
            [
                4.450851049941403e-07,
                1.2098655392871682e-06,
                1.3709567165530083e-06,
                1.2098662604247682e-06,
                9.422448185478557e-07,
                5.715005151574337e-07,
                1.9947297215043796e-06,
                1.2098655392662613e-06,
                1.2098655392871682e-06,
                1.067702615468225e-06
            ],
            [
                1.7603432133136672e-06,
                7.338213304363436e-07,
                3.4663257978465195e-07,
                1.2098653950480359e-06,
                4.450848927637999e-07,
                1.994729245917502e-06,
                5.043476486915964e-07,
                1.5534975693933505e-06,
                9.422449308748773e-07,
                5.71500651413193e-07
            ],
            [
                4.450849988811838e-07,
                5.715005832872586e-07,
                1.3709572068354007e-06,
                1.3709573702722555e-06,
                1.370957860567974e-06,
                1.2098655392871682e-06,
                9.422448185435711e-07,
                1.0677032518748838e-06,
                1.067703251864202e-06,
                8.315284241650899e-07
            ],
            [
                NaN,
                5.043472879540142e-07,
                5.71500651413193e-07,
                9.422448185534261e-07,
                2.7535694384882703e-05,
                1.0677032518785256e-06,
                1.9947297215043796e-06,
                3.726638839833152e-06,
                2.7535704231844484e-05,
                1.3007123813382511e-05
            ],
            [
                5.043476486915964e-07,
                7.338213304363436e-07,
                7.338212429537553e-07,
                1.2098659719757836e-06,
                9.422442569315887e-07,
                NaN,
                9.422448185510695e-07,
                9.422450432014836e-07,
                1.0677032518785256e-06,
                2.561281600076256e-06
            ],
            [
                5.715004470313855e-07,
                6.475949526020042e-07,
                1.0677028700363782e-06,
                7.338211554783522e-07,
                1.3709572068179446e-06,
                2.9023116391477434e-06,
                5.715007195447234e-07,
                4.450851580555361e-07,
                5.715005832886879e-07,
                3.4663257978638593e-07
            ],
            [
                1.5534983101602148e-06,
                6.962255419868303e-06,
                9.422444815765128e-07,
                9.42244930862237e-07,
                5.715005832886879e-07,
                7.889263526345123e-06,
                5.422218969858371e-06,
                7.889265407327733e-06,
                3.726638395634011e-06,
                7.88926446679691e-06
            ],
            [
                1.8553919030858602e-07,
                1.2098662604291696e-06,
                2.561281905390075e-06,
                4.222834954778007e-06,
                NaN,
                3.7266410611296085e-06,
                7.338211554783522e-07,
                2.2603234895372223e-06,
                1.2098661162056318e-06,
                3.726641061085547e-06
            ],
            [
                9.422445939002803e-07,
                8.315280276607289e-07,
                9.422442569315887e-07,
                9.422445939032799e-07,
                1.7603440527222532e-06,
                5.715004470295662e-07,
                5.04347287955046e-07,
                2.1024341622426268e-07,
                1.3709570434178922e-06,
                6.475947210031623e-07
            ],
            [
                2.699578096393206e-07,
                3.466327037548308e-07,
                5.043475284430694e-07,
                2.3823685319244518e-07,
                6.475947210012481e-07,
                8.315283250371857e-07,
                4.450849458200093e-07,
                5.715003107715166e-07,
                7.3382080556433e-07,
                2.382368815916736e-07
            ],
            [
                1.7603434231705793e-06,
                4.785093353909723e-06,
                6.962256249606473e-06,
                1.7603440527046419e-06,
                4.785092783371756e-06,
                2.2603242978665707e-06,
                3.726638395611981e-06,
                3.2887478892504536e-06,
                7.889262585728421e-06,
                2.9023126771227976e-06
            ],
            [
                2.1024326584639497e-07,
                3.466325797888292e-07,
                2.1024329090867228e-07,
                2.382369951932796e-07,
                3.4663278639738526e-07,
                1.6373766672973748e-07,
                3.927862939126708e-07,
                1.0677027427600627e-06,
                2.6995784182073116e-07,
                4.450852111148132e-07
            ],
            [
                3.0590215399183813e-07,
                3.0590215399183813e-07,
                3.927862470899887e-07,
                1.0677029973192638e-06,
                1.8925145985895816e-05,
                4.450849988811838e-07,
                1.6373768624837685e-07,
                5.715005832827105e-07,
                7.338209805224048e-07,
                2.3823693839290317e-07
            ],
            [
                4.2228339479858295e-06,
                1.47389854857293e-05,
                1.994730434735237e-06,
                4.785096776468749e-06,
                2.2603251062270446e-06,
                1.5534981249574276e-06,
                1.2098662603499435e-06,
                5.715006514105942e-07,
                1.3709576971425944e-06,
                1.9947306726358406e-06
            ],
            [
                9.422450431989127e-07,
                1.7603427936335396e-06,
                1.3709568799919866e-06,
                5.043476486915964e-07,
                1.3709572068522336e-06,
                9.422450432014836e-07,
                2.561282516066741e-06,
                5.043474081993875e-07,
                1.0677029973192638e-06,
                1.3007128464961824e-05
            ],
            [
                2.2603242978665707e-06,
                6.144173869558639e-06,
                5.715003107755449e-07,
                4.539787947345257e-05,
                4.2228324377740105e-06,
                1.0129993395217047e-05,
                1.5534973841895917e-06,
                8.315281267882195e-07,
                1.9947292459347367e-06,
                1.0677032518748838e-06
            ],
            [
                1.2098658277335738e-06,
                6.475947982037486e-07,
                1.9947304348703948e-06,
                3.288749849477628e-06,
                2.2603242978665707e-06,
                1.3709576971379186e-06,
                1.760342793638743e-06,
                1.0677026154806063e-06,
                1.2098659719716573e-06,
                2.902313369111213e-06
            ],
            [
                1.7603427935967163e-06,
                1.760344052714248e-06,
                1.9947301969471416e-06,
                1.0677024881980089e-06,
                1.3709573702647743e-06,
                1.5534977545603963e-06,
                6.144177531381426e-06,
                1.3709576971425944e-06,
                1.0677026154730804e-06,
                2.561281905376098e-06
            ],
            [
                8.315284241650899e-07,
                6.1441760667392215e-06,
                4.785094494628999e-06,
                0.0004305570920088367,
                9.422443692489024e-07,
                1.1478765389222573e-05,
                3.059021904571643e-07,
                8.31527928532683e-07,
                3.7266388398585725e-06,
                1.9947299592933255e-06
            ],
            [
                2.699578740032504e-07,
                2.6995774527718623e-07,
                2.1024334103581732e-07,
                NaN,
                1.637377057680051e-07,
                1.1253509497883659e-07,
                2.10243290909724e-07,
                8.764242227418718e-08,
                1.1253522913127183e-07,
                1.275190732904469e-07
            ],
            [
                1.3709573702822306e-06,
                5.422217677078203e-06,
                1.209865827740176e-06,
                4.785096776468749e-06,
                1.3709573702722555e-06,
                4.450851580555361e-07,
                4.222834451327159e-06,
                2.9023130231176453e-06,
                8.315278294072958e-07,
                2.902311639183378e-06
            ],
            [
                2.2603248367656408e-06,
                8.939695238536645e-06,
                5.422220908925639e-06,
                9.422450431989127e-07,
                1.5534975693933505e-06,
                6.1441760667392215e-06,
                1.9947297215125433e-06,
                9.422450431989127e-07,
                3.288748673319648e-06,
                2.5612812946681295e-06
            ],
            [
                6.475947210012481e-07,
                1.994730672668496e-06,
                2.561283432035425e-06,
                1.5534983101393749e-06,
                3.927862939126708e-07,
                1.0677024881980089e-06,
                1.3709567165530083e-06,
                3.927862002641863e-07,
                1.0677028700363782e-06,
                2.9023119851781017e-06
            ],
            [
                4.450851049941403e-07,
                7.338209805224048e-07,
                5.04347468323289e-07,
                2.4300243631272052e-05,
                6.962253759828703e-06,
                2.382370235922541e-07,
                1.994729721482609e-06,
                4.222834954687752e-06,
                4.450852111148132e-07,
                2.902312677150514e-06
            ],
            [
                7.338211554688417e-07,
                8.315277302819205e-07,
                5.422218969895357e-06,
                4.785092783519724e-06,
                5.422220262636381e-06,
                4.4508505193932864e-07,
                3.120191137659974e-05,
                1.760343213335281e-06,
                7.889266347715168e-06,
                5.043473480730849e-07
            ],
            [
                4.450851049959619e-07,
                2.1024344128660572e-07,
                2.3823685319244518e-07,
                2.699578096393206e-07,
                3.059022269250683e-07,
                2.102434162245973e-07,
                3.9278634073732336e-07,
                3.4663262110803996e-07,
                3.927863875616689e-07,
                2.382369383923073e-07
            ],
            [
                6.475951069932288e-07,
                3.466325797896173e-07,
                7.338209805170655e-07,
                6.475948753991907e-07,
                8.315281267882195e-07,
                6.475946437781423e-07,
                2.1024341622426268e-07,
                1.209865827740176e-06,
                5.715002426460124e-07,
                9.422450432014836e-07
            ],
            [
                1.3709568799823232e-06,
                8.315283250371857e-07,
                4.450849458218309e-07,
                6.475949526003845e-07,
                7.338209805240734e-07,
                1.2098653950656417e-06,
                8.315278294072958e-07,
                5.043472879540142e-07,
                5.715006514167015e-07,
                6.475950297993789e-07
            ],
            [
                3.927862939126708e-07,
                4.450850519403407e-07,
                1.2751907329024393e-07,
                2.1024334103505245e-07,
                2.6995784182140636e-07,
                2.6995790618252024e-07,
                5.04347528440776e-07,
                1.2098662604247682e-06,
                3.059021904571643e-07,
                2.1024336609724313e-07
            ],
            [
                5.043475885674441e-07,
                9.422442569208767e-07,
                9.422448185510695e-07,
                1.5534983101549167e-06,
                1.3709575337078829e-06,
                1.2098662604247682e-06,
                1.2098662604049616e-06,
                2.5612812946890944e-06,
                5.715007195447234e-07,
                1.5534983101602148e-06
            ],
            [
                2.1024334103505245e-07,
                2.1024329090867228e-07,
                3.0590226339061185e-07,
                2.102433159684668e-07,
                7.338209805200689e-07,
                2.3823699519143784e-07,
                9.931195693628605e-08,
                2.1024329090867228e-07,
                1.4449800373065699e-07,
                2.3823685319244518e-07
            ],
            [
                1.1253512180925583e-07,
                3.0590226339061185e-07,
                1.4449798650551755e-07,
                2.3823688159291947e-07,
                2.1024336609843824e-07,
                2.3823696679327928e-07,
                1.8553914607267268e-07,
                2.1024331597262577e-07,
                6.023569166654288e-08,
                1.4449798650551755e-07
            ],
            [
                2.2603242978665707e-06,
                1.3709573702722555e-06,
                1.5534977545603963e-06,
                5.715006514151423e-07,
                1.5534983101478522e-06,
                8.315279285205827e-07,
                6.475946437928669e-07,
                2.9023133690980155e-06,
                7.338207180661203e-07,
                1.7603427935678977e-06
            ],
            [
                3.05902336324494e-07,
                2.5612828213934817e-06,
                3.466327863945479e-07,
                3.927862470899887e-07,
                5.043475885674441e-07,
                7.338212429582604e-07,
                5.043476486915964e-07,
                3.059022269250683e-07,
                NaN,
                1.067703379154416e-06
            ],
            [
                2.902313369111213e-06,
                2.2603242978871282e-06,
                NaN,
                4.222834954753043e-06,
                1.5534984953298217e-06,
                3.288750633488963e-06,
                7.889262585814522e-06,
                9.422443692574719e-07,
                2.9023123311055552e-06,
                3.288748281329893e-06
            ],
            [
                1.3709568799760888e-06,
                7.338212429537553e-07,
                1.760343423160973e-06,
                1.5534984953298217e-06,
                7.338213304283347e-07,
                1.760343423160973e-06,
                5.043472879525233e-07,
                3.927862470861484e-07,
                2.9023112932177327e-06,
                5.043474683204221e-07
            ],
            [
                1.5534975693869924e-06,
                1.855391681898159e-07,
                2.1024329090781183e-07,
                2.90231233114251e-06,
                5.715007195447234e-07,
                8.315278294072958e-07,
                8.315283250371857e-07,
                1.8553910183607374e-07,
                4.450851580555361e-07,
                1.855391681898159e-07
            ],
            [
                2.5612831267086116e-06,
                1.3709567165530083e-06,
                7.889261645355786e-06,
                0.99992032697287,
                1.1478770862589836e-05,
                2.4300252320622747e-05,
                2.1444943301674863e-05,
                2.9023126771227976e-06,
                3.2887478892683997e-06,
                6.962253759904688e-06
            ],
            [
                1.3709570434178922e-06,
                9.4224425692559e-07,
                1.760344052714248e-06,
                1.2098659719788098e-06,
                2.9023126771227976e-06,
                1.7603436330179102e-06,
                1.5534984953453635e-06,
                1.5534975693933505e-06,
                4.2228339479858295e-06,
                2.5612828213934817e-06
            ],
            [
                1.3709573702722555e-06,
                9.422448185510695e-07,
                9.422442569290178e-07,
                5.715003107715166e-07,
                1.3709567165461505e-06,
                6.962255419931625e-06,
                7.338207180864763e-07,
                5.715006514151423e-07,
                5.043474683204221e-07,
                1.3709575337125585e-06
            ],
            [
                1.3709570434178922e-06,
                7.338209805224048e-07,
                1.370957860567974e-06,
                5.043476486915964e-07,
                1.2098656835076114e-06,
                1.3709576971379186e-06,
                3.2887490653408545e-06,
                1.2098658277451275e-06,
                5.715005151606823e-07,
                2.260324836787226e-06
            ],
            [
                7.338207180864763e-07,
                5.715003789017068e-07,
                9.422444815765128e-07,
                6.475947210012481e-07,
                9.422448185510695e-07,
                6.475951069985296e-07,
                1.7603434231705793e-06,
                6.475949525981759e-07,
                3.9278634073732336e-07,
                1.3709575337125585e-06
            ],
            [
                4.785096776468749e-06,
                1.3709568799679844e-06,
                7.338209805224048e-07,
                4.450852111148132e-07,
                5.715003107755449e-07,
                4.450848927637999e-07,
                2.3823702359290413e-07,
                1.067703379154416e-06,
                1.7603434231705793e-06,
                2.260324836776948e-06
            ],
            [
                5.043474081993875e-07,
                7.338213304363436e-07,
                0.9999962733589441,
                2.699577774560111e-07,
                6.475948754012522e-07,
                5.715002426486762e-07,
                1.3709573702722555e-06,
                4.450849988811838e-07,
                4.222831934379152e-06,
                3.4663249714612693e-07
            ],
            [
                1.0677024882009222e-06,
                1.0677028700422047e-06,
                1.994729721518893e-06,
                1.0677026154806063e-06,
                2.6995790618469934e-07,
                1.444979692800516e-07,
                7.889263526345123e-06,
                1.275191036933194e-07,
                1.30071315662049e-05,
                3.288749457383046e-06
            ],
            [
                3.4663249714612693e-07,
                6.475947982037486e-07,
                2.102434412875379e-07,
                5.715003789046955e-07,
                1.370957860576702e-06,
                8.764242227380856e-08,
                5.715006514176113e-07,
                1.6373766672973748e-07,
                4.450852111148132e-07,
                3.466326211105621e-07
            ],
            [
                1.5534983101602148e-06,
                8.315283250371857e-07,
                2.9023112932045342e-06,
                1.0677033791583005e-06,
                8.939694172770212e-06,
                2.902310947208574e-06,
                4.450849988798682e-07,
                1.0677024881980089e-06,
                2.260324297853209e-06,
                2.2603234895176927e-06
            ],
            [
                1.5534973842076057e-06,
                9.422444815792981e-07,
                5.71500515159253e-07,
                6.475949526020042e-07,
                6.475945666051092e-07,
                8.315281267861397e-07,
                3.2887502415767434e-06,
                5.422217677152175e-06,
                3.059022269250683e-07,
                1.5534977545886537e-06
            ],
            [
                5.715005832886879e-07,
                3.4663278639892215e-07,
                5.043472278322555e-07,
                3.927862470899887e-07,
                3.4663249714451116e-07,
                4.450851580555361e-07,
                4.450850519403407e-07,
                2.6995774527718623e-07,
                1.9947304348862686e-06,
                3.4663249714612693e-07
            ],
            [
                1.6373762769138607e-07,
                2.382368531929327e-07,
                6.475945666051092e-07,
                NaN,
                1.1253518888531272e-07,
                2.69957906184239e-07,
                4.450848927650143e-07,
                6.962254589978262e-06,
                6.475945666051092e-07,
                5.715003107767143e-07
            ],
            [
                4.450849458218309e-07,
                1.5534975693792215e-06,
                1.2098658277451275e-06,
                2.699576809143613e-07,
                7.338210679909462e-07,
                8.315281267861397e-07,
                1.9947299593014888e-06,
                1.2098661161982042e-06,
                5.043476486915964e-07,
                5.04347468323289e-07
            ],
            [
                NaN,
                4.785096206076165e-06,
                9.422447062294175e-07,
                5.715003789033962e-07,
                8.315281267834927e-07,
                5.422218323487975e-06,
                8.315281267882195e-07,
                2.9023116391978967e-06,
                7.889261645427538e-06,
                7.889259764359722e-06
            ],
            [
                2.5612834320214477e-06,
                3.2887494574518405e-06,
                1.9947294837154625e-06,
                1.2098659719757836e-06,
                2.902313023130843e-06,
                8.315277302788957e-07,
                1.553497199007048e-06,
                2.2603242978871282e-06,
                2.5612828213934817e-06,
                1.2098658277451275e-06
            ],
            [
                1.0677033791437343e-06,
                1.0677024881887838e-06,
                1.994730197090463e-06,
                9.422444815765128e-07,
                NaN,
                5.715005151606823e-07,
                6.475945666033422e-07,
                2.9023116391675407e-06,
                2.2603237589676295e-06,
                3.7266406168624155e-06
            ],
            [
                3.0590215399183813e-07,
                9.422450431989127e-07,
                4.785094494811783e-06,
                1.0677024882009222e-06,
                7.338208055664991e-07,
                6.962257909785973e-06,
                NaN,
                2.102434412875379e-07,
                3.9278634073732336e-07,
                5.715002426475718e-07
            ],
            [
                3.059021175261338e-07,
                1.4449796928021588e-07,
                1.1253506814842375e-07,
                9.93120161310289e-08,
                6.475949526003845e-07,
                1.2098652508347793e-06,
                1.4449802095666915e-07,
                1.4449805540740185e-07,
                7.734416698849138e-08,
                1.4449805540763184e-07
            ],
            [
                7.889265407090955e-06,
                3.726639728348526e-06,
                2.7535687818640727e-05,
                5.4222209089700225e-06,
                1.6701423835320418e-05,
                4.222832941034507e-06,
                7.889262585814522e-06,
                4.0063677865600476e-05,
                1.4738980215352592e-05,
                3.726641061027928e-06
            ],
            [
                1.3709573702856596e-06,
                8.315279285351409e-07,
                1.0677029973219343e-06,
                7.338207180898968e-07,
                1.5534973842076057e-06,
                3.927862470899887e-07,
                1.0677026154806063e-06,
                2.561281600086738e-06,
                8.315279285351409e-07,
                1.855391239547094e-07
            ],
            [
                1.0677028700363782e-06,
                8.315278294072958e-07,
                1.3709576971379186e-06,
                5.715003789017068e-07,
                7.338212429537553e-07,
                6.475950297942253e-07,
                8.315281267834927e-07,
                5.043474081993875e-07,
                1.0677024881980089e-06,
                1.3709573702722555e-06
            ],
            [
                2.5612825160562587e-06,
                3.7266388398585725e-06,
                1.994729245917502e-06,
                2.902312677104321e-06,
                6.144177531660828e-06,
                3.2887490653408545e-06,
                4.785094494783494e-06,
                2.9023116390421582e-06,
                2.9023133690637e-06,
                9.422447062202052e-07
            ],
            [
                1.7603440527286572e-06,
                1.7603434231705793e-06,
                8.31528126775552e-07,
                1.2098661161927025e-06,
                9.422447062202052e-07,
                7.338211554783522e-07,
                1.2098661161927025e-06,
                1.5534979397500702e-06,
                1.760344052714248e-06,
                2.3823688159291947e-07
            ],
            [
                8.315280276546789e-07,
                5.715005832853093e-07,
                1.760343633031919e-06,
                6.475946437966953e-07,
                4.450848927637999e-07,
                4.450851580555361e-07,
                7.338209805200689e-07,
                8.315284241597959e-07,
                3.466325797888292e-07,
                2.3823693839290317e-07
            ],
            [
                5.715005832827105e-07,
                5.71500515159253e-07,
                5.715003107715166e-07,
                7.338208055664991e-07,
                6.475949525981759e-07,
                5.71500515159253e-07,
                6.475949525981759e-07,
                1.0677026154730804e-06,
                8.315281267834927e-07,
                5.715007195431641e-07
            ],
            [
                7.338213304363436e-07,
                1.0677029973219343e-06,
                5.715007195447234e-07,
                6.475947210031623e-07,
                1.3709567165617364e-06,
                1.5534981249697903e-06,
                8.315277302841894e-07,
                NaN,
                5.043472879540142e-07,
                1.5534983101393749e-06
            ],
            [
                1.8553907971855875e-07,
                1.275190580890061e-07,
                9.931189774187203e-08,
                2.382368531929327e-07,
                1.6373770576776313e-07,
                8.764244316973974e-08,
                9.931189774187203e-08,
                1.8553914607267268e-07,
                4.691161005609407e-08,
                1.1253525596174225e-07
            ],
            [
                2.6995774527577444e-07,
                1.7603430034743913e-06,
                3.466326624336003e-07,
                3.927862939126708e-07,
                2.6995771309523475e-07,
                1.4449795205429202e-07,
                5.715002426486762e-07,
                3.927860597945825e-07,
                2.2603240284371276e-06,
                1.8553919030858602e-07
            ],
            [
                1.6373766672973748e-07,
                2.382370235933104e-07,
                2.699576809143613e-07,
                3.059022269250683e-07,
                1.6373776432509826e-07,
                5.043472879540142e-07,
                2.6995784182140636e-07,
                5.043475885674441e-07,
                1.855391239544352e-07,
                2.1024326584639497e-07
            ],
            [
                2.9023109472244114e-06,
                9.422447062202052e-07,
                8.315284241560147e-07,
                2.9023109471689794e-06,
                4.7850933538313875e-06,
                1.3709572068422585e-06,
                1.3709576971425944e-06,
                1.0677032518748838e-06,
                1.5534981249496567e-06,
                2.2603234895289998e-06
            ],
            [
                8.315284241597959e-07,
                2.2603234895372223e-06,
                3.726638395634011e-06,
                1.7603434231777837e-06,
                1.994729483723626e-06,
                2.6995774527718623e-07,
                1.8925141473978602e-05,
                3.927860597945825e-07,
                1.5534971990126997e-06,
                1.5534984953510149e-06
            ],
            [
                5.715003789017068e-07,
                1.0677032518785256e-06,
                3.927863875584984e-07,
                3.05902263389638e-07,
                2.699578740011634e-07,
                1.3709572068422585e-06,
                3.466327037539638e-07,
                5.043475284430694e-07,
                2.1024329090781183e-07,
                5.043472879481655e-07
            ],
            [
                1.760343423160973e-06,
                1.2098662604247682e-06,
                1.9947297215043796e-06,
                3.288750241561788e-06,
                5.422218323487975e-06,
                2.902310947190096e-06,
                1.2098655392871682e-06,
                3.2887482813149375e-06,
                4.222832941142044e-06,
                8.315281267834927e-07
            ],
            [
                1.3709575337078829e-06,
                1.7603434231833873e-06,
                5.715003789017068e-07,
                6.475951069932288e-07,
                1.209865827740176e-06,
                3.726639728262097e-06,
                1.0677032518700286e-06,
                8.315281267861397e-07,
                5.715003789033962e-07,
                9.422448185534261e-07
            ],
            [
                5.715005151574337e-07,
                1.5534981249697903e-06,
                1.3709570434178922e-06,
                1.9947304348703948e-06,
                1.7603432133136672e-06,
                2.9023109472244114e-06,
                1.3709575337078829e-06,
                6.475945666051092e-07,
                1.7603436330179102e-06,
                1.7603427936263351e-06
            ],
            [
                9.422450431989127e-07,
                8.31527928532683e-07,
                9.422443692489024e-07,
                5.1442213660804794e-05,
                4.222833444590791e-06,
                9.422448185534261e-07,
                1.3709575336947905e-06,
                1.067703379154416e-06,
                1.8925157266089433e-05,
                3.466327863983311e-07
            ],
            [
                5.715004470313855e-07,
                6.475947210012481e-07,
                6.475947209985977e-07,
                1.2098655392871682e-06,
                2.902312677137316e-06,
                8.315280276546789e-07,
                7.338209805224048e-07,
                1.3709573702647743e-06,
                9.422442569208767e-07,
                2.5612831266946347e-06
            ],
            [
                3.288749065423109e-06,
                3.288748281295496e-06,
                2.9023126771227976e-06,
                2.260324836776948e-06,
                1.760344052714248e-06,
                2.260324297853209e-06,
                2.260325375664839e-06,
                1.2098659719524008e-06,
                5.715003107755449e-07,
                1.0129988564716393e-05
            ],
            [
                1.9947292459347367e-06,
                2.5612822107167428e-06,
                1.5534975693933505e-06,
                1.2098659719716573e-06,
                7.338207180864763e-07,
                3.2887482813149375e-06,
                1.9947297215125433e-06,
                1.2098656835224664e-06,
                1.3709567165617364e-06,
                1.3709568799823232e-06
            ],
            [
                5.715007195431641e-07,
                1.8553910183607374e-07,
                5.715007195431641e-07,
                8.315281267834927e-07,
                4.450848927650143e-07,
                1.2098656835136636e-06,
                3.9278638755456876e-07,
                5.71500242637956e-07,
                1.2098652508287273e-06,
                7.338212429582604e-07
            ],
            [
                1.2098662604247682e-06,
                8.315281267861397e-07,
                7.338212429504183e-07,
                5.043472879540142e-07,
                1.5534979397740895e-06,
                NaN,
                1.7603438428740716e-06,
                4.4508505193932864e-07,
                3.927862002663297e-07,
                7.338207180864763e-07
            ],
            [
                1.5534979397740895e-06,
                1.9947297215043796e-06,
                3.288747889178668e-06,
                2.5612828213818346e-06,
                1.3709573702647743e-06,
                1.2098653950656417e-06,
                1.3709576971379186e-06,
                1.300713156582635e-05,
                1.2098655392871682e-06,
                7.889262585814522e-06
            ],
            [
                1.370957860567974e-06,
                7.338213304316717e-07,
                2.5612834320214477e-06,
                7.338209805224048e-07,
                3.7266401725681614e-06,
                1.0677032518748838e-06,
                6.475950298011458e-07,
                1.0677032518785256e-06,
                2.699577774585891e-07,
                1.7603434231777837e-06
            ]
        ]
    },
    {
        "q_id": "10076_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998874648245,
                0.9999993916409634,
                0.9999996940978462,
                0.9999988634358835,
                0.9999999273418182,
                0.9999996743688586,
                0.9999998942830358,
                0.9999998461826405,
                0.9999992661789323,
                0.9999980052709928
            ],
            [
                0.9999995818810776,
                0.9999972735307071,
                0.9999998144608762,
                0.9999993916409637,
                0.9999988634365616,
                0.999999802494586,
                0.9999991148431757,
                0.9999994631249963,
                0.9999998362623529,
                0.999999789756659
            ],
            [
                0.9999991148429648,
                0.9999988634360194,
                0.9999983463110077,
                0.9999972735297333,
                0.999999526209499,
                0.9999989322972583,
                0.9999995549148422,
                0.999999746398073,
                0.9999994631249964,
                0.9999995549147361
            ],
            [
                0.9999972735284308,
                0.999999581881277,
                0.9999993524054337,
                0.9999998257022045,
                0.9999949062968224,
                0.9999994284992807,
                0.9999993916408185,
                0.9999997897565587,
                0.9999997463981938,
                2.1024336609874897e-07
            ],
            [
                2.902312677137316e-06,
                8.315282259138311e-07,
                1.7603440527286572e-06,
                1.3007133116732079e-05,
                2.4300243631890864e-05,
                1.0677029973219343e-06,
                6.144176799334096e-06,
                1.3709572068522336e-06,
                5.043476486924565e-07,
                1.2098653950656417e-06
            ],
            [
                0.9999995549148422,
                0.9999997761970247,
                0.9999992188518564,
                0.9999998362622943,
                0.9999995262093294,
                0.9999994284996895,
                0.9999989322970042,
                0.9999989969857928,
                0.9999987121047856,
                0.9999992661787572
            ],
            [
                0.9999993524048937,
                0.9999988634358837,
                0.999998932296749,
                0.9999992188516701,
                0.9999981261248423,
                0.9999977396754361,
                0.9999991148433868,
                0.9999985406237806,
                0.9999991148431763,
                0.9999995262092164
            ],
            [
                0.9999969105066641,
                0.9999981261239491,
                0.9999974387174877,
                0.9999978766215414,
                0.9999991148427539,
                0.9999991148433871,
                0.999998629042142,
                0.999995504816293,
                0.999999114842965,
                0.999998126125065
            ],
            [
                0.9999969105062944,
                0.9999995262096121,
                0.999999495652592,
                0.9999945777810587,
                0.9999995549150548,
                0.9999991148429646,
                0.9999983463100218,
                0.9999989969854344,
                0.9999967112497635,
                0.9999996072138936
            ],
            [
                2.144495864106235e-05,
                4.222834451403972e-06,
                8.93969843573914e-06,
                3.7266383956509585e-06,
                0.9999992188515767,
                1.892514373029853e-05,
                8.939697370069891e-06,
                1.7603425837903113e-06,
                2.7535691103314177e-05,
                1.892514373029853e-05
            ],
            [
                1.4738978458623327e-05,
                4.785094494811783e-06,
                0.9999992188516695,
                1.3007123813559956e-05,
                2.2603242978943238e-06,
                5.4222202626709005e-06,
                0.9999994631250604,
                1.994729483729522e-06,
                0.9999989969856736,
                1.7603425837903113e-06
            ],
            [
                8.315277302841894e-07,
                0.9999990577554065,
                1.1253513522391131e-07,
                0.9999997761970247,
                0.9999998642566542,
                0.9999994956527722,
                0.9999989322967485,
                0.9999997897567091,
                0.9999998144609423,
                0.9999969105062911
            ],
            [
                4.222832437798974e-06,
                0.9999996310113282,
                2.5612828213934817e-06,
                0.9999991684719729,
                2.699578096393206e-07,
                0.9999798543092856,
                0.9999996310114598,
                6.144173869603344e-06,
                0.9999990577557439,
                3.466327450765785e-07
            ],
            [
                0.9999546021314297,
                0.9999995262094422,
                0.9999977396759727,
                0.9999990577550697,
                0.9999991148433867,
                5.043472879540142e-07,
                0.9999984465022463,
                6.605214470327124e-05,
                0.9999977396757036,
                0.9999989322972576
            ],
            [
                0.99999926617867,
                3.927863407379485e-07,
                0.9999990577557435,
                0.9999993524049704,
                0.9999997463982241,
                0.9999991148427534,
                0.9999984465016912,
                0.9999987121044777,
                0.9999990577551819,
                0.9999993524050477
            ],
            [
                5.043475885696228e-07,
                1.7603425837903113e-06,
                1.0129995810463632e-05,
                7.889263526409699e-06,
                1.0129995810463632e-05,
                8.939693107288474e-06,
                0.9999998555019619,
                1.760343213335281e-06,
                0.9999995818812273,
                1.1478770862882149e-05
            ],
            [
                0.9999985406232594,
                0.9999993916407465,
                0.9999977396759773,
                0.9999994284997582,
                0.999998996985913,
                0.9999993106387092,
                0.9999993524051258,
                0.9999972735287644,
                0.9999987901340286,
                0.9999991684717753
            ],
            [
                0.9999994631249323,
                0.999998996985434,
                0.9999994631248045,
                0.9999989322968761,
                0.9999989969856736,
                0.999999802494586,
                0.999999057755631,
                0.999999789756659,
                0.999999761763147,
                0.9999996743686645
            ],
            [
                0.9999970976866337,
                0.9999997300423191,
                0.9999997761970248,
                0.9999869928731019,
                0.9999960330140878,
                0.9999997761972116,
                5.715004470295662e-07,
                0.9999997126314811,
                0.9999986290431205,
                0.9999993106390368
            ],
            [
                0.9999988634358834,
                0.9999994956527123,
                0.9999986290427941,
                0.9999977396754348,
                0.9999994631248684,
                0.9999991148428592,
                0.999999730042094,
                0.9999995262094423,
                0.9999992661787572,
                0.9999987901340288
            ],
            [
                0.9999998461826222,
                0.999999495652592,
                0.9999997761971582,
                0.9999996310113719,
                0.9999997463981636,
                0.9999990577550698,
                0.9999998257021421,
                0.9999997126314126,
                0.999999653367379,
                0.9999995818813269
            ],
            [
                0.9999995549148953,
                0.9999992661788452,
                0.9999995549151075,
                0.9999988634361546,
                0.9999995549148953,
                0.9999986290432847,
                0.9999988634358835,
                0.9999991148426481,
                0.9999987901344616,
                0.9999994956525922
            ],
            [
                0.9999989322967491,
                0.9999997617630048,
                0.9999991684715762,
                0.9999952149072205,
                0.9999997300421261,
                0.9999997463982242,
                0.999999855502048,
                0.9999964991455894,
                0.9999988634358836,
                0.9999997126315153
            ],
            [
                0.99999967436882,
                0.999999894282998,
                0.9999997463981636,
                0.9999996072136594,
                0.9999992188517629,
                0.9999986290421403,
                0.9999969105048204,
                0.999997593896515,
                0.9999987121046318,
                0.9999989969861518
            ],
            [
                0.9999985406230842,
                0.9999975938979506,
                2.4300232043987867e-05,
                6.605215257197525e-05,
                0.9999960330126718,
                0.9999960330140966,
                0.9999952149043712,
                0.9999938558246754,
                0.9999985406230842,
                1.4738987243478167e-05
            ],
            [
                0.9999993106391193,
                0.9999996940978096,
                0.9999934595596619,
                0.9999999006880904,
                0.9999972735290813,
                0.9999898700102484,
                0.9999997761970784,
                0.999999526209273,
                0.9999992661786701,
                0.9999997300422226
            ],
            [
                0.9999989322971304,
                0.9999996072139403,
                0.9999991148428594,
                0.9999993916411085,
                0.9999969105040818,
                0.9999988634358841,
                0.9999998802069444,
                0.9999988634358835,
                0.9999994631247403,
                0.9999997761970515
            ],
            [
                3.9278605979534166e-07,
                1.7603425837903113e-06,
                2.3823693839325527e-07,
                9.422443692574719e-07,
                1.5534984953552536e-06,
                1.2098659719788098e-06,
                5.715002426486762e-07,
                6.144177531811707e-06,
                NaN,
                5.043472278322555e-07
            ],
            [
                0.9999995549150544,
                0.999999391640891,
                0.9999991684718739,
                0.9999984465022459,
                0.9999992188513905,
                0.9999988634362901,
                0.9999989969857933,
                0.9999988634366964,
                0.9999996533675031,
                0.9999989969856732
            ],
            [
                0.9999945777829797,
                0.9999296881336839,
                0.9999974387180968,
                0.9999993524054338,
                4.539786865090791e-05,
                0.999999581881327,
                0.999999814460876,
                0.9999982396559483,
                0.9999546021208747,
                0.9999955048173619
            ],
            [
                0.999994577782976,
                0.9999996310113719,
                0.9999996072137063,
                0.9999996533674615,
                0.999999789756659,
                0.9999892166865171,
                0.9999991148433864,
                0.9999992188515765,
                0.9999989969859121,
                0.9999988634360192
            ],
            [
                0.9999998362623723,
                0.999999168472072,
                0.9999996743688975,
                0.9999975938973765,
                0.9999991684719726,
                0.9999998144608762,
                0.9999998461827322,
                0.9999999123575046,
                0.9999970976876705,
                0.9999998555020309
            ],
            [
                0.9999999123575569,
                0.9999998461827322,
                0.9999989969861516,
                0.999993037741268,
                0.9999987121052458,
                0.9999989969859123,
                0.9999981261250648,
                0.9999998144609645,
                0.9999996310114159,
                0.999999872480942
            ],
            [
                5.4222183235249605e-06,
                0.9999998362623334,
                0.9999996743687422,
                3.2887506336235617e-06,
                6.1441767993788005e-06,
                0.9999969105051854,
                3.2887494574832472e-06,
                1.147876812620341e-05,
                3.72663883989755e-06,
                1.0129987357517693e-05
            ],
            [
                0.9999997300422226,
                0.9999992188514834,
                0.9999993524051247,
                2.3823682479292225e-07,
                0.9999991684715761,
                0.999998446502061,
                0.999999495652532,
                0.9999986290429576,
                0.9999998257021422,
                0.9999977396762434
            ],
            [
                0.9999999006879957,
                0.9999997761971848,
                0.9999997617630049,
                0.9999998555019618,
                0.999997593896802,
                0.9999995818813767,
                3.927862002663297e-07,
                0.9999998724809723,
                0.9999996743688586,
                0.9999997300421581
            ],
            [
                1.209865827752005e-06,
                7.889259764517575e-06,
                1.3709575337159875e-06,
                3.059021904580685e-07,
                NaN,
                1.994729483729522e-06,
                0.9999251538001105,
                3.05902263391829e-07,
                2.1024331597152624e-07,
                1.3709573702856596e-06
            ],
            [
                0.9999991684721711,
                0.9999986290424678,
                0.9999985406234334,
                0.9999995818812772,
                0.9999991148427539,
                0.9999985406234331,
                0.9999983463106132,
                0.9999987901337409,
                0.9999984465016926,
                0.9999983463104166
            ],
            [
                0.9999997463981032,
                0.9999983463098235,
                0.9999991684721712,
                0.9999996533672552,
                0.9999981261248423,
                0.9999994631248043,
                0.9999995262094987,
                0.9999997463981939,
                0.9999934595635699,
                0.9999978766205277
            ],
            [
                0.9999978766207799,
                0.999999674368781,
                0.9999994956525321,
                0.9999991148428592,
                0.999998540624302,
                7.338211554783522e-07,
                0.9999993524054336,
                0.9999987121044785,
                0.9999986290424672,
                0.9999996072137063
            ],
            [
                1.0677029973158649e-06,
                2.260324836776948e-06,
                1.1253516205489029e-07,
                1.2098659719757836e-06,
                1.2751901248454963e-07,
                8.764244316973974e-08,
                3.9278610661545617e-07,
                1.6373762769138607e-07,
                6.825597214718257e-08,
                2.561282516066741e-06
            ],
            [
                0.9999988634362907,
                0.9999994956527123,
                0.9999910603026433,
                0.9999991148431759,
                0.9999994956524118,
                0.9999981261243955,
                0.99999886343629,
                0.9999991148432811,
                0.999998629043285,
                0.9999987121044782
            ],
            [
                0.9999970976866375,
                0.9999916019279843,
                0.9999972735307099,
                0.9999983463110093,
                0.9999972735290821,
                0.9999975938982367,
                0.9999970976890551,
                0.999998790134462,
                0.9999992188516703,
                0.9999964991447547
            ],
            [
                0.9999984465020616,
                9.422442569315887e-07,
                0.9999987901338849,
                0.9999987901338849,
                0.9999987121041712,
                0.9999987901341738,
                0.9999989322970035,
                0.9999989322970039,
                0.9999984465015058,
                0.9999993106387085
            ],
            [
                5.3157837044597743e-08,
                3.2241839428313264e-08,
                7.734428685047173e-08,
                9.931200429212718e-08,
                3.2241847115356483e-08,
                7.734418542875216e-08,
                6.475950297993789e-07,
                4.139934586278605e-08,
                8.764254764780641e-08,
                9.931202796993203e-08
            ],
            [
                0.9999991148431755,
                0.9999987901343173,
                0.9999970976883633,
                0.9999996310114159,
                0.9999991148432811,
                0.9999978766217928,
                0.9999977396748962,
                0.9999997617631184,
                0.999998790134318,
                0.9999952149072232
            ],
            [
                0.9999996940978826,
                0.9999992661787575,
                0.9999992188516699,
                0.999999653367379,
                0.9999989969861511,
                0.9999994956523516,
                0.9999992661789324,
                0.9999983463108101,
                0.9999997300421261,
                0.999999218851856
            ],
            [
                0.9999996072137999,
                0.9999998461826037,
                0.9999993916411085,
                0.9999993106387904,
                0.9999997300422548,
                0.9999994631250603,
                0.9999998555019618,
                0.9999982396563681,
                0.9999983463096268,
                0.9999949062925735
            ],
            [
                3.927863875616689e-07,
                1.2098661162056318e-06,
                1.209866260432471e-06,
                3.72663883989755e-06,
                4.450848927658745e-07,
                4.22283545819819e-06,
                2.9023119851899796e-06,
                1.0129987357407137e-05,
                2.2603234895372223e-06,
                2.902312331170226e-06
            ],
            [
                0.9999987901340298,
                0.9999992188517633,
                0.9999995549148424,
                0.9999994956524119,
                0.9999980052700431,
                0.9999991148432823,
                0.9999998024946801,
                0.9999993106386265,
                0.9999990577557443,
                0.9999997761971583
            ],
            [
                0.9999964991460067,
                5.715003789046955e-07,
                0.9999994631250604,
                0.9999992661790201,
                0.9999985406236062,
                0.9999992661788449,
                0.9999885212278025,
                0.9999993106386262,
                0.9999993524054339,
                0.9999994284996897
            ],
            [
                0.9999869928684861,
                0.9999985406236062,
                0.9999987121046319,
                0.9999986290429579,
                0.9999972735290834,
                0.99999963101146,
                0.9999995549148953,
                0.9999994284997576,
                0.9999988634365613,
                0.999997593896802
            ],
            [
                0.9999990577549576,
                0.9999989322975126,
                0.9999978766210358,
                0.999996273358946,
                0.9999989322968766,
                0.9999996310115481,
                0.9999994284994173,
                0.9999987121043249,
                0.9999986290423052,
                0.9999989322966221
            ],
            [
                0.9999997126314469,
                0.9999990577555189,
                0.9999998942830485,
                0.9999992661791952,
                0.9999997761971849,
                0.999998346310021,
                0.9999995262094422,
                0.9999970976873266,
                0.9999996743686257,
                0.9999998461826405
            ],
            [
                0.9999997761970515,
                0.9999998024946095,
                0.9999989322975125,
                0.9999994631249323,
                0.9999998461827322,
                0.9999980052705182,
                0.9999892166890795,
                0.9999996072138466,
                0.9999957771655542,
                0.9999996940977368
            ],
            [
                1.6373768624837685e-07,
                7.734414854792722e-08,
                0.9999957771660551,
                0.9999949062968251,
                0.9999998942830485,
                0.9999938558246726,
                0.999998629042794,
                0.9999988634362897,
                1.8553919030776337e-07,
                0.9999992188512971
            ],
            [
                1.994729721518893e-06,
                7.338210680021253e-07,
                1.4738983729535602e-05,
                5.144219527356777e-05,
                2.5612831267202583e-06,
                1.7603432133296774e-06,
                3.2887506336235617e-06,
                1.012999218776902e-05,
                2.90231094723893e-06,
                1.0129987357407137e-05
            ],
            [
                0.9999989322971305,
                0.9999993524050477,
                0.9999984465026168,
                0.9999989969857929,
                0.9999995262092728,
                0.9999994284996897,
                0.9999978766210331,
                0.9999988634365612,
                0.9999972735297326,
                0.9999996940976272
            ],
            [
                0.9999995818812769,
                0.9999983463108097,
                0.9999955048162824,
                6.475947210031623e-07,
                0.9999885212277811,
                0.9999994956525318,
                3.9278610661902853e-07,
                0.9999990577551818,
                0.9999980052705176,
                1.2751910369275402e-07
            ],
            [
                0.9999977396754343,
                0.9999997126315153,
                0.9999993106387906,
                0.9999978766207791,
                0.9999771719974607,
                0.9999998642567351,
                0.9999998555019963,
                0.9999995818812272,
                0.9999997463982241,
                0.9999988634365607
            ],
            [
                0.9999980052698054,
                0.9999993916409637,
                2.3823696679327928e-07,
                0.9999967112497617,
                3.288749065423109e-06,
                0.9999960330145703,
                0.9999989969862718,
                0.9999991684715763,
                0.9999996533672139,
                0.999998346310613
            ],
            [
                0.9999998024946095,
                0.9999998724810027,
                0.9999977396765122,
                0.9999989969860317,
                0.9999998555019791,
                0.9999997897567091,
                0.9999998642566542,
                0.9999999006880075,
                0.9999997617629764,
                0.999999653367379
            ],
            [
                7.338208930460318e-07,
                6.475947982037486e-07,
                6.475945666063607e-07,
                2.6995774527718623e-07,
                5.715002426486762e-07,
                8.315277302857965e-07,
                9.422445939054222e-07,
                5.715002426486762e-07,
                1.7603430034867993e-06,
                2.2603234895372223e-06
            ],
            [
                0.9999972735300564,
                0.999948557792693,
                0.9999934595604404,
                0.999999607213753,
                0.999997876622045,
                0.9999977396746254,
                0.9999998257020798,
                1.8553905759969634e-07,
                0.9999925887166048,
                0.999998712105092
            ],
            [
                2.9023109472494878e-06,
                1.8925148241872038e-05,
                8.315281267882195e-07,
                7.889261645427538e-06,
                1.5534981249697903e-06,
                6.47595107001401e-07,
                1.0677029973219343e-06,
                2.260324567337161e-06,
                4.539788488274408e-05,
                4.785093924389007e-06
            ],
            [
                0.9999995549151076,
                0.9999990577549575,
                0.9999992661792824,
                0.9999994284994173,
                0.9999996940978462,
                0.9999996743688199,
                0.9999989969862718,
                0.9999997617630901,
                0.9999955048179008,
                0.9999989969859127
            ],
            [
                1.8925157266089433e-05,
                1.209865539298447e-06,
                2.9023109472494878e-06,
                3.7266379514061143e-06,
                3.7266410611465547e-06,
                2.9023112932296107e-06,
                1.0129993395336818e-05,
                2.2603248367949354e-06,
                2.9023112932296107e-06,
                6.962258739796719e-06
            ],
            [
                0.9999997617630333,
                0.9999993524048933,
                0.9999989322973851,
                0.9999993106387906,
                0.9999998144608762,
                0.9999997897565838,
                0.999999872480942,
                0.9999999176675338,
                0.9999997300422869,
                0.9999995818813767
            ],
            [
                0.9999949062950075,
                0.9999995549149484,
                3.7266401726173067e-06,
                9.422449308774482e-07,
                0.9999970976866348,
                0.9999942280820419,
                0.9999994631251885,
                0.9999991684721714,
                0.9999934595635795,
                7.338208930460318e-07
            ],
            [
                0.9999998942830233,
                0.999999900688055,
                0.9999997761972116,
                0.9999995549147359,
                0.9999998144609645,
                0.9999998642567028,
                0.9999960330131434,
                0.9999992661789323,
                0.9999986290432844,
                0.9999986290431214
            ],
            [
                0.9999997126314811,
                0.9999996940976639,
                0.9999997126313784,
                0.9999997126314126,
                0.9999993106387904,
                0.9999972735287597,
                0.9999989969856733,
                0.9999992661789326,
                0.9999998362622552,
                0.9999998144609203
            ],
            [
                0.9999724642959031,
                0.9999982396565785,
                0.9999992188515772,
                0.9999990577552945,
                0.9999986290426303,
                0.9999997761971582,
                0.9999975938968043,
                0.9999997617631754,
                0.999999746398073,
                0.9999992188514838
            ],
            [
                1.994729483729522e-06,
                1.3709576971463352e-06,
                5.043475885696228e-07,
                5.715006514176113e-07,
                8.315279285370317e-07,
                1.209865827752005e-06,
                8.315281267882195e-07,
                1.7603438428848787e-06,
                7.338209805240734e-07,
                3.2887506336235617e-06
            ],
            [
                0.9999987901338847,
                4.2228319344021954e-06,
                6.144173137170873e-06,
                4.785093924389007e-06,
                0.9999994956525922,
                6.962256249935742e-06,
                2.2603248367949354e-06,
                5.422220909041528e-06,
                1.0677029973219343e-06,
                5.715006514176113e-07
            ],
            [
                0.9999985406241285,
                3.2887502415438413e-06,
                0.9999969105066595,
                0.9999975938985235,
                5.715003107767143e-07,
                0.9999974387174864,
                0.999998446502062,
                0.9999843104447184,
                9.422448185534261e-07,
                0.9999972735284336
            ],
            [
                0.9999985406243022,
                0.9999986290423036,
                0.999999789756609,
                0.9999996533674202,
                0.9999996310115921,
                0.999998005269329,
                0.9999992188517629,
                0.9999996743687422,
                0.9999990577555193,
                0.9999993916410364
            ],
            [
                0.9999989969856733,
                2.699577774585891e-07,
                0.9999998024947273,
                0.9999991684721714,
                0.9999996072136597,
                0.9999993916406736,
                0.9999986290431214,
                0.9999997761970784,
                0.9999969105066592,
                0.9999997300423191
            ],
            [
                2.69957906184239e-07,
                2.5612834320563895e-06,
                8.315277302857965e-07,
                1.2098656835224664e-06,
                1.2098659719788098e-06,
                4.785096776499213e-06,
                6.144175334468545e-06,
                3.726637951387472e-06,
                2.2603240284371276e-06,
                9.422445939054222e-07
            ],
            [
                0.9999993106386262,
                0.9999970976866364,
                0.9999938558224852,
                0.9999996533674617,
                0.9999980052707562,
                0.9999982396559487,
                0.9999989969861515,
                0.9999970976890595,
                0.9999957771650511,
                0.9999952149066543
            ],
            [
                0.9999978766210343,
                0.9999993524048933,
                0.9999983463100215,
                0.9999984465015055,
                0.9999993524052795,
                0.9999975938982371,
                0.9999975938970898,
                0.9999993916411812,
                0.9999985406236063,
                0.9999989969860318
            ],
            [
                0.9999998144608098,
                2.3823688159291947e-07,
                0.9999993524054338,
                0.999994906293788,
                6.144173869603344e-06,
                0.9999982396569981,
                0.9999988634358834,
                0.9999955048162896,
                0.9999981261250649,
                0.9999945777810533
            ],
            [
                0.9999997897567342,
                0.999998540623606,
                0.9999992661791947,
                0.9999997126314811,
                0.9999998802069445,
                0.9999998461826954,
                0.9999998642566543,
                0.9999997463981636,
                0.9999993916410361,
                0.9999988634365612
            ],
            [
                6.962256249885085e-06,
                0.9999991148429646,
                0.9999994631251242,
                9.422443692489024e-07,
                0.9999996743686647,
                0.999999730042094,
                0.9999997897566341,
                0.9999981261239473,
                0.9999970976869799,
                0.999999310639037
            ],
            [
                0.9999910603015856,
                0.9999993106390371,
                0.9999994956527122,
                0.9999992661790202,
                0.9999991148428591,
                0.9999994631251886,
                0.9999972735303819,
                0.9999998362622358,
                0.9999996072136125,
                0.999999776197105
            ],
            [
                0.9999998942830737,
                0.999999168471874,
                0.9999993916406734,
                0.9999938558261472,
                0.9999998461827138,
                0.9999934595635677,
                0.9999992188519493,
                0.9999998642566542,
                0.9999994956526521,
                0.9999998362623528
            ],
            [
                0.9999982396565784,
                0.9999989969860325,
                0.9999832985822482,
                1.5534975693979422e-06,
                0.999998932296876,
                0.9999967112509422,
                0.9999964991455907,
                0.999999057755519,
                0.9999985406234337,
                0.9999996533675032
            ],
            [
                0.9999998024946566,
                0.9999998144608983,
                0.9999997126314468,
                0.9999993524054338,
                0.9999996743686644,
                0.9999999067051166,
                0.9999989969855537,
                0.9999998555020307,
                0.9999993916407459,
                0.9999991684716754
            ],
            [
                0.9999993106389549,
                0.999998790134606,
                0.9999991684720723,
                0.9999997126315496,
                0.9999985406232582,
                0.9999996072137062,
                5.8291293348093234e-05,
                0.9999969105048193,
                0.9999989969856733,
                0.999997739675434
            ],
            [
                0.9999993524050479,
                0.9999987901337404,
                0.9999997897566589,
                0.999999746398073,
                0.9999996533672963,
                0.9999998257021006,
                0.9999996533672963,
                0.9999999176674848,
                0.999999789756684,
                0.999999825702163
            ],
            [
                0.9999977396757037,
                0.9999997126314126,
                0.9999988634365606,
                0.9999960330131418,
                0.9999991684719727,
                0.9999975938976611,
                0.9999996533672549,
                0.9999994956525919,
                0.9999998362623332,
                0.9999992661790196
            ],
            [
                0.9999997463980427,
                0.9999984465018765,
                0.9999985406243025,
                0.9999991148426481,
                0.9999983463108096,
                0.9999989322971309,
                0.9999989322975128,
                0.9999985406241289,
                0.999999352405357,
                0.9999996940978826
            ],
            [
                6.144176066943187e-06,
                1.5534971990169383e-06,
                2.561282210740037e-06,
                3.466326624336003e-07,
                3.7266388398585725e-06,
                9.422445939054222e-07,
                7.889265407327733e-06,
                4.450852111155216e-07,
                2.2603251062450327e-06,
                7.889265407327733e-06
            ],
            [
                0.999999730042287,
                0.9999988634360193,
                0.9999994956527726,
                0.9999983463106127,
                0.9999991684718739,
                1.8925143729575624e-05,
                0.9999996072138467,
                0.9999996072136127,
                8.315284241650899e-07,
                0.9999984465026169
            ],
            [
                1.994729008151319e-06,
                3.7266379514061143e-06,
                3.288749849529972e-06,
                3.466326624336003e-07,
                2.9023133691217714e-06,
                6.144177531811707e-06,
                4.785092783519724e-06,
                1.5534984953552536e-06,
                4.785095065232451e-06,
                4.2228319344021954e-06
            ],
            [
                0.9999989969861518,
                0.9999987901343173,
                0.999998932296749,
                0.9999969105051894,
                0.9999988634360197,
                0.9999988634358834,
                1.9947301970972664e-06,
                0.9999993524052022,
                0.9999988634357486,
                0.9999994284995538
            ],
            [
                0.9999987901341734,
                0.999999789756609,
                0.999999631011504,
                0.9999995262094987,
                0.999999607213753,
                0.9999987121049387,
                0.9999998874649051,
                0.9999998024945624,
                0.9999998024946566,
                0.9999991684716755
            ],
            [
                4.22283545819819e-06,
                1.4738983729535602e-05,
                2.7535700947920753e-05,
                2.1444953527476883e-05,
                8.939697369980456e-06,
                1.4738985486506781e-05,
                0.9999993524049708,
                1.6701421845361053e-05,
                2.260325106237323e-06,
                1.9947304348862686e-06
            ],
            [
                0.9999997300421584,
                0.9999975938982357,
                0.9999904837517206,
                0.9999990577555189,
                0.9999981261248418,
                0.9999960330136178,
                0.9999996743686645,
                0.9999988634361545,
                0.9999997463980126,
                0.9999996072138467
            ],
            [
                0.9999993524051253,
                0.9999982396559505,
                0.9999980052702843,
                0.9999992661790202,
                0.9999995549148424,
                0.9999995549150015,
                0.9999990577550697,
                0.9999996310115482,
                0.9999996533675031,
                0.9999997126314812
            ],
            [
                1.994729483729522e-06,
                1.209866260432471e-06,
                1.3709578605729614e-06,
                NaN,
                2.5612831267202583e-06,
                2.561281294760143e-06,
                1.5534975693979422e-06,
                1.6701415872385704e-05,
                8.315280276607289e-07,
                7.338212429582604e-07
            ],
            [
                0.99999916847227,
                0.9999995262095551,
                0.9999994631249322,
                0.9999997761971849,
                0.9999995262095552,
                0.9999993916409635,
                0.9999996310114159,
                0.9999986290426305,
                0.999999495652652,
                0.9999974387174871
            ],
            [
                3.05902263391829e-07,
                8.315278294114555e-07,
                3.05902336324494e-07,
                NaN,
                3.059022998581767e-07,
                3.466325797900508e-07,
                3.059022998581767e-07,
                2.902312331170226e-06,
                7.338207180898968e-07,
                5.043475885696228e-07
            ],
            [
                0.9999997126313784,
                9.422445939054222e-07,
                0.9999989969860323,
                1.3007133116909523e-05,
                3.288747889284851e-06,
                6.962253760024999e-06,
                5.4222183235249605e-06,
                1.670142980920999e-05,
                1.5534984953552536e-06,
                0.9999997463981335
            ],
            [
                1.0129988565084915e-05,
                7.889264466868659e-06,
                2.2603251062450327e-06,
                0.9999997463981031,
                0.9999995549150013,
                5.422217030781934e-06,
                0.9999991684719727,
                2.9023109472494878e-06,
                0.9999998362622943,
                2.9023116392097746e-06
            ],
            [
                1.7603440527286572e-06,
                0.9999994284992811,
                0.9999996533674204,
                0.9999990577550707,
                0.9999974387184031,
                0.9999997300421584,
                0.999999712631447,
                0.9999974387187089,
                0.9999988634360193,
                0.9999989969854343
            ],
            [
                NaN,
                0.9999999067050054,
                0.9999994284995533,
                0.9999999006881497,
                0.999999802494586,
                0.9999999273418962,
                0.9999999067049943,
                0.9999993916411085,
                0.9999999123575672,
                0.9999997463982241
            ],
            [
                0.9999993916406735,
                0.9999955048173534,
                0.9999993524053565,
                0.9999990577551822,
                0.9999991684721714,
                0.9999986290429578,
                0.9999996533673378,
                0.9999995818813767,
                0.9999994284992806,
                0.9999995262095552
            ],
            [
                0.9999978766207804,
                0.9999993106391192,
                0.9999990577550696,
                0.9999982396572077,
                0.999999266179195,
                0.9999967112505466,
                0.9999997761971849,
                0.9999990577552942,
                0.9999994284996895,
                0.9999997463982241
            ],
            [
                0.9999993106389546,
                0.9999994284996894,
                0.9999996533674204,
                0.9999991684721713,
                0.999999802494586,
                0.9999996940977367,
                3.9278610661902853e-07,
                0.999997593897949,
                0.9999994284993489,
                0.9999993524049704
            ],
            [
                0.9999990577554063,
                0.9999997126315154,
                0.9999992661787572,
                0.9999994284995531,
                0.999997876621793,
                0.9999980052707559,
                0.9999998144609425,
                0.9999942280772298,
                0.9999996743688586,
                0.9999989969854343
            ],
            [
                0.9999934595612292,
                0.9999972735300561,
                0.999998239656578,
                0.9999988634364254,
                3.4663262111182307e-07,
                0.9999993524048931,
                0.999999218851949,
                0.9999986290427946,
                0.9999987121052458,
                0.9999987901346062
            ],
            [
                0.9999987901338853,
                0.9999974387184062,
                1.994729721518893e-06,
                0.9999921107346329,
                0.999998446501876,
                2.3823690999290963e-07,
                0.9999978766217937,
                2.6995784182140636e-07,
                0.999998629042304,
                0.9999989322972583
            ],
            [
                0.9999998724809116,
                9.931189774187203e-08,
                0.9999972735290809,
                0.9999998144609203,
                0.9999994631248043,
                0.9999993916408183,
                0.9999998362623138,
                0.9999998362623724,
                0.9999980052695664,
                0.9999832985801673
            ],
            [
                0.9999994631251884,
                0.9999993106387084,
                0.9999992661792824,
                7.338212429582604e-07,
                0.9999995262094987,
                0.9999992188512974,
                0.9999991684718738,
                0.999999428499349,
                0.9999988634358836,
                0.9999930377445897
            ],
            [
                0.9999998802069159,
                0.9999992661786702,
                0.9999996940976638,
                0.9999992661787577,
                0.9999998362623528,
                0.999999712631344,
                0.999999674368781,
                0.999999653367255,
                0.999999814460876,
                0.9999978766217923
            ],
            [
                0.9999997126313441,
                0.9999995262092729,
                0.9999997126314127,
                0.9999989969857931,
                0.9999986290429574,
                0.9999996940978099,
                0.9999985406230847,
                0.9999992661786704,
                0.999999789756659,
                0.9999974387165705
            ],
            [
                4.785096206076165e-06,
                1.370957860576702e-06,
                3.927860597945825e-07,
                5.715003789046955e-07,
                1.5534977545886537e-06,
                2.561281294760143e-06,
                2.7535704231844484e-05,
                5.043472879525233e-07,
                4.450851580566494e-07,
                1.994730197090463e-06
            ],
            [
                0.9999996743687035,
                0.9999983463106126,
                0.9999962733598337,
                0.999998932296749,
                0.9999993106389546,
                0.9999972735307071,
                0.999999218851856,
                0.9999990577555191,
                0.9999993106388724,
                0.9999994956524718
            ],
            [
                0.9999987121047852,
                0.9999994631250603,
                0.9999994631249962,
                0.9999997761971849,
                0.9999992661787576,
                0.9999998024947272,
                0.9999985406243016,
                0.9999981261246181,
                0.9999997761972116,
                2.102434412875379e-07
            ],
            [
                1.067703124601679e-06,
                0.99999691050666,
                3.726639284144195e-06,
                4.785096206076165e-06,
                7.33821330437595e-07,
                2.561281294760143e-06,
                0.9999997300421584,
                2.2603245673443566e-06,
                5.043474683240344e-07,
                1.9947301970972664e-06
            ],
            [
                0.9999798543164187,
                0.9999995549150542,
                0.9999724643122437,
                0.9999998802068873,
                0.9999996533674202,
                0.9999986290426316,
                0.9999991148428591,
                NaN,
                0.9999999634651836,
                0.9999996940978096
            ],
            [
                7.338212429594283e-07,
                5.71500719545698e-07,
                6.475946438055299e-07,
                4.22283545819819e-06,
                8.939694172957213e-06,
                1.2098661162056318e-06,
                6.475949526020042e-07,
                3.4663249714612693e-07,
                1.5534971990169383e-06,
                5.715006514176113e-07
            ],
            [
                9.422447062294175e-07,
                0.9999877809225509,
                0.9999843104466033,
                1.3709567165617364e-06,
                5.04347287955046e-07,
                9.422450432030903e-07,
                1.012998977264307e-05,
                0.9999967112509379,
                0.999997273530058,
                0.999982221454541
            ],
            [
                0.9999989322973851,
                0.9999962733611647,
                0.9999993106387904,
                0.9999991684718738,
                0.9999992188517631,
                0.9999996743687034,
                0.9999998144608098,
                0.9999990577551819,
                0.9999998802068873,
                0.9999987121044781
            ],
            [
                0.9999991148426481,
                0.9999998257022045,
                0.00010889696121576468,
                0.9999996310115918,
                0.9999997617630616,
                0.9999996072139403,
                0.999999581881277,
                0.9999997463981939,
                0.9999999226557131,
                0.999999653367379
            ],
            [
                0.9999998461827322,
                0.99999911484307,
                0.9999997617631186,
                0.9999910602994488,
                0.9999983463098239,
                1.1253525596174225e-07,
                3.059021175261338e-07,
                0.999999266178845,
                2.5612834320563895e-06,
                0.9999985406236063
            ],
            [
                1.994729483723626e-06,
                2.699576809143613e-07,
                1.0677027427624903e-06,
                1.5534979397790343e-06,
                1.994729721518893e-06,
                4.450848927658745e-07,
                1.5534984953552536e-06,
                5.043472278322555e-07,
                4.4508505193932864e-07,
                3.059022998581767e-07
            ]
        ]
    },
    {
        "q_id": "9828_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.3823693839325527e-07,
                2.5612831267202583e-06,
                7.734428685047173e-08,
                2.1024329090929374e-07,
                6.475950298021765e-07,
                0.9999910603026364,
                2.2603234895372223e-06,
                3.927863407379485e-07,
                3.9278629391427843e-07,
                4.450848927658745e-07
            ],
            [
                1.3709572068522336e-06,
                1.0677028700363782e-06,
                7.889262585886274e-06,
                5.715007195431641e-07,
                6.47594798194325e-07,
                2.2603251062450327e-06,
                6.1441746020359e-06,
                3.726638839878908e-06,
                3.288748281329893e-06,
                2.9023133690980155e-06
            ],
            [
                3.059022998576899e-07,
                2.1024329090929374e-07,
                8.764247451307293e-08,
                1.8553903548231313e-07,
                9.93118503859575e-08,
                7.338212429582604e-07,
                8.764255809528314e-08,
                4.4508494582314646e-07,
                7.734423152941018e-08,
                2.3823685319244518e-07
            ],
            [
                7.734415776836702e-08,
                7.338211554783522e-07,
                7.734418542875216e-08,
                7.734421308914719e-08,
                5.315780535989972e-08,
                0.9999885212346231,
                1.1253518888464745e-07,
                1.6373764721072816e-07,
                0.9999955048200321,
                0.9999996940977002
            ],
            [
                5.715005151606823e-07,
                8.764245361752286e-08,
                2.102434412875379e-07,
                6.023569884718319e-08,
                2.699576809143613e-07,
                0.9998766054549523,
                1.4449805540740185e-07,
                1.6373768624837685e-07,
                0.9999921107383591,
                4.450848927650143e-07
            ],
            [
                2.102434412871794e-07,
                1.275190276859705e-07,
                1.4449795205429202e-07,
                0.9993736659073271,
                4.139939521459479e-08,
                1.6373766672973748e-07,
                2.3823685319244518e-07,
                1.8553919030776337e-07,
                3.466325797888292e-07,
                3.4663266243308805e-07
            ],
            [
                5.043474081993875e-07,
                0.9999994284996894,
                1.8553905760062447e-07,
                1.9947292459347367e-06,
                2.1024334103352274e-07,
                5.715005832872586e-07,
                8.315281267861397e-07,
                8.764244316973974e-08,
                1.2098662604247682e-06,
                0.9999987121043241
            ],
            [
                0.999990483743783,
                1.1253506814797596e-07,
                1.0677032518748838e-06,
                0.9999994631251242,
                1.0,
                1.6373770576776313e-07,
                3.9278610661902853e-07,
                5.043473480766399e-07,
                1.2751905808881762e-07,
                0.9999998942829602
            ],
            [
                0.9999990577556311,
                0.9999646437493915,
                0.9999995818812272,
                0.9999999067051388,
                0.9999997300421904,
                0.9999990577551819,
                0.9999251537998894,
                0.9999970976869785,
                0.9999970976883624,
                0.9999999358793409
            ],
            [
                4.4508505193932864e-07,
                8.315278294114555e-07,
                2.2603251062450327e-06,
                1.5534977545886537e-06,
                5.315781803390236e-08,
                1.5534977545886537e-06,
                1.2098652508424818e-06,
                2.260324567337161e-06,
                7.338208930460318e-07,
                1.9947304348862686e-06
            ],
            [
                9.422448185534261e-07,
                1.5534981249697903e-06,
                1.2098661162023305e-06,
                1.2098656835224664e-06,
                3.927862002663297e-07,
                1.7603434231777837e-06,
                1.8553907971855875e-07,
                2.1024339116134898e-07,
                3.059022998576899e-07,
                3.1201922533564516e-05
            ],
            [
                0.9999810748427593,
                2.2603242978871282e-06,
                1.7603434231833873e-06,
                1.760342793638743e-06,
                2.6995784182140636e-07,
                2.902312677150514e-06,
                2.1024336609874897e-07,
                1.3709576971463352e-06,
                3.466327037553825e-07,
                7.734414854823498e-08
            ],
            [
                8.764249540862797e-08,
                1.0677026154774503e-06,
                1.209866260432471e-06,
                6.825602910433871e-08,
                3.059021539909339e-07,
                1.8553916819032217e-07,
                4.450849458218309e-07,
                2.38237023590304e-07,
                0.999996910506659,
                1.855391239544352e-07
            ],
            [
                2.90231233114251e-06,
                1.3709570434178922e-06,
                1.209865683518615e-06,
                8.31528424162821e-07,
                3.726638839833152e-06,
                9.422443692555439e-07,
                1.5534971990126997e-06,
                2.561283432035425e-06,
                1.067703379154416e-06,
                1.994730672668496e-06
            ],
            [
                2.6995784182140636e-07,
                7.73442776300517e-08,
                4.4508510499737865e-07,
                1.6373766672973748e-07,
                2.1024341622426268e-07,
                0.9999417087489033,
                1.6373766672973748e-07,
                2.1024341622426268e-07,
                0.9999996310114159,
                6.475948753991907e-07
            ],
            [
                0.9999995262092163,
                1.2751899728286965e-07,
                1.0677027427624903e-06,
                0.9999339478557259,
                7.734416698849138e-08,
                2.382369667929001e-07,
                9.422450431989127e-07,
                1.4449798650551755e-07,
                3.059022269250683e-07,
                3.0590237279032884e-07
            ],
            [
                0.9999980052702792,
                3.059022998576899e-07,
                2.1024331597262577e-07,
                8.764247451307293e-08,
                9.931190958076104e-08,
                9.931190958076104e-08,
                1.8553907971855875e-07,
                7.338213304363436e-07,
                1.1253516205489029e-07,
                1.8553907971855875e-07
            ],
            [
                5.4222176771176554e-06,
                2.69957906184239e-07,
                1.4449798650551755e-07,
                3.927862470899887e-07,
                0.9999982396569971,
                4.139934092743992e-08,
                2.6995774527718623e-07,
                7.338208930460318e-07,
                1.8553912395262116e-07,
                1.4449795205429202e-07
            ],
            [
                0.9998911030529425,
                1.4449805540763184e-07,
                2.382368531929327e-07,
                0.9999980052700412,
                2.102434162245973e-07,
                1.2751908849167202e-07,
                9.931195693628605e-08,
                0.9999885212346264,
                8.764249540862797e-08,
                2.699577774585891e-07
            ],
            [
                3.466327450756327e-07,
                1.8553903548231313e-07,
                5.315784971839039e-08,
                1.6373766672973748e-07,
                2.6995784182140636e-07,
                1.1253510839355284e-07,
                1.1253514863968147e-07,
                1.637377643243723e-07,
                1.4449798650569826e-07,
                1.4449805540740185e-07
            ],
            [
                1.1253513522447425e-07,
                2.5612812947508257e-06,
                2.102434412871794e-07,
                0.9999984465020608,
                3.4663266243308805e-07,
                2.3823690999290963e-07,
                5.043476486915964e-07,
                1.637377448057981e-07,
                6.60521604406802e-05,
                3.9278610661902853e-07
            ],
            [
                5.043476486915964e-07,
                1.1253510839355284e-07,
                3.46632497145457e-07,
                0.9999885212305261,
                1.0,
                2.1024336609843824e-07,
                1.4449805540740185e-07,
                6.825601283086733e-08,
                3.0590215399183813e-07,
                7.734424996967756e-08
            ],
            [
                6.023569884718319e-08,
                2.3823696679230424e-07,
                1.1253513522447425e-07,
                3.927862002663297e-07,
                3.9278615344178325e-07,
                3.059021175255426e-07,
                1.125352291309328e-07,
                0.9999999358793867,
                1.2098656835224664e-06,
                6.475947210031623e-07
            ],
            [
                0.9999546021152665,
                1.444980726324838e-07,
                2.1024329090929374e-07,
                7.734414854792722e-08,
                0.999972464315538,
                2.1024326584582131e-07,
                1.8553916819032217e-07,
                1.670142582682936e-05,
                1.8553910183548312e-07,
                1.4449798650476187e-07
            ],
            [
                1.8553907971855875e-07,
                0.9999994631248682,
                2.1024326584639497e-07,
                8.764245361752286e-08,
                1.444979692797559e-07,
                2.102433159721477e-07,
                0.9999785550413892,
                9.931193325852072e-08,
                1.2751905808881762e-07,
                3.059023363231725e-07
            ],
            [
                3.466327450756327e-07,
                0.9999970976890542,
                0.9999983463100202,
                5.315783704433184e-08,
                0.9999798543116193,
                8.315279285351409e-07,
                6.023574911170301e-08,
                1.637377448057981e-07,
                5.715003789046955e-07,
                2.6995774527657245e-07
            ],
            [
                1.994729245917502e-06,
                2.699577774585891e-07,
                6.475945666051092e-07,
                1.275190124842887e-07,
                0.9999925887192517,
                3.9278610661902853e-07,
                3.466327037548308e-07,
                1.8553907971855875e-07,
                1.3709572068522336e-06,
                3.9278610661902853e-07
            ],
            [
                9.422449308716635e-07,
                5.043476486915964e-07,
                4.785096206047877e-06,
                5.043476486915964e-07,
                0.9999546021151707,
                0.9999599363030796,
                8.315277302857965e-07,
                4.222832941193893e-06,
                0.9999977396748947,
                7.734418542875216e-08
            ],
            [
                8.315281267861397e-07,
                2.699578740032504e-07,
                4.450850519403407e-07,
                1.2751901248454963e-07,
                0.9999989969861514,
                1.1478764021029928e-05,
                1.444979692800516e-07,
                3.927862002663297e-07,
                0.9999994631247402,
                1.27519088491875e-07
            ],
            [
                5.422220909009474e-06,
                4.450852111148132e-07,
                4.450849988811838e-07,
                9.931192141912081e-08,
                1.855391681906175e-07,
                3.9278605979534166e-07,
                0.9999991148428589,
                0.9999962733598291,
                5.043472278299047e-07,
                9.931190958076104e-08
            ],
            [
                2.561282210740037e-06,
                4.222835458175145e-06,
                1.9947301970972664e-06,
                4.222832437798974e-06,
                1.6373764721072816e-07,
                3.059022998576899e-07,
                3.7266401726173067e-06,
                4.2228319344021954e-06,
                2.6995784182140636e-07,
                1.3709567165579959e-06
            ],
            [
                0.999925153764171,
                0.9999998874648917,
                7.734421308914719e-08,
                0.9999756997477143,
                3.466325384661554e-07,
                7.338209805224048e-07,
                0.9999910603037089,
                4.785093353940187e-06,
                5.04347528446051e-07,
                0.9999925887210248
            ],
            [
                0.9999869928684486,
                7.734423152895294e-08,
                0.9999957771665579,
                0.9999987121052454,
                0.9999989322966212,
                0.9999994956525318,
                0.9999964991460055,
                0.9999980052707548,
                0.9999996072136593,
                0.9999988634361542
            ],
            [
                7.734424996967756e-08,
                1.444979692797559e-07,
                8.764243272157922e-08,
                1.4449805540740185e-07,
                5.043472879540142e-07,
                2.102434412871794e-07,
                9.422443692574719e-07,
                1.6373770576776313e-07,
                0.9999546021207438,
                1.855391239544352e-07
            ],
            [
                7.338213304363436e-07,
                1.8553916819032217e-07,
                1.3709568799919866e-06,
                1.7603425837903113e-06,
                5.04347468323289e-07,
                0.9999982396567872,
                2.2603234895372223e-06,
                5.043475885674441e-07,
                2.5612812947508257e-06,
                0.9999852610127736
            ],
            [
                3.46632497145457e-07,
                1.8553916819032217e-07,
                1.2098662604291696e-06,
                5.71500515159253e-07,
                3.059022998576899e-07,
                4.450848927650143e-07,
                8.315278294114555e-07,
                0.999986992871545,
                6.475945666051092e-07,
                1.8553907971855875e-07
            ],
            [
                4.4508494582314646e-07,
                0.9999546021098557,
                1.6373776432509826e-07,
                2.699577774585891e-07,
                1.6373762769138607e-07,
                2.6995784182140636e-07,
                0.9999983463108095,
                9.931202796957073e-08,
                0.9999810748450194,
                2.6995784182140636e-07
            ],
            [
                3.466326211105621e-07,
                6.825598028392069e-08,
                7.734424996967756e-08,
                1.4449795205389775e-07,
                6.475950297993789e-07,
                0.9999998942830233,
                2.102434412871794e-07,
                5.043472278299047e-07,
                3.059022998576899e-07,
                8.764249540810985e-08
            ],
            [
                0.999995214903798,
                1.0129987357407137e-05,
                1.4449805540740185e-07,
                7.338207180898968e-07,
                8.764245361752286e-08,
                1.637377448057981e-07,
                0.9999151889591094,
                1.855391239544352e-07,
                3.927860597945825e-07,
                1.8553907971855875e-07
            ],
            [
                1.2751899728286965e-07,
                0.9999599362888338,
                1.8553907971855875e-07,
                1.6373762769138607e-07,
                1.4449798650476187e-07,
                0.9999998144609646,
                1.6373766672973748e-07,
                5.043476486915964e-07,
                0.9999998362622747,
                0.9999993524050476
            ],
            [
                9.931198061405701e-08,
                5.715002426475718e-07,
                9.931199245292204e-08,
                3.466325797896173e-07,
                1.27519088491875e-07,
                7.734416698849138e-08,
                3.059022269250683e-07,
                5.3157830707696514e-08,
                5.04347468323289e-07,
                1.2751904288739315e-07
            ],
            [
                3.466327037539638e-07,
                8.764255809528314e-08,
                1.8553907971855875e-07,
                1.6373770576776313e-07,
                1.4449805540740185e-07,
                5.715005832886879e-07,
                9.931193325852072e-08,
                3.927862002663297e-07,
                5.043476486902204e-07,
                1.444980209564556e-07
            ],
            [
                2.382368531929327e-07,
                8.31527928532683e-07,
                0.9999646437493537,
                1.2751901248454963e-07,
                1.4449798650551755e-07,
                0.9999938558275997,
                3.0590237279032884e-07,
                2.6995774527718623e-07,
                0.9999952149055077,
                0.9999921107374196
            ],
            [
                1.1253512180925583e-07,
                3.466326211113502e-07,
                0.9999994631250603,
                3.466327450765785e-07,
                2.902312331170226e-06,
                0.9999785550439653,
                2.102434412871794e-07,
                8.764247451307293e-08,
                2.6995771309523475e-07,
                5.04347468323289e-07
            ],
            [
                4.450852111148132e-07,
                0.9999960330140888,
                0.9999987121049384,
                0.9998766054258917,
                1.4449805540651476e-07,
                0.9999934595619995,
                4.450848927658745e-07,
                2.3823693839057394e-07,
                1.637377448057981e-07,
                1.8553916819032217e-07
            ],
            [
                2.382369667929001e-07,
                2.699576809143613e-07,
                0.9999997463980427,
                4.4508494582405734e-07,
                0.9999945777803863,
                3.05902336324494e-07,
                2.3823702359290413e-07,
                0.999998446502246,
                3.927862470899887e-07,
                0.9999546021206696
            ],
            [
                1.1253521571574156e-07,
                2.382369667929001e-07,
                2.3823702359290413e-07,
                0.9999687980812584,
                1.444980209564556e-07,
                6.825608606148807e-08,
                3.0590237279032884e-07,
                3.653479031523475e-08,
                3.466325797888292e-07,
                1.4449805540700758e-07
            ],
            [
                0.9999992661792821,
                2.10243290909724e-07,
                3.059022269250683e-07,
                0.9999810748562998,
                0.9999998942829351,
                0.9999996072136593,
                0.9999930377420956,
                1.2751899728286965e-07,
                9.931195693628605e-08,
                0.9999999468421756
            ],
            [
                1.444980726324838e-07,
                1.4449805540740185e-07,
                2.3823702359290413e-07,
                7.734414854792722e-08,
                7.734419464850171e-08,
                3.9278634073732336e-07,
                2.382369667929001e-07,
                2.1024339116082313e-07,
                5.715003789033962e-07,
                7.73441946488886e-08
            ],
            [
                7.734416698849138e-08,
                4.450848927637999e-07,
                1.855391239544352e-07,
                6.475945666033422e-07,
                2.382369667929001e-07,
                3.0590215399183813e-07,
                0.9999151889285838,
                1.637377448057981e-07,
                3.9278624708775595e-07,
                1.6373762769138607e-07
            ],
            [
                2.10243290909724e-07,
                1.1253513522447425e-07,
                7.73442776300517e-08,
                8.764245361752286e-08,
                3.059021904580685e-07,
                1.855391018347238e-07,
                4.450852641717689e-07,
                2.3823696679230424e-07,
                2.6995774527718623e-07,
                2.382368247909451e-07
            ],
            [
                0.9999993106386261,
                3.4663249714325014e-07,
                1.855391018347238e-07,
                2.1024336609843824e-07,
                0.999999391641181,
                0.9999981261243943,
                1.444980209564556e-07,
                3.059023363231725e-07,
                1.3709572068478697e-06,
                1.0677032518748838e-06
            ],
            [
                9.931187406410953e-08,
                3.9278610661902853e-07,
                3.059022269250683e-07,
                1.5534975693979422e-06,
                7.338213304363436e-07,
                5.043476486915964e-07,
                1.444980209564556e-07,
                2.10243290909724e-07,
                0.9999977396759725,
                0.9999989322966212
            ],
            [
                0.9999974387171798,
                0.9999998257021214,
                0.9999952149066499,
                1.6373764721072816e-07,
                5.043476486924565e-07,
                0.9999952149037965,
                3.0590226339061185e-07,
                2.1024341622426268e-07,
                8.315282259138311e-07,
                4.4508505193791187e-07
            ],
            [
                2.699577774585891e-07,
                2.1024331597262577e-07,
                1.5534975693979422e-06,
                3.0590237279032884e-07,
                2.6995774527657245e-07,
                1.444979692800516e-07,
                5.043476486915964e-07,
                2.699577774585891e-07,
                2.1024326584680133e-07,
                1.444980209564556e-07
            ],
            [
                5.715002426486762e-07,
                1.8553905760062447e-07,
                3.466327450765785e-07,
                0.9999999500627738,
                0.9999999176675142,
                0.9999969105051857,
                3.4663266243111764e-07,
                3.288749457469787e-06,
                1.855391681906175e-07,
                0.9999810748540496
            ],
            [
                4.450852641717689e-07,
                2.102434412871794e-07,
                2.382369667929001e-07,
                1.6373776432509826e-07,
                1.4449805540740185e-07,
                0.9999967112509364,
                0.9999930377454158,
                9.931189774187203e-08,
                0.9999756997477279,
                1.4449795205429202e-07
            ],
            [
                2.699577774585891e-07,
                2.1024326584582131e-07,
                1.637377643243723e-07,
                2.5612828213690224e-06,
                0.9999989969857924,
                1.6373766672973748e-07,
                5.04347408197782e-07,
                4.4508494582314646e-07,
                3.059021175261338e-07,
                9.931190958076104e-08
            ],
            [
                0.9999983463104144,
                2.1024339116082313e-07,
                5.71500719545698e-07,
                1.8553916819032217e-07,
                1.2751899728286965e-07,
                1.5534984953552536e-06,
                0.9999996072138935,
                3.466326211105621e-07,
                9.931202796957073e-08,
                0.999998932297385
            ],
            [
                0.9999999226557869,
                1.6373766672973748e-07,
                1.1253516205489029e-07,
                0.9999945777790955,
                3.9278610661902853e-07,
                1.6373776432509826e-07,
                3.927862939113312e-07,
                6.825600469412533e-08,
                1.8553907971855875e-07,
                0.9999991684717744
            ],
            [
                3.9278615344178325e-07,
                1.637377643243723e-07,
                5.715003789033962e-07,
                2.561282210740037e-06,
                2.3823690999160957e-07,
                9.422450431989127e-07,
                5.043472879540142e-07,
                3.9278634073625165e-07,
                2.1024339116082313e-07,
                2.5612819054028872e-06
            ],
            [
                1.4449795205429202e-07,
                6.023578501491997e-08,
                1.4449798650551755e-07,
                3.059021175261338e-07,
                1.8553916819032217e-07,
                9.422448185534261e-07,
                8.764247451307293e-08,
                1.8553903548231313e-07,
                8.764245361752286e-08,
                3.927862470899887e-07
            ],
            [
                0.9999962733611614,
                0.9999987121043247,
                0.9999998024946095,
                0.9999992188516699,
                0.999997593896514,
                0.9999942280772269,
                0.9999984465022467,
                0.9999991148429646,
                0.9999995818813269,
                0.9999998144608098
            ],
            [
                0.9999986290423034,
                0.9999998555020135,
                0.9999998802069873,
                0.9999988634364252,
                0.9999998642567189,
                0.9999339478715392,
                0.9999991684720719,
                0.9999969105044493,
                0.9999998461826222,
                0.9999996940978096
            ],
            [
                6.144176066901277e-06,
                1.637376862489725e-07,
                3.4663274507713016e-07,
                8.315277302857965e-07,
                1.3709567165617364e-06,
                3.9278610661902853e-07,
                2.699578096403948e-07,
                1.2098659719788098e-06,
                9.422448185534261e-07,
                4.4508494582314646e-07
            ],
            [
                1.067703124601679e-06,
                1.4449805540740185e-07,
                8.315283250371857e-07,
                3.466326211113502e-07,
                9.931195693628605e-08,
                2.3823685319244518e-07,
                4.450852111148132e-07,
                2.3823682479292225e-07,
                2.1024331597262577e-07,
                4.4508505193932864e-07
            ],
            [
                0.999993855823204,
                0.9999151889185779,
                0.9999869928761931,
                0.9999869928699945,
                4.4508494582405734e-07,
                0.9999485577802837,
                1.1253521571574156e-07,
                0.9999687980849645,
                0.9999989322967484,
                1.1253521571574156e-07
            ],
            [
                2.5612825160096693e-06,
                0.999954602142343,
                1.2751905808881762e-07,
                2.699576809143613e-07,
                2.1024334103505245e-07,
                0.9999687980738688,
                1.4449800373065699e-07,
                9.422443692555439e-07,
                2.3823702359290413e-07,
                1.2751899728311609e-07
            ],
            [
                3.466326211113502e-07,
                8.764249540862797e-08,
                1.4449798650551755e-07,
                2.6995784182140636e-07,
                4.450850519403407e-07,
                1.8925143729575624e-05,
                7.734423152941018e-08,
                3.9278634073732336e-07,
                2.1024339116168358e-07,
                0.9999997300423191
            ],
            [
                2.1024339116134898e-07,
                1.637377448057981e-07,
                2.3823702359290413e-07,
                5.715002426460124e-07,
                9.93118503859575e-08,
                0.9999974387168749,
                1.444979692800516e-07,
                8.764245361752286e-08,
                6.475950297993789e-07,
                4.450849988798682e-07
            ],
            [
                0.9999869928699925,
                1.275190124842887e-07,
                2.6995784182140636e-07,
                1.8553919030776337e-07,
                3.466325797888292e-07,
                1.8553903548231313e-07,
                1.1253518888531272e-07,
                3.4663253846718004e-07,
                8.764241182605906e-08,
                3.9278615344178325e-07
            ],
            [
                3.466325797888292e-07,
                2.6995774527718623e-07,
                5.04347528446051e-07,
                8.764245361752286e-08,
                0.9999921107383583,
                5.715003107755449e-07,
                0.9999984465015053,
                3.927862470899887e-07,
                3.059021175261338e-07,
                4.450852111148132e-07
            ],
            [
                0.9999985406232577,
                9.931190958076104e-08,
                1.4449795205429202e-07,
                6.023572038882162e-08,
                1.4449805540740185e-07,
                6.825604537781398e-08,
                1.2751899728286965e-07,
                0.9999756997506227,
                1.1253510839355284e-07,
                1.6373770576776313e-07
            ],
            [
                0.99999345956044,
                1.8553910183607374e-07,
                1.444980209564556e-07,
                3.466327037548308e-07,
                1.2751910369275402e-07,
                2.3823685319244518e-07,
                2.1024341622426268e-07,
                1.2751905808881762e-07,
                1.4449802095609418e-07,
                3.927862002654366e-07
            ],
            [
                9.422445939054222e-07,
                1.1478769494396542e-05,
                1.8553905760062447e-07,
                1.5534981249697903e-06,
                3.2887502415767434e-06,
                5.04347287955046e-07,
                6.475950298011458e-07,
                3.726639284144195e-06,
                1.855391239539711e-07,
                6.475950298011458e-07
            ],
            [
                1.1253513522447425e-07,
                1.8553916819032217e-07,
                0.9999994284997575,
                3.927862470899887e-07,
                2.1024339116134898e-07,
                1.275190276859705e-07,
                7.734423152941018e-08,
                1.855391239539711e-07,
                6.825598842065202e-08,
                0.9999687980924009
            ],
            [
                1.444980209564556e-07,
                4.1399375473868e-08,
                1.2751904288710323e-07,
                3.0590222692437275e-07,
                1.27519088491875e-07,
                8.764247451307293e-08,
                2.1024339116134898e-07,
                2.3823702359290413e-07,
                2.6995774527718623e-07,
                0.9998911031042987
            ],
            [
                0.989013058745722,
                3.466325384661554e-07,
                2.561281600076256e-06,
                1.5534983101644536e-06,
                6.962253760024999e-06,
                8.315278294114555e-07,
                4.785096776499213e-06,
                2.699576809143613e-07,
                1.209866260432471e-06,
                1.1478765389368729e-05
            ],
            [
                9.931189774187203e-08,
                2.6995784182140636e-07,
                1.6373764721072816e-07,
                3.2241850958880614e-08,
                1.7603438428800754e-06,
                0.9999810748495427,
                1.553497754583709e-06,
                3.4663249714612693e-07,
                5.043476486915964e-07,
                0.9999998802069587
            ],
            [
                5.715005832872586e-07,
                0.9999925887219021,
                1.8553916819032217e-07,
                2.3823690999290963e-07,
                3.466327037548308e-07,
                1.4449805540740185e-07,
                0.9999934595651194,
                5.043476486902204e-07,
                1.1253520230052635e-07,
                8.764244316973974e-08
            ],
            [
                3.0590237279032884e-07,
                3.9278634073732336e-07,
                1.2751905808881762e-07,
                2.1024341622426268e-07,
                9.931201612997889e-08,
                3.05902190458764e-07,
                1.0677027427600627e-06,
                3.9278615344178325e-07,
                5.043474081993875e-07,
                9.422443692555439e-07
            ],
            [
                1.1253514863909295e-07,
                2.1024339116082313e-07,
                1.855390354818069e-07,
                8.315281267861397e-07,
                6.475945666051092e-07,
                2.3823693839154895e-07,
                1.4449798650551755e-07,
                5.715005832886879e-07,
                1.637377057673536e-07,
                2.102433410343832e-07
            ],
            [
                0.9999984465015054,
                0.9999987121047846,
                0.9999993524052792,
                3.466327037539638e-07,
                0.9999910602994395,
                2.6995768091383957e-07,
                0.9999994284994851,
                2.3823685319244518e-07,
                4.450852111148132e-07,
                7.73441946488886e-08
            ],
            [
                8.764245361752286e-08,
                1.4449807263287805e-07,
                0.9999977396765107,
                2.5612812947508257e-06,
                1.1253513522447425e-07,
                3.059021539909339e-07,
                1.1253512180925583e-07,
                0.9999546021368835,
                1.444979692797559e-07,
                1.1253514863968147e-07
            ],
            [
                4.139936560330104e-08,
                2.1024331597262577e-07,
                1.855391460719133e-07,
                3.9278615344178325e-07,
                1.6373766672973748e-07,
                1.444979692800516e-07,
                1.125352291309328e-07,
                1.6373770576776313e-07,
                3.466326211113502e-07,
                9.931188590255539e-08
            ],
            [
                2.69957906184239e-07,
                5.04347287955046e-07,
                1.4449805540740185e-07,
                1.1253508156363576e-07,
                3.059021175261338e-07,
                1.6373776432509826e-07,
                1.3709576971425944e-06,
                0.9999934595612234,
                3.059021175261338e-07,
                3.05902190458764e-07
            ],
            [
                0.999992110737421,
                0.9999962733620512,
                0.9999990577557434,
                0.9999982396567876,
                0.9999981261250638,
                0.9999991684722699,
                0.9999969105044489,
                0.9999970976876703,
                0.9999981261243942,
                0.9999885212291598
            ],
            [
                7.889262585886274e-06,
                1.3709572068522336e-06,
                0.9999996743688586,
                2.2603242978871282e-06,
                0.9999962733602732,
                0.9999998642566381,
                0.999999946842163,
                0.99999926617867,
                0.9999997761970247,
                4.785093353940187e-06
            ],
            [
                1.125352291309328e-07,
                1.6373764721072816e-07,
                3.7266410611296085e-06,
                2.3823688159291947e-07,
                1.6373764721072816e-07,
                2.699578096393206e-07,
                0.999968798073793,
                3.927860597945825e-07,
                1.8553919030858602e-07,
                1.6373770576776313e-07
            ],
            [
                3.9278634073625165e-07,
                3.059022269250683e-07,
                8.764245361752286e-08,
                7.734424996967756e-08,
                0.9999964991443354,
                1.4449798650551755e-07,
                1.637377057673536e-07,
                1.8553919030858602e-07,
                9.422447062294175e-07,
                1.0677027427624903e-06
            ],
            [
                0.00013982202416902017,
                2.1024336609724313e-07,
                3.927862939126708e-07,
                4.450852641717689e-07,
                8.764245361752286e-08,
                4.450851580555361e-07,
                0.9999993524050477,
                9.931193325852072e-08,
                1.2751908849167202e-07,
                3.466327037548308e-07
            ],
            [
                2.2603234895053587e-06,
                1.067703379154416e-06,
                0.9999832985761833,
                2.6995777745711594e-07,
                4.450852641717689e-07,
                5.043472879540142e-07,
                1.637377448057981e-07,
                9.422445939002803e-07,
                5.043476486902204e-07,
                6.47594566597747e-07
            ],
            [
                0.9999994956524717,
                0.9999898700102373,
                2.561281905390075e-06,
                2.6995784182073116e-07,
                3.927862470890063e-07,
                7.734424996967756e-08,
                1.2751899728286965e-07,
                5.04347528446051e-07,
                2.382369667929001e-07,
                1.637377448057981e-07
            ],
            [
                3.05902190458764e-07,
                1.3709572068522336e-06,
                1.8553907971855875e-07,
                0.9999977396762422,
                0.9999852610180403,
                3.466327450765785e-07,
                2.3823688159291947e-07,
                3.4663266243308805e-07,
                0.9999975938965144,
                8.315284241650899e-07
            ],
            [
                7.734423152941018e-08,
                1.2751899728311609e-07,
                1.4449800373065699e-07,
                2.1024341622426268e-07,
                3.927860597945825e-07,
                1.8553905760024476e-07,
                2.1024344128584085e-07,
                0.9999952149072192,
                0.9999952149043679,
                5.715007195447234e-07
            ],
            [
                0.9999998555019447,
                0.9999546021259818,
                0.9999982396561575,
                5.04347468323289e-07,
                1.0677032518814388e-06,
                9.931199245292204e-08,
                1.7603438428800754e-06,
                0.9999910603015711,
                0.9998415638038571,
                1.8553905760062447e-07
            ],
            [
                9.931190958076104e-08,
                2.6995790618469934e-07,
                7.338208055664991e-07,
                1.1253514863968147e-07,
                1.067703124601679e-06,
                2.6995771309523475e-07,
                3.653479031523475e-08,
                1.2751908849167202e-07,
                3.927862470899887e-07,
                1.444980726324838e-07
            ],
            [
                2.6995768091310296e-07,
                0.9999998724809571,
                1.275190580884987e-07,
                1.6373764721039308e-07,
                9.931193325852072e-08,
                1.8553910183607374e-07,
                8.31528424162821e-07,
                6.02357419307143e-08,
                0.9999916019239712,
                1.4449805540740185e-07
            ],
            [
                2.69957906184239e-07,
                1.2751901248454963e-07,
                0.9999921107336578,
                9.931190958076104e-08,
                1.855391239544352e-07,
                8.764244316973974e-08,
                1.8553903548231313e-07,
                3.4663249714612693e-07,
                1.2751908849167202e-07,
                2.382369951932796e-07
            ],
            [
                4.1399365603508136e-08,
                7.73441946488886e-08,
                1.4449807263312446e-07,
                3.4663266243308805e-07,
                3.466326624336003e-07,
                1.2751908849167202e-07,
                1.855391239544352e-07,
                1.4449805540763184e-07,
                3.9278634073732336e-07,
                1.1253509497835043e-07
            ],
            [
                7.734418542875216e-08,
                2.10243290909724e-07,
                1.6373762769138607e-07,
                1.8553919030858602e-07,
                0.9999989322975121,
                9.931192141912081e-08,
                0.9999992188517626,
                1.8553903548231313e-07,
                3.46632497145457e-07,
                1.4449798650551755e-07
            ],
            [
                0.999996273359386,
                0.9999995818810776,
                0.9999987901341728,
                3.9278634073732336e-07,
                0.9999986290427937,
                0.9999993524048933,
                0.9999983463100205,
                0.9999999586006443,
                0.9999994284993488,
                0.9999985406236054
            ],
            [
                2.1024336609843824e-07,
                1.444980209564556e-07,
                2.1024341622426268e-07,
                1.275190276859705e-07,
                1.7603434231777837e-06,
                2.382369667929001e-07,
                7.338208055664991e-07,
                9.931190958076104e-08,
                1.1253526937656726e-07,
                2.3823696679230424e-07
            ],
            [
                4.4508494582405734e-07,
                0.999986992871545,
                1.2098659719788098e-06,
                3.927860597945825e-07,
                9.422442569315887e-07,
                9.422443692555439e-07,
                4.222834954778007e-06,
                6.144173869603344e-06,
                2.69957906184239e-07,
                1.0677028700422047e-06
            ],
            [
                9.931193325797878e-08,
                6.825608606148807e-08,
                3.466326211105621e-07,
                0.9999983463104145,
                2.102433410343832e-07,
                0.9999997761971048,
                2.382369667929001e-07,
                1.855391239544352e-07,
                1.275190580884987e-07,
                1.444980209564556e-07
            ],
            [
                0.9999998362623138,
                0.999997438717791,
                0.999999554914789,
                0.9999998874649184,
                0.9999998802069302,
                0.9999997463980125,
                0.9999994956525319,
                0.999999802494633,
                0.9999981261246172,
                0.9999998362623528
            ],
            [
                0.9999992188513903,
                3.927861066170637e-07,
                2.3823685319244518e-07,
                0.9999972735287559,
                6.475948754012522e-07,
                0.999994577780387,
                1.275191036933194e-07,
                2.3823682479181176e-07,
                3.059022998576899e-07,
                3.0590237279032884e-07
            ],
            [
                7.338209805240734e-07,
                1.760343633031919e-06,
                3.9278638756099906e-07,
                6.475947982022763e-07,
                1.3709572068478697e-06,
                3.0590215399183813e-07,
                1.4449803818215767e-07,
                4.450851580566494e-07,
                8.315281267882195e-07,
                1.637377643243723e-07
            ],
            [
                2.2603234895372223e-06,
                1.4449798650551755e-07,
                0.999999653367255,
                1.2751905808881762e-07,
                1.4449798650551755e-07,
                2.3823702359290413e-07,
                0.999999653367503,
                3.059022998576899e-07,
                0.9999785550516269,
                2.2603242978871282e-06
            ],
            [
                1.7603440527222532e-06,
                1.0677032518814388e-06,
                9.422444815792981e-07,
                5.422220909009474e-06,
                0.9999980052695653,
                1.8553907971855875e-07,
                5.715005832886879e-07,
                2.6995774527718623e-07,
                3.466327450756327e-07,
                5.715005832886879e-07
            ],
            [
                8.315284241650899e-07,
                0.9999998362623334,
                3.288749457469787e-06,
                1.3709576971425944e-06,
                1.4449805540740185e-07,
                8.315279285351409e-07,
                0.9999978766215387,
                0.999999746398073,
                3.288749457469787e-06,
                3.9278610661902853e-07
            ],
            [
                1.2751902768568054e-07,
                2.699577774585891e-07,
                0.9998911030786539,
                0.999903897585457,
                1.855391239539711e-07,
                6.475945666051092e-07,
                2.699577774585891e-07,
                3.0590237279032884e-07,
                0.9999957771665577,
                8.764247451307293e-08
            ],
            [
                3.46632497145457e-07,
                3.927862470899887e-07,
                1.6373770576776313e-07,
                3.059022269250683e-07,
                1.4449795205429202e-07,
                1.5534984953453635e-06,
                1.2751905808881762e-07,
                2.1024339116134898e-07,
                1.855391239544352e-07,
                1.6373766672973748e-07
            ],
            [
                7.734423152941018e-08,
                1.1253513522447425e-07,
                9.931187406410953e-08,
                0.9999942280772222,
                8.764255809528314e-08,
                1.1253509497835043e-07,
                1.275190884913241e-07,
                1.2751905808881762e-07,
                1.4449805540700758e-07,
                1.4449807263312446e-07
            ],
            [
                6.475947210046347e-07,
                4.4508505193932864e-07,
                0.9999986290421399,
                0.9999980052695658,
                0.999999814460876,
                0.9999938558261332,
                2.3823696679230424e-07,
                0.999999814460876,
                2.1024331597262577e-07,
                9.931187406410953e-08
            ],
            [
                2.2603248367949354e-06,
                1.444979692800516e-07,
                3.059022269250683e-07,
                3.4663249714612693e-07,
                1.3709568799919866e-06,
                1.0677026154806063e-06,
                9.93120161306789e-08,
                5.715005151606823e-07,
                1.2751905808881762e-07,
                6.475950298011458e-07
            ],
            [
                9.931188590255539e-08,
                2.6995768091310296e-07,
                1.2751908849167202e-07,
                2.699578096393206e-07,
                8.764241182641775e-08,
                2.3823685319244518e-07,
                6.023571320847322e-08,
                0.9999916019289772,
                1.6373766672973748e-07,
                9.931193325852072e-08
            ],
            [
                1.8553905760062447e-07,
                2.3823690999290963e-07,
                3.927860597945825e-07,
                1.8553905760024476e-07,
                4.450852111148132e-07,
                1.2751899728286965e-07,
                1.637377448057981e-07,
                0.9999969105055536,
                2.6995784182140636e-07,
                1.275190276859705e-07
            ],
            [
                1.7603440527222532e-06,
                1.855391239539711e-07,
                0.9999982396574171,
                0.9999938558224725,
                3.466327450756327e-07,
                1.8553916819032217e-07,
                1.2098656835224664e-06,
                3.0590237279032884e-07,
                7.734423152941018e-08,
                5.715007195447234e-07
            ],
            [
                5.043474081993875e-07,
                1.637376862471855e-07,
                8.764251630363003e-08,
                8.764247451307293e-08,
                5.715002426460124e-07,
                1.8553910183607374e-07,
                3.059023363231725e-07,
                3.466327450756327e-07,
                1.4449805540651476e-07,
                2.430025232128576e-05
            ],
            [
                0.9999646437451547,
                6.023571320847322e-08,
                5.715007195447234e-07,
                2.6995774527657245e-07,
                1.2751908849167202e-07,
                3.059021175247079e-07,
                1.8553905760062447e-07,
                1.4449798650551755e-07,
                2.3823702359290413e-07,
                2.382369667929001e-07
            ],
            [
                8.315279285370317e-07,
                1.855391681906175e-07,
                1.3709573702822306e-06,
                3.46632497145457e-07,
                3.726639284144195e-06,
                1.2098659719788098e-06,
                3.059022269250683e-07,
                3.288747889284851e-06,
                2.260324567337161e-06,
                1.5534973842076057e-06
            ],
            [
                1.6373762769138607e-07,
                0.999997593896514,
                1.0677026154730804e-06,
                8.315279285351409e-07,
                1.2751899728286965e-07,
                3.466327450756327e-07,
                3.9278634073732336e-07,
                2.102433159721477e-07,
                8.315277302857965e-07,
                3.05902190458764e-07
            ],
            [
                6.023571320847322e-08,
                1.2751899728286965e-07,
                2.1024341622426268e-07,
                2.3823702359290413e-07,
                3.0590215399183813e-07,
                0.9999988634360187,
                7.338212429562581e-07,
                1.1253512180925583e-07,
                1.1253509497883659e-07,
                1.6373764721072816e-07
            ],
            [
                2.102433159721477e-07,
                3.059021175255426e-07,
                2.69957906184239e-07,
                7.734418542875216e-08,
                0.9999993524051248,
                2.3823690999290963e-07,
                0.9999970976880166,
                3.466327450765785e-07,
                9.931186222482958e-08,
                1.2751908849167202e-07
            ],
            [
                3.0590237279032884e-07,
                2.260324567337161e-06,
                5.715004470313855e-07,
                1.4449795205429202e-07,
                0.9999869928746524,
                3.4663262110945863e-07,
                9.422448185435711e-07,
                1.6373772528581146e-07,
                1.3709567165579959e-06,
                4.450852111148132e-07
            ],
            [
                3.466327037539638e-07,
                3.927862939126708e-07,
                1.8553907971855875e-07,
                4.4508505193932864e-07,
                5.715003789033962e-07,
                1.444980726324838e-07,
                1.6373768624837685e-07,
                9.931195693628605e-08,
                1.637377448057981e-07,
                1.855391239539711e-07
            ],
            [
                6.475947210031623e-07,
                3.059022269250683e-07,
                1.6373764721072816e-07,
                1.4449795205429202e-07,
                1.1253512180925583e-07,
                1.8553903548231313e-07,
                2.6995784182140636e-07,
                0.9999962733593845,
                5.043472879540142e-07,
                1.5534975693933505e-06
            ]
        ]
    },
    {
        "q_id": "9307_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            126,
            127
        ],
        "rewards": [
            [
                0.9999981261252882,
                0.9999997126314811,
                1.994729721518893e-06,
                0.9999987121046323,
                0.999999864256719,
                0.9999991148432813,
                0.9999997761970782,
                1.4738985486265496e-05,
                0.9999994631249962,
                0.9999991684717746
            ],
            [
                4.222831934286977e-06,
                1.0129989771823107e-05,
                3.726638395415398e-06,
                1.6701421843720577e-05,
                2.9023133689924295e-06,
                1.6701421844085127e-05,
                3.2887506333812835e-06,
                2.3823693839290317e-07,
                5.422217030032353e-06,
                2.2603251062270446e-06
            ],
            [
                8.315278294114555e-07,
                1.637377448057981e-07,
                1.5534975693979422e-06,
                4.222835458175145e-06,
                3.2887478892504536e-06,
                4.785093924330255e-06,
                1.7603436330259153e-06,
                3.4663278639892215e-07,
                3.0590237279085045e-07,
                7.338208930460318e-07
            ],
            [
                1.760343003481596e-06,
                2.1024326584582131e-07,
                1.4449803818215767e-07,
                1.8553910183674878e-07,
                3.059022269250683e-07,
                1.4449805540740185e-07,
                1.855391239539711e-07,
                2.3823688159291947e-07,
                2.3823688159237777e-07,
                1.275190428875671e-07
            ],
            [
                3.927862470899887e-07,
                2.6995787400282076e-07,
                7.338209805240734e-07,
                2.2603253756874524e-06,
                7.889266347715168e-06,
                2.6995784182140636e-07,
                3.05902190458764e-07,
                1.0677026154806063e-06,
                5.715003789046955e-07,
                8.315281267861397e-07
            ],
            [
                1.8553919030826963e-07,
                1.4449798650551755e-07,
                7.338213304363436e-07,
                3.059021175255426e-07,
                3.4663253846718004e-07,
                1.1253517547010071e-07,
                8.76424013786396e-08,
                7.73441946488886e-08,
                5.715003789033962e-07,
                3.466327450756327e-07
            ],
            [
                0.9999991148429644,
                0.9999986290429573,
                2.1444950971601277e-05,
                0.9999984465024314,
                4.450848927658745e-07,
                1.4449805540763184e-07,
                1.444980209564556e-07,
                1.8553905760024476e-07,
                7.734414854823498e-08,
                2.3823688159237777e-07
            ],
            [
                1.4738981972564636e-05,
                0.9999997617631469,
                8.939694172957213e-06,
                1.3709572068522336e-06,
                5.422218969895357e-06,
                1.3709568799919866e-06,
                5.043472278322555e-07,
                2.699578096403948e-07,
                1.0677032518814388e-06,
                8.315282259138311e-07
            ],
            [
                3.4663266243308805e-07,
                3.288747889284851e-06,
                2.3823688159291947e-07,
                2.2603240284371276e-06,
                1.0677026154806063e-06,
                1.1253509497883659e-07,
                1.855391239544352e-07,
                0.9999934595612275,
                0.999998712105093,
                7.338211554783522e-07
            ],
            [
                0.9999993524051248,
                0.9999964991460052,
                0.9999993916406734,
                0.9999983463096263,
                0.9999992661792823,
                0.9999992188517629,
                0.999998629043284,
                0.9999994284992806,
                0.9999991684717744,
                0.9999991148426478
            ],
            [
                2.561282516066741e-06,
                6.475945666033422e-07,
                8.315284241650899e-07,
                0.9999997761970248,
                0.0007096703874599275,
                2.6995787400282076e-07,
                2.1024334103581732e-07,
                2.2603251062270446e-06,
                0.9999998724809875,
                8.939698435657833e-06
            ],
            [
                1.5534975693979422e-06,
                NaN,
                0.9999974387171833,
                2.753568453792444e-05,
                1.3007130015677909e-05,
                1.3709567165617364e-06,
                8.939695238634211e-06,
                6.144172404738491e-06,
                4.4508515805735777e-07,
                1.3709576971463352e-06
            ],
            [
                2.699577774585891e-07,
                2.5612834320563895e-06,
                8.315277302841894e-07,
                1.3709578605729614e-06,
                1.0677028700422047e-06,
                4.4508494582405734e-07,
                3.059021175261338e-07,
                1.4449802095666915e-07,
                3.927862002663297e-07,
                4.4508494582405734e-07
            ],
            [
                2.1444953527944967e-05,
                0.9999987121049386,
                6.144172404738491e-06,
                1.5534981249697903e-06,
                2.7535704232595768e-05,
                0.9999995549151074,
                5.715002426475718e-07,
                1.30071315662049e-05,
                0.999999607213753,
                3.4663274507713016e-07
            ],
            [
                0.9999998024946095,
                0.9999991148431754,
                0.9999999176675437,
                0.9999999176675436,
                0.9999997463981939,
                0.9999999500627798,
                0.999999789756634,
                0.9999999176674454,
                0.9999998874648648,
                0.9999993524054336
            ],
            [
                0.999996033012203,
                0.9999989969860326,
                0.9999988634361546,
                0.9999987901340288,
                0.9999983463096276,
                0.9999984465020617,
                0.9999981261250644,
                0.9999994631249326,
                0.9999972735290821,
                0.9999992661790199
            ],
            [
                4.2228339479858295e-06,
                2.90231094723893e-06,
                8.315277302841894e-07,
                3.288747889284851e-06,
                0.9999977396748958,
                1.5534984953552536e-06,
                1.9947297215125433e-06,
                0.9999934595619989,
                9.422443692527585e-07,
                2.2603253756956754e-06
            ],
            [
                1.275190276859705e-07,
                4.450852641737424e-07,
                2.1024336609874897e-07,
                2.6995784182183607e-07,
                3.4663278639892215e-07,
                2.5612812947508257e-06,
                6.144172404738491e-06,
                3.0590237279085045e-07,
                6.475947982037486e-07,
                5.71500515161527e-07
            ],
            [
                1.6701421845361053e-05,
                4.006370174664993e-05,
                1.6373764721039308e-07,
                2.5612819054133693e-06,
                0.9999921107393043,
                1.855391239547094e-07,
                2.382370235933104e-07,
                9.931189774187203e-08,
                3.059022998576899e-07,
                2.1024334103581732e-07
            ],
            [
                2.3823696679327928e-07,
                5.043474082005342e-07,
                4.785093924362895e-06,
                4.450852641737424e-07,
                1.209865539295696e-06,
                1.2098653950692178e-06,
                0.0017007222699154446,
                7.73441946488886e-08,
                1.209865827752005e-06,
                1.3007130015677909e-05
            ],
            [
                0.9999998024947037,
                3.466325797900508e-07,
                4.785093924389007e-06,
                0.9999945777810352,
                1.6373772528704005e-07,
                3.059021175261338e-07,
                0.9999995818813268,
                3.466327863983311e-07,
                1.8553907971879076e-07,
                0.9999990577554064
            ],
            [
                0.9999986290431205,
                0.9999995549148951,
                1.855391681906175e-07,
                0.999998629043121,
                0.9999993106388725,
                0.9999983463102179,
                0.9999955048178895,
                0.9999978766222984,
                0.999998346310612,
                0.9999994284996213
            ],
            [
                0.9999992188518558,
                2.382369951932796e-07,
                5.829128640005915e-05,
                2.10243290909724e-07,
                6.144177531767002e-06,
                1.209865539295696e-06,
                3.059021175261338e-07,
                2.75356878194421e-05,
                1.7603425837855082e-06,
                1.4449805540763184e-07
            ],
            [
                3.535626336072768e-05,
                0.999998346310021,
                0.9999994631247406,
                0.999996711251724,
                7.889266347715168e-06,
                0.9999969105055573,
                3.2887482813149375e-06,
                0.9999975938976639,
                4.006370174344354e-05,
                5.4222176771176554e-06
            ],
            [
                0.9999994284997575,
                0.9999994284994169,
                0.9999990577551819,
                0.999998346310612,
                0.9999994631251883,
                0.9999993524051249,
                0.999999802494586,
                0.9999996072138936,
                0.9999994631249962,
                0.9999993106391191
            ],
            [
                0.9999962733607275,
                0.9999987901343181,
                0.999999310639202,
                0.9999990577557447,
                0.9999991148430711,
                0.9999980052698068,
                0.9999982396570009,
                0.9999989322970045,
                0.9999978766223019,
                0.9999985406241292
            ],
            [
                0.9999994956524717,
                7.338212429582604e-07,
                0.9999992188513903,
                1.3709575337159875e-06,
                1.5534979397790343e-06,
                1.1253509497883659e-07,
                7.88926446679691e-06,
                7.73442776303243e-08,
                0.9999991148427534,
                9.931187406410953e-08
            ],
            [
                3.466327863983311e-07,
                1.0677033791612137e-06,
                3.9278610661902853e-07,
                1.012999460278499e-05,
                2.5612828213934817e-06,
                1.994729008145876e-06,
                2.9023126771227976e-06,
                9.422448185510695e-07,
                3.288750241561788e-06,
                0.9999952149049404
            ],
            [
                3.059022998576899e-07,
                5.422217030747413e-06,
                5.715005832886879e-07,
                9.422445939032799e-07,
                4.785095635655362e-06,
                3.059021175255426e-07,
                6.962257909842961e-06,
                3.0590215399183813e-07,
                0.999979854299605,
                3.927862470899887e-07
            ],
            [
                4.450849988798682e-07,
                9.422445939032799e-07,
                1.2098653950656417e-06,
                8.315277302857965e-07,
                3.927862002654366e-07,
                6.475947210031623e-07,
                2.6995784182140636e-07,
                6.475947210031623e-07,
                5.043475885674441e-07,
                3.466327037548308e-07
            ],
            [
                0.9999989969860319,
                3.0590237279085045e-07,
                0.9999997126315153,
                1.5534984953510149e-06,
                0.9999989322966215,
                6.475947210031623e-07,
                1.637376862489725e-07,
                2.5612831267202583e-06,
                0.999998996985434,
                2.3823699519290042e-07
            ],
            [
                1.0677024881980089e-06,
                1.994730434879465e-06,
                3.927860597945825e-07,
                4.450851580540182e-07,
                3.059023363231725e-07,
                3.288750241561788e-06,
                1.5534983101602148e-06,
                9.422445939002803e-07,
                5.71500515159253e-07,
                5.04347468323289e-07
            ],
            [
                1.8553905759969634e-07,
                1.1253509497835043e-07,
                1.5534983101602148e-06,
                3.288749065423109e-06,
                1.1478766757561534e-05,
                1.6373770576776313e-07,
                1.1253521571574156e-07,
                6.962253760024999e-06,
                1.7603434231777837e-06,
                1.0677028700363782e-06
            ],
            [
                0.9999989969859122,
                0.9999992661791947,
                0.9999997617631469,
                0.9999992188514834,
                2.75356812556058e-05,
                4.450852641737424e-07,
                0.9999994631248041,
                2.4300237837960777e-05,
                1.2098653950692178e-06,
                0.9999998024946802
            ],
            [
                0.9999986290429573,
                1.7603425837855082e-06,
                2.6995774527718623e-07,
                6.475947210031623e-07,
                6.475951069985296e-07,
                6.475947210031623e-07,
                0.999998126124394,
                1.370957860576702e-06,
                6.475945666051092e-07,
                6.144173869558639e-06
            ],
            [
                3.466325797888292e-07,
                1.760343213335281e-06,
                0.9999988634357477,
                1.1478770862882149e-05,
                0.9999982396574172,
                1.4738978458140753e-05,
                5.04347287955046e-07,
                8.939695238536645e-06,
                2.4300249425247723e-05,
                0.9999930377412638
            ],
            [
                0.9999986290431205,
                0.9999994956525919,
                0.9999996743687422,
                0.9999991684720718,
                0.9999992661789323,
                0.9999997126315497,
                0.999999653367255,
                0.9999994284996895,
                0.999999266178845,
                0.9999996940977732
            ],
            [
                3.4663278639892215e-07,
                0.9999983463110068,
                6.475946438055299e-07,
                8.764254764780641e-08,
                3.9278605979534166e-07,
                3.059022269250683e-07,
                2.699576809143613e-07,
                1.27519088491875e-07,
                2.102434162245973e-07,
                2.1024326584680133e-07
            ],
            [
                5.715004470313855e-07,
                3.4663253846718004e-07,
                1.6373776432509826e-07,
                1.8553903548231313e-07,
                1.1253517547010071e-07,
                2.1024341622426268e-07,
                7.734414854823498e-08,
                1.6373772528677946e-07,
                1.125351083940518e-07,
                1.6373764721072816e-07
            ],
            [
                0.9999995818812273,
                0.9999991684720718,
                1.637376862489725e-07,
                1.2098662604291696e-06,
                0.99999879013374,
                0.9999994631250603,
                1.3007126914435202e-05,
                0.9999996533672963,
                0.9999978766222983,
                0.9999995262093857
            ],
            [
                1.9947299593014888e-06,
                0.9999999397642365,
                0.9999999358793332,
                0.9999999715466392,
                0.9999999317439546,
                0.9999998461826037,
                0.9999998362622358,
                0.9999999611088627,
                0.999999955930589,
                0.9999997463981031
            ],
            [
                0.999999789756634,
                0.9999998942829729,
                0.9999994631249323,
                0.9999996940977731,
                0.9999998461826222,
                0.9999994631250603,
                0.9999898700078189,
                0.999999554914789,
                0.999999310638626,
                0.9999994631251242
            ],
            [
                2.1024341622426268e-07,
                4.450849988811838e-07,
                0.9999997761970781,
                0.9999995818813269,
                0.9999997761971048,
                4.4508494582405734e-07,
                0.9999997617630049,
                0.9999949062962145,
                0.9999995549150013,
                3.059022269250683e-07
            ],
            [
                6.475950298021765e-07,
                0.9999998461826037,
                4.450852111155216e-07,
                2.699578096403948e-07,
                0.9999980052698038,
                1.553497754583709e-06,
                5.8291272497207844e-05,
                0.9999993916409634,
                4.450851580555361e-07,
                0.9999998144608762
            ],
            [
                0.9999989969857925,
                0.9999989969857926,
                0.9999993524052022,
                0.9999993106388727,
                0.9999987901341729,
                0.9999996743686257,
                0.9999991148433868,
                0.9999994631248041,
                0.9999990577551818,
                0.999998712104171
            ],
            [
                5.422217677152175e-06,
                0.999992110736493,
                2.1024336609874897e-07,
                5.422220262636381e-06,
                2.2603251062270446e-06,
                1.855391681906175e-07,
                3.4663278639892215e-07,
                2.1024326584582131e-07,
                1.0677029973192638e-06,
                3.4663278639892215e-07
            ],
            [
                0.9999988634360203,
                0.9999984465022473,
                0.9999993916406738,
                0.9999989969855549,
                0.9999995262095553,
                0.9999995262092735,
                0.9999983463110073,
                0.999998346310613,
                0.9999949062962206,
                0.999999526209443
            ],
            [
                2.5612834320563895e-06,
                1.6373772528677946e-07,
                0.999993855825401,
                3.4663253846718004e-07,
                2.561283126728994e-06,
                2.5612834320563895e-06,
                3.288749849529972e-06,
                0.9999988634358832,
                6.475948753991907e-07,
                5.422220909041528e-06
            ],
            [
                0.9999994956527725,
                0.9999991684719727,
                0.9999994631251882,
                0.9999997617631753,
                0.999999730042287,
                0.999999266179195,
                0.999999310638626,
                0.9999995262093858,
                0.9999986290426306,
                0.9999992661792824
            ],
            [
                3.059022998576899e-07,
                2.561281600086738e-06,
                4.450848927658745e-07,
                4.450848927658745e-07,
                8.939699501416646e-06,
                1.994729008145876e-06,
                1.2751901248454963e-07,
                2.902313023130843e-06,
                6.475946438055299e-07,
                3.72663883989755e-06
            ],
            [
                3.2887506335906595e-06,
                6.475951069961737e-07,
                9.422449308748773e-07,
                0.9999995262095551,
                4.450849988811838e-07,
                3.927862002654366e-07,
                4.450849988798682e-07,
                2.69957906184239e-07,
                3.7266388398585725e-06,
                3.726637951367137e-06
            ],
            [
                1.8553919030858602e-07,
                0.9999983463104151,
                1.444979692800516e-07,
                0.9999980052709929,
                1.8553910183649565e-07,
                7.734418542875216e-08,
                0.9999930377404428,
                0.9999995262094987,
                2.1024341622426268e-07,
                0.999999814460854
            ],
            [
                0.9999986290421409,
                1.994729721518893e-06,
                6.475947210031623e-07,
                5.715005832872586e-07,
                0.9999992188516701,
                6.9622595696935874e-06,
                3.927862470899887e-07,
                5.043472879525233e-07,
                1.3007128465151102e-05,
                2.2603251062270446e-06
            ],
            [
                0.9999975938976616,
                0.9999988634366964,
                0.9999996940977002,
                0.9999991148428589,
                3.059022998581767e-07,
                1.2098652508424818e-06,
                8.31527928532683e-07,
                7.338212429582604e-07,
                2.90231094723893e-06,
                0.9999987901346055
            ],
            [
                6.475947210046347e-07,
                1.3709568799823232e-06,
                1.5534973842076057e-06,
                5.043476486915964e-07,
                3.9278634073625165e-07,
                1.7603427936335396e-06,
                1.9947292459265734e-06,
                9.422447062270609e-07,
                1.0677032518785256e-06,
                5.043474683204221e-07
            ],
            [
                2.561281600086738e-06,
                1.5534984953552536e-06,
                0.9999992188519491,
                1.370957860576702e-06,
                5.043472879540142e-07,
                7.889265407327733e-06,
                2.382369951932796e-07,
                5.04347287955046e-07,
                0.9999998144608319,
                2.902312677150514e-06
            ],
            [
                0.9999992188515767,
                0.9999992188516696,
                0.9999985406236055,
                0.9999991684717745,
                0.9999993524049703,
                0.9999998024947037,
                0.999999746398073,
                0.9999983463098234,
                0.9999987901337404,
                0.9999995549150013
            ],
            [
                0.0002959572059428831,
                9.610242646245866e-05,
                2.7535697666401535e-05,
                0.00026119024754499347,
                0.00020342690098001725,
                0.00043055714311273843,
                0.00029595724129079026,
                7.889260704732132e-06,
                6.605212894856585e-05,
                1.4738987243236881e-05
            ],
            [
                1.1253506814842375e-07,
                3.726639284125553e-06,
                0.0015011825226723756,
                8.315282259138311e-07,
                2.6995790618469934e-07,
                0.999998996986271,
                9.422447062294175e-07,
                1.9947301970972664e-06,
                0.9999994284994851,
                6.475945666051092e-07
            ],
            [
                0.9999978766205257,
                0.9999957771675629,
                4.450850519403407e-07,
                0.9999952149055068,
                0.9999995818811772,
                0.999954602136841,
                0.9999962733611617,
                0.999999789756609,
                4.450848927658745e-07,
                0.9999967112513275
            ],
            [
                2.1444940745839484e-05,
                0.999998996986152,
                5.04347468323289e-07,
                0.9999967112517255,
                3.466326211113502e-07,
                1.7603430034867993e-06,
                2.382368531929327e-07,
                1.6373764721072816e-07,
                0.9999982396574177,
                0.9999991148426489
            ],
            [
                1.275190580884987e-07,
                7.73441946488886e-08,
                6.1441746020359e-06,
                1.6373764721039308e-07,
                1.8553905760062447e-07,
                7.734418542875216e-08,
                1.8553905760062447e-07,
                1.4449802095609418e-07,
                2.102434412875379e-07,
                0.9999997463981334
            ],
            [
                2.902312331170226e-06,
                1.6373770576776313e-07,
                3.9278634073732336e-07,
                3.7266401726173067e-06,
                1.6373762769138607e-07,
                0.9999910603005058,
                2.2603234895372223e-06,
                3.0590215399183813e-07,
                5.715003789033962e-07,
                0.9999957771645459
            ],
            [
                3.7266410611296085e-06,
                1.9947292459347367e-06,
                9.422442569315887e-07,
                6.962255419868303e-06,
                6.1441746020359e-06,
                1.9947292459347367e-06,
                3.288749457469787e-06,
                1.8925148241872038e-05,
                3.7266410611296085e-06,
                1.3709573702822306e-06
            ],
            [
                1.637377448057981e-07,
                1.2098653950656417e-06,
                0.999997876622045,
                0.9999996072136594,
                5.715007195431641e-07,
                2.561282210740037e-06,
                2.382368531929327e-07,
                0.9999993916409635,
                4.450848927621807e-07,
                3.4663249714612693e-07
            ],
            [
                0.99999926617867,
                0.999999631011372,
                0.9999997126315496,
                0.9999997463980125,
                0.9999993916408185,
                0.9999997126313783,
                0.9999998144609424,
                0.9999998802069017,
                0.9999991684716755,
                0.9999997617631187
            ],
            [
                0.999999814460854,
                0.9999980052707552,
                0.9999998555019618,
                0.9999997617631184,
                0.9999998724809116,
                0.999999631011416,
                0.9999996072138466,
                0.9999982396567874,
                0.999999872480942,
                0.9999998257021422
            ],
            [
                0.9999990577555187,
                2.260323758987159e-06,
                0.9999996310114159,
                0.9999987901343169,
                0.9999997126315496,
                0.999999730042287,
                0.9999994284997575,
                0.9999989322972578,
                0.9999998461826771,
                0.9999994284996894
            ],
            [
                6.1441746020359e-06,
                2.3823693839325527e-07,
                1.5534979397790343e-06,
                0.9999997761970248,
                4.006371129615879e-05,
                1.6701419854156377e-05,
                3.9278615344178325e-07,
                4.450852641717689e-07,
                9.422449308716635e-07,
                1.3709570434122812e-06
            ],
            [
                9.422442569315887e-07,
                4.450852111148132e-07,
                5.715003789046955e-07,
                1.3709576971463352e-06,
                2.1024341622426268e-07,
                6.825600469412533e-08,
                7.734423152941018e-08,
                0.9999997463980729,
                0.999993855826865,
                9.931185038635267e-08
            ],
            [
                1.1253513522447425e-07,
                1.1253512180925583e-07,
                3.059022269250683e-07,
                3.059022998576899e-07,
                2.1024341622426268e-07,
                6.825601283086733e-08,
                1.2751905808881762e-07,
                8.315279285351409e-07,
                8.764245361752286e-08,
                7.734423152941018e-08
            ],
            [
                0.9999989322973848,
                0.999999218851949,
                0.9999970976876704,
                6.475949526020042e-07,
                0.9999986290426303,
                0.9999997761970781,
                7.338210680002898e-07,
                0.9999986290432838,
                0.9999997126314126,
                3.4663266243308805e-07
            ],
            [
                5.715007195447234e-07,
                0.9999967112521114,
                7.338207180898968e-07,
                8.315284241650899e-07,
                2.3823693839325527e-07,
                9.422447062294175e-07,
                0.9999945777803864,
                1.147876812620341e-05,
                4.450848927658745e-07,
                0.9999999226558146
            ],
            [
                3.726639728370556e-06,
                2.561281600086738e-06,
                3.726638839878908e-06,
                4.450849988811838e-07,
                5.043476486915964e-07,
                1.0677027427569065e-06,
                1.5534983101602148e-06,
                4.539785241676547e-05,
                4.450848927658745e-07,
                3.466327450765785e-07
            ],
            [
                3.288747889284851e-06,
                1.0677029973192638e-06,
                6.962255419931625e-06,
                1.9947299592933255e-06,
                1.5534975693933505e-06,
                0.9999986290424676,
                2.2603242978871282e-06,
                5.043475885696228e-07,
                2.9023119851899796e-06,
                1.3007128465151102e-05
            ],
            [
                0.9999989322966213,
                0.9999993524054336,
                6.475945666051092e-07,
                1.30071315662049e-05,
                9.931187406410953e-08,
                0.999999391640891,
                0.9999998024947272,
                4.4508494582405734e-07,
                1.8553914607267268e-07,
                9.422442569315887e-07
            ],
            [
                3.120190021657421e-05,
                0.99999345955966,
                1.3007123812980299e-05,
                2.5612828213818346e-06,
                0.0002034269977368796,
                3.2887486733420804e-06,
                1.0129988563914856e-05,
                6.962255419804982e-06,
                6.144176799166453e-06,
                2.1444948413814623e-05
            ],
            [
                0.9999957771670647,
                0.9999981261237241,
                0.9999904837460722,
                0.9999967112509391,
                0.999998239655949,
                0.9999930377454319,
                0.9999957771670659,
                1.3709575337078829e-06,
                8.31527928532683e-07,
                0.9999151889290281
            ],
            [
                7.338209805224048e-07,
                3.466327037539638e-07,
                6.475951069985296e-07,
                1.760343003481596e-06,
                9.422444815765128e-07,
                9.422448185510695e-07,
                1.7603438428740716e-06,
                6.475945666051092e-07,
                1.5534971990126997e-06,
                2.1024331597262577e-07
            ],
            [
                1.067703379154416e-06,
                8.315281267800897e-07,
                1.3709570434054234e-06,
                5.715005832872586e-07,
                1.0677028700363782e-06,
                1.0677027427569065e-06,
                1.994730197071414e-06,
                7.338213304363436e-07,
                2.9023133690821773e-06,
                9.422442569315887e-07
            ],
            [
                6.475950298011458e-07,
                1.275190428875671e-07,
                2.1024334103581732e-07,
                9.931193325852072e-08,
                7.734415776836702e-08,
                3.059021175255426e-07,
                4.785095635655362e-06,
                2.102433159721477e-07,
                0.0005527786818807164,
                2.1024326584639497e-07
            ],
            [
                1.2098659719716573e-06,
                9.422442569315887e-07,
                3.466325384661554e-07,
                6.475951070002966e-07,
                3.059022998569248e-07,
                0.9999991148426479,
                1.8553916819032217e-07,
                5.715007195431641e-07,
                1.637377057673536e-07,
                3.0590215399183813e-07
            ],
            [
                1.7603427936335396e-06,
                0.9999993106391195,
                2.2603242978871282e-06,
                0.9999982396574179,
                0.9999990577550701,
                1.7603440527286572e-06,
                0.9999938558261504,
                0.9999986290421414,
                0.99999921885167,
                0.9999991684721716
            ],
            [
                1.275190276859705e-07,
                0.9999974387171805,
                1.553498124964492e-06,
                1.012999581021488e-05,
                0.9999980052698058,
                0.9999938558232041,
                6.962259569630266e-06,
                0.9999942280792922,
                0.9999810748450335,
                0.9999925887227922
            ],
            [
                0.00012339463384858465,
                3.927862939126708e-07,
                1.3007131566015624e-05,
                0.0002305067706362583,
                9.422449308748773e-07,
                1.4738983729535602e-05,
                4.785093353940187e-06,
                5.715003107755449e-07,
                0.9999986290424667,
                7.338211554783522e-07
            ],
            [
                6.47595107001401e-07,
                7.734418542875216e-08,
                3.4663278639892215e-07,
                1.7603432133296774e-06,
                3.466326624336003e-07,
                1.5534984953552536e-06,
                1.444980381819277e-07,
                1.6373770576776313e-07,
                1.444979692800516e-07,
                2.10243290909724e-07
            ],
            [
                3.927863875616689e-07,
                5.422218323487975e-06,
                6.144175334468545e-06,
                0.9999994284992809,
                0.9999996072136129,
                0.999999391641109,
                3.9278605979534166e-07,
                1.7603434231777837e-06,
                3.288749065423109e-06,
                7.889260704968913e-06
            ],
            [
                5.422217676654099e-06,
                3.2887502415438413e-06,
                1.8925155008528632e-05,
                0.9999916019249881,
                2.5612834320214477e-06,
                6.144172404587612e-06,
                0.9999970976866354,
                1.0129994602057158e-05,
                2.9023123311055552e-06,
                3.726639284050988e-06
            ],
            [
                0.9999983463110095,
                0.9999892166891503,
                0.999997593897671,
                0.9999945777829998,
                0.9999967112517291,
                0.9999972735294093,
                0.999996910505191,
                0.9999983463110083,
                0.9999984465028033,
                0.9999986290427958
            ],
            [
                2.3823696679327928e-07,
                3.466325384661554e-07,
                9.931185038635267e-08,
                4.139940508508409e-08,
                9.422445939002803e-07,
                0.9999989969862707,
                3.288749457469787e-06,
                2.5612825160271407e-06,
                1.7603427936079236e-06,
                1.6373776432481905e-07
            ],
            [
                0.9999995262094988,
                1.6373764721072816e-07,
                2.102434412875379e-07,
                0.9999992661787575,
                0.9999997463980729,
                1.4449807263312446e-07,
                0.9999978766217941,
                4.0063701745046735e-05,
                2.6995774527718623e-07,
                2.1024331597262577e-07
            ],
            [
                7.338213304363436e-07,
                2.102434412875379e-07,
                1.2098653950692178e-06,
                1.6373764721072816e-07,
                9.422445939032799e-07,
                4.4508526417298334e-07,
                6.475945666051092e-07,
                1.7603434231777837e-06,
                9.422445939032799e-07,
                1.760343213335281e-06
            ],
            [
                2.2603251062270446e-06,
                NaN,
                1.0677029973192638e-06,
                6.605216831371112e-05,
                5.422219616228845e-06,
                2.9023119851781017e-06,
                1.4738981972323349e-05,
                3.7266388398585725e-06,
                1.994730672668496e-06,
                3.726639284125553e-06
            ],
            [
                0.9999997897565839,
                0.9999990577554074,
                0.9999994631249964,
                8.315277302841894e-07,
                0.9999988634362914,
                0.9999980052707568,
                0.999999310638873,
                0.9999992661791951,
                0.9999995549150015,
                0.999999114842965
            ],
            [
                0.9999997617629766,
                0.999998712105246,
                0.9999974387187079,
                2.382370235933104e-07,
                1.275190580890061e-07,
                2.699576809143613e-07,
                0.9999996743687422,
                0.9999987121043248,
                3.927863875616689e-07,
                1.2098661162056318e-06
            ],
            [
                4.785093924362895e-06,
                5.4222209089700225e-06,
                0.9999985406232575,
                1.9947292459347367e-06,
                1.4449798650551755e-07,
                1.994729008145876e-06,
                3.466325797888292e-07,
                3.9278605979534166e-07,
                3.9278615344178325e-07,
                1.994729008145876e-06
            ],
            [
                0.9999969105040811,
                0.999999746398073,
                1.275190580890061e-07,
                6.144177531767002e-06,
                0.9999987121041714,
                0.9999995549150545,
                0.99999963101146,
                1.637376862489725e-07,
                0.9999994956527124,
                2.6995790618469934e-07
            ],
            [
                0.9999992661789322,
                2.7535694384081332e-05,
                7.338210680021253e-07,
                6.475947210031623e-07,
                4.785095065204162e-06,
                0.999999554914842,
                1.3709570434178922e-06,
                5.043473480777865e-07,
                1.6701421845361053e-05,
                0.999999653367379
            ],
            [
                1.3007130015488633e-05,
                4.4508510499849186e-07,
                0.9999996533672136,
                0.999998996986271,
                0.9999998555020481,
                0.999998932297003,
                6.144176799334096e-06,
                4.450852111148132e-07,
                0.999999352405279,
                0.9999994284997575
            ],
            [
                5.144221366885164e-05,
                1.6373768624874915e-07,
                2.561283432035425e-06,
                0.9999974387165733,
                0.999995214903804,
                0.9999969105066618,
                0.9999974387171859,
                0.999994577779098,
                0.9999981261243952,
                1.3709576971379186e-06
            ],
            [
                8.939695238634211e-06,
                0.9999957771670626,
                1.0677026154806063e-06,
                1.0677027427600627e-06,
                3.059022998576899e-07,
                0.9999975938976616,
                1.0677031245990084e-06,
                0.9999993106389549,
                3.120191881423529e-05,
                0.9999996072137062
            ],
            [
                9.610244939803353e-05,
                2.2603251062450327e-06,
                8.315281267861397e-07,
                1.5534973842076057e-06,
                0.9999964991439307,
                5.715003107767143e-07,
                3.0590237279085045e-07,
                6.475949526020042e-07,
                0.999997273530059,
                1.994729008145876e-06
            ],
            [
                0.999999218851949,
                0.9999997126314126,
                0.9999997761970516,
                0.9999993916406735,
                0.9999997126314469,
                0.999998712104478,
                0.9999996533672965,
                0.9999995549150543,
                0.9999998642566381,
                0.9999996310115039
            ],
            [
                2.2603237589779086e-06,
                4.785095635655362e-06,
                3.9278605979534166e-07,
                3.9278610661902853e-07,
                6.475946438055299e-07,
                4.4508510499849186e-07,
                1.4449800373065699e-07,
                4.2228339479858295e-06,
                9.422450431989127e-07,
                3.9278634073732336e-07
            ],
            [
                2.753569766795419e-05,
                1.4449803818215767e-07,
                1.8553914607267268e-07,
                0.9999955048194968,
                3.4663249714612693e-07,
                1.0677024882009222e-06,
                4.4508510499849186e-07,
                1.067703124601679e-06,
                4.450852641737424e-07,
                5.1442201405453086e-05
            ],
            [
                1.8553907971855875e-07,
                0.9999989969861522,
                0.9999986290426321,
                1.1478764021029928e-05,
                5.144220140264605e-05,
                1.209865539295696e-06,
                1.7603438428800754e-06,
                0.9999989322972582,
                6.962257079832313e-06,
                4.450850519403407e-07
            ],
            [
                1.9947297215125433e-06,
                1.1478770862735993e-05,
                5.043476486915964e-07,
                1.275190580890061e-07,
                4.4508510499737865e-07,
                5.715002426475718e-07,
                8.315284241650899e-07,
                3.466326211105621e-07,
                2.3823690999290963e-07,
                5.715003107755449e-07
            ],
            [
                5.422217030707961e-06,
                5.422219616184461e-06,
                1.7603434231777837e-06,
                2.260324836787226e-06,
                1.5534984953453635e-06,
                1.5534975693933505e-06,
                1.300712536350655e-05,
                2.7535700948722127e-05,
                2.260325375664839e-06,
                6.144172404587612e-06
            ],
            [
                6.144172404738491e-06,
                0.9999994284996212,
                4.4508494582405734e-07,
                1.5534975693979422e-06,
                9.422445939054222e-07,
                2.102434162245973e-07,
                3.059021175261338e-07,
                4.450851580566494e-07,
                3.059022998581767e-07,
                3.288749065423109e-06
            ],
            [
                4.450849988811838e-07,
                3.288749065423109e-06,
                1.209865539295696e-06,
                8.315281267861397e-07,
                2.3823702359290413e-07,
                1.0677024881980089e-06,
                5.043476486915964e-07,
                0.9999993916406734,
                0.999999495652652,
                4.4508494582405734e-07
            ],
            [
                3.0590237279085045e-07,
                6.475947982037486e-07,
                1.067702870039777e-06,
                1.7603432133296774e-06,
                2.1444943302181958e-05,
                1.7603438428800754e-06,
                4.785093924362895e-06,
                4.2228334445658276e-06,
                2.90231094723893e-06,
                8.315281267882195e-07
            ],
            [
                1.3709576971425944e-06,
                5.043472879540142e-07,
                3.466327863983311e-07,
                0.9999981261241708,
                1.8925157265710765e-05,
                4.539789029616496e-05,
                0.999998629042957,
                3.7266401726173067e-06,
                1.0129987357287368e-05,
                1.4738985486265496e-05
            ],
            [
                0.999999554914736,
                0.999999310638955,
                0.9999991148428593,
                0.9999995818811775,
                0.9999996533672139,
                0.9999997126314126,
                0.9999994284995533,
                0.999999653367379,
                0.9999985406232587,
                0.999999310638955
            ],
            [
                1.6373770576776313e-07,
                4.450849988811838e-07,
                0.9999992188514841,
                3.4663266243308805e-07,
                0.9999989322966223,
                5.715005151606823e-07,
                3.927860597945825e-07,
                3.927862002663297e-07,
                9.422448185534261e-07,
                5.715002426486762e-07
            ],
            [
                5.04347468323289e-07,
                0.9999991684715763,
                3.0590237279085045e-07,
                0.9999984465026166,
                4.222834954778007e-06,
                0.9999977396765112,
                8.939694172867777e-06,
                0.9999987121043242,
                0.9999996310116359,
                1.994730672675753e-06
            ],
            [
                4.450851580566494e-07,
                3.0590215399183813e-07,
                3.2887478892683997e-06,
                1.4738980215352592e-05,
                7.338212429582604e-07,
                1.3007126914435202e-05,
                1.994730434879465e-06,
                2.3823696679230424e-07,
                4.4508510499849186e-07,
                1.7603438428800754e-06
            ],
            [
                0.9999997463981636,
                1.5534973842076057e-06,
                5.715002426486762e-07,
                3.4663278639892215e-07,
                2.6995774527718623e-07,
                2.382370235933104e-07,
                4.450852641737424e-07,
                1.8553916819032217e-07,
                3.466326624336003e-07,
                4.450848927658745e-07
            ],
            [
                9.422442569290178e-07,
                3.466327037548308e-07,
                4.006370174344354e-05,
                2.1444953527944967e-05,
                0.9999996310115479,
                3.927860597945825e-07,
                1.637377448057981e-07,
                2.699577774585891e-07,
                4.785094494783494e-06,
                1.0129992187658463e-05
            ],
            [
                0.9999999067050832,
                0.9999991684719726,
                0.9999997897565588,
                0.999999554914789,
                0.9999999273418702,
                0.9999998874648648,
                0.9999999006879721,
                0.999995214907219,
                0.9999977396765118,
                0.9999998942829225
            ],
            [
                6.475950297993789e-07,
                3.466327450756327e-07,
                5.715003107767143e-07,
                5.715002426460124e-07,
                7.338208055664991e-07,
                6.475951070002966e-07,
                1.8553907971855875e-07,
                3.4663253846718004e-07,
                3.4663266243308805e-07,
                8.315277302819205e-07
            ],
            [
                4.450849988811838e-07,
                3.726638839878908e-06,
                9.422445939032799e-07,
                7.88926446679691e-06,
                2.6995774527718623e-07,
                7.338209805200689e-07,
                9.422449308774482e-07,
                8.315284241650899e-07,
                1.6701423835624208e-05,
                2.561281600076256e-06
            ],
            [
                0.9999972735300569,
                0.99999911484307,
                0.9999997126313783,
                0.9999978766222981,
                0.9999925887192515,
                2.6995774527657245e-07,
                0.9999984465022462,
                0.9999995549150544,
                0.9999960330155108,
                0.999999631011592
            ],
            [
                0.9999970976869812,
                0.9999904837483473,
                0.9999945777784526,
                0.9999955048168329,
                1.0129992187658463e-05,
                0.9999916019310011,
                8.939697369882888e-06,
                0.9999970976873295,
                0.9999938558276132,
                2.260325106237323e-06
            ]
        ]
    },
    {
        "q_id": "10155_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.260323758987159e-06,
                4.139934586278605e-08,
                4.222834954801051e-06,
                8.939695238634211e-06,
                9.422447062294175e-07,
                4.450852111155216e-07,
                0.999999746398073,
                5.043473480777865e-07,
                2.260323758987159e-06,
                3.05902336324494e-07
            ],
            [
                0.9999832985821908,
                0.99999385582248,
                4.139936066832438e-08,
                0.9999996533673376,
                0.9999822214418523,
                0.9999993524053565,
                0.9999992188517629,
                0.9998601778644641,
                1.0677026154806063e-06,
                3.927862470899887e-07
            ],
            [
                0.9999998642566543,
                0.9999996533672139,
                0.9999998362622358,
                0.9999980052695665,
                0.9999997761971582,
                0.9999996072138935,
                0.9999994956525321,
                0.9999998144608762,
                0.9999993106391192,
                0.9999996310114599
            ],
            [
                0.9999997463981637,
                0.9999994631251244,
                0.9999997761971315,
                0.999999922655787,
                0.9999993524052795,
                0.9999997761971848,
                0.9999991684718738,
                0.9999998802069445,
                0.9999987901340291,
                0.999999776197025
            ],
            [
                0.9999996940977002,
                0.9999997617631754,
                0.9999997300420939,
                0.9999997617631186,
                0.9999997300422548,
                0.9999997617630334,
                0.999999746398073,
                0.999999631011372,
                0.9999997463980428,
                0.9999998942830863
            ],
            [
                0.9999997463981939,
                0.9999996310114159,
                0.999999674368781,
                0.999999495652592,
                0.9999996072138467,
                0.9999994956527123,
                0.9999989969861519,
                0.9999995818811773,
                0.9999990577551819,
                0.9999993916408191
            ],
            [
                9.422442569315887e-07,
                8.315280276580819e-07,
                5.04347468323289e-07,
                8.315277302788957e-07,
                6.475947982037486e-07,
                5.043476486924565e-07,
                4.222835458044565e-06,
                1.0677031245990084e-06,
                5.043473480777865e-07,
                4.4508494582405734e-07
            ],
            [
                0.9999995818810776,
                0.9999998362623334,
                0.9999995818813768,
                0.9999996940977003,
                0.9999994631251884,
                0.9999997761971849,
                0.9999969105051869,
                0.9999995818811276,
                0.999999730042287,
                0.9999995549150545
            ],
            [
                8.764247451307293e-08,
                0.9999997126313441,
                0.999983298578184,
                0.999994906293786,
                7.734416698849138e-08,
                0.9999978766212857,
                5.04347528446051e-07,
                0.9999942280799757,
                3.726637951387472e-06,
                0.9999822214397118
            ],
            [
                1.994729483705484e-06,
                0.9999993106387084,
                0.9999898700041949,
                0.9999991148432811,
                0.9999996072138936,
                0.9999964991443369,
                0.999999428499349,
                1.7603427936335396e-06,
                0.9999994631248044,
                0.9999967112513289
            ],
            [
                0.9999972735303825,
                0.9999989322966213,
                0.9999989322971304,
                0.9999987901341729,
                1.6701429808632785e-05,
                0.99999743871779,
                0.9999993106392012,
                0.9999964991451721,
                5.043472879540142e-07,
                0.999998239657207
            ],
            [
                0.9999978766220479,
                0.9999996940977732,
                0.9999996072136595,
                0.9999995262094987,
                0.9999994956525321,
                0.9999994631249324,
                1.8553919030826963e-07,
                0.9999996533674619,
                0.9999995262093295,
                0.9999997897565839
            ],
            [
                0.9999972735284319,
                0.999999653367255,
                0.9999988634358838,
                0.9999982396574176,
                0.9999991684715767,
                0.9999987121047854,
                0.9999990577549575,
                0.9999993524050479,
                0.9999991148433871,
                0.9999983463104156
            ],
            [
                1.275190580884987e-07,
                1.1253513522447425e-07,
                6.475945666033422e-07,
                1.8553916819032217e-07,
                9.931193325852072e-08,
                6.023569884718319e-08,
                4.139934092760465e-08,
                8.764242227418718e-08,
                0.9999987901340285,
                9.931187406410953e-08
            ],
            [
                8.764254764749753e-08,
                7.338213304363436e-07,
                2.382370235933104e-07,
                1.6373766672973748e-07,
                3.927860597935108e-07,
                1.275190732904469e-07,
                2.6995774527657245e-07,
                5.04347528446051e-07,
                9.931190958076104e-08,
                8.315281267882195e-07
            ],
            [
                0.9999997300422228,
                0.9999995818813269,
                0.9999997126314126,
                0.9999996940978098,
                0.9999987901344618,
                0.9999996072139403,
                0.9999996072136127,
                0.9999996310113719,
                0.999999653367503,
                0.9999997300421904
            ],
            [
                0.9999995549150545,
                0.9999987121052463,
                0.9999987121043247,
                0.9999984465026185,
                0.9999987901337409,
                0.999999391640674,
                0.9999992188517633,
                0.9999995549147896,
                0.9999996533674206,
                0.9999991148428596
            ],
            [
                0.9999998024947273,
                0.9999997897567091,
                0.9999997761972116,
                0.9999997617629766,
                0.9999999006879958,
                0.9999998642566866,
                0.9999994284996213,
                0.9999998555020309,
                0.999999825702163,
                0.999999631011636
            ],
            [
                6.825601283086733e-08,
                8.764249540862797e-08,
                4.1399365603508136e-08,
                1.4449798650551755e-07,
                8.764245361752286e-08,
                5.315787506598473e-08,
                1.8553919030776337e-07,
                1.4449795205429202e-07,
                0.9999998802069445,
                5.715003107755449e-07
            ],
            [
                4.4508515805735777e-07,
                1.4449805540763184e-07,
                1.8553919030858602e-07,
                3.9278629391427843e-07,
                2.699578740032504e-07,
                2.1024334103581732e-07,
                1.4449798650551755e-07,
                9.422444815814404e-07,
                2.3823690999323465e-07,
                1.275190580890061e-07
            ],
            [
                0.9999999273418095,
                0.9999992188517628,
                0.9999997761970248,
                0.9999993524049704,
                0.9999989969857925,
                0.9999994631248043,
                0.9999984465022466,
                0.9999995549147891,
                0.9999998802069302,
                0.9999975938985225
            ],
            [
                0.9999998362622943,
                0.9999997300421903,
                0.9999997617631184,
                0.9999990577551823,
                0.9999994284992808,
                0.9999997463981334,
                0.9999998555019275,
                0.9999996940976639,
                0.999999495652532,
                0.9999996072138468
            ],
            [
                0.9999997897565839,
                0.9999996072138935,
                0.9999996072137531,
                0.9999996310115479,
                0.9999992188514835,
                0.9999983463104151,
                0.9999992661786699,
                0.999999730042094,
                0.999999310638626,
                0.9999989969857929
            ],
            [
                0.9999843104503214,
                0.9999986290426309,
                0.9999998362622747,
                0.9999994956525319,
                0.9999995549147891,
                0.9999997897565589,
                5.71500515159253e-07,
                0.9999994284994851,
                0.9999978766205263,
                0.9999996533673378
            ],
            [
                0.9999981261252876,
                6.475947982037486e-07,
                0.9999986290427939,
                0.00015843627371237145,
                0.9999981261243951,
                0.00037998453231794627,
                0.9999984465026169,
                0.999999391640746,
                0.999999114842648,
                0.9999798543044002
            ],
            [
                8.315280276626197e-07,
                0.9999987121041709,
                4.450852641737424e-07,
                6.475950298011458e-07,
                1.6373766672973748e-07,
                2.1024331597262577e-07,
                3.927863875616689e-07,
                0.9999990577556311,
                0.9999996072137529,
                2.699578740032504e-07
            ],
            [
                0.9999989322966223,
                0.9999987901343202,
                0.9999982396565804,
                0.9999991148427542,
                0.9999985406237808,
                0.999999310639202,
                0.999999218851391,
                0.9999991148429651,
                0.9999984465018767,
                0.9999980052695684
            ],
            [
                0.999999057755631,
                0.9999993106389548,
                0.9999984465026165,
                0.9999992188514836,
                0.9999980052698041,
                0.9999995818811773,
                0.9999997463981334,
                0.9999991148429646,
                0.9999993916408187,
                0.9999975938970888
            ],
            [
                0.9999756997564258,
                3.224186633297071e-08,
                6.475947210031623e-07,
                1.4449798650569826e-07,
                5.3157811697009444e-08,
                2.3823690999290963e-07,
                2.699577774585891e-07,
                1.994729008145876e-06,
                9.931194509740267e-08,
                6.475947210046347e-07
            ],
            [
                0.9999980052695658,
                0.999999631011328,
                0.999977172000163,
                1.2098656835224664e-06,
                0.9999995818810777,
                0.9999998724809571,
                0.9999969105044494,
                0.9999996743688199,
                0.999999900687972,
                0.9999997126315496
            ],
            [
                7.889261645355786e-06,
                2.6995790618469934e-07,
                6.962259569630266e-06,
                9.931187406410953e-08,
                1.760343633031919e-06,
                8.315282259138311e-07,
                3.927862002663297e-07,
                1.6373774480605869e-07,
                8.315281267882195e-07,
                1.7603425837855082e-06
            ],
            [
                0.9999994284997579,
                0.9999996533672137,
                0.9999994631251244,
                0.9999996310114161,
                0.999999864256719,
                0.9999995262094991,
                0.9999992188518559,
                0.9999978766207798,
                0.9999975938968029,
                0.9999942280786042
            ],
            [
                0.999999428499417,
                0.999999114842859,
                0.9999996743686645,
                0.9999994284994851,
                0.99999926617867,
                0.9999994956524717,
                0.9999995549147362,
                0.9999996533674206,
                0.9999990577555192,
                0.9999993524053564
            ],
            [
                1.3709576971379186e-06,
                2.260325106237323e-06,
                2.561282821106957e-06,
                8.315284241650899e-07,
                1.3709575337016483e-06,
                1.8553916819032217e-07,
                4.22283394786293e-06,
                1.5534977545886537e-06,
                2.2603245673155757e-06,
                8.31527928532683e-07
            ],
            [
                3.726641061085547e-06,
                3.726638395634011e-06,
                8.315283250371857e-07,
                3.0590226339061185e-07,
                1.3007130015299356e-05,
                2.9023133690980155e-06,
                2.2603240283888175e-06,
                3.2887482813149375e-06,
                7.889261645355786e-06,
                2.1444958640087166e-05
            ],
            [
                3.927861066170637e-07,
                3.0590237279032884e-07,
                1.012999581021488e-05,
                7.734419464850171e-08,
                2.6995768091310296e-07,
                2.6995790618252024e-07,
                3.059021539909339e-07,
                4.450849988798682e-07,
                1.6373762769138607e-07,
                8.764245361752286e-08
            ],
            [
                0.9999983463096284,
                0.9999986290432844,
                0.9999982396572094,
                0.9999984465015069,
                0.99999905775552,
                0.9999992188514842,
                0.9999991684718744,
                0.9999974387177953,
                0.9999987121049391,
                0.9999975938973765
            ],
            [
                0.9999999123574523,
                0.9999993524053566,
                0.9999999397642221,
                1.4449798650476187e-07,
                0.9999999123574838,
                0.9999999006880312,
                0.9999994956527122,
                0.9999988634358837,
                1.0,
                0.9999991684717744
            ],
            [
                0.9999997761971049,
                4.450848927658745e-07,
                0.9999992661786699,
                0.9999997300421261,
                0.9999996533674204,
                0.9999986290432842,
                0.9999997761971583,
                0.9999999176674357,
                0.9999998802069302,
                0.9999998942830358
            ],
            [
                0.9999998874647977,
                7.338211554783522e-07,
                0.9999998024946095,
                0.9999999067050165,
                9.61024150359243e-05,
                0.9999999468421186,
                0.9999998942828973,
                0.9999960330140877,
                0.9999985406230837,
                1.0
            ],
            [
                8.315282259138311e-07,
                5.715003107767143e-07,
                4.4508494582314646e-07,
                1.3007130014873483e-05,
                1.0677029973192638e-06,
                1.5534984953453635e-06,
                1.2098656835224664e-06,
                9.422450432014836e-07,
                2.2603240284371276e-06,
                1.553498124964492e-06
            ],
            [
                0.9999988634362899,
                0.9999916019239719,
                0.999998540623084,
                0.9999982396572072,
                0.9999991684722701,
                0.9999990577552943,
                0.9999832985741985,
                0.9999994956523517,
                0.9999945777829752,
                0.9999983463096278
            ],
            [
                0.9999994284997576,
                0.9999996533673379,
                0.9999877809269364,
                0.9999994284994852,
                0.9999996072137064,
                0.9999984465016912,
                0.9999960330126729,
                0.9999994956525322,
                0.9999996310114161,
                0.9999995549149483
            ],
            [
                2.1024334103581732e-07,
                1.4449805540740185e-07,
                7.734424996967756e-08,
                1.275190276859705e-07,
                1.2751905808881762e-07,
                6.023569166654288e-08,
                7.73442776303243e-08,
                3.653479902594117e-08,
                1.6373770576776313e-07,
                1.6373766672888118e-07
            ],
            [
                0.9999974387180964,
                2.260325106237323e-06,
                2.5612819054028872e-06,
                3.059022269250683e-07,
                1.994730672668496e-06,
                1.7603440527222532e-06,
                2.9023109472244114e-06,
                2.5612825160562587e-06,
                1.4449795205429202e-07,
                0.9999151889193432
            ],
            [
                0.9999998874649185,
                0.9999999226558146,
                0.9999978766205265,
                0.9999994284994169,
                0.999989870004224,
                0.9999999006880312,
                0.9999999067050499,
                1.0,
                0.999999825702163,
                9.422445939032799e-07
            ],
            [
                0.9999771720004492,
                1.4738985486265496e-05,
                0.9999989322970038,
                0.9999996940977004,
                0.9999852610216472,
                0.9999991148432813,
                0.9999991148427537,
                4.450852111135988e-07,
                6.475950298011458e-07,
                0.9999993916408186
            ],
            [
                0.9999998024946802,
                0.9999999067049832,
                0.999999653367255,
                0.9999998024946802,
                0.9999925887174842,
                0.999998712105092,
                0.9999998461826222,
                0.9999957771655567,
                1.637377057673536e-07,
                2.2603242978778778e-06
            ],
            [
                0.9999994631249324,
                0.9999994956523519,
                0.9999997463982241,
                0.9999997897566841,
                0.9999989969860322,
                1.444979692800516e-07,
                0.9999987901338846,
                0.9999996072136597,
                0.9999994631248685,
                0.999999526209612
            ],
            [
                0.9999997761970782,
                0.9999983463106122,
                0.9999997126313783,
                0.9999997463980427,
                0.9999998942830862,
                0.9999993524054338,
                0.9999998555020307,
                0.9999997126314811,
                0.9999996940977368,
                0.9999999067051499
            ],
            [
                0.999999554915108,
                0.9999993916408186,
                0.999999653367255,
                0.999998932296622,
                0.9999996533674618,
                0.9999996940978099,
                0.9999991684717748,
                0.9999984465015065,
                0.9999987121044787,
                0.9999991684722704
            ],
            [
                9.931189774187203e-08,
                0.99999743871657,
                0.9999991684715762,
                0.9999980052709934,
                0.9999997300421583,
                0.999941708748489,
                0.9999756997622682,
                0.9999985406237794,
                0.9999949062943949,
                0.9999992188517629
            ],
            [
                0.9999993524050478,
                1.300712536408621e-05,
                9.422443692574719e-07,
                5.043475885696228e-07,
                9.422447062294175e-07,
                3.9278629391427843e-07,
                0.9999984465026166,
                7.338208055680009e-07,
                1.4449802095666915e-07,
                1.8553907971879076e-07
            ],
            [
                0.9999995818811773,
                0.9999997761971583,
                0.9999989322971304,
                0.9999996940977732,
                0.9999994284996896,
                0.9999993106389551,
                0.9999997463981939,
                0.9999978766220452,
                0.9999997126313783,
                0.9999997300421261
            ],
            [
                0.9999964991464257,
                0.9999921107393137,
                2.1444953526969788e-05,
                0.9999986290431212,
                0.999998346310612,
                0.9999980052707561,
                0.9999962733593925,
                0.9999987121050925,
                0.9999993106391192,
                0.9999877809210977
            ],
            [
                0.9999993524049704,
                0.9999997761971049,
                0.9999987901337404,
                0.9999998555019963,
                0.9999993524053564,
                0.9999997897567091,
                0.9999998555019619,
                0.9999994284993488,
                0.9999997300421584,
                0.9999992188512972
            ],
            [
                0.9999989322966213,
                0.9999989969861512,
                0.9999993916407461,
                0.9999993524048936,
                0.9999997897565589,
                0.9999997617631186,
                0.9999997897565589,
                0.9999991148431756,
                0.9999990577550696,
                0.9999996743687811
            ],
            [
                0.9999993524052021,
                0.9999985406236058,
                1.99472900813862e-06,
                0.9999995262095555,
                0.999998996985434,
                0.9999967112497608,
                5.715007195447234e-07,
                0.999999674368781,
                0.9999994956527724,
                0.9999992661787572
            ],
            [
                0.9999987901344614,
                4.450851049917114e-07,
                2.382368531929327e-07,
                3.927860597945825e-07,
                1.2751908849167202e-07,
                6.475946438055299e-07,
                8.315284241650899e-07,
                3.05902117523595e-07,
                2.699576809143613e-07,
                3.726637951387472e-06
            ],
            [
                0.9999997761971582,
                0.9999994284995531,
                0.9999998024945624,
                0.9999998724810027,
                0.9999998024946801,
                0.9999998802068873,
                0.9999999176675044,
                0.9999998257021838,
                0.999999814460876,
                0.9999999176674848
            ],
            [
                0.9999992188519491,
                1.855391239547094e-07,
                2.699578096403948e-07,
                8.7642558095602e-08,
                6.825601283086733e-08,
                0.9999995549147891,
                4.4508515805735777e-07,
                3.7266379514061143e-06,
                0.999998446502061,
                3.4663262111182307e-07
            ],
            [
                0.9999995549149482,
                0.9999988634364257,
                0.9999994956524718,
                0.999999653367379,
                0.9999988634365613,
                0.9999995549147359,
                0.9999996940978098,
                0.9999995549149484,
                0.9999985406237799,
                0.9999995262095552
            ],
            [
                0.9999997897565588,
                0.9999916019269721,
                0.9999832985702187,
                0.9999930377445887,
                0.9999987901340284,
                0.9999998362622748,
                0.9999945777803902,
                1.0,
                7.338209805224048e-07,
                0.9999999468421883
            ],
            [
                3.4663278639892215e-07,
                1.2751905808881762e-07,
                7.338212429582604e-07,
                7.338208930460318e-07,
                1.209866260432471e-06,
                5.04347468323289e-07,
                1.4449802095666915e-07,
                2.102434412875379e-07,
                6.475947210046347e-07,
                1.994729483729522e-06
            ],
            [
                0.9999967112509373,
                0.999999761763147,
                0.9999992188517629,
                0.9999987901338847,
                0.9999998642566705,
                0.9999998257021422,
                0.9999991684722703,
                0.9999997463980428,
                0.9999980052702793,
                0.9999987901346055
            ],
            [
                1.1253508156363576e-07,
                8.7642558095602e-08,
                1.6373766672973748e-07,
                4.139941495546278e-08,
                4.691160446380562e-08,
                1.637377057680051e-07,
                4.139934092760465e-08,
                6.023578501513224e-08,
                6.825608606172863e-08,
                7.734414854823498e-08
            ],
            [
                1.275190732904469e-07,
                4.691162683297406e-08,
                7.734424996967756e-08,
                6.475945666051092e-07,
                1.4449807263312446e-07,
                1.725784003388814e-08,
                7.338208055664991e-07,
                2.2603251062013478e-06,
                9.422445939032799e-07,
                1.6373770576776313e-07
            ],
            [
                0.9999992188514834,
                0.9999989969857929,
                0.9999995262094987,
                0.9999985406234323,
                0.9999989322966214,
                0.9999993524049706,
                0.9999988634360192,
                0.9999977396754343,
                0.9999986290426309,
                0.9999986290429571
            ],
            [
                0.9999997126314125,
                0.9999992188513904,
                0.9999975938968018,
                0.9999988634361545,
                0.9999986290421405,
                0.9999996743686257,
                0.9999986290424668,
                0.9999997463981032,
                0.9999988634364254,
                0.9999974387184026
            ],
            [
                1.1253512180925583e-07,
                2.845337441546675e-08,
                8.315278294097538e-07,
                0.9999994631249323,
                0.9999996533673376,
                1.3709578605729614e-06,
                6.475946438055299e-07,
                6.475946438055299e-07,
                2.10243290909724e-07,
                2.382370235933104e-07
            ],
            [
                0.9999982396574174,
                0.9999990577549573,
                0.9999980052698054,
                0.9999991148432809,
                0.9999997463980125,
                0.9999996743687034,
                0.9999996533674204,
                0.9999997761971583,
                0.9999993916408911,
                0.9999993524054337
            ],
            [
                0.999999746398073,
                0.9999997897566842,
                0.9999997761971317,
                0.999999746398073,
                0.999999776197105,
                0.9999993106386267,
                0.9999997126313785,
                0.9999995549150548,
                0.9999996310115481,
                0.999999428499349
            ],
            [
                0.9999980052709935,
                0.9999996072138468,
                0.9999978766222984,
                5.043474683220276e-07,
                0.9999969105040821,
                0.9999989969862708,
                0.9999986290426306,
                0.9999962733593882,
                0.999999168472171,
                0.9999974387171806
            ],
            [
                0.9999998257020799,
                0.9999997126315496,
                0.9999981261243952,
                0.9999996743688199,
                0.9999970976883641,
                0.9999993524048935,
                0.9999994284996214,
                0.9999998257020799,
                0.9999998874648917,
                0.9999999067051054
            ],
            [
                0.9999996533672552,
                0.9999996940977731,
                0.9999994631251244,
                0.9999989969861518,
                0.9999997300421904,
                0.9999988634362899,
                0.9999996533674205,
                0.9999993106386262,
                0.9999997126314469,
                0.9999995549148422
            ],
            [
                0.9999986290421398,
                1.0677026154730804e-06,
                9.931195693628605e-08,
                8.315283250343497e-07,
                7.338210680021253e-07,
                5.04347287955046e-07,
                8.315281267882195e-07,
                7.338211554801876e-07,
                1.5534977545886537e-06,
                9.422442569315887e-07
            ],
            [
                1.0,
                0.999999946842182,
                1.0,
                0.9999998874647978,
                0.9999988634357481,
                0.9999998144608097,
                0.9999997897566841,
                1.0,
                0.9999998802069159,
                0.9999992661791948
            ],
            [
                0.9999996072136594,
                0.9999978766217924,
                0.9999986290426306,
                0.9999994284997575,
                0.9999983463108093,
                0.9999969105051869,
                0.999999495652532,
                0.9999983463110066,
                0.9999987121044779,
                0.9999983463110066
            ],
            [
                0.9999993916408909,
                0.9999996533672137,
                0.999999653367379,
                0.9999997761970781,
                0.9999994631247402,
                0.9999992188515764,
                0.9999999226558423,
                0.9999994956526522,
                0.9999995818812272,
                0.9999998642566866
            ],
            [
                0.9999991148431755,
                0.9999989969862713,
                0.9999992661790199,
                0.999999607213753,
                0.9999990577557435,
                0.999999631011504,
                0.9999994631251244,
                0.9999984465028022,
                0.9999994956524717,
                5.422220262636381e-06
            ],
            [
                0.9999996310115481,
                0.9999994631247405,
                0.9999996310116359,
                0.9999996743688975,
                0.9999997617631753,
                0.9999994631249323,
                0.9999993106387084,
                0.9999993106386259,
                0.9999998461826589,
                0.9999997126315497
            ],
            [
                0.9999986290429573,
                0.9999998362623529,
                0.9999999067049831,
                0.9999998802069159,
                2.5612825160562587e-06,
                0.9999998144608098,
                0.9999997126314469,
                0.9999999176674357,
                0.99999787662078,
                0.9999997617631184
            ],
            [
                4.539787406003298e-05,
                0.9999981261237256,
                0.9999980052695674,
                0.9999972735297338,
                0.9999977396762431,
                0.9999970976869834,
                0.9999960330145659,
                0.9999985406230841,
                0.9999949062968353,
                0.9999945777791
            ],
            [
                1.275190276859705e-07,
                2.1024336609874897e-07,
                0.9999997463980427,
                1.5534977545886537e-06,
                0.9999997126313441,
                3.927863875616689e-07,
                3.927862002663297e-07,
                1.370957860576702e-06,
                1.3709575337125585e-06,
                1.0677032518814388e-06
            ],
            [
                0.9999996940977367,
                0.9999996533672963,
                0.9999998144609203,
                0.9999998724809571,
                0.9999998802069874,
                1.0,
                0.9999993524049708,
                0.9999998555019963,
                0.9999996940976272,
                0.9999997897565589
            ],
            [
                0.9999992661788449,
                0.9999988634360188,
                0.9999998144608098,
                0.99999911484307,
                0.9999994284997579,
                0.9999990577550694,
                0.9999994284996213,
                0.999999776197025,
                0.999999352405202,
                2.561282210729555e-06
            ],
            [
                2.699577774585891e-07,
                2.1024334103581732e-07,
                0.9999852610233338,
                0.9999998555019447,
                0.999999789756609,
                1.1478770862882149e-05,
                3.059022998581767e-07,
                0.9999251537824881,
                0.9999516743680866,
                0.9999995262094987
            ],
            [
                2.699577774585891e-07,
                7.889259764517575e-06,
                6.475947982037486e-07,
                1.2751901248454963e-07,
                1.8553903548231313e-07,
                2.10243290909724e-07,
                1.0677028700363782e-06,
                3.466325797888292e-07,
                2.1024326584639497e-07,
                1.27519088491875e-07
            ],
            [
                0.999999391640891,
                0.9999997761970515,
                0.999999495652592,
                0.9999995818811275,
                0.9999998724809875,
                0.9999996940977004,
                0.9999994631248683,
                0.9999998144608762,
                0.9999998144608319,
                0.9999984465024312
            ],
            [
                0.9999998942829729,
                0.9999999006881497,
                0.9999999123575255,
                0.9999998874647575,
                0.9999999317440116,
                0.9999998257020799,
                0.9999998642567189,
                0.9999998555019963,
                0.9999998362623138,
                0.9999999067050609
            ],
            [
                6.825598028392069e-08,
                1.8553907971855875e-07,
                7.73441946488886e-08,
                8.76424013786396e-08,
                9.931189774187203e-08,
                9.93120161310289e-08,
                1.7603425837855082e-06,
                2.382369667929001e-07,
                2.1024331597262577e-07,
                8.7642558095602e-08
            ],
            [
                8.7642516304188e-08,
                0.9999988634360188,
                0.0001398221408903759,
                0.9999986290426305,
                1.2751899728311609e-07,
                2.144495608378187e-05,
                9.931189774187203e-08,
                0.9999984465028018,
                3.927862470899887e-07,
                1.8553914607267268e-07
            ],
            [
                0.999999864256719,
                0.9999997761971582,
                0.9999992661792824,
                0.9999994956527724,
                0.9999996940978098,
                0.999999554914736,
                0.9999991684721711,
                0.9999998724808964,
                0.9999994956523515,
                0.9999996533672137
            ],
            [
                0.9999998461826038,
                0.9999998942830862,
                0.9999997300421904,
                0.9999992661791074,
                0.9999999317439954,
                0.9999999176674848,
                0.999997876620529,
                0.9999998257022046,
                0.9999998144609424,
                1.0677031245953668e-06
            ],
            [
                1.6373776432509826e-07,
                1.5534984953552536e-06,
                5.043476486915964e-07,
                9.931190958076104e-08,
                3.466327450765785e-07,
                4.450848927650143e-07,
                1.275190580890061e-07,
                2.102434162245973e-07,
                5.043476486924565e-07,
                3.0590237279032884e-07
            ],
            [
                0.999999495652713,
                0.9999992188515773,
                0.9999993106392022,
                0.9999982396561606,
                0.999997739675706,
                0.9999990577556322,
                0.9999985406232583,
                9.422443692574719e-07,
                0.999999057754958,
                0.9999987901347502
            ],
            [
                0.999999776197105,
                0.9999996533672965,
                0.9999996533673379,
                0.9999997617631754,
                0.9999993524049706,
                0.9999994956524717,
                0.9999991684715764,
                0.9999996743687424,
                0.9999995262095552,
                0.999999352405125
            ],
            [
                0.9999921107345985,
                0.9999994284996896,
                0.9999983463106128,
                0.9999546021210246,
                0.9999251537463385,
                0.9999992188516696,
                0.99999743871657,
                0.9999982396574175,
                0.9999869928746634,
                0.9999898700090257
            ],
            [
                1.1253521571574156e-07,
                0.9999994956526522,
                0.9999995549150543,
                0.9999997126313441,
                0.999999730042287,
                0.9999992188516699,
                0.9999997126313441,
                0.9999997617630617,
                0.9999996310113719,
                0.9999996743688975
            ],
            [
                5.043472278322555e-07,
                4.4508510499849186e-07,
                3.9278629391427843e-07,
                8.315278294097538e-07,
                8.315278294114555e-07,
                2.561281600086738e-06,
                0.9999998461826037,
                9.422445939002803e-07,
                5.043473480777865e-07,
                3.05902336324494e-07
            ],
            [
                0.9999996940978098,
                0.9999992188519494,
                0.9999995262093294,
                0.999998540623606,
                0.999998932297258,
                0.9999989969862711,
                0.9999996310114161,
                0.9999991148427537,
                0.9999995818811276,
                0.9999995818812272
            ],
            [
                8.315279285351409e-07,
                1.3007126914612648e-05,
                9.422442569334097e-07,
                9.422445939002803e-07,
                3.288747889284851e-06,
                2.9023116392097746e-06,
                5.1442201405453086e-05,
                NaN,
                2.2603248367949354e-06,
                8.939695238536645e-06
            ],
            [
                1.1253520230052635e-07,
                1.725784003388814e-08,
                7.73441946488886e-08,
                7.734418542875216e-08,
                2.5110002900238917e-08,
                8.764247451307293e-08,
                7.734421308914719e-08,
                5.315787506598473e-08,
                8.764247451307293e-08,
                1.2751908849167202e-07
            ],
            [
                0.9999771719920187,
                0.9999999123575568,
                0.9999934595596592,
                0.9999999226557131,
                0.999972464312258,
                0.9999982396572074,
                0.9999997126313441,
                1.6373766672973748e-07,
                0.9999989322967485,
                2.1024329090929374e-07
            ],
            [
                2.561281600086738e-06,
                5.043475885696228e-07,
                6.962259569750576e-06,
                0.9999949062943938,
                0.9999993106388727,
                0.9999992188512972,
                0.9999991148428589,
                0.999998126125065,
                0.9999992661786699,
                1.3709576971463352e-06
            ],
            [
                1.1253512180925583e-07,
                0.9999942280785998,
                5.043474081993875e-07,
                7.338209805200689e-07,
                1.1253518888464745e-07,
                3.0590215399183813e-07,
                0.9999916019259717,
                0.999998346310612,
                0.9999984465026163,
                0.9999955048162824
            ],
            [
                0.9999995262092163,
                0.9999997463981335,
                0.9999998555019619,
                0.9999996533673791,
                0.99999921885167,
                0.9999995818813269,
                0.9999997617630334,
                0.9999996533672963,
                0.9999996533672552,
                0.9999992188516701
            ],
            [
                0.9999810748427765,
                0.9999975938982354,
                0.9999994284997576,
                0.9999998257022046,
                0.9999991684722703,
                0.9999972735287557,
                0.999998932297258,
                0.9999983463102181,
                0.9999988634361545,
                0.9999982396569979
            ],
            [
                3.059022269250683e-07,
                4.53978524104898e-05,
                1.275190580890061e-07,
                9.422445939002803e-07,
                6.475945666051092e-07,
                1.4449807263312446e-07,
                5.715005832872586e-07,
                1.8553903548231313e-07,
                2.6995790618350237e-07,
                1.27519088491875e-07
            ],
            [
                0.9999994956524717,
                0.9999997897567343,
                0.9999997897566341,
                0.9999998802069587,
                0.9999994631247403,
                0.9999997463980428,
                0.999999653367503,
                0.9999994631247404,
                0.9999996940978096,
                0.9999998362622553
            ],
            [
                0.9999998024946095,
                0.9999997463980729,
                0.9999998555019619,
                0.9999930377445828,
                0.9999982396567869,
                0.9999998461826222,
                0.9999998144608983,
                0.9999998362623724,
                0.9999998257020798,
                0.9999995818814266
            ],
            [
                0.9999964991460114,
                0.9999993106390375,
                0.9999985406236066,
                0.9999998642566866,
                0.9999993106386265,
                0.9999991684721716,
                0.9999988634358843,
                0.9999969105048208,
                0.9999986290421424,
                0.9999991684715767
            ],
            [
                2.6995784182140636e-07,
                8.315280276626197e-07,
                2.5612819054133693e-06,
                0.9999993106388726,
                8.315284241650899e-07,
                0.9999989322966217,
                4.22283545819819e-06,
                1.4449805540763184e-07,
                0.9999986290427945,
                1.5534981249697903e-06
            ],
            [
                2.382368815916736e-07,
                9.931196877456114e-08,
                0.9999934595604438,
                0.9999993106386261,
                9.931200429111105e-08,
                7.338208055664991e-07,
                2.3823693839290317e-07,
                8.764247451259466e-08,
                0.9999925887192533,
                9.42244930862237e-07
            ],
            [
                0.9999995262096116,
                0.9999997126314811,
                0.9999987901346062,
                0.9999993916406734,
                0.9999974387177911,
                0.999999653367255,
                0.9999992661791947,
                0.9999990577554064,
                0.9999997897565838,
                0.9999992188516696
            ],
            [
                0.9999995549151076,
                0.9999995262092728,
                0.999999554914736,
                0.999999581881277,
                0.9999993916411812,
                0.999999746398194,
                0.999999428499417,
                0.99999967436882,
                0.9999996533675031,
                0.9999993916406735
            ],
            [
                0.9999994284995533,
                0.9999998724809115,
                8.764249540862797e-08,
                0.9999985406237804,
                7.734418542875216e-08,
                0.9999992188513906,
                0.9999999226558053,
                0.9999998461827139,
                0.999989870012671,
                0.9999972735297317
            ],
            [
                0.9999975938973756,
                0.999999825702059,
                0.9999987901340288,
                0.9999986290427939,
                0.9999989969862709,
                0.9999995549149482,
                0.9999993916411812,
                0.999999631011548,
                0.9999995262095552,
                0.9999992188517631
            ],
            [
                0.9999992188517629,
                0.9999987121044779,
                0.9999994284996214,
                7.889262585886274e-06,
                0.9999980052700426,
                3.726639284144195e-06,
                0.9999993106386262,
                0.9999993916411811,
                0.9999994631247404,
                0.9999980052702794
            ],
            [
                0.9999998362622747,
                0.9999994284996212,
                0.9999997300422225,
                0.9999995818813268,
                0.9999996072138467,
                0.9999969105051854,
                0.9999989322975121,
                0.9999997897565838,
                0.9999991684716754,
                0.9999998802069017
            ],
            [
                3.4663249714451116e-07,
                1.444980209564556e-07,
                5.043475885674441e-07,
                2.6995790618469934e-07,
                2.3823690999160957e-07,
                5.04347468318358e-07,
                2.6995768091310296e-07,
                1.6373774480535133e-07,
                7.338209805224048e-07,
                2.3823696679230424e-07
            ],
            [
                4.785095635655362e-06,
                0.9999998024947273,
                6.825609419848033e-08,
                5.715006514176113e-07,
                1.760343213335281e-06,
                1.7603427936335396e-06,
                0.9999997126315153,
                6.023571320847322e-08,
                9.422448185534261e-07,
                6.475949526020042e-07
            ],
            [
                0.9999999176675829,
                0.9999996533672137,
                0.9999996310113719,
                0.9999994631249964,
                0.9999996533674618,
                0.9999994956527124,
                0.9999993916411813,
                0.9999997126315496,
                0.99999691050666,
                0.9999995818814267
            ],
            [
                0.9999999434137097,
                0.9999997897566341,
                0.9999985406236057,
                0.9999998024945861,
                0.9999998802069445,
                0.9999832985741994,
                0.9999646437369977,
                0.9999998642567351,
                0.999999900687984,
                0.9999986290432842
            ],
            [
                5.71500515159253e-07,
                1.5534975693933505e-06,
                1.6373772528677946e-07,
                2.5612812947508257e-06,
                4.785092783454444e-06,
                7.889263526345123e-06,
                0.9999981261250638,
                0.9999916019289833,
                1.2751905808881762e-07,
                2.6995771309523475e-07
            ],
            [
                3.466327037539638e-07,
                0.9999994631251885,
                0.9999989322968765,
                7.889264466639056e-06,
                1.1478764020560142e-05,
                1.1478764020883773e-05,
                0.9999975938965165,
                0.9999987121043249,
                2.4300249425247723e-05,
                3.120192625175911e-05
            ],
            [
                1.4738988999940381e-05,
                3.53562549305363e-05,
                6.962254589781966e-06,
                0.9999996310115039,
                0.9999998461826223,
                3.2887498494551953e-06,
                6.144173869502757e-06,
                4.785094494750855e-06,
                5.422219616140078e-06,
                4.785095065093186e-06
            ],
            [
                1.1253513522447425e-07,
                0.9999980052700421,
                2.6995768091310296e-07,
                3.0590226338838606e-07,
                0.9999988634358834,
                1.8553903548231313e-07,
                2.3823702359138736e-07,
                1.4449800373065699e-07,
                8.764254764749753e-08,
                6.023573475041126e-08
            ]
        ]
    },
    {
        "q_id": "9884_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            4,
            7,
            9,
            10,
            11,
            13,
            16,
            18,
            21,
            22,
            24,
            25,
            27,
            28,
            29,
            32,
            35,
            38,
            41,
            43,
            45,
            48,
            52,
            55,
            56,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            84,
            86,
            87,
            89,
            92,
            94,
            98,
            99,
            100,
            102,
            104,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                4.222834954801051e-06,
                NaN,
                7.338209805200689e-07,
                7.889265407327733e-06,
                6.962257909842961e-06,
                NaN,
                9.422442569334097e-07,
                1.3709575337159875e-06,
                NaN,
                6.962257079889302e-06
            ],
            [
                7.338213304363436e-07,
                4.450851580540182e-07,
                9.422450432014836e-07,
                1.2098656835224664e-06,
                8.315281267861397e-07,
                5.043475885696228e-07,
                1.7603438428848787e-06,
                7.338209805240734e-07,
                1.9947301970972664e-06,
                3.059021175261338e-07
            ],
            [
                1.994730672668496e-06,
                2.2603234895289998e-06,
                1.067703379154416e-06,
                2.2603242978665707e-06,
                1.9947297215043796e-06,
                2.2603242978778778e-06,
                6.475947210031623e-07,
                2.2603237589779086e-06,
                5.715002426486762e-07,
                1.5534975693933505e-06
            ],
            [
                5.043472879525233e-07,
                4.785093353940187e-06,
                1.7603425837855082e-06,
                NaN,
                1.5534975693979422e-06,
                1.3709572068522336e-06,
                5.043472879525233e-07,
                1.4738978458382043e-05,
                1.553498124964492e-06,
                2.902312331170226e-06
            ],
            [
                2.561281600086738e-06,
                3.7266410611296085e-06,
                9.422444815792981e-07,
                2.2603251062450327e-06,
                7.338212429582604e-07,
                3.2887482813149375e-06,
                1.99472900813862e-06,
                9.422448185534261e-07,
                7.338210680021253e-07,
                6.475946438055299e-07
            ],
            [
                8.939693107190907e-06,
                6.144176799227922e-06,
                NaN,
                NaN,
                1.7603434231777837e-06,
                5.422221555414699e-06,
                3.5356238073889594e-05,
                1.994729008145876e-06,
                2.9023130230846496e-06,
                1.994729483694599e-06
            ],
            [
                1.2098662604291696e-06,
                9.422450432014836e-07,
                3.466326211113502e-07,
                2.561282210740037e-06,
                9.422443692555439e-07,
                9.422450431989127e-07,
                4.22283545819819e-06,
                NaN,
                0.0002959572413768997,
                1.0677029973192638e-06
            ],
            [
                3.466326211113502e-07,
                6.475945666051092e-07,
                8.315278294097538e-07,
                9.422448185510695e-07,
                8.315282259138311e-07,
                3.05902190458764e-07,
                4.4508526417298334e-07,
                8.315277302841894e-07,
                9.422443692555439e-07,
                3.9278634073732336e-07
            ],
            [
                1.670141786295194e-05,
                2.561281294644835e-06,
                1.7603434231505666e-06,
                9.422444815814404e-07,
                5.043475885696228e-07,
                4.785092783519724e-06,
                NaN,
                1.5534975693869924e-06,
                7.484622725903504e-05,
                6.475945666051092e-07
            ],
            [
                4.2228319344021954e-06,
                5.422220909009474e-06,
                5.422218969895357e-06,
                NaN,
                1.4738976701652988e-05,
                1.2098659719757836e-06,
                NaN,
                1.0129988565084915e-05,
                7.889265407327733e-06,
                4.222831934379152e-06
            ],
            [
                9.422450431989127e-07,
                1.0677032518785256e-06,
                8.939698435657833e-06,
                1.2098662604247682e-06,
                6.962254589914941e-06,
                1.3709568799823232e-06,
                6.475949525981759e-07,
                1.2098662604126641e-06,
                1.7603427936335396e-06,
                6.475950297942253e-07
            ],
            [
                1.2098662604291696e-06,
                NaN,
                NaN,
                1.3709575337016483e-06,
                9.422445939032799e-07,
                5.715007195447234e-07,
                4.450851580566494e-07,
                2.2603253756956754e-06,
                6.962258739796719e-06,
                6.475949526020042e-07
            ],
            [
                7.338210680021253e-07,
                1.4738980215593877e-05,
                NaN,
                8.315284241650899e-07,
                1.7603430034867993e-06,
                6.962255419931625e-06,
                8.315277302841894e-07,
                2.2603253756956754e-06,
                9.422450431989127e-07,
                8.315283250371857e-07
            ],
            [
                7.338207180898968e-07,
                2.2603253756956754e-06,
                2.561282821402217e-06,
                2.7535691103314177e-05,
                2.2603234895372223e-06,
                6.962259569750576e-06,
                1.994729008145876e-06,
                1.3709572068553509e-06,
                4.785096206076165e-06,
                2.902312331170226e-06
            ],
            [
                NaN,
                4.785093924389007e-06,
                2.1444945858485726e-05,
                5.715005832886879e-07,
                1.7603438428848787e-06,
                1.0677028700363782e-06,
                4.450852111135988e-07,
                6.475947982037486e-07,
                5.715003789033962e-07,
                4.785093353940187e-06
            ],
            [
                1.7603440527286572e-06,
                1.0677032518700286e-06,
                1.0677027427600627e-06,
                7.338209805170655e-07,
                5.715006514105942e-07,
                5.715006514176113e-07,
                4.450849988811838e-07,
                9.422443692555439e-07,
                2.2603234895372223e-06,
                3.726640172537657e-06
            ],
            [
                0.0019267347027284668,
                3.288749849498565e-06,
                1.5534971990126997e-06,
                1.8925150497435443e-05,
                6.962254589781966e-06,
                1.0129987357407137e-05,
                2.144495097113319e-05,
                2.9023116391477434e-06,
                4.785093353940187e-06,
                8.939696304213768e-06
            ],
            [
                1.0677029973192638e-06,
                6.962256249885085e-06,
                NaN,
                6.144177531811707e-06,
                9.422447062202052e-07,
                7.338213304316717e-07,
                4.785095065204162e-06,
                1.5534979397740895e-06,
                3.288747889284851e-06,
                3.288749457469787e-06
            ],
            [
                8.315282259051341e-07,
                2.2603242978665707e-06,
                5.715004470313855e-07,
                1.8925157265710765e-05,
                7.338208930421943e-07,
                8.93970056668775e-06,
                NaN,
                2.1444953526969788e-05,
                4.785094494783494e-06,
                7.338207180864763e-07
            ],
            [
                5.71500719545698e-07,
                1.209866260432471e-06,
                8.315281267861397e-07,
                2.382369667929001e-07,
                5.715002426475718e-07,
                1.9947292459406333e-06,
                3.4663274507713016e-07,
                7.338208930460318e-07,
                1.6373774480605869e-07,
                3.059022998581767e-07
            ],
            [
                2.5612825160271407e-06,
                2.9023112932045342e-06,
                1.5534971989992774e-06,
                2.5612822107167428e-06,
                1.209866260432471e-06,
                1.012998977198894e-05,
                3.4663262111182307e-07,
                1.2098659719788098e-06,
                1.9947292459265734e-06,
                4.222835458148261e-06
            ],
            [
                1.5534975693979422e-06,
                1.8925152753790864e-05,
                4.2228329411708495e-06,
                5.422219616184461e-06,
                4.222834451355964e-06,
                6.962254589914941e-06,
                5.422218969818919e-06,
                2.902310947208574e-06,
                5.422217030747413e-06,
                8.315279285351409e-07
            ],
            [
                1.0677026154730804e-06,
                6.475949525981759e-07,
                1.0677032518748838e-06,
                1.0129994602895546e-05,
                7.338213304083124e-07,
                3.288750241561788e-06,
                9.422447062294175e-07,
                3.927862470816829e-07,
                NaN,
                1.0677026154619133e-06
            ],
            [
                4.22283545808297e-06,
                6.475945666063607e-07,
                6.144175334015912e-06,
                8.315282259138311e-07,
                1.760343633031919e-06,
                2.6995784182183607e-07,
                1.6701419853518415e-05,
                5.715003789017068e-07,
                3.466325797888292e-07,
                3.46632497145457e-07
            ],
            [
                1.1478766757404937e-05,
                2.1444956082767684e-05,
                0.00017952794494541173,
                2.2603242978213447e-06,
                4.785093924330255e-06,
                2.9023116391477434e-06,
                8.939694172957213e-06,
                1.8925148241080285e-05,
                8.939695238536645e-06,
                2.9023133690425823e-06
            ],
            [
                3.7266401726173067e-06,
                1.3709578605729614e-06,
                1.9947292459347367e-06,
                1.553497199007048e-06,
                3.7266406168827523e-06,
                7.88926446679691e-06,
                3.2887478892683997e-06,
                6.144177531767002e-06,
                2.9023109472244114e-06,
                1.2098656835224664e-06
            ],
            [
                1.7603427936335396e-06,
                2.90231094723893e-06,
                1.067702870039777e-06,
                4.222832437798974e-06,
                8.315279285351409e-07,
                7.338208930460318e-07,
                7.338211554801876e-07,
                1.0677026154806063e-06,
                3.288749065423109e-06,
                1.9947301970972664e-06
            ],
            [
                7.338207180838067e-07,
                6.475949526003845e-07,
                5.043474081993875e-07,
                3.927862939113312e-07,
                1.76034300345598e-06,
                5.715003107715166e-07,
                5.715003107715166e-07,
                2.6995790618252024e-07,
                5.043473480730849e-07,
                8.315282259009745e-07
            ],
            [
                1.8925141473186853e-05,
                8.939700566801578e-06,
                0.00010889688337946374,
                1.012999097997104e-05,
                4.785096206013061e-06,
                5.422217677078203e-06,
                7.338212429582604e-07,
                6.144174601879434e-06,
                1.8925143729575624e-05,
                0.00020342707066267436
            ],
            [
                6.475947982037486e-07,
                3.4663278639892215e-07,
                8.939696304311336e-06,
                3.4663262110803996e-07,
                3.2887502415767434e-06,
                5.043472879504592e-07,
                2.260324028427877e-06,
                1.4449807263312446e-07,
                2.1024336609843824e-07,
                3.9278610661902853e-07
            ],
            [
                3.2887506336235617e-06,
                3.4663278639892215e-07,
                4.006369219393695e-05,
                2.902312677137316e-06,
                NaN,
                3.72663883989755e-06,
                4.222834954778007e-06,
                3.288750241561788e-06,
                5.422220909009474e-06,
                1.2098661162056318e-06
            ],
            [
                4.222833444590791e-06,
                3.7266406168827523e-06,
                2.561282516066741e-06,
                4.22283545819819e-06,
                8.315279285351409e-07,
                1.9947304348862686e-06,
                4.4508510499849186e-07,
                1.2098656835224664e-06,
                1.4738983729535602e-05,
                1.5534971990169383e-06
            ],
            [
                4.222834954778007e-06,
                3.466327863983311e-07,
                1.5534975693979422e-06,
                1.9947301970972664e-06,
                3.059021175261338e-07,
                3.288749457409966e-06,
                2.561281905390075e-06,
                5.043473480777865e-07,
                2.902310947190096e-06,
                2.5612812947508257e-06
            ],
            [
                6.962258739796719e-06,
                NaN,
                5.04347468323289e-07,
                8.315282259089153e-07,
                3.726637951387472e-06,
                5.8291251656508296e-05,
                3.2887506336086064e-06,
                4.222834954778007e-06,
                1.3709572068522336e-06,
                NaN
            ],
            [
                8.315281267882195e-07,
                1.147876812574406e-05,
                3.0590237279085045e-07,
                4.450851580566494e-07,
                2.1024334103553052e-07,
                5.422219616228845e-06,
                2.3823688159237777e-07,
                1.3709576971463352e-06,
                3.059022998576899e-07,
                5.043472278312808e-07
            ],
            [
                1.8553905760062447e-07,
                3.05902190458764e-07,
                1.8553907971879076e-07,
                3.466326211113502e-07,
                5.043476486915964e-07,
                1.4449805540763184e-07,
                1.8553919030858602e-07,
                3.927863875616689e-07,
                1.637376862489725e-07,
                2.382369951932796e-07
            ],
            [
                1.9947304348862686e-06,
                1.209865827740176e-06,
                5.715003789033962e-07,
                8.315280276546789e-07,
                4.785095635655362e-06,
                3.059022269254856e-07,
                5.715005832895975e-07,
                6.475950297971703e-07,
                4.222833947932061e-06,
                8.315279285370317e-07
            ],
            [
                2.5612812947508257e-06,
                1.670141786325573e-05,
                1.3709575337078829e-06,
                1.760343003481596e-06,
                2.5612834320470717e-06,
                2.5612831267202583e-06,
                4.222833947960866e-06,
                6.144173869558639e-06,
                1.3709573702822306e-06,
                1.6701419854156377e-05
            ],
            [
                3.535624228698939e-05,
                1.7603427936335396e-06,
                1.0677027427600627e-06,
                1.0677032518785256e-06,
                3.2887506336235617e-06,
                1.3007131566015624e-05,
                3.7266379513434106e-06,
                8.939695238634211e-06,
                5.715003107767143e-07,
                NaN
            ],
            [
                1.4738983729535602e-05,
                1.9947306726594253e-06,
                2.9023109472244114e-06,
                4.222833947897496e-06,
                1.892515501014656e-05,
                1.9947304348595095e-06,
                3.2887478892683997e-06,
                1.7603434231777837e-06,
                3.726639728348526e-06,
                3.53562422882756e-05
            ],
            [
                NaN,
                NaN,
                6.475945666033422e-07,
                6.475949526020042e-07,
                NaN,
                5.422217030747413e-06,
                1.3709572068522336e-06,
                3.4663249714451116e-07,
                1.553498495338299e-06,
                NaN
            ],
            [
                2.2603251062450327e-06,
                NaN,
                7.338210680021253e-07,
                9.422448185534261e-07,
                9.422445939032799e-07,
                1.7603425837855082e-06,
                2.902312331170226e-06,
                2.2603245673155757e-06,
                1.2098659719757836e-06,
                6.962254589978262e-06
            ],
            [
                9.931195693628605e-08,
                1.4449798650551755e-07,
                2.3823690999323465e-07,
                6.475946438055299e-07,
                4.4508526417298334e-07,
                1.637377057680051e-07,
                2.3823688159291947e-07,
                3.0590237279085045e-07,
                5.422218969895357e-06,
                1.5534977545886537e-06
            ],
            [
                5.422217677152175e-06,
                5.71500515159253e-07,
                4.222832437677995e-06,
                1.3709567165617364e-06,
                5.422217677152175e-06,
                9.610240358212368e-05,
                6.962259569750576e-06,
                2.7535694385633984e-05,
                8.93969843573914e-06,
                2.5612831266946347e-06
            ],
            [
                1.7603434231505666e-06,
                1.5534984953298217e-06,
                3.288749457409966e-06,
                2.2603242978871282e-06,
                2.3823699519035448e-07,
                3.726638839878908e-06,
                2.561282210729555e-06,
                1.5534975693792215e-06,
                1.0677031245905116e-06,
                1.994729721469003e-06
            ],
            [
                0.0,
                NaN,
                1.7603440527334603e-06,
                3.4663278639892215e-07,
                NaN,
                6.475947982037486e-07,
                8.315279285351409e-07,
                5.4222202626709005e-06,
                1.3709568799919866e-06,
                NaN
            ],
            [
                4.785092783519724e-06,
                6.962257909842961e-06,
                2.5612819054133693e-06,
                2.9023116391978967e-06,
                1.1478769494250387e-05,
                2.9023119851635836e-06,
                2.90231094723893e-06,
                NaN,
                2.902312331170226e-06,
                2.90231094723893e-06
            ],
            [
                1.0677024881980089e-06,
                4.78509392429544e-06,
                2.4300249423965898e-05,
                6.1441731370702875e-06,
                7.889264466639056e-06,
                6.962255419931625e-06,
                4.222835458148261e-06,
                5.422219616184461e-06,
                1.300712846477255e-05,
                6.144173136952939e-06
            ],
            [
                1.6701429808632785e-05,
                5.422218969818919e-06,
                5.422218969818919e-06,
                4.222832437747125e-06,
                1.5534984953453635e-06,
                1.0677031245905116e-06,
                1.1478765389222573e-05,
                4.785096206013061e-06,
                1.0129990980100021e-05,
                2.9023112931873767e-06
            ],
            [
                2.561282210729555e-06,
                2.5612819054028872e-06,
                6.9622587397397306e-06,
                2.430023204460668e-05,
                1.7603434231705793e-06,
                1.0677027427600627e-06,
                2.7535704231043113e-05,
                3.5356238071317175e-05,
                1.7603438428660665e-06,
                4.785092783415276e-06
            ],
            [
                1.2751908849167202e-07,
                1.0677028700422047e-06,
                1.8553907971855875e-07,
                1.6373766672973748e-07,
                2.6995790618469934e-07,
                1.4449805540763184e-07,
                2.3823690999290963e-07,
                3.466326211113502e-07,
                2.382370235933104e-07,
                1.4449805540651476e-07
            ],
            [
                9.422442569208767e-07,
                3.927860597945825e-07,
                2.5612812947508257e-06,
                4.785096206076165e-06,
                4.785096776468749e-06,
                4.222832941193893e-06,
                2.2603234895176927e-06,
                2.260324836776948e-06,
                1.3709576971425944e-06,
                NaN
            ],
            [
                4.006367786720367e-05,
                NaN,
                1.760342793638743e-06,
                5.715007195447234e-07,
                NaN,
                5.422217030781934e-06,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                6.475947982037486e-07,
                1.3709573702822306e-06,
                1.760344052714248e-06,
                6.475945666051092e-07,
                6.962257909785973e-06,
                7.338209805224048e-07,
                9.422442569315887e-07,
                1.2098655392811161e-06,
                3.726641061109272e-06,
                8.31528424162821e-07
            ],
            [
                NaN,
                1.209865827752005e-06,
                1.760342793638743e-06,
                NaN,
                NaN,
                NaN,
                4.785094494811783e-06,
                2.2603234895372223e-06,
                6.144176066943187e-06,
                NaN
            ],
            [
                5.4222176771176554e-06,
                NaN,
                2.699578096403948e-07,
                0.0009110510256005003,
                1.6701421845057263e-05,
                6.962256249821764e-06,
                7.889266347636241e-06,
                3.7266392840781026e-06,
                3.726641061109272e-06,
                4.785095635624897e-06
            ],
            [
                1.2098661161927025e-06,
                5.043473480777865e-07,
                3.05902336324494e-07,
                7.338208055680009e-07,
                1.3709576971425944e-06,
                8.315278294114555e-07,
                5.043474081993875e-07,
                4.450848927658745e-07,
                6.475951069932288e-07,
                NaN
            ],
            [
                1.1478770862882149e-05,
                2.260324567337161e-06,
                8.939696304311336e-06,
                9.422442569315887e-07,
                1.760343213335281e-06,
                1.99472900813862e-06,
                2.902312677137316e-06,
                9.422445939054222e-07,
                1.0677029973158649e-06,
                1.760343003481596e-06
            ],
            [
                1.0129989772412744e-05,
                1.0677031245905116e-06,
                1.5534975693933505e-06,
                2.561282210701601e-06,
                3.2887482812506295e-06,
                8.939696304213768e-06,
                3.288749457432399e-06,
                8.939697369785323e-06,
                3.2887490653408545e-06,
                4.785095635592258e-06
            ],
            [
                1.3709575336947905e-06,
                5.4222183235249605e-06,
                3.4663262110945863e-07,
                4.4508494582405734e-07,
                1.0677026154806063e-06,
                5.715002426475718e-07,
                NaN,
                1.2098662604126641e-06,
                1.2098653950656417e-06,
                6.9622579096593295e-06
            ],
            [
                NaN,
                1.3709575337159875e-06,
                3.4663274507713016e-07,
                NaN,
                3.05902336324494e-07,
                NaN,
                1.0129987357517693e-05,
                NaN,
                5.715005832895975e-07,
                7.338208055680009e-07
            ],
            [
                3.288749065423109e-06,
                1.1478764021029928e-05,
                6.1441767993788005e-06,
                NaN,
                NaN,
                4.785093924389007e-06,
                NaN,
                1.7603430034867993e-06,
                3.7266401726359486e-06,
                3.9278605979534166e-07
            ],
            [
                1.6701427816728442e-05,
                4.222832437747125e-06,
                1.1478769493916314e-05,
                7.484623620251482e-05,
                1.8925141472360678e-05,
                7.889263526093993e-06,
                4.006369219393695e-05,
                4.222833947897496e-06,
                8.939694172770212e-06,
                2.9023116391978967e-06
            ],
            [
                2.7535694384081332e-05,
                7.889266347786918e-06,
                3.7266379512518984e-06,
                4.222835458002318e-06,
                5.422219616228845e-06,
                7.889259764359722e-06,
                2.1444940744318203e-05,
                2.9023119851635836e-06,
                4.785092783519724e-06,
                2.1444953522913026e-05
            ],
            [
                1.553497754583709e-06,
                3.288748281295496e-06,
                2.9023126771227976e-06,
                4.785095635624897e-06,
                3.288749849477628e-06,
                2.561283432035425e-06,
                1.2098658277451275e-06,
                NaN,
                4.785094494750855e-06,
                1.5534977545886537e-06
            ],
            [
                8.315280276626197e-07,
                3.466326211113502e-07,
                6.475947210046347e-07,
                9.422447062294175e-07,
                9.422448185510695e-07,
                1.5534979397829198e-06,
                1.7603427936335396e-06,
                NaN,
                7.338213304363436e-07,
                4.450850519403407e-07
            ],
            [
                2.2603251062450327e-06,
                1.3709567165617364e-06,
                1.0677029973219343e-06,
                6.475947982037486e-07,
                3.9278610661902853e-07,
                4.22283545819819e-06,
                1.2098653950656417e-06,
                9.422445939032799e-07,
                4.4508494582405734e-07,
                3.7266397283908927e-06
            ],
            [
                1.9947292459347367e-06,
                NaN,
                1.994730434879465e-06,
                5.4222183235249605e-06,
                6.962257909501028e-06,
                3.2887482811908074e-06,
                3.2887498495150166e-06,
                3.726639728370556e-06,
                2.260325106237323e-06,
                1.5534977545886537e-06
            ],
            [
                6.144175334468545e-06,
                2.2603242978871282e-06,
                2.260325106237323e-06,
                1.6701425826525565e-05,
                1.7603425837791042e-06,
                5.1442195268327955e-05,
                1.1478768125911099e-05,
                2.260324836776948e-06,
                6.144176066850984e-06,
                7.338210680021253e-07
            ],
            [
                2.9023123311583482e-06,
                1.892514598551715e-05,
                1.0677026154806063e-06,
                2.144494585801764e-05,
                NaN,
                0.00013982202424632715,
                NaN,
                2.7535700949523498e-05,
                7.889263526345123e-06,
                1.300712846411008e-05
            ],
            [
                8.315282259117513e-07,
                8.315282259151545e-07,
                3.9278605979011705e-07,
                8.315279285370317e-07,
                3.72663883989755e-06,
                2.382368531929327e-07,
                2.699577774585891e-07,
                1.9947299593078385e-06,
                3.2887506336086064e-06,
                1.9947292459347367e-06
            ],
            [
                NaN,
                1.2098662604291696e-06,
                NaN,
                1.209865539295696e-06,
                1.5534983101602148e-06,
                9.422449308716635e-07,
                5.715005832886879e-07,
                1.994729483723626e-06,
                1.5534971990126997e-06,
                3.2887498495150166e-06
            ],
            [
                7.889266347786918e-06,
                2.1024339116168358e-07,
                3.7266379514061143e-06,
                5.043475284468537e-07,
                2.699576809143613e-07,
                3.927862002663297e-07,
                6.475950298021765e-07,
                3.288749457469787e-06,
                2.561281294760143e-06,
                3.726638395611981e-06
            ],
            [
                4.539789029616496e-05,
                8.315283250394546e-07,
                8.315282259138311e-07,
                1.3709573702822306e-06,
                9.422448185388577e-07,
                6.475951069932288e-07,
                3.9278610661902853e-07,
                3.05902117523595e-07,
                2.6995784182140636e-07,
                3.927862002625787e-07
            ],
            [
                4.2228329411708495e-06,
                1.3709568799823232e-06,
                3.059022998576899e-07,
                5.715003107655392e-07,
                1.5534975693869924e-06,
                1.5534975693792215e-06,
                1.9947306726358406e-06,
                1.3709575337078829e-06,
                5.715005832853093e-07,
                NaN
            ],
            [
                1.1253508156363576e-07,
                3.653479031538012e-08,
                4.691162683297406e-08,
                1.1253512180925583e-07,
                6.023571320847322e-08,
                1.1253508156363576e-07,
                5.315784971839039e-08,
                3.224187402001668e-08,
                4.1399375473868e-08,
                4.139938534423022e-08
            ]
        ]
    },
    {
        "q_id": "9861_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                1.5534971990169383e-06,
                1.4449798650551755e-07,
                3.4663278639892215e-07,
                1.3709573702856596e-06,
                0.00026119024774258443,
                3.9278634073732336e-07,
                0.999998932296876,
                3.927863875616689e-07,
                6.475946438055299e-07,
                3.7266383956509585e-06
            ],
            [
                0.9999982396567892,
                0.9999975938965187,
                3.1201907657271834e-05,
                0.9999987901338867,
                0.9999986290432857,
                0.9999988634358843,
                0.9999962733589599,
                0.9999982396572089,
                0.9999978766205351,
                1.0677026154806063e-06
            ],
            [
                2.2603242978871282e-06,
                4.450849988811838e-07,
                3.466325797888292e-07,
                3.466327450744504e-07,
                3.466326624322211e-07,
                5.715004470313855e-07,
                5.715006514151423e-07,
                2.6995790618350237e-07,
                7.338211554783522e-07,
                2.2603253756956754e-06
            ],
            [
                1.760343633031919e-06,
                0.999998932297131,
                1.6373776432509826e-07,
                8.315284241650899e-07,
                1.0677029973219343e-06,
                8.315277302841894e-07,
                0.9999938558247091,
                1.2098652508424818e-06,
                0.9999970976883652,
                0.9999985406236083
            ],
            [
                1.3007123813193233e-05,
                1.6701427817730953e-05,
                5.422221555340727e-06,
                7.88926446679691e-06,
                4.785092783519724e-06,
                2.5612812947508257e-06,
                3.288750241561788e-06,
                6.962257909785973e-06,
                6.962259569750576e-06,
                4.785096206076165e-06
            ],
            [
                0.9999986290424682,
                0.9999982396567896,
                0.9999981261241744,
                0.9999974387180995,
                0.999999266178845,
                0.999999607213753,
                0.9999983463104168,
                0.9999985406239547,
                0.9999977396762448,
                0.9999981261250672
            ],
            [
                5.04347468323289e-07,
                2.1024336609874897e-07,
                5.043475885696228e-07,
                1.067703124601679e-06,
                5.71500515161527e-07,
                5.715002426486762e-07,
                1.209865827752005e-06,
                3.4663278639892215e-07,
                2.382370235933104e-07,
                3.059022269254856e-07
            ],
            [
                1.3709575337159875e-06,
                3.059022269254856e-07,
                8.315279285370317e-07,
                6.47594875403829e-07,
                NaN,
                1.6373762769187936e-07,
                2.1024334103581732e-07,
                3.9278629391427843e-07,
                1.5534983101644536e-06,
                8.315284241665078e-07
            ],
            [
                0.9999992188513903,
                0.9999997897566592,
                0.9999997300421261,
                0.9999997617630049,
                0.9999995818812272,
                0.9999997761971315,
                0.9999967112521146,
                0.9999997463981334,
                0.999999057755182,
                0.9999991148428591
            ],
            [
                NaN,
                NaN,
                6.962257079889302e-06,
                2.1024331597288867e-07,
                1.3709572068553509e-06,
                3.466326624336003e-07,
                8.31528325040778e-07,
                1.994729008151319e-06,
                7.338210680032098e-07,
                3.288749849529972e-06
            ],
            [
                7.338208055680009e-07,
                9.422443692574719e-07,
                9.422442569334097e-07,
                1.9947292459406333e-06,
                3.927862470905692e-07,
                9.422442569334097e-07,
                2.382368815932174e-07,
                1.0677026154827912e-06,
                5.715002426486762e-07,
                3.927862470905692e-07
            ],
            [
                5.043472879540142e-07,
                7.338210680021253e-07,
                1.0677024882009222e-06,
                5.715005151606823e-07,
                6.962254589978262e-06,
                3.466327037548308e-07,
                4.450848927650143e-07,
                3.466326211113502e-07,
                4.450848927650143e-07,
                8.315277302857965e-07
            ],
            [
                0.9999978766212881,
                0.9999989969856738,
                0.9999991148427537,
                0.9999987121047859,
                0.9999972735287644,
                0.9999945777790987,
                0.9999978766223011,
                0.9999996072136595,
                0.9999985406232597,
                0.9999942280813554
            ],
            [
                3.535624650279074e-05,
                1.760342793638743e-06,
                4.222834954801051e-06,
                3.466326211113502e-07,
                1.1253512180925583e-07,
                4.222834954801051e-06,
                3.7266401726359486e-06,
                2.10243290909724e-07,
                2.2603240284371276e-06,
                2.699578740032504e-07
            ],
            [
                2.2603253756956754e-06,
                8.939697369882888e-06,
                2.9023112932177327e-06,
                0.9999981261250663,
                1.0677033791612137e-06,
                4.0063696967815485e-05,
                4.222833444590791e-06,
                1.147877359957198e-05,
                9.422448185534261e-07,
                1.5534973842076057e-06
            ],
            [
                1.0677029973219343e-06,
                0.999998712105094,
                0.9999983463096273,
                2.1024336609843824e-07,
                0.9999993524052024,
                0.9999992188514837,
                0.9999987901346064,
                0.9999998942829477,
                0.9999993524051249,
                0.9999997126314468
            ],
            [
                7.338208055680009e-07,
                2.5612834320563895e-06,
                8.315279285370317e-07,
                8.315284241665078e-07,
                1.3709575337159875e-06,
                2.561283126728994e-06,
                2.1024331597288867e-07,
                7.889265407327733e-06,
                4.4508494582405734e-07,
                2.3823690999323465e-07
            ],
            [
                3.9278634073732336e-07,
                3.05902263391829e-07,
                3.927863875616689e-07,
                5.715002426486762e-07,
                1.637377448057981e-07,
                3.927862470899887e-07,
                2.69957906184239e-07,
                2.1024336609874897e-07,
                3.059022998581767e-07,
                2.1024334103581732e-07
            ],
            [
                5.71500515161527e-07,
                1.2098656835252174e-06,
                3.288749849529972e-06,
                NaN,
                1.7603425837903113e-06,
                1.994729008151319e-06,
                4.222834451403972e-06,
                9.422450432030903e-07,
                2.5612834320563895e-06,
                9.422443692574719e-07
            ],
            [
                1.3709575337159875e-06,
                1.9947292459406333e-06,
                5.71500515161527e-07,
                3.7266379514061143e-06,
                1.0677024882029858e-06,
                7.33821330437595e-07,
                9.422450432030903e-07,
                1.3709572068553509e-06,
                3.288749849529972e-06,
                7.338208055680009e-07
            ],
            [
                0.999998446502802,
                0.9999991148432811,
                0.9999994956527123,
                0.9999997126315153,
                0.999999495652652,
                0.999998629042631,
                0.9999991148430707,
                0.9999994956524116,
                0.999999391640891,
                0.9999986290424676
            ],
            [
                0.999999057755182,
                0.999998126125066,
                0.9999986290427942,
                0.9999986290431221,
                0.9999967112505479,
                0.999998712104325,
                0.9999987901338845,
                0.9999990577554069,
                0.9999987121046323,
                0.9999988634357486
            ],
            [
                1.994730434879465e-06,
                4.222833444590791e-06,
                2.9023126771227976e-06,
                2.9023133690980155e-06,
                3.4663278639738526e-07,
                2.260324028427877e-06,
                6.144173137126169e-06,
                4.785094494750855e-06,
                1.5534984953453635e-06,
                4.222834954778007e-06
            ],
            [
                8.315277302857965e-07,
                3.9278620026686556e-07,
                1.994729483729522e-06,
                9.422443692574719e-07,
                1.4449803818215767e-07,
                1.8553907971879076e-07,
                7.338209805240734e-07,
                4.450850519409479e-07,
                3.927863407379485e-07,
                6.475950298021765e-07
            ],
            [
                2.7535687820994754e-05,
                5.422217677152175e-06,
                6.962259569750576e-06,
                2.699576809143613e-07,
                6.1441767993788005e-06,
                5.715006514176113e-07,
                7.338208055680009e-07,
                1.637377057680051e-07,
                1.5534983101644536e-06,
                3.4663274507713016e-07
            ],
            [
                1.012999098021058e-05,
                2.902312331170226e-06,
                4.785094494811783e-06,
                1.1478764020883773e-05,
                1.7603440527286572e-06,
                8.315277302841894e-07,
                1.209865539295696e-06,
                1.5534973842076057e-06,
                1.7603434231833873e-06,
                6.144175334468545e-06
            ],
            [
                5.715006514176113e-07,
                5.422220262636381e-06,
                8.315277302857965e-07,
                2.699577130960941e-07,
                1.760343213335281e-06,
                5.043475885696228e-07,
                3.2887502415767434e-06,
                6.47595107001401e-07,
                3.466326624336003e-07,
                1.3709576971463352e-06
            ],
            [
                1.3709576971463352e-06,
                6.1441746020359e-06,
                1.0677029973219343e-06,
                2.6995774527718623e-07,
                1.7603440527334603e-06,
                7.338208055680009e-07,
                6.475946438055299e-07,
                1.2098661162056318e-06,
                2.5612834320563895e-06,
                3.927863875616689e-07
            ],
            [
                1.760342793638743e-06,
                5.71500719545698e-07,
                2.2603248367949354e-06,
                5.715005832895975e-07,
                7.338212429582604e-07,
                5.71500515161527e-07,
                4.785095635655362e-06,
                1.3709575337159875e-06,
                7.338211554813555e-07,
                7.338212429594283e-07
            ],
            [
                0.9999992661787577,
                0.9999992188512976,
                0.9999986290432854,
                0.9999989322973857,
                0.9999981261243952,
                0.9999990577551825,
                0.9999988634365632,
                0.9999982396565811,
                0.999998996985674,
                0.9999987121041719
            ],
            [
                6.475945666063607e-07,
                NaN,
                5.043474082012222e-07,
                3.927862470905692e-07,
                8.31528325040778e-07,
                2.699578096403948e-07,
                2.1024331597288867e-07,
                2.699578740032504e-07,
                1.0677027427624903e-06,
                1.3709575337159875e-06
            ],
            [
                6.47595107001401e-07,
                NaN,
                8.315278294114555e-07,
                1.0129994602895546e-05,
                3.466326624336003e-07,
                1.760342793638743e-06,
                NaN,
                5.715006514176113e-07,
                5.715004470326849e-07,
                9.422443692574719e-07
            ],
            [
                2.902312677150514e-06,
                1.760342793638743e-06,
                1.5534973842076057e-06,
                1.0677027427624903e-06,
                1.209866260432471e-06,
                1.2098659719788098e-06,
                5.715002426486762e-07,
                1.994729721518893e-06,
                9.422443692574719e-07,
                1.0677027427624903e-06
            ],
            [
                0.9999993524051249,
                0.9999980052698069,
                0.9999987121043261,
                0.9999984465015076,
                0.999999114842754,
                0.9999987121041718,
                0.9999991684717748,
                0.9999990577557442,
                0.9999988634365625,
                0.9999996533673792
            ],
            [
                6.475949526020042e-07,
                7.338213304363436e-07,
                1.0677027427600627e-06,
                5.043472879525233e-07,
                2.102434412875379e-07,
                8.315281267861397e-07,
                4.450849458218309e-07,
                3.4663262110945863e-07,
                3.4663266243111764e-07,
                5.715007195431641e-07
            ],
            [
                6.825608606148807e-08,
                4.4508510499737865e-07,
                5.04347287955046e-07,
                2.382368531929327e-07,
                1.6373772528704005e-07,
                3.059021175261338e-07,
                1.637377448057981e-07,
                3.059022998581767e-07,
                2.69957906184239e-07,
                4.4508505193932864e-07
            ],
            [
                0.999997438717488,
                0.9999993524053565,
                0.999997097686635,
                0.9999989322966216,
                0.9999992661787572,
                0.9999993916409636,
                0.9999989322966217,
                0.999999057755744,
                0.9999945777810482,
                0.9999964991464249
            ],
            [
                4.785094494750855e-06,
                6.144172404587612e-06,
                5.422218323399208e-06,
                5.422221555340727e-06,
                1.4738978457041559e-05,
                8.939697369671496e-06,
                2.561283432035425e-06,
                3.1201900215552636e-05,
                6.144174601935314e-06,
                1.300712691403299e-05
            ],
            [
                0.9999978766205269,
                0.9999934595651283,
                0.9999991684715767,
                0.9999978766205289,
                0.999995777168076,
                0.9999724643123923,
                0.9999983463102188,
                0.9999982396565789,
                0.9999964991464284,
                0.999999057755182
            ],
            [
                8.315284241650899e-07,
                6.144176799334096e-06,
                1.5534977545886537e-06,
                1.5534981249697903e-06,
                4.4508494582405734e-07,
                1.2098662604291696e-06,
                1.7603427936335396e-06,
                9.422450432014836e-07,
                1.5534971990126997e-06,
                9.422445939032799e-07
            ],
            [
                0.9999970976866419,
                0.99999905775507,
                0.9999972735294101,
                0.999996711251731,
                0.9999992661790207,
                0.9999982396574192,
                0.9999975938976671,
                0.9999981261239522,
                0.9999869928654289,
                0.9999992188512976
            ],
            [
                0.9999996940976272,
                0.9999997126313441,
                0.9999994956525923,
                0.9999991148426494,
                0.9999994631248684,
                0.9999949062950081,
                0.9999997126315497,
                0.9999962733602769,
                0.9999984465024331,
                0.9999988634357495
            ],
            [
                0.9999997463982241,
                0.9999996743687035,
                0.9999996072136125,
                0.9999997300421261,
                0.9999987121050925,
                0.9999993106387084,
                0.9999990577554071,
                0.9999989969856734,
                0.9999986290431212,
                0.9999952149060868
            ],
            [
                0.9999988634358844,
                0.999998712104325,
                0.9999996072138468,
                0.9999996072138467,
                0.9999987121043251,
                0.9999930377404486,
                0.9999987121047862,
                0.9999978766207808,
                0.9999417087208847,
                0.9999997761970516
            ],
            [
                2.2603245673443566e-06,
                3.927863407379485e-07,
                6.47595107001401e-07,
                2.102434162245973e-07,
                9.422444815814404e-07,
                1.3709572068522336e-06,
                1.760342793638743e-06,
                5.043475284468537e-07,
                3.288749457469787e-06,
                8.315277302857965e-07
            ],
            [
                3.535624650150453e-05,
                0.9999910603047922,
                3.2887498495150166e-06,
                5.043474081993875e-07,
                0.9999974387177946,
                1.0129990980100021e-05,
                7.338212429582604e-07,
                3.535626757524533e-05,
                3.2887490653872164e-06,
                6.605212894856585e-05
            ],
            [
                9.422442569334097e-07,
                3.059022269254856e-07,
                9.422443692574719e-07,
                1.8553907971879076e-07,
                6.47594952603035e-07,
                2.10243290909963e-07,
                2.3823690999323465e-07,
                3.466325384682834e-07,
                2.3823690999323465e-07,
                1.4449796928021588e-07
            ],
            [
                0.9999978766223011,
                4.450851049991497e-07,
                5.4222183235249605e-06,
                1.0677028700422047e-06,
                2.3823688159291947e-07,
                2.6995774527718623e-07,
                1.2751899728311609e-07,
                0.9999990577551825,
                6.475945666063607e-07,
                0.9999986290421407
            ],
            [
                1.7603425837903113e-06,
                1.209865539298447e-06,
                3.0590219045914655e-07,
                NaN,
                7.338207180898968e-07,
                3.7266383956509585e-06,
                6.47595107001401e-07,
                3.05902190458764e-07,
                3.9278629391427843e-07,
                1.3007134667436886e-05
            ],
            [
                5.715006514176113e-07,
                5.043475885696228e-07,
                3.927862470905692e-07,
                1.209865539298447e-06,
                9.422443692574719e-07,
                1.855391239547094e-07,
                7.338209805240734e-07,
                3.927863407379485e-07,
                1.3709576971463352e-06,
                8.315277302857965e-07
            ],
            [
                0.9999991684722703,
                0.9999967112505511,
                0.9999992188516701,
                0.9999975938965165,
                0.9999994631248045,
                0.9999989969857933,
                0.9999982396567901,
                0.9999984465018783,
                0.9999985406232589,
                0.9999980052705233
            ],
            [
                0.9999989322966214,
                0.9999994631251241,
                0.9999992188515768,
                0.9999987901341728,
                0.9999978766207813,
                0.9999992661787576,
                0.9999994284994853,
                0.999998126124845,
                0.9999955048162882,
                0.9999993524053564
            ],
            [
                0.9999997463980124,
                6.475945666063607e-07,
                1.3007125363908762e-05,
                0.9999983463100229,
                0.9999987901344625,
                6.605214470327124e-05,
                1.4449800373118268e-07,
                1.275191036933194e-07,
                1.6373776432509826e-07,
                0.9999810748587965
            ],
            [
                1.0677024882029858e-06,
                3.0590219045914655e-07,
                9.422443692574719e-07,
                2.10243290909963e-07,
                5.715006514176113e-07,
                3.466326624336003e-07,
                8.315277302857965e-07,
                6.47595107001401e-07,
                1.275190124846946e-07,
                3.4663274507713016e-07
            ],
            [
                1.2098661162056318e-06,
                7.33821330437595e-07,
                1.5534973842076057e-06,
                2.3823693839325527e-07,
                5.715002426486762e-07,
                5.043472278322555e-07,
                8.315284241665078e-07,
                3.466326624336003e-07,
                1.9947301970972664e-06,
                3.466325797900508e-07
            ],
            [
                0.9999934595627845,
                1.760343213335281e-06,
                2.2603251062450327e-06,
                0.9999978766212859,
                3.12019039369228e-05,
                0.9999945777797477,
                0.999997438716573,
                6.144175334468545e-06,
                4.785095635655362e-06,
                1.5534984953552536e-06
            ],
            [
                1.209865827752005e-06,
                8.315277302841894e-07,
                2.1444940745839484e-05,
                1.670142980893658e-05,
                1.5534983101644536e-06,
                3.05902190458764e-07,
                1.3709567165617364e-06,
                1.012998977264307e-05,
                2.90231094723893e-06,
                3.288747889284851e-06
            ],
            [
                0.9999898700126635,
                0.9999990577554072,
                0.9999972735287583,
                0.9999987121050934,
                0.9999972735290862,
                0.9999975938970911,
                0.9999980052700455,
                0.9999986290427945,
                0.9999992188519492,
                0.9999998024947038
            ],
            [
                7.338213304363436e-07,
                9.422445939054222e-07,
                1.5534981249697903e-06,
                3.466326211113502e-07,
                4.785095065232451e-06,
                3.1201922535494165e-05,
                1.7603425837903113e-06,
                1.5534984953552536e-06,
                2.6995790618469934e-07,
                2.2603234895372223e-06
            ],
            [
                0.999996910506666,
                0.9999985406236086,
                0.999999114843176,
                0.9999992661786704,
                0.9999984465015068,
                0.9999992661787581,
                0.9999993916411092,
                0.999997876621793,
                0.9999997463980729,
                0.9999975938985337
            ],
            [
                8.315277302857965e-07,
                5.715003789046955e-07,
                9.422443692574719e-07,
                3.2887506336086064e-06,
                5.043472879525233e-07,
                4.222832941193893e-06,
                5.04347468323289e-07,
                4.785095065232451e-06,
                9.422445939032799e-07,
                3.05902336324494e-07
            ],
            [
                8.315278294114555e-07,
                1.6373766672973748e-07,
                2.5612834320563895e-06,
                1.8553914607267268e-07,
                3.466326624336003e-07,
                7.338212429594283e-07,
                6.47594952603035e-07,
                3.05902263391829e-07,
                1.2098656835252174e-06,
                1.7603425837903113e-06
            ],
            [
                9.422448185534261e-07,
                5.04347287955046e-07,
                0.9999977396757057,
                1.0677032518814388e-06,
                2.1024336609843824e-07,
                3.059022998581767e-07,
                3.4663249714612693e-07,
                2.6995790618469934e-07,
                1.9947299593078385e-06,
                2.6995784182140636e-07
            ],
            [
                4.450851049991497e-07,
                3.0590219045914655e-07,
                3.059022269254856e-07,
                8.315278294114555e-07,
                2.3823682479317953e-07,
                1.1253524254650944e-07,
                3.4663262111182307e-07,
                2.561282821402217e-06,
                3.9278629391427843e-07,
                8.315284241665078e-07
            ],
            [
                4.4508494582405734e-07,
                6.962254589978262e-06,
                1.760343213335281e-06,
                8.315281267882195e-07,
                2.5612828213934817e-06,
                6.475947210046347e-07,
                3.7266406168827523e-06,
                4.785093353940187e-06,
                1.0677029973192638e-06,
                8.315280276626197e-07
            ],
            [
                3.466326624336003e-07,
                5.71500515161527e-07,
                1.9947301970972664e-06,
                1.3709576971463352e-06,
                NaN,
                1.209865827752005e-06,
                1.7603425837903113e-06,
                4.450850519409479e-07,
                2.3823688159291947e-07,
                8.315284241665078e-07
            ],
            [
                0.9999996940978827,
                0.9999994631251883,
                0.9999994631249324,
                0.9999993106389549,
                0.9999997463981636,
                0.999999730042094,
                0.9999995818812772,
                0.9999994284994851,
                0.9999983463106135,
                0.9999998024946566
            ],
            [
                1.4738980215593877e-05,
                NaN,
                1.994729483729522e-06,
                3.288748673376478e-06,
                1.7603434231833873e-06,
                8.939700567094277e-06,
                NaN,
                0.9999970976883638,
                NaN,
                3.2887506336235617e-06
            ],
            [
                7.88926446679691e-06,
                0.9999983463100212,
                0.9999978766207807,
                0.9999995818811774,
                0.9999969105055572,
                0.9999969105040838,
                0.9999934595620341,
                0.9999952149049423,
                0.9999992188516696,
                0.9999904837460956
            ],
            [
                0.9999987901341748,
                2.1024326584639497e-07,
                1.760343003481596e-06,
                5.715006514151423e-07,
                9.422444815765128e-07,
                5.043474081993875e-07,
                1.3709576971425944e-06,
                3.0590215399183813e-07,
                5.715003107755449e-07,
                0.9999852610233815
            ],
            [
                1.0677032518814388e-06,
                5.715002426486762e-07,
                1.30071315662049e-05,
                8.315284241665078e-07,
                2.3823682479292225e-07,
                3.0590219045914655e-07,
                9.422448185534261e-07,
                4.450848927658745e-07,
                5.715003107767143e-07,
                4.450848927658745e-07
            ],
            [
                2.4300232045225487e-05,
                2.3823693839290317e-07,
                9.422442569315887e-07,
                1.3709568799919866e-06,
                1.2751899728311609e-07,
                3.466327037548308e-07,
                1.7603438428800754e-06,
                9.931198061405701e-08,
                2.902313023130843e-06,
                6.475950298021765e-07
            ],
            [
                0.9999706884685834,
                0.9999986290427954,
                0.9999977396762434,
                0.9999985406243022,
                0.9999949062956144,
                0.9999904837505995,
                1.4738976701652988e-05,
                0.9999974387187102,
                0.9999987121044778,
                2.1444948415296896e-05
            ],
            [
                0.999999057755407,
                5.829128639666634e-05,
                1.3709576971425944e-06,
                8.315281267861397e-07,
                0.9999984465024345,
                1.2098656835224664e-06,
                4.785093924362895e-06,
                0.9999991684720723,
                0.9999989322967493,
                2.902310947208574e-06
            ],
            [
                2.260324028427877e-06,
                NaN,
                2.1024334103505245e-07,
                4.450850519403407e-07,
                4.4508494582405734e-07,
                4.4508510499849186e-07,
                1.5534983101602148e-06,
                7.338211554783522e-07,
                8.315284241650899e-07,
                3.927860597945825e-07
            ],
            [
                0.9999986290427944,
                0.9999988634361549,
                0.9999989969854353,
                0.9999986290431218,
                0.9999987121047862,
                0.9999987901343181,
                0.9999989969861521,
                0.9999975938979525,
                0.9999969105044529,
                0.9999996743688974
            ],
            [
                0.9999949062925821,
                0.999999266178845,
                0.9999962733616131,
                0.9999996533674615,
                0.999998629043284,
                0.9999981261241709,
                0.9999997126315153,
                0.9999991148431754,
                0.9999978766210321,
                0.9999994956525319
            ],
            [
                0.9999994631251242,
                0.9999921107393217,
                0.9999964991439203,
                0.999995777166564,
                0.9999996072138466,
                0.9999995818812769,
                0.9999993524048932,
                0.9999964991460079,
                0.9999852610145428,
                0.9999151889389276
            ],
            [
                0.9999990577552945,
                0.9999992661792824,
                0.9999964991468434,
                0.9999994631249324,
                0.9999986290424671,
                0.9999992188519494,
                0.9999987901347499,
                0.9999982396559498,
                0.9999992661789325,
                0.9999990577550699
            ],
            [
                0.999999266179195,
                0.9999997126313441,
                0.9999991148428589,
                0.9999994631248682,
                0.9999995549148952,
                0.9999994956527727,
                0.999998996985554,
                0.9999996072139404,
                0.9999993106391193,
                0.999998790133741
            ],
            [
                0.9999962733598321,
                5.8291272497207844e-05,
                1.4738985486506781e-05,
                0.0001398220575534256,
                1.0677028700422047e-06,
                9.422442569315887e-07,
                1.0129989772532511e-05,
                0.00017952798776403812,
                4.5397874064161706e-05,
                9.61024379351396e-05
            ],
            [
                0.9999983463102181,
                0.9999990577551819,
                0.9999993916406736,
                0.9999992188512972,
                0.999999674368742,
                0.9999994956524115,
                0.9999993524048936,
                0.9999995549148952,
                0.9999997897565588,
                0.9999995818814267
            ],
            [
                3.927862470899887e-07,
                2.699576809143613e-07,
                1.8553916819032217e-07,
                5.715003107767143e-07,
                1.147877359957198e-05,
                2.3823696679327928e-07,
                3.0590237279032884e-07,
                1.6373776432509826e-07,
                1.855391681898159e-07,
                3.059022998576899e-07
            ],
            [
                7.338209805200689e-07,
                3.059022269250683e-07,
                7.338213304363436e-07,
                2.5612828213934817e-06,
                1.5534971990126997e-06,
                1.5534971990126997e-06,
                6.475945666063607e-07,
                1.0677032518785256e-06,
                2.382370235922541e-07,
                5.715005832886879e-07
            ],
            [
                0.9999991148431757,
                0.9999993916408185,
                0.9999996743687035,
                0.9999991684718739,
                0.9999993524054337,
                0.9999989969859123,
                0.9999995549149482,
                0.9999989322968762,
                0.9999994631251246,
                0.9999995818814266
            ],
            [
                0.9999992661788452,
                0.9999982396569991,
                0.9999986290427947,
                0.999996711250157,
                0.9999975938965165,
                0.9999978766217945,
                0.9999969105059262,
                0.9999982396565793,
                0.9999989969859128,
                0.9999969105066624
            ],
            [
                1.8553919030858602e-07,
                1.0677028700422047e-06,
                3.4663262111182307e-07,
                3.466327037553825e-07,
                1.9947301970972664e-06,
                1.209866260432471e-06,
                8.31528325040778e-07,
                5.715006514176113e-07,
                7.338207180898968e-07,
                1.0677027427624903e-06
            ],
            [
                1.0129987357407137e-05,
                2.5612828213934817e-06,
                1.5534983101602148e-06,
                1.5534973842030142e-06,
                6.144176799334096e-06,
                2.902312677137316e-06,
                3.726638395634011e-06,
                6.144173869558639e-06,
                6.9622595696935874e-06,
                0.0
            ],
            [
                6.144175334468545e-06,
                2.902312677150514e-06,
                2.90231094723893e-06,
                2.902312677150514e-06,
                5.043474683240344e-07,
                6.475947210046347e-07,
                2.902312331170226e-06,
                3.4663262111182307e-07,
                5.715007195447234e-07,
                1.5534975693979422e-06
            ],
            [
                8.481104140395962e-05,
                7.889266347786918e-06,
                3.726638839878908e-06,
                1.2098659719757836e-06,
                4.222834451382849e-06,
                2.260325106237323e-06,
                5.715007195447234e-07,
                1.0677027427600627e-06,
                1.9947297215125433e-06,
                8.315283250394546e-07
            ],
            [
                6.47595107001401e-07,
                7.338209805240734e-07,
                2.2603253756956754e-06,
                2.9023112932177327e-06,
                6.475947210046347e-07,
                1.5534971990169383e-06,
                1.0677033791612137e-06,
                2.699576809143613e-07,
                1.5534983101644536e-06,
                8.315279285370317e-07
            ],
            [
                5.04347287955046e-07,
                7.338208055680009e-07,
                6.475947982037486e-07,
                NaN,
                4.450848927658745e-07,
                1.370957860576702e-06,
                8.315280276626197e-07,
                3.288747889284851e-06,
                1.370957860576702e-06,
                8.315279285370317e-07
            ],
            [
                1.012998977264307e-05,
                3.927860597945825e-07,
                2.9023119851899796e-06,
                1.6373762769138607e-07,
                5.3157830707696514e-08,
                NaN,
                1.1253512180925583e-07,
                2.5612819054133693e-06,
                3.9278615344178325e-07,
                2.102434412875379e-07
            ],
            [
                1.9947292459347367e-06,
                1.7603438428800754e-06,
                7.338208930460318e-07,
                1.760343213335281e-06,
                1.994729721518893e-06,
                2.9023116392097746e-06,
                1.5534983101602148e-06,
                3.2887498495150166e-06,
                7.889266347786918e-06,
                3.7266401726359486e-06
            ],
            [
                5.043475885696228e-07,
                5.715006514176113e-07,
                3.466326624336003e-07,
                7.338212429594283e-07,
                8.315279285370317e-07,
                4.450851049991497e-07,
                3.4663274507713016e-07,
                0.999998712104786,
                8.315277302857965e-07,
                1.3709576971463352e-06
            ],
            [
                7.734423152941018e-08,
                2.6995784182183607e-07,
                3.0590237279032884e-07,
                1.1253518888531272e-07,
                7.734421308914719e-08,
                8.764247451307293e-08,
                1.1253513522447425e-07,
                3.05902336324494e-07,
                1.4449795205429202e-07,
                3.653482951291499e-08
            ],
            [
                1.5534973842076057e-06,
                0.999998346310021,
                1.5534975693979422e-06,
                1.5534975693979422e-06,
                5.043476486915964e-07,
                7.889260704968913e-06,
                1.5534983101602148e-06,
                1.3709573702822306e-06,
                0.9999969105044507,
                0.9999988634364263
            ],
            [
                2.430024652792821e-05,
                0.9999995262092731,
                9.422447062294175e-07,
                2.3823693839325527e-07,
                6.475945666063607e-07,
                1.444980209564556e-07,
                0.9999994631249323,
                3.466326624336003e-07,
                0.999998996985434,
                0.9999916019290662
            ],
            [
                0.9999995818813269,
                0.999999653367255,
                0.9999998461826589,
                0.9999993106389549,
                0.9999996743686259,
                0.9999989322966215,
                0.9999974387187094,
                0.9999992188513905,
                0.999999428499417,
                0.999999168472171
            ],
            [
                0.9999989322972584,
                0.999999310639037,
                0.9999997617631469,
                0.9999996072136126,
                0.9999994284994853,
                0.999993037741276,
                0.9999996940977732,
                0.9999995262094987,
                0.9999995262094987,
                0.9999993106386262
            ],
            [
                0.9999996310115479,
                0.9999974387184024,
                3.72663883989755e-06,
                0.9999992661791071,
                2.2603242978943238e-06,
                1.9947299593078385e-06,
                0.9999969105059269,
                2.561283126728994e-06,
                0.0010322310985772072,
                5.043473480777865e-07
            ],
            [
                2.2603242978778778e-06,
                1.8553914607267268e-07,
                2.699578096403948e-07,
                8.315280276626197e-07,
                3.927863407379485e-07,
                5.043475885696228e-07,
                1.855391681906175e-07,
                2.699578096403948e-07,
                1.2098661162056318e-06,
                1.1253526937697666e-07
            ],
            [
                0.9999938558246945,
                0.9999964991464304,
                0.9999980052709952,
                0.9999960330122138,
                0.9999974387177969,
                0.9999977396746282,
                0.9999993106390371,
                0.9999988634361549,
                0.9999982396572091,
                0.9999975938973785
            ],
            [
                0.9999994631250602,
                0.9999989969862711,
                0.9999985406243018,
                0.9999987901343174,
                0.9999993916410362,
                0.9999962733602914,
                0.9999994631251885,
                0.9999984465015068,
                0.9999992661792826,
                0.9999969105040835
            ],
            [
                3.059022998581767e-07,
                1.3709567165617364e-06,
                1.370957860576702e-06,
                8.315277302857965e-07,
                1.3709567165617364e-06,
                7.338208055680009e-07,
                1.637376862489725e-07,
                1.209865827752005e-06,
                6.475947210046347e-07,
                2.699578096403948e-07
            ],
            [
                8.315278294114555e-07,
                5.043474683240344e-07,
                2.10243290909963e-07,
                9.931189774187203e-08,
                NaN,
                5.043474082012222e-07,
                NaN,
                6.475950298021765e-07,
                5.715006514176113e-07,
                4.450852111155216e-07
            ],
            [
                0.9999987901344625,
                0.9999822214418772,
                5.715005832895975e-07,
                0.9999988634360197,
                6.144172404738491e-06,
                9.422450432014836e-07,
                2.561281294760143e-06,
                6.475947210046347e-07,
                0.9999945777829864,
                0.9999756997535258
            ],
            [
                4.222834451403972e-06,
                1.5534983101602148e-06,
                2.2603245673443566e-06,
                3.288747889284851e-06,
                3.288749849529972e-06,
                2.9023116392097746e-06,
                1.5534984953552536e-06,
                1.012999218776902e-05,
                7.338207180898968e-07,
                1.0677028700422047e-06
            ],
            [
                4.22283545819819e-06,
                1.1478769494542698e-05,
                1.994729008145876e-06,
                1.3007130015677909e-05,
                0.999974132566297,
                2.2603234895372223e-06,
                1.3007128464961824e-05,
                1.012999098021058e-05,
                0.9999930377429479,
                0.9999904837438028
            ],
            [
                0.9999986290429594,
                0.999999057755182,
                0.9999991148426483,
                0.9999998874648917,
                0.9999988634357494,
                0.9999994956523516,
                0.999999218851577,
                0.9999991148429647,
                0.9999994956524118,
                0.9999987901341737
            ],
            [
                9.422444815814404e-07,
                1.5534981249736758e-06,
                1.2098659719788098e-06,
                2.3823688159291947e-07,
                7.338212429582604e-07,
                1.2098661162056318e-06,
                5.715002426486762e-07,
                2.9023112932177327e-06,
                2.699577774589574e-07,
                9.422449308774482e-07
            ],
            [
                0.9999994631248684,
                0.9999987121041726,
                0.9999997126315154,
                0.9999990577557436,
                0.9999995262095551,
                0.9999978766215396,
                0.9999989969861518,
                0.9999989969857933,
                0.9999993916411812,
                0.9999990577556316
            ],
            [
                6.475945666063607e-07,
                7.338211554813555e-07,
                4.4508515805735777e-07,
                1.0677027427624903e-06,
                4.450851049991497e-07,
                1.637376862489725e-07,
                4.4508515805735777e-07,
                1.855390576008354e-07,
                9.422444815814404e-07,
                9.931200429212718e-08
            ],
            [
                0.00010889689638175376,
                8.315277302857965e-07,
                2.9023119851899796e-06,
                4.2228339479858295e-06,
                7.889264466868659e-06,
                6.1441767993788005e-06,
                5.422220909009474e-06,
                4.222832941193893e-06,
                1.7603430034867993e-06,
                7.338208055680009e-07
            ],
            [
                1.209865827752005e-06,
                7.889264466868659e-06,
                1.0677026154806063e-06,
                1.0677033791612137e-06,
                2.561281294760143e-06,
                2.561281600086738e-06,
                1.0677032518814388e-06,
                2.2603253756956754e-06,
                2.561281600086738e-06,
                6.144177531811707e-06
            ],
            [
                0.9999910603005279,
                0.9999993106392013,
                0.9999990577550699,
                0.9999967112509376,
                0.9999982396569974,
                0.9999987121044784,
                0.9999877809225471,
                0.999998629042631,
                0.9999982396561601,
                5.043476486924565e-07
            ],
            [
                0.9999982396567888,
                0.9999981261241742,
                0.9999978766217951,
                0.9999983463110071,
                0.999999352405048,
                0.9999994631251248,
                0.9999982396565809,
                0.999998629042468,
                0.9999970976880241,
                0.9999986290429581
            ],
            [
                NaN,
                5.144219527094787e-05,
                0.9999987121049404,
                0.9999983463108094,
                2.5612831267202583e-06,
                1.0677032518785256e-06,
                0.9999989969861515,
                0.9999877809196837,
                1.9947292459347367e-06,
                0.999998446502802
            ],
            [
                0.9999992661786706,
                0.999999057755407,
                0.9999991148426499,
                0.00012339456028720406,
                0.9999989969857938,
                0.9999942280806782,
                0.9999988634362899,
                0.9999957771645545,
                0.9999982396572109,
                0.9999987121046333
            ],
            [
                5.043475284468537e-07,
                4.4508499888275247e-07,
                2.1024339116168358e-07,
                NaN,
                5.71500515161527e-07,
                1.7603425837903113e-06,
                2.561283126728994e-06,
                8.315278294114555e-07,
                2.3823682479317953e-07,
                2.3823690999323465e-07
            ],
            [
                3.726637951387472e-06,
                5.04347528446051e-07,
                1.7603434231833873e-06,
                1.3709568799919866e-06,
                5.043476486915964e-07,
                2.2603240284371276e-06,
                7.338209805224048e-07,
                7.338209805224048e-07,
                1.5534971990126997e-06,
                5.043474081993875e-07
            ]
        ]
    },
    {
        "q_id": "9707_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            23,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            68,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            100,
            101,
            102,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            117,
            118,
            119,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.450851580540182e-07,
                5.04347287955046e-07,
                5.715003107767143e-07,
                6.475950298011458e-07,
                1.7603434231777837e-06,
                4.450849988811838e-07,
                1.9947292459347367e-06,
                4.450848927621807e-07,
                6.475945666033422e-07,
                2.2603242978778778e-06
            ],
            [
                0.9999970976876722,
                0.9999980052693288,
                0.9999991684721709,
                0.9999980052693287,
                0.9999987901340284,
                0.999998126124841,
                0.9999983463098236,
                0.999998790134461,
                0.9999964991451746,
                2.1024341622426268e-07
            ],
            [
                1.2098661162023305e-06,
                2.382369951932796e-07,
                1.0677032518814388e-06,
                2.6995774527718623e-07,
                1.1253525596134564e-07,
                7.338209805240734e-07,
                1.067702870039777e-06,
                5.715005832872586e-07,
                5.04347468323289e-07,
                5.715003107767143e-07
            ],
            [
                NaN,
                2.902312677137316e-06,
                NaN,
                0.9999978766220471,
                1.2098652508287273e-06,
                NaN,
                6.962255419931625e-06,
                4.450852641737424e-07,
                9.422447062294175e-07,
                8.315279285351409e-07
            ],
            [
                4.222834954778007e-06,
                4.78509278348926e-06,
                3.288750241561788e-06,
                1.0677027427600627e-06,
                1.7603434231833873e-06,
                3.7266410611296085e-06,
                1.5534981249697903e-06,
                3.7266410611296085e-06,
                2.9023116391978967e-06,
                2.561281294760143e-06
            ],
            [
                8.315281267882195e-07,
                2.382369951932796e-07,
                1.7603434231833873e-06,
                1.2098659719757836e-06,
                9.422444815814404e-07,
                4.785092783519724e-06,
                6.475945666063607e-07,
                3.059021175261338e-07,
                9.422443692574719e-07,
                6.475947210046347e-07
            ],
            [
                7.338208055664991e-07,
                1.3709573702778664e-06,
                1.4738976701652988e-05,
                2.5612819054133693e-06,
                NaN,
                8.315278294114555e-07,
                1.1478766757853845e-05,
                6.962257079889302e-06,
                NaN,
                1.994729008151319e-06
            ],
            [
                2.902311639183378e-06,
                0.9999969105040821,
                3.927860597945825e-07,
                1.9947304348595095e-06,
                0.9999962733607202,
                0.9999977396765137,
                0.9999969105055552,
                6.475946438022905e-07,
                0.999941708741982,
                0.9999952149072294
            ],
            [
                1.5534977545603963e-06,
                1.209865539295696e-06,
                9.422449308716635e-07,
                1.9947292459347367e-06,
                1.7603436330259153e-06,
                4.222834451355964e-06,
                1.7603427936335396e-06,
                1.0677029973192638e-06,
                1.5534975693979422e-06,
                1.760343423160973e-06
            ],
            [
                1.5534975693869924e-06,
                3.726637951387472e-06,
                7.484626297142789e-05,
                9.422450431989127e-07,
                NaN,
                4.78509278348926e-06,
                1.2098656835224664e-06,
                5.715002426475718e-07,
                2.4300249425247723e-05,
                1.2098658277335738e-06
            ],
            [
                4.785094494750855e-06,
                7.338212429504183e-07,
                1.8925152754169532e-05,
                1.4738976701411704e-05,
                NaN,
                2.5612812947508257e-06,
                8.481105151274973e-05,
                9.422445939032799e-07,
                2.4300237838535383e-05,
                2.260324028427877e-06
            ],
            [
                2.5612831267202583e-06,
                1.1478765389368729e-05,
                2.260323758987159e-06,
                1.012998977264307e-05,
                8.939698435657833e-06,
                3.726639728348526e-06,
                6.962257909842961e-06,
                5.144221980055201e-05,
                4.0063682641226247e-05,
                1.0677028700422047e-06
            ],
            [
                7.889264466725156e-06,
                1.7603427936263351e-06,
                2.382369383923073e-07,
                5.715004470313855e-07,
                1.0677033791583005e-06,
                4.785093924362895e-06,
                2.5612828213934817e-06,
                8.315277302819205e-07,
                3.288749457469787e-06,
                6.962257909785973e-06
            ],
            [
                8.315283250394546e-07,
                1.1253508156363576e-07,
                1.2751908849167202e-07,
                2.2603242978871282e-06,
                2.2603251062450327e-06,
                2.102434162245973e-07,
                0.9998911031038947,
                0.9999969105055536,
                1.2098653950656417e-06,
                3.05902263391829e-07
            ],
            [
                1.553498124964492e-06,
                1.4449798650569826e-07,
                3.2887506336235617e-06,
                1.370957860567974e-06,
                3.4663278639892215e-07,
                2.382369383923073e-07,
                6.475945666033422e-07,
                6.475950298011458e-07,
                3.059021904580685e-07,
                9.422443692489024e-07
            ],
            [
                1.8553919030858602e-07,
                3.4663249714612693e-07,
                2.1024334103581732e-07,
                3.927862002654366e-07,
                NaN,
                1.1253526937697666e-07,
                1.4449798650551755e-07,
                2.382368531929327e-07,
                3.0590237279085045e-07,
                3.9278610661902853e-07
            ],
            [
                7.338208055664991e-07,
                6.475951069985296e-07,
                9.422443692527585e-07,
                1.0677026154730804e-06,
                1.3007123813382511e-05,
                5.715005832886879e-07,
                1.0677032518748838e-06,
                1.3709576971425944e-06,
                9.422448185510695e-07,
                1.994730434879465e-06
            ],
            [
                4.450852641737424e-07,
                1.370957860576702e-06,
                1.0677033791612137e-06,
                6.475945666051092e-07,
                1.994729721518893e-06,
                1.7603434231833873e-06,
                6.1441746020359e-06,
                7.338207180898968e-07,
                4.78509278348926e-06,
                1.012999098021058e-05
            ],
            [
                2.260324028427877e-06,
                1.4449805540763184e-07,
                4.7850950649408664e-06,
                4.785094494716039e-06,
                3.726639284103523e-06,
                3.2887490653408545e-06,
                1.5534979397740895e-06,
                9.422444815765128e-07,
                1.994729483705484e-06,
                2.2603245673155757e-06
            ],
            [
                1.994729721518893e-06,
                1.760343213335281e-06,
                8.315281267861397e-07,
                8.3152792852928e-07,
                4.785094494811783e-06,
                6.144177531811707e-06,
                2.5612825160562587e-06,
                1.3709567165530083e-06,
                2.5612828213934817e-06,
                9.422445939032799e-07
            ],
            [
                1.0129994602895546e-05,
                2.699577452775239e-07,
                9.422447062294175e-07,
                9.422444815814404e-07,
                2.1024336609843824e-07,
                2.382370235933104e-07,
                2.1024336609874897e-07,
                1.209866260432471e-06,
                1.5534984953552536e-06,
                NaN
            ],
            [
                1.0677032518785256e-06,
                7.338210680021253e-07,
                1.5534975693933505e-06,
                1.5534975693933505e-06,
                8.315280276626197e-07,
                1.3709568799919866e-06,
                1.7603438428800754e-06,
                1.5534981249697903e-06,
                5.04347528446051e-07,
                1.8553919030858602e-07
            ],
            [
                NaN,
                6.47595107001401e-07,
                5.715006514176113e-07,
                8.315277302857965e-07,
                4.4508494582405734e-07,
                7.338210680021253e-07,
                2.699576809143613e-07,
                8.315278294114555e-07,
                1.370957860576702e-06,
                2.382370235933104e-07
            ],
            [
                1.994729483705484e-06,
                2.5612828213934817e-06,
                9.422444815765128e-07,
                6.475945666051092e-07,
                1.5534981249397663e-06,
                1.3709570434122812e-06,
                1.9947299593078385e-06,
                NaN,
                2.9023112932045342e-06,
                2.902312677137316e-06
            ],
            [
                6.47594566594213e-07,
                1.444979692800516e-07,
                1.2098661161927025e-06,
                8.31528424162821e-07,
                NaN,
                3.0590226339061185e-07,
                1.9947292459265734e-06,
                5.04347528446051e-07,
                5.043475284430694e-07,
                1.7603436330259153e-06
            ],
            [
                9.422447062294175e-07,
                1.1253518888531272e-07,
                1.994730197090463e-06,
                8.315277302841894e-07,
                6.475945666051092e-07,
                5.04347528446051e-07,
                9.422442569315887e-07,
                1.637377448057981e-07,
                2.1024331597262577e-07,
                4.450852111148132e-07
            ],
            [
                5.422217677152175e-06,
                4.2228319344021954e-06,
                6.144173137170873e-06,
                0.00023050663330540923,
                6.962256249885085e-06,
                0.9999960330145606,
                1.4738983729535602e-05,
                2.1444943302650045e-05,
                6.144175334468545e-06,
                2.4300243631890864e-05
            ],
            [
                2.3823693839290317e-07,
                NaN,
                NaN,
                1.3709568799919866e-06,
                5.715003107767143e-07,
                8.764254764780641e-08,
                1.1253526937697666e-07,
                1.2751908849167202e-07,
                6.475946438055299e-07,
                1.637376862489725e-07
            ],
            [
                7.338209805240734e-07,
                0.9999981261252873,
                0.9999987121052455,
                0.9999989322968759,
                2.102434412875379e-07,
                0.999998932297258,
                0.9999985406236068,
                0.9999993524054337,
                0.9999991148429646,
                1.2098652508424818e-06
            ],
            [
                1.6373772528704005e-07,
                8.315281267834927e-07,
                8.315281267861397e-07,
                1.0677027427525368e-06,
                3.466326624322211e-07,
                1.0677029973192638e-06,
                2.90231094723893e-06,
                9.422448185510695e-07,
                3.9278615344178325e-07,
                1.0677032518748838e-06
            ],
            [
                5.715003789033962e-07,
                9.422442569315887e-07,
                3.726639728370556e-06,
                7.889261645269683e-06,
                1.5534971990126997e-06,
                1.3709570434178922e-06,
                6.605212107986466e-05,
                1.2098656835224664e-06,
                5.829126555256903e-05,
                2.430025232128576e-05
            ],
            [
                NaN,
                2.9023112932177327e-06,
                4.785094494811783e-06,
                4.785093924389007e-06,
                NaN,
                NaN,
                2.9023119851899796e-06,
                NaN,
                5.422221555414699e-06,
                NaN
            ],
            [
                8.315282259138311e-07,
                1.2098656835224664e-06,
                9.422448185510695e-07,
                4.450850519403407e-07,
                4.4508505193932864e-07,
                8.315277302857965e-07,
                4.222834954801051e-06,
                1.3709568799919866e-06,
                1.0129989772532511e-05,
                1.6373774480605869e-07
            ],
            [
                3.726637951387472e-06,
                5.4222183235249605e-06,
                1.5534984953552536e-06,
                2.382368531929327e-07,
                4.450849988798682e-07,
                2.561282516066741e-06,
                2.2603253756956754e-06,
                1.2098661162056318e-06,
                5.043476486924565e-07,
                1.3709575337159875e-06
            ],
            [
                3.7266397283908927e-06,
                4.785095635655362e-06,
                1.1478768126057254e-05,
                1.0677027427600627e-06,
                5.422219616265831e-06,
                8.315277302857965e-07,
                4.222833444590791e-06,
                3.288749457469787e-06,
                5.04347528446051e-07,
                1.5534983101602148e-06
            ],
            [
                1.3007133116732079e-05,
                5.715003789046955e-07,
                6.144176799334096e-06,
                NaN,
                1.7603427936263351e-06,
                5.04347468323289e-07,
                1.3709570434219446e-06,
                2.902312677150514e-06,
                2.102434412875379e-07,
                4.222834954778007e-06
            ],
            [
                5.715005151606823e-07,
                5.715003107767143e-07,
                3.466325797896173e-07,
                1.370957860576702e-06,
                1.637377057673536e-07,
                3.726637951387472e-06,
                1.5534975693979422e-06,
                1.6373770576776313e-07,
                1.5534971990169383e-06,
                NaN
            ],
            [
                1.4449807263312446e-07,
                8.764242227418718e-08,
                1.637377057680051e-07,
                1.855391681906175e-07,
                2.5612828213934817e-06,
                1.8553903548231313e-07,
                1.99472900813862e-06,
                1.9947301970972664e-06,
                3.9278629391427843e-07,
                3.2887502415767434e-06
            ],
            [
                7.338211554783522e-07,
                1.0677024881980089e-06,
                9.422445939032799e-07,
                4.450848927650143e-07,
                1.067702615468225e-06,
                9.422450431989127e-07,
                3.2887482813149375e-06,
                1.0677024881980089e-06,
                2.2603234895176927e-06,
                7.338207180864763e-07
            ],
            [
                3.927862470899887e-07,
                1.5534975693979422e-06,
                4.785093353940187e-06,
                3.7266401726359486e-06,
                5.422217030781934e-06,
                NaN,
                1.7603427936335396e-06,
                1.5534981249697903e-06,
                3.9278615344178325e-07,
                1.2098652508424818e-06
            ],
            [
                8.315283250394546e-07,
                3.53562422882756e-05,
                2.6995790618469934e-07,
                NaN,
                2.561282210740037e-06,
                8.315277302841894e-07,
                5.043475885696228e-07,
                3.12019225345861e-05,
                NaN,
                1.6373766672973748e-07
            ],
            [
                3.466325797896173e-07,
                2.7535694385633984e-05,
                1.0677032518814388e-06,
                2.7535700950274782e-05,
                2.1024336609843824e-07,
                1.473898900066424e-05,
                1.0677032518748838e-06,
                0.0021827164088344124,
                0.9995121429473526,
                0.006692850967625253
            ],
            [
                1.2098656835224664e-06,
                7.338212429537553e-07,
                NaN,
                7.338212429537553e-07,
                6.1441746020359e-06,
                1.994730197071414e-06,
                1.7603438428800754e-06,
                7.88926446679691e-06,
                1.99472924590571e-06,
                3.288748673360027e-06
            ],
            [
                3.72663883989755e-06,
                2.9023119851899796e-06,
                8.315277302857965e-07,
                NaN,
                8.315279285370317e-07,
                1.275190732904469e-07,
                8.315277302857965e-07,
                1.067703124601679e-06,
                8.315278294114555e-07,
                1.5534983101644536e-06
            ],
            [
                0.9999985406232579,
                1.7603432133032607e-06,
                0.999999912357442,
                0.9999994956525919,
                6.144176066901277e-06,
                0.9999724643157163,
                0.9999983463102179,
                1.209865827752005e-06,
                0.9999925887166048,
                0.9999962733620543
            ],
            [
                7.338208930460318e-07,
                3.466326624336003e-07,
                2.6995774527718623e-07,
                6.475947210046347e-07,
                1.5534973842076057e-06,
                3.05902190458764e-07,
                3.0590237279085045e-07,
                5.043473480777865e-07,
                3.466325384678894e-07,
                3.466326624336003e-07
            ],
            [
                2.2603234895289998e-06,
                3.7266410611296085e-06,
                1.0677028700363782e-06,
                2.9023116391978967e-06,
                1.0677027427600627e-06,
                2.5612812947508257e-06,
                1.2098662604291696e-06,
                2.902311639183378e-06,
                2.9023112932177327e-06,
                4.222833444590791e-06
            ],
            [
                0.9999994631249961,
                0.9999977396751644,
                0.9999984465026167,
                0.9999992188514835,
                0.9999982396572069,
                0.9999969105055547,
                2.6995771309523475e-07,
                0.9999981261239469,
                0.9999977396748951,
                0.9999995549150543
            ],
            [
                1.1253513522447425e-07,
                NaN,
                3.9278610661902853e-07,
                3.9278605979534166e-07,
                0.9996200154273983,
                1.2751899728311609e-07,
                2.6995784182183607e-07,
                1.8925148242250705e-05,
                1.1478769494542698e-05,
                1.0129988565084915e-05
            ],
            [
                NaN,
                6.825597214718257e-08,
                7.734424996967756e-08,
                6.825598028392069e-08,
                5.3157811697009444e-08,
                6.825600469412533e-08,
                7.73441946488886e-08,
                7.734414854823498e-08,
                1.1253509497883659e-07,
                5.043473480777865e-07
            ],
            [
                3.927862002625787e-07,
                9.422443692555439e-07,
                6.475949526020042e-07,
                1.5534979397790343e-06,
                1.7603427936335396e-06,
                1.0677032518748838e-06,
                6.475947210031623e-07,
                3.466327037553825e-07,
                5.043473480777865e-07,
                3.466325797888292e-07
            ],
            [
                4.450848927658745e-07,
                3.059022269254856e-07,
                1.855391239544352e-07,
                8.315284241665078e-07,
                5.043475885696228e-07,
                3.9278629391427843e-07,
                1.994729008151319e-06,
                3.05902263391829e-07,
                8.315278294114555e-07,
                2.102434162245973e-07
            ],
            [
                5.715004470313855e-07,
                6.962256249821764e-06,
                1.6701427817730953e-05,
                1.3709576971425944e-06,
                NaN,
                2.382369667929001e-07,
                7.88926446679691e-06,
                1.9947294837154625e-06,
                2.5612816000646084e-06,
                NaN
            ],
            [
                1.5534975693979422e-06,
                2.2603234895372223e-06,
                5.715003789046955e-07,
                6.962258739796719e-06,
                NaN,
                3.46632497145457e-07,
                7.889259764517575e-06,
                5.715003789046955e-07,
                1.7603438428800754e-06,
                6.475949526020042e-07
            ],
            [
                4.139934092760465e-08,
                2.1024334103581732e-07,
                1.1253516205489029e-07,
                3.9278629391427843e-07,
                5.3157887739943563e-08,
                1.1253509497883659e-07,
                4.4508515805735777e-07,
                2.699576809143613e-07,
                5.71500719545698e-07,
                6.475947982037486e-07
            ],
            [
                3.7266410611296085e-06,
                1.8925143729954285e-05,
                NaN,
                1.0129993395336818e-05,
                1.0129994602895546e-05,
                1.4738978458623327e-05,
                2.2603242978871282e-06,
                6.962257909785973e-06,
                2.2603234895289998e-06,
                2.9023130231176453e-06
            ],
            [
                0.0001795279663377456,
                4.7850944945245504e-06,
                1.5534981249697903e-06,
                9.422443692489024e-07,
                5.422221555296344e-06,
                0.0003353500311432834,
                5.715003107715166e-07,
                NaN,
                2.4300249425247723e-05,
                1.067703251864202e-06
            ],
            [
                6.475950298011458e-07,
                2.382368531929327e-07,
                6.475948754012522e-07,
                9.931186222523604e-08,
                8.764254764780641e-08,
                1.2751910369275402e-07,
                1.2098659719757836e-06,
                1.2751905808881762e-07,
                9.422444815814404e-07,
                2.3823702359290413e-07
            ],
            [
                8.315279285351409e-07,
                NaN,
                2.144495864059426e-05,
                7.889262585886274e-06,
                1.4738976701411704e-05,
                5.422220262636381e-06,
                2.144495608424996e-05,
                NaN,
                1.1478765389368729e-05,
                NaN
            ],
            [
                0.00017952803058267475,
                8.481103129578775e-05,
                1.3709575337159875e-06,
                4.006371129776199e-05,
                1.855391239544352e-07,
                1.9947292459347367e-06,
                1.8553910183674878e-07,
                5.04347468323289e-07,
                NaN,
                6.475947982037486e-07
            ],
            [
                7.889265407255982e-06,
                1.0129987357407137e-05,
                2.7535694383279957e-05,
                3.2887478892504536e-06,
                1.5534975693869924e-06,
                6.144177531767002e-06,
                1.209865250822125e-06,
                1.7603436330179102e-06,
                1.9947299592933255e-06,
                1.7603432133136672e-06
            ],
            [
                6.475947982037486e-07,
                4.450849988811838e-07,
                4.785094494783494e-06,
                9.422448185534261e-07,
                2.9023119851781017e-06,
                4.222834954778007e-06,
                1.0677029973192638e-06,
                1.7603425837903113e-06,
                2.260323758987159e-06,
                4.785096206076165e-06
            ],
            [
                6.82560779249779e-08,
                2.1024336609874897e-07,
                3.0590219045914655e-07,
                2.3823693839325527e-07,
                4.450852641737424e-07,
                NaN,
                4.4508515805735777e-07,
                5.043475885696228e-07,
                3.4663278639892215e-07,
                NaN
            ],
            [
                1.7603427936335396e-06,
                5.043472879525233e-07,
                6.144174601991196e-06,
                1.7603430034743913e-06,
                6.475945666051092e-07,
                5.715003107738556e-07,
                6.475946438022905e-07,
                1.4738989000422955e-05,
                1.0677028700266676e-06,
                2.2603237589676295e-06
            ],
            [
                3.7266410611296085e-06,
                3.726639728348526e-06,
                3.2887506336086064e-06,
                7.889264466725156e-06,
                6.475950298011458e-07,
                1.9947301970813926e-06,
                4.4508505193791187e-07,
                2.260324836776948e-06,
                8.315284241650899e-07,
                7.338209805224048e-07
            ],
            [
                0.9999982396561583,
                4.222834954778007e-06,
                0.9999967112493695,
                1.5534975693979422e-06,
                3.288750241561788e-06,
                6.9622587397397306e-06,
                0.00026119034110431625,
                3.288748281329893e-06,
                1.209865539295696e-06,
                0.9999962733620525
            ],
            [
                1.2098658277451275e-06,
                1.994729721518893e-06,
                1.0677024882009222e-06,
                7.338213304363436e-07,
                6.475946438055299e-07,
                5.715003107767143e-07,
                6.475947982037486e-07,
                NaN,
                NaN,
                8.315279285351409e-07
            ],
            [
                2.102434412871794e-07,
                7.338212429582604e-07,
                4.450848927658745e-07,
                4.450852111155216e-07,
                1.4449805540740185e-07,
                7.338208055664991e-07,
                2.6995790618469934e-07,
                5.715005832886879e-07,
                1.9947292459347367e-06,
                3.466326624336003e-07
            ],
            [
                3.4663274507713016e-07,
                0.9999785550516355,
                4.4508494582405734e-07,
                0.0003799845775099843,
                1.2751904288739315e-07,
                1.4449805540740185e-07,
                0.9999852610163193,
                1.6701425827133152e-05,
                3.466326624336003e-07,
                5.043475885696228e-07
            ],
            [
                7.889266347786918e-06,
                1.7603434231833873e-06,
                1.3007123813382511e-05,
                1.0677029973219343e-06,
                1.209865827752005e-06,
                3.927862002663297e-07,
                2.4300252321904572e-05,
                1.0677033791612137e-06,
                0.9998977001003153,
                5.422217677152175e-06
            ],
            [
                8.315279285351409e-07,
                1.5534981249697903e-06,
                7.3382080556433e-07,
                1.994730197090463e-06,
                5.715003789046955e-07,
                9.422450432014836e-07,
                4.4508494582405734e-07,
                9.422450431989127e-07,
                1.7603434231833873e-06,
                1.0677033791612137e-06
            ],
            [
                1.0677027427600627e-06,
                2.260323758987159e-06,
                3.7266410611296085e-06,
                NaN,
                5.422217030781934e-06,
                4.450849988811838e-07,
                4.0063701745046735e-05,
                1.8925157266089433e-05,
                4.222833444590791e-06,
                8.93969950132721e-06
            ],
            [
                3.927862470899887e-07,
                1.3709572068522336e-06,
                7.338208055680009e-07,
                1.0677033791612137e-06,
                1.0677033791612137e-06,
                3.927863407379485e-07,
                2.9023119851781017e-06,
                2.5612819054133693e-06,
                2.2603248367949354e-06,
                1.0677026154827912e-06
            ],
            [
                1.7603430034867993e-06,
                2.2603234895372223e-06,
                2.102434162245973e-07,
                8.315279285351409e-07,
                4.222833444590791e-06,
                NaN,
                5.715003789046955e-07,
                2.5612819054133693e-06,
                NaN,
                1.3709568799919866e-06
            ],
            [
                1.30071315662049e-05,
                1.3007130015677909e-05,
                6.144174601991196e-06,
                3.288748673376478e-06,
                1.209865539295696e-06,
                1.5534975693933505e-06,
                1.3709567165461505e-06,
                1.7603438428740716e-06,
                1.2098653950656417e-06,
                3.726639284144195e-06
            ],
            [
                5.715003789046955e-07,
                6.475950298011458e-07,
                4.139940508508409e-08,
                3.2887486733420804e-06,
                2.9023130231176453e-06,
                0.9999962733589415,
                1.637377448057981e-07,
                3.9278629391427843e-07,
                5.715005151606823e-07,
                1.2098659719757836e-06
            ],
            [
                6.023578501513224e-08,
                6.9622587397397306e-06,
                1.275190276859705e-07,
                2.699578096403948e-07,
                NaN,
                1.1253524254650944e-07,
                3.466326624336003e-07,
                1.637376862489725e-07,
                6.023577783447482e-08,
                6.475949526020042e-07
            ],
            [
                5.04347287955046e-07,
                9.422442569315887e-07,
                5.04347528446051e-07,
                1.0677029973219343e-06,
                3.927862470899887e-07,
                5.04347468323289e-07,
                9.422442569315887e-07,
                1.2751902768612997e-07,
                NaN,
                NaN
            ],
            [
                1.0677029973219343e-06,
                7.484624513510494e-05,
                0.0002611904033454894,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                1.6373764721072816e-07,
                4.0063701745046735e-05
            ],
            [
                6.475945666051092e-07,
                7.734423152941018e-08,
                1.4449805540740185e-07,
                1.2098656835076114e-06,
                1.9947299592933255e-06,
                1.209866260432471e-06,
                2.102434412875379e-07,
                9.931189774187203e-08,
                9.422448185534261e-07,
                1.4449798650551755e-07
            ],
            [
                1.444979692800516e-07,
                3.927862002663297e-07,
                4.450852641737424e-07,
                3.059021175261338e-07,
                2.6995790618469934e-07,
                4.450848927658745e-07,
                NaN,
                5.04347528446051e-07,
                8.315283250394546e-07,
                8.315284241650899e-07
            ],
            [
                5.715007195431641e-07,
                2.1024336609843824e-07,
                4.785094494783494e-06,
                1.3709575337125585e-06,
                8.315281267861397e-07,
                2.753568453792444e-05,
                1.7603432133296774e-06,
                1.9947292459347367e-06,
                4.785095635624897e-06,
                5.422217030747413e-06
            ],
            [
                8.939693107288474e-06,
                1.9947292459347367e-06,
                4.785093353874907e-06,
                6.962253760024999e-06,
                6.962255419868303e-06,
                4.785093353940187e-06,
                6.144177531767002e-06,
                3.726639728370556e-06,
                2.2603248367656408e-06,
                1.9947297215043796e-06
            ],
            [
                1.670142980920999e-05,
                7.889266347786918e-06,
                1.2098659719788098e-06,
                7.889260704968913e-06,
                6.144176066943187e-06,
                1.7603425837855082e-06,
                8.315284241650899e-07,
                5.422218969895357e-06,
                5.422220262636381e-06,
                3.288749457469787e-06
            ],
            [
                4.222834451382849e-06,
                7.484624512911504e-05,
                7.889261645427538e-06,
                6.605214470327124e-05,
                2.9023119851899796e-06,
                6.60521446989462e-05,
                2.753568782024347e-05,
                4.785096776499213e-06,
                3.288749065423109e-06,
                6.9622587397397306e-06
            ],
            [
                9.422448185534261e-07,
                NaN,
                4.4508526417298334e-07,
                7.338210679979539e-07,
                3.927862939136532e-07,
                2.699576809143613e-07,
                1.0677032518814388e-06,
                1.3709570434219446e-06,
                4.4508510499849186e-07,
                1.6373764721072816e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                8.315277302841894e-07,
                4.450850519403407e-07,
                7.338210680021253e-07,
                NaN,
                1.8553919030858602e-07,
                3.4663278639892215e-07,
                1.3709572068522336e-06
            ],
            [
                6.962257909842961e-06,
                0.9999938558224762,
                0.9999925887219074,
                8.939697369980456e-06,
                0.9999599363127138,
                8.315279285351409e-07,
                0.9999251537820864,
                1.012998977264307e-05,
                7.889265407327733e-06,
                0.999860177893202
            ],
            [
                2.2603253756874524e-06,
                1.2098662604291696e-06,
                7.338213304363436e-07,
                9.422444815765128e-07,
                9.422442569315887e-07,
                7.338209805240734e-07,
                1.3709573702822306e-06,
                1.5534983101602148e-06,
                1.7603436330259153e-06,
                9.422443692555439e-07
            ],
            [
                3.05902336324494e-07,
                3.466325797896173e-07,
                4.4508515805735777e-07,
                2.6995784182183607e-07,
                8.764241182641775e-08,
                3.9278629391427843e-07,
                1.8553914607267268e-07,
                5.715003789046955e-07,
                2.90231094723893e-06,
                2.2603234895372223e-06
            ],
            [
                3.2887506336235617e-06,
                1.209865827752005e-06,
                2.902313023130843e-06,
                1.0677026154806063e-06,
                9.422447062294175e-07,
                1.370957860576702e-06,
                5.715006514176113e-07,
                3.535624650279074e-05,
                8.315280276626197e-07,
                6.475947210046347e-07
            ],
            [
                9.61024035541569e-05,
                5.043475284430694e-07,
                1.0677024881980089e-06,
                1.4738981972082061e-05,
                1.2098655392871682e-06,
                6.144174601991196e-06,
                7.889260704732132e-06,
                1.2098653950656417e-06,
                4.2228329411708495e-06,
                2.9023133690980155e-06
            ],
            [
                3.9278615344178325e-07,
                6.475947210012481e-07,
                6.144175334468545e-06,
                1.3709576971425944e-06,
                6.475949525981759e-07,
                3.0590226339061185e-07,
                3.927860597945825e-07,
                9.422445939002803e-07,
                1.2098658277451275e-06,
                8.315280276607289e-07
            ],
            [
                9.931193325852072e-08,
                2.3823696679327928e-07,
                5.04347468323289e-07,
                1.3709567165579959e-06,
                4.450852641737424e-07,
                8.315277302841894e-07,
                2.6995790618469934e-07,
                8.315279285370317e-07,
                5.715006514176113e-07,
                NaN
            ],
            [
                4.450848927650143e-07,
                1.5534983101602148e-06,
                1.8553916819032217e-07,
                1.5534979397592542e-06,
                1.5534979397740895e-06,
                6.475947982037486e-07,
                2.260324028372372e-06,
                3.7266406167827664e-06,
                1.0677027427569065e-06,
                3.7266388398585725e-06
            ],
            [
                1.8553916819032217e-07,
                9.422442569315887e-07,
                1.855391239539711e-07,
                3.9278605979534166e-07,
                3.4663278639892215e-07,
                4.450850519403407e-07,
                1.2751905808881762e-07,
                1.0677027427600627e-06,
                2.6995784182140636e-07,
                3.466325797896173e-07
            ],
            [
                3.4663249714612693e-07,
                5.043474081993875e-07,
                1.275190580890061e-07,
                1.2751899728311609e-07,
                3.059022269254856e-07,
                9.931189774187203e-08,
                NaN,
                1.2098662604291696e-06,
                5.043472278322555e-07,
                1.8553907971855875e-07
            ],
            [
                1.0129987357407137e-05,
                1.7603438428800754e-06,
                1.6701421845361053e-05,
                2.260324567337161e-06,
                1.3709572068522336e-06,
                1.3709572068522336e-06,
                9.422443692555439e-07,
                6.1441746020359e-06,
                4.785094494811783e-06,
                2.6995774527718623e-07
            ],
            [
                1.5534971990169383e-06,
                3.7266383956509585e-06,
                1.3709572068553509e-06,
                3.7266397283908927e-06,
                1.0677029973192638e-06,
                9.422450432014836e-07,
                1.994730672668496e-06,
                4.450848927658745e-07,
                1.0677032518814388e-06,
                5.71500719545698e-07
            ],
            [
                5.422220909009474e-06,
                9.422442569315887e-07,
                2.5612812947380135e-06,
                8.315282259009745e-07,
                1.370956716529941e-06,
                7.889262585886274e-06,
                1.0677028700363782e-06,
                2.9023112931873767e-06,
                5.043472879481655e-07,
                8.315281267800897e-07
            ],
            [
                2.561281294760143e-06,
                8.315277302841894e-07,
                NaN,
                5.043476486924565e-07,
                NaN,
                NaN,
                1.8553907971855875e-07,
                1.637376862489725e-07,
                6.475946438055299e-07,
                8.7642516304188e-08
            ],
            [
                4.222832941142044e-06,
                5.043472879540142e-07,
                8.315281267834927e-07,
                7.889266347715168e-06,
                5.715007195431641e-07,
                4.222835458148261e-06,
                5.422220262636381e-06,
                4.785095065232451e-06,
                1.5534975693869924e-06,
                7.338213304363436e-07
            ],
            [
                8.315282259138311e-07,
                2.7535700949523498e-05,
                0.9999822214545244,
                3.288747889284851e-06,
                4.222834954778007e-06,
                5.422220262636381e-06,
                2.902312677137316e-06,
                2.5612812947508257e-06,
                1.5534975693979422e-06,
                4.785093353940187e-06
            ],
            [
                6.475950298011458e-07,
                3.466327450765785e-07,
                3.05902263391829e-07,
                3.466327037548308e-07,
                1.3709575337159875e-06,
                7.73441946488886e-08,
                1.4449805540763184e-07,
                1.637377057673536e-07,
                3.05902336324494e-07,
                3.0590219045914655e-07
            ],
            [
                7.338207180898968e-07,
                5.4222215552470286e-06,
                1.760342793638743e-06,
                2.561282210729555e-06,
                0.999915188959582,
                1.012998735687278e-05,
                9.422442569315887e-07,
                6.962258739796719e-06,
                3.2887482811908074e-06,
                1.209865539295696e-06
            ],
            [
                NaN,
                1.2098661162023305e-06,
                2.699578740032504e-07,
                7.338208055664991e-07,
                1.7603440527286572e-06,
                6.825608606172863e-08,
                1.8553907971855875e-07,
                8.7642526752214e-08,
                7.338210680021253e-07,
                2.6995790618469934e-07
            ],
            [
                2.5612812947508257e-06,
                1.9947292459347367e-06,
                4.2228329411708495e-06,
                1.209865827740176e-06,
                2.9023109472244114e-06,
                1.3709576971379186e-06,
                7.889261645427538e-06,
                4.785096206076165e-06,
                1.99472900813862e-06,
                1.3709575337016483e-06
            ]
        ]
    },
    {
        "q_id": "9108_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.9947299592933255e-06,
                2.10243290909963e-07,
                2.902312677084523e-06,
                1.670141985245514e-05,
                1.3709570434122812e-06,
                1.9947292459265734e-06,
                4.450852111148132e-07,
                8.315278294097538e-07,
                6.962257909501028e-06,
                1.0677026154827912e-06
            ],
            [
                9.931189774187203e-08,
                7.734423152941018e-08,
                1.760344052693435e-06,
                2.382369951932796e-07,
                7.484620052444058e-05,
                9.931187406410953e-08,
                1.1253508156363576e-07,
                2.3823688159291947e-07,
                7.338207180801359e-07,
                8.76424013786396e-08
            ],
            [
                8.764247451307293e-08,
                NaN,
                1.1253508156363576e-07,
                1.994729721518893e-06,
                3.653481209178873e-08,
                0.999998126124841,
                2.6995774527718623e-07,
                3.288749457469787e-06,
                4.4508515805735777e-07,
                0.9999898700041975
            ],
            [
                4.450851049991497e-07,
                0.9999997463980427,
                1.637377057680051e-07,
                0.9999996743688199,
                0.9999964991464237,
                8.764241182641775e-08,
                2.699578096403948e-07,
                8.7642558095602e-08,
                3.653482951291499e-08,
                1.4449800373118268e-07
            ],
            [
                1.1253521571574156e-07,
                1.637377057680051e-07,
                7.734416698849138e-08,
                1.3709567165617364e-06,
                1.6373764721039308e-07,
                1.4738976701411704e-05,
                1.6373776432509826e-07,
                1.275191036933194e-07,
                8.764244316973974e-08,
                1.4449805540763184e-07
            ],
            [
                2.3823696679230424e-07,
                2.1024336609843824e-07,
                2.6995774527577444e-07,
                9.93120161310289e-08,
                1.4449805540763184e-07,
                1.2751899728311609e-07,
                3.0590237279085045e-07,
                3.4663249714612693e-07,
                1.4449805540763184e-07,
                2.1024326584639497e-07
            ],
            [
                1.370957860576702e-06,
                5.715005832886879e-07,
                1.994729483723626e-06,
                2.382368531929327e-07,
                1.067703124601679e-06,
                6.475947210046347e-07,
                1.2098658277489788e-06,
                NaN,
                1.760343423160973e-06,
                5.715007195447234e-07
            ],
            [
                0.9999785550542091,
                0.9999756997680439,
                1.6373770576776313e-07,
                0.9999898700090465,
                0.9999687980813098,
                0.9999942280813522,
                1.637376862489725e-07,
                8.764254764780641e-08,
                0.9999990577551819,
                7.338208055680009e-07
            ],
            [
                6.962256249885085e-06,
                2.902310947208574e-06,
                5.043474081993875e-07,
                1.3709576971425944e-06,
                3.7266410611296085e-06,
                2.2603240284371276e-06,
                9.422443692446175e-07,
                1.2098658277451275e-06,
                4.785095065232451e-06,
                2.260324028427877e-06
            ],
            [
                2.382370235933104e-07,
                2.382369951932796e-07,
                2.382370235933104e-07,
                4.450852111155216e-07,
                2.699578740032504e-07,
                4.4508494582405734e-07,
                2.699578096403948e-07,
                5.715002426486762e-07,
                1.0677026154827912e-06,
                NaN
            ],
            [
                3.466327450765785e-07,
                7.338212429582604e-07,
                1.4449795205457127e-07,
                8.315277302841894e-07,
                3.4663253846718004e-07,
                3.0590237279032884e-07,
                5.715005832886879e-07,
                5.043476486915964e-07,
                6.475947210031623e-07,
                1.4449795205429202e-07
            ],
            [
                1.994729483729522e-06,
                9.610244940712274e-05,
                1.892514373029853e-05,
                9.931202796993203e-08,
                2.382370235933104e-07,
                1.5534984953552536e-06,
                1.5534979397829198e-06,
                3.059021175261338e-07,
                3.466325797900508e-07,
                6.023576347299818e-08
            ],
            [
                1.0677027427600627e-06,
                7.338209805240734e-07,
                6.475947210031623e-07,
                2.699578096403948e-07,
                3.466325384682834e-07,
                1.994729483729522e-06,
                1.5534977545886537e-06,
                3.0590237279085045e-07,
                9.422447062294175e-07,
                7.338207180898968e-07
            ],
            [
                8.31528424162821e-07,
                2.2603242978778778e-06,
                6.475947210046347e-07,
                6.475946438055299e-07,
                3.288749457409966e-06,
                1.3709567165579959e-06,
                2.2603240284371276e-06,
                5.715002426486762e-07,
                1.7603434231241496e-06,
                8.764241182641775e-08
            ],
            [
                NaN,
                2.3823690999323465e-07,
                6.475945666063607e-07,
                2.699578096393206e-07,
                5.043475885696228e-07,
                1.3007126914612648e-05,
                2.2603242978871282e-06,
                5.043475885696228e-07,
                6.475948754028718e-07,
                6.475945666063607e-07
            ],
            [
                NaN,
                2.699577774589574e-07,
                0.9999974387187072,
                3.059022998581767e-07,
                3.9278620026686556e-07,
                1.637377057680051e-07,
                1.1253506814842375e-07,
                3.9278620026686556e-07,
                2.3823696679327928e-07,
                2.382368815932174e-07
            ],
            [
                2.382369667929001e-07,
                1.6373776432509826e-07,
                8.31528325040778e-07,
                7.734421308914719e-08,
                6.475950298011458e-07,
                1.0677033791612137e-06,
                3.653482951291499e-08,
                2.382368531929327e-07,
                2.3823688159291947e-07,
                1.6373770576776313e-07
            ],
            [
                3.4663249714612693e-07,
                1.8553916819032217e-07,
                4.450851580555361e-07,
                1.8553910183607374e-07,
                2.699578096393206e-07,
                8.764249540862797e-08,
                2.1024334103505245e-07,
                1.2098656835224664e-06,
                2.1024341622426268e-07,
                6.023573475041126e-08
            ],
            [
                5.043475885674441e-07,
                4.4508510499737865e-07,
                3.466325384661554e-07,
                1.1253514863968147e-07,
                3.927862002663297e-07,
                1.2098656835224664e-06,
                3.927862002654366e-07,
                2.6995784182140636e-07,
                1.6373772528677946e-07,
                5.043473480766399e-07
            ],
            [
                3.059023727894942e-07,
                3.927862470899887e-07,
                5.043475885696228e-07,
                5.043472879540142e-07,
                2.1024334103581732e-07,
                7.338209805240734e-07,
                3.927862470899887e-07,
                9.931189774187203e-08,
                2.2603245673443566e-06,
                2.6995790618469934e-07
            ],
            [
                2.6995771309523475e-07,
                8.764249540862797e-08,
                1.2751905808881762e-07,
                9.422445939054222e-07,
                4.4508494582405734e-07,
                1.6373764721039308e-07,
                7.338208055664991e-07,
                1.6373764721072816e-07,
                1.2751899728286965e-07,
                1.8553907971855875e-07
            ],
            [
                3.927862002641863e-07,
                1.8553916819032217e-07,
                1.6373764720990908e-07,
                1.1253521571574156e-07,
                3.059021539909339e-07,
                2.382369667929001e-07,
                4.4508494582405734e-07,
                1.8553910183607374e-07,
                1.8553903548231313e-07,
                1.8553903548231313e-07
            ],
            [
                3.9278610661902853e-07,
                2.7535704232595768e-05,
                5.715006514167015e-07,
                2.699577774585891e-07,
                6.475947210046347e-07,
                5.71500719545698e-07,
                5.043473480777865e-07,
                5.04347528446051e-07,
                2.382369951932796e-07,
                3.927862002663297e-07
            ],
            [
                8.764254764780641e-08,
                6.825602910433871e-08,
                8.764253719911533e-08,
                1.275190580890061e-07,
                1.275190732904469e-07,
                5.315789407666425e-08,
                1.8553907971855875e-07,
                4.691162683297406e-08,
                8.764245361752286e-08,
                1.637377448057981e-07
            ],
            [
                3.0590237279032884e-07,
                5.043475885696228e-07,
                3.0590215399183813e-07,
                9.422448185534261e-07,
                4.450852111148132e-07,
                3.927862002663297e-07,
                4.450850519403407e-07,
                5.715006514176113e-07,
                1.637377448057981e-07,
                9.422447062294175e-07
            ],
            [
                9.422444815726566e-07,
                6.825608606172863e-08,
                1.6373766672973748e-07,
                3.0590237279085045e-07,
                1.6373776432509826e-07,
                1.8553919030858602e-07,
                4.4508494582405734e-07,
                1.4449807263312446e-07,
                9.422445939054222e-07,
                4.691164920214251e-08
            ],
            [
                3.9278615344178325e-07,
                3.466325797896173e-07,
                2.3823688159237777e-07,
                2.1024334103581732e-07,
                3.4663278639892215e-07,
                3.059022998581767e-07,
                2.1024339116082313e-07,
                1.6373766672973748e-07,
                1.637376862489725e-07,
                2.3823690999290963e-07
            ],
            [
                1.4449807263312446e-07,
                3.9278629391427843e-07,
                2.699578740032504e-07,
                2.699577130960941e-07,
                4.450850519409479e-07,
                3.9278629391427843e-07,
                2.699577130960941e-07,
                1.2751902768612997e-07,
                2.1024334103581732e-07,
                1.760342793638743e-06
            ],
            [
                8.315277302841894e-07,
                4.4508494582405734e-07,
                3.05902190458764e-07,
                9.422450431912e-07,
                7.338210679949506e-07,
                6.475949526020042e-07,
                3.927862470899887e-07,
                2.699578740032504e-07,
                3.4663278639892215e-07,
                1.0677032518785256e-06
            ],
            [
                9.931189774187203e-08,
                2.2603234895372223e-06,
                NaN,
                9.931199245322124e-08,
                1.9947299593078385e-06,
                1.3709567165617364e-06,
                1.3709567165530083e-06,
                4.4508510499849186e-07,
                5.715003107767143e-07,
                1.855391681906175e-07
            ],
            [
                5.715006514176113e-07,
                4.4508515805735777e-07,
                5.043475885696228e-07,
                1.4449805540740185e-07,
                7.338207180898968e-07,
                3.0590219045914655e-07,
                1.760342793638743e-06,
                4.450852641737424e-07,
                1.3709568799919866e-06,
                1.5534983101602148e-06
            ],
            [
                5.043475885674441e-07,
                8.315281267861397e-07,
                2.9023133690980155e-06,
                1.5534975693933505e-06,
                4.450848927650143e-07,
                1.1478769494542698e-05,
                2.9023116391978967e-06,
                4.450849988811838e-07,
                9.422444815765128e-07,
                6.475951069985296e-07
            ],
            [
                6.475947210046347e-07,
                2.102434412875379e-07,
                5.715002426486762e-07,
                5.715003789046955e-07,
                2.1024336609843824e-07,
                2.699577774585891e-07,
                1.2098656835252174e-06,
                3.927863875616689e-07,
                2.2603253756956754e-06,
                1.994729721518893e-06
            ],
            [
                1.760343003481596e-06,
                2.3823685319320354e-07,
                1.892515049819277e-05,
                9.931190958076104e-08,
                3.4663262111182307e-07,
                7.338208930460318e-07,
                1.6373762769187936e-07,
                9.93120161310289e-08,
                8.31527928532683e-07,
                6.825608606172863e-08
            ],
            [
                2.260323758987159e-06,
                5.043473480777865e-07,
                1.8553907971855875e-07,
                8.315284241650899e-07,
                1.637376862489725e-07,
                3.466325797896173e-07,
                6.475948753991907e-07,
                8.764249540862797e-08,
                2.1024326584639497e-07,
                1.637377448057981e-07
            ],
            [
                2.1024336609874897e-07,
                3.059022998576899e-07,
                7.338207180898968e-07,
                2.5612819054133693e-06,
                1.7603425837903113e-06,
                1.7603425837903113e-06,
                1.8925155009767892e-05,
                7.33821330437595e-07,
                7.338208055680009e-07,
                5.043476486915964e-07
            ],
            [
                0.9999978766222984,
                1.855391681906175e-07,
                NaN,
                1.994729483729522e-06,
                NaN,
                1.855391681906175e-07,
                3.2887498495150166e-06,
                7.734418542875216e-08,
                0.00010889694829665246,
                5.71500719545698e-07
            ],
            [
                1.8553919030776337e-07,
                2.3823688159237777e-07,
                6.475950298011458e-07,
                2.382369667929001e-07,
                2.2603234895372223e-06,
                2.3823693839325527e-07,
                1.5534973842076057e-06,
                1.637377057673536e-07,
                4.78509563555309e-06,
                3.059021904571643e-07
            ],
            [
                1.0677027427525368e-06,
                2.6995768091310296e-07,
                2.382369667929001e-07,
                4.4508494582405734e-07,
                4.691162683297406e-08,
                7.3382080556433e-07,
                4.4508494582405734e-07,
                5.715002426486762e-07,
                3.05902263391829e-07,
                0.9999970976883632
            ],
            [
                1.994729483729522e-06,
                1.2098659719788098e-06,
                3.9278634073732336e-07,
                3.2887506336235617e-06,
                7.889265407327733e-06,
                2.382368531929327e-07,
                3.288749849529972e-06,
                2.102434412875379e-07,
                5.422219616265831e-06,
                4.785095635655362e-06
            ],
            [
                5.315784971839039e-08,
                2.102433159721477e-07,
                4.691167716359673e-08,
                1.2751910369275402e-07,
                7.734423152941018e-08,
                6.825598842035714e-08,
                1.8553916819032217e-07,
                3.224188555067886e-08,
                1.6373762769138607e-07,
                3.224187402001668e-08
            ],
            [
                3.059022269250683e-07,
                2.1024326584582131e-07,
                1.3709567165579959e-06,
                5.043476486915964e-07,
                6.825598842065202e-08,
                6.825609419848033e-08,
                2.382369383923073e-07,
                4.450849988780466e-07,
                5.04347528440776e-07,
                2.3823699519143784e-07
            ],
            [
                6.47595107001401e-07,
                1.1253509497883659e-07,
                7.73441946488886e-08,
                1.6373764721072816e-07,
                1.0677026154806063e-06,
                1.5534979397740895e-06,
                NaN,
                5.422220909009474e-06,
                0.0002959572061151019,
                3.224187402001668e-08
            ],
            [
                1.2098656835252174e-06,
                9.422442569334097e-07,
                3.927860597935108e-07,
                1.3709576971463352e-06,
                5.715007195447234e-07,
                2.2603251062450327e-06,
                1.370957860576702e-06,
                2.902313023130843e-06,
                1.9947304348862686e-06,
                1.994729721518893e-06
            ],
            [
                1.0677026154806063e-06,
                7.338210680021253e-07,
                8.315278294114555e-07,
                1.209865539295696e-06,
                9.422448185510695e-07,
                1.5534984953552536e-06,
                1.3709572068522336e-06,
                2.3823688159291947e-07,
                1.2098653950692178e-06,
                9.422445939054222e-07
            ],
            [
                5.715003788993679e-07,
                3.9278610661822475e-07,
                1.7603434231241496e-06,
                1.0677024881941248e-06,
                3.059021175261338e-07,
                2.9023116391675407e-06,
                8.315282259117513e-07,
                4.450851580566494e-07,
                6.475950297993789e-07,
                5.715005832886879e-07
            ],
            [
                5.04347287955046e-07,
                7.889266347715168e-06,
                2.1024339116168358e-07,
                1.7603440527334603e-06,
                5.715003789046955e-07,
                5.043472278322555e-07,
                0.9999785550414317,
                1.9947304348862686e-06,
                3.059022998576899e-07,
                1.3007123813382511e-05
            ],
            [
                5.715006514105942e-07,
                4.5397857828200684e-05,
                0.9999978766215395,
                0.9999962733616096,
                3.059021175255426e-07,
                0.9999296881589637,
                6.023579219579052e-08,
                0.9999771720029281,
                6.1441746020359e-06,
                1.7603438428800754e-06
            ],
            [
                3.4663249714612693e-07,
                1.444979692800516e-07,
                1.6373766672973748e-07,
                7.734421308914719e-08,
                2.1024326584639497e-07,
                0.002182716935705145,
                0.9999962733589424,
                4.2228319344021954e-06,
                0.9999646437368436,
                0.9999960330136178
            ],
            [
                5.043475885696228e-07,
                9.42244930862237e-07,
                1.0677028700422047e-06,
                7.338211554813555e-07,
                1.994729483705484e-06,
                0.9999989322970033,
                0.99998615399217,
                1.994729008145876e-06,
                0.9999945777823281,
                9.422447062240614e-07
            ],
            [
                3.059023363231725e-07,
                1.275190580884987e-07,
                2.6995768091310296e-07,
                1.8553907971813685e-07,
                2.6995768091310296e-07,
                1.275190124842887e-07,
                1.855391239544352e-07,
                1.8553910183548312e-07,
                5.04347528446051e-07,
                2.1024339116082313e-07
            ],
            [
                2.699578096403948e-07,
                6.023569166654288e-08,
                9.931187406410953e-08,
                1.8553907971855875e-07,
                2.1024334103581732e-07,
                9.931185038635267e-08,
                3.466326624336003e-07,
                6.825598842065202e-08,
                1.444979692800516e-07,
                2.699576809143613e-07
            ],
            [
                1.855391681906175e-07,
                1.1253525596174225e-07,
                1.994729721518893e-06,
                1.637376862489725e-07,
                5.04347287955046e-07,
                9.422445938861406e-07,
                2.2603234895372223e-06,
                3.927863407379485e-07,
                3.466326624336003e-07,
                3.927862470905692e-07
            ],
            [
                3.4663249714612693e-07,
                1.4449803818215767e-07,
                1.6373762769187936e-07,
                3.927862939126708e-07,
                3.059021175261338e-07,
                2.6995784182140636e-07,
                2.1024334103505245e-07,
                1.444979692800516e-07,
                2.3823690999290963e-07,
                2.10243290909724e-07
            ],
            [
                1.6373762769187936e-07,
                0.9999992661789323,
                6.47595107001401e-07,
                0.9999975938973759,
                2.561282821402217e-06,
                3.9278620026686556e-07,
                2.6995784182183607e-07,
                0.9999998555019962,
                5.715002426486762e-07,
                5.715006514176113e-07
            ],
            [
                6.144172404738491e-06,
                4.785094494811783e-06,
                0.9999942280779286,
                1.5534973842076057e-06,
                7.484623621395011e-05,
                2.902312331170226e-06,
                0.9999942280793228,
                1.8925148242250705e-05,
                3.726639284144195e-06,
                6.144172404738491e-06
            ],
            [
                1.444980209564556e-07,
                3.0590237279085045e-07,
                2.3823685319244518e-07,
                2.699577774585891e-07,
                9.422447062294175e-07,
                4.450852641737424e-07,
                2.1024334103505245e-07,
                1.1253516205489029e-07,
                1.444980209564556e-07,
                2.1024331597262577e-07
            ],
            [
                3.288750241561788e-06,
                6.962257909842961e-06,
                8.315281267882195e-07,
                5.715003107755449e-07,
                8.315281267800897e-07,
                8.315281267834927e-07,
                6.475950298011458e-07,
                1.3709568799919866e-06,
                1.3709576971463352e-06,
                1.3709575337159875e-06
            ],
            [
                1.3709575337159875e-06,
                4.450852641737424e-07,
                1.8553907971855875e-07,
                1.8553916819032217e-07,
                6.825600469412533e-08,
                2.1024341622426268e-07,
                1.1253509497883659e-07,
                7.734414854823498e-08,
                1.067703124601679e-06,
                3.9278610661902853e-07
            ],
            [
                0.0003353501513165474,
                1.0677027427600627e-06,
                0.0001398221242266438,
                2.1444945858485726e-05,
                0.999997876621793,
                1.5534971990169383e-06,
                5.422219616265831e-06,
                NaN,
                3.288748281329893e-06,
                1.855391239547094e-07
            ],
            [
                2.699578096403948e-07,
                2.9023119851899796e-06,
                5.71500719545698e-07,
                3.9278629391427843e-07,
                NaN,
                1.3007130015677909e-05,
                1.0129993395336818e-05,
                NaN,
                2.26032402841657e-06,
                1.275190732904469e-07
            ],
            [
                1.4449805540700758e-07,
                6.825601283086733e-08,
                5.04347287955046e-07,
                1.125352291309328e-07,
                6.023569166654288e-08,
                3.466326211105621e-07,
                2.3823693839325527e-07,
                1.444979692797559e-07,
                1.1253526937697666e-07,
                8.764249540862797e-08
            ],
            [
                3.059021175255426e-07,
                1.6373766672973748e-07,
                5.715003107755449e-07,
                2.3823699519290042e-07,
                2.1024334103581732e-07,
                1.444980209564556e-07,
                1.0677033791612137e-06,
                1.8553910183607374e-07,
                2.6995774527657245e-07,
                4.450850519403407e-07
            ],
            [
                0.9999991148432811,
                0.9999992188514834,
                0.9999925887219043,
                0.9999898700114443,
                1.6373772528704005e-07,
                6.825609419848033e-08,
                0.9999992188518558,
                6.825608606172863e-08,
                3.466326624336003e-07,
                0.9999969105055533
            ],
            [
                1.994730197071414e-06,
                3.7266406168624155e-06,
                1.9947304348703948e-06,
                7.338212429582604e-07,
                1.5534975693869924e-06,
                1.6701415872385704e-05,
                1.7603434231777837e-06,
                7.889263526345123e-06,
                1.5534984953453635e-06,
                8.315284241560147e-07
            ],
            [
                1.2098659719788098e-06,
                2.10243290909724e-07,
                8.93969950132721e-06,
                2.260324836787226e-06,
                5.043476486924565e-07,
                1.2098659719788098e-06,
                4.4508510499849186e-07,
                8.315283250394546e-07,
                2.430024073523505e-05,
                8.315278294097538e-07
            ],
            [
                3.927863407379485e-07,
                6.475946438055299e-07,
                1.4449807263312446e-07,
                1.6373772528704005e-07,
                1.8553914607267268e-07,
                1.6373764721072816e-07,
                1.6373766672973748e-07,
                2.3823688159291947e-07,
                1.1253512180925583e-07,
                5.715006514176113e-07
            ],
            [
                1.8925148242250705e-05,
                9.931186222523604e-08,
                3.466326624336003e-07,
                1.209865827752005e-06,
                6.144176066943187e-06,
                NaN,
                1.209866260432471e-06,
                7.33821330437595e-07,
                0.9999843104521745,
                2.699577452775239e-07
            ],
            [
                1.637377643243723e-07,
                6.825601283086733e-08,
                4.691167716359673e-08,
                3.224185864592658e-08,
                3.653483822348123e-08,
                2.3823690999323465e-07,
                8.764242227418718e-08,
                3.653481209178873e-08,
                1.2751905808881762e-07,
                0.9999994284992807
            ],
            [
                3.9278605979534166e-07,
                9.931189774187203e-08,
                1.3007126914435202e-05,
                1.3709573702856596e-06,
                3.726638839878908e-06,
                1.4449795205429202e-07,
                3.9278605979534166e-07,
                1.1478766757853845e-05,
                7.338212429582604e-07,
                3.72663883989755e-06
            ],
            [
                5.4222183234485234e-06,
                8.315283250371857e-07,
                1.3709572068522336e-06,
                2.1024339116168358e-07,
                4.450849458218309e-07,
                2.5612831267202583e-06,
                1.5534979397740895e-06,
                NaN,
                5.715003789017068e-07,
                3.9278615344178325e-07
            ],
            [
                5.04347528440776e-07,
                1.9947292459347367e-06,
                4.450852111148132e-07,
                5.715003107755449e-07,
                3.059021175261338e-07,
                8.315283250394546e-07,
                4.450848927650143e-07,
                3.9278634073732336e-07,
                7.484624512911504e-05,
                1.8553916819032217e-07
            ],
            [
                6.475950298021765e-07,
                NaN,
                1.855391681906175e-07,
                1.7603434231833873e-06,
                3.4663262111182307e-07,
                1.3007126914612648e-05,
                1.0677029973219343e-06,
                1.27519088491875e-07,
                5.043475284468537e-07,
                0.9999952149055236
            ],
            [
                5.715004470295662e-07,
                5.043472278322555e-07,
                1.3709570434178922e-06,
                NaN,
                5.043473480777865e-07,
                1.7603434231777837e-06,
                7.338208055664991e-07,
                1.0677027427600627e-06,
                1.0129993395217047e-05,
                1.209866260432471e-06
            ],
            [
                1.5534981249697903e-06,
                5.043475284430694e-07,
                5.715005832853093e-07,
                5.715003788993679e-07,
                1.8553919030776337e-07,
                1.2098659719757836e-06,
                3.059022269250683e-07,
                3.927860597945825e-07,
                2.3823702359290413e-07,
                9.422444815726566e-07
            ],
            [
                5.043472879540142e-07,
                5.422217030781934e-06,
                8.315281267882195e-07,
                2.753568782024347e-05,
                3.288748281329893e-06,
                1.209865539295696e-06,
                2.7535700950274782e-05,
                5.715004470313855e-07,
                1.994729721518893e-06,
                1.5534977545886537e-06
            ],
            [
                2.10243290909724e-07,
                2.382369951932796e-07,
                8.315281267882195e-07,
                4.450848927658745e-07,
                5.715003789046955e-07,
                1.5534973842076057e-06,
                7.889261645427538e-06,
                4.222832437798974e-06,
                6.023578501513224e-08,
                2.699578096403948e-07
            ],
            [
                1.2751901248454963e-07,
                1.2751899728286965e-07,
                2.1024331597262577e-07,
                3.927863407379485e-07,
                2.699577774585891e-07,
                4.222834954801051e-06,
                3.059022269250683e-07,
                2.69957906184239e-07,
                1.444979692800516e-07,
                1.6373776432509826e-07
            ],
            [
                5.04347528446051e-07,
                1.8553919030858602e-07,
                7.338211554813555e-07,
                8.31528325040778e-07,
                1.3709572068522336e-06,
                1.2751907329024393e-07,
                3.466325797900508e-07,
                1.1253513522447425e-07,
                2.3823685319244518e-07,
                5.043472278322555e-07
            ],
            [
                1.0677028700422047e-06,
                2.1024334103581732e-07,
                1.760342793638743e-06,
                3.927863407379485e-07,
                5.715003107767143e-07,
                5.3157837044597743e-08,
                3.9278629391427843e-07,
                4.450848927658745e-07,
                9.422444815814404e-07,
                1.3007123813382511e-05
            ],
            [
                NaN,
                5.043472278322555e-07,
                2.3823690999323465e-07,
                1.2098659719788098e-06,
                3.05902190458764e-07,
                7.338209805240734e-07,
                0.9999898700078282,
                1.0677032518814388e-06,
                1.8553910183674878e-07,
                0.0010322308515277655
            ],
            [
                1.5534984953552536e-06,
                2.3823693839325527e-07,
                1.3709573702778664e-06,
                2.382370235933104e-07,
                3.927862470905692e-07,
                3.927860597945825e-07,
                2.1024334103581732e-07,
                3.4663278639892215e-07,
                1.9947297215043796e-06,
                1.3709576971463352e-06
            ],
            [
                5.71500651413193e-07,
                1.2098652508347793e-06,
                1.7603425837702984e-06,
                NaN,
                1.9947299593014888e-06,
                1.7603425837606927e-06,
                NaN,
                3.2887502415438413e-06,
                1.3709567165530083e-06,
                7.338211554783522e-07
            ],
            [
                3.927863407379485e-07,
                5.422217030781934e-06,
                5.043476486924565e-07,
                1.1253509497883659e-07,
                1.637376862489725e-07,
                6.825608606172863e-08,
                3.9278629391427843e-07,
                1.275190428875671e-07,
                1.6701423836262173e-05,
                1.2751899728311609e-07
            ],
            [
                3.7266410611296085e-06,
                1.2751910369310194e-07,
                8.764247451307293e-08,
                2.1024336609874897e-07,
                NaN,
                0.999998712104171,
                7.338207180898968e-07,
                6.825606165129312e-08,
                3.05902190458764e-07,
                3.059022998576899e-07
            ],
            [
                7.889263526409699e-06,
                6.144172404693786e-06,
                6.962256249935742e-06,
                3.535626336201389e-05,
                8.764253720001207e-08,
                6.962257909842961e-06,
                2.102434412875379e-07,
                5.043473480777865e-07,
                6.475947210046347e-07,
                1.5534979397829198e-06
            ],
            [
                0.009708476445658299,
                1.7603434231833873e-06,
                5.715003789046955e-07,
                4.4508510499849186e-07,
                1.067703124601679e-06,
                1.6373776432509826e-07,
                NaN,
                6.962256249885085e-06,
                3.726639284144195e-06,
                7.338212429582604e-07
            ],
            [
                1.275190124842887e-07,
                7.338211554783522e-07,
                2.1024334103352274e-07,
                1.6373766672888118e-07,
                1.855391239539711e-07,
                1.8553905760062447e-07,
                2.6995771309523475e-07,
                1.6373766672973748e-07,
                6.47595107001401e-07,
                5.715007195431641e-07
            ],
            [
                9.93120161310289e-08,
                0.9999810748518104,
                6.475946438055299e-07,
                0.9999964991464234,
                1.275190580890061e-07,
                2.1024336609874897e-07,
                3.466326211113502e-07,
                2.1024326584702836e-07,
                9.931186222523604e-08,
                1.275189972832538e-07
            ],
            [
                1.275190732904469e-07,
                1.4449800373065699e-07,
                5.043474081993875e-07,
                2.1024334103505245e-07,
                2.5612828213934817e-06,
                5.04347528446051e-07,
                1.8553916819032217e-07,
                2.2603234895372223e-06,
                2.3823685319244518e-07,
                1.8553910183607374e-07
            ],
            [
                9.931186222523604e-08,
                6.825604537781398e-08,
                1.2751902768612997e-07,
                3.05902263391829e-07,
                1.5534977545886537e-06,
                1.5534973842076057e-06,
                0.9999970976866346,
                1.6373776432509826e-07,
                7.338208930460318e-07,
                6.825598028392069e-08
            ],
            [
                3.224185864592658e-08,
                1.0677026154827912e-06,
                1.370957860576702e-06,
                4.450850519409479e-07,
                0.9999869928746471,
                4.4508515805735777e-07,
                0.9999546021261099,
                5.04347287955046e-07,
                3.0590226339061185e-07,
                1.1253525596134564e-07
            ],
            [
                1.2098662604126641e-06,
                9.931189774187203e-08,
                1.5534971989992774e-06,
                2.561282210740037e-06,
                0.9997388097925888,
                5.715007195447234e-07,
                9.422450431912e-07,
                1.0677033791583005e-06,
                1.8553919030858602e-07,
                1.012999218776902e-05
            ],
            [
                1.275190428875671e-07,
                7.734428685047173e-08,
                2.1024334103581732e-07,
                1.2098652508424818e-06,
                3.466325797900508e-07,
                2.102434162245973e-07,
                9.931202796993203e-08,
                3.466325797900508e-07,
                9.93120161310289e-08,
                9.422444815814404e-07
            ],
            [
                2.102433660979124e-07,
                2.6995790618350237e-07,
                3.9278634073625165e-07,
                7.338212429537553e-07,
                6.47594952595231e-07,
                5.715007195431641e-07,
                7.338209805200689e-07,
                NaN,
                4.2228339479858295e-06,
                3.0590215399183813e-07
            ],
            [
                5.043472278322555e-07,
                1.5534981249697903e-06,
                7.338212429582604e-07,
                2.382369951932796e-07,
                5.715005832886879e-07,
                9.422449308774482e-07,
                5.715002426475718e-07,
                3.4663278639892215e-07,
                2.6995774527718623e-07,
                5.043473480777865e-07
            ],
            [
                5.715002426486762e-07,
                3.05902336324494e-07,
                1.8553905760062447e-07,
                2.3823693839325527e-07,
                2.3823688159291947e-07,
                1.994729483729522e-06,
                6.962258739796719e-06,
                3.05902336324494e-07,
                6.475945666063607e-07,
                7.734421308914719e-08
            ],
            [
                2.1024336609874897e-07,
                1.1253522913127183e-07,
                1.1253524254615121e-07,
                1.2751905808881762e-07,
                3.9278605979534166e-07,
                8.764249540862797e-08,
                4.450852641737424e-07,
                7.734421308914719e-08,
                6.47595107001401e-07,
                1.8553910183674878e-07
            ],
            [
                8.315284241597959e-07,
                4.450848927650143e-07,
                5.715005151606823e-07,
                9.422448185510695e-07,
                1.067702870039777e-06,
                7.338209805224048e-07,
                2.260323758939877e-06,
                6.475950298011458e-07,
                1.5534984953453635e-06,
                9.422445939032799e-07
            ],
            [
                5.71500719545698e-07,
                1.855391239544352e-07,
                4.222832941193893e-06,
                8.764242227418718e-08,
                2.6995774527718623e-07,
                1.4449803818215767e-07,
                5.043475284468537e-07,
                3.9278629391427843e-07,
                3.059022998576899e-07,
                3.927863407379485e-07
            ],
            [
                1.8553905760062447e-07,
                2.6995768091383957e-07,
                4.450851580540182e-07,
                1.2751901248454963e-07,
                2.1024331597262577e-07,
                1.1253513522447425e-07,
                3.059022998569248e-07,
                8.764244316973974e-08,
                2.6995784182140636e-07,
                5.71500242637956e-07
            ],
            [
                7.734425919002834e-08,
                1.1253525596174225e-07,
                1.275189972832538e-07,
                2.699577452775239e-07,
                9.422450432030903e-07,
                3.927862470905692e-07,
                1.1253524254650944e-07,
                6.82560779249779e-08,
                2.3823690999323465e-07,
                3.466326624336003e-07
            ],
            [
                2.3823685319244518e-07,
                2.6995774527657245e-07,
                1.8553919030776337e-07,
                8.7642516304188e-08,
                2.6995768091310296e-07,
                2.3823682479181176e-07,
                3.05902263389638e-07,
                2.3823688159237777e-07,
                3.9278634073732336e-07,
                1.855390354818069e-07
            ],
            [
                5.315784971839039e-08,
                1.8553916819032217e-07,
                6.825602910433871e-08,
                1.4449805540763184e-07,
                1.4449798650551755e-07,
                1.1253521571574156e-07,
                2.1024334103581732e-07,
                1.1253513522447425e-07,
                4.691162124067829e-08,
                5.3157830707696514e-08
            ],
            [
                3.466327037512053e-07,
                2.3823688159237777e-07,
                3.059022269250683e-07,
                5.043475885657239e-07,
                1.8553919030776337e-07,
                2.6995771309523475e-07,
                7.338207180864763e-07,
                3.46632497145457e-07,
                3.9278634073625165e-07,
                2.102434412871794e-07
            ],
            [
                7.73441946488886e-08,
                5.043476486924565e-07,
                5.043473480777865e-07,
                1.1253508156363576e-07,
                8.764241182641775e-08,
                8.315279285370317e-07,
                1.8553910183674878e-07,
                1.4449803818215767e-07,
                2.102434162245973e-07,
                2.102434162245973e-07
            ],
            [
                1.5534975693979422e-06,
                0.9999989322975127,
                0.9999989969856733,
                5.043476486924565e-07,
                0.9999785550542803,
                5.715002426486762e-07,
                1.27519088491875e-07,
                1.3709575337159875e-06,
                0.999994577779095,
                5.715005832886879e-07
            ],
            [
                1.760342793638743e-06,
                3.9278605979534166e-07,
                1.6373762769138607e-07,
                5.04347468323289e-07,
                6.475950298011458e-07,
                4.4508515805735777e-07,
                3.927861534431675e-07,
                7.734418542875216e-08,
                3.466325797896173e-07,
                5.715003789046955e-07
            ],
            [
                3.059022269250683e-07,
                1.0677028700422047e-06,
                NaN,
                7.33821330437595e-07,
                3.9278610661902853e-07,
                7.338207180898968e-07,
                1.0677028700422047e-06,
                7.338207180898968e-07,
                NaN,
                5.71500719545698e-07
            ],
            [
                1.6373774480605869e-07,
                1.7603434231777837e-06,
                1.760343003481596e-06,
                6.475950298011458e-07,
                6.475947210046347e-07,
                1.8553914607267268e-07,
                2.1024339116168358e-07,
                2.699576809143613e-07,
                3.05902336324494e-07,
                1.4449807263312446e-07
            ],
            [
                8.76424013786396e-08,
                8.764244316973974e-08,
                2.3823688159291947e-07,
                2.6995771309523475e-07,
                3.059022998576899e-07,
                0.9999785550465765,
                3.059021904571643e-07,
                5.715002426486762e-07,
                1.855391681883394e-07,
                7.338212429582604e-07
            ],
            [
                5.715007195447234e-07,
                6.475948754012522e-07,
                4.450852111135988e-07,
                1.8553905760062447e-07,
                3.059022998581767e-07,
                1.3709568799879344e-06,
                5.715003789017068e-07,
                3.9278605979208185e-07,
                9.422449308774482e-07,
                6.023574911170301e-08
            ],
            [
                0.9999667857900172,
                0.9999930377413037,
                0.00037998453217423387,
                1.8925155009767892e-05,
                1.9947292459347367e-06,
                0.9999957771665686,
                8.315281267882195e-07,
                1.444979692800516e-07,
                2.5612828213934817e-06,
                1.9947297215125433e-06
            ],
            [
                3.6534838223576766e-08,
                6.023576347299818e-08,
                9.93118503859575e-08,
                4.139936066832438e-08,
                6.825598028392069e-08,
                3.224186633297071e-08,
                1.1253514863909295e-07,
                1.275190124846946e-07,
                3.653481209178873e-08,
                7.734421308914719e-08
            ],
            [
                1.8553905760062447e-07,
                1.637377448057981e-07,
                4.450848927658745e-07,
                3.9278605979208185e-07,
                3.927861066170637e-07,
                3.466325797888292e-07,
                3.9278634073732336e-07,
                2.1024339116082313e-07,
                3.4663253846473677e-07,
                2.1024331597288867e-07
            ],
            [
                2.102434412875379e-07,
                1.1253512180925583e-07,
                1.1253524254650944e-07,
                1.4449795205472734e-07,
                8.76424013786396e-08,
                2.3823685319320354e-07,
                6.962258739796719e-06,
                9.931202796993203e-08,
                9.422449308748773e-07,
                1.9947301970972664e-06
            ],
            [
                4.450852111148132e-07,
                3.4663278639892215e-07,
                7.889259764517575e-06,
                6.144176799283803e-06,
                1.5534977545886537e-06,
                6.475947210046347e-07,
                3.2887502415767434e-06,
                NaN,
                6.144175334468545e-06,
                8.315279285351409e-07
            ],
            [
                1.0677032518814388e-06,
                5.043472278322555e-07,
                1.209865827752005e-06,
                0.9999832985823819,
                3.466327450756327e-07,
                4.222834954801051e-06,
                1.3007123813382511e-05,
                3.9278605979534166e-07,
                3.927863407379485e-07,
                1.2751908849167202e-07
            ],
            [
                5.315783704433184e-08,
                3.65348425788669e-08,
                6.023578501491997e-08,
                1.4449800373118268e-07,
                0.9999972735303807,
                8.764242227418718e-08,
                1.27519088491875e-07,
                7.734418542875216e-08,
                9.931195693628605e-08,
                8.7642558095602e-08
            ],
            [
                1.444980726324838e-07,
                9.931185038635267e-08,
                1.6373770576776313e-07,
                2.382369383923073e-07,
                1.444980209564556e-07,
                3.2241847115356483e-08,
                1.8553903548231313e-07,
                6.023574911170301e-08,
                3.466326211105621e-07,
                5.315789407685159e-08
            ],
            [
                8.31528325040778e-07,
                6.475950297942253e-07,
                1.5534984953510149e-06,
                5.422218323487975e-06,
                5.422219616228845e-06,
                4.4508515805199415e-07,
                1.637377643243723e-07,
                8.315277302788957e-07,
                1.760343633031919e-06,
                5.715006514105942e-07
            ],
            [
                5.422218969895357e-06,
                1.444980209564556e-07,
                9.931195693628605e-08,
                4.450852641717689e-07,
                3.9278634073732336e-07,
                5.715006514167015e-07,
                1.8553905760062447e-07,
                3.9278634073625165e-07,
                9.931189774187203e-08,
                1.2098659719757836e-06
            ],
            [
                3.466326211113502e-07,
                1.3709573702822306e-06,
                NaN,
                7.338208055680009e-07,
                1.9947301970972664e-06,
                4.450850519403407e-07,
                1.8553919030858602e-07,
                2.3823690999290963e-07,
                2.3823699519290042e-07,
                1.760343213335281e-06
            ],
            [
                0.9999991684720717,
                0.9999999273418009,
                0.9999982396563679,
                0.999998346310218,
                0.9999993916411085,
                0.9999724643024782,
                0.9999998942829225,
                2.1024331597288867e-07,
                0.9999994956524115,
                0.999997593896514
            ],
            [
                1.8553910183674878e-07,
                3.2887506336235617e-06,
                1.444980209564556e-07,
                1.4449795205472734e-07,
                3.6534838223576766e-08,
                6.825606978822427e-08,
                2.3823702359290413e-07,
                5.315781803390236e-08,
                2.3823696679230424e-07,
                1.4449802095666915e-07
            ]
        ]
    },
    {
        "q_id": "9906_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            62,
            63,
            64,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            99,
            100,
            102,
            104,
            105,
            106,
            108,
            109,
            110,
            113,
            115,
            117,
            118,
            120,
            122,
            123,
            126,
            127
        ],
        "rewards": [
            [
                2.5612825160562587e-06,
                1.3709567165461505e-06,
                9.42244930862237e-07,
                1.2098662603499435e-06,
                2.1024329090867228e-07,
                3.9278634072866033e-07,
                3.7266383955882547e-06,
                1.2098659719524008e-06,
                3.927862938956128e-07,
                7.338208055664991e-07
            ],
            [
                NaN,
                3.466327450765785e-07,
                4.450852641717689e-07,
                1.444980209564556e-07,
                5.04347468323289e-07,
                9.422448185534261e-07,
                2.699576809143613e-07,
                6.475951069961737e-07,
                3.726639728370556e-06,
                8.315283250394546e-07
            ],
            [
                1.9947292459265734e-06,
                0.9999981261241725,
                0.9999991684719737,
                0.999987780919632,
                0.9999987121049396,
                5.715005832886879e-07,
                0.9999995818811774,
                0.999986992870012,
                NaN,
                0.9999981261250663
            ],
            [
                8.315279285351409e-07,
                3.2887478892504536e-06,
                1.994730434879465e-06,
                3.059022998576899e-07,
                NaN,
                9.422442569208767e-07,
                NaN,
                1.8925150497435443e-05,
                6.475950297971703e-07,
                4.450851580540182e-07
            ],
            [
                0.9998911030783592,
                3.7266406168624155e-06,
                0.00010889687040094255,
                3.5356250712032926e-05,
                3.288749849498565e-06,
                0.9998911031174975,
                1.3709578605617394e-06,
                1.3007125363719486e-05,
                0.9980732654727851,
                1.994729245917502e-06
            ],
            [
                0.9999955048194996,
                0.9999916019239846,
                NaN,
                NaN,
                1.209865827752005e-06,
                0.9999970976887114,
                1.855391239544352e-07,
                1.6373766672973748e-07,
                4.450848927658745e-07,
                0.9999810748540507
            ],
            [
                2.260325375664839e-06,
                1.3709568799760888e-06,
                4.785095065132354e-06,
                2.260324567302214e-06,
                1.370957697068717e-06,
                1.7603427936263351e-06,
                2.561282210701601e-06,
                4.222832941142044e-06,
                1.3709570434122812e-06,
                1.3709578605617394e-06
            ],
            [
                4.4508494582405734e-07,
                4.450852111148132e-07,
                1.670142980893658e-05,
                3.726638839878908e-06,
                4.450850519403407e-07,
                NaN,
                1.0677026154806063e-06,
                5.04347468323289e-07,
                7.338213304363436e-07,
                1.8553907971855875e-07
            ],
            [
                0.9999892166904293,
                0.9999910603005178,
                0.9999869928731228,
                0.9999417087420795,
                2.6995771309523475e-07,
                NaN,
                1.7603427936335396e-06,
                8.315278294097538e-07,
                8.315280276626197e-07,
                1.5534975693979422e-06
            ],
            [
                1.0677033791583005e-06,
                1.0677031245990084e-06,
                0.00017952803055133065,
                3.059022269250683e-07,
                5.422219616228845e-06,
                5.144220140264605e-05,
                1.3007133116732079e-05,
                4.2228329411708495e-06,
                1.6701421844753466e-05,
                NaN
            ],
            [
                5.043475284430694e-07,
                8.315281267706361e-07,
                2.5612816000646084e-06,
                0.9999832985822034,
                4.222833444590791e-06,
                0.9999892166891021,
                5.043472879540142e-07,
                7.88926446679691e-06,
                3.927862002654366e-07,
                6.475947210012481e-07
            ],
            [
                5.715004470295662e-07,
                1.0677029973192638e-06,
                1.760344052714248e-06,
                8.315281267834927e-07,
                3.05902117523595e-07,
                2.561281600076256e-06,
                1.2098653950480359e-06,
                1.6373762769138607e-07,
                3.927862002641863e-07,
                8.315279285351409e-07
            ],
            [
                6.144172404693786e-06,
                1.7603434231833873e-06,
                8.315284241650899e-07,
                2.2603242978871282e-06,
                1.4738989000422955e-05,
                7.338208055664991e-07,
                3.059022269250683e-07,
                1.5534981249697903e-06,
                1.8553905760062447e-07,
                1.855391681906175e-07
            ],
            [
                NaN,
                1.855391239544352e-07,
                7.338208055680009e-07,
                2.69957906184239e-07,
                6.023569884718319e-08,
                1.1253510839355284e-07,
                1.8553907971855875e-07,
                5.715005151606823e-07,
                2.102434412871794e-07,
                8.315282259138311e-07
            ],
            [
                5.715007195431641e-07,
                9.422448185388577e-07,
                5.715007195431641e-07,
                1.7603432132784448e-06,
                4.22283545819819e-06,
                5.043475885674441e-07,
                4.450849458218309e-07,
                5.043474081993875e-07,
                2.9023126771227976e-06,
                3.0590215399183813e-07
            ],
            [
                4.539785241676547e-05,
                0.0003353500713116092,
                1.3709573702822306e-06,
                6.475951069985296e-07,
                1.0677024882009222e-06,
                1.7603427936335396e-06,
                0.9999898700054419,
                1.7603440527286572e-06,
                1.3709573702822306e-06,
                5.715004470243685e-07
            ],
            [
                2.260324297853209e-06,
                1.0677032518748838e-06,
                1.9947306726358406e-06,
                1.2098661161927025e-06,
                2.2603242978778778e-06,
                6.475947210012481e-07,
                1.209865539274514e-06,
                2.2603234894745224e-06,
                1.209865250822125e-06,
                1.5534979397500702e-06
            ],
            [
                9.422447062270609e-07,
                2.6995774527657245e-07,
                6.475950298011458e-07,
                8.481103128838341e-05,
                2.69957906184239e-07,
                NaN,
                2.561283432035425e-06,
                7.338209805240734e-07,
                8.315282259138311e-07,
                6.475950297971703e-07
            ],
            [
                NaN,
                1.0677028700363782e-06,
                4.2228329411708495e-06,
                8.315277302747361e-07,
                4.785095635624897e-06,
                1.2098653950606901e-06,
                NaN,
                1.1478768126057254e-05,
                4.785093353940187e-06,
                3.7266379513434106e-06
            ],
            [
                0.0001795279021267955,
                2.902310947208574e-06,
                1.3007125363293615e-05,
                7.338212429504183e-07,
                2.2603240283888175e-06,
                1.0677028700320085e-06,
                6.962254589851619e-06,
                8.315284241597959e-07,
                1.553497754577351e-06,
                1.994730434879465e-06
            ],
            [
                1.76034300345598e-06,
                1.5534979397677313e-06,
                1.3709573702778664e-06,
                2.2603234895289998e-06,
                1.067702870039777e-06,
                6.962256249885085e-06,
                2.9023119851635836e-06,
                3.288749457432399e-06,
                1.7603432133136672e-06,
                1.994729245917502e-06
            ],
            [
                1.0677032518748838e-06,
                7.338207180864763e-07,
                1.0677026154730804e-06,
                1.7603438428660665e-06,
                2.9023119851781017e-06,
                4.450851580540182e-07,
                2.561281600076256e-06,
                8.315281267800897e-07,
                3.05902336324494e-07,
                4.785096776468749e-06
            ],
            [
                9.422449308716635e-07,
                4.785093353909723e-06,
                5.715007195410849e-07,
                1.2098653950606901e-06,
                3.2887490653872164e-06,
                2.561281600076256e-06,
                8.315282259089153e-07,
                1.0677024881980089e-06,
                3.535624650150453e-05,
                6.475951069985296e-07
            ],
            [
                6.475950297971703e-07,
                1.3709576971379186e-06,
                1.5534981249574276e-06,
                1.5534971989907999e-06,
                3.7266383955611403e-06,
                1.9947299593014888e-06,
                8.315277302788957e-07,
                8.315284241597959e-07,
                6.144172404693786e-06,
                1.067703251864202e-06
            ],
            [
                0.9999877809240245,
                0.9999869928684806,
                3.726638839806038e-06,
                1.1478765389368729e-05,
                0.9999822214439745,
                6.962254589914941e-06,
                3.2887478892504536e-06,
                0.9999869928653669,
                7.889265407177056e-06,
                1.7603425837791042e-06
            ],
            [
                2.902313369111213e-06,
                4.22283545819819e-06,
                3.288747889284851e-06,
                7.338208930460318e-07,
                1.0677026154806063e-06,
                2.5612812947508257e-06,
                2.902312677150514e-06,
                6.475948754012522e-07,
                3.7266410611296085e-06,
                3.288750241561788e-06
            ],
            [
                0.9999994284996214,
                0.9999997463980124,
                0.9999994284994169,
                0.9999998461826956,
                0.9999998642567353,
                0.9999989322975129,
                0.9999996072138467,
                0.999999266179195,
                0.9999998461827139,
                0.9999998144608541
            ],
            [
                1.5534983101478522e-06,
                3.726638839878908e-06,
                0.999373665763629,
                1.2098659719757836e-06,
                5.04347528446051e-07,
                1.3709576971425944e-06,
                6.475950298011458e-07,
                0.9999756997593063,
                1.855391239544352e-07,
                2.2603234895176927e-06
            ],
            [
                2.699576809143613e-07,
                1.2098659719788098e-06,
                1.1253525596174225e-07,
                2.10243290909724e-07,
                4.450849988811838e-07,
                1.3709567165579959e-06,
                8.764241182641775e-08,
                3.0590222692437275e-07,
                6.825600469412533e-08,
                6.475946438055299e-07
            ],
            [
                1.0129987357407137e-05,
                1.0677032518785256e-06,
                1.89251527534122e-05,
                8.93969950101825e-06,
                1.3709567165579959e-06,
                2.144495863958007e-05,
                3.53562549305363e-05,
                1.9947294837154625e-06,
                1.0129989772532511e-05,
                3.2887478892683997e-06
            ],
            [
                0.9999991684718736,
                0.9999989322971305,
                0.9999998024947037,
                0.9999991148427537,
                0.9999993916408186,
                0.9999822214460816,
                0.9999999358793332,
                0.9999996940977003,
                0.9999992661786701,
                0.9999981261239482
            ],
            [
                6.475951069985296e-07,
                1.3709568799879344e-06,
                4.2228324377740105e-06,
                4.450851580540182e-07,
                3.4663262110189246e-07,
                1.670141786325573e-05,
                6.962257909722651e-06,
                NaN,
                3.4663249714325014e-07,
                1.0677027427600627e-06
            ],
            [
                1.9947304348862686e-06,
                1.3709567165579959e-06,
                6.144175334468545e-06,
                2.902313023130843e-06,
                4.222834954753043e-06,
                3.726638395611981e-06,
                NaN,
                1.7603438428740716e-06,
                8.939698435657833e-06,
                6.9622587397397306e-06
            ],
            [
                5.715005151606823e-07,
                1.6373764721072816e-07,
                7.338208930460318e-07,
                2.1024331597262577e-07,
                7.338208055680009e-07,
                1.7603438428800754e-06,
                2.3823690999160957e-07,
                6.475949526020042e-07,
                2.6995790618469934e-07,
                3.927862470899887e-07
            ],
            [
                1.5534983101478522e-06,
                4.785095065232451e-06,
                1.2098656835136636e-06,
                3.288748281295496e-06,
                NaN,
                NaN,
                1.2098659719716573e-06,
                2.260323758987159e-06,
                1.553498124964492e-06,
                1.9947304348595095e-06
            ],
            [
                1.1253526937697666e-07,
                1.3007130015677909e-05,
                6.144175334468545e-06,
                0.9999934595643505,
                1.2098659719757836e-06,
                2.102434412875379e-07,
                0.9997694931786816,
                1.3007133116732079e-05,
                0.9999646437536146,
                2.6995771309523475e-07
            ],
            [
                7.338209805170655e-07,
                4.2228334445370225e-06,
                3.05902263389638e-07,
                6.47594566597747e-07,
                0.9999687980776082,
                5.043472879504592e-07,
                1.7603434231777837e-06,
                9.422444815679433e-07,
                1.99472900813862e-06,
                1.9947304348703948e-06
            ],
            [
                2.5612812947508257e-06,
                5.715005151606823e-07,
                6.144176799334096e-06,
                7.338207180864763e-07,
                1.3709567165579959e-06,
                6.962259569630266e-06,
                7.338210680021253e-07,
                1.9947299593014888e-06,
                1.1478768126057254e-05,
                6.144175334468545e-06
            ],
            [
                NaN,
                NaN,
                0.0001233945896995423,
                2.260324836696773e-06,
                2.9023130231176453e-06,
                1.0677026154774503e-06,
                1.8925157264919016e-05,
                NaN,
                8.315282259089153e-07,
                4.222832941034507e-06
            ],
            [
                2.699577774560111e-07,
                9.422449308774482e-07,
                7.338210680002898e-07,
                9.422445939002803e-07,
                7.338208055664991e-07,
                8.315279285370317e-07,
                1.067702870039777e-06,
                3.9278615343901467e-07,
                1.0677032518785256e-06,
                4.450852111100568e-07
            ],
            [
                2.699578740032504e-07,
                2.5612834320470717e-06,
                2.1024331597262577e-07,
                1.370957860576702e-06,
                NaN,
                1.8553919030858602e-07,
                2.9023109472244114e-06,
                4.4508494582405734e-07,
                6.475947982037486e-07,
                2.4300234941261454e-05
            ],
            [
                1.2098656835224664e-06,
                5.715003107767143e-07,
                1.9947301970972664e-06,
                5.715003107755449e-07,
                9.422442569315887e-07,
                1.9947292459347367e-06,
                8.76424013786396e-08,
                8.315281267882195e-07,
                6.475945666051092e-07,
                1.2098661162023305e-06
            ],
            [
                2.9023109471689794e-06,
                4.450849458179853e-07,
                2.561282210701601e-06,
                1.2098659719524008e-06,
                1.9947299592570416e-06,
                5.422217030663578e-06,
                2.5612828213352452e-06,
                1.3709572068354007e-06,
                1.9947294837154625e-06,
                2.260325375634003e-06
            ],
            [
                3.726638839878908e-06,
                1.5534981249697903e-06,
                7.338208055664991e-07,
                2.382369951932796e-07,
                2.902312677150514e-06,
                5.715003789046955e-07,
                1.5534983101549167e-06,
                1.2098658277451275e-06,
                1.7603434231833873e-06,
                8.315282259089153e-07
            ],
            [
                6.475946438055299e-07,
                1.0677029973192638e-06,
                4.785095635655362e-06,
                4.5397852414783676e-05,
                8.315283250371857e-07,
                1.1478770862735993e-05,
                NaN,
                1.994729008145876e-06,
                1.760344052714248e-06,
                NaN
            ],
            [
                1.3709568799823232e-06,
                8.31528424162821e-07,
                4.785092783415276e-06,
                1.3709572068272963e-06,
                1.3709568799679844e-06,
                9.422444815679433e-07,
                1.3709575336530204e-06,
                3.059021904571643e-07,
                NaN,
                1.5534971989992774e-06
            ],
            [
                5.04347468318358e-07,
                6.962253759904688e-06,
                6.962255419728997e-06,
                7.889263526266196e-06,
                5.422218969818919e-06,
                2.2603234895289998e-06,
                3.288747889229516e-06,
                2.561282821352716e-06,
                2.4300249423965898e-05,
                2.7535704231043113e-05
            ],
            [
                1.6373764721072816e-07,
                0.9999942280792852,
                0.9999982396565779,
                0.9999969105044493,
                0.9999993106389546,
                0.9999980052700417,
                NaN,
                0.999997273530381,
                0.9999993916408185,
                1.209866260432471e-06
            ],
            [
                2.9023133690980155e-06,
                1.1478772231086046e-05,
                5.715003107755449e-07,
                5.422220262555012e-06,
                4.785094494783494e-06,
                0.00012339463384858465,
                NaN,
                1.0129994602895546e-05,
                9.422442569315887e-07,
                0.9999810748427816
            ],
            [
                1.0677024881941248e-06,
                2.5612825160562587e-06,
                2.2603245673279107e-06,
                1.2098662604192665e-06,
                3.059023363207381e-07,
                1.0677024881829577e-06,
                3.7266392840781026e-06,
                1.2098655392871682e-06,
                6.475950297971703e-07,
                1.2098662604192665e-06
            ],
            [
                2.9023119851635836e-06,
                1.2098656835076114e-06,
                1.3709576971242028e-06,
                1.370956716529941e-06,
                7.889259764273619e-06,
                2.2603242978665707e-06,
                1.2098656835136636e-06,
                9.422442569208767e-07,
                1.0677028700266676e-06,
                1.2098662604126641e-06
            ],
            [
                2.2603242978871282e-06,
                NaN,
                2.260325106237323e-06,
                1.670142980893658e-05,
                8.93969950132721e-06,
                0.9999785550542108,
                0.9999843104465592,
                6.1441746020359e-06,
                5.043473480777865e-07,
                4.78509563555309e-06
            ],
            [
                1.2751905808881762e-07,
                4.4508510499737865e-07,
                7.338213304363436e-07,
                3.466326211113502e-07,
                1.855391239544352e-07,
                4.450848927650143e-07,
                3.535626757524533e-05,
                6.962257909785973e-06,
                1.275190276859705e-07,
                2.90231094723893e-06
            ],
            [
                2.90231233114251e-06,
                4.2228324375512536e-06,
                1.9947301970587145e-06,
                1.6373776432509826e-07,
                2.2603234894560207e-06,
                6.962253759581752e-06,
                1.3709570433885908e-06,
                7.88926258532661e-06,
                5.715004470313855e-07,
                5.4222202623972055e-06
            ],
            [
                2.144494841482881e-05,
                2.9023133690637e-06,
                1.3709572068272963e-06,
                6.962259569560613e-06,
                6.9622579096593295e-06,
                8.315284241597959e-07,
                3.726638839833152e-06,
                6.962254589978262e-06,
                1.994729721482609e-06,
                3.726641061085547e-06
            ],
            [
                NaN,
                8.939696304213768e-06,
                7.338208930460318e-07,
                3.927862002663297e-07,
                1.0677029973192638e-06,
                2.699577774585891e-07,
                6.144173137170873e-06,
                5.715003107755449e-07,
                0.999993459561226,
                5.715002426486762e-07
            ],
            [
                6.9622595696935874e-06,
                6.475948753965404e-07,
                6.962256249758443e-06,
                2.5612825160271407e-06,
                1.7603436330091044e-06,
                2.2603248367656408e-06,
                2.2603234895289998e-06,
                9.422443692527585e-07,
                1.0677024881887838e-06,
                3.726639284103523e-06
            ],
            [
                5.043472879504592e-07,
                1.2751907329024393e-07,
                5.715003107715166e-07,
                6.475948753930064e-07,
                5.715003107755449e-07,
                7.338207180864763e-07,
                3.05902226922147e-07,
                1.3709568799679844e-06,
                2.3823699519143784e-07,
                5.715007195431641e-07
            ],
            [
                0.9999985406237798,
                5.043474683156057e-07,
                0.9999975938979507,
                4.450852111120808e-07,
                8.939698435560267e-06,
                3.05902190458764e-07,
                1.0677026154730804e-06,
                8.315283250305684e-07,
                0.9999970976887097,
                8.315278294038928e-07
            ],
            [
                2.382370235922541e-07,
                0.9999921107402436,
                2.2603234895289998e-06,
                3.4663274507713016e-07,
                1.994729008145876e-06,
                1.9947299593014888e-06,
                NaN,
                0.9999038975743094,
                8.31527928532683e-07,
                3.46632497145457e-07
            ],
            [
                5.715004470295662e-07,
                2.4300234940642642e-05,
                0.9999980052700431,
                0.9999975938970905,
                6.475947982002148e-07,
                2.382368531929327e-07,
                0.9999949062931872,
                0.9999996072136126,
                0.9999987901344621,
                1.2751905808881762e-07
            ],
            [
                2.260324836787226e-06,
                0.9999938558261342,
                0.9998766054555789,
                3.0590237279085045e-07,
                1.8553916819032217e-07,
                7.338208055664991e-07,
                1.8553905760062447e-07,
                1.994729008145876e-06,
                4.785095635655362e-06,
                3.9278605979534166e-07
            ],
            [
                2.561282516066741e-06,
                2.260324567337161e-06,
                5.4222183235249605e-06,
                1.5534971990169383e-06,
                1.2098659719788098e-06,
                8.315277302841894e-07,
                3.288748281329893e-06,
                1.5534971990169383e-06,
                7.889262585886274e-06,
                1.209866260432471e-06
            ],
            [
                2.9023133690821773e-06,
                2.4300234940642642e-05,
                2.1024344128584085e-07,
                1.7603434231777837e-06,
                6.475945666009864e-07,
                8.315279285251204e-07,
                5.715002426460124e-07,
                5.043474081993875e-07,
                4.785093924362895e-06,
                3.0590215399183813e-07
            ],
            [
                8.31528424151477e-07,
                6.144175334468545e-06,
                NaN,
                1.7603425837702984e-06,
                1.2098653950656417e-06,
                2.5612825160562587e-06,
                1.2098659719716573e-06,
                2.902312677137316e-06,
                2.2603242978871282e-06,
                2.9023119851266288e-06
            ],
            [
                5.422217030747413e-06,
                5.715005832886879e-07,
                6.02357921955714e-08,
                7.338212429562581e-07,
                7.734425918979532e-08,
                1.4449807263312446e-07,
                6.475949526020042e-07,
                1.6373764720990908e-07,
                2.1024339116168358e-07,
                1.5381734119776652e-07
            ],
            [
                1.2098656835224664e-06,
                0.9999724642958198,
                1.760343633031919e-06,
                0.9999974387184019,
                0.9999546021260809,
                3.9278634073732336e-07,
                4.539787947345257e-05,
                3.927863407379485e-07,
                1.0129987357287368e-05,
                4.222834954778007e-06
            ],
            [
                4.450852641717689e-07,
                3.466327037539638e-07,
                4.450852111148132e-07,
                1.5534979397790343e-06,
                4.450849988798682e-07,
                6.144173137126169e-06,
                8.315279285370317e-07,
                6.9622595696935874e-06,
                9.422445939002803e-07,
                6.475947982022763e-07
            ],
            [
                2.260325375664839e-06,
                1.9947297214182054e-06,
                1.370956716529941e-06,
                2.2603248366762157e-06,
                2.561282515988704e-06,
                7.338210679909462e-07,
                1.7603430034311638e-06,
                1.0677028700053041e-06,
                2.2603237589676295e-06,
                2.561281599914358e-06
            ],
            [
                0.9999869928685208,
                0.9999861539922063,
                0.9999251537554344,
                1.8925143729162536e-05,
                3.288750241561788e-06,
                0.9999339478558854,
                0.9999810748428879,
                0.9999925887219299,
                4.785094494716039e-06,
                0.9999646437454659
            ],
            [
                9.422447062294175e-07,
                3.288749457469787e-06,
                8.315279285351409e-07,
                0.0013250221890673188,
                9.422444815792981e-07,
                4.4508494582405734e-07,
                4.450852641737424e-07,
                3.0590237279032884e-07,
                8.939695238536645e-06,
                4.0063711294555596e-05
            ],
            [
                2.6995790618469934e-07,
                7.338208055680009e-07,
                2.6995771309333195e-07,
                1.275190884913241e-07,
                1.0677024881829577e-06,
                6.825598842065202e-08,
                9.422442569315887e-07,
                5.715003107767143e-07,
                3.927860597945825e-07,
                2.382369667929001e-07
            ],
            [
                0.9990889487421272,
                5.422220262636381e-06,
                2.1024339116134898e-07,
                3.927863875616689e-07,
                5.422220262599396e-06,
                2.6995774527718623e-07,
                1.3007130015488633e-05,
                0.9996200155288483,
                8.315282259138311e-07,
                3.726637951367137e-06
            ],
            [
                2.5612828213818346e-06,
                2.260324028427877e-06,
                8.939697369882888e-06,
                2.9023130230846496e-06,
                1.4738980215352592e-05,
                7.889259764445822e-06,
                2.753568782024347e-05,
                1.3709575337078829e-06,
                2.4300232042706045e-05,
                8.315281267800897e-07
            ],
            [
                2.5612825160271407e-06,
                2.9023109471689794e-06,
                2.260324836776948e-06,
                8.315280276456036e-07,
                1.300712536350655e-05,
                7.484620943960125e-05,
                1.553497384196656e-06,
                NaN,
                1.99473067264854e-06,
                3.726639728348526e-06
            ],
            [
                4.2228324377740105e-06,
                4.450849988798682e-07,
                3.927860597935108e-07,
                NaN,
                3.288750241561788e-06,
                2.382368247924618e-07,
                6.475947210031623e-07,
                1.3709576971425944e-06,
                2.9023116391978967e-06,
                3.927860597945825e-07
            ],
            [
                5.043475284430694e-07,
                1.7603434231705793e-06,
                3.726641061085547e-06,
                1.994729008145876e-06,
                4.4508510499849186e-07,
                1.5534971990126997e-06,
                2.260324836776948e-06,
                1.2098652508347793e-06,
                3.4663249714451116e-07,
                5.043475284430694e-07
            ],
            [
                1.5534977545603963e-06,
                1.7603440527286572e-06,
                6.475950298011458e-07,
                3.7266401726173067e-06,
                7.338208055536515e-07,
                4.785093924330255e-06,
                9.422450432014836e-07,
                1.067702870039777e-06,
                1.7603438428800754e-06,
                4.222833444590791e-06
            ],
            [
                4.785092783454444e-06,
                3.2887478892055875e-06,
                4.222833444506298e-06,
                6.962256249758443e-06,
                4.785095065171522e-06,
                0.0001584361981391736,
                1.8925150496609267e-05,
                1.5534975693601474e-06,
                3.2887478891487563e-06,
                8.939698435454571e-06
            ],
            [
                8.315280276546789e-07,
                0.9998766054704178,
                2.260324836776948e-06,
                8.31528126775552e-07,
                4.785095635592258e-06,
                1.5534979397740895e-06,
                1.012999581021488e-05,
                0.9999339478635177,
                3.2887482813149375e-06,
                9.422447062202052e-07
            ],
            [
                1.4738983728784933e-05,
                1.994730197090463e-06,
                4.539789028757721e-05,
                2.2603242978377903e-06,
                2.7535687818640727e-05,
                5.715005832853093e-07,
                7.88926352599354e-06,
                NaN,
                2.260324567337161e-06,
                1.4738976701411704e-05
            ],
            [
                6.144172404520556e-06,
                8.315277302788957e-07,
                1.55349775456958e-06,
                2.260325375677174e-06,
                1.3709572068354007e-06,
                9.422447062240614e-07,
                1.2098652508287273e-06,
                1.99472924590571e-06,
                7.338207180864763e-07,
                2.56128282131428e-06
            ],
            [
                1.760343423160973e-06,
                7.889262585886274e-06,
                1.7603425837855082e-06,
                1.7603440527222532e-06,
                8.93969950132721e-06,
                1.9947304348595095e-06,
                6.962254589781966e-06,
                1.2098662604192665e-06,
                6.9622595696935874e-06,
                1.994729721482609e-06
            ],
            [
                1.9947301970972664e-06,
                2.3823682479292225e-07,
                6.825598842065202e-08,
                2.3823688159291947e-07,
                NaN,
                1.444979692797559e-07,
                2.5612831267202583e-06,
                1.444979692800516e-07,
                6.144172404693786e-06,
                1.8553907971855875e-07
            ],
            [
                1.3709573702822306e-06,
                6.144177531811707e-06,
                4.4508510499849186e-07,
                1.994729483723626e-06,
                3.4663278639892215e-07,
                9.422447062294175e-07,
                1.0677033791612137e-06,
                9.422447062294175e-07,
                5.715003789046955e-07,
                3.4663274507713016e-07
            ],
            [
                0.9999985406234321,
                0.9999945777816805,
                0.9999994631248044,
                0.999999057755182,
                0.9999994284992807,
                0.9999977396751641,
                0.9999994631249963,
                0.9999995262093293,
                0.9999996940978826,
                0.9999992188513903
            ],
            [
                1.0677024882009222e-06,
                0.9998204721024677,
                1.2098659719757836e-06,
                4.785094494783494e-06,
                7.734423152941018e-08,
                0.9999945777803902,
                1.8553903548231313e-07,
                0.9999892166890878,
                1.6373766672973748e-07,
                0.9999969105051869
            ],
            [
                6.475949526020042e-07,
                1.3709568799760888e-06,
                2.5612825160271407e-06,
                3.9278605979208185e-07,
                2.5612831267202583e-06,
                1.2098659719716573e-06,
                4.785094494783494e-06,
                6.962259569630266e-06,
                1.6701421845057263e-05,
                3.0590226339061185e-07
            ],
            [
                1.0677027427600627e-06,
                5.043472278255469e-07,
                1.3709575337078829e-06,
                3.4663249714451116e-07,
                8.315284241597959e-07,
                1.0677032518748838e-06,
                3.9278634073732336e-07,
                8.315281267861397e-07,
                8.315283250394546e-07,
                3.0590237278838124e-07
            ],
            [
                8.939700567004841e-06,
                1.4738983729294318e-05,
                5.715006514151423e-07,
                1.0677032518785256e-06,
                5.04347348075149e-07,
                0.9998415637931242,
                1.2098661161927025e-06,
                9.422449308748773e-07,
                8.315277302819205e-07,
                7.3382080556433e-07
            ],
            [
                3.2887490653872164e-06,
                5.422219616184461e-06,
                2.5612825160562587e-06,
                6.962255419868303e-06,
                1.0129990980100021e-05,
                5.4222209089700225e-06,
                5.82912516391202e-05,
                1.994730197090463e-06,
                2.902312677137316e-06,
                6.144176799227922e-06
            ],
            [
                1.3709572068422585e-06,
                0.9999980052709931,
                0.9999945777803882,
                0.9999852610233151,
                0.9999832985821608,
                0.9999687980775306,
                3.0590237278838124e-07,
                0.999959936307953,
                5.04347528446051e-07,
                0.9999981261252878
            ],
            [
                0.999999310639037,
                0.9999999067050276,
                0.9999996072137999,
                0.9999987901344618,
                0.999999310639037,
                0.9999995818813268,
                0.9999995262094422,
                0.9999992661788448,
                0.9999997300423192,
                0.9999974387187077
            ],
            [
                0.9999990577557439,
                0.9999990577554074,
                0.9999988634364265,
                0.9999986290424677,
                0.999999114842648,
                0.999999114843387,
                0.999999352405125,
                0.9999987901337405,
                0.9999982396559495,
                0.9999992661788449
            ],
            [
                8.93969950132721e-06,
                1.5534983101602148e-06,
                4.785092783454444e-06,
                7.889259764445822e-06,
                1.994729483705484e-06,
                4.450852111135988e-07,
                6.962254589914941e-06,
                6.1441724044534996e-06,
                3.726638395415398e-06,
                1.6701415872385704e-05
            ],
            [
                1.9947292459265734e-06,
                NaN,
                2.9023133690980155e-06,
                NaN,
                NaN,
                NaN,
                8.315279285351409e-07,
                7.338207180864763e-07,
                NaN,
                2.5612825160271407e-06
            ],
            [
                2.5612816000145246e-06,
                2.5612812947077304e-06,
                8.315278293838516e-07,
                1.994729008105057e-06,
                9.422447062094932e-07,
                1.370956716529941e-06,
                2.561282210701601e-06,
                2.5612812947077304e-06,
                1.2098659719601033e-06,
                2.2603234895176927e-06
            ],
            [
                1.7603440527286572e-06,
                7.338207180801359e-07,
                8.939698435657833e-06,
                NaN,
                1.9947292459347367e-06,
                8.939693107288474e-06,
                3.288749457469787e-06,
                8.315281267834927e-07,
                NaN,
                2.260325106237323e-06
            ],
            [
                8.93969950132721e-06,
                8.31527928532683e-07,
                1.5534971990126997e-06,
                2.5612819054028872e-06,
                1.2098652508424818e-06,
                9.422444815765128e-07,
                2.4300252321904572e-05,
                1.4738983729294318e-05,
                3.059022998576899e-07,
                2.5612812947508257e-06
            ],
            [
                6.475951069985296e-07,
                0.9999852610180717,
                1.9947292459347367e-06,
                1.2098659719716573e-06,
                1.855390354818069e-07,
                8.315284241650899e-07,
                0.9999938558224848,
                0.9999869928653787,
                5.71500515151976e-07,
                1.3709568799823232e-06
            ],
            [
                3.288750241561788e-06,
                1.5534973842076057e-06,
                7.484620943960125e-05,
                8.315279285351409e-07,
                1.5534975693979422e-06,
                8.315281267882195e-07,
                1.275190580890061e-07,
                1.3709576971425944e-06,
                7.338209805240734e-07,
                1.209866260432471e-06
            ]
        ]
    },
    {
        "q_id": "10169_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.999997097688016,
                0.9999955048194951,
                0.999968798077524,
                0.9999992661786697,
                0.9999997463982241,
                1.5534984953453635e-06,
                0.9999910603069019,
                2.2603234895289998e-06,
                0.9999991684718734,
                2.3823696679327928e-07
            ],
            [
                4.785096206076165e-06,
                0.9999962733589399,
                0.999999554914789,
                0.9999999317439465,
                0.9999996310115039,
                0.9999997126313441,
                0.9999978766215384,
                0.9999995818813269,
                0.9999994956527123,
                0.9999998257021421
            ],
            [
                0.999995777164544,
                4.2228334445658276e-06,
                9.422449308716635e-07,
                2.9023116391675407e-06,
                0.00015843629234288536,
                1.8925145985895816e-05,
                0.9999949062943951,
                0.9999957771645442,
                1.3007134667070165e-05,
                9.422443692489024e-07
            ],
            [
                0.9999997126313097,
                0.9999999500628393,
                0.9999999586006394,
                1.9947299593014888e-06,
                0.9999985406239534,
                0.9999999530883283,
                0.9999999067050276,
                0.999999855501979,
                1.994729483723626e-06,
                0.9999999176675142
            ],
            [
                0.9999999123575255,
                0.9999994956525318,
                0.9999997126315154,
                4.450848927658745e-07,
                0.9999996072137062,
                0.9999997617631753,
                0.9999997761970515,
                0.9999993524052793,
                0.9999999123575151,
                3.288748281329893e-06
            ],
            [
                0.9999999677581451,
                0.9999999273417836,
                0.9999997761971315,
                0.9998415638404773,
                0.9999997300420939,
                0.9999999748900211,
                0.9999952149072182,
                0.999999922655833,
                0.9999999006880076,
                8.315283250394546e-07
            ],
            [
                0.9999983463110057,
                0.9999945777790944,
                0.9999996533674617,
                0.9999998874647977,
                2.5612834320214477e-06,
                0.9999998362622357,
                0.9999999273418182,
                0.9999945777790937,
                0.9999996940977003,
                1.3709573702822306e-06
            ],
            [
                0.9999996072138467,
                0.9999997617630333,
                0.9999994956524116,
                0.999999428499485,
                9.422443692555439e-07,
                0.9999997126315153,
                0.9999998144608981,
                0.9999998724810027,
                0.9999996743688975,
                2.382369951932796e-07
            ],
            [
                0.9999994284994851,
                0.99999976176309,
                0.9999999634651618,
                0.9999994956526521,
                3.288749065423109e-06,
                0.9999996743688586,
                0.9999999397642724,
                0.9999998942829098,
                0.9999997300423192,
                0.9999996940977732
            ],
            [
                1.209865827752005e-06,
                0.9999967112493678,
                0.9999996072136593,
                1.5534975693979422e-06,
                0.9999998642566866,
                1.9947299593078385e-06,
                0.9999993106387081,
                0.9999930377429243,
                0.9999987121052454,
                1.3709576971463352e-06
            ],
            [
                0.9999996940977367,
                0.9999999123575672,
                0.9999989969860319,
                0.9999999611088487,
                0.9999756997650787,
                0.9999996072136593,
                0.9999997897567342,
                0.9999997897566089,
                0.999999802494586,
                0.9999989969861512
            ],
            [
                0.999996499146422,
                0.9999991684719727,
                0.9999992661792823,
                0.9999962733602752,
                0.9999983463100206,
                5.715004470313855e-07,
                0.999999114842648,
                0.9999980052693285,
                0.9999994284995533,
                0.9999989969856729
            ],
            [
                2.1024326584639497e-07,
                0.999999653367255,
                2.6995771309523475e-07,
                0.9999994956527123,
                0.9999992661791948,
                0.9999992661789323,
                0.9999998144608097,
                0.9999996072139403,
                0.9999994631249324,
                2.382369667929001e-07
            ],
            [
                0.9999687980961007,
                0.9999997617629764,
                5.043473480777865e-07,
                0.9999993916406734,
                0.999995214904937,
                0.9999999559305891,
                0.9999992661790197,
                0.9999999358794174,
                0.9999998802069017,
                0.9999724643089319
            ],
            [
                0.9999997126315496,
                0.9999994284996214,
                0.9999998024946095,
                0.9999996310116359,
                0.9999997617631753,
                0.9999995549151075,
                0.9999998144608098,
                0.9999991148430705,
                0.9999997761971315,
                0.9999996940978098
            ],
            [
                1.4738983728490028e-05,
                0.9999991148432809,
                0.9999967112509363,
                0.999991060303701,
                0.999985261016281,
                8.939696304213768e-06,
                2.6995777745711594e-07,
                5.043472879504592e-07,
                1.553498124964492e-06,
                1.5534975693979422e-06
            ],
            [
                0.9999999006880668,
                0.9999998362623334,
                0.9999998802069302,
                0.9999998144609203,
                0.9999997126315496,
                0.9999999317439873,
                0.9999988634362897,
                0.9999993524054336,
                0.999999825702059,
                0.9999996940978826
            ],
            [
                0.9999985406234317,
                0.9999989322972576,
                0.999999391641036,
                0.9999999006881259,
                0.9999999656787284,
                0.9999998362623529,
                6.475947982037486e-07,
                0.9999991148433864,
                6.475950297971703e-07,
                0.999999931743979
            ],
            [
                0.9999996533673791,
                0.9999998642566866,
                0.9999898700054018,
                8.31527928532683e-07,
                0.9999962733611617,
                9.422450431989127e-07,
                0.999998790134173,
                5.715003107767143e-07,
                7.338213304363436e-07,
                0.9999987121050918
            ],
            [
                0.9999996072136126,
                4.450852111148132e-07,
                5.422220909009474e-06,
                4.4508494582405734e-07,
                1.3709575337016483e-06,
                0.9999996533672963,
                0.9998766054699672,
                0.999999554914789,
                0.9999934595651165,
                0.9999999067051388
            ],
            [
                7.734425918979532e-08,
                0.9999991684722699,
                0.9999995262096116,
                0.9999969105062899,
                0.9999997300421583,
                0.9999990577554064,
                0.9999995262093292,
                0.999999653367379,
                0.9999998802069302,
                0.9999999317439628
            ],
            [
                0.9999993916407459,
                0.9999999226557593,
                0.9999991148430698,
                0.9999999123575359,
                0.9999997617630049,
                0.9999981261243938,
                0.9999964991451701,
                3.2887482813149375e-06,
                0.9999991684720717,
                2.902312331170226e-06
            ],
            [
                0.9999983463104151,
                0.9999987901343169,
                0.9999994956524118,
                0.9999998555019619,
                0.9999981261248408,
                0.9999998144608098,
                0.9999998362622553,
                0.999999554914842,
                0.9999997617630049,
                0.9999945777790966
            ],
            [
                6.475951069932288e-07,
                4.450851580540182e-07,
                4.450851580540182e-07,
                1.6373770576776313e-07,
                3.05902117523595e-07,
                4.450849458218309e-07,
                0.9999995262096116,
                0.9999991148427533,
                3.4663266242969896e-07,
                3.9278624708775595e-07
            ],
            [
                0.9999993916407459,
                0.9999987901340288,
                0.9999998257021838,
                0.9999987901344611,
                0.9999996533673376,
                0.9999985406243014,
                0.999997876621792,
                1.067703124601679e-06,
                0.9999994631249962,
                0.9999997463981334
            ],
            [
                0.9998601778605337,
                2.5612828213818346e-06,
                0.9999996940978461,
                0.9999964991451697,
                0.9999934595627773,
                0.9999339478242106,
                6.47594566597747e-07,
                3.726638839833152e-06,
                2.2603251062270446e-06,
                0.9999151889487421
            ],
            [
                0.9999852610162793,
                0.9999999397642796,
                0.9999910603058317,
                2.260324567337161e-06,
                1.3709575337159875e-06,
                0.9999599363126164,
                6.475947982037486e-07,
                0.9999999434137705,
                0.9999988634364251,
                3.466327037548308e-07
            ],
            [
                0.9999999530883843,
                1.5534983101602148e-06,
                0.9999998362623723,
                0.9999985406243014,
                0.9999993106387902,
                0.9999996310115038,
                0.9999996072138466,
                0.9999997897565838,
                1.3709576971425944e-06,
                0.999999814460876
            ],
            [
                0.9999921107393097,
                0.9999994956527725,
                0.999999391640891,
                0.9999993106387084,
                0.999999310639037,
                0.9999996533672965,
                5.715005832886879e-07,
                0.9999985406234314,
                0.9999998802069587,
                0.999999218851856
            ],
            [
                4.785096206076165e-06,
                0.9999983463102172,
                0.9999996743687422,
                0.9999997300421261,
                0.9999983463102176,
                0.9999997300420939,
                1.275190580884987e-07,
                0.9999994284996895,
                1.2751904288739315e-07,
                0.9999997126313783
            ],
            [
                0.9999999226558238,
                0.9999997300422547,
                0.9999997761971048,
                1.0,
                0.9999995549150013,
                0.9999995262096116,
                0.9999998257020798,
                0.9999994631250603,
                0.9999996743688586,
                0.9999997463982241
            ],
            [
                1.7603430034867993e-06,
                2.90231094723893e-06,
                3.9278615343901467e-07,
                1.1253521571574156e-07,
                1.8553907971813685e-07,
                1.5534971990126997e-06,
                9.931198061405701e-08,
                2.1024336609843824e-07,
                9.931188590255539e-08,
                4.4508494582405734e-07
            ],
            [
                0.9999998874648112,
                0.9999785550439377,
                1.0677033791495609e-06,
                6.144172404587612e-06,
                2.2603251061849014e-06,
                5.422217677078203e-06,
                2.902313023063532e-06,
                3.288747889229516e-06,
                7.338208055664991e-07,
                1.300713001508642e-05
            ],
            [
                0.9999987901343186,
                0.9999969105066605,
                0.999998629043121,
                0.9999982396559484,
                0.999996499143919,
                0.9999991684718738,
                0.999992110739305,
                0.9999993106391195,
                0.9999952149037985,
                0.9999756997651224
            ],
            [
                0.9999980052707546,
                0.9999991148430699,
                1.9947301970972664e-06,
                0.9999994284994169,
                0.9999998024946095,
                0.9999993916411085,
                0.9999999468421186,
                0.9999997126313097,
                0.9999999358794402,
                0.999999825702163
            ],
            [
                0.9999980052702792,
                0.9999989322966213,
                0.9999996072138936,
                0.9999998024946095,
                0.9999996940978826,
                0.9999997300422547,
                0.9999994631249324,
                0.9999997463981939,
                0.9999974387168743,
                0.9999997463982241
            ],
            [
                2.3823682479292225e-07,
                0.9999967112509355,
                0.9999989322967484,
                9.931198061405701e-08,
                0.9999869928746471,
                3.9278634073732336e-07,
                0.9999977396759722,
                0.9999832985781667,
                1.5534971990126997e-06,
                4.222834954801051e-06
            ],
            [
                3.9278634073625165e-07,
                0.9999996533674617,
                0.9999997761971582,
                0.9999995262093292,
                0.9999991684720716,
                0.9999995549151074,
                0.9999995262094987,
                0.9999995262095551,
                0.9999998642566542,
                0.9999998642566866
            ],
            [
                0.9999994284995531,
                0.9999993524051248,
                0.9999994631249963,
                0.999999674368781,
                0.9999998724809267,
                0.9999994631249962,
                0.9999998874647574,
                0.9999994956525919,
                0.9999997300420939,
                0.9999985406232574
            ],
            [
                6.475948753991907e-07,
                6.475949526003845e-07,
                0.9999945777816793,
                0.9999930377462434,
                0.000261190278863158,
                0.9999985406243013,
                0.9999993106390368,
                2.430024073461624e-05,
                0.9999992661792821,
                8.939695238536645e-06
            ],
            [
                0.9999999123575046,
                0.9999869928746499,
                0.9999945777823265,
                8.31527928532683e-07,
                0.9999999176674356,
                5.043472278322555e-07,
                7.338210679979539e-07,
                2.144495608424996e-05,
                0.9999999611088811,
                0.9999998257021421
            ],
            [
                3.4663253846718004e-07,
                2.4300232043987867e-05,
                1.0677033791612137e-06,
                0.9999982396565773,
                2.9023119851781017e-06,
                1.760342793638743e-06,
                0.9999967112513277,
                0.9999991148430699,
                0.9999930377454123,
                9.422448185534261e-07
            ],
            [
                1.2751910369275402e-07,
                1.8553907971813685e-07,
                6.475948753991907e-07,
                5.043473480777865e-07,
                5.715003789046955e-07,
                1.5534975693979422e-06,
                2.3823682479181176e-07,
                3.927862002654366e-07,
                2.5612819054133693e-06,
                2.1024326584582131e-07
            ],
            [
                1.0,
                0.9999997126315153,
                0.9999996940978825,
                0.9999998024946801,
                0.9999999434137232,
                0.999999967758103,
                1.2098656835224664e-06,
                1.9947297215125433e-06,
                0.9999998642566219,
                0.9999999559306259
            ],
            [
                0.9999997463980427,
                0.999995777166055,
                0.9999798543140238,
                4.450849988811838e-07,
                4.4508510499849186e-07,
                1.0677029973158649e-06,
                5.04347287955046e-07,
                0.9999981261241704,
                0.9999999006879958,
                0.999991060304771
            ],
            [
                0.9999995262092727,
                0.9999999176675338,
                0.9999999123575046,
                0.9999999434137907,
                0.999999310638626,
                0.9999998461826405,
                1.0677033791583005e-06,
                7.338211554783522e-07,
                0.9999999123574524,
                2.6995768091383957e-07
            ],
            [
                0.9999992661788448,
                0.9999994284996214,
                0.9999995549149483,
                0.9999991684719727,
                0.9999989969857928,
                0.9999981261243942,
                0.999997097688363,
                0.9999993916409637,
                0.9999989969854339,
                0.9999986290431208
            ],
            [
                0.9999925887210168,
                0.9999996940976638,
                0.9999998024946801,
                0.9999998144609203,
                0.9999997617631469,
                0.9999996072136594,
                0.9999995549151074,
                0.9999997761971582,
                0.9999998362622943,
                0.9999996072137999
            ],
            [
                0.9999967112505449,
                0.9999969105055547,
                3.927860597935108e-07,
                0.9999996072137062,
                0.9999975938985223,
                0.9999989969861515,
                0.9999967112521133,
                0.9999992661790199,
                0.9999977396762424,
                3.288749849498565e-06
            ],
            [
                0.999999114843281,
                0.9999988634358834,
                0.9999991148426479,
                0.9999984465018759,
                0.999998446501876,
                0.9999975938982347,
                0.9999990577557438,
                0.9999995549148422,
                0.9999949062925725,
                0.9999981261241706
            ],
            [
                0.9999999358793485,
                8.315280276626197e-07,
                0.9999998362622748,
                0.9999997761971849,
                0.9999999697115588,
                0.9999999634651705,
                1.9947299593078385e-06,
                0.9999999358794174,
                0.9999977396757027,
                2.1024341622426268e-07
            ],
            [
                0.9999852610215542,
                0.9999981261246172,
                0.9999964991443351,
                0.9999986290424667,
                0.9999987901347493,
                0.9999989322968756,
                0.9999993524053563,
                0.9999997761970781,
                0.9999997300422547,
                8.315277302857965e-07
            ],
            [
                0.9999997300423191,
                0.9999992188513902,
                0.9999997300423192,
                0.9999952149037962,
                0.9999996743688975,
                0.9999997761970515,
                0.9999997761971582,
                0.9999997617631186,
                0.9999992188515765,
                0.9999998461827139
            ],
            [
                0.9999988634361542,
                5.043476486924565e-07,
                3.2887506336086064e-06,
                7.338209805240734e-07,
                0.9999999226558238,
                0.99999577716555,
                0.9999938558254022,
                0.9995694428637637,
                0.999997097688362,
                0.999992110733657
            ],
            [
                0.9999998555019791,
                0.9999999123574629,
                0.9999999468421059,
                1.0,
                0.9999999176675044,
                0.999999931743971,
                5.04347528446051e-07,
                1.3709575337159875e-06,
                0.9999997617631469,
                0.9999997761970515
            ],
            [
                3.466327450756327e-07,
                1.4449798650551755e-07,
                2.382368247924618e-07,
                2.3823688159291947e-07,
                2.6995784182073116e-07,
                1.2751907329024393e-07,
                2.6995790618350237e-07,
                0.9999646437619848,
                8.764244316973974e-08,
                0.999998996985673
            ],
            [
                0.9999998802069587,
                0.9999999176674651,
                0.9999999586006443,
                0.9999962733607171,
                0.9999978766220446,
                1.0,
                0.9999998642566542,
                0.9999999226558423,
                0.9999999176675044,
                0.9999852610110139
            ],
            [
                0.9999996743686645,
                0.9999997126314125,
                6.475946438055299e-07,
                0.9999992188518558,
                0.999999789756634,
                0.9999997761972116,
                0.9999995818811275,
                0.9999999006879721,
                0.9999999226558146,
                0.9999997463981334
            ],
            [
                0.999972464312229,
                0.9999997897567342,
                0.9999974387187065,
                0.9999983463104146,
                0.9999980052707548,
                0.9999997300422226,
                7.338211554783522e-07,
                5.71500651413193e-07,
                0.9999996940978095,
                0.9999996310115038
            ],
            [
                0.9999996310115918,
                0.9999994284992806,
                0.9999998362623334,
                0.999999789756659,
                0.9999995262095552,
                0.9999999358793562,
                0.9999998942828973,
                0.9999998942829602,
                0.9999998362623334,
                0.9999998724809267
            ],
            [
                0.9999998724809419,
                0.9999986290423033,
                0.9999996940976638,
                6.023575629235017e-08,
                0.999999554914789,
                1.3709568799919866e-06,
                2.699578096393206e-07,
                0.999998790134461,
                1.1253526937656726e-07,
                0.9999997761970782
            ],
            [
                3.288749849529972e-06,
                6.962256249885085e-06,
                8.939693107288474e-06,
                2.90231094723893e-06,
                1.5534975693979422e-06,
                6.475950298011458e-07,
                6.9622537599680095e-06,
                3.0590237279032884e-07,
                3.9278615344178325e-07,
                1.5534984953552536e-06
            ],
            [
                1.5534979397740895e-06,
                0.9999975938970875,
                0.9999986290423033,
                0.9999992188514834,
                2.9023133690637e-06,
                0.9999930377454136,
                1.7603434231705793e-06,
                0.9999995818813268,
                3.9278634073625165e-07,
                0.9999982396561575
            ],
            [
                0.9999989322975121,
                2.9023133690980155e-06,
                0.9999970976883624,
                1.2098656835252174e-06,
                1.1253526937656726e-07,
                0.9999996533673376,
                0.9999985406237792,
                0.999999057755631,
                0.9999995818811773,
                0.9999945777816792
            ],
            [
                0.9999977396765116,
                0.9999997897567091,
                0.9999984465024312,
                0.9999724642990765,
                0.9999996072136593,
                0.9999724643023523,
                0.9999998461826956,
                0.999999730042287,
                0.9999955048194963,
                0.9999994956523514
            ],
            [
                0.9999993524052019,
                9.422444815814404e-07,
                0.9999996533672136,
                5.715006514176113e-07,
                0.9999970976869775,
                0.9999998802069302,
                0.9999978766205266,
                1.3709567165617364e-06,
                0.9999995818813766,
                0.9999945777790935
            ],
            [
                0.9999832985721999,
                0.9999993106392012,
                0.9999991684718734,
                0.9999984465028016,
                0.9999989322972576,
                0.9999984465022459,
                0.9999938558254012,
                0.9999967112497594,
                0.9999994284993488,
                0.9999984465016902
            ],
            [
                0.9999975938985225,
                0.9999724643155044,
                0.9999934595612249,
                0.9999994284996896,
                0.999999581881277,
                0.999996910505186,
                0.9999988634362903,
                0.999992110735537,
                0.999997876622298,
                0.9999869928715521
            ],
            [
                0.9999995262096116,
                0.9999987121044779,
                0.9999949062968243,
                0.9999957771650468,
                4.4508510499849186e-07,
                0.9999994284996894,
                6.475947982002148e-07,
                0.9999991148433864,
                0.9999992661788447,
                0.999999789756659
            ],
            [
                3.0590237279085045e-07,
                0.9999999273418788,
                0.9999952149066473,
                0.9999995818811274,
                0.999999631011416,
                0.9999994631248682,
                0.0001233946191118875,
                0.9999999273417836,
                0.9999984465028013,
                1.2098661162056318e-06
            ],
            [
                0.9999984465016903,
                0.999998790133884,
                2.7535694384081332e-05,
                0.9999785550592712,
                0.9999993916411085,
                0.9999921107383578,
                0.9999983463108089,
                0.9999998724809875,
                0.9999987121044775,
                0.9999962733607182
            ],
            [
                0.9999995549150014,
                0.9999993916409636,
                0.9999996940978098,
                0.9999996743686257,
                0.9999998802068873,
                0.9999999273417749,
                0.9999992188518559,
                0.9999993916406734,
                0.9999972735297313,
                0.9999998257020798
            ],
            [
                6.475945666051092e-07,
                1.2751905808881762e-07,
                9.931200429181105e-08,
                1.4449802095609418e-07,
                3.0590237279032884e-07,
                3.288750241561788e-06,
                1.6373774480605869e-07,
                1.6373766672973748e-07,
                5.043474683220276e-07,
                2.1024326584639497e-07
            ],
            [
                0.9999987901337398,
                9.422448185510695e-07,
                3.0590237279032884e-07,
                0.9999994284995531,
                1.0677026154806063e-06,
                3.466325797888292e-07,
                0.9999993106387903,
                0.9999977396754334,
                0.9999938558239374,
                4.4508494582405734e-07
            ],
            [
                0.9999987901337404,
                1.5534977545886537e-06,
                0.9999974387184017,
                2.2603251062450327e-06,
                6.47595107001401e-07,
                4.785093924389007e-06,
                0.9999980052693284,
                5.4222209089700225e-06,
                0.9999974387168753,
                2.561281294760143e-06
            ],
            [
                0.9999910603026397,
                0.9999955048200321,
                0.999997097687324,
                0.9999996310115479,
                2.699578740032504e-07,
                0.9999983463106119,
                0.9999980052702793,
                2.90231233114251e-06,
                0.9999980052709929,
                0.999999674368781
            ],
            [
                0.99999976176309,
                7.338210680002898e-07,
                0.9999546021477497,
                0.9999957771665569,
                6.475950298011458e-07,
                0.9999994284993488,
                8.315282259089153e-07,
                0.9999999176675829,
                0.9999977396754337,
                1.2098661162056318e-06
            ],
            [
                0.9999930377412649,
                0.9999546021206042,
                1.1253513522447425e-07,
                0.9999998802068873,
                0.9999997463981334,
                0.9999994631251883,
                1.0677029973192638e-06,
                0.9999999123575464,
                0.9999998642566542,
                0.9999999500627857
            ],
            [
                0.9999987121044777,
                0.9999984465024312,
                3.466327037553825e-07,
                2.5612831267202583e-06,
                0.9999982396565776,
                0.9999977396748944,
                0.9999984465018757,
                0.9999981261237239,
                0.9999998642566543,
                1.209865827752005e-06
            ],
            [
                0.9999996743687034,
                0.999999674368781,
                0.999999352405202,
                0.9999995262093857,
                0.9999999468421124,
                0.9999996310113279,
                0.9999996743688586,
                0.9999998024946566,
                0.9999990577551818,
                0.9999989969854337
            ],
            [
                0.999999730042287,
                0.9999998024946566,
                0.9999996743688199,
                0.9999996072138467,
                0.999999789756659,
                0.9999998362623138,
                0.9999997463982241,
                0.9999998461826038,
                0.9999996743688199,
                0.9999996940978826
            ],
            [
                1.0677024881829577e-06,
                4.4508515805199415e-07,
                1.3709568799592562e-06,
                3.2887478892055875e-06,
                5.04347348075149e-07,
                1.6373766672821107e-07,
                1.5534973841592143e-06,
                2.5612828213352452e-06,
                3.927862939113312e-07,
                2.2603251062013478e-06
            ],
            [
                0.9999999358793562,
                8.315284241650899e-07,
                0.9999999226557225,
                0.9999999273418269,
                2.102434412875379e-07,
                0.9999999358793562,
                1.3709567165579959e-06,
                0.9999977396751643,
                0.9999999317439546,
                0.9999998555019447
            ],
            [
                0.9999994631251242,
                0.9999996743686645,
                0.9999998724809571,
                0.9999998802069873,
                0.9999996743686645,
                0.9999995818811275,
                0.999999961108858,
                0.9999999123574629,
                4.4508510499849186e-07,
                0.9999998257020798
            ],
            [
                1.7603425837855082e-06,
                0.9999999397642796,
                0.9999984465028013,
                0.9999987901344611,
                1.9947299593078385e-06,
                0.9999995262093292,
                0.9999994284992807,
                0.9999962733616057,
                5.715002426460124e-07,
                0.9999996310115479
            ],
            [
                1.6373766672973748e-07,
                0.9999994956526521,
                1.275190276859705e-07,
                0.9999997617630333,
                2.3823688159291947e-07,
                0.9999992188514835,
                0.9999997300421583,
                1.275190124842887e-07,
                1.2751907329024393e-07,
                0.9999994631251883
            ],
            [
                0.999995777167565,
                8.315277302857965e-07,
                0.9999999123574732,
                0.9999994956523514,
                9.422449308716635e-07,
                0.9999997126314811,
                0.9999999434137434,
                0.9999991148427533,
                0.9999993524051247,
                1.3709567165617364e-06
            ],
            [
                0.9999989969856732,
                0.9999983463096261,
                1.0677029973192638e-06,
                1.067703124601679e-06,
                7.338208930460318e-07,
                6.475947982037486e-07,
                8.31527928532683e-07,
                6.475947982002148e-07,
                3.46632497145457e-07,
                0.999999554914842
            ],
            [
                0.999999653367255,
                0.999999802494586,
                0.9999998024946566,
                0.9999997761972116,
                1.0,
                5.043474683220276e-07,
                0.9999984465015049,
                0.9999952149049368,
                0.9999945777823255,
                0.9999994956527724
            ],
            [
                1.147876812574406e-05,
                9.422443692489024e-07,
                7.338211554783522e-07,
                5.422219616184461e-06,
                1.4738985486265496e-05,
                8.31527928532683e-07,
                4.450851580540182e-07,
                1.3709570434054234e-06,
                4.4508505193386385e-07,
                1.2098652508347793e-06
            ],
            [
                0.99999916847227,
                0.9999995818813767,
                0.9999998874648917,
                0.9999997300423191,
                0.9999998942829854,
                0.9999998461827139,
                0.9999999397642437,
                5.715004470313855e-07,
                0.9999999358794249,
                0.9999998874648648
            ],
            [
                2.9023133690980155e-06,
                9.422443692574719e-07,
                2.90231094723893e-06,
                0.9999962733607167,
                0.9999990577550694,
                1.2098658277451275e-06,
                0.9999810748450078,
                0.9999982396567876,
                0.9999885212359889,
                0.9999967112513278
            ],
            [
                7.338213304363436e-07,
                0.9999996743688586,
                0.9999995549151075,
                0.9999997300423192,
                0.9999991684719727,
                0.9999996940978461,
                0.999999746398073,
                0.9999995818812769,
                0.9999998024945626,
                0.9999996940978826
            ],
            [
                0.9999998362622943,
                0.9999997463981334,
                0.9999999732705411,
                0.999999789756659,
                0.9999998942829225,
                1.6373770576776313e-07,
                0.9999999656787038,
                0.9999999397642939,
                6.475945666051092e-07,
                0.9999998461826956
            ],
            [
                0.9999991684721707,
                0.9999983463104145,
                0.9999998874648514,
                0.9999991684718734,
                0.9999995262093857,
                0.9999989969860317,
                2.382369667929001e-07,
                0.9999992661791947,
                1.209865539295696e-06,
                0.9999992661792823
            ],
            [
                5.715004470243685e-07,
                0.9999999226558423,
                8.315277302747361e-07,
                3.46632497145457e-07,
                6.962257909722651e-06,
                0.9999852610145312,
                1.3709572068478697e-06,
                8.31528424162821e-07,
                5.043472879504592e-07,
                0.9999991684719726
            ],
            [
                0.9999999176675632,
                0.9999999176675535,
                0.9999996743686257,
                0.999999391641036,
                0.9999999067051388,
                0.9999999317439139,
                0.9999997300422869,
                1.0,
                0.9999999634651443,
                0.9999995262095551
            ],
            [
                0.9999991148433863,
                0.9999999067049942,
                0.9999989322972574,
                7.889261645427538e-06,
                0.9999997300421904,
                0.9999998144608319,
                0.9999991148427534,
                0.9999996743688586,
                0.9999997463981636,
                0.9999993524053564
            ],
            [
                0.9999991684718734,
                0.9999724642958062,
                0.999999554914842,
                0.9999925887183683,
                0.9999984465015055,
                2.699578740032504e-07,
                0.9999832985702217,
                1.209865827752005e-06,
                0.9999972735294054,
                6.144175334468545e-06
            ],
            [
                6.962255419931625e-06,
                0.9999999358793868,
                0.9999996940977002,
                0.9999997300421261,
                0.9999999317439872,
                0.9999996533673791,
                0.9999990577550695,
                0.9999998144609203,
                0.9999996743686645,
                9.422447062294175e-07
            ],
            [
                0.9999997761970516,
                0.9999996940978462,
                0.9999996533673376,
                0.9999998257022045,
                0.9999998024946801,
                0.9999996072137999,
                0.9999992188513903,
                0.9999999226557224,
                0.9999998724809571,
                9.422445939054222e-07
            ],
            [
                3.726639728370556e-06,
                0.9999998461826772,
                0.9999999006881023,
                0.9999985406239533,
                0.999999310639119,
                0.9999991684719726,
                0.999999653367379,
                0.9999952149072189,
                0.9999993916411085,
                0.9999993524052019
            ],
            [
                1.3709575337159875e-06,
                0.9999999468421377,
                0.9999995549150543,
                0.9999994631250602,
                0.9999998144609424,
                0.9999999715466527,
                0.999999428499485,
                0.9999978766210325,
                0.9999999067050053,
                0.999988521235993
            ],
            [
                0.9999987901341728,
                0.9999996940978096,
                0.999998346310612,
                0.9999995262095551,
                0.9999975938985222,
                0.9999996533674204,
                0.9999996072137999,
                0.9999995818811275,
                0.9999997300421262,
                0.9999987901337403
            ],
            [
                7.889263526180094e-06,
                9.422448185534261e-07,
                0.9999898700041956,
                0.9999983463108092,
                1.7603430034743913e-06,
                1.8925155008941717e-05,
                4.222831934379152e-06,
                0.9999921107374189,
                0.999999057754957,
                1.760343213322473e-06
            ],
            [
                0.9999994631251242,
                0.999999789756609,
                0.999999495652532,
                1.760343213335281e-06,
                0.9999974387177905,
                0.9999996743686257,
                0.9999983463100204,
                0.9999998144608098,
                0.9999999358793409,
                0.999999825702059
            ],
            [
                0.9999998024946566,
                0.9999998724809419,
                0.9999999176675437,
                0.9999996310116358,
                0.9999995549149483,
                2.5612828213934817e-06,
                0.9999998724809116,
                0.999999653367255,
                0.9999999656786834,
                0.9999998144609646
            ],
            [
                0.9999981261241703,
                0.9999898700114427,
                0.9999869928684512,
                0.9999998144609424,
                2.5612834320470717e-06,
                3.927860597945825e-07,
                0.9999998144609645,
                1.209865827752005e-06,
                0.9999832985741877,
                0.9999996940978095
            ],
            [
                0.9999992661792823,
                0.9999999176674456,
                0.9999995818814266,
                0.9999996072137063,
                0.9999984465026167,
                0.9999997897567092,
                0.9999999006881378,
                0.9999999067050498,
                0.9999996743686645,
                0.9999996743687422
            ],
            [
                1.4449798650417048e-07,
                0.9999993106386259,
                7.338209805170655e-07,
                7.338211554783522e-07,
                0.9999990577550695,
                0.9999986290424667,
                0.9999967112513288,
                2.6995790618252024e-07,
                8.764246406483893e-08,
                4.4508510499737865e-07
            ],
            [
                3.059023727894942e-07,
                0.9999996072136593,
                1.8553905760024476e-07,
                0.9999997617631752,
                2.102433660979124e-07,
                0.9999986290432838,
                0.9999970976890539,
                0.9999992661792821,
                0.9999989969859122,
                0.9999998024945624
            ],
            [
                0.9999998642566542,
                0.9999997761970781,
                0.9999999273418096,
                0.9999998555019619,
                0.9999987901338843,
                0.9999996310116359,
                1.3709568799919866e-06,
                0.9999998642566542,
                7.338208055664991e-07,
                0.9999417087067525
            ],
            [
                0.9999996533672137,
                0.999999730042287,
                0.9999991148432811,
                0.9999995262095551,
                0.9999999434137232,
                2.6995774527657245e-07,
                0.9999997463981938,
                1.4449802095609418e-07,
                0.9999988634357478,
                0.9999955048178889
            ],
            [
                2.2603234895372223e-06,
                1.6373772528704005e-07,
                0.9999938558275983,
                7.338207180898968e-07,
                1.1478764021029928e-05,
                6.475947210046347e-07,
                0.9999972735294057,
                0.9999938558275976,
                2.6995784182183607e-07,
                0.9999949062931803
            ],
            [
                0.9999997897565588,
                0.9999996072137529,
                3.927862939126708e-07,
                0.9999997897566089,
                0.9999995818813766,
                0.9999993524050477,
                0.9999997463981032,
                0.9999997617630901,
                0.9999996533672963,
                0.99999976176309
            ],
            [
                3.927863875584984e-07,
                0.99999926617867,
                0.9999992188512972,
                2.7535704231043113e-05,
                0.999996273359829,
                0.9999996533674617,
                0.9999724643187772,
                0.9999724643154891,
                0.9999898700078206,
                0.999996273360718
            ],
            [
                0.9999998724809572,
                0.9999998642566704,
                0.9999995549150543,
                0.9999998802069159,
                1.370957860576702e-06,
                0.9999997463980125,
                0.9999938558261331,
                0.9999993106386259,
                0.9999996533672136,
                0.9999985406232574
            ],
            [
                0.9999997126313098,
                0.9999995549147359,
                0.9999996072139403,
                0.9999996940978096,
                0.9999982396567875,
                0.9999993524051248,
                0.9999996940977367,
                0.9999998642566866,
                0.9999997126313441,
                0.9999995818814266
            ],
            [
                0.9999962733616059,
                0.9999997761970248,
                0.9999960330136155,
                0.9999999226557408,
                0.9999999500627917,
                0.9999998362623332,
                0.9999999123575881,
                0.9999993524048931,
                0.9999999067051277,
                0.9999995818814265
            ],
            [
                0.9999999397642724,
                0.9999998802069587,
                0.9999998724808963,
                0.9999999358793714,
                0.9999989969862708,
                0.9999999358793715,
                0.9999998802069444,
                0.9999930377437527,
                0.9999998461826405,
                0.9999997761971048
            ],
            [
                3.4663278639892215e-07,
                9.422443692574719e-07,
                0.9999930377437534,
                0.9999687980998331,
                3.466327450765785e-07,
                0.9999980052702792,
                2.6995784182073116e-07,
                0.99999671124976,
                5.715002426486762e-07,
                0.999998239657207
            ],
            [
                1.6373764721072816e-07,
                3.7266401726359486e-06,
                6.475950298021765e-07,
                1.5534981249736758e-06,
                4.4508510499737865e-07,
                2.2603248367949354e-06,
                1.1253512180925583e-07,
                3.466327037548308e-07,
                2.382369383923073e-07,
                0.9999945777829717
            ],
            [
                0.9999997126314126,
                0.9999998642566704,
                0.9999995262093858,
                0.9999995262095552,
                0.9999993524049705,
                0.9999998642567351,
                0.9999996743688976,
                0.9999989969861512,
                0.9999978766217915,
                0.9999998024946095
            ],
            [
                1.0,
                0.9999999656786915,
                0.9999998144609203,
                0.999999887464905,
                8.315277302857965e-07,
                0.9999996310114599,
                9.422448185534261e-07,
                5.043474081993875e-07,
                1.9947304348862686e-06,
                0.9999999397642508
            ],
            [
                0.9999994956525919,
                0.9999938558246686,
                3.466327450756327e-07,
                0.9999910602994412,
                0.9999992661787572,
                0.9999980052707551,
                0.9999969105048169,
                0.9999945777823265,
                1.760343213335281e-06,
                0.9999980052702793
            ],
            [
                0.9999995262093292,
                9.422444815814404e-07,
                0.9999994631251241,
                0.999989870012655,
                0.9999996310114159,
                0.999999653367255,
                0.9999995262096116,
                0.9999810748450123,
                0.9999993106389548,
                0.9999995818811773
            ],
            [
                0.999999581881277,
                0.9999998555020307,
                0.9999994631247402,
                0.9999999732705411,
                0.9999997897566841,
                0.9999998144609645,
                0.9999998802069159,
                0.9999995262096116,
                0.9999995262095552,
                0.9999995262094422
            ],
            [
                0.9999977396762417,
                0.9999994956525919,
                2.5612828213934817e-06,
                0.999995777165047,
                0.9999998257021838,
                0.9999993106387082,
                0.9999962733616065,
                0.9999989969861514,
                0.9999991148430699,
                5.043476486915964e-07
            ]
        ]
    },
    {
        "q_id": "9639_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                9.422443692446175e-07,
                7.889266347715168e-06,
                2.7535700949523498e-05,
                8.315281267706361e-07,
                4.450849988758202e-07,
                4.785093924330255e-06,
                1.3709576970949014e-06,
                3.726639284017094e-06,
                4.222832437747125e-06,
                0.9999822214502913
            ],
            [
                2.1024341622426268e-07,
                3.726640616748873e-06,
                0.9998204721024677,
                2.2603237589542675e-06,
                4.22283394786293e-06,
                6.144174601879434e-06,
                2.2603234895053587e-06,
                3.288747889229516e-06,
                4.222835458148261e-06,
                2.9023119851266288e-06
            ],
            [
                3.653483822348123e-08,
                2.102433159721477e-07,
                1.275190732904469e-07,
                3.059023363231725e-07,
                5.715005832886879e-07,
                1.2098652508424818e-06,
                4.4508494582314646e-07,
                5.715005832886879e-07,
                5.04347468323289e-07,
                2.102434162245973e-07
            ],
            [
                0.9999991684719726,
                0.999998712104171,
                0.9999993916409634,
                1.7603436330179102e-06,
                1.9947304348332037e-06,
                0.9999988634358835,
                0.9999921107402471,
                0.9999977396754336,
                0.9999993106389546,
                2.9023112932177327e-06
            ],
            [
                5.71500515159253e-07,
                2.6995771309523475e-07,
                2.6995771309523475e-07,
                2.6995777745711594e-07,
                3.9278634073625165e-07,
                2.1024336609843824e-07,
                6.475948754012522e-07,
                5.715003788993679e-07,
                7.338208055664991e-07,
                0.9999998461826222
            ],
            [
                1.209865539295696e-06,
                7.484625403938018e-05,
                1.7603434231833873e-06,
                4.4508510499737865e-07,
                0.9999974387168746,
                6.962257909722651e-06,
                0.999998346310415,
                0.999992110740242,
                3.05902263391829e-07,
                3.726638395634011e-06
            ],
            [
                2.1024336609724313e-07,
                7.338207180864763e-07,
                5.043475284447896e-07,
                1.2751908849088918e-07,
                5.71500515159253e-07,
                1.4449805540740185e-07,
                2.3823688159237777e-07,
                5.715007195447234e-07,
                0.9998911030401033,
                1.275190580884987e-07
            ],
            [
                4.222831934352267e-06,
                5.422217676797111e-06,
                3.288749849477628e-06,
                0.9999996072137999,
                0.9999988634357478,
                0.9999987121052456,
                0.999999872480942,
                0.999999789756634,
                2.260324836776948e-06,
                2.6995774527657245e-07
            ],
            [
                4.450852111135988e-07,
                2.6995784182073116e-07,
                5.04347468323289e-07,
                4.450849988811838e-07,
                8.315281267861397e-07,
                1.9947304348703948e-06,
                4.4508505193932864e-07,
                6.475948754012522e-07,
                3.927861066170637e-07,
                5.715005151606823e-07
            ],
            [
                1.9947306726594253e-06,
                3.2887482812745586e-06,
                1.8553919030776337e-07,
                3.05902117523595e-07,
                1.0677032518700286e-06,
                4.2228339479858295e-06,
                6.144173869379821e-06,
                5.043475885674441e-07,
                1.8553907971758842e-07,
                3.4663266243111764e-07
            ],
            [
                1.4449803818215767e-07,
                2.1024331597262577e-07,
                0.9999964991447547,
                0.9999822214503417,
                0.9999952149066486,
                4.785093353874907e-06,
                0.9999962733602751,
                6.825605351455307e-08,
                0.9999910603026405,
                9.931193325852072e-08
            ],
            [
                3.9278634073625165e-07,
                5.04347528440776e-07,
                1.5534971989992774e-06,
                3.059021539909339e-07,
                3.466326211113502e-07,
                8.315281267834927e-07,
                1.553498124964492e-06,
                1.3709568799823232e-06,
                1.760344052714248e-06,
                5.71500515159253e-07
            ],
            [
                1.4738981969615573e-05,
                3.059022998576899e-07,
                0.9999980052695664,
                0.9999985406232579,
                5.715007195447234e-07,
                3.05902190458764e-07,
                0.9999930377437558,
                8.315283250371857e-07,
                3.927861066170637e-07,
                2.699577774585891e-07
            ],
            [
                0.0009110511271666856,
                0.9999984465020608,
                0.9999991148426479,
                8.315282259117513e-07,
                0.9999898700066155,
                3.4663266243308805e-07,
                1.2098659719601033e-06,
                7.338209805240734e-07,
                0.9999934595643404,
                5.043476486915964e-07
            ],
            [
                0.9999832985702217,
                0.999948557798764,
                0.999994228079285,
                5.043472879540142e-07,
                1.275190124842887e-07,
                2.102433159721477e-07,
                4.4508494582405734e-07,
                0.9999810748427624,
                5.043472879540142e-07,
                1.2751908849167202e-07
            ],
            [
                3.4663266243111764e-07,
                1.0677029973056687e-06,
                8.31528424151477e-07,
                9.422443692489024e-07,
                1.275190732904469e-07,
                4.450851580540182e-07,
                3.7266383955611403e-06,
                5.04347348075149e-07,
                6.475951069961737e-07,
                5.422217676925328e-06
            ],
            [
                1.444980726324838e-07,
                0.999995214907219,
                5.715003789033962e-07,
                0.9999997617630617,
                2.699578740032504e-07,
                1.5534975693933505e-06,
                5.715006514167015e-07,
                0.9999977396748948,
                5.043473480730849e-07,
                0.9999970976890543
            ],
            [
                1.3709572068354007e-06,
                3.466325384661554e-07,
                3.466326211113502e-07,
                0.9999997897567091,
                5.04347348075149e-07,
                0.9999987901337399,
                0.9999989969861515,
                4.450851580566494e-07,
                4.450849988798682e-07,
                7.338208930421943e-07
            ],
            [
                0.999999802494633,
                0.9999983463098234,
                0.9999957771660546,
                0.9999989969854337,
                0.9999999176675142,
                0.9999996940978825,
                0.9999977396751643,
                0.9999995262094987,
                4.450848927650143e-07,
                2.90231094723893e-06
            ],
            [
                2.561282821352716e-06,
                1.7603436330259153e-06,
                4.4508515805199415e-07,
                9.42244256915735e-07,
                3.05902263389638e-07,
                1.7603430034743913e-06,
                5.043473480730849e-07,
                4.450849458200093e-07,
                1.5534981249397663e-06,
                1.994730434847717e-06
            ],
            [
                7.889262585886274e-06,
                6.605214468549049e-05,
                0.9999989969856731,
                9.422447062270609e-07,
                5.043473480766399e-07,
                3.4663253846718004e-07,
                1.300713311614059e-05,
                1.3007128464559612e-05,
                3.466326211105621e-07,
                1.0129994602222992e-05
            ],
            [
                0.9999983463106116,
                3.726638395634011e-06,
                0.9999996743688586,
                0.9999994284992806,
                6.962253759581752e-06,
                0.9999998555019275,
                0.9999885212264089,
                0.9999646437409129,
                0.9999962733602733,
                0.9999997761970515
            ],
            [
                1.0677029973158649e-06,
                4.222831934156396e-06,
                0.9999687980924558,
                8.315283250371857e-07,
                0.9999687980962317,
                4.222834954687752e-06,
                NaN,
                0.9999970976887085,
                5.71500515159253e-07,
                3.288747889229516e-06
            ],
            [
                0.9999949062943949,
                1.9947306726594253e-06,
                5.043476486915964e-07,
                0.9999991148432809,
                4.4508494582405734e-07,
                2.2603237589676295e-06,
                3.927862002654366e-07,
                1.9947292459265734e-06,
                0.9998766053971976,
                8.315283250394546e-07
            ],
            [
                4.450849988798682e-07,
                2.10243290909724e-07,
                1.370957860567974e-06,
                6.1441760667392215e-06,
                5.715005832872586e-07,
                3.9278610661545617e-07,
                2.6995774527657245e-07,
                3.0590226338838606e-07,
                2.3823688159237777e-07,
                1.3709575337016483e-06
            ],
            [
                2.7535694382378416e-05,
                0.9999998362622943,
                8.315277302788957e-07,
                0.9999993106388725,
                0.9999985406234317,
                0.9999994631248682,
                1.76034300345598e-06,
                0.9999974387174848,
                2.5612834320214477e-06,
                5.043472879540142e-07
            ],
            [
                4.222833444506298e-06,
                4.222831934352267e-06,
                2.260325106237323e-06,
                2.561281600076256e-06,
                2.260324836776948e-06,
                NaN,
                3.288749849477628e-06,
                4.785092783519724e-06,
                6.144176066901277e-06,
                1.5534979397592542e-06
            ],
            [
                0.9999898700066134,
                2.561281600049467e-06,
                0.9999974387177908,
                0.9999930377437612,
                1.2098655392921197e-06,
                3.9278624708775595e-07,
                9.422449308673789e-07,
                9.422450431912e-07,
                0.9999997897567091,
                1.0677026154730804e-06
            ],
            [
                5.043474081993875e-07,
                1.8553916819032217e-07,
                1.27519088491875e-07,
                1.553498124964492e-06,
                1.855391681906175e-07,
                5.715005832853093e-07,
                2.3823685319244518e-07,
                3.726639284017094e-06,
                4.4508494582314646e-07,
                9.422445939002803e-07
            ],
            [
                2.9023133690980155e-06,
                8.31527928532683e-07,
                1.0677029973158649e-06,
                2.9023112931688987e-06,
                3.2887502415243994e-06,
                3.7266383955882547e-06,
                7.338207180864763e-07,
                2.5612822107167428e-06,
                1.9947297215125433e-06,
                6.962254589705982e-06
            ],
            [
                9.422448185510695e-07,
                0.9999945777829724,
                3.4663249714451116e-07,
                1.0677027427525368e-06,
                3.4663249714612693e-07,
                3.4663249714451116e-07,
                5.04347468323289e-07,
                6.475951069808602e-07,
                1.9947299592933255e-06,
                1.9947304348703948e-06
            ],
            [
                1.4449805540763184e-07,
                4.785095635592258e-06,
                1.275190580884987e-07,
                5.04347468323289e-07,
                9.422443692489024e-07,
                3.927860597945825e-07,
                2.3823682479181176e-07,
                3.466325797888292e-07,
                5.043472879540142e-07,
                8.31527928532683e-07
            ],
            [
                3.05902263391829e-07,
                0.9999885212291495,
                3.4663266243111764e-07,
                2.6995790618469934e-07,
                2.3823688159237777e-07,
                2.6995784182073116e-07,
                2.6995787400208416e-07,
                4.450850519403407e-07,
                1.444980209564556e-07,
                7.338208930421943e-07
            ],
            [
                0.9999877809269205,
                4.785093924156175e-06,
                0.999998540623606,
                0.9999999006880905,
                0.9999997761970515,
                4.4508494582314646e-07,
                0.9999993916410361,
                1.7603427936335396e-06,
                1.209866260432471e-06,
                9.422445939032799e-07
            ],
            [
                4.785093924156175e-06,
                3.9278615344178325e-07,
                5.04347528446051e-07,
                0.9999997463982241,
                3.466325797888292e-07,
                8.764240137829087e-08,
                2.3823690999290963e-07,
                3.92786293909545e-07,
                1.444979692800516e-07,
                2.1024339116134898e-07
            ],
            [
                2.69957906184239e-07,
                2.699577774585891e-07,
                3.4663266243308805e-07,
                0.9999930377429276,
                1.0677031245953668e-06,
                6.475946438022905e-07,
                3.0590237279032884e-07,
                0.9999861539905092,
                0.9999983463102178,
                3.466326211105621e-07
            ],
            [
                3.726641061109272e-06,
                5.043476486902204e-07,
                4.78509563555309e-06,
                6.475947982022763e-07,
                2.5612822107167428e-06,
                1.012999460251781e-05,
                8.939696304002375e-06,
                6.962255419728997e-06,
                0.9999885212346231,
                4.78509392429544e-06
            ],
            [
                3.7266388397721442e-06,
                0.999972464299136,
                8.939700566289352e-06,
                7.88926164518358e-06,
                1.2098662604291696e-06,
                3.726638839806038e-06,
                3.9278634073625165e-07,
                6.9622579092224155e-06,
                1.994729008145876e-06,
                7.889264466445326e-06
            ],
            [
                1.6373762769138607e-07,
                6.144176799227922e-06,
                3.2887490653872164e-06,
                0.9999955048194976,
                0.9999949062962169,
                0.9999995549149482,
                0.9999990577557434,
                0.999998629042794,
                7.338212429562581e-07,
                1.9947297215043796e-06
            ],
            [
                1.994730197071414e-06,
                0.9999667858094627,
                3.726641061027928e-06,
                2.260324028404236e-06,
                4.222831934379152e-06,
                0.9999962733602746,
                0.9999910603069072,
                2.2603251062147097e-06,
                5.4222170304318e-06,
                3.2887498493983645e-06
            ],
            [
                1.4449805540585765e-07,
                2.3823690999290963e-07,
                3.4663253846316044e-07,
                6.144175333926503e-06,
                2.561282210740037e-06,
                6.962256249517824e-06,
                2.2603245672867952e-06,
                2.902310947190096e-06,
                1.0677027427471959e-06,
                0.9999969105044483
            ],
            [
                9.931189774187203e-08,
                3.059022269250683e-07,
                0.9999993916407459,
                2.1024329090929374e-07,
                0.9999980052707553,
                0.9999996533672137,
                1.7603425837791042e-06,
                NaN,
                3.46632497145457e-07,
                7.338211554783522e-07
            ],
            [
                3.9278610661545617e-07,
                3.9278634073732336e-07,
                8.315277302788957e-07,
                4.450849458218309e-07,
                1.637377057673536e-07,
                3.9278634073732336e-07,
                4.450849988811838e-07,
                5.715002426460124e-07,
                4.450851580540182e-07,
                0.9999993106391191
            ],
            [
                0.9999998024946802,
                0.9999996310115918,
                0.9999998144608981,
                5.422220262505697e-06,
                0.9999996533674204,
                0.9999998942830485,
                1.0,
                0.9999981261241709,
                2.902311985146426e-06,
                0.9999999656786874
            ],
            [
                5.043473480766399e-07,
                1.7603425837791042e-06,
                4.4508510499737865e-07,
                0.9999921107393015,
                0.9999997617630616,
                1.5534971990126997e-06,
                2.2603242978778778e-06,
                1.7603438428800754e-06,
                4.222831934352267e-06,
                2.2603253756874524e-06
            ],
            [
                1.994730434879465e-06,
                3.7266406168624155e-06,
                1.1478765389065974e-05,
                2.260324297853209e-06,
                7.338207180864763e-07,
                2.9023109472244114e-06,
                3.2887482812506295e-06,
                0.9999987901340287,
                8.315281267800897e-07,
                0.9999877809181776
            ],
            [
                1.3709575337078829e-06,
                1.5534983101478522e-06,
                4.785094494672519e-06,
                8.939697369671496e-06,
                1.3709575337016483e-06,
                6.475948753930064e-07,
                1.7603436330179102e-06,
                3.535626336072768e-05,
                0.9999967112513286,
                0.9999975938965142
            ],
            [
                0.9999980052693281,
                0.9999981261252878,
                3.4663274507713016e-07,
                3.9278610661822475e-07,
                7.338212429582604e-07,
                1.6373770576776313e-07,
                1.4449802095609418e-07,
                0.9999962733598314,
                0.99999385582394,
                0.9999599363031495
            ],
            [
                1.0677029973158649e-06,
                7.338213304363436e-07,
                7.889260704968913e-06,
                1.6701421845361053e-05,
                9.422443692555439e-07,
                5.422220262505697e-06,
                1.0677032518785256e-06,
                1.0129995809929273e-05,
                1.9947294837154625e-06,
                3.059021539909339e-07
            ],
            [
                0.9999982396574173,
                0.999995777165049,
                6.475945666063607e-07,
                2.6995768091383957e-07,
                4.450852641737424e-07,
                3.466327450765785e-07,
                5.043474081957179e-07,
                4.4508494582314646e-07,
                1.8553905760062447e-07,
                0.9999038975969499
            ],
            [
                8.31527928532683e-07,
                1.6373776432509826e-07,
                2.6995790618252024e-07,
                2.5612825160562587e-06,
                9.422448185510695e-07,
                9.422443692555439e-07,
                8.315277302788957e-07,
                1.5534971990169383e-06,
                1.2098653950551882e-06,
                1.0677029973192638e-06
            ],
            [
                0.9999986290426303,
                3.7266406168403854e-06,
                1.067703379154416e-06,
                4.2228324377164004e-06,
                2.5612831267086116e-06,
                0.9999251537651426,
                2.9023109472244114e-06,
                2.9023126771227976e-06,
                4.78509392429544e-06,
                2.5612828213690224e-06
            ],
            [
                2.3823682479181176e-07,
                4.4508515805199415e-07,
                4.450851580566494e-07,
                4.450849458218309e-07,
                1.994730434879465e-06,
                3.927861066170637e-07,
                2.902312677104321e-06,
                3.927860597945825e-07,
                1.4449796928021588e-07,
                2.382368531929327e-07
            ],
            [
                1.275190580884987e-07,
                6.144175334418252e-06,
                9.422445939002803e-07,
                6.962253759828703e-06,
                4.222834954687752e-06,
                2.3823699519290042e-07,
                1.637377448057981e-07,
                1.3709570434178922e-06,
                2.902310947208574e-06,
                8.939700566143004e-06
            ],
            [
                6.962256249758443e-06,
                4.222833947820683e-06,
                8.93969630362837e-06,
                6.962257079775324e-06,
                6.144173136729416e-06,
                2.3823699519143784e-07,
                3.288749849477628e-06,
                7.338207180864763e-07,
                3.059022269250683e-07,
                8.315279285149107e-07
            ],
            [
                1.760343842833246e-06,
                4.222832941111319e-06,
                2.5612815999679353e-06,
                0.9999970976873246,
                3.7266379512518984e-06,
                3.726639728224814e-06,
                2.2603248367173307e-06,
                1.4738978456049602e-05,
                4.222834954514924e-06,
                2.2603245673155757e-06
            ],
            [
                3.927861066170637e-07,
                2.5612828213690224e-06,
                3.466326211105621e-07,
                0.9999995818813767,
                3.059021539909339e-07,
                0.9999934595612212,
                3.9278605979534166e-07,
                0.9999992661789323,
                0.9999964991460052,
                3.0590237279085045e-07
            ],
            [
                8.315282259089153e-07,
                5.043472879540142e-07,
                3.059022998576899e-07,
                1.8553907971855875e-07,
                2.5612812947077304e-06,
                6.962256249429175e-06,
                1.370957860567974e-06,
                2.6995774527718623e-07,
                2.5612828213934817e-06,
                1.9947301970813926e-06
            ],
            [
                0.9999994956526521,
                0.9999992661791071,
                0.9999970976887079,
                3.927861534406222e-07,
                3.9278615344178325e-07,
                4.4508526416286326e-07,
                0.9999988634357477,
                0.999989870004201,
                0.999996033014561,
                5.043472879540142e-07
            ],
            [
                0.9999987901347496,
                0.9999934595596613,
                3.927862470899887e-07,
                4.222832941142044e-06,
                0.9999981261250644,
                2.260325375650449e-06,
                1.300713466619476e-05,
                1.067702870039777e-06,
                1.5534977545886537e-06,
                0.999993855826873
            ],
            [
                1.3709575337078829e-06,
                3.927862002641863e-07,
                2.699578096393206e-07,
                4.450852641737424e-07,
                6.475949526020042e-07,
                3.466327037548308e-07,
                1.0677026154774503e-06,
                1.994729245878497e-06,
                2.2603234894560207e-06,
                8.315282259117513e-07
            ],
            [
                5.8291293348093234e-05,
                2.6995774527718623e-07,
                6.475947210031623e-07,
                4.4508494582314646e-07,
                9.422442569290178e-07,
                5.04347528446051e-07,
                0.9999852610145271,
                1.9947299593078385e-06,
                7.338211554783522e-07,
                8.315279285351409e-07
            ],
            [
                3.059022998569248e-07,
                0.9999964991464227,
                3.927862470899887e-07,
                4.450851580540182e-07,
                3.2887502415438413e-06,
                5.043476486902204e-07,
                0.9999997617630333,
                0.9999974387187069,
                1.2098653950606901e-06,
                1.5534975693933505e-06
            ],
            [
                0.9999994631251882,
                2.1444945852673643e-05,
                2.6995784182183607e-07,
                2.1024341622426268e-07,
                0.9999934595619993,
                4.222834954561012e-06,
                3.7266397281434697e-06,
                8.764247451307293e-08,
                2.9023126771227976e-06,
                4.4508510499737865e-07
            ],
            [
                0.9999964991447547,
                4.450852641717689e-07,
                4.450851580566494e-07,
                3.927861534406222e-07,
                0.999997097688017,
                7.338211554783522e-07,
                5.043472879540142e-07,
                1.1253509497883659e-07,
                7.3382080556433e-07,
                4.450851580540182e-07
            ],
            [
                0.9999898700114461,
                0.999995777166558,
                4.785095065171522e-06,
                1.2098662604247682e-06,
                3.726638395611981e-06,
                5.043474081931949e-07,
                1.30071315662049e-05,
                1.8553905759969634e-07,
                1.6701427818034747e-05,
                1.0677028700363782e-06
            ],
            [
                0.9999994284992806,
                0.999999554914842,
                0.9999989969859123,
                9.422450431989127e-07,
                0.9999975938979487,
                3.927862002654366e-07,
                0.9999992188514835,
                0.9999972735287553,
                0.9999957771645462,
                3.288748281329893e-06
            ],
            [
                2.561282210740037e-06,
                2.1024344128584085e-07,
                6.023576347299818e-08,
                3.9278615343901467e-07,
                5.715003107755449e-07,
                6.475949525919915e-07,
                4.450849458200093e-07,
                2.699577130944368e-07,
                0.9999646437409151,
                5.043476486902204e-07
            ],
            [
                2.1024341622426268e-07,
                2.102434412871794e-07,
                1.3709573702822306e-06,
                1.99472924590571e-06,
                1.855391460719133e-07,
                3.059022269250683e-07,
                3.466326211113502e-07,
                1.4449805540740185e-07,
                1.444979692797559e-07,
                2.1024326584639497e-07
            ],
            [
                3.7266383955611403e-06,
                8.939696304002375e-06,
                1.7603440527286572e-06,
                4.450851580540182e-07,
                2.1024341622368903e-07,
                2.6995784182140636e-07,
                8.315283250371857e-07,
                6.144177531660828e-06,
                1.8553910183607374e-07,
                1.5534983101602148e-06
            ],
            [
                5.04347408197782e-07,
                1.8553907971855875e-07,
                5.715003789046955e-07,
                4.4508510499849186e-07,
                3.0590237279032884e-07,
                3.927862002663297e-07,
                1.855391239544352e-07,
                7.338207180864763e-07,
                5.043472879540142e-07,
                0.9999910603058337
            ],
            [
                0.9999982396574175,
                0.9999987121043247,
                0.9999934595620018,
                7.3382080556433e-07,
                7.338212429562581e-07,
                1.2098659719601033e-06,
                0.9999994284994169,
                0.9999945777810344,
                0.9999998555019618,
                8.315282259089153e-07
            ],
            [
                0.9999997761970781,
                1.994730197090463e-06,
                1.8553905760024476e-07,
                0.9999998642566381,
                0.9999972735303806,
                0.9999885212359879,
                0.9999989322975121,
                0.9999993524049704,
                0.9999980052702796,
                3.0590226339137693e-07
            ],
            [
                0.9999724642991594,
                0.9999986290427939,
                7.889259764273619e-06,
                0.9999785550593431,
                1.9947294837154625e-06,
                7.889266347636241e-06,
                1.99472900813862e-06,
                4.785094494750855e-06,
                0.9999987121046313,
                5.4222202624563834e-06
            ],
            [
                0.9999993524054336,
                0.9999987121047851,
                0.14804719051380197,
                4.450850519403407e-07,
                2.1024339116168358e-07,
                3.0590237279032884e-07,
                0.9999921107374213,
                3.9278615344178325e-07,
                0.9999993524051247,
                0.9999970976866323
            ],
            [
                1.8553919030776337e-07,
                4.450849988811838e-07,
                9.422449308748773e-07,
                2.3823682479181176e-07,
                5.715004470295662e-07,
                3.9278610661822475e-07,
                6.475948753991907e-07,
                1.4449798650476187e-07,
                6.475947210031623e-07,
                1.0677027427569065e-06
            ],
            [
                4.2228334445658276e-06,
                1.370957860567974e-06,
                0.9999974387184011,
                7.338207180838067e-07,
                0.9999984465016905,
                5.715006514105942e-07,
                7.338213304316717e-07,
                1.855390354818069e-07,
                3.059021539909339e-07,
                5.043475885657239e-07
            ],
            [
                3.4663249714325014e-07,
                9.42244818532859e-07,
                0.9999992661786697,
                0.9999869928762076,
                0.9999994956524116,
                2.9023133690637e-06,
                0.9999756997651137,
                2.5612825160562587e-06,
                2.9023133690425823e-06,
                3.2887502415243994e-06
            ],
            [
                3.726639283901856e-06,
                5.715004470313855e-07,
                4.006368263787411e-05,
                6.1441746017453204e-06,
                2.9023112932177327e-06,
                3.466327037553825e-07,
                0.9999981261248407,
                3.7266401726173067e-06,
                3.9278638755992735e-07,
                3.4663262110945863e-07
            ],
            [
                0.9999942280820402,
                3.927860597945825e-07,
                1.2751908849167202e-07,
                3.0590226339061185e-07,
                4.785096776433933e-06,
                3.9278624708775595e-07,
                3.726640616748873e-06,
                1.855391239544352e-07,
                2.699576809143613e-07,
                1.5534979397677313e-06
            ],
            [
                3.0590237279032884e-07,
                3.059021539909339e-07,
                4.450852641717689e-07,
                2.102433159721477e-07,
                4.4508494582314646e-07,
                6.475946438055299e-07,
                5.715002426460124e-07,
                1.637377643243723e-07,
                0.9999485577864516,
                NaN
            ],
            [
                2.561282210729555e-06,
                1.637377057673536e-07,
                0.999997438718708,
                0.9999957771650498,
                2.5612828213818346e-06,
                0.999997876621792,
                0.9999994956524115,
                0.9999339478400403,
                0.9999991684719728,
                0.9999994956523515
            ],
            [
                0.9999985406243013,
                5.715002426460124e-07,
                3.4663266243111764e-07,
                5.715005832798517e-07,
                3.7266388397721442e-06,
                1.8553905760024476e-07,
                8.31528424151477e-07,
                2.1024344128584085e-07,
                8.315284241597959e-07,
                1.8553910183548312e-07
            ],
            [
                5.04347528446051e-07,
                3.4663278639892215e-07,
                5.715002426460124e-07,
                7.338207180864763e-07,
                9.422449308716635e-07,
                1.6373762769138607e-07,
                9.422443692489024e-07,
                3.466326211105621e-07,
                1.0677027427569065e-06,
                8.315282259138311e-07
            ],
            [
                2.2603237589779086e-06,
                5.422220262636381e-06,
                0.9999151889189469,
                4.222834954753043e-06,
                0.9999992188515764,
                5.715005832872586e-07,
                4.785095065132354e-06,
                4.785096776394765e-06,
                0.9999998942829854,
                4.785096206047877e-06
            ],
            [
                5.42222090882208e-06,
                2.26032402841657e-06,
                7.338208930421943e-07,
                3.9278615344178325e-07,
                3.927860597945825e-07,
                1.300713001508642e-05,
                1.0677024881941248e-06,
                1.2751908849167202e-07,
                1.9947306726594253e-06,
                2.9023130230846496e-06
            ],
            [
                0.9999987121043243,
                2.3823702359290413e-07,
                0.9999998144608098,
                0.9999986290424668,
                1.2098662604247682e-06,
                0.9999724643023993,
                9.422445939032799e-07,
                0.9999988634361543,
                5.715005832872586e-07,
                1.3709570434178922e-06
            ],
            [
                2.6995768091310296e-07,
                0.9999982396559489,
                5.04347408197782e-07,
                6.475947210012481e-07,
                8.764245361752286e-08,
                0.9999991684715764,
                2.1024339116082313e-07,
                1.2751902768612997e-07,
                5.043476486902204e-07,
                0.9999977396746261
            ],
            [
                0.9999993916411811,
                3.466326211105621e-07,
                2.6995784182073116e-07,
                0.9999985406237795,
                3.0590237279032884e-07,
                0.9999997300422226,
                1.9947292459265734e-06,
                0.9999997617631184,
                7.338210679979539e-07,
                0.9999969105059225
            ],
            [
                0.9999949062950023,
                2.5612819054028872e-06,
                0.9999980052695662,
                0.9999983463108092,
                0.9999996743688199,
                0.9999997300421904,
                0.9999999530883509,
                6.144176066850984e-06,
                2.260324836787226e-06,
                2.9023119851635836e-06
            ],
            [
                3.0590237279032884e-07,
                5.715002426460124e-07,
                8.315282259089153e-07,
                6.475951069961737e-07,
                2.69957906184239e-07,
                3.9278634073625165e-07,
                3.2887490652810324e-06,
                4.450849988798682e-07,
                2.699578096393206e-07,
                7.338211554725124e-07
            ],
            [
                3.466327450756327e-07,
                6.475947981975644e-07,
                7.338207180801359e-07,
                7.338213304316717e-07,
                1.6373762769138607e-07,
                8.315278294001114e-07,
                3.927860597945825e-07,
                2.6995771309523475e-07,
                8.315284241650899e-07,
                4.450851580540182e-07
            ],
            [
                6.475948753965404e-07,
                0.9999964991451707,
                5.04347468323289e-07,
                1.7603425837903113e-06,
                7.338207180838067e-07,
                2.1024331597152624e-07,
                2.9023112932177327e-06,
                6.47594566597747e-07,
                3.059022998569248e-07,
                1.0677029973158649e-06
            ],
            [
                1.125352291309328e-07,
                3.0590215399183813e-07,
                1.275190580884987e-07,
                3.0590237279032884e-07,
                1.6373764721039308e-07,
                5.043473480766399e-07,
                5.043472879540142e-07,
                5.043476486902204e-07,
                3.4663253846718004e-07,
                3.466327450765785e-07
            ],
            [
                1.6373776432481905e-07,
                4.450852641717689e-07,
                1.8553907971855875e-07,
                2.9023109472244114e-06,
                0.9999989969861515,
                1.0677033791583005e-06,
                2.2603242978778778e-06,
                1.3709567165579959e-06,
                0.9999978766205265,
                8.31527928532683e-07
            ],
            [
                0.9999982396569975,
                0.9999546021478132,
                3.059023363231725e-07,
                0.9999992188518558,
                2.2603234895289998e-06,
                2.382369667929001e-07,
                0.9999989969859123,
                1.2751905808881762e-07,
                0.9999960330150337,
                0.9999992188513902
            ],
            [
                1.4449800373065699e-07,
                2.382368815916736e-07,
                3.288748281329893e-06,
                1.2098653950656417e-06,
                4.450852111148132e-07,
                3.4663249714451116e-07,
                1.067703379154416e-06,
                9.422445939032799e-07,
                1.4449798650551755e-07,
                1.3709572068422585e-06
            ],
            [
                0.9999983463100206,
                0.9999995549147891,
                0.9999989322975124,
                0.9999964991455893,
                0.9999993916408184,
                0.9999996072136126,
                0.9999970976890553,
                0.99999911484307,
                0.9999892166839398,
                0.9999981261248406
            ],
            [
                1.0677024882009222e-06,
                4.785095635592258e-06,
                3.059021175247079e-07,
                1.9947301970587145e-06,
                2.699578096399958e-07,
                1.147876675548402e-05,
                1.9947306725451314e-06,
                2.260325375664839e-06,
                1.2098661162023305e-06,
                1.5534975693869924e-06
            ],
            [
                5.715006514167015e-07,
                0.9999997126314126,
                3.05902263389638e-07,
                0.9999997463981637,
                0.9999998874648112,
                3.726638839878908e-06,
                6.144173869502757e-06,
                4.450849988811838e-07,
                1.2098661161982042e-06,
                5.043476486915964e-07
            ],
            [
                7.889263526180094e-06,
                3.0590215399183813e-07,
                8.939700567004841e-06,
                1.0677029973192638e-06,
                1.0677026154730804e-06,
                0.9999975938982352,
                0.9999960330126689,
                2.9023133690980155e-06,
                0.9999930377454167,
                1.7603425837702984e-06
            ],
            [
                0.9999861539905098,
                0.9999151889397297,
                4.222835458117536e-06,
                0.9999916019239695,
                0.9999960330150338,
                0.9999970976883642,
                0.9999921107355408,
                0.9999964991468407,
                0.9999898700126572,
                0.9999945777816798
            ],
            [
                0.9999993106391191,
                0.9999993524049704,
                0.9999996940978825,
                1.8553916819032217e-07,
                0.9999785550516243,
                0.9999999273418442,
                2.1024331597262577e-07,
                0.9999985406243014,
                2.6995787400282076e-07,
                4.450852641717689e-07
            ],
            [
                0.9999981261248405,
                2.260324028404236e-06,
                1.2098652508391807e-06,
                0.00013982204085104992,
                2.1024336609843824e-07,
                4.450849988798682e-07,
                2.561281905376098e-06,
                1.4738976700661033e-05,
                3.288748281295496e-06,
                4.450850519403407e-07
            ],
            [
                2.5612825160562587e-06,
                2.5612812947380135e-06,
                0.9999982396561582,
                0.9999978766212864,
                0.9999998461827322,
                2.1444948412137308e-05,
                1.553497754583709e-06,
                0.9999994956526521,
                1.3007126913346863e-05,
                0.9999756997564273
            ],
            [
                0.9999985406234316,
                6.475951069961737e-07,
                3.7266383955882547e-06,
                3.4663266243111764e-07,
                9.422447062294175e-07,
                7.338213304283347e-07,
                0.9999955048162814,
                0.9999969105055534,
                2.382370235922541e-07,
                0.9999977396751644
            ],
            [
                3.2887490653109436e-06,
                3.7266401721817755e-06,
                6.1441724044534996e-06,
                5.422218323399208e-06,
                1.2098662604192665e-06,
                2.2603245672025095e-06,
                1.8925145982866508e-05,
                4.7850939242083995e-06,
                9.422448185435711e-07,
                1.994729959224386e-06
            ],
            [
                2.3823688159237777e-07,
                2.3823682479181176e-07,
                1.8553905760024476e-07,
                3.466327037553825e-07,
                2.699576809143613e-07,
                1.6373774480605869e-07,
                2.699578740032504e-07,
                1.8553919030776337e-07,
                5.715004470326849e-07,
                1.4449798650551755e-07
            ],
            [
                0.9999982396563682,
                1.637376862489725e-07,
                7.338210680002898e-07,
                0.9999997300421261,
                0.9999985406236057,
                3.059021175247079e-07,
                0.9999967112521129,
                0.9998766054261466,
                0.9999910603005165,
                2.3823702359290413e-07
            ],
            [
                4.785094494628999e-06,
                1.5534984953510149e-06,
                1.670141587141357e-05,
                0.9999993524052792,
                0.9999038976212503,
                0.999997739675434,
                2.902311293147782e-06,
                8.939700566289352e-06,
                0.9999977396754345,
                6.962257909323729e-06
            ],
            [
                1.9947297215125433e-06,
                8.315281267800897e-07,
                4.450851580540182e-07,
                1.370956716529941e-06,
                7.338208055536515e-07,
                4.450851580540182e-07,
                4.785095635592258e-06,
                1.2098655392811161e-06,
                4.450851580540182e-07,
                1.012999581021488e-05
            ],
            [
                3.927862939113312e-07,
                7.73441946488886e-08,
                2.3823682479181176e-07,
                3.4663266243111764e-07,
                1.1253510839355284e-07,
                6.475947210031623e-07,
                4.450849458200093e-07,
                2.382369951932796e-07,
                3.4663249714325014e-07,
                5.715004470272272e-07
            ],
            [
                2.6995784182140636e-07,
                1.6373776432509826e-07,
                3.7266401725681614e-06,
                0.9999869928684451,
                0.9999687980850205,
                0.9999955048184253,
                3.466326211113502e-07,
                3.288749457409966e-06,
                0.9999969105040807,
                0.9999852610127797
            ],
            [
                3.4663249714612693e-07,
                5.715005832886879e-07,
                3.9278605979534166e-07,
                2.1024331597262577e-07,
                1.6373772528704005e-07,
                8.315282259089153e-07,
                6.475950298011458e-07,
                2.6995771309523475e-07,
                5.043473480777865e-07,
                4.450848927650143e-07
            ],
            [
                6.475946438022905e-07,
                0.999998863436019,
                2.6995768091310296e-07,
                0.9999952149066499,
                7.338213304316717e-07,
                4.450849988798682e-07,
                3.9278634073625165e-07,
                0.9999898700102432,
                0.9999997617630049,
                0.9999977396757038
            ],
            [
                0.9999993524052021,
                4.222834954687752e-06,
                1.7603434231097403e-06,
                8.315280276607289e-07,
                0.9999687980998635,
                0.9999945777790956,
                3.2887494574518405e-06,
                0.9999972735284307,
                0.9999989969857926,
                1.1478772230762415e-05
            ],
            [
                0.9999999273417662,
                0.999995214907219,
                1.370957860576702e-06,
                0.999995504820034,
                8.315284241650899e-07,
                0.9999998362623332,
                0.9999996940977732,
                0.9999998461827322,
                2.5612816000646084e-06,
                0.9999995549147891
            ],
            [
                0.9999832985722319,
                0.9999989969862708,
                0.9999997463982241,
                7.338212429562581e-07,
                0.999996910505187,
                0.9999898700066143,
                3.12019002122609e-05,
                0.9999885212264098,
                0.9999910603026411,
                0.9999339478561958
            ],
            [
                3.05902263389638e-07,
                2.561281905376098e-06,
                1.2098661162023305e-06,
                6.96225956921868e-06,
                1.2098652508391807e-06,
                3.0590222692437275e-07,
                2.561282210701601e-06,
                2.6995777745711594e-07,
                3.466327450756327e-07,
                1.2098662604291696e-06
            ],
            [
                4.450848927650143e-07,
                5.715007195410849e-07,
                2.382369667929001e-07,
                0.9999985406234317,
                2.3823696679230424e-07,
                0.9999984465024314,
                2.382368247924618e-07,
                2.382369667914917e-07,
                1.6373762769138607e-07,
                0.9999785550414078
            ],
            [
                5.422218969720291e-06,
                5.715003788993679e-07,
                1.994729721482609e-06,
                6.475951069932288e-07,
                3.9278634073098236e-07,
                8.315277302747361e-07,
                3.9278634072866033e-07,
                1.3709572068272963e-06,
                7.889264466725156e-06,
                2.2603248367656408e-06
            ],
            [
                0.9999942280806658,
                4.785096205930373e-06,
                3.0590237279032884e-07,
                0.9999916019289823,
                2.5612825160271407e-06,
                7.889260704732132e-06,
                7.889265406904397e-06,
                2.9023116391978967e-06,
                1.2098652508347793e-06,
                3.7266392839832006e-06
            ],
            [
                0.9999994631250603,
                3.466325797888292e-07,
                3.466325797888292e-07,
                7.338213304283347e-07,
                0.9999970976873245,
                3.466327037539638e-07,
                1.2098656835076114e-06,
                3.059023727894942e-07,
                5.043472879540142e-07,
                0.9999885212264218
            ],
            [
                6.962254589978262e-06,
                3.059022269250683e-07,
                4.785096776303374e-06,
                1.0129987357517693e-05,
                7.889260704968913e-06,
                6.962255419931625e-06,
                6.962257909842961e-06,
                3.288747889284851e-06,
                4.22283545819819e-06,
                3.059023727894942e-07
            ],
            [
                2.9023130231176453e-06,
                2.6995774527657245e-07,
                4.78509392429544e-06,
                4.450850519403407e-07,
                1.0677032518700286e-06,
                1.5534971990126997e-06,
                4.222833947897496e-06,
                3.7266388396128453e-06,
                7.338207180838067e-07,
                3.2887486733420804e-06
            ],
            [
                3.288750241500471e-06,
                8.939695238439078e-06,
                6.144176066672166e-06,
                7.338208930421943e-07,
                6.144177531811707e-06,
                6.9622579095833456e-06,
                7.338210680002898e-07,
                6.962257909785973e-06,
                3.288750633545794e-06,
                6.9622537599680095e-06
            ],
            [
                5.043475885657239e-07,
                2.260324028427877e-06,
                6.475948753991907e-07,
                9.422448185435711e-07,
                5.043473480730849e-07,
                5.715006514105942e-07,
                8.315282259089153e-07,
                7.3382080556433e-07,
                5.715006514105942e-07,
                1.5534979397592542e-06
            ],
            [
                0.9999988634358834,
                0.9999987901346056,
                0.9999978766210325,
                2.3823702359290413e-07,
                0.9999967112497602,
                0.999997097688017,
                0.9999982396574175,
                0.9999998144608099,
                0.9999962733589428,
                3.4663249714451116e-07
            ]
        ]
    },
    {
        "q_id": "9527_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            97,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                9.931186222523604e-08,
                3.466327450765785e-07,
                1.3709572068553509e-06,
                3.9278620026686556e-07,
                4.4508494582405734e-07,
                1.4449796928021588e-07,
                3.059022269254856e-07,
                1.4449796928021588e-07,
                5.043474683240344e-07,
                6.47595107001401e-07
            ],
            [
                0.9999988634360193,
                0.9999995262093859,
                0.999999712631447,
                0.9999997300423193,
                1.0,
                0.9999997300423193,
                0.9999997300422551,
                0.9999997617629766,
                0.9999992188514847,
                0.999998863436292
            ],
            [
                8.7642516304188e-08,
                6.825597214691097e-08,
                1.27519088491875e-07,
                1.8553907971855875e-07,
                1.4449795205429202e-07,
                2.1024336609843824e-07,
                1.1253516205489029e-07,
                1.8553903548231313e-07,
                3.466326624336003e-07,
                9.931190958076104e-08
            ],
            [
                0.9999982396570003,
                0.9999986290432861,
                0.9999989969862721,
                0.9999969105044567,
                0.999998932296877,
                0.9999992188515772,
                0.999998790134174,
                0.9999993106387919,
                0.9999990577551832,
                1.3709567165617364e-06
            ],
            [
                0.9999992188517628,
                0.9999989969855534,
                0.9999997761971317,
                0.9999989969861515,
                0.9999989969855538,
                0.9999986290432845,
                0.9999996940977732,
                0.9999987121049387,
                0.99999967436882,
                0.9999997761970782
            ],
            [
                6.144173137126169e-06,
                8.315279285351409e-07,
                8.315281267834927e-07,
                2.430024073333442e-05,
                1.7603440527222532e-06,
                4.222832941142044e-06,
                1.0677032518785256e-06,
                9.422444815792981e-07,
                4.450851580555361e-07,
                4.222834954778007e-06
            ],
            [
                5.04347468323289e-07,
                7.33821330437595e-07,
                3.4663274507713016e-07,
                1.994730672668496e-06,
                2.382370235933104e-07,
                2.699577774585891e-07,
                2.1024336609843824e-07,
                5.715005832895975e-07,
                1.3709567165617364e-06,
                2.3823690999323465e-07
            ],
            [
                0.9999972735300623,
                0.9999972735290871,
                0.999998863435749,
                2.561283432035425e-06,
                0.9999980052693495,
                0.9999957771650536,
                1.5534983101478522e-06,
                0.9999978766207834,
                0.9999992188515777,
                0.9999964991447732
            ],
            [
                0.9999993916411817,
                0.9999994631248686,
                0.9999996310115042,
                0.9999988634358844,
                0.9999988634364264,
                0.9999985406232589,
                0.9999994631249969,
                0.9999996310114603,
                0.9999987901338858,
                0.999998629042796
            ],
            [
                2.10243290909963e-07,
                2.382368815932174e-07,
                0.9999994956526523,
                2.699578740032504e-07,
                3.466326624336003e-07,
                6.47594952603035e-07,
                1.0677026154827912e-06,
                1.855390576008354e-07,
                1.4449802095666915e-07,
                5.043475885696228e-07
            ],
            [
                6.962255419931625e-06,
                7.88926070489716e-06,
                8.315277302788957e-07,
                3.288749457469787e-06,
                5.422220909009474e-06,
                6.1441746020359e-06,
                2.5612834320470717e-06,
                6.144173869603344e-06,
                7.889260704818233e-06,
                3.726639728370556e-06
            ],
            [
                0.9999986290421413,
                0.9999980052702806,
                0.9999985406243039,
                0.9999991684718745,
                0.9999987901337412,
                5.043476486915964e-07,
                0.9999991148430707,
                3.4663249714612693e-07,
                0.9999938558261559,
                0.9999986290426308
            ],
            [
                0.9999983463106122,
                0.9999989322972577,
                0.9999982396563679,
                0.9999985406243022,
                0.9999983463110069,
                0.9999981261250666,
                0.9999984465026165,
                0.9999980052702807,
                0.9999991684720719,
                0.9999972735303816
            ],
            [
                8.315283250394546e-07,
                6.475950298011458e-07,
                9.422444815814404e-07,
                8.315278294114555e-07,
                2.5612834320563895e-06,
                1.1253520230052635e-07,
                1.9947301970972664e-06,
                1.0677024882009222e-06,
                1.3709576971463352e-06,
                8.315278294114555e-07
            ],
            [
                0.9999997761970248,
                0.9999996743688201,
                0.999999746398194,
                0.999999352405048,
                1.2751905808881762e-07,
                1.8553910183674878e-07,
                0.9999998024945626,
                0.9999993524051253,
                0.9999997463981334,
                0.9999993916407461
            ],
            [
                2.1024336609874897e-07,
                2.1024334103581732e-07,
                1.1253513522447425e-07,
                2.3823696679327928e-07,
                9.931187406410953e-08,
                2.3823685319244518e-07,
                8.764241182641775e-08,
                1.27519088491875e-07,
                6.825602910433871e-08,
                1.4449802095666915e-07
            ],
            [
                2.561282821402217e-06,
                2.9023116392097746e-06,
                1.5534971990169383e-06,
                7.889261645427538e-06,
                8.315280276626197e-07,
                2.561283126728994e-06,
                2.2603234895372223e-06,
                3.72663883989755e-06,
                1.5534973842076057e-06,
                9.422445939054222e-07
            ],
            [
                0.9999964991468474,
                0.9999991148429654,
                1.9947292459347367e-06,
                3.7266401725935817e-06,
                0.9999992188513912,
                0.9999974387177942,
                0.9999987901338853,
                6.475946437996402e-07,
                0.00026119027880236077,
                1.1478764020727177e-05
            ],
            [
                0.9999993916409637,
                0.9999997300421904,
                0.9999992661786702,
                0.9999998642567351,
                0.9999998802069302,
                0.9999987901338849,
                0.9999998555020481,
                0.9999995818814268,
                0.9999994284992809,
                0.9999995549147362
            ],
            [
                1.8925155009767892e-05,
                3.535624650021832e-05,
                1.7603440527222532e-06,
                1.7603427936183298e-06,
                1.0677026154730804e-06,
                1.7603436330179102e-06,
                1.0677032518748838e-06,
                1.760343003481596e-06,
                3.726639728370556e-06,
                1.2098662604291696e-06
            ],
            [
                1.994730434879465e-06,
                5.829127250060064e-05,
                1.3709570434178922e-06,
                5.715004470313855e-07,
                1.8925143729954285e-05,
                6.14417753171671e-06,
                5.422219616265831e-06,
                5.715003107767143e-07,
                2.5612828213690224e-06,
                4.2228334445370225e-06
            ],
            [
                9.422444815792981e-07,
                1.3007123813382511e-05,
                5.715006514151423e-07,
                2.5612825160562587e-06,
                4.222832437798974e-06,
                1.067703124601679e-06,
                5.715006514151423e-07,
                7.338209805200689e-07,
                1.067703124601679e-06,
                8.31528424146183e-07
            ],
            [
                6.475947210031623e-07,
                6.475947982037486e-07,
                7.338207180898968e-07,
                1.7603438428800754e-06,
                1.5534975693979422e-06,
                2.699576809143613e-07,
                4.450850519403407e-07,
                7.338210680021253e-07,
                8.315281267861397e-07,
                7.338212429562581e-07
            ],
            [
                2.6995768091310296e-07,
                3.05902117523595e-07,
                3.9278634073732336e-07,
                9.931187406368048e-08,
                3.059021904571643e-07,
                2.1024336609638268e-07,
                3.0590222692437275e-07,
                4.450852641717689e-07,
                2.3823685319174098e-07,
                3.466327037512053e-07
            ],
            [
                6.825598028392069e-08,
                1.275190580890061e-07,
                9.931202796993203e-08,
                1.7603434231833873e-06,
                5.715006514176113e-07,
                1.4449798650569826e-07,
                1.1253525596174225e-07,
                1.275190124846946e-07,
                1.9947292459406333e-06,
                2.3823685319320354e-07
            ],
            [
                2.561282516042282e-06,
                5.04347287955046e-07,
                3.7266383955882547e-06,
                1.6373774480605869e-07,
                1.7603438428800754e-06,
                2.902313369111213e-06,
                6.144175334468545e-06,
                1.3007125363908762e-05,
                4.539788488687281e-05,
                2.902312677137316e-06
            ],
            [
                0.9999964991451721,
                0.9999981261246187,
                0.9999921107383887,
                0.9999970976866337,
                3.288749065423109e-06,
                0.999999168472073,
                0.9999952149038003,
                0.9999989322970035,
                0.9999984465028031,
                0.9999990577552943
            ],
            [
                2.5612831267202583e-06,
                8.315281267882195e-07,
                4.2228339479858295e-06,
                1.0129993395336818e-05,
                1.209865539295696e-06,
                1.5534981249697903e-06,
                2.2603251062450327e-06,
                3.72663883989755e-06,
                1.0677026154806063e-06,
                3.927862002663297e-07
            ],
            [
                1.6373764721072816e-07,
                2.1024341622426268e-07,
                1.7603438428848787e-06,
                1.1253524254650944e-07,
                6.962258739796719e-06,
                5.422217030781934e-06,
                7.734425919002834e-08,
                2.6995771309523475e-07,
                3.05902263391829e-07,
                3.7266379514061143e-06
            ],
            [
                0.9999982396572079,
                0.9999993524050478,
                0.9999986290432848,
                0.9999986290426305,
                4.222832941193893e-06,
                5.043473480766399e-07,
                1.2751901248454963e-07,
                0.9999987901344618,
                0.9999994956527725,
                5.043472879540142e-07
            ],
            [
                0.9999984465016911,
                1.1478772231086046e-05,
                0.9999996743686257,
                0.999997739675435,
                6.605215257630029e-05,
                6.962259569750576e-06,
                0.9999989322975126,
                0.9999983463104162,
                0.9999993524050481,
                0.999999168472171
            ],
            [
                1.444980209564556e-07,
                9.422450431989127e-07,
                3.0590237279032884e-07,
                1.8553905760024476e-07,
                9.93120161310289e-08,
                1.275190580890061e-07,
                1.2751899728286965e-07,
                2.3823690999160957e-07,
                1.855391239539711e-07,
                5.715003789046955e-07
            ],
            [
                1.637377057680051e-07,
                1.4449805540740185e-07,
                5.715003107767143e-07,
                0.9999991684721712,
                0.9999994284996218,
                4.450852111155216e-07,
                3.5356238073889594e-05,
                4.450848927658745e-07,
                5.715005832895975e-07,
                4.450852641737424e-07
            ],
            [
                4.139940014976854e-08,
                1.1861128494392035e-08,
                1.2751907328949007e-07,
                1.275190580884987e-07,
                1.1253506814797596e-07,
                2.845334728018925e-08,
                6.023578501513224e-08,
                1.1253512180925583e-07,
                3.224187402001668e-08,
                2.215950777364157e-08
            ],
            [
                0.9999994284996899,
                0.9999992661788453,
                0.9999996533673795,
                0.9999993524053566,
                1.3709572068522336e-06,
                0.999999428499758,
                1.209865827752005e-06,
                0.999999114843176,
                0.9999993916409639,
                0.9999992188519494
            ],
            [
                0.9999992188516699,
                0.9999992661787576,
                0.9999994956526523,
                0.9999995818813767,
                0.9999993524051248,
                0.9999996310115039,
                0.9999996743687811,
                0.9999993524050477,
                0.9999992661791951,
                0.9999989969855543
            ],
            [
                0.9999985406234352,
                0.9999993524049711,
                0.9999987901340305,
                0.9999990577556325,
                0.9999983463102192,
                0.9999993524050484,
                0.9999974387184072,
                5.422220262636381e-06,
                0.9999982396572121,
                0.9999970976883716
            ],
            [
                3.2887502415767434e-06,
                1.5534977545886537e-06,
                1.7603438428800754e-06,
                3.2887506336235617e-06,
                3.726638839878908e-06,
                3.288750241561788e-06,
                1.9947301970972664e-06,
                2.902312331170226e-06,
                4.222834451382849e-06,
                1.994730197090463e-06
            ],
            [
                3.7266401726359486e-06,
                5.715007195447234e-07,
                1.2098658277451275e-06,
                6.144176799334096e-06,
                5.043472879540142e-07,
                8.939700567094277e-06,
                1.8925150497848527e-05,
                1.3709568799919866e-06,
                1.0129988564974359e-05,
                8.939698435657833e-06
            ],
            [
                2.1024334103581732e-07,
                0.9999997897566841,
                0.9999997897566841,
                0.9999996072137066,
                0.9999998362622553,
                1.4449807263312446e-07,
                0.9999996310115481,
                8.764245361752286e-08,
                0.9999989322968774,
                0.9999994284996898
            ],
            [
                6.962257909722651e-06,
                2.430024652792821e-05,
                1.7603434231777837e-06,
                3.9278634073732336e-07,
                6.144173869502757e-06,
                4.2228334445658276e-06,
                2.902312677137316e-06,
                2.5612812947508257e-06,
                0.00023050679794415073,
                2.9023109472244114e-06
            ],
            [
                0.9999989969861519,
                0.9999993106390379,
                0.9999989322968768,
                0.9999986290432858,
                0.999999581881377,
                0.9999992661788452,
                0.9999989969857936,
                0.9999992661791951,
                0.999999266178758,
                0.9999994956524118
            ],
            [
                1.6373770576776313e-07,
                1.5534981249736758e-06,
                1.2751901248454963e-07,
                1.0677033791583005e-06,
                2.561281294760143e-06,
                8.315282259117513e-07,
                1.6373770576776313e-07,
                7.734425918979532e-08,
                4.691161005609407e-08,
                7.734414854823498e-08
            ],
            [
                0.9999988634361575,
                0.9999977396757079,
                0.9999972735284425,
                0.9999989322968773,
                0.9999989322975145,
                0.9999994631250604,
                0.9999980052698083,
                7.338208930460318e-07,
                0.9999991148433877,
                0.9999983463108106
            ],
            [
                0.9999991684716756,
                0.9999955048184265,
                0.9999978766210332,
                0.9999964991451754,
                0.005911067515464108,
                1.8925141473599938e-05,
                1.4738989000422955e-05,
                0.9999981261243962,
                0.9999995262096117,
                0.999999428499485
            ],
            [
                2.1024336609843824e-07,
                5.043472879525233e-07,
                2.699577774585891e-07,
                8.315277302857965e-07,
                2.2603253756956754e-06,
                1.6373776432509826e-07,
                1.1253518888531272e-07,
                7.73442776303243e-08,
                1.6373766672973748e-07,
                3.466327863983311e-07
            ],
            [
                1.4449800373098553e-07,
                1.1253512180925583e-07,
                9.422445939032799e-07,
                4.4508510499849186e-07,
                5.715005832872586e-07,
                6.825608606172863e-08,
                3.05902336324494e-07,
                3.9278629391427843e-07,
                6.475950298011458e-07,
                9.931202796993203e-08
            ],
            [
                1.760343633031919e-06,
                3.288748281329893e-06,
                0.0001233946191424094,
                3.7266410611296085e-06,
                5.715005832886879e-07,
                1.5534984953552536e-06,
                1.275190276859705e-07,
                0.0001584362925687936,
                3.927863407379485e-07,
                3.927862470899887e-07
            ],
            [
                2.6995784182140636e-07,
                8.315282259138311e-07,
                6.47595107001401e-07,
                3.059022998581767e-07,
                2.6995774527718623e-07,
                4.450851580566494e-07,
                1.2098656835224664e-06,
                0.999998932297005,
                1.0677033791612137e-06,
                1.1478772231086046e-05
            ],
            [
                1.637376862489725e-07,
                2.3823702359290413e-07,
                9.422443692555439e-07,
                9.931202796993203e-08,
                9.422447062240614e-07,
                1.2098661162023305e-06,
                1.4738978457041559e-05,
                3.4663253846718004e-07,
                1.4449796928021588e-07,
                1.760343213335281e-06
            ],
            [
                0.9999993916409637,
                9.931186222523604e-08,
                9.931202796957073e-08,
                1.4449802095609418e-07,
                9.931187406410953e-08,
                7.73441946488886e-08,
                1.6373764721072816e-07,
                7.734415776836702e-08,
                4.139935079796334e-08,
                1.2751901248454963e-07
            ],
            [
                4.785094494783494e-06,
                2.5612828213934817e-06,
                1.3007133116732079e-05,
                1.0129993395336818e-05,
                2.260325106237323e-06,
                3.2887506336086064e-06,
                1.1478764021029928e-05,
                8.939698435560267e-06,
                1.1478768125911099e-05,
                1.5534984953453635e-06
            ],
            [
                0.9999989969861516,
                0.9999984465018764,
                2.3823690999323465e-07,
                0.9999987901338842,
                0.9999993524051249,
                0.9999994284997576,
                0.9999989969856733,
                0.9999992188519493,
                0.9999993916406735,
                0.9999998642566219
            ],
            [
                2.10243290909724e-07,
                4.6911638017556955e-08,
                1.6373770576776313e-07,
                9.931187406410953e-08,
                5.3157887739943563e-08,
                1.4449798650569826e-07,
                3.059021175261338e-07,
                1.4449798650551755e-07,
                1.444979692797559e-07,
                6.023574911170301e-08
            ],
            [
                0.9999993106389553,
                3.4663274507713016e-07,
                5.043475885696228e-07,
                5.715006514176113e-07,
                1.7603425837903113e-06,
                0.999999218851577,
                0.9999982396565792,
                7.338208930460318e-07,
                1.1253526937697666e-07,
                1.5534984953552536e-06
            ],
            [
                0.9999972735303877,
                0.9999990577551825,
                0.9999983463096265,
                0.9999987901344632,
                0.9999982396567899,
                0.9999985406241285,
                0.9999987121047886,
                0.9999969105040896,
                0.9999981261243952,
                0.9999989969855545
            ],
            [
                0.9999983463100214,
                0.9999981261248424,
                0.9999984465015096,
                0.9999988634362913,
                0.9999989969859141,
                0.9999987901337424,
                0.9999992661792829,
                0.999998346310812,
                0.9999972735290849,
                0.9999987901341737
            ],
            [
                0.9999938558239656,
                0.9999988634364263,
                3.466326624336003e-07,
                0.010986940545880577,
                0.9998911030869344,
                0.9999988634360206,
                3.120190765625026e-05,
                5.043475885696228e-07,
                2.7535704231844484e-05,
                NaN
            ],
            [
                5.715002426486762e-07,
                5.04347287955046e-07,
                1.8553903548231313e-07,
                2.3823696679230424e-07,
                1.1253525596174225e-07,
                1.855391239544352e-07,
                4.450852641737424e-07,
                3.0590226339137693e-07,
                3.46632497145457e-07,
                6.825604537781398e-08
            ],
            [
                0.9999997463980127,
                0.9999997300421585,
                0.9999994956527126,
                0.9999996940977368,
                0.9999995549150017,
                0.9999996072136598,
                0.9999995818811277,
                0.9999996940976641,
                0.9999995818811778,
                0.9999995262093297
            ],
            [
                1.7603425837903113e-06,
                8.315278294114555e-07,
                0.9999990577557436,
                0.9999991148428594,
                0.9999980052707553,
                0.9999993524051248,
                0.9999985406232584,
                2.9023112932296107e-06,
                0.9999992188515769,
                0.9999993106387907
            ],
            [
                3.059022998576899e-07,
                8.315277302788957e-07,
                1.2098661162056318e-06,
                2.3823696679327928e-07,
                2.1024341622426268e-07,
                3.0590237279085045e-07,
                1.855391681906175e-07,
                1.6373762769138607e-07,
                3.466325797896173e-07,
                1.2098653950656417e-06
            ],
            [
                4.450850519403407e-07,
                0.9999991684719731,
                0.999999168471775,
                0.9999998024947273,
                1.3709575337159875e-06,
                0.9999997300423192,
                3.059021175261338e-07,
                0.9999980052695667,
                0.9999995262092731,
                0.9999997761970782
            ],
            [
                0.9999974387187107,
                0.9999994284997575,
                0.9999993106390379,
                0.9999993916408917,
                0.9999974387184041,
                0.9999989322967494,
                0.9999993106392018,
                0.999999266178933,
                0.9999994956524116,
                0.9999986290432865
            ],
            [
                0.9999994284995534,
                0.9999989969862713,
                0.9999978766222997,
                0.9999977396754391,
                0.9999987121046318,
                0.999999789756659,
                0.9999985406241282,
                0.9999992188512974,
                1.5534971990126997e-06,
                0.9999989969855537
            ],
            [
                0.9999991148430702,
                0.9999994631249969,
                2.561281600086738e-06,
                0.9999995818812774,
                0.9999981261237251,
                0.9999991148430705,
                0.999999495652412,
                2.2603234895372223e-06,
                0.9999992661789332,
                0.999998346309628
            ],
            [
                0.99999911484307,
                0.9999983463104154,
                0.9999987901344618,
                0.9999991684715762,
                0.9999991148432811,
                0.9999994631251883,
                0.9999989969854346,
                0.9999987901337407,
                0.9999991684715761,
                0.999999168472171
            ],
            [
                0.9999984465022503,
                8.764242227418718e-08,
                4.222832941142044e-06,
                3.466325384678894e-07,
                0.9999993916407461,
                2.3823688159291947e-07,
                5.715003789046955e-07,
                8.315278294114555e-07,
                5.043476486924565e-07,
                0.9999986290423053
            ],
            [
                1.6701421845361053e-05,
                0.9999995262093292,
                1.3007134667436886e-05,
                0.9999986290429574,
                0.9999949062931875,
                0.9999995262092167,
                0.9999997463980124,
                0.9999983463100224,
                0.9999964991464237,
                0.9999985406237812
            ],
            [
                8.764254764780641e-08,
                2.1024334103581732e-07,
                3.7266410611296085e-06,
                2.3823690999290963e-07,
                1.6373772528704005e-07,
                3.9278634073732336e-07,
                2.9023119851899796e-06,
                1.4449805540740185e-07,
                1.27519088491875e-07,
                8.93969950132721e-06
            ],
            [
                5.715002426486762e-07,
                5.043473480777865e-07,
                1.0677024882009222e-06,
                1.6701415872385704e-05,
                3.059022269250683e-07,
                2.102434162245973e-07,
                5.04347287955046e-07,
                2.1444950971601277e-05,
                5.04347287955046e-07,
                0.999997438717796
            ],
            [
                0.9999993916407459,
                0.9999998024946095,
                0.9999989322972578,
                0.9999982396563679,
                0.9999985406232578,
                0.9999980052700426,
                0.9999993106392014,
                0.9999995262094987,
                0.9999992188515766,
                0.9999974387187072
            ],
            [
                6.962257909722651e-06,
                0.9999977396757042,
                8.315282259051341e-07,
                0.9999925887201432,
                4.785096206076165e-06,
                4.222832941142044e-06,
                8.315282259117513e-07,
                2.2603234895053587e-06,
                2.3823690999323465e-07,
                2.382369951932796e-07
            ],
            [
                2.2603251062450327e-06,
                0.9999993916411813,
                1.994729483729522e-06,
                2.902312677150514e-06,
                2.260324028443809e-06,
                5.71500719545698e-07,
                1.2098653950716937e-06,
                6.962259569750576e-06,
                9.422444815814404e-07,
                0.999999581881078
            ],
            [
                5.715002426486762e-07,
                1.0677028700422047e-06,
                8.315277302857965e-07,
                3.05902263391829e-07,
                7.338209805240734e-07,
                6.144175334468545e-06,
                5.71500719545698e-07,
                1.0677032518814388e-06,
                1.9947292459347367e-06,
                4.4508515805735777e-07
            ],
            [
                0.9999988634357516,
                0.9999983463096292,
                0.99999931063912,
                0.9999993524049712,
                0.9999983463108123,
                0.9999986290424687,
                0.9999984465018767,
                0.9999983463098248,
                6.475950298011458e-07,
                2.699578096393206e-07
            ],
            [
                4.222834451382849e-06,
                5.043476486915964e-07,
                1.2098655392921197e-06,
                4.450850519403407e-07,
                7.88926070489716e-06,
                6.475947210031623e-07,
                1.370957860576702e-06,
                1.760343633031919e-06,
                1.0677033791612137e-06,
                3.288749457469787e-06
            ],
            [
                3.059021175261338e-07,
                2.260324836776948e-06,
                4.450848927650143e-07,
                8.764241182641775e-08,
                5.715005151574337e-07,
                1.855391681906175e-07,
                0.9999982396559481,
                2.102434412875379e-07,
                7.734418542875216e-08,
                6.475951070002966e-07
            ],
            [
                0.00048785712210106994,
                0.9999981261246192,
                0.9999992188514847,
                2.9023133690637e-06,
                0.00010889696125141565,
                0.9999983463096304,
                2.902310947208574e-06,
                2.9023116391978967e-06,
                6.605215255419451e-05,
                1.994729245917502e-06
            ],
            [
                6.825598028392069e-08,
                3.059021175261338e-07,
                1.855391239547094e-07,
                9.931195693628605e-08,
                9.931187406410953e-08,
                1.1253526937697666e-07,
                1.637376862489725e-07,
                1.1253512180925583e-07,
                1.8553910183674878e-07,
                3.059022998576899e-07
            ],
            [
                0.999999057755744,
                0.9999974387171808,
                0.999984310448437,
                0.9999994284995533,
                0.9999996940978096,
                0.9999998942829477,
                0.9999996940978096,
                0.9999997463981938,
                0.9999996533672139,
                0.9999996310114599
            ],
            [
                1.9947299592933255e-06,
                5.71500515161527e-07,
                4.450848927658745e-07,
                1.3709570434219446e-06,
                3.0590233632400716e-07,
                2.699576809143613e-07,
                1.2751901248454963e-07,
                2.1024334103581732e-07,
                8.315278294114555e-07,
                3.2887494574518405e-06
            ],
            [
                3.4663278639265633e-07,
                5.043472879525233e-07,
                3.466325797888292e-07,
                2.102433410343832e-07,
                5.043472879525233e-07,
                7.338209805224048e-07,
                5.715005832886879e-07,
                3.9278634073625165e-07,
                3.4663249714612693e-07,
                3.466325797888292e-07
            ],
            [
                0.9999997617630334,
                0.9999994956525923,
                0.9999994956527727,
                0.9999993916408187,
                0.9999995818811773,
                0.9999995818810778,
                0.9999993916411812,
                0.9999997463980125,
                0.9999996940978827,
                0.9999989969861516
            ],
            [
                1.0677024882009222e-06,
                1.6373766672973748e-07,
                1.855391239544352e-07,
                8.315284241650899e-07,
                1.637376862489725e-07,
                2.699576809143613e-07,
                6.475947982037486e-07,
                1.760342793638743e-06,
                6.825602910433871e-08,
                7.338209805240734e-07
            ],
            [
                6.475946438055299e-07,
                3.059021175261338e-07,
                4.4508515805735777e-07,
                2.102434412875379e-07,
                3.4663262111182307e-07,
                2.102434412875379e-07,
                3.466326624336003e-07,
                1.2098659719788098e-06,
                1.067703124601679e-06,
                2.699578096403948e-07
            ],
            [
                0.9999982396567895,
                3.7266406168827523e-06,
                2.7535694384882703e-05,
                0.9999945777816962,
                0.9999646437371967,
                7.889259764517575e-06,
                0.9999974387168816,
                2.902313369111213e-06,
                0.9999990577549576,
                0.9999985406230847
            ],
            [
                0.9999996940976638,
                0.9999997463981939,
                0.999999057754958,
                0.9999993524052023,
                0.9999996533672553,
                0.9999994956527123,
                0.9999991684721714,
                0.9999995262092167,
                0.9999992661791077,
                0.99999976176309
            ],
            [
                6.825600469412533e-08,
                3.059022998581767e-07,
                5.043475885696228e-07,
                1.4449802095666915e-07,
                6.475946438055299e-07,
                3.4663249714612693e-07,
                1.4449803818215767e-07,
                4.450848927658745e-07,
                5.043472278322555e-07,
                6.023569166654288e-08
            ],
            [
                0.9999986290424693,
                1.855391239547094e-07,
                8.315281267882195e-07,
                2.102434412875379e-07,
                0.999998629042796,
                8.315278294114555e-07,
                8.764247451307293e-08,
                1.8553905760062447e-07,
                1.4449800373118268e-07,
                0.9999967112509435
            ],
            [
                0.9999991684715768,
                6.962257079832313e-06,
                0.9999994284993495,
                0.9999994631248689,
                0.9999996072136128,
                0.999999266179108,
                0.9999997300420942,
                0.9999993524050483,
                0.9999992661792833,
                0.9999995818810781
            ],
            [
                1.0677029973219343e-06,
                2.382370235933104e-07,
                3.05902190458764e-07,
                1.4449798650551755e-07,
                4.785093924389007e-06,
                4.22283545819819e-06,
                1.6373774480605869e-07,
                9.422443692574719e-07,
                2.260323758987159e-06,
                1.4449805540740185e-07
            ],
            [
                2.902312677137316e-06,
                0.9999962733616232,
                5.043474082005342e-07,
                1.8553905760062447e-07,
                0.9999980052693314,
                5.04347468323289e-07,
                0.9999987901343188,
                0.9999986290426327,
                5.043476486902204e-07,
                0.9999970976869845
            ],
            [
                0.9999998642567028,
                0.9999997761970781,
                0.9999997300421583,
                0.9999994284995534,
                0.9999997761971582,
                0.9999998555020135,
                0.9999997897565588,
                0.9999995549151075,
                0.9999996940977002,
                0.9999991148429648
            ],
            [
                3.4663278639892215e-07,
                1.6373770576683237e-07,
                0.9999995262096117,
                1.855391239544352e-07,
                0.999999526209499,
                0.9999997463980731,
                0.9999994631248684,
                3.059021175261338e-07,
                0.9999998144609645,
                1.0677033791612137e-06
            ],
            [
                2.10243290909724e-07,
                1.2751908849167202e-07,
                2.1024334103581732e-07,
                8.764242227418718e-08,
                3.4663262111182307e-07,
                1.6373766672994222e-07,
                8.315278294114555e-07,
                2.6995790618469934e-07,
                5.71500719545698e-07,
                2.699576809143613e-07
            ],
            [
                5.715003789033962e-07,
                2.6995784182140636e-07,
                2.699578740011634e-07,
                3.4663249714451116e-07,
                2.3823685319244518e-07,
                1.2098652508424818e-06,
                6.475948754012522e-07,
                6.475947982002148e-07,
                1.209866260432471e-06,
                2.699578096393206e-07
            ],
            [
                5.043474081993875e-07,
                4.450851049991497e-07,
                3.05902336324494e-07,
                1.209865827752005e-06,
                1.3709568799919866e-06,
                6.475948754012522e-07,
                5.715003789046955e-07,
                3.466325797896173e-07,
                5.71500719545698e-07,
                5.715005151606823e-07
            ],
            [
                0.9999994631247404,
                0.9999995549148425,
                0.999999310638873,
                0.9999994284996896,
                0.9999992661787579,
                0.9999983463096274,
                0.9999998024947272,
                0.9999978766205293,
                0.9999987121041721,
                0.9999994631249326
            ],
            [
                0.999997273528757,
                0.9999852610129021,
                1.7603427936263351e-06,
                1.8553910183607374e-07,
                0.999984310442818,
                0.9999910603005111,
                5.043476486915964e-07,
                0.9999952149049439,
                7.88926070489716e-06,
                0.999998446502247
            ],
            [
                0.999997438718707,
                0.9999987901346057,
                0.999999391640746,
                0.9999993106389549,
                0.9999997126313784,
                0.9999983463106129,
                0.9999996072138937,
                0.9999995262093857,
                0.9999994284996213,
                0.9999987901344615
            ],
            [
                7.734415776836702e-08,
                0.9999991148428601,
                1.2098661162056318e-06,
                NaN,
                0.006692849995562132,
                0.9999991148428604,
                6.475946438055299e-07,
                0.9999995818810778,
                1.8553919030858602e-07,
                6.475947982037486e-07
            ],
            [
                8.315284241597959e-07,
                6.9622537599680095e-06,
                3.7266401726359486e-06,
                8.939699501416646e-06,
                2.2603251062450327e-06,
                1.3709576971379186e-06,
                4.450852111148132e-07,
                2.5612834320563895e-06,
                1.147876812620341e-05,
                4.222832437798974e-06
            ],
            [
                5.715002426475718e-07,
                0.9999964991455894,
                3.466326211113502e-07,
                1.27519088491875e-07,
                0.9999970976873269,
                0.9999910603005375,
                1.855391239544352e-07,
                0.9999892166826582,
                8.764244316973974e-08,
                1.8553919030858602e-07
            ],
            [
                8.315281267882195e-07,
                1.9947299593078385e-06,
                6.475950298021765e-07,
                5.043473480777865e-07,
                1.0677033791612137e-06,
                1.209865827752005e-06,
                1.7603440527334603e-06,
                3.05902263391829e-07,
                3.4663274507713016e-07,
                3.4663274507713016e-07
            ],
            [
                9.422449308774482e-07,
                7.338212429582604e-07,
                9.4224425692559e-07,
                2.2603234895372223e-06,
                9.422450431954847e-07,
                5.422220262636381e-06,
                1.5534981249697903e-06,
                8.315280276626197e-07,
                0.9999646437326821,
                4.785093924362895e-06
            ],
            [
                4.450848927650143e-07,
                1.0677028700422047e-06,
                5.715007195447234e-07,
                2.902312677150514e-06,
                1.5534981249697903e-06,
                2.2603251062450327e-06,
                2.699578096403948e-07,
                1.0677024881980089e-06,
                4.785095065204162e-06,
                1.994729721518893e-06
            ],
            [
                0.9999987121046329,
                0.9999977396749004,
                0.9999974387165749,
                0.9999991684720729,
                0.999998996985913,
                0.9999988634365624,
                0.9999984465015072,
                0.9999990577556317,
                0.9999985406230854,
                0.9999991684721722
            ],
            [
                1.6373770576776313e-07,
                2.6995787400282076e-07,
                7.734418542875216e-08,
                6.825608606172863e-08,
                1.4449802095666915e-07,
                6.825608606172863e-08,
                3.466326211105621e-07,
                5.3157887739943563e-08,
                8.7642558095602e-08,
                5.3157830707696514e-08
            ],
            [
                2.9023112932296107e-06,
                0.999997876622048,
                0.9999975938982426,
                1.9947299593078385e-06,
                0.9999945777797551,
                1.0677029973219343e-06,
                0.9999984465022485,
                0.999997273530385,
                0.9999977396754364,
                0.9999995549150015
            ],
            [
                0.9999987901340299,
                0.9999983463110077,
                0.9999986290432857,
                0.9999983463104168,
                0.9999993106389558,
                0.9999993106386276,
                0.9999983463104176,
                0.9999975938979544,
                0.9999977396765175,
                0.9999995262093297
            ],
            [
                0.9999989969861531,
                0.9999989969854343,
                0.9999975938968091,
                0.9999992661788457,
                2.2603251062450327e-06,
                0.9999994956526523,
                0.9999989969859132,
                0.9999994284997581,
                0.9999980052695681,
                0.9999992188518564
            ],
            [
                0.999999114842648,
                1.7603438428740716e-06,
                7.338213304283347e-07,
                0.9999977396762454,
                0.9999994956525322,
                0.9999417087491798,
                0.9999934595604543,
                0.9999934595635656,
                2.10243290909963e-07,
                3.927862470899887e-07
            ],
            [
                3.9278610661902853e-07,
                8.315283250394546e-07,
                0.9999989322975126,
                2.1024341622426268e-07,
                9.422445939032799e-07,
                3.2887502415767434e-06,
                4.4508510499849186e-07,
                3.0590237279032884e-07,
                2.1024326584639497e-07,
                9.422448185534261e-07
            ],
            [
                3.466325797888292e-07,
                3.466326211113502e-07,
                6.475950298011458e-07,
                7.338212429582604e-07,
                1.6373770576776313e-07,
                7.338208055664991e-07,
                2.382369383923073e-07,
                6.475945666051092e-07,
                2.69957906184239e-07,
                2.6995774527718623e-07
            ],
            [
                1.0677029973219343e-06,
                1.067703124601679e-06,
                7.33821330437595e-07,
                3.9278629391427843e-07,
                9.422443692574719e-07,
                3.059022269254856e-07,
                9.422442569334097e-07,
                7.338212429594283e-07,
                1.5534984953552536e-06,
                5.043475885696228e-07
            ],
            [
                2.6995774527718623e-07,
                0.9999995262093859,
                6.475949526020042e-07,
                3.4663249714612693e-07,
                0.9999977396759736,
                0.9999989322973851,
                0.9999996940977367,
                0.9999983463098238,
                0.9999993524050478,
                0.9999980052705191
            ],
            [
                0.9999997126314811,
                0.9999996072136127,
                0.9999996743686645,
                0.9999996940978826,
                0.9999996533672552,
                0.9999997126314469,
                0.9999995818810777,
                0.9999972735290834,
                0.9999991148433868,
                0.9999992188519491
            ],
            [
                0.9999957771675723,
                0.9999978766212944,
                0.9999984465026197,
                0.9999980052702825,
                0.9999984465015064,
                0.9999967112513368,
                2.9023112932045342e-06,
                0.9999970976880239,
                0.9999957771680756,
                0.9999877809240341
            ],
            [
                0.999999352405434,
                0.9999996072139409,
                0.9999994284996219,
                0.9999996743687036,
                0.9999992661788457,
                0.9999989322966222,
                0.9999995818812774,
                0.9999994284996898,
                0.9999995818810781,
                0.9999985406243043
            ],
            [
                1.1253512180925583e-07,
                0.9999996533674619,
                0.999998629042468,
                0.9999993524052795,
                3.466326624336003e-07,
                0.9999994631248683,
                1.4449805540763184e-07,
                3.466327037553825e-07,
                1.8553914607267268e-07,
                0.9999996743688588
            ],
            [
                2.1024331597288867e-07,
                1.275189972832538e-07,
                3.2241889394209404e-08,
                2.1024336609874897e-07,
                1.8553907971879076e-07,
                1.6373764721091427e-07,
                7.73442776303243e-08,
                9.931199245322124e-08,
                9.931200429212718e-08,
                9.931199245322124e-08
            ],
            [
                9.422444815814404e-07,
                3.9278610661902853e-07,
                2.382370235933104e-07,
                2.3823688159291947e-07,
                2.3823693839325527e-07,
                2.10243290909724e-07,
                1.1478772231232203e-05,
                6.962254589978262e-06,
                8.481106162154104e-05,
                8.481104140395962e-05
            ],
            [
                1.3709568799760888e-06,
                2.9023109471689794e-06,
                2.26032402841657e-06,
                1.2098659719716573e-06,
                8.939696304311336e-06,
                4.006371129615879e-05,
                8.939693107190907e-06,
                1.012999460278499e-05,
                2.5612816000646084e-06,
                2.2603251062013478e-06
            ]
        ]
    },
    {
        "q_id": "9199_mmlu_physics",
        "cot_ids": [
            0,
            1,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            94,
            95,
            96,
            98,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999996072136595,
                0.9999993916407459,
                0.9999994284993491,
                0.9999995818812771,
                0.9999983463098246,
                0.99999963101146,
                0.9999997897565588,
                0.9999998642566704,
                0.9999996072137531,
                0.9999995262092164
            ],
            [
                0.9999996743687424,
                0.9999993916411088,
                0.9999986290431208,
                0.9999995818811276,
                0.9999994631249325,
                0.999999789756634,
                0.9999994631251244,
                0.9999991684715768,
                0.9999985406234323,
                0.9999992188516699
            ],
            [
                5.8291272497207844e-05,
                5.829127944184748e-05,
                6.962257079832313e-06,
                3.2887486733420804e-06,
                1.1478769494250387e-05,
                0.00010889689633501143,
                2.2603237589779086e-06,
                4.222833947932061e-06,
                4.78509278348926e-06,
                0.00013982207417849628
            ],
            [
                1.0,
                0.9999997761971049,
                0.9999998555019274,
                0.9999987901337405,
                0.9999997463982241,
                0.9999996310113719,
                0.9999993106387904,
                0.9999998257022045,
                0.9999997761970782,
                0.9999997300421261
            ],
            [
                0.999998712105246,
                0.9999985406241281,
                0.9999995818813767,
                0.9999994284996216,
                0.9999987901343179,
                0.9999996072136595,
                0.9999992661789326,
                0.999998446501692,
                0.9999993916407459,
                0.9999994631248045
            ],
            [
                2.5612812947508257e-06,
                1.99472900813862e-06,
                1.994729483723626e-06,
                7.338212429582604e-07,
                1.5534984953453635e-06,
                6.962255419868303e-06,
                3.726638395634011e-06,
                1.670142980893658e-05,
                8.31528424162821e-07,
                2.561282516066741e-06
            ],
            [
                0.9999992661787579,
                0.9999986290427949,
                0.9999969105048186,
                0.9999988634362906,
                0.9999986290424683,
                0.9999996310115481,
                0.99999963101146,
                0.9999995262096119,
                0.9999984465026178,
                0.9999995818810778
            ],
            [
                0.9999999006879958,
                0.9999904837517358,
                0.9999993524053568,
                0.9999999358793562,
                0.9999999067051055,
                0.9999997463981637,
                0.9999992188519499,
                0.9999998461827322,
                0.9999998802069445,
                0.9999991684721713
            ],
            [
                7.338208055664991e-07,
                0.9999955048200396,
                1.760343213335281e-06,
                2.382369951932796e-07,
                0.9999975938982386,
                3.05902336324494e-07,
                5.715002426486762e-07,
                8.315281267882195e-07,
                3.726639284144195e-06,
                4.006368741670684e-05
            ],
            [
                0.999999168471973,
                0.999996273359389,
                0.9999991684718739,
                0.9999995818810776,
                0.9999991148430709,
                0.9999993524052024,
                0.9999992188519495,
                0.999999428499758,
                0.9999993524050482,
                0.9999995818811774
            ],
            [
                0.9999992661791951,
                0.9999993106390371,
                0.99999921885167,
                0.9999986290424677,
                0.9999994631250606,
                0.9999996940977368,
                0.9999997761970248,
                0.9999998362623334,
                0.9999998555019274,
                0.9999993916407461
            ],
            [
                0.9999999067049943,
                0.9999998257020799,
                0.9999998874648917,
                0.9999995262096119,
                0.9999998362622553,
                0.9999992661789326,
                0.9999997126315153,
                0.9999993106386263,
                0.9999999067050164,
                0.9999997761970781
            ],
            [
                NaN,
                0.999994906294404,
                0.9986749775536717,
                0.9999756997564206,
                0.9999916019260076,
                0.9999930377437641,
                0.999993459559675,
                0.999992110738376,
                0.9999962733607293,
                0.9999832985781901
            ],
            [
                3.05902190458764e-07,
                5.715006514176113e-07,
                3.0590237279085045e-07,
                6.475946438055299e-07,
                3.9278629391427843e-07,
                8.315277302857965e-07,
                2.699578096403948e-07,
                9.422445939054222e-07,
                5.715006514176113e-07,
                3.059022998581767e-07
            ],
            [
                7.88926446679691e-06,
                0.9999992661789326,
                0.9999991148426481,
                5.422220909009474e-06,
                0.9999952149055077,
                5.715005832886879e-07,
                7.338212429582604e-07,
                0.9999981261250657,
                0.9999964991468397,
                7.338209805240734e-07
            ],
            [
                0.9999997463980427,
                0.9999995818810778,
                0.9999995818812273,
                0.99999967436882,
                0.9999996310116359,
                0.9999997463982241,
                0.999999653367255,
                0.9999996533675031,
                0.9999992188514838,
                0.9999997761971849
            ],
            [
                1.4738980214280206e-05,
                0.9999972735297359,
                1.1478766757237902e-05,
                3.2887506336086064e-06,
                9.422447062202052e-07,
                1.1478764020560142e-05,
                1.067703379154416e-06,
                9.422448185478557e-07,
                0.9999945777810632,
                1.5534981249574276e-06
            ],
            [
                1.2098659719757836e-06,
                4.785096776499213e-06,
                2.5612819054028872e-06,
                8.31527928532683e-07,
                1.9947299593078385e-06,
                3.927862002663297e-07,
                3.288748673376478e-06,
                NaN,
                1.3709576971463352e-06,
                8.315280276626197e-07
            ],
            [
                1.3709578605729614e-06,
                1.209866260432471e-06,
                6.475947210031623e-07,
                1.0677032518814388e-06,
                9.422443692555439e-07,
                6.475947210046347e-07,
                9.422443692555439e-07,
                4.4508494582405734e-07,
                1.275190276859705e-07,
                1.5534977545886537e-06
            ],
            [
                0.9999974387180984,
                0.9999982396565834,
                0.9999993106390374,
                0.999998446502063,
                0.999999266179108,
                0.9999993916409642,
                0.999999057755183,
                0.9999990577549579,
                0.9999991684717755,
                0.99999879013475
            ],
            [
                0.9999992188516699,
                0.9999964991460057,
                0.9999987121046318,
                0.9999990577552947,
                0.9999972735287562,
                0.9999998555019791,
                0.9999992661792821,
                0.999999825702059,
                0.9999997897565839,
                0.9999993916411088
            ],
            [
                2.1024331597262577e-07,
                1.3709567165617364e-06,
                1.8553919030858602e-07,
                2.3823690999290963e-07,
                2.699578740032504e-07,
                1.8553907971855875e-07,
                8.764244316973974e-08,
                9.931186222523604e-08,
                1.444979692800516e-07,
                1.6373766672973748e-07
            ],
            [
                2.7535694384882703e-05,
                3.9278634073732336e-07,
                0.9999993524049706,
                5.71500651413193e-07,
                0.9999964991443374,
                3.7266406168624155e-06,
                6.605213682159303e-05,
                2.3823693839290317e-07,
                5.715007195447234e-07,
                1.994729483723626e-06
            ],
            [
                0.999999825702059,
                0.999999526209386,
                0.9999998942829729,
                0.9999997617631469,
                0.9999991148431758,
                0.9999996940977002,
                0.9999997300420941,
                0.9999992661791954,
                0.999999789756659,
                0.9999994284994171
            ],
            [
                0.999999900687984,
                0.9999996533672549,
                1.892514598551715e-05,
                0.9999998942829855,
                0.999999631011416,
                0.9999994284992808,
                2.5612834320470717e-06,
                0.9999997761971049,
                0.9999997897567091,
                0.9999998257020799
            ],
            [
                3.726638839833152e-06,
                1.994730434879465e-06,
                1.2098659719757836e-06,
                0.9999977396746264,
                2.5612825160271407e-06,
                1.5534975693933505e-06,
                2.5612825160271407e-06,
                1.370956716529941e-06,
                3.2887478892683997e-06,
                1.2098658277451275e-06
            ],
            [
                0.9999998802068873,
                0.9999993916409637,
                1.0,
                0.9999998802069017,
                0.9999998642567351,
                0.9999999226557962,
                0.9999998257020799,
                0.9999997897567342,
                0.999999428499349,
                0.999999927341801
            ],
            [
                2.6995774527718623e-07,
                1.067703124601679e-06,
                5.715005832895975e-07,
                3.466327037553825e-07,
                7.338208055680009e-07,
                2.382368531929327e-07,
                2.699578740032504e-07,
                5.715006514176113e-07,
                3.466325797896173e-07,
                5.043476486924565e-07
            ],
            [
                1.5534975693869924e-06,
                1.5534975693792215e-06,
                1.5534975693933505e-06,
                8.315278294072958e-07,
                1.3709572068478697e-06,
                2.9023119851781017e-06,
                2.561283432035425e-06,
                4.450848927650143e-07,
                1.3709575337078829e-06,
                1.3709570434178922e-06
            ],
            [
                1.209866260432471e-06,
                1.0677032518814388e-06,
                1.6373764721072816e-07,
                3.059021904580685e-07,
                6.475946438055299e-07,
                1.3709573702822306e-06,
                1.7603440527286572e-06,
                1.6373764721072816e-07,
                1.5534983101644536e-06,
                7.338209805240734e-07
            ],
            [
                0.9999999067050832,
                0.9999987121044788,
                0.9999994956526521,
                0.9999997300421584,
                0.9999996072138,
                0.999998932297131,
                0.999999581881277,
                0.9999993524048935,
                0.999999631011372,
                0.9999980052709941
            ],
            [
                2.561281600086738e-06,
                8.315281267882195e-07,
                1.2098661162056318e-06,
                2.1024331597262577e-07,
                3.05902263391829e-07,
                3.726639284125553e-06,
                3.466327037539638e-07,
                2.5612819054133693e-06,
                6.962257079832313e-06,
                4.450848927650143e-07
            ],
            [
                0.9999997897566341,
                0.9999996310113282,
                0.9999998555019275,
                0.9999998362623334,
                0.9999997761970782,
                0.9999996310116361,
                0.9999997617631753,
                0.9999998362622944,
                0.9999997617630334,
                0.9999987121047863
            ],
            [
                9.422442569315887e-07,
                1.370957860576702e-06,
                4.450848927650143e-07,
                3.466327863983311e-07,
                0.9999949062925797,
                6.475947210031623e-07,
                4.2228339479858295e-06,
                1.5534971990126997e-06,
                7.338213304363436e-07,
                1.3709576971425944e-06
            ],
            [
                0.9999993106386263,
                0.9999989969859125,
                0.9999996072136128,
                0.9999975938982367,
                0.9999995549148425,
                0.999994577778467,
                0.9999991148428595,
                0.9999994631248045,
                0.9999993106386265,
                0.9999987901341739
            ],
            [
                1.7603427936263351e-06,
                6.144177531811707e-06,
                1.2098658277451275e-06,
                4.2228329411708495e-06,
                1.0677027427624903e-06,
                9.422447062270609e-07,
                1.760343213335281e-06,
                2.9023133690980155e-06,
                7.338213304363436e-07,
                3.9278610661902853e-07
            ],
            [
                0.9999992661791077,
                0.9999996310116359,
                0.9999996533672552,
                0.9999996940976273,
                0.9999993916410365,
                0.999999730042094,
                0.9999996940976639,
                0.9999998024947037,
                0.9999987901344622,
                0.9999997126313784
            ],
            [
                3.059022998576899e-07,
                1.2098659719757836e-06,
                2.1024331597262577e-07,
                2.1024341622426268e-07,
                5.043476486915964e-07,
                2.1024334103505245e-07,
                2.6995771309523475e-07,
                2.260324567337161e-06,
                1.855391239544352e-07,
                1.7603438428740716e-06
            ],
            [
                NaN,
                1.0677032518814388e-06,
                2.561283432035425e-06,
                3.927862002663297e-07,
                1.994730672675753e-06,
                7.338208055664991e-07,
                5.043476486915964e-07,
                3.726639728348526e-06,
                2.5612812947508257e-06,
                2.561282210729555e-06
            ],
            [
                0.9999999226557778,
                0.9999999226558146,
                0.9999999123575777,
                0.9999999226557224,
                1.0,
                0.9999999067051055,
                0.9999998802069873,
                0.9999999317440116,
                0.999999906705072,
                0.9999998802069587
            ],
            [
                0.9999997300422229,
                0.9999998144609645,
                0.9999997300421907,
                0.9999998642566866,
                0.9999998144608983,
                0.999999789756609,
                0.9999999067050721,
                0.9999996743688975,
                0.9999998144608098,
                0.9999998874648112
            ],
            [
                1.5534981249697903e-06,
                5.829126555256903e-05,
                5.4222209089700225e-06,
                1.0129993394811673e-05,
                4.2228349547223175e-06,
                2.382368247924618e-07,
                6.9622537599680095e-06,
                3.927862470899887e-07,
                2.260323489490968e-06,
                1.4738980215352592e-05
            ],
            [
                2.699576809143613e-07,
                4.22283545819819e-06,
                3.05902263391829e-07,
                3.059022998581767e-07,
                3.05902190458764e-07,
                2.1024339116168358e-07,
                2.3823690999323465e-07,
                4.4508515805735777e-07,
                7.338209805240734e-07,
                4.450852111155216e-07
            ],
            [
                7.338208055680009e-07,
                1.994730672675753e-06,
                9.422448185510695e-07,
                7.338213304363436e-07,
                7.889262585886274e-06,
                1.7603434231833873e-06,
                6.962258739796719e-06,
                5.04347468323289e-07,
                4.785094494783494e-06,
                7.338212429582604e-07
            ],
            [
                0.9999998461826406,
                0.9999998642567351,
                0.9999998257021422,
                0.9999998257022045,
                0.999999495652532,
                0.9999995549147891,
                0.9999996072139405,
                0.9999993524049706,
                0.9999996072138936,
                0.9999996533673791
            ],
            [
                2.1024344128660572e-07,
                2.1024341622368903e-07,
                5.043475284430694e-07,
                5.04347348075149e-07,
                3.2887494574518405e-06,
                5.043475885674441e-07,
                1.1478773599425825e-05,
                2.699577774560111e-07,
                3.927860597935108e-07,
                3.9278634073732336e-07
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999123575778,
                0.9999998942830863,
                0.9999999611088534,
                0.9999999358793409,
                0.9999999067050276
            ],
            [
                0.9999993524052022,
                0.9999996940978826,
                0.9999998144608762,
                0.9999996310114599,
                0.9999996940978462,
                1.0677027427624903e-06,
                0.9999998144608762,
                0.9999998024946567,
                0.9999997761971583,
                0.9999997300423191
            ],
            [
                0.9999997126314468,
                0.9999994284996213,
                0.9999892166865116,
                0.9999998362622553,
                2.699577774589574e-07,
                0.9999977396748952,
                0.9999989322968759,
                0.9999993916410361,
                0.999999607213753,
                0.9999994956527123
            ],
            [
                2.102434162245973e-07,
                6.475949526020042e-07,
                3.466325797888292e-07,
                2.3823682479292225e-07,
                2.6995774527718623e-07,
                6.475949526020042e-07,
                1.8553905760062447e-07,
                2.102434162245973e-07,
                8.939698435657833e-06,
                1.8553914607267268e-07
            ],
            [
                1.1478768126057254e-05,
                6.1441746020359e-06,
                3.288749849529972e-06,
                3.7266410611296085e-06,
                1.5534973842076057e-06,
                5.715005151606823e-07,
                2.5612812947508257e-06,
                2.3823688159291947e-07,
                6.475949526020042e-07,
                1.3709567165617364e-06
            ],
            [
                0.9999997897567342,
                0.9999985406230842,
                0.9999992661790201,
                0.9999995818812774,
                0.9999996743687035,
                0.9999986290421414,
                0.9999988634358841,
                0.9999997300420941,
                0.9999994631250604,
                0.9999992661792824
            ],
            [
                0.9999993524050479,
                0.9999991684715765,
                0.9999999176674749,
                0.9999994284997576,
                0.9999996072138936,
                0.9999994284994851,
                0.9999998024947037,
                0.9999998144609205,
                0.9999991148426485,
                0.9999987121050923
            ],
            [
                0.9999986290432851,
                0.999998863435749,
                0.9999995549147362,
                0.9999994284994175,
                0.9999989969856742,
                0.9999992661788456,
                0.9999987121052469,
                0.9999992661792829,
                0.9999989322971319,
                0.9999987121052472
            ],
            [
                3.4663249714612693e-07,
                9.4224425692559e-07,
                2.6995771309523475e-07,
                2.102434412875379e-07,
                1.2751904288739315e-07,
                6.475947210031623e-07,
                3.927862002663297e-07,
                5.043475284468537e-07,
                1.855391681906175e-07,
                3.927862002663297e-07
            ],
            [
                0.9999996940977004,
                0.9999994631248685,
                0.9999997126314469,
                0.9999999226558515,
                0.9999999176674945,
                0.9999997761971317,
                0.9999997300421585,
                0.9999998874648379,
                0.9999998144608762,
                0.9999997617631753
            ],
            [
                NaN,
                0.9999991684716757,
                0.9999991148432813,
                0.9999995262093857,
                0.9999996940978462,
                0.9999994284996215,
                0.9999994631248684,
                0.999999310639119,
                0.9999990577555191,
                0.9999987121047852
            ],
            [
                0.999999114843387,
                0.999998996986032,
                0.9999985406234345,
                0.9999990577555196,
                0.9999981261248434,
                0.9999996533674618,
                0.9999975938965205,
                0.9999985406230847,
                0.9999992661786704,
                0.9999990577554074
            ],
            [
                3.927860597935108e-07,
                1.7603438428740716e-06,
                0.9999967112509373,
                3.9278605979208185e-07,
                3.4663262110945863e-07,
                3.9278615344178325e-07,
                1.2098655392871682e-06,
                4.785093353940187e-06,
                4.450849988811838e-07,
                1.3709567165579959e-06
            ],
            [
                3.9278605979534166e-07,
                3.05902190458764e-07,
                1.6373770576776313e-07,
                1.6373766672973748e-07,
                2.382370235933104e-07,
                5.715005832886879e-07,
                2.699576809143613e-07,
                2.382369667929001e-07,
                3.059021175261338e-07,
                3.466325797896173e-07
            ],
            [
                1.0,
                0.9999996940977003,
                1.0,
                0.9999997761970248,
                0.9999999586006443,
                1.0,
                0.9999999697115804,
                0.9999999677581529,
                0.9999997126315154,
                0.9999995549148952
            ],
            [
                0.9999921107383813,
                3.7266410611296085e-06,
                0.9999981261239501,
                6.605213682591808e-05,
                2.382369951932796e-07,
                0.9999978766210336,
                1.7603434231833873e-06,
                2.430025232128576e-05,
                4.539785241676547e-05,
                6.475948754012522e-07
            ],
            [
                0.9999996310115039,
                0.999999730042287,
                0.9999998724809116,
                0.9999999397643083,
                0.9999993524049704,
                0.999999825702059,
                0.999999917667524,
                0.999999495652532,
                0.9999997617630049,
                0.9999995262093858
            ],
            [
                3.2887482813149375e-06,
                3.2887502415438413e-06,
                1.6701417863559525e-05,
                1.7603436330179102e-06,
                6.475949525919915e-07,
                6.475949525981759e-07,
                3.72664061681327e-06,
                1.0677024881980089e-06,
                1.7603436330091044e-06,
                7.338209805200689e-07
            ],
            [
                4.4508515805735777e-07,
                7.338208055680009e-07,
                1.0677026154827912e-06,
                8.315277302857965e-07,
                3.7266401726359486e-06,
                1.209866260432471e-06,
                2.2603251062450327e-06,
                5.043474683240344e-07,
                6.475950298011458e-07,
                2.9023119851899796e-06
            ],
            [
                5.715003107755449e-07,
                2.561283432035425e-06,
                4.2228339479858295e-06,
                1.760342793638743e-06,
                3.466327863983311e-07,
                5.04347528446051e-07,
                1.2098658277451275e-06,
                2.3823688159291947e-07,
                5.043472879540142e-07,
                4.222833444590791e-06
            ],
            [
                0.9999994956524717,
                0.9999993524048936,
                0.9999989969862711,
                0.9999994284994851,
                0.9999995818810776,
                0.9999991684721712,
                0.9999989969857929,
                0.999999653367255,
                0.9999997463981334,
                0.9999989969857926
            ],
            [
                6.023572038912295e-08,
                0.9999998724809115,
                0.9999998642566704,
                1.1253509497883659e-07,
                3.9278629391427843e-07,
                1.1253509497883659e-07,
                0.9999997761972116,
                0.9999998724809875,
                0.9999998024947273,
                0.9999996072136594
            ],
            [
                1.5534973842030142e-06,
                0.9999997126314468,
                3.927862939126708e-07,
                0.9999996310116359,
                0.9999998461827322,
                5.715004470313855e-07,
                0.9999994284997575,
                6.475947982022763e-07,
                0.9999997617630333,
                0.9999997761970515
            ],
            [
                0.9999991684716758,
                0.9999993916411816,
                0.99999967436882,
                0.9999987901340291,
                0.9999998257021837,
                0.9999991684715767,
                0.9999987901344616,
                0.9999994956524718,
                0.9999997761971317,
                0.9999996072136593
            ],
            [
                1.6373776432509826e-07,
                2.102434412875379e-07,
                3.466326624336003e-07,
                3.059021175261338e-07,
                5.715005832886879e-07,
                9.422447062294175e-07,
                2.699578740032504e-07,
                5.043476486924565e-07,
                4.4508510499849186e-07,
                2.382368531929327e-07
            ],
            [
                0.9999996072137063,
                0.9999997126313441,
                0.9999999226557131,
                0.9999997761970515,
                0.9999998461826956,
                0.9999998555019963,
                1.0,
                0.9999999273417836,
                0.999999653367503,
                0.9999998724809419
            ],
            [
                6.144176799334096e-06,
                1.5534981249697903e-06,
                5.043476486915964e-07,
                7.338209805240734e-07,
                5.715002426475718e-07,
                1.7603438428800754e-06,
                9.422448185510695e-07,
                2.5612828213818346e-06,
                4.4508510499849186e-07,
                1.5534977545886537e-06
            ],
            [
                1.1478769494396542e-05,
                1.1478772231086046e-05,
                8.315280276626197e-07,
                1.99472900813862e-06,
                5.144220753172505e-05,
                4.006370652067535e-05,
                8.939695238634211e-06,
                4.785093924389007e-06,
                3.288747889284851e-06,
                0.9999991684722709
            ],
            [
                3.059022998581767e-07,
                1.6373764721072816e-07,
                0.9999996310114599,
                1.855391239547094e-07,
                4.450852111155216e-07,
                1.8553910183674878e-07,
                0.9999997300421584,
                3.466325797900508e-07,
                6.825597214718257e-08,
                5.043472278322555e-07
            ],
            [
                4.4508515805735777e-07,
                5.043472278322555e-07,
                2.699577452775239e-07,
                3.0590237279085045e-07,
                2.1024331597288867e-07,
                2.699578096403948e-07,
                4.4508515805735777e-07,
                2.699578740032504e-07,
                3.05902336324494e-07,
                1.275190428875671e-07
            ],
            [
                1.6373764721072816e-07,
                2.1024331597262577e-07,
                5.715007195447234e-07,
                2.382369951932796e-07,
                2.1024326584639497e-07,
                1.855391239544352e-07,
                2.6995771309523475e-07,
                1.6373770576776313e-07,
                1.637377448057981e-07,
                2.6995790618469934e-07
            ],
            [
                0.9999997897565839,
                0.9999994631248046,
                0.9999998257022045,
                0.9999991684718741,
                0.9999997463980428,
                0.999999776197025,
                0.9999987901347509,
                0.9999997617631187,
                NaN,
                0.9999998144609646
            ],
            [
                0.9999997463980427,
                0.999999168472171,
                0.9999997761970248,
                0.999999631011548,
                0.9999996940977004,
                0.9999996072137062,
                0.9999996533674617,
                0.9999997300421904,
                0.999999730042287,
                0.9999996940978461
            ],
            [
                0.9999996940976272,
                0.9999996940977367,
                0.9999997617630617,
                0.9999997761971849,
                0.9999998257021006,
                0.9999997617631184,
                0.999999653367255,
                0.9999998362622943,
                0.9999996072137999,
                0.9999996310113719
            ],
            [
                0.999999802494633,
                0.9999992661790198,
                0.9999993524053569,
                0.9999994284993488,
                0.9999993524048932,
                0.9999989969861516,
                0.999999495652532,
                0.9999998724809267,
                0.9999997761970515,
                0.9999995262092164
            ],
            [
                0.9999998257020799,
                0.9999996940976638,
                0.9999997300421584,
                0.9999995262092165,
                0.999999894282998,
                0.9999997126314126,
                0.9999993916406738,
                0.9999989322972577,
                0.9999996940976638,
                0.9999995818811773
            ],
            [
                0.9999999317440279,
                0.9999997761972116,
                0.9999998642566866,
                0.9999998802069873,
                0.9999996940976273,
                0.9999998874648782,
                0.999999946842163,
                0.9999998802069731,
                0.9999999468421377,
                0.9999999006880904
            ],
            [
                3.0590237279032884e-07,
                0.9999997897565839,
                1.2751905808881762e-07,
                9.931198061405701e-08,
                3.9278634073732336e-07,
                1.4449805540700758e-07,
                5.04347528446051e-07,
                0.9999998461827139,
                0.9999987901343173,
                0.9999996743688199
            ],
            [
                1.5534973842076057e-06,
                1.8553910183674878e-07,
                1.4449798650569826e-07,
                1.760342793638743e-06,
                6.825600469412533e-08,
                4.450852641737424e-07,
                2.6995784182183607e-07,
                3.466325384678894e-07,
                1.209865827752005e-06,
                1.855391239547094e-07
            ],
            [
                9.422450431989127e-07,
                1.3709572068478697e-06,
                2.5612816000646084e-06,
                1.6373774480535133e-07,
                8.315279285351409e-07,
                1.8553910183607374e-07,
                8.315278294072958e-07,
                1.2098662604291696e-06,
                2.5612816000646084e-06,
                8.315279285370317e-07
            ],
            [
                2.382369383923073e-07,
                9.422450432014836e-07,
                2.5612819054133693e-06,
                3.288747889284851e-06,
                8.315280276626197e-07,
                1.9947301970972664e-06,
                3.288749065423109e-06,
                2.2603248367949354e-06,
                3.059022998576899e-07,
                4.450852641737424e-07
            ],
            [
                1.855390576008354e-07,
                4.450852641737424e-07,
                9.422443692574719e-07,
                3.927863875616689e-07,
                NaN,
                3.9278629391427843e-07,
                2.6995784182183607e-07,
                5.715005832895975e-07,
                5.715005832895975e-07,
                1.4449805540763184e-07
            ],
            [
                1.5534971990169383e-06,
                6.475945666051092e-07,
                3.726638395634011e-06,
                1.3709568799919866e-06,
                1.5534971990169383e-06,
                1.9947292459347367e-06,
                6.962258739796719e-06,
                1.8553907971855875e-07,
                1.209866260432471e-06,
                6.962259569750576e-06
            ],
            [
                0.9999997761971315,
                0.9999992188512974,
                0.9999993916408187,
                0.9999994284996898,
                0.9999832985783159,
                0.9999991148432811,
                0.9999995262094987,
                0.9999997761972116,
                0.9999994284994853,
                0.9999991148428595
            ],
            [
                5.71500515161527e-07,
                6.475945666063607e-07,
                7.338208055680009e-07,
                8.315279285370317e-07,
                5.043475885696228e-07,
                5.043476486924565e-07,
                2.9023116392097746e-06,
                3.05902263391829e-07,
                1.5534979397829198e-06,
                5.043475885696228e-07
            ],
            [
                1.8553910183674878e-07,
                2.561281294760143e-06,
                1.5534983101644536e-06,
                6.47595107001401e-07,
                1.8925157266089433e-05,
                1.3007130015488633e-05,
                9.422442569334097e-07,
                5.422221555414699e-06,
                1.855391239547094e-07,
                7.338209805224048e-07
            ],
            [
                0.9999997617631186,
                0.999999814460854,
                0.9999996940978462,
                0.9999997897566841,
                0.9999997300423192,
                0.9999998802069731,
                0.9999990577550695,
                0.9999998257021837,
                0.9999996072139403,
                0.9999997300423191
            ],
            [
                0.9999997300421584,
                0.999999730042255,
                0.999999746398194,
                0.9999995818812772,
                0.9999997761972117,
                0.9999995549147893,
                0.999999802494586,
                0.9999991684718739,
                0.9999995262093296,
                0.9999996940978098
            ],
            [
                7.338213304363436e-07,
                3.059022269250683e-07,
                2.260323758987159e-06,
                7.338213304363436e-07,
                5.043473480777865e-07,
                8.315284241650899e-07,
                9.422449308774482e-07,
                5.715005151606823e-07,
                1.5534975693933505e-06,
                7.338211554783522e-07
            ],
            [
                4.450852111155216e-07,
                3.05902336324494e-07,
                1.4449800373118268e-07,
                3.05902263391829e-07,
                1.2751902768612997e-07,
                7.338207180898968e-07,
                2.102434412875379e-07,
                2.102434412875379e-07,
                4.4508515805735777e-07,
                2.382369951932796e-07
            ],
            [
                3.9278634073732336e-07,
                6.475949526020042e-07,
                5.715006514176113e-07,
                3.0590237279032884e-07,
                3.927863875616689e-07,
                5.715002426486762e-07,
                1.2751899728286965e-07,
                1.5534975693979422e-06,
                3.7266397283908927e-06,
                3.059022998576899e-07
            ],
            [
                0.999999894282935,
                0.9999998642566704,
                0.9999999273418355,
                0.9999998362622357,
                0.9999999176675338,
                0.9999999006880312,
                0.999999814460876,
                0.9999999434137841,
                0.9999998874648514,
                0.999999900687972
            ],
            [
                0.9999993524053572,
                0.9999997897567092,
                0.9999995549148956,
                0.9999995262095558,
                0.9999989322970045,
                0.9999975938976671,
                0.9999998257020799,
                0.9999992188512978,
                0.9999995549148956,
                0.9999997617629766
            ],
            [
                0.9999998942830862,
                0.9999998024946801,
                0.9999998461826956,
                0.9999992188519491,
                0.9999998874647843,
                0.999999554914789,
                0.9999991684722701,
                0.9999998144608319,
                0.999999855501979,
                0.9999997761971582
            ],
            [
                6.47595107001401e-07,
                2.382369951932796e-07,
                4.450850519403407e-07,
                3.05902263391829e-07,
                2.699577774585891e-07,
                2.382370235933104e-07,
                3.9278620026686556e-07,
                5.715003107767143e-07,
                3.059022269250683e-07,
                1.6373774480605869e-07
            ],
            [
                0.9999998257020798,
                0.9999998362622943,
                0.999999802494586,
                0.9999998144608983,
                0.9999997761970781,
                0.9999998362622943,
                0.999999554914842,
                0.9999997897567091,
                0.9999997463981032,
                0.9999997761971848
            ],
            [
                0.9999999317440035,
                0.9999999176674749,
                1.0,
                1.0,
                0.9999998802069873,
                0.9999998802069017,
                0.9999998942828973,
                0.9999999067050943,
                1.0,
                0.9999999358794096
            ],
            [
                0.9999998144608099,
                0.9999983463110089,
                0.9999995549148953,
                0.9999999067051054,
                0.9999995818814267,
                0.9999996940977367,
                0.9999994631248046,
                0.9999998942829098,
                0.9999996533673379,
                0.999999218851763
            ],
            [
                3.7266406168827523e-06,
                5.422217030747413e-06,
                0.00012339463384858465,
                1.3709572068522336e-06,
                4.222833444590791e-06,
                6.144177531767002e-06,
                4.785093924330255e-06,
                2.260325106237323e-06,
                5.422220262599396e-06,
                4.222831934379152e-06
            ],
            [
                1.9947297215125433e-06,
                4.2228319344021954e-06,
                1.760342793638743e-06,
                7.889263526409699e-06,
                5.8291251656508296e-05,
                6.962253760024999e-06,
                3.288749065423109e-06,
                1.7603434231833873e-06,
                7.889262585886274e-06,
                1.994729008145876e-06
            ],
            [
                2.382369383923073e-07,
                1.27519088491875e-07,
                2.1024326584639497e-07,
                3.46632497145457e-07,
                4.450848927658745e-07,
                2.3823699519290042e-07,
                3.0590226339061185e-07,
                3.466327863983311e-07,
                8.764247451307293e-08,
                1.6373776432509826e-07
            ],
            [
                3.2887506336086064e-06,
                2.5612812947508257e-06,
                1.994730672675753e-06,
                3.7266410611296085e-06,
                2.902313023130843e-06,
                2.5612812947508257e-06,
                6.475947210031623e-07,
                2.7535697667202906e-05,
                2.902312677150514e-06,
                3.288747889284851e-06
            ],
            [
                0.9999999226557869,
                0.9999998642566381,
                0.9999998257020591,
                0.9999999006880076,
                0.9999998024946332,
                0.999999872480942,
                0.9999997897567343,
                0.9999998642566219,
                0.9999998874648514,
                0.9999998874647575
            ],
            [
                0.9999996533672137,
                0.999999789756684,
                0.9999995262095552,
                0.9999998362623334,
                0.9999997300421904,
                0.9999986290421405,
                0.9999993524050479,
                0.9999998144608319,
                0.9999996072138001,
                0.9999993916407461
            ],
            [
                0.9999990577552953,
                0.9999991148426481,
                0.9999986290424676,
                0.9999989969862721,
                0.9999984465022478,
                0.9999995262094427,
                0.999999495652472,
                0.9999994284993493,
                0.9999991148426486,
                0.9999990577550707
            ],
            [
                2.699578096403948e-07,
                7.338208055680009e-07,
                4.450848927658745e-07,
                3.4663262111182307e-07,
                1.8553919030858602e-07,
                6.475949526020042e-07,
                5.04347287955046e-07,
                4.450852641737424e-07,
                1.6373764721072816e-07,
                4.450852641737424e-07
            ],
            [
                1.670142582682936e-05,
                1.1478772231086046e-05,
                7.889263526266196e-06,
                1.0677028700363782e-06,
                7.338208055579897e-07,
                7.889260704818233e-06,
                2.260325106237323e-06,
                4.222833947932061e-06,
                3.2887478892504536e-06,
                2.260324567337161e-06
            ],
            [
                0.9999999176674454,
                0.9999999123575465,
                0.9999998802069587,
                0.9999997463982241,
                0.9999998642567351,
                0.9999987901343173,
                0.9999997617631753,
                0.9999997463981637,
                0.9999999358793639,
                0.9999997897565588
            ]
        ]
    },
    {
        "q_id": "9217_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                5.04347528440776e-07,
                1.7603440527222532e-06,
                1.0129988564974359e-05,
                4.4508505193932864e-07,
                1.8553919030776337e-07,
                2.382369667929001e-07,
                2.699577774560111e-07,
                2.1024326584582131e-07,
                2.6995774527718623e-07,
                5.715006514176113e-07
            ],
            [
                1.994730434879465e-06,
                4.4508494582314646e-07,
                1.8553903548231313e-07,
                9.931186222523604e-08,
                6.475950298011458e-07,
                0.705785040214066,
                2.3823696679230424e-07,
                1.8553916819032217e-07,
                3.466325797896173e-07,
                0.9999952149043669
            ],
            [
                0.9999485577864307,
                9.931199245292204e-08,
                0.9999869928700016,
                4.450849458200093e-07,
                0.9999599362983708,
                0.9999898700090285,
                2.5612825160271407e-06,
                0.999988521234617,
                1.6373774480479287e-07,
                0.9999852610215548
            ],
            [
                3.9278605979534166e-07,
                8.315281267882195e-07,
                3.9278610661902853e-07,
                5.043476486915964e-07,
                3.0590215399183813e-07,
                9.422445939054222e-07,
                8.315282259138311e-07,
                1.067703379154416e-06,
                6.475950297971703e-07,
                2.3823688159237777e-07
            ],
            [
                5.422220909009474e-06,
                3.927863407379485e-07,
                0.9999949062925721,
                0.9991959139866451,
                3.288750241561788e-06,
                0.9999852610145286,
                0.9999910602994398,
                1.0677028700422047e-06,
                1.5534971990126997e-06,
                1.2098652508424818e-06
            ],
            [
                3.059021539909339e-07,
                0.9999869928653452,
                0.9999967112513277,
                0.9999962733602731,
                1.6373764721039308e-07,
                0.9999934595627781,
                0.9999967112517204,
                0.9999898700114401,
                2.10243290909724e-07,
                0.9999987121046312
            ],
            [
                7.338213304363436e-07,
                1.370957860576702e-06,
                2.6995790618252024e-07,
                8.315279285351409e-07,
                0.9999910602994382,
                1.0677027427624903e-06,
                0.9999756997534994,
                0.9999810748495163,
                0.9999945777797399,
                5.043472278322555e-07
            ],
            [
                0.9999934595619981,
                0.9999910603037021,
                0.9999885212305166,
                2.3823690999290963e-07,
                2.1024334103553052e-07,
                0.9999885212318911,
                0.9999485577620417,
                0.9999869928730976,
                5.043474683220276e-07,
                0.9999967112513283
            ],
            [
                0.9999987901347497,
                0.9999991148427534,
                0.9999988634364251,
                0.9999994631248682,
                9.422447062150634e-07,
                2.699577774585891e-07,
                0.9999942280813493,
                0.9999970976866323,
                0.9999942280799734,
                0.9999967112505443
            ],
            [
                0.9999980052707556,
                0.9999995262094987,
                0.9999992661790198,
                5.043475885674441e-07,
                0.9999990577556315,
                3.288749065406658e-06,
                0.999999712631344,
                6.475947210046347e-07,
                8.31527928532683e-07,
                0.9999989969860318
            ],
            [
                0.9999962733593845,
                0.9999952149032255,
                0.9999957771680675,
                0.9999957771670611,
                0.9999967112497598,
                0.9999967112521122,
                0.999995777165047,
                0.999993855824668,
                0.9999957771665575,
                0.9999974387174848
            ],
            [
                3.288747889284851e-06,
                0.9999251537908458,
                0.9999885212264108,
                1.3709572068354007e-06,
                3.466326211105621e-07,
                6.9622587397397306e-06,
                0.9999832985702161,
                6.962257079889302e-06,
                0.9999938558254013,
                0.9999832985801692
            ],
            [
                1.5534977545384963e-06,
                0.9999988634364252,
                0.9999987121050922,
                3.2887482812745586e-06,
                0.9999993524052793,
                0.9999980052702794,
                0.9999993524050477,
                0.999999310639119,
                0.9999995818814266,
                0.9999921107383635
            ],
            [
                3.0590229985449037e-07,
                6.475947982002148e-07,
                2.6995790618252024e-07,
                1.8553919030708836e-07,
                3.4663266243111764e-07,
                3.2887494574832472e-06,
                2.1024326584582131e-07,
                2.699577774560111e-07,
                1.1253506814797596e-07,
                1.444980726324838e-07
            ],
            [
                2.1024339116082313e-07,
                0.9999997300421262,
                0.999988521230513,
                0.9999994956527122,
                3.059021904580685e-07,
                0.9999962733598291,
                1.6373766672888118e-07,
                0.9999945777829724,
                3.059021175247079e-07,
                2.1024336609843824e-07
            ],
            [
                0.9999687980886571,
                1.9947299593078385e-06,
                3.7266401726359486e-06,
                0.9999869928730976,
                0.9999910603036979,
                5.043473480777865e-07,
                3.927863407379485e-07,
                2.69957906184239e-07,
                3.927863407379485e-07,
                1.2098656835224664e-06
            ],
            [
                0.9999989969860319,
                0.9999995818813269,
                0.9999997463980125,
                0.9999989969859122,
                0.9999991684718735,
                0.999998540623432,
                5.71500651413193e-07,
                5.04347528440776e-07,
                0.9999992188516695,
                0.9999997463982241
            ],
            [
                0.9999999067049832,
                0.9999869928746487,
                0.999998239657417,
                0.9999989969860319,
                0.9999999006880786,
                6.825597214718257e-08,
                0.9999999123575569,
                0.999998629043284,
                0.9999998724809419,
                0.9999998461826588
            ],
            [
                0.9999852610215635,
                0.9999934595619995,
                2.382369383923073e-07,
                6.475947982002148e-07,
                0.9999967112517216,
                0.999995777166054,
                0.9999934595651181,
                8.315281267882195e-07,
                0.9999962733616063,
                0.9999898700054067
            ],
            [
                7.734428685047173e-08,
                1.8553914607237736e-07,
                2.102433159721477e-07,
                3.466326211105621e-07,
                6.475946438042047e-07,
                1.1253512180925583e-07,
                1.4738980214280206e-05,
                5.71500515159253e-07,
                1.855391239544352e-07,
                8.764241182641775e-08
            ],
            [
                0.9999987901343169,
                0.9999998874648782,
                0.999999802494586,
                0.9999998642566866,
                0.9999993524052794,
                0.9999997897566841,
                0.9999995262095552,
                0.9999974387187074,
                0.9999869928668924,
                0.9999983463096264
            ],
            [
                0.9999930377454146,
                1.3709572068422585e-06,
                3.059022269250683e-07,
                5.04347468323289e-07,
                2.902313023039776e-06,
                0.9999852610127696,
                0.9999921107374183,
                1.1478769494396542e-05,
                0.9999930377429245,
                0.9999921107402411
            ],
            [
                8.939693107288474e-06,
                4.785093924389007e-06,
                1.9947299593078385e-06,
                6.144176066943187e-06,
                5.422218969895357e-06,
                4.22283545819819e-06,
                1.7603425837903113e-06,
                6.144176066943187e-06,
                4.785095065232451e-06,
                7.734421308914719e-08
            ],
            [
                0.9999997897566841,
                0.999998346309824,
                0.9999997897565588,
                8.315277302857965e-07,
                0.999999887464932,
                0.9999970976887079,
                0.9999989969857928,
                0.999999581881277,
                0.9999991148428589,
                0.9999957771665605
            ],
            [
                6.825598028392069e-08,
                5.315788140303327e-08,
                5.715005832872586e-07,
                5.043472879540142e-07,
                5.04347287955046e-07,
                0.999991060300508,
                3.927862002654366e-07,
                5.043474683220276e-07,
                2.382368531929327e-07,
                1.1253506814842375e-07
            ],
            [
                0.9999885212332509,
                1.1253514863909295e-07,
                0.9999994631249962,
                1.8553905760024476e-07,
                0.9999930377454167,
                0.9999910603015734,
                0.9999251538003523,
                0.9999960330121968,
                0.999975699747736,
                0.9999994631249961
            ],
            [
                2.3823682479181176e-07,
                4.450852641717689e-07,
                0.9999952149037974,
                1.4449802095609418e-07,
                1.1253510839355284e-07,
                2.3823688159237777e-07,
                3.0590215399183813e-07,
                4.450851580540182e-07,
                0.9999960330131428,
                0.9999934595596613
            ],
            [
                4.450850519403407e-07,
                0.9999964991451723,
                1.0129987357020188e-05,
                4.785095065171522e-06,
                0.9999996743688199,
                2.3823690999290963e-07,
                0.9999938558224728,
                0.9999930377454169,
                3.2887506336086064e-06,
                0.9999978766222983
            ],
            [
                0.9999724643122624,
                0.9999771720056161,
                9.422445939032799e-07,
                0.9999599362888593,
                0.9999964991447529,
                0.9999987121044777,
                0.9999985406237794,
                0.9999994631249962,
                0.999998346309626,
                0.9999975938973751
            ],
            [
                0.9999988634361544,
                0.9999995262092728,
                0.9999998874648246,
                0.9999989969857924,
                0.9999998461826588,
                9.422448185435711e-07,
                0.9999999273418961,
                0.9999996072136125,
                0.9999997126315496,
                0.9999975938973745
            ],
            [
                0.9999978766210328,
                0.9999970976866327,
                2.3823696679230424e-07,
                3.466325384661554e-07,
                0.9999993916411811,
                0.9999997463981032,
                0.9999975938985237,
                0.9999975938985232,
                0.9999978766222989,
                0.9999995549148951
            ],
            [
                0.9999646437577896,
                8.315284241650899e-07,
                0.999999391641036,
                1.8925143728749452e-05,
                0.9999962733620507,
                5.043473480777865e-07,
                0.9999810748517819,
                0.9999990577554064,
                0.9999992188515765,
                0.9999852610233203
            ],
            [
                4.222834451327159e-06,
                8.31528424162821e-07,
                0.9999646437451162,
                3.927862470899887e-07,
                0.9999852610197931,
                2.6995784182073116e-07,
                0.9997694933150904,
                0.9995694430199438,
                0.9999687980961285,
                3.466325797888292e-07
            ],
            [
                3.927862002654366e-07,
                0.999996499146839,
                4.450852111148132e-07,
                0.9999546021260809,
                0.999996499146422,
                0.9999417087487099,
                0.9999724643187934,
                1.2098652508424818e-06,
                0.9999869928669063,
                2.561281600076256e-06
            ],
            [
                0.9999993106390371,
                0.9999995262092729,
                0.9999960330155095,
                1.760343213335281e-06,
                0.9999974387174859,
                0.9999995549148951,
                0.9999992661792826,
                0.9999996940977732,
                0.9999995262094987,
                0.9999972735297326
            ],
            [
                9.422449308716635e-07,
                0.9999970976876709,
                2.382368815916736e-07,
                3.466327037512053e-07,
                0.999997876622045,
                0.9999982396563678,
                8.93970056668775e-06,
                8.315283250371857e-07,
                0.9999969105062908,
                0.9999974387174855
            ],
            [
                4.222831934379152e-06,
                5.715006514176113e-07,
                7.338212429562581e-07,
                9.931190958076104e-08,
                1.994729721518893e-06,
                1.8553910183649565e-07,
                2.2603248367949354e-06,
                9.931185038635267e-08,
                3.72663883989755e-06,
                4.450850519403407e-07
            ],
            [
                3.9278629391427843e-07,
                1.0677029973056687e-06,
                2.902312677150514e-06,
                3.46632497145457e-07,
                5.71500719545698e-07,
                3.466326211113502e-07,
                6.475945666051092e-07,
                2.10243290909724e-07,
                1.7603434231777837e-06,
                1.3709568799879344e-06
            ],
            [
                0.9999997761971582,
                0.9999998362622747,
                0.9999975938973746,
                0.9999945777790938,
                0.9999986290423033,
                0.999992110735543,
                0.9999898700041968,
                0.9999969105055532,
                0.9999997463981032,
                0.999999712631344
            ],
            [
                1.444979692797559e-07,
                0.9999930377429237,
                3.288749849529972e-06,
                3.9278634073625165e-07,
                1.0677026154806063e-06,
                9.93118503859575e-08,
                6.475947982037486e-07,
                1.9947299593078385e-06,
                6.144172404738491e-06,
                6.962255419931625e-06
            ],
            [
                4.4508499888275247e-07,
                9.422448185534261e-07,
                3.05902263391829e-07,
                7.734421308914719e-08,
                1.855391239547094e-07,
                1.2751908849167202e-07,
                1.7603434231833873e-06,
                3.927862002663297e-07,
                2.6995790618350237e-07,
                1.2751905808881762e-07
            ],
            [
                0.9999994284994851,
                0.9999925887201394,
                1.855391239544352e-07,
                0.9999967112513296,
                0.9999997300421262,
                2.3823702359290413e-07,
                0.9999993106386261,
                0.9999998024945624,
                0.9999997897566341,
                0.9999993524049705
            ],
            [
                0.9999994631251242,
                0.9999993916407459,
                0.9999996072139402,
                0.9999984465020607,
                0.9999996533672549,
                0.9999987901346055,
                0.9999988634362899,
                1.8553916819032217e-07,
                0.9999999067049943,
                1.0
            ],
            [
                1.6373766672973748e-07,
                5.043476486915964e-07,
                2.5612831267202583e-06,
                3.4663253846718004e-07,
                1.637377057673536e-07,
                2.102433159721477e-07,
                1.855391239539711e-07,
                1.209865827752005e-06,
                4.450850519403407e-07,
                1.5534984953552536e-06
            ],
            [
                0.9999925887210236,
                0.9999985406237798,
                0.9999989322966212,
                1.3709568799919866e-06,
                0.9999945777784524,
                3.05902226923399e-07,
                0.9999977396762427,
                0.9999988634365609,
                0.9999986290432842,
                0.9999984465018756
            ],
            [
                0.9999987901340286,
                0.9999970976883632,
                0.999999428499417,
                0.9999999176675829,
                3.9278634073625165e-07,
                1.4449798650476187e-07,
                0.9999992188512973,
                0.9999998257021838,
                0.9999996533672963,
                0.9999999176675338
            ],
            [
                1.4449802095609418e-07,
                2.3823685319244518e-07,
                2.5612825159677387e-06,
                0.9999724643056915,
                3.927862002654366e-07,
                8.315279285351409e-07,
                1.637377448057981e-07,
                7.338213304316717e-07,
                2.1444948409679848e-05,
                0.9999843104559187
            ],
            [
                9.422448185435711e-07,
                1.5534977545603963e-06,
                1.2098659719601033e-06,
                1.5534975693869924e-06,
                5.422219616184461e-06,
                1.8925157265710765e-05,
                3.7266406167827664e-06,
                1.760343423160973e-06,
                7.338213304316717e-07,
                2.561282210701601e-06
            ],
            [
                4.222834954801051e-06,
                4.785096206076165e-06,
                0.00010889688339134737,
                1.1478766757718129e-05,
                2.2603251062147097e-06,
                8.939699501416646e-06,
                8.939693107288474e-06,
                8.93969843573914e-06,
                3.2887502415767434e-06,
                0.999999495652592
            ],
            [
                3.9278615344178325e-07,
                9.931193325852072e-08,
                5.043474683220276e-07,
                9.422450431989127e-07,
                8.315283250394546e-07,
                1.2751899728311609e-07,
                3.059021175247079e-07,
                1.3709568799919866e-06,
                1.2751905808881762e-07,
                3.9278624708775595e-07
            ],
            [
                0.9999885212346216,
                0.9999921107355378,
                0.9999938558246705,
                0.99997246431224,
                8.315278294114555e-07,
                1.8553910183674878e-07,
                0.9999852610127773,
                0.9999417087208126,
                0.9999822214460572,
                0.9999934595620003
            ],
            [
                4.222835458148261e-06,
                2.9023123311583482e-06,
                2.5612819054133693e-06,
                9.422447062294175e-07,
                1.0677028700422047e-06,
                1.7603434231833873e-06,
                2.2603245673443566e-06,
                6.962257909842961e-06,
                3.726638839878908e-06,
                1.2098661162056318e-06
            ],
            [
                0.9999983463108094,
                0.9999957771645454,
                0.9999974387187064,
                0.9999993916406735,
                0.9999977396751648,
                0.9999994631250604,
                0.9999974387165704,
                0.9999969105066595,
                0.9999921107383655,
                6.023576347299818e-08
            ],
            [
                2.6995790618252024e-07,
                1.6373770576776313e-07,
                1.275190276859705e-07,
                1.2751910369275402e-07,
                8.315278294097538e-07,
                1.637377448057981e-07,
                6.962253760024999e-06,
                1.4449795205429202e-07,
                1.6373764721039308e-07,
                4.4508510499737865e-07
            ],
            [
                0.9999993916411085,
                0.9999952149055082,
                0.9999967112521122,
                0.9999998555020307,
                0.999989870004203,
                0.9999942280799743,
                0.9999930377437547,
                0.9999992188514835,
                0.9999949062943932,
                0.9999810748540369
            ],
            [
                0.9999997126313783,
                0.9999980052700412,
                0.9999930377462445,
                1.1253509497883659e-07,
                5.715006514151423e-07,
                2.102434412875379e-07,
                0.9999964991455874,
                1.5534975693979422e-06,
                0.9999993524052792,
                0.999996033014561
            ],
            [
                0.9999970976876701,
                0.999992110733659,
                0.9999687980812632,
                0.9999785550592795,
                0.9999910602994387,
                0.9999852610233118,
                0.9999485578049669,
                1.9947301970972664e-06,
                0.9999852610145223,
                0.9999852610110147
            ],
            [
                0.9999989322973848,
                0.9999998874648246,
                1.8553907971855875e-07,
                6.475945666033422e-07,
                3.466326211105621e-07,
                0.9999993106391191,
                1.8553905760062447e-07,
                0.9999994956527123,
                0.999996033014087,
                0.9999885212305183
            ],
            [
                1.275190276859705e-07,
                2.102434412871794e-07,
                2.3823696679230424e-07,
                1.444980209564556e-07,
                4.139936560330104e-08,
                9.931196877517082e-08,
                1.275190580884987e-07,
                1.1253512180925583e-07,
                1.2751905808881762e-07,
                2.10243290909724e-07
            ],
            [
                4.450849988798682e-07,
                5.04347528440776e-07,
                2.6995777745711594e-07,
                3.2887494574518405e-06,
                0.9999970976876701,
                1.6373766672888118e-07,
                3.059022998569248e-07,
                1.6373764721072816e-07,
                8.315278294038928e-07,
                2.1024339116082313e-07
            ],
            [
                2.1024331597262577e-07,
                3.288749457469787e-06,
                3.9278605979534166e-07,
                2.90231094723893e-06,
                1.9947292459347367e-06,
                1.9947304348862686e-06,
                1.3709570434178922e-06,
                3.059022269254856e-07,
                4.450852111148132e-07,
                2.902312677150514e-06
            ],
            [
                1.7603430034867993e-06,
                0.9999877809225577,
                2.2603242978665707e-06,
                0.9999991148430702,
                0.9999949062962169,
                5.715003789017068e-07,
                0.9999996940977732,
                0.9999988634357481,
                0.9999997761971849,
                0.999999114843387
            ],
            [
                0.9999996940976638,
                0.99999834631002,
                7.338210679979539e-07,
                0.9999984465022461,
                0.9999982396559483,
                3.466325384661554e-07,
                6.475949526003845e-07,
                1.2098662604291696e-06,
                6.962254589978262e-06,
                4.450849988798682e-07
            ],
            [
                0.9999982396572077,
                0.9999999176675239,
                0.9999996533673376,
                0.9999986290423036,
                0.9999957771650491,
                0.999999554914789,
                0.9999994956527724,
                0.9999992661788449,
                0.9999999067050609,
                0.9999967112505455
            ],
            [
                0.999999428499485,
                0.9999957771660547,
                0.9999989969854338,
                9.422448185435711e-07,
                0.999997097687324,
                0.9999972735300563,
                0.9999987121041709,
                0.9999981261250638,
                0.9999988634364254,
                0.9999989969860318
            ],
            [
                1.444980726324838e-07,
                1.855391681891831e-07,
                9.931189774187203e-08,
                1.7603440527286572e-06,
                0.9999952149037975,
                0.9999982396574171,
                3.466327450756327e-07,
                0.9999934595612181,
                0.9999938558224711,
                0.9999993106389546
            ],
            [
                0.9999960330150337,
                0.9999981261243942,
                0.9999998874649184,
                1.5534971990126997e-06,
                3.7266379513162962e-06,
                2.561282516066741e-06,
                0.9999997617630616,
                0.9999988634366962,
                0.9999995549148951,
                0.9999996743688975
            ],
            [
                1.1253516205489029e-07,
                5.715002426486762e-07,
                1.2751908849088918e-07,
                3.059021904580685e-07,
                1.275190580884987e-07,
                3.059021175261338e-07,
                7.338210680021253e-07,
                5.043475885696228e-07,
                0.9999957771675643,
                0.9999852610110133
            ],
            [
                0.999995214903227,
                0.9999852610145374,
                0.9999977396757029,
                0.9999724643122437,
                0.9999921107345991,
                0.9999785550464995,
                0.9999038975510843,
                3.726637951387472e-06,
                0.9999921107383596,
                0.9999989969861512
            ],
            [
                0.00010889690932541937,
                3.2887502415767434e-06,
                0.9999975938973745,
                5.422217030781934e-06,
                1.5534983101644536e-06,
                4.785092783545836e-06,
                4.785092783519724e-06,
                3.288748281329893e-06,
                5.043473480766399e-07,
                7.889266347786918e-06
            ],
            [
                3.466327450756327e-07,
                1.8553919030776337e-07,
                2.3823685319244518e-07,
                5.715005832872586e-07,
                1.6373766672973748e-07,
                3.059022269250683e-07,
                1.6373776432481905e-07,
                1.855391239539711e-07,
                9.422445939002803e-07,
                3.0590237278532086e-07
            ],
            [
                0.9999994956527123,
                0.9999993916408911,
                0.9999967112505452,
                0.9999975938979496,
                0.9999985406236058,
                0.9999984465024315,
                0.999999653367503,
                0.9999996072137531,
                0.9999996310114599,
                0.9999996743688586
            ],
            [
                5.043476486915964e-07,
                1.8553903548231313e-07,
                0.9999810748472785,
                1.6373776432481905e-07,
                7.734414854823498e-08,
                0.9999251537818918,
                0.9999930377462469,
                9.931188590255539e-08,
                9.931193325852072e-08,
                0.9999925887219027
            ],
            [
                3.927861066170637e-07,
                1.8553919030776337e-07,
                1.4449805540740185e-07,
                2.3823690999160957e-07,
                9.931190958076104e-08,
                1.2098661161982042e-06,
                5.71500651413193e-07,
                1.4449802095609418e-07,
                3.2887502415767434e-06,
                5.043474082005342e-07
            ],
            [
                0.9999687980924427,
                2.69957906184239e-07,
                0.9999960330131427,
                1.8553905760024476e-07,
                1.8553905760024476e-07,
                0.9999989969859122,
                0.9999986290431203,
                0.9999724642958162,
                2.1024326584639497e-07,
                0.9999898700090272
            ],
            [
                5.715002426460124e-07,
                2.102433159721477e-07,
                0.9999925887165994,
                0.9999852610180504,
                1.1253524254615121e-07,
                0.9999904837437793,
                7.73441946488886e-08,
                5.71500515159253e-07,
                3.059021175247079e-07,
                3.9278615344178325e-07
            ],
            [
                0.9999998802069444,
                0.9999997617629764,
                0.9999977396757035,
                0.9999984465016905,
                0.9999991148427535,
                0.9999898700078206,
                0.9999985406237795,
                0.9999996940977731,
                0.9999993524054336,
                0.9999991148433864
            ],
            [
                0.9999993106390368,
                0.9999972735300555,
                0.9999981261237235,
                3.927860597945825e-07,
                0.9999151889794307,
                0.9999945777790935,
                5.043476486883855e-07,
                0.999997097688016,
                0.9999910603005041,
                0.9999785550593026
            ],
            [
                2.6995784182073116e-07,
                1.2751899728286965e-07,
                2.102433159721477e-07,
                6.475949526020042e-07,
                6.825598842035714e-08,
                1.1253526937656726e-07,
                1.209865539295696e-06,
                2.382368247924618e-07,
                1.0677026154806063e-06,
                5.043473480777865e-07
            ],
            [
                1.147876812620341e-05,
                0.9999992661789325,
                0.9999998724809115,
                0.9999997897567342,
                9.422447062294175e-07,
                4.222834451403972e-06,
                3.726639284144195e-06,
                4.785092783519724e-06,
                1.994729008151319e-06,
                6.82560128305259e-08
            ],
            [
                1.5534971990169383e-06,
                3.7266410611465547e-06,
                4.4508510499849186e-07,
                1.209865827752005e-06,
                1.2751901248454963e-07,
                1.209865827752005e-06,
                1.9947301970972664e-06,
                9.422444815814404e-07,
                8.315279285351409e-07,
                1.1253509497883659e-07
            ],
            [
                5.043474683220276e-07,
                0.9999969105062905,
                3.927861066170637e-07,
                1.3007130015488633e-05,
                4.450849458218309e-07,
                5.715003789017068e-07,
                1.0677029973192638e-06,
                3.05902263389638e-07,
                0.9999986290427935,
                4.450852111148132e-07
            ],
            [
                5.715003789046955e-07,
                1.1253510839355284e-07,
                0.999986992874644,
                0.9999930377437558,
                2.6995784182140636e-07,
                0.999988521231884,
                6.023576347299818e-08,
                0.9999988634366962,
                0.9999978766212857,
                0.9999756997564174
            ],
            [
                0.9999921107383618,
                0.999981074851781,
                1.5534983101602148e-06,
                0.999994577781033,
                0.9999852610145286,
                2.561281600086738e-06,
                0.999992110736478,
                5.422217677152175e-06,
                0.9999974387171804,
                0.9999852610180398
            ],
            [
                1.1253510839355284e-07,
                0.9999962733616057,
                0.9999921107355387,
                0.9999930377437543,
                5.043476486902204e-07,
                0.999988521235987,
                0.9999994956523515,
                0.9999934595612191,
                2.6995777745711594e-07,
                0.9999898700102391
            ],
            [
                0.9999998642566542,
                0.9999998257021006,
                0.9999999226557132,
                0.9999998942830106,
                0.9999998461827322,
                0.9999998024946801,
                1.637377057673536e-07,
                0.9999998461827322,
                0.9999998724809267,
                0.9999969105055533
            ],
            [
                4.222831934352267e-06,
                0.9999994631249962,
                3.059021539909339e-07,
                0.9999852610198049,
                0.9999974387177906,
                1.4449798650476187e-07,
                8.315282259089153e-07,
                4.2228329411708495e-06,
                2.8453364239757298e-08,
                0.9999960330126686
            ],
            [
                7.338208930443633e-07,
                2.3823696679230424e-07,
                1.1253514863909295e-07,
                3.7266383956509585e-06,
                3.466327450756327e-07,
                1.8553907971855875e-07,
                7.338210680002898e-07,
                9.422444815814404e-07,
                3.9278610661902853e-07,
                7.338210680002898e-07
            ],
            [
                0.9999957771650493,
                1.2098659719716573e-06,
                0.9999930377454153,
                6.475950298011458e-07,
                0.9999957771660564,
                0.9999925887183713,
                0.9999967112513289,
                0.9999955048178886,
                0.9999970976869792,
                0.999993459564337
            ],
            [
                0.9999993106392012,
                0.9999997761971315,
                0.9999998724809875,
                0.9999998874649318,
                0.9999992188513903,
                0.999996273362051,
                0.9999994284996213,
                0.9999986290431208,
                0.9999996310115039,
                0.9999996072137999
            ],
            [
                0.9999970976883635,
                0.9999967112521136,
                0.9999997463982241,
                0.9999995262093859,
                0.9999998874648112,
                0.9999989969857929,
                0.9999998461827322,
                0.9999991684719726,
                0.9999991148427535,
                0.9999997126313441
            ],
            [
                0.9999910603005044,
                1.2751902768478173e-07,
                1.4449805540740185e-07,
                2.102433410343832e-07,
                2.1024326584582131e-07,
                1.4449802095609418e-07,
                3.059021175247079e-07,
                1.8553907971758842e-07,
                1.637377643243723e-07,
                1.4449805540651476e-07
            ],
            [
                7.338208055664991e-07,
                0.9999756997621945,
                1.2098659719757836e-06,
                1.2098661162056318e-06,
                6.144173869558639e-06,
                1.7603425837903113e-06,
                1.0677028700422047e-06,
                1.855391239544352e-07,
                4.4508494582405734e-07,
                2.561282210740037e-06
            ],
            [
                0.9999992661787576,
                1.637377057673536e-07,
                0.9999987901343171,
                0.9999930377454189,
                0.9999957771680701,
                0.9999989969854343,
                0.9999986290429574,
                0.9999960330145632,
                0.9999996743687035,
                0.9999996310116359
            ],
            [
                0.9999898700126519,
                0.9999949062937862,
                0.9999930377454156,
                0.9999724642958349,
                0.999997739675164,
                0.9999930377429237,
                0.9999987901343167,
                0.9999869928668956,
                0.9999994284993488,
                1.3709572068422585e-06
            ],
            [
                0.9999998461826038,
                1.5534979397740895e-06,
                1.8553907971855875e-07,
                7.734425918979532e-08,
                0.9999417087207821,
                3.0590237279085045e-07,
                0.9999756997477232,
                0.9999832985821582,
                1.8553914607237736e-07,
                0.9999994631249322
            ],
            [
                0.9999417087417479,
                0.9999970976869789,
                0.9999995818812272,
                0.9999599362935889,
                0.9999945777790945,
                1.1253506814797596e-07,
                0.9999898700066175,
                0.999993855823937,
                7.338208055664991e-07,
                1.6373766672973748e-07
            ],
            [
                5.043476486902204e-07,
                1.5534977545886537e-06,
                3.059022269250683e-07,
                5.715003788993679e-07,
                1.5534984953510149e-06,
                2.69957906184239e-07,
                1.8553919030776337e-07,
                2.1024326584582131e-07,
                6.475947210031623e-07,
                4.450852641717689e-07
            ],
            [
                2.2603242978778778e-06,
                6.475949526003845e-07,
                7.889259764517575e-06,
                1.6373764721039308e-07,
                8.939699501416646e-06,
                9.93120161306789e-08,
                1.0677026154774503e-06,
                0.0001795279663064015,
                5.715003789033962e-07,
                5.715005832886879e-07
            ],
            [
                0.9999991148429644,
                0.9999977396762418,
                0.9999964991447527,
                1.8925155009354808e-05,
                0.9999832985821646,
                3.466325384661554e-07,
                0.9999832985821582,
                0.9999989969854338,
                0.9999988634366962,
                0.9999995549147891
            ],
            [
                1.4449798650551755e-07,
                2.6995768091310296e-07,
                2.1024336609843824e-07,
                0.9999921107355405,
                5.043472879525233e-07,
                8.764255809528314e-08,
                0.9999980052700419,
                2.3823702359290413e-07,
                3.9278615344178325e-07,
                8.764247451307293e-08
            ],
            [
                3.9278605979208185e-07,
                4.450851049959619e-07,
                4.450849988811838e-07,
                5.043472879525233e-07,
                5.715003788993679e-07,
                3.466327037548308e-07,
                2.6995777745711594e-07,
                2.102433660979124e-07,
                1.5534975693792215e-06,
                8.315279285351409e-07
            ],
            [
                0.9999996743686645,
                0.9999998461826038,
                0.9999990577555189,
                0.9999996743688586,
                0.9999995818811774,
                0.9999995549150543,
                0.9999999123575882,
                0.9999998257021422,
                0.9999995818810777,
                0.9999996072136594
            ],
            [
                0.9999996940978826,
                0.9999992661788448,
                0.9999986290421398,
                0.9999994956523515,
                0.9999996310113279,
                8.7642516304188e-08,
                0.9999996533672137,
                0.9999994956527122,
                0.9999987121049383,
                0.9999997617631752
            ],
            [
                0.9999988634357481,
                0.9999877809181721,
                0.9999988634366964,
                0.9999974387168743,
                0.9999991684719727,
                7.338210679979539e-07,
                6.475945666033422e-07,
                0.999996033015506,
                0.9999991148427534,
                0.9999997300421906
            ],
            [
                0.9999970976866323,
                9.422442569290178e-07,
                0.9999869928715471,
                2.561281600076256e-06,
                0.9999151889288207,
                1.3709568799919866e-06,
                8.315282259138311e-07,
                0.9999985406237795,
                0.9999938558239359,
                1.5534973842030142e-06
            ],
            [
                0.9999810748472882,
                0.9999960330140865,
                3.4663249714612693e-07,
                0.9999960330126686,
                5.04347528446051e-07,
                0.9999921107383588,
                0.9999898700090276,
                1.4449803818215767e-07,
                0.9999972735284304,
                0.9999938558246693
            ],
            [
                0.9999985406234316,
                0.9999925887174875,
                0.9999949062968272,
                1.1253525596055243e-07,
                0.9999992188516696,
                0.9999960330136173,
                0.9999997463980125,
                0.9999994631251884,
                0.9999997300420939,
                0.9999996940976638
            ],
            [
                0.9999967112517197,
                0.9999998362623138,
                2.1024336609843824e-07,
                0.9999969105062902,
                0.9999994284994169,
                0.9999989322966213,
                0.9999955048200321,
                0.9999997126313098,
                0.9999999273417922,
                0.9999934595604392
            ],
            [
                0.9999945777803866,
                0.9999996310115039,
                0.9999996310115039,
                0.9999832985702132,
                0.9999988634364252,
                0.9999967112513277,
                0.99999916847227,
                0.9999646437325065,
                0.9999945777784474,
                0.9999910603015723
            ],
            [
                0.9999985406241276,
                0.9999994631248684,
                0.9999997463980427,
                2.1024341622368903e-07,
                0.9999998724809115,
                0.999999674368781,
                0.9999994631248684,
                0.9999996072138935,
                0.9999942280779109,
                0.999999761763005
            ],
            [
                0.9999993524050476,
                0.9999980052700418,
                0.9999998724809875,
                0.9999997300421262,
                0.9999997761970515,
                0.999994906292574,
                0.9999993524048932,
                0.9999998144608098,
                0.9999995818811276,
                2.9023116392097746e-06
            ],
            [
                0.9999996533674204,
                0.9999997761972116,
                6.475946438055299e-07,
                0.9999992188516696,
                0.9999934595643382,
                0.9999997300420939,
                0.9999997300422548,
                0.9999964991447536,
                0.999999266178845,
                0.9999986290431208
            ],
            [
                5.715003789033962e-07,
                2.699576809143613e-07,
                4.2228339479858295e-06,
                3.059023727894942e-07,
                6.475947210012481e-07,
                3.927860597945825e-07,
                2.3823685319244518e-07,
                9.422448185478557e-07,
                4.450849988811838e-07,
                3.9278629391427843e-07
            ],
            [
                0.9999038975863911,
                0.9999998024945624,
                2.1444940745839484e-05,
                0.9999995262093292,
                0.9999993916411811,
                5.043475284430694e-07,
                0.9999996940978096,
                1.6373766672973748e-07,
                6.475947982037486e-07,
                3.653481209178873e-08
            ],
            [
                0.9999994284993489,
                0.9999998362622357,
                0.999999653367255,
                0.9999994631248041,
                0.9999978766220449,
                0.9999996940977003,
                0.9999998555020135,
                0.9999974387168749,
                0.9999994284996895,
                0.9999998144608762
            ],
            [
                9.422445939054222e-07,
                5.043474683240344e-07,
                1.1253512180925583e-07,
                9.422447062294175e-07,
                2.561281294760143e-06,
                1.1253506814797596e-07,
                3.0590237279085045e-07,
                2.3823693839325527e-07,
                9.422448185534261e-07,
                1.3709575337159875e-06
            ],
            [
                9.931187406368048e-08,
                0.9999991148432809,
                0.9999949062956077,
                2.2603245673443566e-06,
                0.9999986290431203,
                3.46632497145457e-07,
                6.144173137170873e-06,
                0.9999982396565774,
                2.5612834320563895e-06,
                1.3709572068522336e-06
            ],
            [
                0.9999996072136126,
                0.9999974387171805,
                0.9999993524052794,
                0.9999977396748956,
                0.9999987121043247,
                3.059022269250683e-07,
                0.9999994631251884,
                4.450851580540182e-07,
                0.9999985406236063,
                1.1253518888531272e-07
            ],
            [
                1.7603425837606927e-06,
                3.4663266243111764e-07,
                2.6995777745711594e-07,
                3.05902226923399e-07,
                1.5534981249574276e-06,
                6.475951069932288e-07,
                2.6995790618252024e-07,
                5.04347348075149e-07,
                3.05902226923399e-07,
                3.4663253846316044e-07
            ],
            [
                0.9999995262092163,
                2.102433410343832e-07,
                0.9999985406241283,
                0.9999990577557437,
                0.9999987901343173,
                0.9999989969859123,
                0.999999495652592,
                0.9999945777810347,
                0.9999989322966213,
                0.9999989322966213
            ],
            [
                6.475945666063607e-07,
                9.422445939054222e-07,
                0.9999980052702803,
                0.9999997300421583,
                0.9999972735287556,
                0.9999991684718735,
                0.9999999226557776,
                8.3152792852928e-07,
                0.9999980052707556,
                0.9999980052700421
            ],
            [
                1.1253517547010071e-07,
                2.3823702359290413e-07,
                1.4449795205429202e-07,
                5.715006514167015e-07,
                7.734423152941018e-08,
                3.466326211113502e-07,
                5.715005832886879e-07,
                1.4449798650476187e-07,
                3.059021175255426e-07,
                6.023573475041126e-08
            ],
            [
                0.9999994284996895,
                2.102433660979124e-07,
                0.9999986290432843,
                0.9999957771645445,
                0.9999832985801749,
                1.9947292459265734e-06,
                1.2098661162056318e-06,
                3.0590215399183813e-07,
                4.450849988811838e-07,
                0.9999985406230836
            ],
            [
                7.338207180864763e-07,
                1.3709576971463352e-06,
                3.0590215399183813e-07,
                3.9278610661822475e-07,
                2.3823688159291947e-07,
                1.6373766672973748e-07,
                5.715005832895975e-07,
                5.422219616265831e-06,
                8.315283250371857e-07,
                2.2603234895372223e-06
            ],
            [
                1.0129994602895546e-05,
                0.9999949062943931,
                1.6373764721039308e-07,
                0.9999756997506004,
                1.6373762769138607e-07,
                0.9999974387177902,
                3.288747889284851e-06,
                2.2603251062450327e-06,
                0.9999983463104146,
                0.9999992661792823
            ],
            [
                0.9999980052709928,
                0.9999985406236055,
                0.9999993106387902,
                0.9999970976876702,
                0.9999986290426303,
                0.9999962733598307,
                1.3709575337016483e-06,
                0.9999962733616061,
                0.9999997617630616,
                0.999999825702163
            ],
            [
                9.422443692574719e-07,
                0.9999994956527722,
                0.9999967112493682,
                2.6995768091383957e-07,
                1.3709567165617364e-06,
                0.9999991684719727,
                0.9999975938968013,
                4.450849988811838e-07,
                2.2603234895372223e-06,
                7.889264466868659e-06
            ]
        ]
    },
    {
        "q_id": "9570_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            12,
            13,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            29,
            30,
            32,
            34,
            36,
            37,
            39,
            40,
            42,
            43,
            44,
            47,
            48,
            49,
            52,
            53,
            55,
            57,
            60,
            61,
            62,
            66,
            67,
            69,
            70,
            71,
            72,
            75,
            77,
            78,
            80,
            81,
            83,
            87,
            88,
            90,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            101,
            106,
            109,
            111,
            112,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            125
        ],
        "rewards": [
            [
                1.7603438428740716e-06,
                5.715005832827105e-07,
                1.760343213335281e-06,
                8.315284241597959e-07,
                1.2098658277451275e-06,
                1.5534975693869924e-06,
                5.043472879540142e-07,
                4.222831934202483e-06,
                5.043472879540142e-07,
                9.422447062094932e-07
            ],
            [
                1.1253525596174225e-07,
                8.315280276626197e-07,
                1.4449807263312446e-07,
                1.6373774480605869e-07,
                7.889261645427538e-06,
                1.444979692800516e-07,
                7.338207180898968e-07,
                NaN,
                1.8553919030858602e-07,
                1.855391681906175e-07
            ],
            [
                1.2098662604291696e-06,
                8.315277302747361e-07,
                1.3007125363908762e-05,
                NaN,
                2.5612828213818346e-06,
                1.5534984953510149e-06,
                6.144176799283803e-06,
                4.78509278348926e-06,
                1.2098658277181688e-06,
                1.8925141473186853e-05
            ],
            [
                0.9999994631251246,
                0.9999982396572089,
                0.9999994956524719,
                0.9999967112505492,
                0.9999993524053568,
                0.999997593897089,
                0.99999759389795,
                0.9999998642567351,
                0.9999989969857932,
                0.9999989969862716
            ],
            [
                1.0677024882009222e-06,
                8.315278294072958e-07,
                5.422220262636381e-06,
                2.7535704231844484e-05,
                1.0677024882009222e-06,
                1.2098653950656417e-06,
                2.1444940745371397e-05,
                3.927862939126708e-07,
                3.927863875584984e-07,
                1.994730197090463e-06
            ],
            [
                5.71500515159253e-07,
                1.5534979397740895e-06,
                2.382369951932796e-07,
                5.715002426475718e-07,
                2.2603237589779086e-06,
                1.3709573702822306e-06,
                6.475949526020042e-07,
                5.043475284430694e-07,
                7.338210680002898e-07,
                8.315281267882195e-07
            ],
            [
                0.9999962733620552,
                0.9999984465015064,
                6.475947982037486e-07,
                2.1024336609874897e-07,
                2.10243290909724e-07,
                NaN,
                2.4300234941261454e-05,
                9.931193325852072e-08,
                0.00020342699794109547,
                3.059021539909339e-07
            ],
            [
                2.5612819054133693e-06,
                2.3823702359138736e-07,
                1.8553912395160867e-07,
                2.1024336609874897e-07,
                6.023573475041126e-08,
                1.7603434231833873e-06,
                1.1253521571574156e-07,
                2.1024326584639497e-07,
                4.785095635655362e-06,
                6.825606165129312e-08
            ],
            [
                1.0677032518814388e-06,
                5.715004470326849e-07,
                3.466325797896173e-07,
                6.475947210046347e-07,
                5.043473480777865e-07,
                6.144175334418252e-06,
                5.043473480777865e-07,
                1.209866260432471e-06,
                4.450852641737424e-07,
                4.450849458218309e-07
            ],
            [
                0.9999962733620541,
                0.9999986290427941,
                0.9999986290423042,
                0.9999978766215399,
                0.9999986290429586,
                0.9999985406232584,
                0.9999982396563686,
                0.9999949062937941,
                0.9999982396561592,
                0.9999975938976626
            ],
            [
                2.2603234895053587e-06,
                1.9947301970972664e-06,
                6.475950298011458e-07,
                3.2887506336086064e-06,
                2.6995784182140636e-07,
                3.288748673376478e-06,
                1.0677027427600627e-06,
                1.7603425837791042e-06,
                1.4738987243236881e-05,
                4.785093353909723e-06
            ],
            [
                6.023572038912295e-08,
                1.2751904288710323e-07,
                1.637377448057981e-07,
                1.637377448057981e-07,
                3.059021175247079e-07,
                2.6995771309210433e-07,
                5.043476486915964e-07,
                5.715003107767143e-07,
                6.475947210012481e-07,
                1.2751901248454963e-07
            ],
            [
                1.2098655392871682e-06,
                1.2098662604247682e-06,
                6.475951069985296e-07,
                3.7266406168624155e-06,
                1.2098655392811161e-06,
                4.222833947932061e-06,
                2.260324836776948e-06,
                1.760343003481596e-06,
                1.5534981249496567e-06,
                1.7603427936263351e-06
            ],
            [
                8.315280276546789e-07,
                3.927862002625787e-07,
                9.422447062202052e-07,
                1.3709576971160984e-06,
                6.475951069985296e-07,
                8.315284241560147e-07,
                1.2098662604126641e-06,
                5.043475885674441e-07,
                6.47594952595231e-07,
                4.450849458218309e-07
            ],
            [
                2.6995784182140636e-07,
                9.931185038635267e-08,
                0.9999987901344616,
                2.1024336609874897e-07,
                0.9999985406237799,
                0.9999988634364254,
                2.1024334103581732e-07,
                4.4508494582405734e-07,
                5.043472278322555e-07,
                0.9999980052693291
            ],
            [
                1.7603425837855082e-06,
                3.120192625482384e-05,
                4.450848927658745e-07,
                1.8553903548231313e-07,
                0.9999892166878167,
                9.422445939054222e-07,
                6.144173137170873e-06,
                0.00026119040307950143,
                3.7266383956509585e-06,
                6.962254589914941e-06
            ],
            [
                3.0590237279032884e-07,
                3.059021175261338e-07,
                5.715006514176113e-07,
                7.734421308914719e-08,
                3.0590237279085045e-07,
                6.475949526003845e-07,
                1.6373766672973748e-07,
                1.7603438428800754e-06,
                7.338208055680009e-07,
                1.3007134667259441e-05
            ],
            [
                2.1024341622368903e-07,
                3.4663249714612693e-07,
                1.9947304348862686e-06,
                3.0590237279032884e-07,
                1.8553912395338048e-07,
                3.0590226339061185e-07,
                1.5534971990126997e-06,
                2.3823699519290042e-07,
                2.102434412875379e-07,
                2.69957906184239e-07
            ],
            [
                0.9999997300423192,
                0.9999995262092165,
                0.9999996310115041,
                0.9999977396754347,
                0.9999997126315496,
                0.9999995262096117,
                0.9999997300421906,
                0.9999987901340288,
                0.9999995818811774,
                0.9999981261243949
            ],
            [
                0.9999921107383615,
                0.9999989322966212,
                0.9999989322971304,
                0.9999975938982357,
                2.6995784182140636e-07,
                0.9999998362622747,
                0.999992110736482,
                0.9999995549150013,
                0.9999832985741985,
                0.9999992188513903
            ],
            [
                5.04347408197782e-07,
                3.2887506335906595e-06,
                2.260324836776948e-06,
                5.043472879525233e-07,
                2.9023126771227976e-06,
                7.338212429582604e-07,
                1.4449805540740185e-07,
                9.422442569315887e-07,
                1.855391681898159e-07,
                2.382368247924618e-07
            ],
            [
                3.2887482813149375e-06,
                8.315281267800897e-07,
                1.0677031245905116e-06,
                4.4508515805199415e-07,
                3.927863875584984e-07,
                3.927862470790036e-07,
                1.3709568799823232e-06,
                3.059023363221292e-07,
                9.422443692446175e-07,
                5.715005832827105e-07
            ],
            [
                2.1024336609843824e-07,
                1.1253520230080141e-07,
                5.043475885674441e-07,
                5.043474081993875e-07,
                1.855390576008354e-07,
                6.962257909842961e-06,
                3.9278629391427843e-07,
                3.466325797900508e-07,
                2.1024339116168358e-07,
                5.715005151606823e-07
            ],
            [
                7.338213304316717e-07,
                3.927862002641863e-07,
                5.715003789017068e-07,
                3.46632497145457e-07,
                2.2603242978871282e-06,
                3.466325384661554e-07,
                3.120192625482384e-05,
                1.8553910183607374e-07,
                3.0590237278838124e-07,
                3.53562422882756e-05
            ],
            [
                7.338207180884785e-07,
                5.043473480777865e-07,
                7.338207180838067e-07,
                5.04347648680129e-07,
                5.043472879540142e-07,
                7.338209805224048e-07,
                7.338211554783522e-07,
                5.715005151606823e-07,
                3.9278624708775595e-07,
                1.2098658277451275e-06
            ],
            [
                0.999999631011548,
                NaN,
                1.0,
                0.9999998555020136,
                0.9999986290421405,
                0.9999997126314469,
                0.9999991684717745,
                2.8453367631661124e-08,
                0.9999982396574181,
                0.9999995818811275
            ],
            [
                3.927862470899887e-07,
                1.994730434879465e-06,
                8.315279285351409e-07,
                2.902312677137316e-06,
                8.315281267861397e-07,
                1.067703124601679e-06,
                7.889266347715168e-06,
                8.315278294114555e-07,
                8.315277302841894e-07,
                3.0590237279032884e-07
            ],
            [
                2.2603237589676295e-06,
                1.3709576971379186e-06,
                9.422443692489024e-07,
                3.7266401726173067e-06,
                1.553497754583709e-06,
                6.475946438055299e-07,
                1.3709576971425944e-06,
                2.1024341622368903e-07,
                3.466326624322211e-07,
                1.0129988564974359e-05
            ],
            [
                1.3709568799919866e-06,
                2.561282210701601e-06,
                5.715002426486762e-07,
                4.222833444590791e-06,
                5.04347468318358e-07,
                4.785093353940187e-06,
                3.9278610661902853e-07,
                1.9947294837154625e-06,
                7.338213304363436e-07,
                8.939697369980456e-06
            ],
            [
                1.209866260432471e-06,
                1.275190580890061e-07,
                3.059021175261338e-07,
                NaN,
                0.0001584361792827627,
                1.8553919030858602e-07,
                6.475949526020042e-07,
                5.715002426486762e-07,
                5.715005832886879e-07,
                1.4449807263312446e-07
            ],
            [
                NaN,
                7.73442776303243e-08,
                0.00317268335866948,
                0.9999599362937723,
                1.6373776432509826e-07,
                1.5534984953453635e-06,
                3.288749457469787e-06,
                1.067702870039777e-06,
                1.275190580890061e-07,
                1.300713001508642e-05
            ],
            [
                NaN,
                4.0063711294555596e-05,
                0.9999967112497655,
                0.9999960330136249,
                0.999996910504836,
                0.999996033015051,
                7.88926446679691e-06,
                0.9999970976887167,
                0.0002959570648182355,
                2.3823699519290042e-07
            ],
            [
                2.902312677150514e-06,
                1.4449795205429202e-07,
                NaN,
                2.382370235922541e-07,
                1.2098662604291696e-06,
                1.7603430034867993e-06,
                NaN,
                5.715002426486762e-07,
                7.338208055664991e-07,
                2.561282210740037e-06
            ],
            [
                1.3709575337159875e-06,
                2.699578740032504e-07,
                3.7266397283908927e-06,
                1.7603438428800754e-06,
                1.6373770576776313e-07,
                5.043472879540142e-07,
                2.699578740032504e-07,
                3.726638839806038e-06,
                6.475947982037486e-07,
                3.466327037553825e-07
            ],
            [
                6.475949526020042e-07,
                3.535625914363812e-05,
                8.315279285351409e-07,
                0.9999942280779516,
                9.422448185478557e-07,
                2.2603234895053587e-06,
                0.9999916019310062,
                0.9999930377462555,
                1.0677032518814388e-06,
                0.9999925887228189
            ],
            [
                6.475949526020042e-07,
                6.475947982037486e-07,
                8.315283250394546e-07,
                1.8925148242250705e-05,
                5.715003789033962e-07,
                6.605214470327124e-05,
                4.222832437798974e-06,
                6.1441746020359e-06,
                5.422217677152175e-06,
                1.0129993395336818e-05
            ],
            [
                2.69957906184239e-07,
                8.315284241650899e-07,
                1.670142980893658e-05,
                1.5534979397740895e-06,
                4.785093924330255e-06,
                9.422444815765128e-07,
                NaN,
                5.715003789046955e-07,
                7.338209805200689e-07,
                1.0677033791583005e-06
            ],
            [
                3.4663266243111764e-07,
                1.2098659719757836e-06,
                2.561282210740037e-06,
                4.4508505193386385e-07,
                4.4508515805199415e-07,
                5.829128640005915e-05,
                3.466327450756327e-07,
                7.338210679979539e-07,
                5.71500242637956e-07,
                3.2887498495150166e-06
            ],
            [
                0.9999993916410361,
                0.9999994956527123,
                0.9999995818811276,
                0.9999994631250604,
                0.9999990577549573,
                0.9999996533672137,
                0.9999992661789325,
                0.9999989969862708,
                0.9999991684720722,
                0.999997876622045
            ],
            [
                4.4508494582405734e-07,
                1.637376862489725e-07,
                9.931187406410953e-08,
                1.6373764721072816e-07,
                1.855391681906175e-07,
                9.931189774187203e-08,
                2.699578740032504e-07,
                1.1253526937656726e-07,
                7.734423152941018e-08,
                1.275190732904469e-07
            ],
            [
                4.450850519403407e-07,
                2.3823690999290963e-07,
                2.382369383923073e-07,
                1.6373764720990908e-07,
                2.1024341622297196e-07,
                3.05902336324494e-07,
                2.1024331597262577e-07,
                NaN,
                NaN,
                2.6995784182140636e-07
            ],
            [
                1.637376862489725e-07,
                NaN,
                0.9999983463104162,
                1.9947304348862686e-06,
                1.0677026154827912e-06,
                1.760342793638743e-06,
                0.9999995262092728,
                NaN,
                1.7603432133032607e-06,
                1.209865827752005e-06
            ],
            [
                2.561283431986506e-06,
                1.9947299593014888e-06,
                1.7603434231777837e-06,
                8.315277302788957e-07,
                8.315277302747361e-07,
                6.475949525981759e-07,
                NaN,
                1.7603430034655858e-06,
                4.222832941034507e-06,
                1.3709572068522336e-06
            ],
            [
                5.71500515159253e-07,
                9.610242648972629e-05,
                4.785092783519724e-06,
                2.902313369111213e-06,
                5.715007195447234e-07,
                2.2603242978871282e-06,
                4.2228329411708495e-06,
                2.2603253756956754e-06,
                2.6995784182140636e-07,
                3.7266397283908927e-06
            ],
            [
                1.6373770576776313e-07,
                1.275190732904469e-07,
                1.6373766672973748e-07,
                2.69957906184239e-07,
                2.699579061812927e-07,
                5.043472278322555e-07,
                1.1253518888531272e-07,
                2.382370235922541e-07,
                1.1253508156363576e-07,
                5.043475284468537e-07
            ],
            [
                1.2098659719716573e-06,
                3.466325797896173e-07,
                2.2603251062270446e-06,
                1.2098656835076114e-06,
                4.2228339479858295e-06,
                2.902312677150514e-06,
                1.2098662604192665e-06,
                2.9023112932177327e-06,
                6.144172404693786e-06,
                1.855391681906175e-07
            ],
            [
                NaN,
                NaN,
                1.3709567165579959e-06,
                6.144172404693786e-06,
                9.422450431989127e-07,
                1.5534975693933505e-06,
                7.484624512911504e-05,
                2.260323758939877e-06,
                1.0677029972993568e-06,
                3.288749457469787e-06
            ],
            [
                4.691162124067829e-08,
                6.023577783447482e-08,
                3.653482951291499e-08,
                2.8453333712602254e-08,
                4.6911660386730734e-08,
                9.931190958076104e-08,
                6.023572038912295e-08,
                3.2241847115356483e-08,
                2.1024339116168358e-07,
                9.931198061405701e-08
            ],
            [
                4.006371129615879e-05,
                0.999992588721056,
                5.715005151606823e-07,
                0.00015843621702094375,
                1.5534984953552536e-06,
                5.043472278322555e-07,
                0.9999969105048273,
                NaN,
                5.043472278322555e-07,
                2.902313023130843e-06
            ],
            [
                1.0677027427471959e-06,
                5.043476486833397e-07,
                3.059023363207381e-07,
                6.475947209918244e-07,
                7.338213304316717e-07,
                1.3709576971242028e-06,
                2.5612828213934817e-06,
                5.715007195431641e-07,
                1.3709576971242028e-06,
                6.475948754012522e-07
            ],
            [
                0.9999999226557316,
                0.9999960330136155,
                0.9999982396567878,
                1.1253525596174225e-07,
                0.9999998942829098,
                0.9999978766212876,
                0.999998540623606,
                NaN,
                0.9999997463980124,
                0.9999994631249964
            ],
            [
                0.9999996072137064,
                0.9999982396561586,
                0.9999972735290816,
                0.999998446501876,
                0.9999985406237801,
                9.931189774187203e-08,
                0.9999967112497609,
                1.1253509497883659e-07,
                6.023573475041126e-08,
                0.9999981261246188
            ],
            [
                2.1024329090867228e-07,
                1.5534973842076057e-06,
                3.927863875616689e-07,
                4.450852641737424e-07,
                1.760342793638743e-06,
                8.315282259138311e-07,
                4.450852641737424e-07,
                5.71500719545698e-07,
                8.315281267882195e-07,
                3.927863875616689e-07
            ],
            [
                4.1399410020127234e-08,
                2.699576809143613e-07,
                5.315784971839039e-08,
                1.2751899728311609e-07,
                1.855391681906175e-07,
                1.275190884913241e-07,
                3.726638839833152e-06,
                1.1253518888531272e-07,
                8.7642516304188e-08,
                NaN
            ],
            [
                6.1441746020359e-06,
                3.9278605979534166e-07,
                0.0004305569889994219,
                9.422447062270609e-07,
                9.422449308748773e-07,
                7.33821067986608e-07,
                7.338208055664991e-07,
                6.475949526020042e-07,
                1.0677031245990084e-06,
                8.315279285351409e-07
            ],
            [
                0.9999995818814267,
                4.139934092760465e-08,
                0.9999957771670643,
                0.9999998024945624,
                0.999999887464838,
                0.9999991148430701,
                0.9999981261246184,
                0.9999997617630901,
                0.9999975938982377,
                1.0
            ],
            [
                6.475945666051092e-07,
                1.067703124601679e-06,
                5.043475885674441e-07,
                2.9023133690425823e-06,
                1.2098662604247682e-06,
                6.962256249885085e-06,
                1.0129987357287368e-05,
                5.715007195447234e-07,
                6.475950297993789e-07,
                1.2098653950656417e-06
            ],
            [
                1.99472900813862e-06,
                1.1253521571574156e-07,
                8.764254764749753e-08,
                1.6373776432509826e-07,
                0.9999986290421402,
                1.637377057673536e-07,
                0.9999992661787575,
                1.2751904288710323e-07,
                3.466327450765785e-07,
                2.1024336609874897e-07
            ],
            [
                1.275190884913241e-07,
                1.0677028700363782e-06,
                3.9278610661366994e-07,
                5.043475885674441e-07,
                3.4663266242969896e-07,
                2.1024344128488479e-07,
                1.209865250822125e-06,
                1.3709570434178922e-06,
                2.69957906184239e-07,
                2.902313369111213e-06
            ],
            [
                9.422448185435711e-07,
                4.222834451382849e-06,
                5.043472879525233e-07,
                8.315278294001114e-07,
                1.2098659719232413e-06,
                2.699577774585891e-07,
                NaN,
                1.760343213335281e-06,
                2.9023119851781017e-06,
                4.4508510499737865e-07
            ],
            [
                8.315277302857965e-07,
                5.715006514176113e-07,
                6.825598028392069e-08,
                3.466326624336003e-07,
                3.05902263391829e-07,
                2.902312331170226e-06,
                1.1253526937697666e-07,
                2.2603251062450327e-06,
                1.9947299593078385e-06,
                7.338207180898968e-07
            ],
            [
                NaN,
                8.939695238634211e-06,
                5.715003789046955e-07,
                4.2228339479858295e-06,
                2.2603253756956754e-06,
                5.715006514176113e-07,
                3.288747889284851e-06,
                9.422445939054222e-07,
                1.7603434231705793e-06,
                4.450848927650143e-07
            ],
            [
                3.927862002663297e-07,
                8.315280276626197e-07,
                0.9999546021373699,
                1.0677028700422047e-06,
                3.9278605979534166e-07,
                6.023571320847322e-08,
                1.4449796928021588e-07,
                6.023573475041126e-08,
                3.9278610661902853e-07,
                4.450852641737424e-07
            ],
            [
                2.430025232128576e-05,
                7.889260704732132e-06,
                1.5534975693869924e-06,
                7.889262585886274e-06,
                3.120191881321371e-05,
                4.450849988758202e-07,
                NaN,
                5.715002426439334e-07,
                8.315282259009745e-07,
                3.059022998576899e-07
            ],
            [
                2.69957906184239e-07,
                1.8553903548231313e-07,
                1.275190124842887e-07,
                1.1253512180925583e-07,
                2.102433660979124e-07,
                1.1253513522447425e-07,
                2.6995777745711594e-07,
                1.6373774480605869e-07,
                2.382369667929001e-07,
                7.734424996967756e-08
            ],
            [
                1.3709575337125585e-06,
                0.9999986290421407,
                0.9999972735284319,
                8.315282259138311e-07,
                4.450848927658745e-07,
                NaN,
                7.338210680021253e-07,
                1.1253512180925583e-07,
                0.9999985406239542,
                0.9999989322971308
            ],
            [
                8.764245361752286e-08,
                6.023569884718319e-08,
                1.7603438428800754e-06,
                3.05902190458764e-07,
                3.4663266243308805e-07,
                1.27519088491875e-07,
                1.1253512180925583e-07,
                3.0590226339137693e-07,
                4.4508499888219586e-07,
                3.059023363231725e-07
            ],
            [
                6.475950298011458e-07,
                6.475950298011458e-07,
                2.260324567337161e-06,
                4.4508526417298334e-07,
                1.0677024882009222e-06,
                2.1024331597262577e-07,
                3.9278634073732336e-07,
                1.9947299593078385e-06,
                8.315277302788957e-07,
                1.994729483723626e-06
            ],
            [
                5.043472879504592e-07,
                9.4224425692559e-07,
                2.5612812947508257e-06,
                3.7266397283908927e-06,
                8.315281267861397e-07,
                NaN,
                6.475947210031623e-07,
                1.0677029973192638e-06,
                2.9023119851781017e-06,
                1.2098662604247682e-06
            ],
            [
                3.059022998558814e-07,
                3.466327037539638e-07,
                1.4449807263312446e-07,
                3.927860597935108e-07,
                2.1024336609843824e-07,
                2.3823685319244518e-07,
                3.0590215399183813e-07,
                2.1024331597262577e-07,
                1.275190884913241e-07,
                3.9278605979208185e-07
            ],
            [
                1.1478772230929451e-05,
                2.260325375664839e-06,
                2.2603245673155757e-06,
                8.939694172770212e-06,
                NaN,
                NaN,
                6.144176799166453e-06,
                1.370957533676711e-06,
                1.147877359926923e-05,
                1.2098655392871682e-06
            ],
            [
                0.9999925887183699,
                5.043472278322555e-07,
                0.9999974387177917,
                0.9999978766215392,
                0.9999974387180968,
                6.475947982037486e-07,
                0.9999978766220454,
                2.102434412875379e-07,
                0.9999980052702802,
                2.2603240284371276e-06
            ],
            [
                7.734415776836702e-08,
                4.450848927650143e-07,
                1.1253521571574156e-07,
                0.9999885212346264,
                8.764252675194995e-08,
                1.1253506814842375e-07,
                1.855391239544352e-07,
                0.999997097687324,
                1.855391239547094e-07,
                3.466327450756327e-07
            ],
            [
                0.999998005270993,
                0.9999983463110065,
                0.9999832985742024,
                0.9999984465020613,
                0.9999981261237236,
                0.9999982396563681,
                0.00029595717085330824,
                0.9999987121047852,
                0.9999972735284312,
                0.9999916019269763
            ],
            [
                3.0590226338838606e-07,
                3.927862002625787e-07,
                2.3823685318968256e-07,
                4.450850519403407e-07,
                3.4663253846718004e-07,
                3.927863875584984e-07,
                3.9278629390507954e-07,
                3.059023727894942e-07,
                4.4508489275752546e-07,
                3.059021175247079e-07
            ],
            [
                3.4663249714325014e-07,
                2.6995777745711594e-07,
                3.4663249714325014e-07,
                1.8553919030776337e-07,
                9.422443692555439e-07,
                2.699578096393206e-07,
                1.8553914607043678e-07,
                2.6995768091310296e-07,
                2.1024326584582131e-07,
                3.059022998576899e-07
            ],
            [
                1.5534981249574276e-06,
                8.315283250371857e-07,
                1.9947304348703948e-06,
                9.422450431989127e-07,
                8.315278294072958e-07,
                1.3709575337078829e-06,
                2.753568125320169e-05,
                1.3709575337078829e-06,
                1.0129988564974359e-05,
                2.2603242978665707e-06
            ],
            [
                7.338210680021253e-07,
                1.067703124601679e-06,
                7.338208055680009e-07,
                1.4449798650551755e-07,
                2.561281600086738e-06,
                2.1024326584639497e-07,
                NaN,
                3.927862002663297e-07,
                5.043472278322555e-07,
                6.475947210046347e-07
            ],
            [
                1.8553907971855875e-07,
                3.0590215399246414e-07,
                3.0590215399183813e-07,
                1.2098659719757836e-06,
                8.315281267861397e-07,
                1.5534979397790343e-06,
                4.450852111155216e-07,
                2.382369383923073e-07,
                6.475951070002966e-07,
                1.760342793638743e-06
            ],
            [
                0.9999995818812272,
                0.9999990577551823,
                0.9999983463106121,
                0.9999983463110071,
                0.999995777166564,
                0.9999989969860322,
                0.9999988634365611,
                0.9999989969862711,
                0.9999986290424672,
                0.999998346310021
            ]
        ]
    },
    {
        "q_id": "9187_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            7,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            63,
            64,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            83,
            86,
            87,
            88,
            90,
            91,
            92,
            93,
            94,
            95,
            97,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            22,
            62,
            85
        ],
        "rewards": [
            [
                0.9999970976873268,
                0.9999957771650498,
                2.7535694385633984e-05,
                7.73442776300517e-08,
                0.9999989969857928,
                0.9999934595635596,
                1.3709567165617364e-06,
                0.999841563783553,
                0.9999988634365612,
                0.9999916019299838
            ],
            [
                2.699578096403948e-07,
                0.9999994956527724,
                2.9023116392097746e-06,
                1.5534971990169383e-06,
                1.2098656835252174e-06,
                8.315278294114555e-07,
                8.315281267882195e-07,
                1.0677026154827912e-06,
                1.2098659719788098e-06,
                4.450852111155216e-07
            ],
            [
                0.9999981261241712,
                0.9999992188517627,
                0.9999962733589433,
                0.9999952149043678,
                0.9999988634360191,
                0.9999974387184011,
                0.9999996072137062,
                0.9999877809283748,
                0.9999949062937888,
                1.3709567165579959e-06
            ],
            [
                8.93969843573914e-06,
                1.012999218776902e-05,
                2.7535700950274782e-05,
                3.726639284144195e-06,
                7.889266347786918e-06,
                5.422221555414699e-06,
                3.7266406168827523e-06,
                3.2887506336235617e-06,
                6.962257909842961e-06,
                5.422220262636381e-06
            ],
            [
                0.9999724643188244,
                0.999998126124841,
                0.9999485578048546,
                0.9999962733602747,
                0.99999303774542,
                0.9999962733589453,
                0.9999983463100204,
                0.9999980052698041,
                1.9947306726049992e-06,
                3.05902190458764e-07
            ],
            [
                2.9023119851635836e-06,
                3.726639728370556e-06,
                1.5534979397740895e-06,
                2.5612834320470717e-06,
                1.7603425837791042e-06,
                1.2098659719757836e-06,
                1.994729483723626e-06,
                1.2098656835224664e-06,
                4.222831934352267e-06,
                9.422448185478557e-07
            ],
            [
                0.9999969105062906,
                8.315282259138311e-07,
                0.9999987901337404,
                0.9999983463110063,
                0.9999982396559502,
                0.9999988634362903,
                1.067703379154416e-06,
                0.9999957771660656,
                1.0129990980100021e-05,
                5.715002426475718e-07
            ],
            [
                5.422220262599396e-06,
                3.0590215399183813e-07,
                1.0677028700422047e-06,
                1.7603438428740716e-06,
                1.209866260432471e-06,
                1.760343003481596e-06,
                1.2098653950692178e-06,
                1.7603434231833873e-06,
                1.4449800373118268e-07,
                6.475949526020042e-07
            ],
            [
                0.9999988634364255,
                2.2603253756874524e-06,
                0.9999991684715761,
                1.3709568799879344e-06,
                0.00218271664260476,
                6.14417533430649e-06,
                0.9999995818812271,
                0.9999985406230839,
                0.9999983463096264,
                0.9999992188515766
            ],
            [
                3.466327037553825e-07,
                7.734424996967756e-08,
                0.9999994284995531,
                1.6373766672973748e-07,
                9.931190958076104e-08,
                5.3157830707696514e-08,
                6.825608606172863e-08,
                1.1253508156363576e-07,
                9.931193325852072e-08,
                1.1253520230052635e-07
            ],
            [
                2.3823693839057394e-07,
                0.999998005270757,
                3.927862002663297e-07,
                6.023574911170301e-08,
                2.1024341622368903e-07,
                2.102433660979124e-07,
                3.059022269250683e-07,
                2.699577774585891e-07,
                0.9999980052693292,
                3.05902190458764e-07
            ],
            [
                1.3007134667436886e-05,
                1.0129993395336818e-05,
                1.1478770862882149e-05,
                6.144177531811707e-06,
                2.902313023130843e-06,
                6.962257909842961e-06,
                1.3007133116732079e-05,
                1.5534971990126997e-06,
                1.3007123813559956e-05,
                4.785094494811783e-06
            ],
            [
                0.9999991684719731,
                1.125351083940518e-07,
                0.9999984465022463,
                2.102434412875379e-07,
                0.9999987121050924,
                0.9999977396746261,
                1.637376862489725e-07,
                9.422443692555439e-07,
                0.9999985406234325,
                1.9947301970972664e-06
            ],
            [
                1.9947304348862686e-06,
                1.760343633031919e-06,
                8.315284241650899e-07,
                5.043474081993875e-07,
                5.04347468323289e-07,
                2.5612819054133693e-06,
                2.5612819054133693e-06,
                1.5534981249697903e-06,
                1.067703124601679e-06,
                1.3709573702822306e-06
            ],
            [
                0.9999999176675436,
                1.0,
                0.9999975938982354,
                0.9999996533674615,
                1.5534979397677313e-06,
                0.9999997897567091,
                0.9999991684721709,
                0.999991060305847,
                1.0,
                0.9999997300421583
            ],
            [
                0.9999987901338846,
                2.5612812947508257e-06,
                0.9999991148430702,
                0.9999988634361543,
                0.9999999067051499,
                0.9999996072138936,
                0.9999997761970515,
                0.9999984465015056,
                1.8925150497848527e-05,
                0.9999998724809267
            ],
            [
                1.5534975693869924e-06,
                1.9947292459265734e-06,
                4.222834451327159e-06,
                1.147877359926923e-05,
                6.1441731370702875e-06,
                1.9947299593014888e-06,
                2.561281600076256e-06,
                4.222832437747125e-06,
                9.422448185510695e-07,
                1.5534984953453635e-06
            ],
            [
                1.370957860576702e-06,
                3.535624228698939e-05,
                2.90231094723893e-06,
                6.962256249885085e-06,
                1.9947301970972664e-06,
                1.3709567165617364e-06,
                6.47595107001401e-07,
                2.9023119851781017e-06,
                9.422443692527585e-07,
                1.3709576971463352e-06
            ],
            [
                2.561281600086738e-06,
                1.0677032518814388e-06,
                1.5534983101602148e-06,
                4.450849988798682e-07,
                1.9947301970972664e-06,
                0.9999998942829981,
                9.422442569290178e-07,
                3.2887478892683997e-06,
                2.2603248367656408e-06,
                2.430023494002383e-05
            ],
            [
                2.102434162245973e-07,
                2.3823696679327928e-07,
                2.6995774527718623e-07,
                2.6995790618469934e-07,
                9.422449308774482e-07,
                3.0590237279085045e-07,
                3.466325797896173e-07,
                1.0677029973192638e-06,
                3.0590237279085045e-07,
                2.1024341622368903e-07
            ],
            [
                1.670141985446017e-05,
                4.006369219393695e-05,
                0.9999667858052416,
                0.9999930377420954,
                0.9999921107383608,
                0.9999646437620586,
                0.9999930377412629,
                0.9999974387165702,
                0.9998204720563998,
                8.315281267882195e-07
            ],
            [
                5.715003788993679e-07,
                1.0677024882009222e-06,
                1.3709572068522336e-06,
                1.2098658277451275e-06,
                2.902312677137316e-06,
                7.734421308872513e-08,
                5.043472278280699e-07,
                7.338208930391909e-07,
                8.315284241560147e-07,
                1.3709573702822306e-06
            ],
            [
                6.144177531811707e-06,
                2.5612828213934817e-06,
                1.3709570434178922e-06,
                1.9947292459265734e-06,
                1.0677026154730804e-06,
                7.338209805240734e-07,
                1.9947297215125433e-06,
                4.450848927658745e-07,
                1.0677029973192638e-06,
                6.475948754012522e-07
            ],
            [
                6.825606978822427e-08,
                2.1024336609874897e-07,
                1.8553907971879076e-07,
                3.059021175261338e-07,
                NaN,
                8.764241182641775e-08,
                9.931190958076104e-08,
                3.0590219045914655e-07,
                1.0677029973219343e-06,
                1.8553914607267268e-07
            ],
            [
                4.222834954801051e-06,
                2.2603253756956754e-06,
                2.2603253756956754e-06,
                1.7603440527334603e-06,
                1.5534973842076057e-06,
                9.422445939054222e-07,
                1.994729483729522e-06,
                2.2603253756956754e-06,
                1.3709567165617364e-06,
                2.9023119851899796e-06
            ],
            [
                1.3709567165617364e-06,
                4.222833444590791e-06,
                0.9999992661790199,
                0.9999987121044777,
                2.260325106237323e-06,
                3.2887478892504536e-06,
                0.9999967112521141,
                1.99472900813862e-06,
                0.999999391640891,
                0.9999974387177908
            ],
            [
                1.7603440527222532e-06,
                3.7266397283908927e-06,
                1.30071315662049e-05,
                2.90231233114251e-06,
                2.1444950971601277e-05,
                1.553497754577351e-06,
                2.90231094723893e-06,
                1.553497754583709e-06,
                4.539786864876098e-05,
                5.043475885674441e-07
            ],
            [
                1.1253513522447425e-07,
                0.9999962733593852,
                1.3709575337159875e-06,
                0.999664649786143,
                0.9999997126314469,
                1.994729721518893e-06,
                0.9999993106388727,
                4.4508510499849186e-07,
                0.9999994956523516,
                0.9999832985821548
            ],
            [
                2.2603234895372223e-06,
                7.889263526409699e-06,
                1.1478770862882149e-05,
                2.2603248367949354e-06,
                2.561281600086738e-06,
                3.7266401726359486e-06,
                7.338210680021253e-07,
                1.0129993395336818e-05,
                0.999996711250152,
                1.5534971990169383e-06
            ],
            [
                5.422219616228845e-06,
                4.691161005609407e-08,
                2.3823690999323465e-07,
                4.450850519409479e-07,
                1.5534971989992774e-06,
                1.2098659719757836e-06,
                1.994730197090463e-06,
                8.315283250394546e-07,
                8.315283250305684e-07,
                1.637376862489725e-07
            ],
            [
                0.9999962733598294,
                0.9999987901343169,
                0.9999970976876724,
                0.999992110740248,
                1.760343213322473e-06,
                0.9999977396762431,
                0.9999995262095553,
                0.9999599362937163,
                0.9999985406232582,
                0.9999955048184292
            ],
            [
                1.30071315662049e-05,
                7.889264466868659e-06,
                1.8925148242250705e-05,
                1.0129987357517693e-05,
                3.535626336201389e-05,
                4.2228339479858295e-06,
                2.902312331170226e-06,
                0.00010889687041282619,
                1.892514147435727e-05,
                8.939695238536645e-06
            ],
            [
                2.102434412875379e-07,
                0.9999972735297316,
                7.33821330437595e-07,
                3.927863407379485e-07,
                2.1024336609874897e-07,
                5.043476486924565e-07,
                5.715005832895975e-07,
                NaN,
                3.9278620026686556e-07,
                3.05902263391829e-07
            ],
            [
                1.6373768624837685e-07,
                1.3007128465151102e-05,
                3.288747889284851e-06,
                3.53562422882756e-05,
                8.939695238634211e-06,
                2.7535700950274782e-05,
                8.939700567094277e-06,
                1.3709572068522336e-06,
                7.889259764517575e-06,
                2.5612828213934817e-06
            ],
            [
                1.4449795205429202e-07,
                7.734423152941018e-08,
                0.9999996743687422,
                6.023569884718319e-08,
                1.1253512180925583e-07,
                0.999999631011548,
                1.125352291309328e-07,
                2.3823690999290963e-07,
                1.2751908849167202e-07,
                1.8553905760062447e-07
            ],
            [
                2.561281294760143e-06,
                3.7266397283908927e-06,
                6.962257909785973e-06,
                NaN,
                0.0008040857675043072,
                3.288747889284851e-06,
                6.962259569750576e-06,
                1.5534971990169383e-06,
                1.1478766757561534e-05,
                2.26032402841657e-06
            ],
            [
                0.9999974387177925,
                0.999998629042794,
                0.9999996743687811,
                0.9999980052693287,
                5.715007195431641e-07,
                0.9999810748495427,
                0.9999986290426305,
                3.288750241561788e-06,
                0.999998239656578,
                0.9999599362937254
            ],
            [
                5.043475885657239e-07,
                2.2603242978871282e-06,
                6.475947982037486e-07,
                1.4449795205429202e-07,
                6.475949526003845e-07,
                3.927862002663297e-07,
                1.3709570433979422e-06,
                2.2603234895372223e-06,
                5.043472278322555e-07,
                1.1253508156317518e-07
            ],
            [
                5.715005151606823e-07,
                6.475947982037486e-07,
                3.9278610661902853e-07,
                3.927863875616689e-07,
                3.9278605979534166e-07,
                1.209865539295696e-06,
                1.209866260432471e-06,
                3.05902336324494e-07,
                7.338210680021253e-07,
                4.4508510499849186e-07
            ],
            [
                0.9999938558261402,
                0.9999910603026402,
                0.999995777165554,
                0.985936371497521,
                0.9999869928715783,
                0.9998766054423663,
                0.9999667857973896,
                0.999876605455182,
                0.9999910603047723,
                0.9999892166916622
            ],
            [
                1.3007126914612648e-05,
                0.9999339478398847,
                0.9999962733593867,
                0.9999852610215582,
                1.892515049819277e-05,
                0.9999771719947138,
                0.9999869928699985,
                4.785096776499213e-06,
                0.9999771720083174,
                5.422221555414699e-06
            ],
            [
                0.999998932296876,
                0.9999984465020613,
                1.4738985486506781e-05,
                0.9999985406241276,
                0.999996910505555,
                0.9999970976873263,
                0.9999960330140881,
                0.9999978766210333,
                0.9999992188513904,
                0.9999983463106128
            ],
            [
                0.9999942280792881,
                0.9999974387184026,
                0.9999892166877941,
                7.88926446679691e-06,
                0.9999991684717745,
                0.9999904837471876,
                0.999992110736481,
                1.5534971990126997e-06,
                0.9992903296593917,
                0.9999756997679989
            ],
            [
                0.9999988634357478,
                0.9999985406232575,
                0.9999962733589417,
                0.9999998802069016,
                0.9999952149043693,
                0.9999960330145621,
                0.9999982396572072,
                0.9999960330121965,
                0.9999983463106126,
                0.9999852610127751
            ],
            [
                4.785096206076165e-06,
                3.726639284144195e-06,
                1.6701415872659116e-05,
                1.3709575337159875e-06,
                4.2228319344021954e-06,
                2.1444943302650045e-05,
                4.222831934379152e-06,
                3.288749849529972e-06,
                3.288749457469787e-06,
                5.422221555414699e-06
            ],
            [
                8.315279285251204e-07,
                9.422443692555439e-07,
                1.0677029973056687e-06,
                9.422444815765128e-07,
                2.699576809143613e-07,
                0.9999985406232578,
                1.0677032518748838e-06,
                3.120191881525687e-05,
                3.927860597935108e-07,
                NaN
            ],
            [
                1.6701417863559525e-05,
                2.699577774585891e-07,
                9.931186222523604e-08,
                7.338210680021253e-07,
                3.466325797896173e-07,
                1.3709567165617364e-06,
                2.69957906184239e-07,
                1.1478770862882149e-05,
                1.5534984953552536e-06,
                1.0677032518814388e-06
            ],
            [
                9.422444815814404e-07,
                4.785094494811783e-06,
                2.2603253756956754e-06,
                2.5612819054133693e-06,
                2.9023116392097746e-06,
                1.7603425837903113e-06,
                4.22283545819819e-06,
                1.3709575337159875e-06,
                1.0677028700422047e-06,
                8.315279285370317e-07
            ],
            [
                2.7535694385633984e-05,
                1.0129988565084915e-05,
                6.962259569750576e-06,
                4.222834451403972e-06,
                3.7266401726359486e-06,
                1.1478769494542698e-05,
                3.288749065423109e-06,
                1.3007123813382511e-05,
                2.902313023130843e-06,
                1.4738980215352592e-05
            ],
            [
                4.222834451403972e-06,
                3.466327450765785e-07,
                5.043476486915964e-07,
                5.422217677152175e-06,
                3.059021175255426e-07,
                6.962253760024999e-06,
                1.3709572068522336e-06,
                0.9999969105059264,
                3.72663883989755e-06,
                2.561281294760143e-06
            ],
            [
                3.927863407379485e-07,
                2.5612834320563895e-06,
                1.3709572068553509e-06,
                2.9023109472494878e-06,
                9.422450432030903e-07,
                3.059022998581767e-07,
                1.2098661162056318e-06,
                2.9023112932296107e-06,
                2.5612834320563895e-06,
                2.2603245673443566e-06
            ],
            [
                1.99472900813862e-06,
                2.561283126679493e-06,
                5.715006514151423e-07,
                8.939699500766203e-06,
                4.4508505193791187e-07,
                3.9278634073732336e-07,
                3.927862470899887e-07,
                1.2098662604247682e-06,
                1.8553903548231313e-07,
                1.2098661161927025e-06
            ],
            [
                7.734424996967756e-08,
                0.9999957771670633,
                0.9999985406232582,
                1.2751907328949007e-07,
                2.1024336609874897e-07,
                0.9999999123575046,
                6.023578501491997e-08,
                2.1024339116134898e-07,
                1.275190124842887e-07,
                9.931190958076104e-08
            ],
            [
                2.699577774585891e-07,
                3.927862470899887e-07,
                2.382369667929001e-07,
                1.6373770576776313e-07,
                2.3823688159291947e-07,
                1.8553905760062447e-07,
                6.825608606148807e-08,
                3.059022269250683e-07,
                1.637377448057981e-07,
                1.4449800373065699e-07
            ],
            [
                1.637377057680051e-07,
                4.450852641737424e-07,
                2.1024334103581732e-07,
                4.450852111155216e-07,
                6.475946438055299e-07,
                1.4449807263312446e-07,
                1.0677029973219343e-06,
                1.2751901248454963e-07,
                2.382368815932174e-07,
                2.3823696679327928e-07
            ],
            [
                7.338207180898968e-07,
                2.102434162245973e-07,
                0.9999993106392013,
                4.450848927658745e-07,
                2.1024339116168358e-07,
                3.4663274507713016e-07,
                1.5534983101644536e-06,
                0.9999987121052454,
                3.059022998581767e-07,
                3.9278629391427843e-07
            ],
            [
                1.670141587208191e-05,
                8.939698435226916e-06,
                1.1478769494250387e-05,
                0.0001398220574171212,
                0.14804719803168948,
                1.6701429807964442e-05,
                6.9622595696935874e-06,
                NaN,
                1.99472924590571e-06,
                6.144177531660828e-06
            ],
            [
                8.939699501416646e-06,
                3.72663883989755e-06,
                0.00023050677073686453,
                6.962256249935742e-06,
                5.422221555414699e-06,
                1.9947304348862686e-06,
                7.889265407327733e-06,
                4.785094494811783e-06,
                4.22283545819819e-06,
                NaN
            ],
            [
                1.147876812620341e-05,
                1.7603425837903113e-06,
                1.7603425837903113e-06,
                3.2887486733899378e-06,
                1.892515049819277e-05,
                3.2241889394209404e-08,
                6.962259569750576e-06,
                1.1478766757853845e-05,
                4.785095065132354e-06,
                6.144176066943187e-06
            ],
            [
                6.47594952595231e-07,
                1.3709573702722555e-06,
                1.2098658277181688e-06,
                1.3709575337016483e-06,
                3.466327037548308e-07,
                1.760343003481596e-06,
                5.043474081993875e-07,
                1.7603427935518875e-06,
                1.7603434231705793e-06,
                1.2098659719716573e-06
            ],
            [
                1.7603427936263351e-06,
                2.144494841482881e-05,
                1.3709572068422585e-06,
                1.8925157266089433e-05,
                8.939696304311336e-06,
                1.9947301970972664e-06,
                3.7266397283908927e-06,
                1.4738985486506781e-05,
                2.753568782024347e-05,
                4.785095635655362e-06
            ],
            [
                1.3709568799368123e-06,
                7.889266347786918e-06,
                7.889266347786918e-06,
                5.422217677152175e-06,
                0.9999980052702806,
                7.889264466868659e-06,
                2.1444943302181958e-05,
                1.1478768126057254e-05,
                6.962258739796719e-06,
                NaN
            ],
            [
                0.9999969105055541,
                0.9999975938970893,
                0.9999998942829477,
                2.260324836776948e-06,
                0.999999168472072,
                0.9999756997651056,
                3.059022269250683e-07,
                0.9999955048194974,
                0.9999981261237242,
                6.144173869558639e-06
            ],
            [
                3.9278605979534166e-07,
                4.4508515805735777e-07,
                3.0590237279085045e-07,
                9.931195693628605e-08,
                4.785093924389007e-06,
                7.338213304363436e-07,
                8.315281267882195e-07,
                2.3823690999290963e-07,
                3.059021175261338e-07,
                2.6995790618469934e-07
            ],
            [
                1.2751905808881762e-07,
                2.102433660979124e-07,
                1.8553907971855875e-07,
                2.3823702359290413e-07,
                2.6995774527718623e-07,
                1.760344052693435e-06,
                5.715005151606823e-07,
                2.3823696679230424e-07,
                2.3823702359290413e-07,
                3.466327450756327e-07
            ],
            [
                1.209866260432471e-06,
                4.222834451403972e-06,
                1.9947301970972664e-06,
                1.2098661162056318e-06,
                1.3709576971463352e-06,
                1.3709567165617364e-06,
                1.2098661162056318e-06,
                1.3709568799919866e-06,
                7.338210680021253e-07,
                3.2887506336235617e-06
            ],
            [
                1.994730672668496e-06,
                3.288748281295496e-06,
                4.222831934379152e-06,
                1.553497384196656e-06,
                3.726638395611981e-06,
                0.9999964991455884,
                1.4738978458382043e-05,
                1.1478770862589836e-05,
                7.889261645427538e-06,
                6.1441724046434924e-06
            ],
            [
                6.144177531811707e-06,
                3.7266397283908927e-06,
                6.144173137170873e-06,
                2.561281294760143e-06,
                1.7603438428848787e-06,
                1.0129987357517693e-05,
                1.0677027427624903e-06,
                1.994729483729522e-06,
                1.3709573702856596e-06,
                5.043476486924565e-07
            ],
            [
                0.9999724643056681,
                0.999983298578189,
                0.9999974387184015,
                0.9999955048200326,
                8.939696304311336e-06,
                0.9999852610110174,
                0.9999869928746481,
                0.9999861539987621,
                0.9999877809196306,
                0.9999646437367234
            ],
            [
                0.9999998874648112,
                0.9999339478242194,
                0.9999980052693294,
                0.9999999067049943,
                0.9999996533673376,
                0.9999986290424675,
                0.9999985406237799,
                0.9999997300422548,
                1.3709572068522336e-06,
                0.9999995818811276
            ],
            [
                0.9999998642566381,
                3.7266379512518984e-06,
                0.9999869928762091,
                0.9999942280813507,
                0.9999991684721707,
                0.9999991148428589,
                0.9999998144609645,
                3.7266406168403854e-06,
                8.764245361708445e-08,
                0.9999995818812272
            ],
            [
                NaN,
                5.422221555414699e-06,
                5.043472879540142e-07,
                7.338210680021253e-07,
                2.902312331170226e-06,
                4.785093924389007e-06,
                3.9278615344178325e-07,
                2.3823685319244518e-07,
                1.8553910183607374e-07,
                2.3823685319244518e-07
            ],
            [
                2.699576809143613e-07,
                1.6373774480605869e-07,
                2.382369667929001e-07,
                0.9999981261241705,
                0.9999822214418378,
                2.382370235933104e-07,
                0.9999974387171804,
                6.475946438055299e-07,
                0.999998932297258,
                0.999964643757755
            ],
            [
                3.0590237279085045e-07,
                NaN,
                9.422443692574719e-07,
                3.059022998576899e-07,
                6.475946438055299e-07,
                7.33821330437595e-07,
                1.0677024882009222e-06,
                2.260324836787226e-06,
                2.9023116392097746e-06,
                4.4508494582405734e-07
            ],
            [
                0.9999852610162928,
                1.670142383595838e-05,
                0.9964063976103296,
                7.484625405027093e-05,
                0.5621765008857982,
                0.9989677690831685,
                0.1480471999111614,
                NaN,
                3.535625071730638e-05,
                0.9999038976084177
            ],
            [
                2.90231094723893e-06,
                8.315284241597959e-07,
                4.450848927658745e-07,
                2.3823702359290413e-07,
                8.939694172957213e-06,
                1.2098658277451275e-06,
                2.902312677137316e-06,
                2.9023119851635836e-06,
                1.067703379154416e-06,
                3.46632497145457e-07
            ],
            [
                7.338207180898968e-07,
                1.3709572068553509e-06,
                1.3709575337159875e-06,
                1.209865827752005e-06,
                4.450850519409479e-07,
                5.71500515161527e-07,
                3.9278629391427843e-07,
                2.382368815932174e-07,
                3.059021175261338e-07,
                1.7603438428848787e-06
            ],
            [
                5.829127250399344e-05,
                0.9999810748563032,
                1.4738985486506781e-05,
                1.3007123813193233e-05,
                5.829127250399344e-05,
                1.1478765389368729e-05,
                1.8925157266089433e-05,
                0.9999955048178928,
                3.120191137659974e-05,
                4.785096776468749e-06
            ],
            [
                2.7535694385633984e-05,
                6.144173137170873e-06,
                0.9999916019239703,
                2.1444950971601277e-05,
                0.00012339454558103757,
                1.7603425837855082e-06,
                4.785093924389007e-06,
                7.889264466868659e-06,
                NaN,
                NaN
            ],
            [
                1.473898900066424e-05,
                1.6701415872659116e-05,
                6.1441746020359e-06,
                6.144173137170873e-06,
                0.9999972735294065,
                3.726639284144195e-06,
                2.90231094723893e-06,
                5.715003107767143e-07,
                4.222834954778007e-06,
                0.9999151889289528
            ],
            [
                0.9999978766222993,
                0.9999982396563688,
                0.999998629043284,
                4.53978632394714e-05,
                0.9999978766207797,
                0.999998005269805,
                0.9999984465028016,
                0.9999962733602779,
                3.288749849529972e-06,
                0.9999925887183696
            ],
            [
                4.222833947960866e-06,
                1.9947292459347367e-06,
                1.0129988565084915e-05,
                8.939695238634211e-06,
                5.715007195431641e-07,
                1.3007126914245925e-05,
                6.1441746020359e-06,
                0.9999810748495368,
                7.338208930460318e-07,
                6.475945666051092e-07
            ],
            [
                9.931195693628605e-08,
                1.6373762769138607e-07,
                1.855391239544352e-07,
                2.10243290909724e-07,
                1.8553907971855875e-07,
                5.04347408197782e-07,
                1.2751902768612997e-07,
                5.04347287955046e-07,
                1.6373764721072816e-07,
                1.1253517547010071e-07
            ],
            [
                1.5534971990169383e-06,
                4.785095635624897e-06,
                6.475950298011458e-07,
                1.0677028700422047e-06,
                5.71500719545698e-07,
                9.422448185534261e-07,
                1.855391239544352e-07,
                NaN,
                8.315280276626197e-07,
                9.422448185534261e-07
            ],
            [
                4.222833444590791e-06,
                3.726639284125553e-06,
                6.144175334468545e-06,
                1.5534975693933505e-06,
                4.785095635655362e-06,
                9.422443692555439e-07,
                4.785093353940187e-06,
                3.726639728370556e-06,
                1.0129994602895546e-05,
                6.962256249885085e-06
            ],
            [
                4.785093924389007e-06,
                2.5612834320563895e-06,
                3.726639284144195e-06,
                5.422221555414699e-06,
                3.7266379514061143e-06,
                3.288749457469787e-06,
                4.222832437798974e-06,
                6.144177531811707e-06,
                1.6701421845361053e-05,
                1.7603434231833873e-06
            ],
            [
                3.726638839878908e-06,
                1.7603440527222532e-06,
                1.4738976701411704e-05,
                5.715003107738556e-07,
                4.785093353940187e-06,
                5.043474081993875e-07,
                3.5356238073889594e-05,
                1.147877359957198e-05,
                5.422218323487975e-06,
                4.785093924362895e-06
            ],
            [
                3.0590237279085045e-07,
                1.637376862489725e-07,
                3.466325797896173e-07,
                5.715003107767143e-07,
                3.4663249714612693e-07,
                6.47594952603035e-07,
                2.699578096399958e-07,
                1.8553907971855875e-07,
                3.9278629391427843e-07,
                7.338207180898968e-07
            ],
            [
                0.999998863436019,
                6.475946438055299e-07,
                0.9999938558254062,
                0.9999987121050923,
                0.9999989969859122,
                0.9999339478715747,
                0.9999910603005092,
                1.7603440527046419e-06,
                0.9999983463104151,
                0.999991601926971
            ],
            [
                1.147876812620341e-05,
                NaN,
                0.0010322312204213415,
                2.9023119851899796e-06,
                2.1444950971601277e-05,
                0.0001584361603525882,
                1.892514598627448e-05,
                2.7535694385633984e-05,
                6.962253760024999e-06,
                2.9023119851899796e-06
            ],
            [
                6.962257079832313e-06,
                1.6701421845361053e-05,
                2.4300237838535383e-05,
                1.3007134667070165e-05,
                3.535625071730638e-05,
                2.5612819054028872e-06,
                7.88926446679691e-06,
                1.1478766757718129e-05,
                6.144177531767002e-06,
                2.753568782024347e-05
            ],
            [
                2.3823690999290963e-07,
                3.4663249714612693e-07,
                2.1024329090929374e-07,
                3.05902190458764e-07,
                7.338212429582604e-07,
                5.715003789046955e-07,
                3.4663249714612693e-07,
                7.338208055680009e-07,
                2.561281294760143e-06,
                8.764247451307293e-08
            ],
            [
                7.3382080556433e-07,
                NaN,
                2.90231094723893e-06,
                4.222834451403972e-06,
                8.939695238634211e-06,
                3.927861066170637e-07,
                6.962259569750576e-06,
                1.670141786325573e-05,
                1.5534983101602148e-06,
                7.338208055680009e-07
            ],
            [
                0.999997273529408,
                0.99999862904214,
                0.9999938558239402,
                0.9999417087485789,
                2.902312677150514e-06,
                0.9999646437325787,
                1.5534973842076057e-06,
                0.9999980052700421,
                1.9947304348862686e-06,
                3.288749849529972e-06
            ],
            [
                1.3709573702822306e-06,
                4.785093353940187e-06,
                1.3709572068522336e-06,
                3.53562422882756e-05,
                5.043474081993875e-07,
                6.9622595696935874e-06,
                8.315279285370317e-07,
                6.962259569750576e-06,
                9.422448185478557e-07,
                1.8925145985104064e-05
            ],
            [
                0.9999957771675689,
                0.9999921107346014,
                0.999986992873121,
                0.9999925887219043,
                0.9999417087415902,
                0.9999982396567881,
                0.9999832985841778,
                0.9999885212318844,
                0.9971990732754465,
                0.9999949062950065
            ],
            [
                1.9947306726594253e-06,
                0.9999993524053566,
                0.9999998642567353,
                0.9999998724809267,
                0.9999938558246754,
                0.9999852610110236,
                1.2098658277335738e-06,
                0.999998540623954,
                3.92786293909545e-07,
                6.962254589914941e-06
            ],
            [
                5.715006514176113e-07,
                1.855391681906175e-07,
                1.0677026154827912e-06,
                3.4663249714612693e-07,
                5.71500719545698e-07,
                2.382370235933104e-07,
                1.4449805540763184e-07,
                3.059022998581767e-07,
                2.699577774589574e-07,
                2.699578740032504e-07
            ],
            [
                2.3823702359290413e-07,
                1.6373774480605869e-07,
                3.0590219045914655e-07,
                5.715003789046955e-07,
                2.3823693839325527e-07,
                1.8553905760062447e-07,
                7.338207180898968e-07,
                2.1024339116168358e-07,
                9.422443692574719e-07,
                7.338210680021253e-07
            ],
            [
                1.0677027427624903e-06,
                5.715006514176113e-07,
                6.47595107001401e-07,
                2.9023116392097746e-06,
                3.05902336324494e-07,
                1.3709568799919866e-06,
                1.994729721518893e-06,
                1.5534983101644536e-06,
                4.450852641737424e-07,
                1.209865827752005e-06
            ],
            [
                3.726639284144195e-06,
                1.9947299593078385e-06,
                2.382369383923073e-07,
                1.3709576971425944e-06,
                1.5534977545886537e-06,
                3.7266397283908927e-06,
                3.7266383956509585e-06,
                3.466326211113502e-07,
                1.3709567165579959e-06,
                3.2887506336235617e-06
            ],
            [
                9.422447062294175e-07,
                7.338207180864763e-07,
                3.4663274507098256e-07,
                1.0677033791583005e-06,
                4.450852111100568e-07,
                9.422450432014836e-07,
                8.31528126775552e-07,
                3.927860597935108e-07,
                2.699579061812927e-07,
                5.715004470295662e-07
            ],
            [
                0.999991060299451,
                3.927862939126708e-07,
                4.4508505193932864e-07,
                8.315282259009745e-07,
                3.2887506336235617e-06,
                5.043472879525233e-07,
                2.561282210729555e-06,
                9.422444815765128e-07,
                6.1441746020359e-06,
                1.2098659719757836e-06
            ],
            [
                2.260324567337161e-06,
                6.144177531767002e-06,
                2.561282210740037e-06,
                6.144176799334096e-06,
                3.0590215399183813e-07,
                1.012999218776902e-05,
                1.370957860576702e-06,
                3.466327863961242e-07,
                5.715006514167015e-07,
                1.7603430034867993e-06
            ],
            [
                2.699576809143613e-07,
                3.466325797896173e-07,
                3.466325384678894e-07,
                1.2751899728311609e-07,
                9.931193325852072e-08,
                2.3823693839325527e-07,
                6.475947210046347e-07,
                4.450848927650143e-07,
                9.422448185534261e-07,
                3.9278605979534166e-07
            ],
            [
                2.561282210729555e-06,
                1.3709573702856596e-06,
                2.902312331170226e-06,
                2.1024344128488479e-07,
                0.9998911030524702,
                0.04208772746504851,
                7.889264466868659e-06,
                0.9999964991464236,
                1.3007134667436886e-05,
                6.475948753991907e-07
            ],
            [
                5.043472278322555e-07,
                0.9999995549149483,
                9.422444815814404e-07,
                5.715003107767143e-07,
                2.3823699519290042e-07,
                1.0677027427624903e-06,
                1.2098656835224664e-06,
                8.315280276626197e-07,
                1.0677033791612137e-06,
                3.927860597945825e-07
            ],
            [
                0.9999957771655567,
                6.475950298011458e-07,
                0.9999992188515768,
                2.102434162245973e-07,
                6.475947982037486e-07,
                2.9023112932177327e-06,
                0.9999985406237801,
                0.9999994956525922,
                3.927862002663297e-07,
                5.043472278322555e-07
            ],
            [
                1.7603430034867993e-06,
                2.902312331170226e-06,
                9.422445939032799e-07,
                1.0129987357287368e-05,
                4.785092783519724e-06,
                NaN,
                1.3709567165617364e-06,
                1.9947292459347367e-06,
                1.4738989000422955e-05,
                1.6701429808632785e-05
            ],
            [
                3.2887502415767434e-06,
                7.889261645427538e-06,
                4.785095065232451e-06,
                2.9023116392097746e-06,
                2.1444950971601277e-05,
                1.9947299593078385e-06,
                6.144177531811707e-06,
                9.422442569315887e-07,
                6.144173869603344e-06,
                1.1478770862882149e-05
            ],
            [
                2.2603248367949354e-06,
                1.2098658277335738e-06,
                1.3709573702822306e-06,
                1.3709575337125585e-06,
                1.553497384196656e-06,
                5.4222183235249605e-06,
                2.561282210740037e-06,
                6.144177531660828e-06,
                1.7603436330259153e-06,
                4.450848927658745e-07
            ],
            [
                1.2098658277451275e-06,
                1.0677028700363782e-06,
                3.927860597945825e-07,
                1.9947304348862686e-06,
                5.715003107738556e-07,
                9.422448185510695e-07,
                1.3709575337078829e-06,
                2.5612812947508257e-06,
                8.315278294097538e-07,
                5.043474081993875e-07
            ]
        ]
    },
    {
        "q_id": "10016_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.260324567337161e-06,
                9.931187406410953e-08,
                0.9999996533673382,
                4.450852641737424e-07,
                9.610246086092883e-05,
                0.9999993524054345,
                6.962258739796719e-06,
                0.9999997761971318,
                1.1478765389368729e-05,
                0.9999995818812275
            ],
            [
                1.6373776432509826e-07,
                2.1024334103581732e-07,
                1.275190732904469e-07,
                1.8553914607267268e-07,
                5.715005832895975e-07,
                8.315279285370317e-07,
                3.059022998581767e-07,
                1.855391239547094e-07,
                2.3823690999323465e-07,
                4.450852641737424e-07
            ],
            [
                1.0,
                1.0,
                0.9999999358793562,
                0.9999999434137571,
                0.9999998257022046,
                0.9999999611088904,
                1.0,
                0.9999999067050943,
                1.0,
                0.9999998874647307
            ],
            [
                1.0,
                1.0,
                0.9999999176674357,
                0.9999999226558146,
                0.999999922655787,
                0.9999999176674946,
                0.9999998724809419,
                0.9999998874648112,
                0.9999998802069731,
                0.9999998942830358
            ],
            [
                0.9999967112513307,
                0.9999981261237253,
                0.9999964991460107,
                0.9999982396563686,
                0.9999981261239481,
                0.9999967112517222,
                0.999999168471676,
                0.9999987901347502,
                0.9999942280772248,
                0.9999981261243946
            ],
            [
                0.9999999176674651,
                0.9999999123574838,
                1.0,
                0.9999997300421906,
                0.9999998642567353,
                1.0,
                0.9999999006881497,
                1.0,
                0.9999997300421583,
                0.9999999067050165
            ],
            [
                6.475946438055299e-07,
                2.1024336609874897e-07,
                1.6373766672994222e-07,
                5.715003789046955e-07,
                9.422447062294175e-07,
                1.5534984953552536e-06,
                1.5534971990169383e-06,
                3.927862002663297e-07,
                3.4663278639892215e-07,
                3.927862002663297e-07
            ],
            [
                1.0,
                0.9999998724808964,
                0.9999999500627739,
                0.9999999067051054,
                0.9999998024947272,
                1.0,
                0.9999999123575672,
                0.9999999123575882,
                0.9999999358794174,
                1.0
            ],
            [
                5.715003789033962e-07,
                8.31528424162821e-07,
                9.422449308774482e-07,
                7.338210680021253e-07,
                7.338213304363436e-07,
                2.1024326584582131e-07,
                3.927860597945825e-07,
                3.927863875616689e-07,
                7.338212429582604e-07,
                2.1024334103581732e-07
            ],
            [
                0.999999463124805,
                0.9999996940976276,
                0.9999997463981941,
                0.999999789756559,
                0.9999995262093297,
                0.9999997617631471,
                0.9999997126314815,
                0.9999994631250617,
                0.9999996743688979,
                0.9999997300421907
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                0.999999789756659,
                0.9999997300422548,
                0.9999999226557685,
                0.9999998942830106,
                0.9999999732705602,
                0.9999997761971849
            ],
            [
                1.0,
                0.9999999273417923,
                1.0,
                0.9999993106387088,
                0.999999922655787,
                0.9999999006880076,
                0.9999999358793332,
                0.9999999123574523,
                2.699577774585891e-07,
                0.9999999226557225
            ],
            [
                0.9999996743688588,
                0.9999998362622748,
                0.9999997300422871,
                0.9999998144608542,
                1.0,
                0.9999999317439221,
                0.9999997761971051,
                0.9999997761972117,
                0.999999927341827,
                0.9999997761972117
            ],
            [
                0.9999996940978828,
                0.9999998461826589,
                0.9999998024946568,
                0.9999999067051499,
                0.9999999176675044,
                0.9999999067050943,
                0.9999999123575674,
                0.9999997126313784,
                0.999999814460832,
                0.9999999006880432
            ],
            [
                0.9999997761971583,
                0.9999998024946802,
                0.999999917667573,
                0.9999996533674618,
                1.0,
                0.9999998942829855,
                0.9999998724810029,
                0.999999953088334,
                0.9999997126315497,
                0.9999998257021631
            ],
            [
                0.9999969105044505,
                0.9999998874647307,
                0.9999998461826405,
                9.422448185534261e-07,
                0.9999997761970782,
                0.9999980052702804,
                0.9999997761970516,
                0.9999996072137531,
                0.9999995549151076,
                1.8553916819032217e-07
            ],
            [
                1.0,
                1.0,
                0.9999995549150015,
                0.9999998257020799,
                1.0,
                1.0,
                0.9999999273417922,
                0.9999995818813272,
                0.9999994631248686,
                0.9999999434137907
            ],
            [
                1.8553914607128047e-07,
                0.9999852610233456,
                1.012999460278499e-05,
                4.450852111148132e-07,
                8.315278294097538e-07,
                1.0129989772412744e-05,
                0.9999910603015862,
                2.3823702359290413e-07,
                5.82912516497227e-05,
                0.9999945777804141
            ],
            [
                5.422218969769604e-06,
                1.1478766757049986e-05,
                0.00013982212416968073,
                6.9622579095833456e-06,
                3.2887502415243994e-06,
                6.962254589851619e-06,
                7.889264466639056e-06,
                0.9999898700103208,
                0.9999969105062939,
                0.9999969105040847
            ],
            [
                0.9999998144608541,
                0.9999998642567353,
                0.9999998024947273,
                0.9999998362623139,
                0.999999922655833,
                0.9999998024945624,
                0.9999996743687035,
                0.9999998362623334,
                0.9999998257021423,
                0.9999999634651662
            ],
            [
                2.6995784182140636e-07,
                2.1024339116082313e-07,
                4.450852111135988e-07,
                4.450848927650143e-07,
                6.475947982002148e-07,
                3.0590215399183813e-07,
                5.043476486915964e-07,
                3.9278605979208185e-07,
                9.422444815679433e-07,
                2.1024334103505245e-07
            ],
            [
                1.2751901248454963e-07,
                8.764244316973974e-08,
                1.8553910183674878e-07,
                1.209865827752005e-06,
                1.6373774480605869e-07,
                1.0677024882029858e-06,
                1.3709573702856596e-06,
                3.7266379514061143e-06,
                2.699576809143613e-07,
                1.0677026154827912e-06
            ],
            [
                0.9999995549150017,
                0.9999997897566343,
                0.9999996940978828,
                0.9999996310114168,
                0.9999996743687429,
                0.9999994956527133,
                0.999999526209613,
                0.9999996072138005,
                0.9999992661791084,
                0.9999996310113725
            ],
            [
                0.9999999397642293,
                1.0,
                0.9999996533674617,
                0.9999998724809268,
                0.9999998802069731,
                0.9999999067050164,
                0.9999995262094987,
                0.9999999530883452,
                0.9999999397642653,
                0.9999999067050498
            ],
            [
                1.0,
                0.9999999273418789,
                0.999999939764294,
                0.9999999176675829,
                1.0,
                0.9999998802069874,
                0.9999998802069302,
                1.0,
                0.9999999226557316,
                0.9999999176675731
            ],
            [
                0.9999994631248683,
                0.9999999123575672,
                0.9999998802069302,
                0.9999999006880194,
                0.9999998257021422,
                0.9999998724809419,
                0.9999998724809116,
                0.9999999006880076,
                1.0,
                0.9999997126313098
            ],
            [
                1.0,
                0.9999999067050276,
                1.0,
                1.0,
                0.9999998874647844,
                1.0,
                0.9999999500628155,
                0.9999998461826406,
                0.9999999317439221,
                0.9999998257021007
            ],
            [
                1.4449798650569826e-07,
                1.1253525596174225e-07,
                3.927863407379485e-07,
                8.76424013786396e-08,
                1.27519088491875e-07,
                3.466326624336003e-07,
                4.4508515805735777e-07,
                1.855391681906175e-07,
                9.931187406410953e-08,
                2.699578096403948e-07
            ],
            [
                0.999999939764215,
                1.7603430034867993e-06,
                0.00020342702218063233,
                8.939697369980456e-06,
                0.9999998024946566,
                8.315284241650899e-07,
                1.760343213335281e-06,
                8.939695238634211e-06,
                0.9999998555020307,
                1.0
            ],
            [
                1.0,
                0.9999998362623334,
                0.9999998144608984,
                0.9999997897566592,
                0.9999998724810027,
                0.999999674368859,
                0.9999997897566593,
                0.9999998362622944,
                0.9999997463980429,
                0.9999997617630334
            ],
            [
                0.999999864256719,
                0.9999998461826406,
                1.0,
                0.9999998724809268,
                1.0,
                0.9999999123574942,
                0.9999997897566091,
                0.9999997897565588,
                0.9999998362622358,
                1.0
            ],
            [
                0.9999991148427545,
                0.9999992661791081,
                0.9999993106392024,
                0.9999991148433874,
                0.9999991148431768,
                0.9999992188518573,
                0.9999992661788456,
                0.9999994284993492,
                0.9999993524048941,
                0.9999989322971319
            ],
            [
                0.9999998461826222,
                0.9999998461826589,
                0.9999999176674848,
                1.0,
                0.9999998555020135,
                0.9999998024947037,
                0.9999998461826406,
                0.9999997761971317,
                0.9999999358794173,
                1.0
            ],
            [
                0.999999855501962,
                0.999999872480942,
                1.0,
                0.9999998874648112,
                1.0,
                0.9999999176675143,
                0.999999825702163,
                0.9999983463096281,
                0.9999998555019964,
                0.9999997617630619
            ],
            [
                1.0,
                0.9999995818812275,
                0.9999999123575465,
                0.9999998874647441,
                1.0,
                0.9999999530883675,
                1.0,
                1.0,
                0.9999999123574733,
                1.0
            ],
            [
                0.999999846182714,
                1.0,
                0.9999997897566341,
                0.9999997617630051,
                0.9999996310115924,
                0.9999997126314814,
                0.999999939764215,
                1.0,
                0.9999999226557316,
                0.9999998144608985
            ],
            [
                0.9999999358794021,
                0.9999999586006344,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999468421883,
                0.9999999611089136,
                1.0
            ],
            [
                0.9999998642567351,
                0.9999998802069159,
                1.0,
                1.0,
                0.9999999176674553,
                1.0,
                1.0,
                0.9999999358794326,
                1.0,
                1.0
            ],
            [
                0.9999998024947037,
                0.9999999273418616,
                0.9999999226557593,
                0.9999998802069588,
                0.9999999176675239,
                0.9999998724809267,
                1.0,
                1.0,
                0.9999998942829729,
                1.0
            ],
            [
                0.9999998555019447,
                1.0,
                0.9999996940976275,
                0.9999999123575987,
                0.9999997463981033,
                0.9999998724809877,
                0.9999998942829855,
                0.9999999559305681,
                0.9999996533672965,
                0.999999776197025
            ],
            [
                1.0129989772532511e-05,
                1.8925157265710765e-05,
                2.1444940745839484e-05,
                0.99999971263131,
                1.4738981972323349e-05,
                0.9999995262094425,
                1.3007130015488633e-05,
                8.939693107190907e-06,
                3.120191881321371e-05,
                6.475949526020042e-07
            ],
            [
                0.9999999358793409,
                0.9999998555019963,
                0.9999999358794402,
                0.9999996533673792,
                0.9999999530883172,
                0.9999999176674553,
                0.9999997761970516,
                0.9999999500627977,
                1.0,
                0.999999939764294
            ],
            [
                0.9999998724809116,
                0.9999998257021007,
                0.9999996310115041,
                0.9999998144608099,
                0.999999776197185,
                0.9999998802069587,
                0.9999997463982242,
                0.9999997300421906,
                0.9999997761971317,
                0.9999995818811279
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999358793792,
                1.0,
                0.9999999067050165,
                1.0,
                0.9999999397642294,
                0.9999999067050054,
                1.0
            ],
            [
                4.785096206047877e-06,
                4.0063696967815485e-05,
                1.2098659719788098e-06,
                4.222835458148261e-06,
                2.7535694384081332e-05,
                3.120191509592808e-05,
                0.9999989322966218,
                0.9999985406236088,
                2.144495097113319e-05,
                3.1201907657271834e-05
            ],
            [
                0.9999999067050609,
                0.9999999468421313,
                1.0,
                1.0,
                0.9999998642566381,
                0.9999999397642725,
                1.0,
                0.9999998555019274,
                0.9999999067051499,
                0.9999999397642582
            ],
            [
                0.999999694097883,
                0.9999999273418875,
                0.9999994284995539,
                1.0,
                1.0,
                0.9999997897566341,
                0.9999999067051165,
                0.9999998555019619,
                0.9999998461826223,
                1.0
            ],
            [
                0.9999996310115044,
                0.9999997761972117,
                0.9999997617631472,
                1.0,
                0.9999997463982242,
                0.9999995818812776,
                0.9999998024945624,
                0.9999998144608319,
                0.9999998461826406,
                0.9999998724809875
            ],
            [
                0.9999998144608983,
                0.999999846182714,
                0.9999998024946567,
                0.9999999123575465,
                0.9999998724808964,
                0.9999998362622944,
                0.9999999067049943,
                0.9999999317439059,
                0.999999900688055,
                0.9999997617631754
            ],
            [
                0.9999999317440198,
                0.9999998144608099,
                0.999999953088362,
                0.999999776197025,
                0.9999998144608762,
                0.9999997761972117,
                0.999999631011636,
                0.9999999123574419,
                0.9999999397642796,
                0.9999997617630618
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999397643156,
                1.0,
                1.0,
                0.9999999123575151,
                1.0,
                0.9999999067050165,
                0.9999998555019447
            ],
            [
                1.0,
                0.9999998724808964,
                1.0,
                1.0,
                0.9999998024947037,
                0.9999999358794173,
                0.9999998642566219,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                0.999999761763147,
                0.9999999358794021,
                1.0,
                0.9999999123575046,
                0.9999998724808964,
                1.0,
                1.0,
                1.0
            ],
            [
                0.99999994341373,
                0.9999998802069588,
                0.9999994956527128,
                0.9999997126313102,
                0.9999998802069017,
                0.9999997617631754,
                1.0,
                0.9999998362623335,
                0.9999999317440116,
                0.9999998362622748
            ],
            [
                0.9999998874649185,
                0.9999998724808964,
                0.9999997617631754,
                0.999999880206916,
                0.9999999067049831,
                0.9999999067051499,
                0.999999927341801,
                0.9999998257021214,
                0.9999998144609205,
                0.9999998257021008
            ],
            [
                0.9999999317439303,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999997897566841,
                0.9999999434137773,
                0.9999998144608098,
                0.9999998461826772,
                0.9999999500628274,
                0.9999999358793867,
                1.0,
                0.9999999317440197,
                0.9999999006881496,
                0.999999846182604
            ],
            [
                1.0,
                0.999999927341853,
                0.9999998461826223,
                0.9999998144608762,
                0.9999997897566341,
                1.0,
                1.0,
                0.9999999358793792,
                0.9999997617630618,
                0.999999776197025
            ],
            [
                0.9999997300421906,
                1.0,
                0.9999999530884012,
                1.0,
                1.0,
                0.9999996743687424,
                1.0,
                1.0,
                0.9999998942830737,
                0.9999998257021631
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999998257020591,
                0.9999998942830863,
                0.9999997897567344,
                0.9999997761971583,
                0.9999998144609425,
                0.9999998802068875,
                0.9999998144608984,
                0.9999998642567028,
                0.9999998802068873,
                0.9999997761970248
            ],
            [
                0.9999995818813769,
                0.9999995818812772,
                0.9999997617630902,
                0.9999998144608541,
                0.9999995549147894,
                0.9999997300423195,
                0.999999776197025,
                0.9999992661787581,
                0.9999998024945626,
                0.9999998362622358
            ],
            [
                5.4222209089700225e-06,
                1.1478764020883773e-05,
                1.2098659719716573e-06,
                1.9947292459265734e-06,
                2.2603245673155757e-06,
                1.4738988999672284e-05,
                0.9999969105041031,
                3.7266388398585725e-06,
                5.715007195447234e-07,
                9.422443692446175e-07
            ],
            [
                2.5612816000646084e-06,
                3.726638395634011e-06,
                2.3823690999063455e-07,
                7.88926446679691e-06,
                2.7535681254003062e-05,
                4.450852111100568e-07,
                2.5612834320563895e-06,
                9.422445939054222e-07,
                4.785095635655362e-06,
                3.4663266242969896e-07
            ],
            [
                0.9999997300422548,
                0.9999994284992808,
                0.9999992661790201,
                0.9999994631249323,
                0.9999995262094423,
                0.9999996940977733,
                0.9999997300421262,
                0.9999997463980125,
                0.9999998942829603,
                0.9999998144608099
            ],
            [
                0.9999998257020593,
                0.9999998461826038,
                0.999999802494586,
                0.9999998257021008,
                0.9999998362622748,
                0.9999998942829603,
                0.9999997617630619,
                0.9999998555019619,
                0.9999996940978099,
                0.999999607213847
            ],
            [
                0.9999998942829855,
                0.9999997463981637,
                0.999999802494586,
                0.999999825702059,
                0.9999997761971849,
                0.9999997126313098,
                0.9999996940977733,
                0.9999997463981637,
                0.9999999006880549,
                0.999999887464838
            ],
            [
                0.9999885212278025,
                8.939700567094277e-06,
                1.5534977545886537e-06,
                1.3709576971463352e-06,
                1.6373764721072816e-07,
                1.892515501014656e-05,
                1.8553905760062447e-07,
                1.3709567165617364e-06,
                2.5612812947508257e-06,
                0.9999938558224803
            ],
            [
                0.9999998802069017,
                0.9999999123575256,
                0.9999999176675829,
                0.9999999123574732,
                0.99999994341373,
                0.9999998362622358,
                0.999999776197105,
                1.0,
                0.9999999226557962,
                0.9999998874648112
            ],
            [
                0.9999997897567344,
                0.9999998942830359,
                1.0,
                0.9999999176674553,
                0.9999997300423192,
                0.9999997897566592,
                0.9999997126315155,
                0.9999998362622553,
                0.9999998802069017,
                0.9999997463981335
            ],
            [
                0.9999998555019274,
                1.0,
                1.0,
                0.9999998642566543,
                1.0,
                0.9999999176675632,
                0.999999864256719,
                0.9999998555020136,
                0.9999999358793485,
                0.9999998802069588
            ],
            [
                0.999999931743914,
                0.9999999176674848,
                0.9999998724808964,
                0.9999999006880431,
                0.9999998942829603,
                1.0,
                0.9999996743688588,
                0.9999996533672553,
                0.9999999176675436,
                0.9999998362623529
            ],
            [
                0.9999999273418875,
                0.9999998942829477,
                0.9999998555020309,
                0.9999997897566841,
                0.9999997617630618,
                1.0,
                0.9999998257021007,
                1.0,
                0.9999999006879957,
                0.9999997617630902
            ],
            [
                0.9999993524050487,
                0.9999991148430717,
                0.9999991148433883,
                0.9999995549151078,
                0.9999996940978099,
                0.999998932296877,
                0.9999993916408919,
                0.9999994284992813,
                0.9999993916406742,
                0.9999988634360208
            ],
            [
                1.0,
                0.9999998802069873,
                1.0,
                0.999999906705061,
                1.0,
                1.0,
                0.9999999006881142,
                1.0,
                0.999999880206916,
                0.999999906705061
            ],
            [
                8.315278294114555e-07,
                8.764245361752286e-08,
                2.9023119851899796e-06,
                1.3709576971463352e-06,
                3.059021175261338e-07,
                1.6373764720990908e-07,
                1.3709567165617364e-06,
                2.2603248367949354e-06,
                4.785096776499213e-06,
                8.939699501416646e-06
            ],
            [
                0.9999999123574523,
                0.9999997761970782,
                0.9999998257021215,
                0.9999994956527726,
                0.9999998874648917,
                0.9999998144609205,
                1.0,
                0.9999998144608542,
                0.9999997761971317,
                0.9999996940977004
            ],
            [
                0.999999730042094,
                0.9999998024946095,
                0.9999997761971849,
                0.9999995549147892,
                1.0,
                0.9999998555020309,
                0.9999997617630334,
                0.9999998724809419,
                0.9999998144609424,
                0.9999998461826406
            ],
            [
                5.715004470313855e-07,
                4.222834954801051e-06,
                1.6701425827133152e-05,
                1.8925145985895816e-05,
                5.829124471187197e-05,
                3.466327450765785e-07,
                1.0677027427600627e-06,
                2.5612819054133693e-06,
                4.450851580566494e-07,
                2.1024339116082313e-07
            ],
            [
                0.9999997897566841,
                0.9999998874649185,
                0.9999999317440035,
                0.9999998724809267,
                0.9999999468421249,
                0.9999998461827323,
                0.9999998362622359,
                0.9999998874648917,
                0.9999998874647441,
                0.9999999559305996
            ],
            [
                1.0,
                0.9999999500628274,
                1.0,
                0.9999999226558054,
                0.9999999273418703,
                0.9999998555020309,
                1.0,
                0.999999887464771,
                0.9999998642567351,
                0.9999999006880431
            ],
            [
                0.9999997617631186,
                0.9999999434137907,
                0.9999998555020135,
                0.9999998874649185,
                1.0,
                0.9999992188512976,
                0.9999999006880077,
                0.9999998362623334,
                0.9999998144609425,
                0.9999997761970782
            ],
            [
                0.9999991148428605,
                0.9999984465026195,
                0.9999996310115923,
                0.9999992188519521,
                0.9999993524054349,
                0.9999994284994185,
                0.9999996940978829,
                0.9999997463980428,
                0.9999989969857961,
                0.9999993106388739
            ],
            [
                0.9999998724809268,
                0.9999997300421262,
                0.9999998942830359,
                0.9999999067051387,
                0.9999998642566543,
                0.9999998642566219,
                0.9999998024947038,
                0.9999998942828972,
                0.999999931743971,
                0.9999998802069017
            ],
            [
                1.994729483723626e-06,
                2.260324836776948e-06,
                4.222834451355964e-06,
                1.7603438428800754e-06,
                8.315278294072958e-07,
                7.338207180864763e-07,
                6.475950297971703e-07,
                3.726641061085547e-06,
                3.288749849498565e-06,
                1.2098662604291696e-06
            ],
            [
                0.9999998024946096,
                0.9999999176674357,
                0.9999999006881142,
                1.0,
                0.9999997897566593,
                0.9999997126315499,
                0.9999997300422871,
                0.9999998257020591,
                0.9999997897567092,
                0.9999998802069874
            ],
            [
                0.9999999226558054,
                1.0,
                0.9999999176675535,
                0.9999999434137975,
                1.0,
                0.9999998942830359,
                0.999999746398073,
                0.9999999634651444,
                0.9999998144609645,
                0.999999894282935
            ],
            [
                0.9999999397642437,
                0.9999999317439873,
                0.9999996940978096,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999317440036,
                0.9999999358794249,
                1.0
            ],
            [
                3.466325797896173e-07,
                7.889265407255982e-06,
                8.939693107190907e-06,
                2.2603242978871282e-06,
                2.90231094723893e-06,
                1.209865539295696e-06,
                5.04347468323289e-07,
                1.0677032518785256e-06,
                4.450849988798682e-07,
                1.0129989772532511e-05
            ],
            [
                1.0,
                0.9999999123575568,
                1.0,
                0.9999996743688975,
                0.9999998555020135,
                0.9999999176674357,
                0.9999994631249963,
                1.0,
                3.0590222692437275e-07,
                1.0
            ],
            [
                0.9999999397643011,
                0.9999998024946802,
                0.9999998942829477,
                0.9999998802069588,
                0.9999995549147362,
                0.9999996072138002,
                0.9999998461826405,
                0.9999996072137535,
                0.9999998724809877,
                0.9999997617631753
            ],
            [
                0.9999998362623529,
                0.9999996940977368,
                0.999999789756659,
                0.9999998024946332,
                0.9999996743686648,
                0.9999996072138,
                0.9999998362622943,
                0.9999998257020799,
                0.9999996533672553,
                0.9999996072137065
            ],
            [
                0.9999999176675338,
                1.0,
                0.9999998461826406,
                0.9999996940977004,
                0.9999998461826222,
                0.9999999067050832,
                1.0,
                0.9999995818814268,
                0.9999997761970782,
                0.9999998874649185
            ],
            [
                0.9999997897566341,
                0.9999997300421585,
                0.99999967436882,
                0.9999996072137064,
                0.9999998724810027,
                0.9999996743687035,
                0.9999987121047852,
                0.9999998724809268,
                0.9999997126313442,
                0.9999998461826956
            ],
            [
                0.9999999067050498,
                0.9999999397642797,
                0.9999999273418876,
                1.0,
                1.0,
                1.0,
                0.999999939764251,
                1.0,
                0.9999999317439383,
                0.9999999067051388
            ],
            [
                0.9999997761970248,
                0.9999998257021214,
                0.9999996940977368,
                0.9999998942829603,
                0.999999631011548,
                0.9999999067051166,
                0.9999999273418442,
                0.999999631011504,
                0.9999998257021007,
                0.9999997463981334
            ],
            [
                5.71500378896509e-07,
                8.315283250371857e-07,
                1.670141786325573e-05,
                7.338209805170655e-07,
                9.422449308716635e-07,
                4.0063706517323215e-05,
                2.9023119851635836e-06,
                1.892514598551715e-05,
                1.2098653950656417e-06,
                9.422447062270609e-07
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999397643156,
                0.9999999656787325,
                1.0,
                0.9999999559306206,
                1.0
            ],
            [
                9.931190958076104e-08,
                6.475947982037486e-07,
                2.699576809143613e-07,
                2.1024331597262577e-07,
                3.466327450756327e-07,
                3.059021904580685e-07,
                2.3823688159237777e-07,
                2.102434412875379e-07,
                2.382368531929327e-07,
                1.6373766672973748e-07
            ],
            [
                0.9999997463982242,
                0.9999997897566841,
                0.9999999006881496,
                0.9999998802069874,
                0.9999993106392018,
                0.9999998802069445,
                0.9999999067050276,
                0.9999996940977005,
                0.9999996940977733,
                0.9999998461826405
            ],
            [
                1.0,
                1.0,
                0.9999998802069445,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999176675436,
                0.9999999559306101,
                0.9999999317440035
            ],
            [
                0.9999998024946333,
                1.0,
                0.9999998362622748,
                0.9999996533672965,
                0.9999998024945861,
                0.9999993916411088,
                0.999999554914736,
                0.9999997761971583,
                0.9999995818812772,
                0.999999428499758
            ],
            [
                1.0,
                0.9999999397642079,
                0.9999999500627799,
                0.9999998724809268,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                4.4508526417298334e-07,
                5.043472879540142e-07,
                7.338207180898968e-07,
                7.338213304363436e-07,
                2.3823696679327928e-07,
                8.315281267882195e-07,
                2.699576809143613e-07,
                1.6373764721072816e-07,
                0.9999987121049405,
                2.699576809143613e-07
            ],
            [
                0.9999997761970784,
                0.999999825702163,
                0.9999998555019276,
                0.9999998802069017,
                0.9999998724809268,
                0.9999996072139407,
                0.9999997463982244,
                1.0,
                0.999999846182714,
                0.999999814460832
            ],
            [
                0.9999998555019964,
                1.0,
                0.9999998461826038,
                0.9999999586005851,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999559305943
            ],
            [
                0.9999998144608099,
                0.9999997126314812,
                0.9999997463980125,
                0.999999746398194,
                0.9999997617630333,
                0.999999789756609,
                0.9999996072137531,
                0.9999998257020591,
                0.9999997126313099,
                0.9999997617629766
            ],
            [
                0.9999999176675632,
                0.9999997463981637,
                0.9999998362623334,
                1.0,
                0.999999730042094,
                0.9999996533674205,
                0.9999999226558146,
                0.9999999067051054,
                0.9999999123574629,
                0.9999998802069587
            ],
            [
                0.9999995549148425,
                1.0,
                1.0,
                0.9999997617629766,
                0.9999998144609425,
                0.9999996072138938,
                0.9999997463981033,
                0.9999996072136128,
                0.999999607213847,
                1.0
            ],
            [
                1.0,
                0.9999996743686648,
                0.9999998144609203,
                0.9999998257021838,
                0.9999997897566091,
                0.9999997126313099,
                0.999999495652532,
                0.9999997126315497,
                0.9999998461826038,
                0.9999998724810027
            ],
            [
                2.6995784182140636e-07,
                3.466327863983311e-07,
                3.466325797896173e-07,
                1.8553907971758842e-07,
                2.382369667929001e-07,
                1.4449798650551755e-07,
                2.9023126771227976e-06,
                5.715003789046955e-07,
                1.0677026154806063e-06,
                7.338208055664991e-07
            ],
            [
                0.9999997300422871,
                0.9999999123574419,
                0.9999997617631754,
                0.9999999067051055,
                0.9999996310116361,
                0.99999981446081,
                0.9999997463980126,
                0.9999994284995538,
                0.9999997897566091,
                0.9999996533673793
            ],
            [
                0.9999999397642222,
                1.0,
                0.9999998642566381,
                0.9999998362622359,
                0.9999999434137637,
                0.9999999273418962,
                0.9999998461826223,
                0.9999999317439059,
                1.0,
                0.9999999358794021
            ],
            [
                0.9999999067051389,
                0.9999996940978464,
                0.9999998257021837,
                1.0,
                0.9999998874648918,
                0.9999999067050832,
                0.9999999123574733,
                0.999999917667583,
                0.9999999317439059,
                0.9999998461826406
            ],
            [
                1.0,
                0.9999994284994853,
                0.9999998362623334,
                0.999999581881078,
                0.999999730042255,
                0.9999998362622748,
                0.9999994631248685,
                0.9999998257020799,
                0.9999999006881142,
                0.9999998724809875
            ],
            [
                1.0,
                0.9999994284997586,
                0.9999997126313785,
                0.9999997463981941,
                1.0,
                0.9999998024946333,
                0.9999996310115044,
                0.9999998461827323,
                0.9999997463980127,
                0.9999997126315499
            ],
            [
                0.9999998362622553,
                1.9947304348862686e-06,
                7.338208055664991e-07,
                2.3823682479292225e-07,
                1.067703124601679e-06,
                2.3823685319244518e-07,
                5.043474683240344e-07,
                1.2098659719788098e-06,
                5.715003107767143e-07,
                2.699578740032504e-07
            ],
            [
                0.999999776197025,
                0.9999997617630902,
                0.9999998144609203,
                0.9999997617629767,
                1.0,
                0.9999998555020481,
                0.9999995262094425,
                0.9999997761970782,
                0.9999997463980731,
                0.999999581881078
            ],
            [
                0.999999730042287,
                0.9999998461827322,
                0.9999997126314469,
                0.9999995549148952,
                0.9999999559306154,
                0.9999996072137532,
                0.999999935879425,
                0.9999996310113721,
                1.0,
                1.0
            ],
            [
                1.855391239544352e-07,
                1.5534975693869924e-06,
                3.9278605979534166e-07,
                3.05902263391829e-07,
                1.275190732904469e-07,
                3.05902263391829e-07,
                2.3823690999323465e-07,
                2.6995774527718623e-07,
                3.9278605979208185e-07,
                2.3823690999323465e-07
            ],
            [
                2.6995790618469934e-07,
                9.422443692574719e-07,
                6.023571320847322e-08,
                9.931190958076104e-08,
                1.209865827752005e-06,
                6.475946438055299e-07,
                5.043476486924565e-07,
                1.6373764721072816e-07,
                1.3709575337159875e-06,
                1.4449800373118268e-07
            ],
            [
                1.0,
                0.9999999226558424,
                0.99999994341373,
                0.9999999176675634,
                1.0,
                1.0,
                0.9999998642566704,
                1.0,
                0.9999999226557408,
                1.0
            ],
            [
                1.0,
                1.0,
                0.999999917667475,
                0.9999999358794096,
                0.9999999176674848,
                1.0,
                0.9999998802069445,
                0.9999998257021838,
                0.9999999006881259,
                0.9999998724809877
            ]
        ]
    },
    {
        "q_id": "10298_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999999123575255,
                0.9999995818813767,
                0.9999997126314469,
                0.9999999358794021,
                0.9999999067051499,
                0.9999998942829602,
                0.9999995818814265,
                0.9999999468421503,
                0.9999997761972116,
                0.9999996743686257
            ],
            [
                0.9999998802069159,
                0.9999999273417923,
                0.9999998144608541,
                0.999999906705061,
                0.9999995262094422,
                0.999999922655833,
                0.9999998802069587,
                0.9999997617631469,
                0.9999996940978461,
                0.999999917667573
            ],
            [
                0.9999998642566219,
                0.9999997300423192,
                0.9999996940978827,
                0.9999998642567351,
                0.9999997617631752,
                0.999999674368781,
                0.9999997761970248,
                0.9999998874647977,
                0.9999997617631184,
                0.9999998642567351
            ],
            [
                0.9999997617631753,
                0.9999999176675535,
                0.9999998461826589,
                0.9999999123575255,
                0.9999998942829981,
                0.9999998802069017,
                0.9999998257022045,
                0.9999998257021422,
                0.9999999434137704,
                0.9999999677581145
            ],
            [
                0.9999995818813767,
                0.9999993524049705,
                0.9999986290427939,
                0.999998712104171,
                9.422448185435711e-07,
                0.9999991148432811,
                0.9999985406230838,
                0.9999997126313783,
                7.338210679979539e-07,
                0.9999984465022463
            ],
            [
                0.999999310639119,
                0.9999999500627857,
                0.9999995262092728,
                0.9999993524049705,
                0.9999999434137571,
                0.9999998461827322,
                0.9999999006880668,
                0.9999998362623529,
                0.999999653367503,
                1.0
            ],
            [
                0.9999999067050831,
                0.9999999176674553,
                0.9999994956527122,
                0.9999998642566219,
                0.9999998461826038,
                0.9999993106386259,
                0.999999712631344,
                0.9999996072136125,
                1.9947299592933255e-06,
                0.9999997126315496
            ],
            [
                0.9999997617630334,
                2.2603237589676295e-06,
                0.9999983463110063,
                0.9999989969857926,
                0.999999802494586,
                4.450849988798682e-07,
                0.9999993524054335,
                0.999999894283061,
                0.999999391641036,
                0.9999997617630049
            ],
            [
                0.9999994284997575,
                0.9999996072137063,
                0.9999996940978096,
                0.9999999559305733,
                0.9999996310116359,
                0.999999789756634,
                0.9999994956525919,
                0.9999998642566381,
                0.9999998642567189,
                0.9999997761970248
            ],
            [
                0.9999995549150543,
                0.999999894282935,
                0.9999998642566704,
                0.9999991148433865,
                0.9999991684718736,
                0.9999999634651575,
                1.0,
                0.999999887464771,
                0.9999997300420939,
                0.9999999586006542
            ],
            [
                0.9999999500627916,
                0.9999999317440116,
                0.9999999317440279,
                0.9999998555020135,
                0.999999653367379,
                0.9999999067051276,
                0.9999998461826222,
                0.9999998461826222,
                0.9999999176674357,
                0.9999995549149482
            ],
            [
                0.9999998724809116,
                0.9999999067051165,
                0.9999999358794327,
                0.999999814460854,
                0.9999997126314811,
                0.9999999273418616,
                0.9999998642567351,
                0.999999391641036,
                0.9999998802069731,
                0.9999998874649051
            ],
            [
                0.9999999123574419,
                0.9999999123574941,
                0.999999825702059,
                0.9999996940976273,
                0.9999998642566866,
                0.9999998724808964,
                0.9999999067051388,
                0.9999998802069873,
                0.9999997761972116,
                0.9999997897567091
            ],
            [
                0.9999998724809116,
                0.9999999273417663,
                0.9999998024947273,
                0.9999999397642868,
                0.9999999067051499,
                0.9999999559305733,
                0.9999997126313098,
                0.9999999530883675,
                0.9999999123574419,
                0.9999999434137233
            ],
            [
                0.9999995549151074,
                0.9999999434137435,
                0.9999996072137999,
                0.9999997463980427,
                0.9999998874649318,
                0.9999999586006245,
                0.9999998942829098,
                0.9999996940976272,
                0.9999998461826405,
                0.9999997617631469
            ],
            [
                0.9999997761970782,
                0.9999997897566341,
                0.999999931743971,
                0.9999997897565839,
                0.9999997897567092,
                0.9999999067050276,
                0.9999997761971049,
                0.9999998724810027,
                0.9999998942830862,
                0.9999996310115039
            ],
            [
                0.9999991148433868,
                0.999999554914842,
                0.9999994631251246,
                0.9999999226558146,
                0.999998629043121,
                0.9999977396748951,
                0.9999998642566381,
                0.9999996940977003,
                5.715007195447234e-07,
                0.9999994956526522
            ],
            [
                0.9999999006879721,
                0.9999998555020481,
                0.9999998802069017,
                0.9999998144608983,
                0.9999998024946566,
                0.9999996310114599,
                0.9999999123574836,
                0.9999998642567351,
                0.9999998461826956,
                0.9999998461826222
            ],
            [
                1.0,
                0.9999998942829602,
                0.9999999634651574,
                0.9999999559306259,
                0.9999999176674848,
                0.9999998802068873,
                0.9999999715466256,
                0.9999998257021837,
                0.9999998802069017,
                0.9999999397643156
            ],
            [
                0.9999998642566381,
                0.9999998362622747,
                0.9999999006881378,
                0.9999999611088719,
                0.9999999434137165,
                0.9999999358793562,
                0.9999999468421249,
                0.9999999123575568,
                0.9999998144608319,
                0.9999992188518559
            ],
            [
                0.9999999358794173,
                0.9999998942830233,
                0.9999998802068873,
                0.9999999358793638,
                0.9999999530883563,
                0.9999999123574733,
                0.9999998257021422,
                0.9999998461827139,
                0.9999998362623138,
                0.9999999176675829
            ],
            [
                0.9999998942829603,
                0.9999999317440116,
                0.9999999397643011,
                0.9999999067051165,
                0.9999999559306101,
                0.9999998874649185,
                0.9999997463981939,
                0.9999987121046312,
                0.9999998642566866,
                0.9999999358794021
            ],
            [
                0.999999943413757,
                0.9999998942829602,
                0.9999999317439302,
                0.9999999006880905,
                0.9999998642566381,
                0.9999998555019275,
                0.9999999176674651,
                0.9999997761970515,
                0.9999999067050498,
                0.9999999434137232
            ],
            [
                0.9999994284995533,
                0.9999995262096119,
                0.9999997126315497,
                0.9999997126314469,
                0.9999960330140883,
                0.9999998144609424,
                0.9999996533673376,
                0.9999997463981032,
                0.9999996072138937,
                0.9999993106386261
            ],
            [
                0.9999998461827322,
                0.999999712631344,
                0.9999997617630617,
                0.9999994284997575,
                0.9999998802069873,
                0.999999814460854,
                0.9999997126315153,
                0.9999997897567092,
                0.9999996940976272,
                0.9999998257020798
            ],
            [
                0.9999998724809572,
                0.9999998802069302,
                0.9999999530883452,
                0.9999998555020307,
                0.9999996743687034,
                0.999999825702163,
                0.9999998555020481,
                0.9999998257021006,
                0.9999995818813767,
                0.9999999397642365
            ],
            [
                0.9999998802069445,
                0.9999995549151075,
                0.9999999123575151,
                0.9999998874649051,
                0.9999998024946566,
                0.9999999176674945,
                0.999999931743979,
                0.9999998144609424,
                0.9999999434137368,
                0.9999999358793332
            ],
            [
                0.99999976176309,
                0.9999998257020798,
                0.9999998802069587,
                0.9999996310113279,
                0.9999996533672549,
                0.9999996940976638,
                0.9999998144608098,
                0.9999998257021421,
                0.9999998942828972,
                0.9999998724809116
            ],
            [
                0.9999998461827322,
                0.9999999176675142,
                0.9999999434137434,
                0.9999999226557592,
                0.9999998144608098,
                0.9999999397643083,
                0.9999998802069159,
                0.9999999715466392,
                0.9999999500628036,
                0.9999999317440198
            ],
            [
                0.9999997617631469,
                0.9999999500628274,
                0.9999998362622357,
                0.9999999559306312,
                0.9999999123574838,
                0.9999998642566704,
                0.9999997617631469,
                0.9999994956523516,
                0.9999999006880195,
                0.9999998024946802
            ],
            [
                0.9999995262093858,
                0.999999802494633,
                0.9999995818813269,
                0.999999917667573,
                0.9999997300422226,
                0.9999998461826405,
                0.9999998024946566,
                0.999999814460876,
                0.9999999176675142,
                0.9999998362623723
            ],
            [
                0.9999999273418702,
                0.9999999656787406,
                0.9999998942830233,
                0.9999998724809267,
                0.9999998555019446,
                0.9999998874649318,
                0.9999998642566381,
                0.9999998461827322,
                0.9999998461826037,
                0.9999999500627798
            ],
            [
                4.450852641717689e-07,
                0.9999997761970515,
                0.9999993524051247,
                0.9999993106388727,
                0.9999994631247403,
                0.9999996533673376,
                0.9999988634361543,
                0.9999997300422226,
                0.9999998024946566,
                0.9999997463981636
            ],
            [
                0.9999998024946095,
                0.9999998257021213,
                0.9999997300423192,
                0.9999997463981636,
                0.9999995262093858,
                0.9999998555020135,
                0.9999997897565588,
                0.9999998642566381,
                0.9999994631248682,
                0.9999996940978098
            ],
            [
                0.9999995262095551,
                0.9999999006880668,
                0.9999997126314469,
                0.9999993916411085,
                0.9999999006880076,
                0.9999999226557962,
                0.9999996743688975,
                0.9999998874648648,
                0.9999998257021422,
                0.9999997617630333
            ],
            [
                5.043476486915964e-07,
                0.9999997463981636,
                6.475948754012522e-07,
                9.422450431954847e-07,
                0.9999997761970516,
                0.999999872480942,
                1.209865539274514e-06,
                0.9999998802069731,
                0.9999996940977731,
                0.9999997463981334
            ],
            [
                0.9999997463981636,
                0.9999996743688975,
                0.9999999123575151,
                0.9999998874647843,
                0.9999995818814266,
                0.9999998724809875,
                0.9999995818813766,
                0.9999997761971849,
                0.9999977396762418,
                0.9999997761970782
            ],
            [
                0.9999999123574628,
                0.9999999530883341,
                0.9999994631248043,
                0.9999998642566704,
                0.9999997617629764,
                0.9999998024947037,
                0.9999994631249323,
                0.9999999500628393,
                0.9999998874648917,
                0.9999999358794173
            ],
            [
                0.9999999067049942,
                0.9999999067050387,
                0.9999998802069873,
                0.999999864256719,
                0.9999999273418096,
                0.999999802494586,
                0.9999999067050054,
                0.9999997761970782,
                0.9999997300421583,
                0.9999999468421187
            ],
            [
                0.9999998555019446,
                0.9999999067049831,
                0.9999998874647977,
                0.999999906705061,
                0.9999999123575046,
                0.9999997761970781,
                0.9999998942830485,
                0.9999997300422548,
                0.9999992661789324,
                0.9999999226558515
            ],
            [
                0.9999999317439954,
                0.999999814460876,
                0.9999998144609424,
                0.9999996533672136,
                0.9999997463981031,
                0.9999999317439872,
                0.9999996940977367,
                0.9999994956527123,
                0.9999999317439546,
                0.999999900688043
            ],
            [
                0.999999310638626,
                0.9999998942828973,
                0.9999996940978462,
                0.999999746398073,
                0.9999997126315153,
                0.9999998802068873,
                0.9999998802069159,
                0.9999998802069873,
                0.9999997617630617,
                0.9999996940977368
            ],
            [
                0.9999998362623138,
                0.9999998802069302,
                0.999999218851856,
                0.999999761763147,
                0.9999998461826589,
                0.9999999067051387,
                0.9999996940976638,
                0.9999999067049942,
                0.9999985406236059,
                0.9999996940977368
            ],
            [
                0.9999999530883508,
                0.9999999226558515,
                0.9999998362622747,
                0.9999997300421904,
                0.9999999006881023,
                0.9999997761971849,
                0.9999994956525319,
                0.9999998642566543,
                0.9999998642566219,
                0.9999997617630049
            ],
            [
                0.9999999500628214,
                0.9999998802069731,
                0.9999997463980427,
                0.9999999123575359,
                0.9999999697115551,
                0.9999999500628571,
                0.9999999468421122,
                0.9999999358794402,
                0.9999999123574523,
                0.9999999123575464
            ],
            [
                0.9999999006881142,
                0.9999999559305995,
                0.9999999226557409,
                1.0,
                0.9999999123574629,
                1.0,
                0.9999998942830862,
                0.9999998257020799,
                0.9999998874648246,
                0.999999900688043
            ],
            [
                0.9999997300421583,
                0.999999730042287,
                0.9999996940978461,
                0.9999993916409635,
                0.9999993106389548,
                0.9999998642566381,
                0.9999994284994169,
                0.9999997617629764,
                0.9999994631250603,
                0.9999994956524718
            ],
            [
                0.9999998461827322,
                0.9999997126314469,
                0.9999999067050388,
                0.9999998024947273,
                0.9999997897565588,
                0.9999999176674356,
                0.9999998144608762,
                0.9999998942830106,
                0.9999999559305733,
                0.9999998642566866
            ],
            [
                0.999999887464932,
                0.9999998874649318,
                0.999999789756634,
                1.0,
                0.9999997463981032,
                0.9999999006880314,
                0.9999999317439547,
                0.9999999226558515,
                0.9999999434137772,
                0.9999999434137637
            ],
            [
                0.9999994284997575,
                0.9999998144608762,
                0.9999995549150543,
                0.9999996533672963,
                0.9999995818813767,
                0.9999994284996894,
                0.9999998942830737,
                0.99999976176309,
                0.9999998802069302,
                0.9999999530883508
            ],
            [
                0.9999997617630901,
                0.999999939764251,
                0.9999998024946801,
                0.9999999530883285,
                0.9999998257020799,
                0.9999999006880431,
                0.9999999067051499,
                0.9999999317439302,
                0.9999998144609645,
                0.9999999468421503
            ],
            [
                1.0,
                0.9999999317439954,
                0.9999999176675632,
                0.9999998942830233,
                1.0,
                0.9999999273418962,
                0.9999999226558238,
                0.9999999397642724,
                0.9999998724810027,
                1.0
            ],
            [
                0.9999998461826038,
                0.9999999006880194,
                0.9999994631249323,
                0.9999999358793944,
                0.999999953088362,
                0.9999999123575778,
                0.9999998461827322,
                0.9999998642566866,
                0.9999997897566089,
                0.9999998362622357
            ],
            [
                0.999999927341801,
                0.9999993106391195,
                0.9999990577549573,
                0.9999997617629766,
                0.9999995549150015,
                0.9999993524051252,
                0.9999969105044513,
                0.9999995262092165,
                0.9999998942829098,
                0.9999998024946095
            ],
            [
                0.9999998362623138,
                0.9999991148430702,
                0.9999995818814267,
                0.9999998874647441,
                0.9999989969862711,
                0.9999997617630901,
                0.9999990577556312,
                0.9999996072137999,
                0.9999997897567091,
                0.9999997897565839
            ],
            [
                0.9999999123575464,
                0.9999994956524717,
                0.9999999764113577,
                0.9999999317439872,
                0.9999998724809723,
                0.9999999226557224,
                0.9999998724808964,
                0.9999997126314468,
                0.999999965678708,
                0.9999999176675239
            ],
            [
                0.9999998555019619,
                0.9999997761970248,
                0.9999999226557685,
                0.9999999226557408,
                0.9999999123574628,
                0.9999998362623332,
                0.9999999500628095,
                0.999999894283061,
                0.9999998942830737,
                0.9999999586006592
            ],
            [
                1.0,
                0.9999998942829225,
                0.9999997897565838,
                0.9999998555019447,
                0.9999999226558423,
                0.9999999006881023,
                0.999999864256719,
                0.9999999273418875,
                0.9999988634362896,
                0.9999999634651444
            ],
            [
                0.9999999530883172,
                0.9999998942830106,
                0.9999998874648379,
                0.9999998874648246,
                0.9999999732705571,
                0.9999999434138109,
                0.9999998257021837,
                0.9999999123574628,
                0.999999802494633,
                0.999999653367379
            ],
            [
                0.9999989322966214,
                0.9999997463981335,
                0.9999996743688199,
                0.9999998942829854,
                0.9999983463102177,
                0.9999999176674848,
                0.9999999176675634,
                0.9999998874647441,
                0.9999993106392014,
                0.9999998555019791
            ],
            [
                0.999999631011328,
                0.9999999468421503,
                0.9999999611089136,
                0.9999998257022045,
                0.9999998724810027,
                0.9999999656787283,
                0.9999998362622552,
                0.9999999006880786,
                0.9999998942830862,
                0.999999887464838
            ],
            [
                0.9999997617630333,
                0.9999998802068873,
                0.9999998257022045,
                0.999999554914789,
                0.9999993916409635,
                0.9999997300421261,
                0.999999802494586,
                0.9999998461826772,
                0.9999997126313098,
                0.9999991684715764
            ],
            [
                1.0,
                0.9999999006881142,
                1.0677029973158649e-06,
                0.9999998802069444,
                0.9999998642567351,
                0.9999997761971582,
                0.9999998802069302,
                0.9999996310114599,
                0.9999998461826405,
                0.9999999123575255
            ],
            [
                0.9999995549150014,
                0.9999998461826405,
                0.999999789756634,
                0.9999995818813269,
                0.9999999006880905,
                0.9999997897565588,
                0.9999995549150543,
                0.999999825702059,
                0.9999998024946801,
                0.9999999176675632
            ],
            [
                0.9999998144609646,
                0.9999999358793791,
                0.9999999176675239,
                0.9999998642567189,
                0.9999996743687034,
                0.9999998942829855,
                0.999999428499485,
                0.9999999358794479,
                0.9999998461826956,
                0.9999999226557962
            ],
            [
                0.9999999397642867,
                1.0,
                0.999999894283061,
                0.9999999176675044,
                0.9999994956525919,
                0.9999999500628155,
                0.9999998362622943,
                0.9999998724809571,
                0.9999996533672963,
                0.9999999067051499
            ],
            [
                0.9999999500627976,
                1.0,
                0.9999998724809875,
                0.9999999468421756,
                0.9999998362622358,
                0.9999999317439059,
                0.9999999176675437,
                0.9999999067051388,
                0.9999998642567028,
                0.9999997126313783
            ],
            [
                0.9999999530883621,
                0.9999997463980125,
                0.9999996743686645,
                1.0,
                0.9999999067049832,
                0.9999998555019619,
                0.9999998555019446,
                0.9999998257021214,
                1.0,
                1.0
            ],
            [
                0.9999998024947037,
                0.9999995262095552,
                0.9999998362622553,
                0.9999998024947038,
                0.9999998642567351,
                0.999999310638626,
                0.9999998461826038,
                0.9999997897567342,
                0.9999998144609425,
                0.9999997300422547
            ],
            [
                0.9999999067049943,
                0.9999996940977368,
                0.9999995549151075,
                0.9999998642567028,
                0.9999998362623334,
                0.9999997897566089,
                0.9999996310113279,
                0.9999996940978096,
                0.9999999123574629,
                0.9999997463981939
            ],
            [
                0.9999997761971049,
                0.9999997617629764,
                0.9999998257022045,
                0.9999999067051499,
                0.9999999006880312,
                0.9999999067050499,
                0.9999999006881259,
                0.9999998257022045,
                0.9999999358794402,
                0.9999999067050165
            ],
            [
                0.9999998555019274,
                0.9999999397642222,
                0.9999999006881142,
                0.999999864256719,
                0.9999999176674454,
                0.9999996310115918,
                0.999999906705061,
                0.9999999176674651,
                0.9999999123575674,
                0.9999998461826772
            ],
            [
                0.9999997463982241,
                0.9999998555019791,
                0.9999993916411811,
                0.999998932296876,
                0.9999996533674617,
                0.9999992661791949,
                0.999999894283061,
                0.9999992188514835,
                0.9999999530883228,
                0.9999998461826038
            ],
            [
                0.9999998461826038,
                0.9999999468421756,
                0.9999998362623724,
                0.9999998362623529,
                0.9999997617630617,
                0.9999998555019791,
                0.9999999226557132,
                0.9999998461827322,
                0.9999998362622552,
                6.962255419931625e-06
            ],
            [
                0.9999993524051247,
                0.9999999358794021,
                0.9999997761972116,
                0.9999997300422869,
                0.9999996940977367,
                0.9999996310115479,
                0.9999996940978826,
                0.9999994631248683,
                0.9999987121044778,
                0.9999999732705602
            ],
            [
                0.9999998802069159,
                0.9999997761971583,
                0.9999997126314468,
                0.999999730042287,
                0.9999996310115039,
                1.0,
                0.9999999317439872,
                0.9999997300423191,
                0.9999996940976273,
                0.9999998144609646
            ],
            [
                0.999999927341801,
                0.9999998802069731,
                0.9999998942829981,
                0.999999917667475,
                0.9999987121041708,
                0.9999998642566219,
                0.999999900688055,
                0.9999998144609646,
                0.9999993916411085,
                0.9999990577555189
            ],
            [
                0.999999965678708,
                0.9999998802069731,
                0.9999999273418182,
                0.9999999067050609,
                0.9999999067050276,
                0.9999999226558515,
                0.9999998724808963,
                0.9999998942830862,
                0.9999999067050943,
                0.9999998461826956
            ],
            [
                0.9999997617631469,
                0.999999900688043,
                0.9999999176675634,
                0.999999900688055,
                0.9999998257020798,
                0.9999998942828973,
                0.9999999176674848,
                0.9999999067051388,
                0.9999998874647977,
                0.9999998874648112
            ],
            [
                0.9999998642566704,
                0.9999999358793867,
                0.999999802494586,
                0.9999999067049832,
                0.9999998642567189,
                0.9999998942830358,
                0.9999999611088672,
                0.9999998874649185,
                0.9999999123574629,
                0.9999999176675634
            ],
            [
                0.9999999006880194,
                0.9999999067050276,
                0.9999999067051276,
                0.9999998362623138,
                0.9999999226557224,
                0.9999996743686257,
                0.9999999468421122,
                0.9999998942830737,
                0.9999999358793944,
                0.999999906705072
            ],
            [
                0.9999999123575672,
                0.9999998874649318,
                0.9999999317439465,
                0.9999999006881377,
                0.999999802494586,
                0.9999998874649185,
                0.9999999226558423,
                0.9999999317440198,
                0.9999999176675535,
                0.9999999397643083
            ],
            [
                0.999999814460854,
                0.9999998257021422,
                0.9999998362623138,
                0.9999998257021422,
                0.9999997126314811,
                0.999999825702059,
                0.9999999358793639,
                0.9999998024946095,
                0.9999998461827138,
                0.9999998144608762
            ],
            [
                0.9999998874649051,
                0.9999999273417662,
                0.9999999634651879,
                0.9999996940976638,
                1.0,
                0.9999997897565588,
                0.999999653367255,
                0.9999998362622747,
                0.9999997761971583,
                0.9999999226557776
            ],
            [
                0.9999997126314811,
                0.9999998362623138,
                0.999999825702059,
                0.9999997761971317,
                0.9999997617630901,
                0.9999994956527725,
                0.9999997761971849,
                0.9999996940977003,
                0.9999996310114599,
                0.9999995262092164
            ],
            [
                0.9999992188517628,
                0.9999996310114598,
                0.9999998257021422,
                0.9999997897567092,
                0.9999998802069874,
                0.9999998802068873,
                0.9999999067050054,
                0.999999789756659,
                0.9999998802069159,
                0.9999998802068873
            ],
            [
                0.9999999067049832,
                0.9999998642566543,
                0.9999998642567028,
                0.9999999123574732,
                0.9999999226557131,
                0.9999999176675142,
                0.9999999067049942,
                0.9999999226557961,
                0.9999999586006196,
                0.9999998724809115
            ],
            [
                0.9999998642566704,
                0.9999999634651487,
                0.999999872480942,
                0.9999998362623332,
                0.9999997897567342,
                0.9999998461826956,
                0.999999554914842,
                0.9999997126314125,
                0.999999495652592,
                0.999999802494586
            ],
            [
                0.9999998555019963,
                0.999999814460876,
                0.9999998461827322,
                0.9999998024945624,
                0.9999995262094987,
                0.999999864256719,
                0.999999846182604,
                0.9999996940977003,
                0.999999887464838,
                0.9999998642566381
            ],
            [
                0.9999997463980124,
                0.9999999123574941,
                0.9999999500627857,
                0.9999998362623334,
                0.9999998724810027,
                0.9999995549150013,
                0.9999999067050388,
                0.9999998642566866,
                0.99999994341373,
                0.9999998461826771
            ],
            [
                0.9999998942829854,
                0.9999999067051387,
                0.9999999317440197,
                0.9999998024947272,
                0.9999999468420996,
                0.9999999006881497,
                0.9999998555019963,
                0.9999999611089136,
                0.9999999123575464,
                0.9999998024947037
            ],
            [
                0.9999998257021837,
                0.9999999358793944,
                0.9999999397642078,
                0.9999999273418962,
                0.999999789756634,
                0.999999917667573,
                0.9999998555020307,
                0.9999998942830233,
                0.9999998642567351,
                0.9999999226557225
            ],
            [
                0.9999997300423192,
                0.9999992188514836,
                0.9999997761970782,
                0.9999998942829225,
                0.9999999006880431,
                0.9999998942828973,
                0.9999999226557962,
                0.9999999226557316,
                0.9999999358793332,
                0.9999996072136594
            ],
            [
                0.9999998555019619,
                0.9999997617631753,
                0.9999997761970248,
                0.9999997463980427,
                0.9999998802069445,
                0.999999730042287,
                0.9999997126313099,
                0.9999997617630901,
                0.9999997617631184,
                0.9999998874647709
            ],
            [
                0.9999998024946332,
                0.9999998724809115,
                0.9999994956527724,
                0.9999998024947038,
                0.9999998362623724,
                0.9999998144608983,
                0.999999927341801,
                0.9999999273418789,
                0.9999999067050165,
                0.9999999358794326
            ],
            [
                0.9999998724808963,
                0.9999999397642724,
                0.9999995262093292,
                0.9999999226557684,
                0.9999998874649051,
                0.9999996072137062,
                1.0,
                0.9999999317440035,
                0.9999998942829225,
                0.9999999006880905
            ],
            [
                0.999999168472171,
                0.999999730042255,
                0.9999995818813767,
                0.9999985406236056,
                0.9999987121050923,
                0.9999992661786699,
                0.9999996072136126,
                0.9999999006881259,
                0.9999969105066592,
                0.999999887464905
            ],
            [
                0.9999999611088904,
                0.9999999123575672,
                0.9999997463981939,
                0.9999998802069302,
                1.0,
                0.9999998461827139,
                0.9999997463982241,
                0.9999999468421503,
                0.9999999358793409,
                0.9999998874648112
            ],
            [
                0.9999994284992806,
                0.9999999067051277,
                7.338209805170655e-07,
                0.9999987901346057,
                0.9999985406232578,
                0.9999995549150544,
                0.9999991684722701,
                0.9999930377429281,
                0.9999989322973851,
                0.9999982396563684
            ],
            [
                0.9999985406232579,
                0.9999975938970883,
                0.9999998461826405,
                0.9999996072139403,
                0.9999998642567028,
                0.9999999697115912,
                0.999999825702059,
                0.999999906705072,
                0.9999999317439627,
                0.9999997897567091
            ],
            [
                0.9999999434138042,
                0.9999999697115622,
                0.9999999397642796,
                0.9999998724809116,
                0.9999998461826771,
                0.9999999434137232,
                0.9999997761971582,
                0.9999996310115479,
                0.999999855501979,
                0.9999999176674749
            ],
            [
                0.9999998802069445,
                0.9999999123575151,
                0.9999999067050609,
                0.9999996743688199,
                0.9999999317439058,
                0.9999999006879721,
                0.9999998144608981,
                0.9999999067050498,
                0.999999946842125,
                0.9999999697115731
            ],
            [
                0.9999998257021213,
                0.9999999067051277,
                0.99999995308839,
                0.999999391641181,
                0.9999997897565588,
                0.9999998461826956,
                0.9999997761971583,
                0.9999999317439384,
                1.0,
                0.9999993916411811
            ],
            [
                0.9999998257021213,
                0.9999999559306259,
                0.9999995818813268,
                0.9999999123575046,
                0.9999999500628274,
                0.9999998461826956,
                0.9999999273418095,
                0.9999999176674945,
                1.0,
                0.9999998942829981
            ],
            [
                0.9999998555019618,
                0.9999992661791951,
                0.9999998555019447,
                0.9999993524053566,
                0.9999982396569977,
                0.9999999317439547,
                0.9999993106391191,
                0.999999730042094,
                0.9999998257021006,
                0.9999996072137999
            ],
            [
                0.9999998461826405,
                0.9999991684716754,
                0.999999310638626,
                0.9999998257021838,
                0.9999992188515765,
                0.9999997300421904,
                0.9999998362622943,
                0.9999998461827139,
                0.9999997126314469,
                0.9999998942830862
            ],
            [
                0.9999999317439058,
                0.9999999273417662,
                0.9999999176674553,
                0.9999997617630617,
                0.9999998724810027,
                0.9999999123575986,
                0.999999712631481,
                0.9999996533672963,
                0.9999999176675632,
                0.9999999397642724
            ],
            [
                0.9999998461827138,
                0.9999998874648379,
                0.9999997761970781,
                0.9999999559306206,
                0.9999998555019619,
                0.999999939764294,
                0.9999998874648245,
                0.9999997617630617,
                0.9999998724809268,
                1.0
            ],
            [
                0.9999995818813269,
                0.9999995818812272,
                0.9999996310115038,
                0.9999998461827322,
                0.9999996940977368,
                1.0,
                0.9999998461826771,
                0.9999999067050721,
                0.9999997761972116,
                0.9999999176675338
            ],
            [
                0.9999998461827138,
                0.9999999006880668,
                0.9999998724808964,
                0.9999998942828973,
                0.9999998257021837,
                0.9999999123575674,
                0.999999946842163,
                0.9999998942829981,
                0.999999802494633,
                0.9999998024946566
            ],
            [
                0.9999998942829981,
                0.9999998144608762,
                0.9999997463981334,
                0.9999996940976638,
                0.9999998802069874,
                0.9999997300423192,
                0.9999998724809268,
                0.9999998461827322,
                0.999999391641036,
                0.9999996533673378
            ],
            [
                0.9999999123575255,
                0.9999999586006048,
                0.9999997617631469,
                0.9999995262094422,
                0.9999998874648112,
                0.9999995549148951,
                0.9999999123574836,
                0.999999900687972,
                0.999999887464932,
                0.9999997761971048
            ],
            [
                1.0,
                0.9999998874648245,
                0.9999999006881142,
                0.9999998555019447,
                0.9999998461826588,
                0.999999391641036,
                0.9999998942830106,
                0.9999999176675731,
                0.999999946842125,
                0.9999998642566542
            ],
            [
                0.9999993106387906,
                0.9999999358793867,
                0.9999997761971849,
                0.9999999006879957,
                0.9999999559305943,
                1.0,
                0.9999998802069017,
                0.9999991148433867,
                0.9999999226557961,
                0.9999998724809572
            ],
            [
                0.9999998144608983,
                0.9999998461826771,
                0.9999999317439139,
                0.9999998362623138,
                0.9999997897566841,
                1.0,
                0.9999994956524116,
                0.9999999586006542,
                0.9999998724810027,
                0.9999999176674945
            ],
            [
                0.9999989322971304,
                0.9999975938970881,
                0.9999998642567351,
                0.9999988634366962,
                0.9999998802069302,
                0.9999997617630901,
                0.999999391641036,
                0.9999993524049704,
                0.9999998024947273,
                0.9999999067051388
            ],
            [
                0.999999168471576,
                0.9999999358794402,
                0.9999997897566089,
                0.9999999397642078,
                0.9999998257021214,
                0.9999999500628155,
                0.9999998724809115,
                0.9999999317439627,
                0.9999999358793409,
                0.9999999067050053
            ],
            [
                0.999999931743979,
                0.9999997463981334,
                0.9999997463980428,
                0.9999998874647709,
                0.9999997300422869,
                0.999999814460876,
                0.9999999123574942,
                0.9999998144608319,
                0.9999998461826222,
                0.9999994956524116
            ],
            [
                0.9999999611088766,
                0.9999999656786874,
                0.9999999468421312,
                0.9999998642566219,
                0.9999998724809419,
                0.9999998874648112,
                0.9999998461827322,
                0.9999998144608981,
                0.999999789756659,
                0.9999999176675338
            ],
            [
                0.9999997463980427,
                0.9999998724810027,
                0.9999998024946095,
                0.9999994956527724,
                0.9999998144609203,
                0.9999999123575778,
                0.9999998362622358,
                0.9999996940977732,
                0.999999917667573,
                0.9999997300423192
            ],
            [
                0.9999998461826956,
                0.9999999176675142,
                0.9999997617631469,
                0.9999997463981031,
                0.9999999067051276,
                0.9999998642566219,
                0.9999999067051499,
                0.9999997463981636,
                0.9999995549150543,
                0.9999998461826588
            ],
            [
                0.9999999500627798,
                0.9999999226557962,
                0.9999998257020591,
                0.9999998942828973,
                0.9999998724809419,
                0.999999887464838,
                0.9999998802068873,
                0.999999931743971,
                0.9999999273418443,
                0.9999999123575046
            ],
            [
                0.9999997897565588,
                0.9999997897567342,
                0.9999996743687811,
                0.9999999559305839,
                0.9999998642567028,
                0.9999999176675338,
                0.9999997463981637,
                0.9999994284993489,
                0.9999996743687422,
                0.999999946842125
            ],
            [
                0.9999999317439954,
                0.999999946842163,
                0.9999997463981939,
                0.9999998362622943,
                0.9999999559305629,
                0.9999998942828973,
                0.9999997617629764,
                0.9999997463981031,
                0.9999998802069873,
                0.9999998461827322
            ],
            [
                0.9999996310115479,
                0.9999994956525321,
                0.9999994284995533,
                0.9999999176675535,
                0.9999993916411811,
                0.9999996940978461,
                0.9999995262093294,
                0.9999997300422548,
                0.9999996310116359,
                0.9999993916408911
            ],
            [
                0.9999991684718734,
                0.9999998257022046,
                0.9999997761971583,
                0.999998996985434,
                0.9999988634366964,
                0.9999984465016907,
                0.999999631011328,
                0.9999996310116359,
                0.9999999067050721,
                0.9999999006880786
            ],
            [
                0.999999922655833,
                0.9999997126315496,
                0.9999999067051055,
                0.9999999500628334,
                0.999999927341827,
                0.9999999123575881,
                0.999999894283061,
                0.9999998802069873,
                0.999999825702163,
                0.9999999176675239
            ],
            [
                0.9999999317439221,
                0.9999998724809875,
                0.9999999397642294,
                0.9999996940976638,
                0.9999972735287567,
                1.0,
                0.9999999358793715,
                0.9999998024947038,
                1.0,
                0.9999996940978826
            ]
        ]
    },
    {
        "q_id": "9420_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999996533672963,
                0.9999996310115918,
                1.1253508156363576e-07,
                0.9999989322973847,
                0.9999997126313783,
                8.7642558095602e-08,
                5.3157811697009444e-08,
                2.3823690999160957e-07,
                1.1253520230052635e-07,
                0.9999996310113719
            ],
            [
                1.994729245878497e-06,
                9.931202796993203e-08,
                8.315277302788957e-07,
                0.9999995262094422,
                0.9999038975629325,
                2.902312677084523e-06,
                1.8553914607267268e-07,
                0.9999974387165697,
                1.7603432133296774e-06,
                3.726639728184142e-06
            ],
            [
                3.927860597945825e-07,
                8.764244316973974e-08,
                0.9999988634364253,
                8.764245361752286e-08,
                0.9999996940977003,
                2.10243290909724e-07,
                2.69957906184239e-07,
                2.382368531929327e-07,
                1.8553903548231313e-07,
                1.275190428875671e-07
            ],
            [
                1.2098652508347793e-06,
                1.5534979397592542e-06,
                1.2098659719601033e-06,
                6.962258739454786e-06,
                1.3709570434054234e-06,
                4.450849988811838e-07,
                1.553498124964492e-06,
                4.450849988798682e-07,
                8.315284241650899e-07,
                9.422445938917108e-07
            ],
            [
                8.315283250150648e-07,
                4.450852111148132e-07,
                1.994729959270648e-06,
                1.760344052650207e-06,
                3.288749457432399e-06,
                5.422219616228845e-06,
                0.999999554914842,
                8.315277302788957e-07,
                1.994729245917502e-06,
                6.9622579096593295e-06
            ],
            [
                1.209865539295696e-06,
                0.9999996743688586,
                0.9999995549150543,
                0.999999825702059,
                0.999999554914842,
                1.2751899728311609e-07,
                2.382369667929001e-07,
                1.6373764721072816e-07,
                0.999999855501979,
                1.8553910183607374e-07
            ],
            [
                0.9999998942830106,
                0.9999998724809874,
                0.9999996072139403,
                2.3823690999290963e-07,
                0.9999998942829098,
                0.9999999273418876,
                0.9999993916408908,
                0.9999999500628631,
                0.9999994631250602,
                0.999999825702163
            ],
            [
                0.9999998802068873,
                6.023574911170301e-08,
                1.8553916819032217e-07,
                1.8553907971758842e-07,
                1.6373770576776313e-07,
                0.9999997300422869,
                0.9999999006880312,
                1.2751910369275402e-07,
                8.764243272157922e-08,
                1.2751901248454963e-07
            ],
            [
                4.450852641737424e-07,
                2.561283432035425e-06,
                2.561283431986506e-06,
                4.222833947897496e-06,
                8.315281267649641e-07,
                0.9999997463981938,
                2.5612825159677387e-06,
                0.0009110510263952278,
                4.785095065171522e-06,
                8.315282259051341e-07
            ],
            [
                0.9999998802069444,
                0.9999998724809875,
                0.9999998942829854,
                0.9999993106386259,
                0.9999996533672963,
                1.4449805540740185e-07,
                2.1024326584582131e-07,
                0.9999997761970782,
                0.9999999397642939,
                0.9999996310114598
            ],
            [
                1.8553912395160867e-07,
                2.3823702359290413e-07,
                0.9999993916406734,
                2.1024336609843824e-07,
                1.6373766672973748e-07,
                2.382368815916736e-07,
                2.1024341622368903e-07,
                0.9999993916406735,
                2.3823699519290042e-07,
                8.764244316973974e-08
            ],
            [
                1.2098659719661556e-06,
                0.9999994631251242,
                1.2098659719601033e-06,
                1.553498495338299e-06,
                8.315284241650899e-07,
                0.9999985406230837,
                3.2887486731641103e-06,
                3.288747889229516e-06,
                1.8553916819032217e-07,
                6.475948754012522e-07
            ],
            [
                1.2751905808881762e-07,
                6.825598842065202e-08,
                0.9999998874648915,
                0.999999825702163,
                0.9999995262095551,
                0.9999992661790197,
                0.9999998642566219,
                0.9999998461826038,
                0.9999996533675028,
                8.764249540862797e-08
            ],
            [
                0.9999995262092728,
                2.3823693839290317e-07,
                1.2098662604247682e-06,
                5.043472879540142e-07,
                0.9999995818814266,
                5.715003107755449e-07,
                2.699577774585891e-07,
                0.9999998724808964,
                0.9999994956527722,
                1.8553907971855875e-07
            ],
            [
                0.999999581881277,
                0.9999997761971848,
                0.9999998362622943,
                2.382369667929001e-07,
                0.9999998144609203,
                0.999996033013142,
                3.927860597945825e-07,
                5.715007195447234e-07,
                0.9999997463981031,
                0.9999997761971049
            ],
            [
                0.9999998724809572,
                0.9999998461827322,
                0.9999996072139403,
                0.9999993524053563,
                0.9999998802069731,
                0.9999996743687422,
                1.2751908849167202e-07,
                0.9999995549150543,
                0.9999993106389548,
                1.2751901248454963e-07
            ],
            [
                5.04347287955046e-07,
                0.9999994631249962,
                0.9999992188513902,
                0.9999997617630049,
                0.9999993106387082,
                0.9999993524049703,
                0.9999995818810776,
                0.9999993106386259,
                1.8553919030776337e-07,
                0.9999996310113279
            ],
            [
                0.9999994631250603,
                0.9999993106388726,
                2.1024326584639497e-07,
                0.999999554914842,
                0.9999994631251884,
                0.9999997617630333,
                2.382370235922541e-07,
                2.75356812513986e-05,
                1.1253516205489029e-07,
                1.1253516205489029e-07
            ],
            [
                7.338208055579897e-07,
                4.785096205830278e-06,
                1.0677029973056687e-06,
                7.338211554464836e-07,
                1.2098652508347793e-06,
                9.42244930849811e-07,
                1.7603432132624344e-06,
                1.2098659719601033e-06,
                1.5534983101549167e-06,
                5.8291251642512995e-05
            ],
            [
                8.764245361752286e-08,
                0.9999999697115515,
                1.8553916819032217e-07,
                0.9999997463980426,
                0.9999997126315496,
                0.9999999273418528,
                0.9999997897567091,
                0.9999996940977002,
                9.931192141912081e-08,
                0.9999999123575151
            ],
            [
                7.3382080556433e-07,
                1.0677024881887838e-06,
                4.4508510499737865e-07,
                3.288750633569722e-06,
                9.422443692390473e-07,
                2.902312677084523e-06,
                4.450849988798682e-07,
                5.043473480766399e-07,
                1.0677031245990084e-06,
                6.962256249682458e-06
            ],
            [
                2.2603242978377903e-06,
                3.2887494571676872e-06,
                1.5534979397592542e-06,
                2.699577774585891e-07,
                7.734416698849138e-08,
                8.315282259089153e-07,
                3.726639283752725e-06,
                7.338207180714596e-07,
                1.9947306726049992e-06,
                1.2098662604049616e-06
            ],
            [
                1.0,
                0.9999998642566219,
                0.9999999067050943,
                4.1399365603508136e-08,
                0.999999310639119,
                0.9999999468421946,
                0.9999998642567351,
                0.9999999500628095,
                1.0,
                0.999999917667524
            ],
            [
                0.9998204720142394,
                2.260325106237323e-06,
                1.5534983101301911e-06,
                0.00013982210756291363,
                6.475946438042047e-07,
                9.422447062294175e-07,
                1.760344052693435e-06,
                6.475946438042047e-07,
                0.9999962733611613,
                2.699576809143613e-07
            ],
            [
                0.9999989322972574,
                0.9999972735307071,
                0.9999988634364252,
                1.6373768624837685e-07,
                1.2751899728311609e-07,
                2.2603251062450327e-06,
                2.3823693839325527e-07,
                4.53978902983119e-05,
                2.699578096393206e-07,
                2.2603248367949354e-06
            ],
            [
                0.9999998874648379,
                0.9999996072139403,
                1.2751901248454963e-07,
                1.8553907971855875e-07,
                0.9999992188512972,
                1.1253518888531272e-07,
                2.5612831267202583e-06,
                0.9999998724809419,
                0.9999994284994851,
                0.9999999500628631
            ],
            [
                5.043476486915964e-07,
                5.043474683220276e-07,
                4.450852641717689e-07,
                1.2098661161982042e-06,
                1.0677029973158649e-06,
                7.338212429562581e-07,
                3.0590215399183813e-07,
                0.9999646437493369,
                2.6995768091310296e-07,
                6.475949525981759e-07
            ],
            [
                8.939699501416646e-06,
                6.1441767993788005e-06,
                6.605212107986466e-05,
                1.209865827752005e-06,
                2.9023109472494878e-06,
                1.6701415872659116e-05,
                1.2098653950716937e-06,
                3.288749849529972e-06,
                2.9023116392097746e-06,
                NaN
            ],
            [
                0.9999998024946801,
                2.3823688159291947e-07,
                0.9999998362623334,
                3.05902190458764e-07,
                0.9999985406241271,
                0.9999997300421904,
                0.9999998362623332,
                1.0,
                0.9999997617630617,
                6.023569884718319e-08
            ],
            [
                9.931193325852072e-08,
                0.9999999226557225,
                0.9999992188516696,
                0.9999995818811772,
                1.4449798650551755e-07,
                0.9999997300420939,
                0.9999998362623723,
                0.9999999273417837,
                0.9999997897567091,
                0.9999997300421904
            ],
            [
                0.9999998362622747,
                0.9999996743686257,
                1.4449805540740185e-07,
                0.9999997126315496,
                1.8553914607267268e-07,
                1.2751901248454963e-07,
                0.9999999273417922,
                2.3823702359290413e-07,
                0.9999998257021422,
                0.9999998724810027
            ],
            [
                9.422442569290178e-07,
                5.043476486902204e-07,
                4.785096776499213e-06,
                8.315277302788957e-07,
                6.475948753930064e-07,
                4.450852111148132e-07,
                0.9999999273418442,
                8.31527928532683e-07,
                8.315280276607289e-07,
                8.939693106873817e-06
            ],
            [
                6.825606978822427e-08,
                2.1024326584639497e-07,
                9.931199245292204e-08,
                0.9999996533674202,
                1.855391239539711e-07,
                0.9999994631249963,
                2.1024326584582131e-07,
                1.4449798650551755e-07,
                1.6373762769138607e-07,
                1.8553907971855875e-07
            ],
            [
                0.9999999634651967,
                0.9999999500628631,
                0.9999996533672137,
                0.9999994284993488,
                3.927862002654366e-07,
                0.9999996533674202,
                1.1253516205489029e-07,
                0.9999999358794021,
                0.9999997761971048,
                0.9999998802069017
            ],
            [
                1.8553919030858602e-07,
                0.9999996533672137,
                9.931189774187203e-08,
                1.8553910183607374e-07,
                0.9999996072137999,
                0.9999998362622747,
                0.9999997897567342,
                1.275190580884987e-07,
                0.9999996310115918,
                0.9999996533672136
            ],
            [
                6.02357921955714e-08,
                0.9999997126314811,
                0.9999993524053564,
                1.275190124842887e-07,
                0.9999998144608319,
                5.71500515159253e-07,
                1.637377643243723e-07,
                0.9999997126315153,
                1.637377057673536e-07,
                1.8553903548231313e-07
            ],
            [
                2.2603234895372223e-06,
                0.9999999273418615,
                2.1024344128584085e-07,
                0.9999993524052019,
                0.9999999176674749,
                0.9999984465026162,
                0.9999998362623529,
                1.1253517547010071e-07,
                0.9999987901341726,
                0.999999607213753
            ],
            [
                2.561282516066741e-06,
                2.9023119851899796e-06,
                9.422444815814404e-07,
                5.422217677152175e-06,
                NaN,
                1.370957860576702e-06,
                7.338207180898968e-07,
                6.962254589978262e-06,
                6.1441767993788005e-06,
                0.9999599362887531
            ],
            [
                1.5534981249397663e-06,
                5.715005832872586e-07,
                0.9999986290426301,
                3.726638395611981e-06,
                1.994729245917502e-06,
                0.9999987901341726,
                9.422442569290178e-07,
                4.4508510499737865e-07,
                9.931195693628605e-08,
                5.043474683220276e-07
            ],
            [
                0.9999999273418443,
                0.9999999006880194,
                0.9999997126313783,
                0.9999993916407458,
                5.71500651413193e-07,
                2.6995784182073116e-07,
                0.9999998362622357,
                3.059021904580685e-07,
                0.9999993106388725,
                0.9999994284995531
            ],
            [
                2.699578740032504e-07,
                2.102433410343832e-07,
                0.999999802494633,
                8.764252675194995e-08,
                1.4449805540740185e-07,
                0.9999996310115039,
                0.9999999176674749,
                0.9999994631249322,
                0.9999986290429569,
                9.931190958076104e-08
            ],
            [
                8.764244316973974e-08,
                1.3709572068522336e-06,
                0.9999995549150543,
                1.444979692800516e-07,
                1.4449803818215767e-07,
                7.73442776303243e-08,
                1.4449798650551755e-07,
                0.999998239657207,
                2.6995784182140636e-07,
                0.9999985406230835
            ],
            [
                1.012999218776902e-05,
                0.9999997463980729,
                0.9999999226557131,
                0.9999999559306153,
                0.9999998144608981,
                0.9999998942830863,
                0.999999653367503,
                0.9999999176675044,
                0.9999999397642796,
                0.9999999500627738
            ],
            [
                0.9999957771670603,
                2.6995774527718623e-07,
                2.3823685318968256e-07,
                0.999999802494586,
                2.1444943302181958e-05,
                0.9999998144609202,
                0.9999998942829854,
                4.450852641737424e-07,
                2.382370235922541e-07,
                3.927862470899887e-07
            ],
            [
                0.9999994956527122,
                0.9999996533674204,
                0.9999994284992807,
                0.9999995818811275,
                0.9999978766207788,
                0.9999995262092727,
                0.9999996533672137,
                0.999999802494633,
                0.9999996072137062,
                0.9999996310113719
            ],
            [
                9.4224425692559e-07,
                1.2098653950606901e-06,
                0.9999832985801602,
                1.8925150497435443e-05,
                1.2098656835076114e-06,
                3.4663253846718004e-07,
                0.9999991684721707,
                1.0677032518785256e-06,
                5.043474683240344e-07,
                1.0129992187253088e-05
            ],
            [
                0.9999869928746625,
                1.0677026154774503e-06,
                0.9999546021476836,
                6.475946438042047e-07,
                1.2098659719716573e-06,
                1.2098653950606901e-06,
                8.315282259138311e-07,
                1.7603440527286572e-06,
                3.927862470899887e-07,
                1.3709572068179446e-06
            ],
            [
                0.9999993916407458,
                5.715002426486762e-07,
                7.338208930443633e-07,
                0.9999999006880431,
                0.9999996310114159,
                0.9999999530883563,
                0.9999997897566089,
                0.999998629043284,
                0.9999998257021422,
                6.475949526020042e-07
            ],
            [
                0.9999999006879721,
                0.999999887464811,
                0.9999998362623724,
                0.9999997897567091,
                0.9999999226557224,
                0.9999994956524115,
                0.9999997897567091,
                0.9999998724809875,
                0.9999996940977003,
                1.473898900066424e-05
            ],
            [
                1.4449798650476187e-07,
                6.825598028392069e-08,
                0.9999997617630617,
                6.825600469412533e-08,
                3.927862470899887e-07,
                1.444980209564556e-07,
                9.931202796957073e-08,
                0.9999996940978825,
                5.315780536011123e-08,
                0.9999998257021628
            ],
            [
                1.5534981249697903e-06,
                0.9999916019289742,
                0.9999724643056483,
                0.9999991684717743,
                0.999998346310809,
                0.9999992188516695,
                1.3709575337159875e-06,
                0.9999942280799732,
                0.9999952149043669,
                5.715003107767143e-07
            ],
            [
                1.0677032518700286e-06,
                9.422450431954847e-07,
                4.7850927830148924e-06,
                1.0129992187400498e-05,
                1.9947304348595095e-06,
                7.338210679949506e-07,
                1.0677032518501217e-06,
                3.72664061671159e-06,
                5.04347348075149e-07,
                3.535626331905454e-05
            ],
            [
                0.9999987901341726,
                2.1024339116168358e-07,
                5.4222183235249605e-06,
                0.9999991684720717,
                0.9999995549151074,
                3.05902263391829e-07,
                0.9999998024947037,
                1.0677026154806063e-06,
                0.9999999317439708,
                0.9999999500628453
            ],
            [
                0.9999997761971048,
                0.9999994956527122,
                0.9999999468421884,
                0.9999997761971582,
                0.9999999067051054,
                0.999999310638708,
                0.9999999006879838,
                0.9999998874649185,
                0.9999994631251242,
                0.9999999226557224
            ],
            [
                0.9999995549150013,
                0.9999999273418788,
                0.9999999468421567,
                0.9999998362622943,
                0.9999999176674848,
                0.9999998942829729,
                0.9999999067050165,
                1.8553905760062447e-07,
                0.9999999358793562,
                0.9999998724809419
            ],
            [
                0.9999999530883564,
                0.9999997761972116,
                0.9999999067051166,
                3.466325797888292e-07,
                2.6995790618252024e-07,
                1.8553905760062447e-07,
                0.9999998461826038,
                0.9999999123575882,
                0.9999999226557316,
                0.9999998024947037
            ],
            [
                0.9999991684717744,
                0.9999999176674749,
                0.9999996072136126,
                0.9999996533674617,
                6.475951069985296e-07,
                0.9999994956527725,
                0.9999989322967487,
                0.9999995262092728,
                0.9875683513649993,
                0.9999998461826222
            ],
            [
                0.9999996940978461,
                9.931185038635267e-08,
                0.9999999176675239,
                0.9999997617631753,
                0.9999995262095551,
                0.9999997761970781,
                0.9999998642566542,
                9.931187406410953e-08,
                0.9999991148430699,
                0.9999997617631186
            ],
            [
                5.04347528446051e-07,
                0.9999998874648112,
                2.3823688159291947e-07,
                0.9999998555020135,
                0.9999998642567028,
                0.9999998802068873,
                0.999999554914736,
                0.9999952149060767,
                0.999999789756684,
                0.9999998461826038
            ],
            [
                0.999999814460876,
                0.9999997463980427,
                0.9999996310114598,
                0.99999976176309,
                0.9999994956524115,
                0.9999997126313441,
                0.9999999067049831,
                0.9999997463982241,
                0.9999999656787121,
                0.9999994956524115
            ],
            [
                1.5534981249574276e-06,
                1.994729245878497e-06,
                8.315280276546789e-07,
                2.5612812946890944e-06,
                3.927862002641863e-07,
                1.5534981249496567e-06,
                1.994730434847717e-06,
                6.475946437996402e-07,
                2.902312677084523e-06,
                1.7603427936079236e-06
            ],
            [
                0.9999998724810027,
                0.9999998942829603,
                0.9999998942830359,
                0.9999999468421186,
                0.9999999358794021,
                7.734414854823498e-08,
                0.9999998724809268,
                1.1253513522447425e-07,
                0.9999989969857926,
                0.9999998257021006
            ],
            [
                0.9999998144609645,
                0.9999997761971315,
                0.999999554914842,
                0.9999999226558515,
                0.9999998802068873,
                0.9999997300423191,
                0.9999990577555187,
                0.9999985406236054,
                0.999999495652592,
                0.9999985406241273
            ],
            [
                0.999999855502048,
                1.4449802095609418e-07,
                2.1024344128660572e-07,
                0.9999997463981032,
                0.9999992661791071,
                0.9999993524052792,
                0.9999995262093292,
                0.9999992661787572,
                1.2751901248454963e-07,
                0.9999993524053564
            ],
            [
                0.9999910603015689,
                2.9023130230846496e-06,
                2.5612834320214477e-06,
                1.7603438428564603e-06,
                0.9999785550413804,
                0.9999987121043239,
                1.1478764021029928e-05,
                1.30071315662049e-05,
                0.9999810748427646,
                1.7603430034655858e-06
            ],
            [
                1.4449807263287805e-07,
                8.315281267834927e-07,
                4.785096776394765e-06,
                1.9947290081177566e-06,
                4.2228324375512536e-06,
                6.962254589528684e-06,
                7.889263526180094e-06,
                3.466327863983311e-07,
                3.0590226339061185e-07,
                6.475948753991907e-07
            ],
            [
                6.475947982022763e-07,
                9.422443692527585e-07,
                7.484621837164364e-05,
                1.2098659719601033e-06,
                1.5534979397592542e-06,
                3.2887506335906595e-06,
                4.222832941142044e-06,
                0.998830489609426,
                1.7603434231705793e-06,
                2.3823690999323465e-07
            ],
            [
                0.9999984465024312,
                0.9999997300423191,
                0.9999998555019275,
                0.9999996310114598,
                0.9999998461827139,
                3.059021175255426e-07,
                0.9999991148428587,
                0.9999998642566381,
                0.9999977396762415,
                0.9999997463981938
            ],
            [
                1.994729721518893e-06,
                2.9023116392097746e-06,
                1.3709572068553509e-06,
                8.315277302857965e-07,
                6.475950298021765e-07,
                3.2887494574832472e-06,
                1.209865827752005e-06,
                2.561281600086738e-06,
                5.422217677152175e-06,
                1.0129987357517693e-05
            ],
            [
                1.994729721469003e-06,
                1.5534979397592542e-06,
                6.144177531532303e-06,
                1.6701429808298613e-05,
                9.422444815792981e-07,
                6.475948753965404e-07,
                2.2603242978665707e-06,
                6.475946438042047e-07,
                1.3709570434122812e-06,
                1.7603432132784448e-06
            ],
            [
                2.102434412871794e-07,
                1.1253512180925583e-07,
                7.338212429464139e-07,
                0.9999999067051054,
                5.043476486915964e-07,
                1.1253525596174225e-07,
                0.9999998257022045,
                0.9999998874648648,
                0.9999993524054336,
                0.9999998802069873
            ],
            [
                0.9999982396565774,
                9.422448185435711e-07,
                0.9999546021152427,
                0.9999987121052453,
                3.927862002663297e-07,
                0.9999756997592791,
                2.3823693839325527e-07,
                0.999998346311006,
                7.889266347786918e-06,
                1.3709570434054234e-06
            ],
            [
                0.9999993106387081,
                6.475945666051092e-07,
                0.999999802494586,
                0.9999998642566381,
                0.9999994631251883,
                0.9999997300420939,
                0.9999999006879838,
                2.1024331597262577e-07,
                9.931188590255539e-08,
                3.46632497145457e-07
            ],
            [
                1.3709575337078829e-06,
                2.6995777745711594e-07,
                3.466327863983311e-07,
                2.5612822106421996e-06,
                3.288748281295496e-06,
                0.9999957771650461,
                1.7603434231705793e-06,
                1.5534981249023245e-06,
                1.2098662604126641e-06,
                1.9947306726594253e-06
            ],
            [
                0.9999994956524118,
                0.9999998144608097,
                0.9999998942830485,
                0.9999997300420939,
                0.9999991148429646,
                1.8553916819032217e-07,
                8.764244316973974e-08,
                0.9999997126314126,
                0.9999986290427936,
                0.9999995549148951
            ],
            [
                0.999999943413784,
                1.6373764721072816e-07,
                0.99999995860059,
                0.9999999434138042,
                0.9999998144609424,
                0.999999973270573,
                0.9999998257021214,
                0.9999993106386259,
                0.9999998642566866,
                0.9999998461827138
            ],
            [
                1.6701423836262173e-05,
                0.9999997897565587,
                2.2603251062450327e-06,
                0.9999978766215383,
                1.3709572068553509e-06,
                5.71500515161527e-07,
                0.9999990577550694,
                0.9999978766215383,
                1.5534979397829198e-06,
                0.9999994631249322
            ],
            [
                3.059021175261338e-07,
                0.999999554914842,
                0.9999996940977731,
                0.999999712631344,
                0.9999997617631469,
                8.7642516304188e-08,
                7.734424996967756e-08,
                1.1253520230052635e-07,
                4.450852111135988e-07,
                0.9999998724809419
            ],
            [
                9.422445939032799e-07,
                0.999992110734597,
                8.315277302841894e-07,
                1.7603425837702984e-06,
                1.2098653950656417e-06,
                1.3709575337125585e-06,
                1.147877359926923e-05,
                8.31528424162821e-07,
                8.31528424151477e-07,
                5.715002426460124e-07
            ],
            [
                0.9999990577554063,
                0.9999996310113279,
                0.9999997300420939,
                0.9999994284995531,
                0.9999995262092162,
                0.9999997897566089,
                0.9999996940978825,
                0.9999998362623528,
                7.734415776836702e-08,
                0.9999996743688586
            ],
            [
                0.9999997617630333,
                0.9999999468421503,
                0.9999999176675632,
                0.9999999226558421,
                1.2751899728311609e-07,
                6.825600469412533e-08,
                5.04347528446051e-07,
                1.6373762769138607e-07,
                0.9999998024945624,
                3.059022269250683e-07
            ],
            [
                0.99999976176309,
                0.9999991684717746,
                5.715006514151423e-07,
                2.1024326584639497e-07,
                7.338212429562581e-07,
                0.9999994956523515,
                0.9999996743686257,
                0.9999996533672137,
                0.9999996072136594,
                0.9999996072137998
            ],
            [
                1.4449807263312446e-07,
                2.3823688159237777e-07,
                1.637377643243723e-07,
                2.3823696679230424e-07,
                0.9999997761970247,
                0.9999994631248682,
                0.9999996743688198,
                3.927862002654366e-07,
                1.8553919030776337e-07,
                6.023574911170301e-08
            ],
            [
                0.9999987901347497,
                0.9999998362623138,
                0.9999990577554064,
                0.999999554914736,
                0.9999991684719726,
                0.9999998874647977,
                0.9999992188519491,
                0.9999994631247403,
                1.1253506814842375e-07,
                0.9999997897565588
            ],
            [
                8.76424013786396e-08,
                2.5612831267202583e-06,
                0.9999999397643011,
                0.99999994341373,
                0.9999999317439872,
                0.9999998461826405,
                0.9999987901337398,
                2.1024341622426268e-07,
                1.8553905760062447e-07,
                0.9999999434137907
            ],
            [
                5.715005151606823e-07,
                0.9999991148427533,
                0.9999975938976611,
                2.561282210729555e-06,
                1.994730434798734e-06,
                1.7603440527046419e-06,
                0.999999391641181,
                9.931195693628605e-08,
                1.553497384180408e-06,
                4.78509563550957e-06
            ],
            [
                6.023572038912295e-08,
                4.222832437747125e-06,
                1.9947292459347367e-06,
                1.0677033791291683e-06,
                1.3709573702566696e-06,
                2.1444945854624007e-05,
                1.2098653950551882e-06,
                0.9999978766205259,
                7.338213304316717e-07,
                1.2098653950656417e-06
            ],
            [
                8.315284241650899e-07,
                1.5534977545384963e-06,
                5.715004470295662e-07,
                3.9278610661822475e-07,
                1.5534979397394734e-06,
                1.3709570434122812e-06,
                1.3709570434122812e-06,
                6.144172404028807e-06,
                7.338210680002898e-07,
                4.4508510499737865e-07
            ],
            [
                3.466326211113502e-07,
                1.3709568799919866e-06,
                8.315283250371857e-07,
                9.422449308774482e-07,
                6.144176066353646e-06,
                1.5534975693869924e-06,
                6.144172404693786e-06,
                6.475945666051092e-07,
                1.3709576971425944e-06,
                2.699576809143613e-07
            ],
            [
                0.9999999559305575,
                1.275190428875671e-07,
                0.9999999006880314,
                0.9999996940978826,
                0.9999998942830737,
                6.825598028392069e-08,
                2.6995784182140636e-07,
                0.9999997300422547,
                0.9999998144609645,
                2.3823685319244518e-07
            ],
            [
                3.466325384661554e-07,
                0.9999996533673378,
                1.6373764721072816e-07,
                2.1024334103505245e-07,
                9.931185038635267e-08,
                0.9999997463981333,
                1.2751899728286965e-07,
                1.637377643243723e-07,
                5.315780536011123e-08,
                0.9999996072137999
            ],
            [
                8.764253720001207e-08,
                3.059022998576899e-07,
                0.9999994956525319,
                8.764247451307293e-08,
                1.2751908849167202e-07,
                8.7642558095602e-08,
                1.1253518888531272e-07,
                1.760343213335281e-06,
                3.224185864592658e-08,
                2.1024336609843824e-07
            ],
            [
                0.9999999317439628,
                0.9999998874647843,
                1.855391239539711e-07,
                3.059022998569248e-07,
                1.637377057673536e-07,
                0.9999999226557869,
                0.9999995818811274,
                4.1399365603508136e-08,
                0.9999996533674617,
                0.999999581881277
            ],
            [
                1.855391239544352e-07,
                3.059022269250683e-07,
                3.4663266243111764e-07,
                1.8553914607267268e-07,
                1.2751908849167202e-07,
                4.450849458200093e-07,
                5.315781803390236e-08,
                2.6995790618469934e-07,
                2.102433410343832e-07,
                2.699577774585891e-07
            ],
            [
                0.9999999176675338,
                0.9999996533672137,
                0.9999998461827322,
                4.450850519403407e-07,
                0.999999631011416,
                0.999999931743914,
                0.9999998461827139,
                0.9999996533673376,
                0.9999999123575464,
                1.6373766672973748e-07
            ],
            [
                6.475949526003845e-07,
                3.7266379512857925e-06,
                6.144174601879434e-06,
                0.9999822214502913,
                1.7603430034655858e-06,
                1.47389854857293e-05,
                2.9023133689924295e-06,
                5.715005832872586e-07,
                1.7603425837791042e-06,
                1.2098659719601033e-06
            ],
            [
                0.9999997897567091,
                1.444979692800516e-07,
                0.9991959141506546,
                0.9999989322971301,
                2.382369667929001e-07,
                0.9999989969854337,
                0.9999989322968756,
                0.9999999123574838,
                9.931189774187203e-08,
                0.9999990577555186
            ],
            [
                0.999999554914842,
                0.9999993524054336,
                0.9999997761970248,
                2.1024331597152624e-07,
                0.9999998257021837,
                0.9999999317439383,
                0.9999997897567091,
                1.4449795205429202e-07,
                4.4508494582405734e-07,
                4.450852641737424e-07
            ],
            [
                8.315281267800897e-07,
                1.8553916819032217e-07,
                1.7603436330091044e-06,
                1.9947301970813926e-06,
                1.3709570433885908e-06,
                1.2098656835136636e-06,
                1.0677031245783732e-06,
                6.475947210012481e-07,
                0.9999869928715466,
                1.4449803818156628e-07
            ],
            [
                0.9999861539971079,
                0.999995777166557,
                6.47594566597747e-07,
                3.059022998569248e-07,
                6.96225873967641e-06,
                1.209865827740176e-06,
                0.9999949062968224,
                1.0677027427525368e-06,
                4.785094494750855e-06,
                0.9999945777810335
            ],
            [
                1.9947290081177566e-06,
                2.2603237589028734e-06,
                8.315282259117513e-07,
                1.1253520230052635e-07,
                6.144173137014406e-06,
                0.9999993916408183,
                3.466327450765785e-07,
                0.9999999123574523,
                8.764249540862797e-08,
                2.9023126771227976e-06
            ],
            [
                0.9999988634365607,
                0.9999998874649051,
                0.9999998642566381,
                0.9997388096294927,
                3.927862002654366e-07,
                2.6995768091383957e-07,
                3.059021175255426e-07,
                0.9999999176675338,
                0.9999999530883787,
                0.9999996940976638
            ],
            [
                0.9999999317439465,
                0.9999993106388727,
                0.9999998942829981,
                0.9999994284993488,
                0.999999887464744,
                0.9999995262092163,
                0.9999998802069159,
                0.9999998555020135,
                0.9999997761971849,
                0.9999999226557317
            ],
            [
                0.9999975938976611,
                0.9999983463108089,
                8.764254764780641e-08,
                2.1024341622426268e-07,
                8.764244316973974e-08,
                0.9999987901338843,
                0.9999972735300554,
                1.0677027427525368e-06,
                9.422443692489024e-07,
                0.9999989322973848
            ],
            [
                0.9999996533672549,
                1.6373770576776313e-07,
                0.999999825702059,
                6.023572038912295e-08,
                0.9999999317439302,
                0.9999991148429643,
                0.9999998874647843,
                7.734416698849138e-08,
                0.9999998461826405,
                0.9999991684716754
            ],
            [
                0.9999991684719726,
                8.31528325040778e-07,
                0.9999997897567091,
                0.9999994956525318,
                0.9999999468421249,
                6.47594952603035e-07,
                0.9999992188518558,
                1.2098656835252174e-06,
                0.9999989969855533,
                2.2603248367949354e-06
            ],
            [
                1.0677026154806063e-06,
                9.422443692555439e-07,
                3.059023727894942e-07,
                0.9999998461826954,
                2.3823702359290413e-07,
                1.6373762769138607e-07,
                0.9999995818810776,
                2.382370235922541e-07,
                1.8553903548231313e-07,
                0.9999994284995531
            ],
            [
                2.699578740032504e-07,
                4.785096775920397e-06,
                2.561282210562998e-06,
                7.338208930460318e-07,
                2.1024341622426268e-07,
                1.0677028700203557e-06,
                0.999998790134606,
                1.3709573702566696e-06,
                6.475947982002148e-07,
                2.902311293147782e-06
            ],
            [
                0.9999998024946566,
                0.9999997617630617,
                0.999999825702059,
                0.9999983463108088,
                0.9999987121041705,
                0.9999992188513901,
                1.2751908849167202e-07,
                0.9999989969856729,
                0.9999996940977002,
                0.9999993106390368
            ],
            [
                0.9999999273418962,
                0.9999996940978461,
                0.9999999226557131,
                0.999999894282935,
                6.825606165129312e-08,
                0.9999997463980426,
                0.999999789756684,
                0.9999974387184007,
                0.9999999067049943,
                0.9999998024947273
            ],
            [
                3.466325797900508e-07,
                0.9999892166903569,
                0.9999996940977731,
                0.999999814460854,
                0.9999998724808963,
                1.1253516205489029e-07,
                0.9999995262092163,
                0.9999997897566589,
                0.9999991684719725,
                7.734424996967756e-08
            ],
            [
                0.9999994631248044,
                0.999999746398073,
                3.466327450765785e-07,
                0.9999997897566841,
                1.7603438428740716e-06,
                9.422443692574719e-07,
                0.9999994631251883,
                0.9999986290432842,
                1.5534973842076057e-06,
                0.9999997897567341
            ],
            [
                0.9999999176675731,
                0.9999998461827139,
                1.637377057673536e-07,
                0.9999985406239532,
                2.382369667929001e-07,
                0.9999997300422226,
                0.9999996072138935,
                0.9999996940977003,
                4.691162683297406e-08,
                0.9999994284992806
            ],
            [
                0.99999976176309,
                0.9999987121049382,
                0.9999984465022456,
                0.9999972735300554,
                0.9999997126313097,
                8.315277302841894e-07,
                0.9999994956523514,
                0.999999352405202,
                0.999981074851767,
                2.102433410343832e-07
            ],
            [
                5.4222215552470286e-06,
                1.994729959270648e-06,
                0.9997694933676536,
                7.338211554758494e-07,
                9.422448185435711e-07,
                5.043474683220276e-07,
                2.4300232032009452e-05,
                1.760344052714248e-06,
                8.315279285351409e-07,
                1.5534981249397663e-06
            ],
            [
                4.78509278348926e-06,
                3.2887506336235617e-06,
                1.994729483729522e-06,
                1.067703124601679e-06,
                1.76034300345598e-06,
                2.7535687818640727e-05,
                1.3007130015299356e-05,
                4.785095065232451e-06,
                1.0677026154827912e-06,
                1.994729008151319e-06
            ],
            [
                1.8553919030776337e-07,
                1.9947292459406333e-06,
                8.315280276626197e-07,
                1.994729483729522e-06,
                0.9999957771670611,
                4.785093924389007e-06,
                3.2887494574832472e-06,
                0.9999991684718733,
                2.2603248367949354e-06,
                0.9999972735290803
            ],
            [
                0.999999814460854,
                0.9999998461826588,
                0.9999980052705167,
                0.9999998642567028,
                1.0,
                0.999999802494633,
                1.0,
                0.9999997617630048,
                0.999999917667524,
                0.9999998024947272
            ],
            [
                0.9999991684720716,
                0.9999999006881141,
                6.475947982037486e-07,
                7.338213304363436e-07,
                2.3823682479181176e-07,
                2.3823702359290413e-07,
                1.2751905808881762e-07,
                1.4449802095609418e-07,
                0.9999970976880155,
                0.9999993106386259
            ],
            [
                0.9999998942830611,
                0.999999931743914,
                0.9999997300422548,
                0.9999998144608762,
                0.9999999123574523,
                0.9999997463982241,
                0.9999998257021422,
                0.999999391640891,
                0.9999999006880312,
                1.637377643243723e-07
            ],
            [
                8.315277302841894e-07,
                2.5612834320214477e-06,
                3.726641061027928e-06,
                2.5612816000646084e-06,
                8.315282259089153e-07,
                5.422218323487975e-06,
                0.9999955048184243,
                1.994729959270648e-06,
                3.2887502415438413e-06,
                1.0677024881941248e-06
            ],
            [
                1.2098662604291696e-06,
                0.9999999586006493,
                7.734419464850171e-08,
                0.9999996743688975,
                0.9999997300421904,
                0.9999997761970781,
                0.999999946842144,
                0.9999998461826956,
                1.1253506814797596e-07,
                0.9999996940976272
            ],
            [
                2.6995790618350237e-07,
                2.1024341622426268e-07,
                5.04347287955046e-07,
                5.043476486915964e-07,
                3.059022269250683e-07,
                1.6373770576776313e-07,
                0.9999910603015708,
                4.450852641717689e-07,
                2.6995784182073116e-07,
                3.46632497145457e-07
            ],
            [
                1.994729959270648e-06,
                2.9023109471452223e-06,
                1.012999218752948e-05,
                1.3709570434054234e-06,
                2.561281600076256e-06,
                6.962254588585202e-06,
                0.9999985406230839,
                2.2603234895176927e-06,
                2.90231233114251e-06,
                2.9023133690637e-06
            ],
            [
                3.466326211105621e-07,
                1.444980209564556e-07,
                5.4222170304318e-06,
                1.553498124964492e-06,
                5.043474081993875e-07,
                1.1253516205489029e-07,
                1.4449802095609418e-07,
                7.338208055664991e-07,
                2.6995768091383957e-07,
                2.5612831267086116e-06
            ],
            [
                0.9999999468421186,
                0.999999917667524,
                0.9999998942830106,
                0.9999998257020798,
                0.9999998144609645,
                0.9999999500627976,
                0.9999999500628274,
                2.699577774585891e-07,
                0.9999999611088487,
                0.9999999176674454
            ],
            [
                8.7642516304188e-08,
                0.9999998724810027,
                0.9999995549148951,
                0.9999996743686257,
                0.9999997761970781,
                0.9999999176675043,
                0.9999998942830485,
                0.9999996072136593,
                0.9999998257021837,
                2.1024336609843824e-07
            ],
            [
                0.9999869928668915,
                4.691160446380562e-08,
                3.653479031538012e-08,
                1.6373766672973748e-07,
                0.9999997617630048,
                0.9999997300420939,
                6.023579219579052e-08,
                0.9999986290432843,
                0.9999999006880312,
                3.653485564473625e-08
            ]
        ]
    },
    {
        "q_id": "9690_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            4,
            5,
            6,
            9,
            11,
            14,
            15,
            17,
            20,
            21,
            23,
            24,
            29,
            30,
            31,
            32,
            33,
            35,
            37,
            38,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            54,
            57,
            61,
            62,
            63,
            66,
            68,
            69,
            70,
            71,
            73,
            74,
            75,
            77,
            82,
            83,
            86,
            88,
            91,
            92,
            93,
            97,
            99,
            101,
            103,
            108,
            112,
            113,
            117,
            118,
            119,
            120,
            121,
            122,
            125,
            126,
            3,
            81,
            100,
            102,
            104,
            105,
            107
        ],
        "rewards": [
            [
                2.561281600049467e-06,
                2.260324297853209e-06,
                5.422220908925639e-06,
                4.78509563546605e-06,
                1.0129995810343862e-05,
                1.1478764020883773e-05,
                1.670141587174774e-05,
                7.484626297687326e-05,
                2.260324836776948e-06,
                1.4738987243478167e-05
            ],
            [
                7.889260704818233e-06,
                2.9023116391978967e-06,
                1.3709567165461505e-06,
                2.90231163910023e-06,
                1.5534971989696065e-06,
                4.785092783454444e-06,
                7.889266347636241e-06,
                5.422220262599396e-06,
                3.7266388398585725e-06,
                3.2887490653408545e-06
            ],
            [
                9.422442569208767e-07,
                1.2751904288710323e-07,
                1.0677032518814388e-06,
                1.4449795205429202e-07,
                2.1024334103505245e-07,
                1.0677026154730804e-06,
                1.2098662604291696e-06,
                9.422445939032799e-07,
                1.3709575337159875e-06,
                1.9947301970972664e-06
            ],
            [
                1.7603425837855082e-06,
                1.7603425837903113e-06,
                8.315282259138311e-07,
                3.466327037548308e-07,
                2.902312677150514e-06,
                NaN,
                8.939696304116203e-06,
                4.222833947960866e-06,
                NaN,
                5.422220908876325e-06
            ],
            [
                2.5612828213934817e-06,
                1.3709572068522336e-06,
                2.9023119851899796e-06,
                8.93969950132721e-06,
                NaN,
                5.422220909009474e-06,
                1.5534981249697903e-06,
                1.0677032518814388e-06,
                6.962255419931625e-06,
                1.8925143729954285e-05
            ],
            [
                2.260325106237323e-06,
                2.2603234895289998e-06,
                1.209866260432471e-06,
                3.288749849529972e-06,
                1.9947297215043796e-06,
                4.785094494783494e-06,
                2.902312331170226e-06,
                3.726638395634011e-06,
                NaN,
                2.902311293147782e-06
            ],
            [
                2.561282210701601e-06,
                2.7535687809124434e-05,
                2.4300234940642642e-05,
                3.288750241374845e-06,
                8.939696304311336e-06,
                2.4300240728958537e-05,
                7.889262585728421e-06,
                8.481104138298063e-05,
                1.3007130014873483e-05,
                5.422217030707961e-06
            ],
            [
                6.962257909722651e-06,
                1.6701427818034747e-05,
                6.144176066795103e-06,
                1.892515501014656e-05,
                2.753568453712307e-05,
                1.0129993395217047e-05,
                2.561281294760143e-06,
                5.422219616265831e-06,
                8.93969843573914e-06,
                6.962257079775324e-06
            ],
            [
                2.260324028427877e-06,
                2.4300237838535383e-05,
                3.2887494574518405e-06,
                1.5534984953453635e-06,
                7.338208930391909e-07,
                4.222834954778007e-06,
                2.90231094723893e-06,
                9.422448185478557e-07,
                2.5612834319655406e-06,
                1.7603438428800754e-06
            ],
            [
                8.939696304213768e-06,
                7.889259764445822e-06,
                1.4738985486265496e-05,
                4.785094494750855e-06,
                3.726638839878908e-06,
                6.144177531767002e-06,
                4.785093924330255e-06,
                3.726638839878908e-06,
                6.962256249821764e-06,
                1.8925155009767892e-05
            ],
            [
                6.475947982037486e-07,
                7.338208055680009e-07,
                1.7603427936335396e-06,
                3.9278610661902853e-07,
                7.889261645427538e-06,
                7.338210680021253e-07,
                3.7266397283908927e-06,
                4.450848927658745e-07,
                7.338211554783522e-07,
                3.05902263391829e-07
            ],
            [
                2.2603234895372223e-06,
                1.3709567165617364e-06,
                1.7603425837903113e-06,
                1.3709570434219446e-06,
                2.9023112932177327e-06,
                1.9947299593078385e-06,
                NaN,
                1.3709567165579959e-06,
                1.3709568799919866e-06,
                1.3709567165579959e-06
            ],
            [
                8.93969950132721e-06,
                1.760343213335281e-06,
                1.30071315662049e-05,
                2.144495608424996e-05,
                1.8925148242250705e-05,
                2.5612831267202583e-06,
                1.994730672675753e-06,
                2.2603234895289998e-06,
                5.043474683204221e-07,
                1.7603440527286572e-06
            ],
            [
                2.5612828213690224e-06,
                2.7535681254003062e-05,
                1.1478772230407462e-05,
                3.535626757524533e-05,
                1.8925150497435443e-05,
                1.3007125363908762e-05,
                3.288749849498565e-06,
                1.670141786295194e-05,
                1.1478764021029928e-05,
                5.422218969818919e-06
            ],
            [
                4.785095635592258e-06,
                2.5612812947508257e-06,
                6.962255419804982e-06,
                3.288747889229516e-06,
                4.78509563555309e-06,
                6.962255419868303e-06,
                1.0129989772532511e-05,
                4.222831934352267e-06,
                2.902311639183378e-06,
                6.962257909842961e-06
            ],
            [
                6.962256249885085e-06,
                1.9947301970972664e-06,
                1.067703124601679e-06,
                1.2098659719788098e-06,
                2.561281600086738e-06,
                6.144172404693786e-06,
                3.0590226339061185e-07,
                5.829127250399344e-05,
                5.422220909009474e-06,
                7.889266347715168e-06
            ],
            [
                5.04347287955046e-07,
                4.785092783519724e-06,
                2.1024334103581732e-07,
                NaN,
                NaN,
                1.0677029973192638e-06,
                1.1478769494542698e-05,
                2.1024334103581732e-07,
                1.7603427936263351e-06,
                NaN
            ],
            [
                2.4300243631272052e-05,
                2.90231163910023e-06,
                1.9947301970451086e-06,
                5.422217030362759e-06,
                NaN,
                NaN,
                1.0677028700363782e-06,
                5.4222209089700225e-06,
                3.120191137659974e-05,
                3.726639728262097e-06
            ],
            [
                2.753568453712307e-05,
                2.260325106237323e-06,
                2.1444953527944967e-05,
                2.1444953527944967e-05,
                2.4300243631890864e-05,
                5.422219616265831e-06,
                1.0129990979842057e-05,
                NaN,
                1.1478765389222573e-05,
                NaN
            ],
            [
                4.222834954778007e-06,
                4.222832941142044e-06,
                5.422217030747413e-06,
                4.785096776468749e-06,
                2.902312331170226e-06,
                1.7603425837702984e-06,
                1.9947292459265734e-06,
                7.338209805224048e-07,
                5.422217030747413e-06,
                NaN
            ],
            [
                2.753568453792444e-05,
                NaN,
                8.939697369980456e-06,
                3.726639728370556e-06,
                6.962256249885085e-06,
                5.4222183235249605e-06,
                NaN,
                4.785092783519724e-06,
                NaN,
                3.7266401726359486e-06
            ],
            [
                6.144176066850984e-06,
                6.962257079775324e-06,
                2.7535681254804434e-05,
                3.726637951367137e-06,
                3.726641061027928e-06,
                7.889264466639056e-06,
                1.1478765389065974e-05,
                1.0129987357158383e-05,
                2.5612812947508257e-06,
                6.962256249821764e-06
            ],
            [
                1.0129995810076682e-05,
                1.147877359872636e-05,
                3.288747889284851e-06,
                2.1444950971601277e-05,
                1.8925152754169532e-05,
                3.5356238073889594e-05,
                5.4222209089700225e-06,
                1.670141786325573e-05,
                1.3007126914435202e-05,
                2.9023133690980155e-06
            ],
            [
                1.0677033791612137e-06,
                3.05902336324494e-07,
                5.715007195447234e-07,
                8.315279285370317e-07,
                8.315281267861397e-07,
                3.059022269250683e-07,
                1.760343633031919e-06,
                9.422450431989127e-07,
                1.7603434231833873e-06,
                5.04347287955046e-07
            ],
            [
                1.5534984953552536e-06,
                3.466327450765785e-07,
                2.6995784182183607e-07,
                5.715003789046955e-07,
                1.4738983729535602e-05,
                3.059022269250683e-07,
                1.5534971990169383e-06,
                8.315279285370317e-07,
                1.209865827752005e-06,
                1.0677026154806063e-06
            ],
            [
                1.994730672675753e-06,
                1.994730672675753e-06,
                1.0677029973192638e-06,
                2.90231094723893e-06,
                2.9023116391978967e-06,
                1.994729483723626e-06,
                6.475948754012522e-07,
                4.2228324377740105e-06,
                7.484622729279634e-05,
                2.5612819054133693e-06
            ],
            [
                6.144172404693786e-06,
                1.7603436330259153e-06,
                5.422220908876325e-06,
                7.889266347715168e-06,
                5.422217030747413e-06,
                1.994730197090463e-06,
                6.962254589978262e-06,
                1.0677029973192638e-06,
                2.753568782024347e-05,
                1.670142980893658e-05
            ],
            [
                4.222834451355964e-06,
                1.3709567165579959e-06,
                8.315283250371857e-07,
                4.785095635624897e-06,
                2.699576809143613e-07,
                1.2098655392921197e-06,
                NaN,
                3.288749065423109e-06,
                8.315281267834927e-07,
                2.260324297853209e-06
            ],
            [
                2.2603234895289998e-06,
                3.288749065423109e-06,
                6.1441746020359e-06,
                2.4300234941880266e-05,
                6.144176799334096e-06,
                0.00010889687041282619,
                2.1444950971601277e-05,
                4.785092783519724e-06,
                5.422219616265831e-06,
                3.288748673376478e-06
            ],
            [
                5.71500515159253e-07,
                3.4663249714612693e-07,
                1.5534973842076057e-06,
                5.715003107755449e-07,
                1.0677032518814388e-06,
                4.450850519403407e-07,
                1.2098658277451275e-06,
                1.5534975693933505e-06,
                7.338211554783522e-07,
                1.0677027427624903e-06
            ],
            [
                2.5612816000145246e-06,
                3.0590237279085045e-07,
                5.043473480777865e-07,
                5.04347287955046e-07,
                3.9278610661902853e-07,
                1.0677029973192638e-06,
                3.927862002663297e-07,
                1.3007126914435202e-05,
                9.422448185534261e-07,
                2.382370235933104e-07
            ],
            [
                1.5534984953510149e-06,
                1.3709570434178922e-06,
                8.315281267882195e-07,
                1.5534984953453635e-06,
                1.2098656835136636e-06,
                1.0677026154806063e-06,
                6.475945666063607e-07,
                1.2098659719757836e-06,
                9.422450431989127e-07,
                5.715003789017068e-07
            ],
            [
                1.0129993395217047e-05,
                2.9023119851899796e-06,
                4.222834954778007e-06,
                3.726638839878908e-06,
                9.422448185510695e-07,
                1.6701419854156377e-05,
                5.422217030707961e-06,
                8.939696304311336e-06,
                4.0063706517323215e-05,
                1.0129989772532511e-05
            ],
            [
                5.422217030614265e-06,
                1.5534975693869924e-06,
                NaN,
                9.4224425692559e-07,
                1.2098661161927025e-06,
                3.2887478892683997e-06,
                4.2228334445658276e-06,
                3.726639728370556e-06,
                5.829126554917624e-05,
                2.9023109472244114e-06
            ],
            [
                7.338209805240734e-07,
                1.2751899728286965e-07,
                6.475948754012522e-07,
                5.043473480777865e-07,
                3.4663249714612693e-07,
                5.715005832853093e-07,
                5.715007195431641e-07,
                2.6995784182183607e-07,
                5.04347287955046e-07,
                1.067703124601679e-06
            ],
            [
                3.288748673376478e-06,
                1.1478770862735993e-05,
                4.785093924362895e-06,
                2.902313369111213e-06,
                1.5534973842076057e-06,
                1.994730672675753e-06,
                1.4738989000422955e-05,
                5.4222183235249605e-06,
                7.338211554801876e-07,
                4.785096206076165e-06
            ],
            [
                1.1253525596174225e-07,
                3.466327450765785e-07,
                3.466327037553825e-07,
                2.382370235933104e-07,
                2.3823685319320354e-07,
                1.8553916819032217e-07,
                9.422442569315887e-07,
                6.475948754012522e-07,
                2.382369667929001e-07,
                1.8553907971855875e-07
            ],
            [
                1.4738976701411704e-05,
                4.785095065132354e-06,
                1.0129990979694647e-05,
                2.7535700947019215e-05,
                1.8925157265332104e-05,
                3.2887482812506295e-06,
                NaN,
                4.222834954778007e-06,
                4.222833947932061e-06,
                4.222834451382849e-06
            ],
            [
                1.0677026154619133e-06,
                1.5534984953199313e-06,
                5.715003107767143e-07,
                4.222831934379152e-06,
                7.338209805240734e-07,
                9.422445939032799e-07,
                6.144172404738491e-06,
                5.715004470313855e-07,
                8.315284241650899e-07,
                5.422220262636381e-06
            ],
            [
                2.5612828213690224e-06,
                6.962257079376403e-06,
                8.939693107093343e-06,
                1.760344052714248e-06,
                4.785096205930373e-06,
                3.7266379513162962e-06,
                1.9947304348703948e-06,
                1.9947299592933255e-06,
                1.5534975693707442e-06,
                8.315277302788957e-07
            ],
            [
                2.260324297853209e-06,
                8.93969736942758e-06,
                6.144175334367959e-06,
                3.288748673360027e-06,
                5.829126554917624e-05,
                3.288749849498565e-06,
                7.889263525663481e-06,
                2.144495608327478e-05,
                4.2228334445370225e-06,
                2.9023133690980155e-06
            ],
            [
                5.422219616265831e-06,
                7.88926540679677e-06,
                8.939693107190907e-06,
                3.466327863983311e-07,
                7.889260704968913e-06,
                1.4738980215352592e-05,
                3.53562422882756e-05,
                2.902312677150514e-06,
                2.7535704232595768e-05,
                1.012998977198894e-05
            ],
            [
                1.7603427936263351e-06,
                1.3007133116732079e-05,
                5.71500651413193e-07,
                6.144173137126169e-06,
                6.962257909785973e-06,
                0.0010322308520079393,
                1.3709576971425944e-06,
                3.726638839878908e-06,
                NaN,
                3.288748673376478e-06
            ],
            [
                2.2603245673279107e-06,
                1.2098662604291696e-06,
                4.450851580555361e-07,
                2.2603237589542675e-06,
                1.3709575336947905e-06,
                7.338209805224048e-07,
                8.939698435657833e-06,
                1.3709576971242028e-06,
                8.31527928532683e-07,
                1.994729483694599e-06
            ],
            [
                1.0677032518785256e-06,
                NaN,
                9.422449308748773e-07,
                1.5534975693707442e-06,
                8.315283250371857e-07,
                8.315283250371857e-07,
                8.315279285370317e-07,
                NaN,
                NaN,
                1.9947294837154625e-06
            ],
            [
                3.466327450765785e-07,
                2.69957906184239e-07,
                7.338208055680009e-07,
                2.6995790618469934e-07,
                8.315280276546789e-07,
                4.450852111148132e-07,
                NaN,
                7.338212429537553e-07,
                NaN,
                3.059021175261338e-07
            ],
            [
                9.422443692574719e-07,
                3.4663278639892215e-07,
                6.825608606172863e-08,
                NaN,
                NaN,
                7.889259764445822e-06,
                NaN,
                NaN,
                5.043475885696228e-07,
                NaN
            ],
            [
                4.785095635624897e-06,
                9.422448185478557e-07,
                2.9023133690980155e-06,
                1.6701415872385704e-05,
                5.422217030707961e-06,
                1.7603432132912532e-06,
                1.067703124601679e-06,
                2.561282210740037e-06,
                8.939696304213768e-06,
                4.785095065232451e-06
            ],
            [
                1.0677029973219343e-06,
                NaN,
                2.902313369111213e-06,
                1.994730197071414e-06,
                6.47595107001401e-07,
                3.9278605979534166e-07,
                6.475950298011458e-07,
                5.715005832853093e-07,
                7.889261645269683e-06,
                1.0677028700422047e-06
            ],
            [
                1.8925143729162536e-05,
                4.785093924362895e-06,
                5.422221555069497e-06,
                3.726638395611981e-06,
                2.9023126771227976e-06,
                6.9622595696935874e-06,
                3.2887482812506295e-06,
                8.939696304002375e-06,
                6.962254589914941e-06,
                1.147876812574406e-05
            ],
            [
                3.12019225345861e-05,
                3.927862939126708e-07,
                1.147877359957198e-05,
                NaN,
                4.222833947774596e-06,
                6.475949525981759e-07,
                1.2098662604291696e-06,
                1.9947292459347367e-06,
                1.8925150497848527e-05,
                6.962254589914941e-06
            ],
            [
                1.4738976701652988e-05,
                2.9023119851899796e-06,
                3.2887502415438413e-06,
                4.785093924330255e-06,
                1.3007131566015624e-05,
                1.1478765389222573e-05,
                4.22283545819819e-06,
                1.0677026154806063e-06,
                9.422443692555439e-07,
                3.2887502415767434e-06
            ],
            [
                9.610240347794738e-05,
                1.5534977545886537e-06,
                1.9947292459347367e-06,
                2.144495608424996e-05,
                2.260324567337161e-06,
                NaN,
                5.422218969818919e-06,
                1.7603436330259153e-06,
                3.726639728370556e-06,
                5.715002426486762e-07
            ],
            [
                3.726641061027928e-06,
                1.2098662604126641e-06,
                2.561282210701601e-06,
                1.3709572068478697e-06,
                4.222835458148261e-06,
                7.889266347715168e-06,
                1.1478769494083349e-05,
                2.5612819054028872e-06,
                1.2098658277451275e-06,
                2.5612812947380135e-06
            ],
            [
                2.2603234895176927e-06,
                4.785094494783494e-06,
                2.260324836776948e-06,
                1.7603434231833873e-06,
                1.994729245917502e-06,
                2.2603234895289998e-06,
                1.2098658277451275e-06,
                3.927863875616689e-07,
                5.715006514151423e-07,
                2.902313023130843e-06
            ],
            [
                8.315283250371857e-07,
                5.715003789046955e-07,
                1.3709568799760888e-06,
                1.5534975693933505e-06,
                5.043476486915964e-07,
                2.260324836787226e-06,
                3.4663249714325014e-07,
                3.4663257978465195e-07,
                1.2098652508424818e-06,
                4.450851049941403e-07
            ],
            [
                2.2603234895176927e-06,
                4.450851049959619e-07,
                4.222833444590791e-06,
                2.2603234895176927e-06,
                4.450851049959619e-07,
                5.043472879525233e-07,
                2.2603242978665707e-06,
                7.88925976418034e-06,
                1.0677032518814388e-06,
                1.0677024881980089e-06
            ],
            [
                3.726640172537657e-06,
                2.260325375664839e-06,
                4.785096205930373e-06,
                1.1478769494396542e-05,
                5.422220908925639e-06,
                1.0129988564974359e-05,
                NaN,
                6.144174601309452e-06,
                6.962253759904688e-06,
                4.222832941072913e-06
            ],
            [
                NaN,
                2.90231094723893e-06,
                1.0129994602895546e-05,
                NaN,
                3.72663883989755e-06,
                NaN,
                8.939698435657833e-06,
                4.785095635655362e-06,
                2.7535700950274782e-05,
                4.222831934352267e-06
            ],
            [
                3.7266410611296085e-06,
                1.0677031245905116e-06,
                1.2098659719757836e-06,
                2.561282516066741e-06,
                1.5534979397740895e-06,
                2.2603237589779086e-06,
                5.715005832827105e-07,
                7.338211554783522e-07,
                1.0677024881980089e-06,
                1.9947292459265734e-06
            ],
            [
                2.2603245673279107e-06,
                3.7266410611296085e-06,
                3.2887482813149375e-06,
                5.715003107755449e-07,
                5.422220262636381e-06,
                1.994729245917502e-06,
                6.962257909785973e-06,
                9.422447062202052e-07,
                3.288748673376478e-06,
                2.561282210729555e-06
            ],
            [
                1.0129988564716393e-05,
                3.7266392840781026e-06,
                5.422221555296344e-06,
                6.962257909722651e-06,
                9.610242645336945e-05,
                3.535625071602016e-05,
                5.422218969858371e-06,
                4.222834954687752e-06,
                NaN,
                1.4738980215111302e-05
            ],
            [
                9.422443692489024e-07,
                6.962254589914941e-06,
                6.475947981975644e-07,
                8.315282259138311e-07,
                6.144172404738491e-06,
                6.475946438055299e-07,
                1.3007134667070165e-05,
                1.7603427936263351e-06,
                4.785092783454444e-06,
                6.475949526020042e-07
            ],
            [
                1.2098656835224664e-06,
                1.5534981249697903e-06,
                3.927862002663297e-07,
                4.785096776499213e-06,
                8.315277302841894e-07,
                9.422443692555439e-07,
                NaN,
                1.760343213335281e-06,
                1.0129994602895546e-05,
                6.144175334367959e-06
            ],
            [
                4.785095635624897e-06,
                2.902312677150514e-06,
                2.5612825160562587e-06,
                5.422218323399208e-06,
                7.889259764359722e-06,
                1.0129995810343862e-05,
                2.9023119850210436e-06,
                1.8925145983795953e-05,
                1.994729483705484e-06,
                1.1478770862735993e-05
            ],
            [
                1.7603434231777837e-06,
                1.5534973841895917e-06,
                2.5612831266946347e-06,
                1.5534975693869924e-06,
                2.5612822107167428e-06,
                2.5612819054028872e-06,
                1.8925145985895816e-05,
                1.8925155009767892e-05,
                3.7266406167827664e-06,
                1.0129995810343862e-05
            ],
            [
                9.422442569315887e-07,
                4.450848927658745e-07,
                1.0677032518785256e-06,
                2.3823699519290042e-07,
                2.3823693839325527e-07,
                5.043474081993875e-07,
                5.422218969818919e-06,
                8.315281267861397e-07,
                5.043475885696228e-07,
                2.260324836776948e-06
            ],
            [
                3.726639728370556e-06,
                2.2603234895176927e-06,
                2.260324567337161e-06,
                1.9947304348703948e-06,
                2.260323758987159e-06,
                6.144172404693786e-06,
                2.902312677150514e-06,
                1.5534984953453635e-06,
                1.012999218776902e-05,
                5.422219616228845e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                6.1441746020359e-06,
                1.3709576971463352e-06,
                0.00017952805197501883,
                6.962259569630266e-06,
                1.8925145985895816e-05,
                1.012998977264307e-05,
                3.726637951387472e-06
            ],
            [
                5.715006514176113e-07,
                4.450850519403407e-07,
                7.338209805200689e-07,
                1.637377448057981e-07,
                4.450852111155216e-07,
                5.04347528446051e-07,
                5.715007195447234e-07,
                3.9278634073732336e-07,
                2.1024331597262577e-07,
                3.4663262110945863e-07
            ],
            [
                4.222834954801051e-06,
                1.99472924590571e-06,
                8.315282259138311e-07,
                6.144175334468545e-06,
                9.422447062294175e-07,
                2.260324836787226e-06,
                NaN,
                3.2887482813149375e-06,
                1.5534975693979422e-06,
                1.0677032518785256e-06
            ],
            [
                8.315277302747361e-07,
                9.42244930862237e-07,
                3.288749457469787e-06,
                2.5612812947508257e-06,
                6.144172404693786e-06,
                3.9278605979011705e-07,
                7.338210679909462e-07,
                5.715006514105942e-07,
                8.315277302649045e-07,
                5.715004470243685e-07
            ],
            [
                2.2603242978871282e-06,
                3.288748281329893e-06,
                NaN,
                2.9023109471689794e-06,
                1.3007123813382511e-05,
                2.2603234895372223e-06,
                4.006369219233375e-05,
                6.1441731370702875e-06,
                4.222834954778007e-06,
                1.3709572068272963e-06
            ],
            [
                1.3709567165579959e-06,
                3.726638839878908e-06,
                7.889261645355786e-06,
                4.4508505193791187e-07,
                2.260325106237323e-06,
                1.0129995810343862e-05,
                1.9947301970972664e-06,
                7.889265407327733e-06,
                NaN,
                3.1201911375578156e-05
            ],
            [
                NaN,
                1.0129988565084915e-05,
                NaN,
                2.902312331125353e-06,
                2.9023133690980155e-06,
                2.9023112932177327e-06,
                2.902313023130843e-06,
                2.5612825160562587e-06,
                4.222832437747125e-06,
                1.2098652508424818e-06
            ],
            [
                1.8925141473978602e-05,
                8.939698435657833e-06,
                4.78509563555309e-06,
                2.9023123311583482e-06,
                2.5612819054133693e-06,
                1.4738987243236881e-05,
                1.0129992187658463e-05,
                1.7603436330179102e-06,
                1.5534975693869924e-06,
                6.144176799283803e-06
            ],
            [
                4.4508505193791187e-07,
                2.9023119851781017e-06,
                7.889264466639056e-06,
                3.927862470899887e-07,
                2.9023119851266288e-06,
                2.5612828213818346e-06,
                3.2887482813149375e-06,
                1.9947297215043796e-06,
                1.3007130014873483e-05,
                5.715005832886879e-07
            ],
            [
                2.2603234895289998e-06,
                1.0677032518785256e-06,
                2.2603242978871282e-06,
                1.994729008145876e-06,
                9.422442569315887e-07,
                1.2098662604247682e-06,
                6.1441767993788005e-06,
                8.315277302841894e-07,
                1.0677024881980089e-06,
                6.144175334468545e-06
            ]
        ]
    },
    {
        "q_id": "9911_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                1.1253521571574156e-07,
                0.9999995549148951,
                0.9999972735290809,
                0.9999993106392012,
                0.9999985406243016,
                0.9999981261239475,
                6.475945666033422e-07,
                2.382369667929001e-07,
                0.999994228079975,
                8.315278294072958e-07
            ],
            [
                0.9999998024947037,
                0.9999982396572072,
                4.222831934379152e-06,
                0.9999997617629766,
                0.9999952149043673,
                1.6373770576776313e-07,
                0.9999981261252877,
                0.9999997300422226,
                0.9999938558254029,
                0.9999756997680169
            ],
            [
                0.9999986290429576,
                0.9999988634366963,
                0.9999997897565587,
                0.9999994284994169,
                0.9999996940978461,
                0.9999964991464226,
                0.9999998461826956,
                0.9999921107364846,
                0.9999969105048173,
                0.9999989322967487
            ],
            [
                5.715004470313855e-07,
                9.422444815765128e-07,
                3.2887498495150166e-06,
                7.338210680021253e-07,
                4.450849988811838e-07,
                6.144176066901277e-06,
                8.315281267882195e-07,
                9.422449308774482e-07,
                3.0590215399183813e-07,
                3.466327863983311e-07
            ],
            [
                2.6995790618350237e-07,
                2.1024326584639497e-07,
                2.1024326584639497e-07,
                3.0590237279032884e-07,
                1.2751908849167202e-07,
                9.931185038635267e-08,
                1.4449795205429202e-07,
                2.3823685319244518e-07,
                8.764244316933122e-08,
                1.8553910183674878e-07
            ],
            [
                0.9999997617630333,
                0.9999995818811773,
                0.9999994956524118,
                0.9999999317439221,
                0.9999995262096117,
                0.9999997300421906,
                0.9999998802069587,
                0.9999995818812771,
                0.9999999226557131,
                0.9999996743686257
            ],
            [
                2.6995784182140636e-07,
                9.422449308748773e-07,
                8.315279285351409e-07,
                0.9999987121047851,
                4.450852111148132e-07,
                7.889263526266196e-06,
                0.9999980052707551,
                3.726638839878908e-06,
                1.3709573702822306e-06,
                4.4508510499849186e-07
            ],
            [
                1.0,
                1.8553907971879076e-07,
                0.9999994956527123,
                0.9999999123574628,
                1.0,
                0.9999996743687034,
                0.9999999677581067,
                0.9999995818812272,
                1.0,
                0.9999997617631469
            ],
            [
                1.1253517547010071e-07,
                8.7642516304188e-08,
                8.764245361752286e-08,
                2.1024341622426268e-07,
                1.1253506814797596e-07,
                8.31528424162821e-07,
                0.9999990577552941,
                3.46632497145457e-07,
                6.023576347299818e-08,
                1.1253526937656726e-07
            ],
            [
                0.9999993524049704,
                0.9999998024946801,
                0.999999554914736,
                0.9999991684720718,
                0.9999984465026165,
                0.9999980052693294,
                1.209865539274514e-06,
                0.9999996310113279,
                3.0590215399183813e-07,
                0.9999995549150544
            ],
            [
                1.0,
                0.9999999176674946,
                0.999999927341827,
                0.9999999006881377,
                0.9999995262093858,
                0.9999998942829225,
                0.9999994284996214,
                1.1253512180925583e-07,
                0.9999998642566704,
                0.9999998724809267
            ],
            [
                0.9999756997622188,
                2.90231094723893e-06,
                3.466327863983311e-07,
                5.043475885674441e-07,
                1.0129994602895546e-05,
                5.043476486915964e-07,
                3.0590215399183813e-07,
                5.04347468323289e-07,
                0.9999975938982363,
                5.715007195447234e-07
            ],
            [
                5.315787506598473e-08,
                1.1253516205489029e-07,
                1.1253516205489029e-07,
                8.764240137829087e-08,
                1.1253518888531272e-07,
                8.7642516304188e-08,
                1.4449795205429202e-07,
                2.382370235922541e-07,
                1.1253513522447425e-07,
                1.2751908849167202e-07
            ],
            [
                3.927860597935108e-07,
                6.475950298011458e-07,
                1.0677032518814388e-06,
                3.466325797888292e-07,
                8.315277302841894e-07,
                2.6995774527577444e-07,
                5.715007195431641e-07,
                7.338208055664991e-07,
                4.4508505193932864e-07,
                3.535626336201389e-05
            ],
            [
                0.9999998461826956,
                0.9999998362622747,
                0.9999998257021837,
                0.9999987121047854,
                6.023568448589658e-08,
                0.9999999226557685,
                0.9999992661789326,
                0.9999999123575881,
                0.9999994956527124,
                0.9999997126314469
            ],
            [
                7.338208055664991e-07,
                5.715004470313855e-07,
                2.3823699519290042e-07,
                4.2228339479858295e-06,
                0.9999980052709927,
                5.043476486915964e-07,
                8.315281267882195e-07,
                3.0590237279032884e-07,
                6.475947210031623e-07,
                4.450852111100568e-07
            ],
            [
                2.3823690999160957e-07,
                2.6995768091310296e-07,
                2.3823690999290963e-07,
                8.76424013786396e-08,
                2.1024326584582131e-07,
                0.9999972735300563,
                1.444980209564556e-07,
                2.3823682479181176e-07,
                1.1253518888531272e-07,
                2.382368247924618e-07
            ],
            [
                0.9999985406241277,
                0.9999981261246186,
                5.8291293344700434e-05,
                0.9999991684722702,
                0.9999957771670646,
                0.9999994631248685,
                0.9999988634358838,
                0.9999986290432844,
                0.9999987121043247,
                0.999998540623954
            ],
            [
                0.9999991148426479,
                0.9999999123574628,
                0.9999995818811773,
                0.9999999067050832,
                0.9999999500628571,
                0.9999998942830106,
                0.9999998802069731,
                0.9999999611088487,
                1.0,
                0.999999958600585
            ],
            [
                0.9999999358793332,
                2.6995768091383957e-07,
                0.9999999656787202,
                0.9999999611088534,
                0.9999995818811275,
                1.0,
                0.9999999226558421,
                0.9999997463981334,
                0.9999999559305733,
                0.9999999434137098
            ],
            [
                1.4449798650551755e-07,
                1.637376862489725e-07,
                5.422217030781934e-06,
                2.6995784182140636e-07,
                3.466325797896173e-07,
                3.466326211113502e-07,
                2.382369951932796e-07,
                2.3823690999290963e-07,
                1.6373776432509826e-07,
                2.382369667929001e-07
            ],
            [
                2.699577774585891e-07,
                2.3823702359290413e-07,
                3.466325797896173e-07,
                3.927862939126708e-07,
                9.93120161306789e-08,
                1.4449798650569826e-07,
                3.927860597945825e-07,
                5.043472278322555e-07,
                2.699576809143613e-07,
                3.9278634073732336e-07
            ],
            [
                1.0129993395217047e-05,
                3.726641061085547e-06,
                4.539786865090791e-05,
                2.5612825160271407e-06,
                3.7266397283231055e-06,
                5.4222209089700225e-06,
                1.2098653950656417e-06,
                6.144176799334096e-06,
                3.9278615344178325e-07,
                2.9023130231176453e-06
            ],
            [
                0.9999974387165704,
                0.9999998724809571,
                0.9999921107355466,
                0.9999998874648515,
                3.466325797896173e-07,
                0.9999988634357482,
                3.9278615344178325e-07,
                0.9999995262096117,
                0.9999989322973853,
                0.9999999123574523
            ],
            [
                0.9999998642567028,
                0.9999998942830358,
                0.9999998362622358,
                0.9999999500627798,
                0.9999997300421584,
                0.999999495652592,
                1.0,
                0.9999992661788449,
                0.9999997126313099,
                0.9999989969854342
            ],
            [
                0.9999985406236057,
                0.9999995549148952,
                6.475950298011458e-07,
                0.9999996072136594,
                6.475949526020042e-07,
                3.0590215399183813e-07,
                1.6373768624837685e-07,
                0.9999756997651039,
                0.9999983463110063,
                0.9999985406234319
            ],
            [
                0.99999995860059,
                0.999999906705061,
                1.0,
                2.3823688159291947e-07,
                0.9999997761972116,
                0.9999999317439546,
                0.9999999697115696,
                1.0,
                0.9999989969856732,
                0.9999999500628453
            ],
            [
                2.382370235933104e-07,
                5.715003107767143e-07,
                4.4508510499849186e-07,
                5.04347528446051e-07,
                3.46632497145457e-07,
                5.715003107755449e-07,
                4.450852111148132e-07,
                3.927860597945825e-07,
                3.059022269250683e-07,
                3.120192625482384e-05
            ],
            [
                8.764249540862797e-08,
                1.4449805540740185e-07,
                1.2751908849167202e-07,
                9.931186222523604e-08,
                1.7603434231833873e-06,
                1.444980209564556e-07,
                1.6373776432509826e-07,
                5.3157830707696514e-08,
                7.73441946488886e-08,
                0.999998863436019
            ],
            [
                0.9999996072139403,
                0.9999934595620038,
                5.422221555296344e-06,
                2.4300249425247723e-05,
                1.5534981249697903e-06,
                0.9999980052709946,
                0.9999983463104153,
                0.9999998257021213,
                9.422450431989127e-07,
                4.450852111135988e-07
            ],
            [
                1.0,
                0.9999999397642293,
                0.9999999123575674,
                0.9999999500627976,
                0.9999998942830358,
                0.9999999358793638,
                0.999999814460876,
                0.9999999434137772,
                0.9999999123575255,
                0.9999999226557778
            ],
            [
                2.3823702359290413e-07,
                1.275191036933194e-07,
                1.125352291309328e-07,
                1.27519088491875e-07,
                2.1024339116082313e-07,
                1.2751908849167202e-07,
                9.931195693628605e-08,
                1.6373774480535133e-07,
                2.3823702359290413e-07,
                3.4663266243111764e-07
            ],
            [
                4.222835458175145e-06,
                1.637377057673536e-07,
                1.4449807263325588e-07,
                7.338210680021253e-07,
                1.6373766672973748e-07,
                1.637377448057981e-07,
                1.1253513522447425e-07,
                2.6995784182183607e-07,
                4.450852111148132e-07,
                8.764244316973974e-08
            ],
            [
                6.475945666051092e-07,
                4.4508494582405734e-07,
                1.067703124601679e-06,
                1.7603425837903113e-06,
                3.05902336324494e-07,
                4.4508494582405734e-07,
                3.0590237279032884e-07,
                7.338209805224048e-07,
                9.422448185534261e-07,
                4.450848927658745e-07
            ],
            [
                0.9999998257021837,
                1.4738985486265496e-05,
                0.9999998802069017,
                0.9999996072136126,
                0.9999997617631753,
                0.9999974387180965,
                0.9999978766215386,
                0.9999995262093292,
                6.475949525919915e-07,
                0.9999975938979493
            ],
            [
                0.9999999317439058,
                0.9999957771665623,
                0.9999998362623138,
                0.99999976176309,
                0.9999999317439627,
                0.9999997761970247,
                0.9999995549147359,
                9.931198061405701e-08,
                0.9999994956525919,
                0.9999996940977732
            ],
            [
                2.6995790618350237e-07,
                2.6995768091310296e-07,
                2.1024344128660572e-07,
                6.9622587397397306e-06,
                1.637377643243723e-07,
                1.2751901248454963e-07,
                1.4449802095666915e-07,
                1.6373776432509826e-07,
                4.1399365603508136e-08,
                0.9999996310114599
            ],
            [
                1.3007126914612648e-05,
                4.222834954687752e-06,
                7.338208930355202e-07,
                3.927861066170637e-07,
                5.1442232053101066e-05,
                1.3709578605617394e-06,
                2.753568782024347e-05,
                1.553498495308628e-06,
                8.939694172656384e-06,
                6.962253759828703e-06
            ],
            [
                2.6995790618350237e-07,
                8.315281267861397e-07,
                5.715004470295662e-07,
                2.699578096393206e-07,
                3.466327037539638e-07,
                2.6995771309523475e-07,
                3.059021904571643e-07,
                3.4663249714325014e-07,
                1.0677028700422047e-06,
                2.260324567337161e-06
            ],
            [
                9.610240358212368e-05,
                0.9999990577549572,
                0.9999989322973851,
                4.222833444590791e-06,
                0.9999995818811275,
                1.6373768624837685e-07,
                0.9999991148428592,
                0.9999970976873263,
                0.9999990577551819,
                0.9999996310116359
            ],
            [
                2.6995784182140636e-07,
                7.338210680021253e-07,
                8.764241182641775e-08,
                1.1253514863909295e-07,
                3.224185864592658e-08,
                8.764249540862797e-08,
                1.6373772528581146e-07,
                8.764249540862797e-08,
                0.9999999634652054,
                0.9999996940977367
            ],
            [
                2.699578740032504e-07,
                0.999999428499485,
                1.5534971990169383e-06,
                1.6373776432509826e-07,
                0.9999993524052793,
                0.9999998724809115,
                1.8925155009767892e-05,
                2.382369951932796e-07,
                8.315278294114555e-07,
                0.999999631011372
            ],
            [
                0.9999996743688199,
                0.9999998942828973,
                0.9999999358793409,
                0.9999978766212856,
                0.9999999317439954,
                3.2887506336086064e-06,
                0.9999977396762421,
                0.9999992188517628,
                0.9999994956527122,
                0.9999996310113719
            ],
            [
                0.9999952149038008,
                3.535626757653154e-05,
                0.9999930377454193,
                0.9999984465020609,
                0.9999994956524718,
                0.9999974387174864,
                0.9999985406234322,
                0.999997593898236,
                7.338210679979539e-07,
                0.9999986290421403
            ],
            [
                0.9999997761970515,
                0.99999862904214,
                0.9999996940978461,
                0.9999998802069873,
                0.9999991148431756,
                0.9999997300421903,
                0.9999993106392013,
                0.9999991684720717,
                0.9999995549148951,
                0.9999998024946566
            ],
            [
                1.855391239547094e-07,
                6.144172404738491e-06,
                2.10243290909724e-07,
                4.450851049991497e-07,
                3.65348425788669e-08,
                1.855391239547094e-07,
                2.699576809143613e-07,
                2.10243290909724e-07,
                3.466325797888292e-07,
                6.962257909785973e-06
            ],
            [
                0.9999970976866344,
                1.1253526937656726e-07,
                3.0590237279032884e-07,
                6.023578501491997e-08,
                0.9999983463110066,
                7.734423152941018e-08,
                1.2098659719757836e-06,
                3.92786293909545e-07,
                1.1253516205489029e-07,
                2.699578096393206e-07
            ],
            [
                2.902313023130843e-06,
                4.785092783519724e-06,
                3.288747889284851e-06,
                1.5534973842076057e-06,
                3.0590215399183813e-07,
                2.382369951932796e-07,
                6.1441746020359e-06,
                6.962254589978262e-06,
                1.1478766757718129e-05,
                1.4449798650417048e-07
            ],
            [
                1.0,
                0.9999997761970248,
                0.9999996072139403,
                0.9999999500628453,
                0.9999975938976611,
                0.9999994631249323,
                0.9999998257022045,
                1.0,
                0.9999999434138042,
                0.9999992188513902
            ],
            [
                7.338210679979539e-07,
                7.338210679909462e-07,
                2.6995790618252024e-07,
                8.315279285149107e-07,
                2.260323489435463e-06,
                3.927863407379485e-07,
                4.4508489275752546e-07,
                3.4663266243111764e-07,
                9.422444815495185e-07,
                4.450849988758202e-07
            ],
            [
                4.139934586278605e-08,
                1.1253524254615121e-07,
                1.637377057673536e-07,
                0.9999962733589413,
                9.931186222523604e-08,
                1.125352291309328e-07,
                2.102434412871794e-07,
                1.4449805540740185e-07,
                8.764244316973974e-08,
                7.734418542875216e-08
            ],
            [
                2.1024326584582131e-07,
                1.8553907971682908e-07,
                2.382369667929001e-07,
                1.6373772528581146e-07,
                2.102433410343832e-07,
                1.2098659719788098e-06,
                3.4663266243111764e-07,
                2.6995768091310296e-07,
                7.889261645090304e-06,
                1.8553903548231313e-07
            ],
            [
                3.4663253846718004e-07,
                2.1024341622426268e-07,
                3.0590237279032884e-07,
                4.450850519403407e-07,
                3.9278615344178325e-07,
                2.3823682479181176e-07,
                1.637377643243723e-07,
                2.6995784182073116e-07,
                2.3823693839290317e-07,
                3.466327450765785e-07
            ],
            [
                1.4449807263312446e-07,
                7.734418542875216e-08,
                1.1253526937656726e-07,
                4.450852111148132e-07,
                1.2751902768612997e-07,
                1.1253512180925583e-07,
                1.8925148242250705e-05,
                9.931189774187203e-08,
                4.6911638017556955e-08,
                1.2751899728286965e-07
            ],
            [
                8.315281267882195e-07,
                1.3709572068522336e-06,
                1.5534975693979422e-06,
                5.715003107767143e-07,
                3.4663274507713016e-07,
                6.962257909842961e-06,
                1.3709570434178922e-06,
                8.315284241665078e-07,
                4.450852111148132e-07,
                9.422443692574719e-07
            ],
            [
                1.8553910183674878e-07,
                3.05902263391829e-07,
                1.6373774480605869e-07,
                1.275190428875671e-07,
                2.1024331597262577e-07,
                1.855391239544352e-07,
                2.6995790618469934e-07,
                3.927863407379485e-07,
                1.855391239544352e-07,
                3.059022269250683e-07
            ],
            [
                1.1253526937656726e-07,
                1.27519073289925e-07,
                1.6373766672888118e-07,
                1.2751907329024393e-07,
                0.999998863435748,
                7.734424996967756e-08,
                1.2751910369275402e-07,
                1.2751899728286965e-07,
                4.1399410020127234e-08,
                1.6373770576776313e-07
            ],
            [
                2.382370235933104e-07,
                3.059023727894942e-07,
                2.382368531929327e-07,
                3.535624650150453e-05,
                1.067703124601679e-06,
                7.484622729279634e-05,
                5.715002426460124e-07,
                4.450849988798682e-07,
                5.715003107755449e-07,
                3.9278605979534166e-07
            ],
            [
                3.466325797896173e-07,
                7.338207180898968e-07,
                7.338207180898968e-07,
                1.2751904288710323e-07,
                2.6995784182183607e-07,
                5.043475885696228e-07,
                4.450852111155216e-07,
                2.102434162245973e-07,
                2.3823693839325527e-07,
                8.315280276626197e-07
            ],
            [
                6.475947210031623e-07,
                3.9278615344178325e-07,
                1.5534973842076057e-06,
                1.3709575337078829e-06,
                2.382369383923073e-07,
                3.05902263391829e-07,
                3.0590215399183813e-07,
                3.0590215399183813e-07,
                2.3823685319244518e-07,
                1.0677026154806063e-06
            ],
            [
                0.9999999397642294,
                1.0,
                0.9999999176675239,
                0.999999391641036,
                0.9999999273418009,
                0.9999999559306049,
                0.9999993916406734,
                0.99999992265575,
                0.9999999006880786,
                0.9999999434137907
            ],
            [
                4.4508515805735777e-07,
                1.994729721518893e-06,
                9.422443692574719e-07,
                1.209866260432471e-06,
                9.422447062294175e-07,
                1.209865827752005e-06,
                1.7603425837903113e-06,
                3.466327037553825e-07,
                1.994729483729522e-06,
                6.47594952603035e-07
            ],
            [
                3.4663278639892215e-07,
                1.6373776432509826e-07,
                1.1253506814842375e-07,
                2.6995784182183607e-07,
                3.9278605979534166e-07,
                4.4508494582405734e-07,
                2.382370235933104e-07,
                1.444979692800516e-07,
                3.927863875616689e-07,
                1.1253518888531272e-07
            ],
            [
                9.422445939032799e-07,
                4.450852111148132e-07,
                5.715004470295662e-07,
                8.939697369980456e-06,
                2.3823702359138736e-07,
                5.043475885674441e-07,
                3.288749849498565e-06,
                2.1024336609638268e-07,
                1.637377643243723e-07,
                1.0677032518814388e-06
            ],
            [
                2.699576809143613e-07,
                2.102433410343832e-07,
                1.4449798650476187e-07,
                1.2751910369275402e-07,
                3.9278605979534166e-07,
                3.05902263389638e-07,
                1.855390354818069e-07,
                1.4449800373065699e-07,
                3.059023363231725e-07,
                2.6995790618252024e-07
            ],
            [
                3.5356238073889594e-05,
                2.699579061812927e-07,
                2.1024336609843824e-07,
                1.9947304348862686e-06,
                3.927860597945825e-07,
                9.422445939002803e-07,
                5.043474081993875e-07,
                2.1024326584639497e-07,
                3.2887506336235617e-06,
                2.1024331597262577e-07
            ],
            [
                0.9999999468421821,
                0.9999995262094987,
                0.9999998642566866,
                0.9999999317439954,
                0.9999999273418355,
                0.9999998642566866,
                0.9999995818811773,
                0.999999581881277,
                0.9999993916411084,
                0.999998932297003
            ],
            [
                0.9999994284996895,
                0.9999996533673378,
                4.222834954778007e-06,
                1.4449805540763184e-07,
                0.9999978766207797,
                9.422442569315887e-07,
                3.9278610661902853e-07,
                0.9999998257021837,
                0.999997593896514,
                0.9999994631248044
            ],
            [
                4.4508494582405734e-07,
                3.466326624336003e-07,
                0.9999991684717743,
                1.473898900066424e-05,
                5.71500651413193e-07,
                1.6373766672994222e-07,
                1.5534973842076057e-06,
                3.05902336324494e-07,
                3.466326211113502e-07,
                6.475945666063607e-07
            ],
            [
                0.9999997126313098,
                0.9999999226557408,
                0.9999998461826405,
                0.9999991684717746,
                0.9999995818812771,
                0.999999653367379,
                0.9999988634365614,
                0.9999989322970031,
                0.9999994956524718,
                0.9999993916410361
            ],
            [
                7.338207180864763e-07,
                2.902312677137316e-06,
                4.222831934379152e-06,
                0.0040701372232347975,
                1.067702615468225e-06,
                1.2098659719757836e-06,
                5.422218323487975e-06,
                1.5534977545886537e-06,
                3.46632497145457e-07,
                1.0129995810463632e-05
            ],
            [
                9.422445939032799e-07,
                1.5534971990126997e-06,
                1.3709572068522336e-06,
                0.9999952149060791,
                5.715004470313855e-07,
                5.043472879540142e-07,
                2.5612828213934817e-06,
                5.043475885674441e-07,
                1.3709570434122812e-06,
                6.475950298011458e-07
            ],
            [
                0.9999999468421059,
                0.9999995262096116,
                0.9999999656786792,
                0.9999999067051054,
                0.9999999748899941,
                1.8553919030858602e-07,
                0.9999999677581067,
                0.999999218851949,
                0.9999988634364254,
                0.9999999397642079
            ],
            [
                5.4222209089700225e-06,
                2.2603234895372223e-06,
                6.475947210012481e-07,
                0.9999990577551819,
                3.05902190458764e-07,
                1.6373764721072816e-07,
                5.422217030747413e-06,
                6.9622537599680095e-06,
                3.059022998576899e-07,
                3.726637951387472e-06
            ],
            [
                0.9999975938976624,
                0.9999987121050924,
                0.9999687980887625,
                0.9999938558232135,
                0.9999949062931808,
                0.9999957771670643,
                0.9999904837471815,
                7.338207180898968e-07,
                0.9999925887227882,
                1.0129993395336818e-05
            ],
            [
                0.9999995818811773,
                0.9999998874649184,
                0.9999997463980729,
                0.999998996985673,
                0.9999992661786699,
                0.9999998642567028,
                0.9999998942829602,
                0.9999993106392012,
                0.9999986290427936,
                0.9999997300423192
            ],
            [
                0.9999992188517628,
                0.9999997463981636,
                0.9999998461826405,
                0.9999997300423192,
                0.9999995262092164,
                0.9999995549149482,
                0.9999998724809724,
                0.9999996072137999,
                0.9999993916409635,
                0.9999992661792824
            ],
            [
                7.338209805224048e-07,
                3.0590237279032884e-07,
                9.422443692555439e-07,
                6.475948754012522e-07,
                1.3709576971463352e-06,
                1.3709568799919866e-06,
                2.10243290909724e-07,
                7.338211554783522e-07,
                3.059022269250683e-07,
                0.9999983463110063
            ],
            [
                1.2751905808881762e-07,
                1.855391239544352e-07,
                0.0002611904343368873,
                1.8553903548231313e-07,
                9.931190958076104e-08,
                0.9999985406243027,
                8.31528424162821e-07,
                5.3157830707696514e-08,
                5.04347528446051e-07,
                1.8553903548231313e-07
            ],
            [
                0.9999998024947272,
                0.9999998724810027,
                0.9999992188519491,
                0.9999985406230836,
                2.699577774585891e-07,
                0.9999989322968758,
                0.9999993106387083,
                0.9999904837437922,
                2.6995790618469934e-07,
                0.9999991684722702
            ],
            [
                6.144176066901277e-06,
                7.889262585886274e-06,
                0.999998712105092,
                6.144172404738491e-06,
                1.0129988565084915e-05,
                1.0,
                6.144173137170873e-06,
                6.962255419931625e-06,
                8.481108184529756e-05,
                1.4738985486506781e-05
            ],
            [
                0.9999999226557869,
                0.9999988634357477,
                0.9999989322975121,
                0.999999391640746,
                0.9999994631248044,
                0.9999996940977367,
                0.9999992661789324,
                0.9999998555019618,
                0.9999957771645454,
                0.9999998942829729
            ],
            [
                1.1253518888531272e-07,
                1.2751904288710323e-07,
                1.444979692800516e-07,
                1.4449800373065699e-07,
                1.4449795205429202e-07,
                1.8553905759969634e-07,
                6.825606165129312e-08,
                1.1253521571574156e-07,
                2.102433660979124e-07,
                7.73442776300517e-08
            ],
            [
                0.9999756997622073,
                1.2098659719788098e-06,
                0.9999983463110063,
                2.382368531929327e-07,
                0.999998996985434,
                0.9999996743686645,
                0.9999980052705181,
                9.931199245292204e-08,
                2.69957906184239e-07,
                8.315282259138311e-07
            ],
            [
                0.9999990577556311,
                0.9999999530883452,
                0.9999997617630333,
                0.9999997761971315,
                0.9999991684720717,
                0.9999998724809115,
                0.9999999006880194,
                0.9999999586006146,
                0.9999997463980125,
                0.9999998642566381
            ],
            [
                8.31527928532683e-07,
                9.422444815765128e-07,
                4.4508510499849186e-07,
                3.466327037539638e-07,
                2.260323758987159e-06,
                9.4224425692559e-07,
                3.927861066170637e-07,
                3.466325384678894e-07,
                6.962257909842961e-06,
                1.0677027427600627e-06
            ],
            [
                0.9999999586006146,
                0.9999998024946095,
                0.9999999006880195,
                0.9999999273418183,
                0.9999994956526522,
                0.9999998724809419,
                0.999999939764294,
                1.0,
                0.9999999358793867,
                0.9999999586006146
            ],
            [
                2.6995784182140636e-07,
                4.450851580555361e-07,
                3.9278615344178325e-07,
                5.043476486915964e-07,
                1.2098655392871682e-06,
                4.4508505193791187e-07,
                3.927862939126708e-07,
                1.9947299592824403e-06,
                3.4663253846718004e-07,
                3.927862939126708e-07
            ],
            [
                NaN,
                0.999999814460876,
                0.9999997761971848,
                0.9999998724809419,
                0.9999997126313097,
                7.338212429594283e-07,
                1.892515501014656e-05,
                1.855390576008354e-07,
                0.9999962733616048,
                0.9999949062956063
            ],
            [
                1.0677027427600627e-06,
                0.9999998144609645,
                0.9999989969856731,
                0.9999990577550695,
                0.9999991684717745,
                0.9999999358793409,
                0.9999999176675731,
                0.9999993106391191,
                0.9999998802068873,
                1.0
            ],
            [
                3.0590237279032884e-07,
                3.0590215399183813e-07,
                2.1024341622426268e-07,
                3.4663249714325014e-07,
                7.338211554783522e-07,
                2.102434162245973e-07,
                1.6373764720990908e-07,
                2.5612816000646084e-06,
                1.637377448057981e-07,
                2.3823702359290413e-07
            ],
            [
                3.653479902594117e-08,
                1.1253520230052635e-07,
                8.764247451307293e-08,
                7.734418542839164e-08,
                1.4449805540763184e-07,
                1.1253520230052635e-07,
                8.764245361752286e-08,
                0.9999969105059213,
                2.6995784182140636e-07,
                2.3823682479181176e-07
            ],
            [
                0.9999998555019791,
                1.0,
                1.6373762769138607e-07,
                0.999999814460876,
                0.9999997617630049,
                0.9999991148430702,
                0.9999980052702813,
                0.9999997897566841,
                0.9999987121050923,
                0.9999997617630334
            ],
            [
                1.6373762769138607e-07,
                2.382370235933104e-07,
                1.2751905808881762e-07,
                1.4449795205429202e-07,
                1.4449805540740185e-07,
                1.4449805540740185e-07,
                2.38237023590304e-07,
                1.1253518888531272e-07,
                2.699577774560111e-07,
                1.4449795205429202e-07
            ],
            [
                4.450850519403407e-07,
                5.04347468323289e-07,
                1.7603438428800754e-06,
                2.102434412875379e-07,
                7.338208055664991e-07,
                2.9023112932296107e-06,
                4.450848927658745e-07,
                2.3823685319174098e-07,
                8.315284241560147e-07,
                1.6373776432509826e-07
            ],
            [
                9.931190958076104e-08,
                9.931185038635267e-08,
                0.9999996072137062,
                4.139934586278605e-08,
                0.9999991148428589,
                0.999999814460854,
                0.9999999273417662,
                4.139935079796334e-08,
                0.9999992661786699,
                0.9999997126315153
            ],
            [
                0.9999998362622357,
                0.9999996940977003,
                0.999999114842648,
                0.9999998642567189,
                0.9999999500628393,
                0.9999995262095552,
                0.9999997463981938,
                0.9999999434138042,
                0.9999999611089043,
                0.999999581881277
            ],
            [
                1.994730672675753e-06,
                2.5612819054133693e-06,
                9.422447062294175e-07,
                1.760342793638743e-06,
                7.338209805240734e-07,
                4.222834451382849e-06,
                6.475946438055299e-07,
                8.315279285370317e-07,
                3.288747889284851e-06,
                4.450852641737424e-07
            ],
            [
                NaN,
                3.2887506336086064e-06,
                4.785096206076165e-06,
                6.1441746018123775e-06,
                1.7603425837606927e-06,
                1.1478765389368729e-05,
                1.7603432132912532e-06,
                6.475946437996402e-07,
                4.450852641656969e-07,
                7.338212429537553e-07
            ],
            [
                0.9999978766220455,
                3.059023727894942e-07,
                2.1024326584639497e-07,
                1.4449800373065699e-07,
                0.9999987121049387,
                0.9999967112521165,
                1.370957860576702e-06,
                3.4663253846473677e-07,
                3.05902117523595e-07,
                1.4449805540700758e-07
            ],
            [
                2.1024329090929374e-07,
                6.475948754012522e-07,
                0.9999991148428589,
                3.4663266243308805e-07,
                1.1253512180925583e-07,
                8.481103128159609e-05,
                2.382369667929001e-07,
                1.8553907971855875e-07,
                1.8553916819032217e-07,
                0.999999607213753
            ],
            [
                3.927863407379485e-07,
                5.043475885696228e-07,
                3.466326624336003e-07,
                2.699577452775239e-07,
                2.6995784182183607e-07,
                2.699578096403948e-07,
                3.059022998581767e-07,
                3.466325797900508e-07,
                3.4663274507713016e-07,
                4.450848927658745e-07
            ],
            [
                0.9999978766217922,
                0.9999996072139403,
                0.9999898700126629,
                0.9999974387177907,
                0.9999982396567879,
                0.9999990577557435,
                6.144174601991196e-06,
                0.0003353500713116092,
                2.3823702359290413e-07,
                0.9999992188513906
            ],
            [
                0.9999998874647441,
                0.9999999358794326,
                0.9999999434137232,
                1.0,
                0.9999999468421187,
                0.9999998555020135,
                0.9999998942828973,
                0.9999999559305891,
                0.9999994284996894,
                0.9999999611088672
            ],
            [
                1.8553907971758842e-07,
                1.275190884913241e-07,
                2.382370235922541e-07,
                4.691160446380562e-08,
                1.2751904288710323e-07,
                1.4449805540740185e-07,
                1.6373774480605869e-07,
                1.2751905808881762e-07,
                1.637377448057981e-07,
                1.1253512180925583e-07
            ],
            [
                1.209865539295696e-06,
                1.3709575337016483e-06,
                5.715007195447234e-07,
                3.9278605979534166e-07,
                5.043472278322555e-07,
                3.120191509274984e-05,
                3.927863407379485e-07,
                1.670141786295194e-05,
                3.7266406168624155e-06,
                3.726638395527247e-06
            ],
            [
                0.9999995818812771,
                1.8553905760062447e-07,
                0.9999861540004142,
                0.9999993524053564,
                0.9999970976890553,
                1.2751908849167202e-07,
                0.9999988634358835,
                0.9999997463982242,
                0.9999981261246178,
                NaN
            ],
            [
                8.315277302841894e-07,
                3.4663249714325014e-07,
                7.734422230883848e-08,
                2.382370235922541e-07,
                1.3709575337078829e-06,
                8.315283250394546e-07,
                5.715003789033962e-07,
                3.927862939126708e-07,
                5.715006514151423e-07,
                2.6995784182073116e-07
            ],
            [
                0.9999999273418355,
                0.9999999317439221,
                1.0,
                0.999999906705061,
                0.9999998362623332,
                1.0,
                1.0,
                0.9999994631249322,
                0.9999964991468396,
                0.9999999559305944
            ],
            [
                1.0677027427600627e-06,
                2.38237023590304e-07,
                1.892515501014656e-05,
                0.00013982214085172238,
                5.715006514151423e-07,
                5.422221555340727e-06,
                4.4508505193791187e-07,
                2.699578096393206e-07,
                2.902312677104321e-06,
                2.2603251062270446e-06
            ],
            [
                2.6995784182183607e-07,
                0.9999967112497616,
                0.9999994284994169,
                0.9999977396765124,
                0.9999981261246176,
                5.04347528446051e-07,
                0.999998239655949,
                0.9999975938970879,
                0.9999989322971308,
                0.9999930377420959
            ],
            [
                1.7603427936335396e-06,
                3.9278605979208185e-07,
                1.7603436330179102e-06,
                8.315278294072958e-07,
                9.422445939002803e-07,
                5.715007195410849e-07,
                8.315278294001114e-07,
                4.78509392429544e-06,
                5.1442238195844654e-05,
                1.7603436330179102e-06
            ],
            [
                0.9999998724809875,
                0.999999607213753,
                0.9999999273418355,
                0.9999997761971849,
                1.0,
                0.999999931743971,
                0.9999996072136593,
                2.3823690999160957e-07,
                0.9999998942830485,
                0.9999997617630049
            ],
            [
                0.9999997761970782,
                0.9999998144609203,
                0.9999998724809875,
                0.9999998257020799,
                5.715007195447234e-07,
                0.9999999123574524,
                0.9999997897567091,
                0.9999997300421906,
                0.9999985406234323,
                0.9999998724809875
            ],
            [
                4.4508505193932864e-07,
                0.9999982396567876,
                3.9278634073625165e-07,
                0.9999989969861512,
                0.9999998144609424,
                0.9999998024946802,
                0.9999982396565784,
                0.999999631011592,
                1.2751901248391176e-07,
                1.2751899728286965e-07
            ],
            [
                0.9999998461827139,
                0.9999993916411086,
                0.9999993524048935,
                0.9999995262092164,
                0.9999996310116359,
                0.9999980052695658,
                0.9999999434137502,
                0.9999999434137434,
                0.9999994631251243,
                0.9999990577551819
            ]
        ]
    },
    {
        "q_id": "10153_mmlu_physics",
        "cot_ids": [
            0,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            38,
            39,
            42,
            44,
            45,
            47,
            51,
            52,
            53,
            54,
            55,
            56,
            58,
            61,
            63,
            64,
            66,
            67,
            68,
            69,
            70,
            71,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            83,
            85,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                7.338210680021253e-07,
                1.7603436330091044e-06,
                1.994730197090463e-06,
                5.715006514176113e-07,
                9.422442569334097e-07,
                1.3709567165617364e-06,
                3.4663274507713016e-07,
                1.0677029973192638e-06,
                5.715005832886879e-07,
                2.1024336609874897e-07
            ],
            [
                1.2098659719716573e-06,
                1.0677029973192638e-06,
                NaN,
                2.5612828213934817e-06,
                1.5534975693979422e-06,
                NaN,
                NaN,
                NaN,
                4.785096776499213e-06,
                6.475949526020042e-07
            ],
            [
                1.9947304348862686e-06,
                5.715005832886879e-07,
                NaN,
                4.450850519403407e-07,
                1.8553907971879076e-07,
                1.5534973842076057e-06,
                NaN,
                1.3007130015488633e-05,
                6.962256249821764e-06,
                1.760342793638743e-06
            ],
            [
                5.04347528446051e-07,
                1.3709567165579959e-06,
                5.715003789046955e-07,
                7.338212429582604e-07,
                5.04347528446051e-07,
                1.5534975693933505e-06,
                3.466327450765785e-07,
                2.5612816000145246e-06,
                2.1444943301674863e-05,
                4.222831934379152e-06
            ],
            [
                1.4449803818215767e-07,
                5.715006514176113e-07,
                8.315278294097538e-07,
                5.043473480777865e-07,
                2.699576809143613e-07,
                6.475947210031623e-07,
                9.422444815814404e-07,
                1.855391681898159e-07,
                NaN,
                2.699578740032504e-07
            ],
            [
                9.422448185534261e-07,
                1.0677026154730804e-06,
                1.5534981249574276e-06,
                9.422448185478557e-07,
                8.939696302652706e-06,
                0.0004305570346422092,
                8.939696304116203e-06,
                9.422450431954847e-07,
                3.288749457432399e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                9.422448185534261e-07,
                2.5612822106421996e-06,
                6.475948753965404e-07,
                5.3157887739943563e-08,
                1.2751902768612997e-07,
                5.715006514176113e-07,
                7.338212429582604e-07
            ],
            [
                9.422448185478557e-07,
                1.2098658277451275e-06,
                1.7603427936263351e-06,
                9.422447062294175e-07,
                1.3709567165579959e-06,
                1.3709575337078829e-06,
                3.288749849477628e-06,
                1.0677028700363782e-06,
                4.78509563546605e-06,
                5.422217677028889e-06
            ],
            [
                1.5534983100920427e-06,
                9.422445938861406e-07,
                1.0677027427525368e-06,
                6.475948754012522e-07,
                1.9947306726358406e-06,
                3.726641061085547e-06,
                7.338209805200689e-07,
                2.561283431916622e-06,
                1.3709575336530204e-06,
                7.338208930391909e-07
            ],
            [
                1.8553919030858602e-07,
                0.9999974387171798,
                6.825602910433871e-08,
                0.9999972735294052,
                0.999978555049068,
                NaN,
                0.9999599363126748,
                1.2751910369343538e-07,
                0.999996273359385,
                0.9999898700126495
            ],
            [
                NaN,
                9.93120161310289e-08,
                6.825608606172863e-08,
                NaN,
                1.5534981249736758e-06,
                1.5534984953552536e-06,
                6.825598842065202e-08,
                4.450851049991497e-07,
                NaN,
                3.0590219045914655e-07
            ],
            [
                2.699578096393206e-07,
                3.059022998581767e-07,
                NaN,
                2.6995771309523475e-07,
                3.466327037548308e-07,
                2.699577774585891e-07,
                5.715003107767143e-07,
                1.8553914607267268e-07,
                1.6373770576776313e-07,
                3.05902263391829e-07
            ],
            [
                1.9947297215125433e-06,
                1.760342793638743e-06,
                3.4663266243308805e-07,
                9.422443692574719e-07,
                7.338212429594283e-07,
                4.4508515805735777e-07,
                3.2887478892055875e-06,
                3.4663274507713016e-07,
                1.067703124601679e-06,
                2.1024336609843824e-07
            ],
            [
                3.059022998576899e-07,
                2.561283432035425e-06,
                1.0677027427624903e-06,
                3.4663253846718004e-07,
                5.043475885696228e-07,
                NaN,
                2.3823696679327928e-07,
                1.9947292459406333e-06,
                0.9999977396754341,
                1.5534973842076057e-06
            ],
            [
                NaN,
                5.715007195431641e-07,
                1.4738985486506781e-05,
                5.715004470295662e-07,
                1.209866260432471e-06,
                3.9278634073625165e-07,
                2.9023123311583482e-06,
                6.475949526003845e-07,
                3.059023727869902e-07,
                1.2098652508347793e-06
            ],
            [
                3.466327863961242e-07,
                4.450848927650143e-07,
                6.475947982037486e-07,
                5.71500719545698e-07,
                4.4508494582405734e-07,
                6.475947982002148e-07,
                6.475951069985296e-07,
                1.4449805540700758e-07,
                7.338208055664991e-07,
                6.475951069985296e-07
            ],
            [
                2.9023119851266288e-06,
                4.7850933538313875e-06,
                1.1478766757718129e-05,
                3.288750241410738e-06,
                2.4300243630653244e-05,
                1.275190732904469e-07,
                2.2603237589676295e-06,
                6.962257909501028e-06,
                4.785095065132354e-06,
                4.78509506499309e-06
            ],
            [
                1.7603434231705793e-06,
                1.9947299593014888e-06,
                2.2603251062270446e-06,
                3.7266392840781026e-06,
                9.422443692489024e-07,
                2.2603234895053587e-06,
                3.288749849477628e-06,
                2.260323489490968e-06,
                1.7603438428660665e-06,
                4.222833444590791e-06
            ],
            [
                8.764254764780641e-08,
                1.1253512180925583e-07,
                1.9947292459347367e-06,
                1.1253509497883659e-07,
                1.637376862489725e-07,
                2.382369951932796e-07,
                1.6373770576776313e-07,
                1.3709576971463352e-06,
                2.102434412875379e-07,
                3.059022269250683e-07
            ],
            [
                8.315281267800897e-07,
                7.338208930391909e-07,
                1.0677032518785256e-06,
                2.6995784182140636e-07,
                4.785096776433933e-06,
                9.422448185534261e-07,
                1.7603440527222532e-06,
                6.475947210031623e-07,
                3.7266383956509585e-06,
                1.2098656835224664e-06
            ],
            [
                2.3823702359290413e-07,
                2.902313369111213e-06,
                6.475949526020042e-07,
                4.450851580555361e-07,
                2.3823693839290317e-07,
                4.4508510499849186e-07,
                1.2098659719757836e-06,
                1.4449800373065699e-07,
                3.288750241561788e-06,
                1.209866260432471e-06
            ],
            [
                9.931193325852072e-08,
                1.4449807263312446e-07,
                1.8553919030858602e-07,
                1.444980209564556e-07,
                1.1253520230052635e-07,
                7.73442776300517e-08,
                1.2751902768612997e-07,
                1.1253522913127183e-07,
                1.6373774480605869e-07,
                1.8553919030858602e-07
            ],
            [
                4.450852111155216e-07,
                9.422442569315887e-07,
                NaN,
                1.1478769494396542e-05,
                5.422218323399208e-06,
                1.0677033791583005e-06,
                3.7266410611296085e-06,
                2.2603251062450327e-06,
                4.222832941111319e-06,
                1.994730434879465e-06
            ],
            [
                8.315282259138311e-07,
                5.04347468323289e-07,
                5.4222183235249605e-06,
                4.0063692172075196e-05,
                3.726637951387472e-06,
                2.5612834320563895e-06,
                6.144172404738491e-06,
                4.450852111148132e-07,
                NaN,
                1.5534984953552536e-06
            ],
            [
                NaN,
                6.1441767993788005e-06,
                2.1024329090867228e-07,
                2.6995777745711594e-07,
                2.699576809143613e-07,
                1.1253508156317518e-07,
                NaN,
                3.2887506336235617e-06,
                0.999959936322372,
                NaN
            ],
            [
                3.7266406168827523e-06,
                3.2887486733420804e-06,
                5.422220908481809e-06,
                2.902312331170226e-06,
                1.637376862489725e-07,
                3.9278634073732336e-07,
                1.760343213335281e-06,
                3.72663883989755e-06,
                2.3823685319244518e-07,
                6.475950297971703e-07
            ],
            [
                0.9999949062925717,
                0.9999724643057024,
                0.999983298578174,
                0.9999898700114427,
                7.734418542875216e-08,
                1.7603434231833873e-06,
                0.9999832985821617,
                0.9999687980923779,
                0.9999646437493717,
                0.999959936298421
            ],
            [
                1.2098658277451275e-06,
                6.962256249682458e-06,
                1.5534984953453635e-06,
                6.962257079705671e-06,
                1.2098661161927025e-06,
                4.222832941142044e-06,
                4.785095635624897e-06,
                3.7266392839832006e-06,
                1.012999460251781e-05,
                6.144173137014406e-06
            ],
            [
                4.4508526417298334e-07,
                1.1253509497883659e-07,
                1.994729721518893e-06,
                2.10243290909724e-07,
                0.9999964991451703,
                7.338208055664991e-07,
                2.3823690999323465e-07,
                3.726639284144195e-06,
                1.637377057680051e-07,
                3.0590215399183813e-07
            ],
            [
                0.4687906266262437,
                1.370957860576702e-06,
                3.535626335686906e-05,
                4.22283545819819e-06,
                1.5534983101602148e-06,
                8.315277302857965e-07,
                2.561281294760143e-06,
                1.8925143729575624e-05,
                2.2603234895372223e-06,
                NaN
            ],
            [
                1.5534973841705173e-06,
                7.889266347715168e-06,
                8.939697369980456e-06,
                3.2887494574518405e-06,
                4.222831934379152e-06,
                7.889262585886274e-06,
                6.1441724044534996e-06,
                8.939696304213768e-06,
                3.927860597935108e-07,
                1.6701425826525565e-05
            ],
            [
                1.1478769493728398e-05,
                1.5534983101478522e-06,
                1.9947306726358406e-06,
                2.561281905390075e-06,
                7.338212429562581e-07,
                NaN,
                8.315281267834927e-07,
                2.5612822107167428e-06,
                1.3709568799823232e-06,
                1.2098659719716573e-06
            ],
            [
                1.6373764721072816e-07,
                3.4663249714612693e-07,
                2.902310947190096e-06,
                3.927862002654366e-07,
                3.0590237279032884e-07,
                2.2603242978778778e-06,
                1.7603434231097403e-06,
                2.260323758882316e-06,
                7.73442776303243e-08,
                1.209865539295696e-06
            ],
            [
                1.3709567165617364e-06,
                8.764253719973308e-08,
                3.05902263391829e-07,
                7.734421308914719e-08,
                1.6373774480479287e-07,
                5.315784971839039e-08,
                1.855391239544352e-07,
                2.5612828213934817e-06,
                3.4663274507713016e-07,
                6.023578501513224e-08
            ],
            [
                2.6995771309523475e-07,
                2.699578740011634e-07,
                4.450848927637999e-07,
                7.338212429537553e-07,
                9.422448185478557e-07,
                2.902312677137316e-06,
                1.8553916819032217e-07,
                2.2603242978778778e-06,
                2.6995771309523475e-07,
                2.6995777745711594e-07
            ],
            [
                6.9622545892184106e-06,
                2.561282210740037e-06,
                4.78509563555309e-06,
                4.450848927658745e-07,
                3.05902190458764e-07,
                4.4508515805735777e-07,
                1.6373772528704005e-07,
                2.9023133689924295e-06,
                7.338207180898968e-07,
                0.9999987901340298
            ],
            [
                1.7603436330259153e-06,
                2.6995784182140636e-07,
                4.450849458200093e-07,
                3.288748281220719e-06,
                6.144176066901277e-06,
                4.450851580555361e-07,
                9.422447062202052e-07,
                2.902312677084523e-06,
                7.338209805224048e-07,
                5.715004470326849e-07
            ],
            [
                3.059023727894942e-07,
                3.4663274507713016e-07,
                1.6373774480535133e-07,
                1.147876812574406e-05,
                7.734423152941018e-08,
                1.444980209564556e-07,
                NaN,
                1.855391681906175e-07,
                5.715007195447234e-07,
                4.450848927650143e-07
            ],
            [
                2.6995790618469934e-07,
                5.715003788993679e-07,
                9.422444815765128e-07,
                4.450852111135988e-07,
                4.450849988798682e-07,
                4.450852111135988e-07,
                3.466326211105621e-07,
                7.889260704968913e-06,
                5.043472879540142e-07,
                8.31528424162821e-07
            ],
            [
                3.4663274507098256e-07,
                2.3823696679230424e-07,
                NaN,
                4.4508515805735777e-07,
                4.4508510498604413e-07,
                8.315283250260307e-07,
                3.7266410611296085e-06,
                5.043476486833397e-07,
                9.422444815814404e-07,
                7.338210679909462e-07
            ],
            [
                4.785096205882502e-06,
                1.760342793638743e-06,
                2.902313023130843e-06,
                7.338208930460318e-07,
                2.699578096393206e-07,
                NaN,
                2.2603242978871282e-06,
                NaN,
                1.6373772528704005e-07,
                3.726640616748873e-06
            ],
            [
                7.338212429582604e-07,
                1.0677032518785256e-06,
                3.4663249714612693e-07,
                2.6995774527718623e-07,
                6.475947210046347e-07,
                4.4508510499849186e-07,
                1.370957860576702e-06,
                2.561282516066741e-06,
                8.315277302841894e-07,
                3.4663249714612693e-07
            ],
            [
                1.3709575337125585e-06,
                2.5612825160562587e-06,
                4.450852641717689e-07,
                2.2603237589676295e-06,
                5.715006514151423e-07,
                1.5534975693979422e-06,
                1.994729483705484e-06,
                1.5534984953453635e-06,
                1.2098662604291696e-06,
                4.450852641717689e-07
            ],
            [
                9.422443692574719e-07,
                5.4222176771176554e-06,
                2.2603251062450327e-06,
                2.9023119851899796e-06,
                1.0677029973192638e-06,
                3.05902263391829e-07,
                6.47595107001401e-07,
                3.05902263391829e-07,
                1.067703124601679e-06,
                2.6995784182140636e-07
            ],
            [
                4.222831934352267e-06,
                3.288749065423109e-06,
                9.422443692555439e-07,
                5.715005832886879e-07,
                3.288749065406658e-06,
                1.994729245917502e-06,
                1.0677032518814388e-06,
                3.7266401725935817e-06,
                2.260325106237323e-06,
                2.2603253756874524e-06
            ],
            [
                1.0677026154827912e-06,
                NaN,
                3.0590237279032884e-07,
                3.927863875616689e-07,
                1.3709576971463352e-06,
                9.422443692574719e-07,
                3.0590237279032884e-07,
                7.338207180898968e-07,
                5.043475885696228e-07,
                3.0590237279032884e-07
            ],
            [
                1.0677028700422047e-06,
                4.785094494811783e-06,
                1.2098659719716573e-06,
                5.043476486915964e-07,
                8.315279285351409e-07,
                1.3709570434122812e-06,
                8.315277302841894e-07,
                1.7603434231777837e-06,
                NaN,
                7.889265406904397e-06
            ],
            [
                NaN,
                1.0677029973219343e-06,
                NaN,
                5.715007195447234e-07,
                1.4449800373118268e-07,
                3.927863407379485e-07,
                3.726639284144195e-06,
                2.260325106237323e-06,
                NaN,
                6.475951069985296e-07
            ],
            [
                NaN,
                NaN,
                1.5534981249697903e-06,
                6.1441746016670885e-06,
                3.2887486733420804e-06,
                4.785096776394765e-06,
                5.4222209089700225e-06,
                5.71500515161527e-07,
                NaN,
                NaN
            ],
            [
                1.3709568799879344e-06,
                2.5612828213934817e-06,
                5.715005832886879e-07,
                3.726639728370556e-06,
                8.315277302841894e-07,
                2.561281905390075e-06,
                1.760342793638743e-06,
                7.338208055664991e-07,
                8.315281267882195e-07,
                2.9023112932045342e-06
            ],
            [
                6.475949526020042e-07,
                2.3823693839325527e-07,
                1.760342793638743e-06,
                7.338211554801876e-07,
                1.7603438428800754e-06,
                3.2887506336235617e-06,
                1.760343213335281e-06,
                5.043474683204221e-07,
                NaN,
                NaN
            ],
            [
                NaN,
                2.3823685319244518e-07,
                4.450849458200093e-07,
                5.422217030555087e-06,
                6.475950298011458e-07,
                2.382369951932796e-07,
                2.4300252321904572e-05,
                1.9947301970813926e-06,
                NaN,
                7.338209805224048e-07
            ],
            [
                1.7603440527286572e-06,
                NaN,
                1.670141786325573e-05,
                7.338211554801876e-07,
                4.4508494582405734e-07,
                4.222832437798974e-06,
                2.10243290909724e-07,
                3.7266406168827523e-06,
                6.144175334418252e-06,
                9.422448185510695e-07
            ],
            [
                1.3709578605455302e-06,
                2.902312331081799e-06,
                1.5534979397740895e-06,
                1.2098661161927025e-06,
                6.475948754012522e-07,
                4.222833947932061e-06,
                3.288750633488963e-06,
                7.338210679979539e-07,
                7.338211554758494e-07,
                5.04347348075149e-07
            ],
            [
                1.2098659719524008e-06,
                3.9278634073732336e-07,
                8.315283250371857e-07,
                7.338212429504183e-07,
                1.7603436330259153e-06,
                5.715004470313855e-07,
                1.4738978458140753e-05,
                1.0677033791437343e-06,
                7.338207180761315e-07,
                7.889262585728421e-06
            ],
            [
                1.9947304348862686e-06,
                3.9278610661902853e-07,
                6.144176066901277e-06,
                1.7603438428740716e-06,
                NaN,
                1.7603440527334603e-06,
                3.05902190458764e-07,
                NaN,
                3.4663274507713016e-07,
                5.043472278322555e-07
            ],
            [
                6.475947210012481e-07,
                5.715005151606823e-07,
                2.1024334103581732e-07,
                1.6373766672973748e-07,
                1.3709567165579959e-06,
                4.4508526417298334e-07,
                6.023568448589658e-08,
                4.450850519403407e-07,
                1.637377057680051e-07,
                3.9278629391427843e-07
            ],
            [
                7.889259764445822e-06,
                2.6995784182140636e-07,
                1.3709573702778664e-06,
                4.222833947960866e-06,
                1.2098655392921197e-06,
                1.9947299593014888e-06,
                2.144495608378187e-05,
                1.7603438428740716e-06,
                3.726637951367137e-06,
                6.962256249821764e-06
            ],
            [
                8.764250585640737e-08,
                0.9999938558254066,
                1.855390576008354e-07,
                0.9999546021314433,
                9.931199245322124e-08,
                8.764250585640737e-08,
                2.6995774527718623e-07,
                1.4449805540740185e-07,
                1.8553905760024476e-07,
                8.764244316973974e-08
            ],
            [
                3.288750241561788e-06,
                1.4738980213985297e-05,
                2.561281600086738e-06,
                4.450851580555361e-07,
                7.338208055664991e-07,
                1.3709573702722555e-06,
                1.5534981249697903e-06,
                5.043474081993875e-07,
                7.88926446679691e-06,
                NaN
            ],
            [
                3.059022998581767e-07,
                2.561283432035425e-06,
                4.222831934379152e-06,
                1.670141786295194e-05,
                6.475949525981759e-07,
                8.315278294072958e-07,
                5.715007195431641e-07,
                6.475949526020042e-07,
                1.994729008145876e-06,
                3.4663266243111764e-07
            ],
            [
                NaN,
                4.785096206076165e-06,
                4.222832437798974e-06,
                4.4508515805735777e-07,
                1.0677029973192638e-06,
                1.994729008145876e-06,
                3.120190393794438e-05,
                4.450849988811838e-07,
                3.927862470899887e-07,
                3.0590237279085045e-07
            ],
            [
                6.962257079553702e-06,
                4.222832437386106e-06,
                5.043474081993875e-07,
                3.288750241473551e-06,
                3.7266401725935817e-06,
                4.450852111135988e-07,
                1.7603425837366772e-06,
                3.2887502414436403e-06,
                4.222833444467892e-06,
                3.0590237279032884e-07
            ],
            [
                1.3709575337078829e-06,
                3.466327037548308e-07,
                1.670142582682936e-05,
                1.9947292459347367e-06,
                1.5534983101602148e-06,
                7.3382080556433e-07,
                2.260324836776948e-06,
                2.5612828213934817e-06,
                1.2098656835136636e-06,
                9.422442569315887e-07
            ],
            [
                1.8925143729954285e-05,
                NaN,
                1.0677032518814388e-06,
                3.927860597945825e-07,
                1.0129987357287368e-05,
                1.3709572068522336e-06,
                8.315281267882195e-07,
                1.2098652508424818e-06,
                3.288748673360027e-06,
                NaN
            ],
            [
                7.338209805240734e-07,
                1.7603434231777837e-06,
                1.7603425837855082e-06,
                3.7266401726173067e-06,
                9.422444815765128e-07,
                2.5612828213934817e-06,
                5.422218969858371e-06,
                2.902311639183378e-06,
                5.715004470313855e-07,
                8.31527928532683e-07
            ],
            [
                2.561281600086738e-06,
                8.315279285370317e-07,
                1.3709575337159875e-06,
                7.338208055680009e-07,
                3.466327037548308e-07,
                4.4508494582405734e-07,
                2.902312677150514e-06,
                6.475950298021765e-07,
                NaN,
                2.6995784182140636e-07
            ],
            [
                4.539786864876098e-05,
                1.1478764020883773e-05,
                NaN,
                1.209865539295696e-06,
                NaN,
                0.9999934595643702,
                7.338211554801876e-07,
                6.144177531767002e-06,
                NaN,
                7.338210680021253e-07
            ],
            [
                3.4663249714451116e-07,
                4.4508494582314646e-07,
                9.422449308716635e-07,
                6.475947209985977e-07,
                2.1024331597152624e-07,
                2.7535700950274782e-05,
                2.3823690999323465e-07,
                3.05902263389638e-07,
                8.315279285370317e-07,
                2.9023112932177327e-06
            ],
            [
                7.73442776303243e-08,
                0.9999975938976613,
                3.653485128944664e-08,
                0.99999385582394,
                0.9999995262092163,
                0.9999852610127759,
                4.139941495546278e-08,
                1.8553907971879076e-07,
                6.023578501513224e-08,
                0.9999910602994384
            ],
            [
                2.2603245673443566e-06,
                1.994729483729522e-06,
                9.931202796993203e-08,
                1.370957860576702e-06,
                3.726639284144195e-06,
                1.3709575337159875e-06,
                6.962257909842961e-06,
                NaN,
                1.855391239544352e-07,
                3.72663883989755e-06
            ],
            [
                9.422450432014836e-07,
                5.04347468323289e-07,
                5.715005832886879e-07,
                2.1024341622426268e-07,
                1.2098653950692178e-06,
                1.637377448057981e-07,
                4.450851580566494e-07,
                9.422444815765128e-07,
                1.760343213335281e-06,
                7.338209805224048e-07
            ],
            [
                1.4449800373098553e-07,
                9.422445939054222e-07,
                8.939696304213768e-06,
                5.043474683204221e-07,
                5.715003788993679e-07,
                NaN,
                2.9023112932045342e-06,
                2.699577774560111e-07,
                1.0677026154619133e-06,
                1.5534977545603963e-06
            ],
            [
                2.260325375650449e-06,
                1.2751901248454963e-07,
                1.6373770576776313e-07,
                3.726638395611981e-06,
                4.785095065204162e-06,
                2.3823688159237777e-07,
                0.9999955048168482,
                5.715007195447234e-07,
                8.315278294072958e-07,
                9.422447062294175e-07
            ],
            [
                3.12019039369228e-05,
                4.78509563550957e-06,
                2.56128159999123e-06,
                2.902312331081799e-06,
                2.2603245673155757e-06,
                2.260324297853209e-06,
                NaN,
                8.939694171331106e-06,
                1.7603427935967163e-06,
                2.9023130230846496e-06
            ],
            [
                1.2098653950656417e-06,
                6.475950298011458e-07,
                5.043474683204221e-07,
                1.0129989772532511e-05,
                5.715005151606823e-07,
                8.939693107190907e-06,
                1.7603427936335396e-06,
                3.288749457469787e-06,
                5.04347528446051e-07,
                3.726638839878908e-06
            ],
            [
                1.8553919030858602e-07,
                1.855391681906175e-07,
                NaN,
                2.1024336609874897e-07,
                1.444979692787374e-07,
                NaN,
                1.8553914607267268e-07,
                2.3823696679327928e-07,
                1.5534975693933505e-06,
                NaN
            ],
            [
                6.475945666051092e-07,
                7.338211554783522e-07,
                3.4663262110945863e-07,
                8.315280276546789e-07,
                2.9023133690980155e-06,
                6.475945666051092e-07,
                8.315280276546789e-07,
                NaN,
                1.067703124601679e-06,
                1.8553907971855875e-07
            ],
            [
                0.9999687980961723,
                0.9999724643089305,
                0.9999785550439584,
                0.9999885212305122,
                0.999975699762233,
                0.9999904837471865,
                0.9999485577926372,
                0.9999599363126659,
                0.9999852610145304,
                0.9999687980998476
            ],
            [
                2.5612812947508257e-06,
                1.209865539295696e-06,
                1.7603425837606927e-06,
                1.4738988999377379e-05,
                2.7535700949523498e-05,
                2.2603234895289998e-06,
                1.5534984953453635e-06,
                1.2098662604126641e-06,
                8.315284241650899e-07,
                4.222834451382849e-06
            ],
            [
                1.0129992187105678e-05,
                2.9023133690637e-06,
                9.422444815765128e-07,
                1.5534981249574276e-06,
                3.2887490653408545e-06,
                4.4508505193791187e-07,
                1.0677027427525368e-06,
                1.0677026154619133e-06,
                1.0677024881980089e-06,
                1.3007123813193233e-05
            ],
            [
                2.2603251061664e-06,
                2.5612831267086116e-06,
                9.422444815765128e-07,
                1.2098661161927025e-06,
                4.222835458175145e-06,
                2.6995784182140636e-07,
                4.785096776499213e-06,
                3.288749849368453e-06,
                2.561283126679493e-06,
                2.1024341622426268e-07
            ],
            [
                1.0677032518748838e-06,
                1.9947304348595095e-06,
                2.9023123310290063e-06,
                1.1253509497883659e-07,
                4.2228324377164004e-06,
                5.71500719545698e-07,
                2.5612812947508257e-06,
                4.7850967763512445e-06,
                1.3709567165530083e-06,
                1.5534973841895917e-06
            ],
            [
                9.422450432014836e-07,
                1.0677027427600627e-06,
                0.0001584361980907647,
                1.0677032518700286e-06,
                2.2603242978871282e-06,
                1.6701423836262173e-05,
                4.22283545819819e-06,
                2.3823690999290963e-07,
                NaN,
                2.3823690999290963e-07
            ],
            [
                5.043472879540142e-07,
                3.0590226339061185e-07,
                5.715005832886879e-07,
                8.315277302841894e-07,
                1.473898900066424e-05,
                2.6995774527718623e-07,
                3.059021904571643e-07,
                2.3823688159291947e-07,
                1.444980209564556e-07,
                1.760343213335281e-06
            ],
            [
                3.7266406168624155e-06,
                3.9278605979534166e-07,
                3.0590226339061185e-07,
                1.2751899728286965e-07,
                5.043474081993875e-07,
                4.450849988811838e-07,
                1.0677031245905116e-06,
                4.4508526417298334e-07,
                3.9278615344178325e-07,
                7.338208055664991e-07
            ],
            [
                1.4449798650551755e-07,
                2.6995784182140636e-07,
                1.9947299592933255e-06,
                2.3823693839290317e-07,
                1.5534981249697903e-06,
                1.8553907971855875e-07,
                1.5534977545886537e-06,
                5.422220262636381e-06,
                1.760342793638743e-06,
                1.5534981249697903e-06
            ],
            [
                4.222834954561012e-06,
                7.338209805200689e-07,
                1.3709575336947905e-06,
                2.4300246525983375e-05,
                6.475946437996402e-07,
                NaN,
                1.553498124964492e-06,
                1.2098659719757836e-06,
                1.892514598551715e-05,
                1.5534975693792215e-06
            ],
            [
                5.715006514176113e-07,
                1.6373764721072816e-07,
                8.7642558095602e-08,
                7.33821330437595e-07,
                1.2751908849167202e-07,
                3.0590215399183813e-07,
                1.8553916819032217e-07,
                2.382369951932796e-07,
                9.931186222482958e-08,
                3.466326211113502e-07
            ],
            [
                4.4508515805735777e-07,
                1.8553914607128047e-07,
                3.0590237279032884e-07,
                1.067703379154416e-06,
                9.610246085253877e-05,
                9.422447062202052e-07,
                4.450852111148132e-07,
                8.315283250394546e-07,
                6.47595107001401e-07,
                3.059023727894942e-07
            ],
            [
                0.9999810748495574,
                0.9999861539954574,
                0.9999771719920209,
                0.999996910506658,
                0.9999898700090321,
                4.450852641737424e-07,
                0.9999960330131438,
                0.9999687980998939,
                0.9999810748472856,
                0.9999925887227862
            ],
            [
                2.260325106237323e-06,
                1.8925148241872038e-05,
                2.902313023101807e-06,
                4.222831934286977e-06,
                5.4222183231674305e-06,
                1.0677029973219343e-06,
                2.2603237589542675e-06,
                9.422444815765128e-07,
                0.00017952803055133065,
                0.999998932297131
            ],
            [
                2.4300249425822333e-05,
                4.539788488687281e-05,
                1.8553914607267268e-07,
                5.422217030781934e-06,
                3.927861066170637e-07,
                3.466326624336003e-07,
                0.9999687980998733,
                0.9999151889287973,
                0.9999898700078206,
                0.9999952149037958
            ],
            [
                6.962254589851619e-06,
                3.120190393794438e-05,
                2.561282210740037e-06,
                7.338209805200689e-07,
                3.288748673360027e-06,
                3.726638395611981e-06,
                1.994730197090463e-06,
                2.3823696679230424e-07,
                4.5397857828200684e-05,
                8.315284241597959e-07
            ],
            [
                0.9999485577744405,
                3.4663274507713016e-07,
                4.4508510499849186e-07,
                3.7266401726359486e-06,
                2.6995774527657245e-07,
                1.3709576971463352e-06,
                1.5534971990169383e-06,
                1.30071315662049e-05,
                7.33821330437595e-07,
                5.043472278312808e-07
            ],
            [
                8.315281267834927e-07,
                4.785093353909723e-06,
                3.288749457432399e-06,
                7.338209805224048e-07,
                5.715005832886879e-07,
                1.0677026154730804e-06,
                2.2603248367512505e-06,
                9.422443692555439e-07,
                6.475947982037486e-07,
                5.422219615750493e-06
            ]
        ]
    },
    {
        "q_id": "9111_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.222834954753043e-06,
                1.5534984953453635e-06,
                8.939699501132077e-06,
                1.2098662604291696e-06,
                9.422444815765128e-07,
                4.785096205973894e-06,
                1.553497754577351e-06,
                1.2098652508287273e-06,
                7.338207180864763e-07,
                1.7603434231777837e-06
            ],
            [
                1.209865827752005e-06,
                3.2887502415767434e-06,
                2.7535694385633984e-05,
                1.3709573702856596e-06,
                1.3007134667436886e-05,
                2.9023116392097746e-06,
                1.994729483729522e-06,
                4.222833444611915e-06,
                8.939695238715516e-06,
                1.760343633036322e-06
            ],
            [
                1.0677032518814388e-06,
                1.2098662604126641e-06,
                2.6995774527718623e-07,
                2.69957906184239e-07,
                2.1024339116168358e-07,
                4.450848927658745e-07,
                2.3823699519290042e-07,
                6.023574911170301e-08,
                2.10243290909724e-07,
                7.73441946488886e-08
            ],
            [
                2.260324028443809e-06,
                1.1478769494542698e-05,
                4.222834451403972e-06,
                8.939700567094277e-06,
                4.785092783545836e-06,
                1.994729483723626e-06,
                7.889263526409699e-06,
                7.889264466868659e-06,
                2.2603248367949354e-06,
                1.209865539298447e-06
            ],
            [
                1.9947304348595095e-06,
                6.475946438022905e-07,
                4.450852641717689e-07,
                1.0677029972920738e-06,
                9.422448185435711e-07,
                1.2098662604291696e-06,
                6.475945666051092e-07,
                3.059022269250683e-07,
                3.927860597945825e-07,
                1.067703379154416e-06
            ],
            [
                0.999998540623779,
                0.9999898700102373,
                0.9999960330140876,
                0.9999992188518558,
                0.9999646437452316,
                0.999997438718095,
                0.9999991684721709,
                0.9999984465020604,
                0.9999992661787572,
                0.9998601778769839
            ],
            [
                1.5534971990169383e-06,
                2.102434412875379e-07,
                1.1478772231086046e-05,
                7.484622728190558e-05,
                0.9999984465015059,
                0.9999417087277416,
                2.1024336609874897e-07,
                0.9999945777829767,
                0.9999898700078271,
                0.999990483747185
            ],
            [
                0.9999996533672962,
                0.999981074856284,
                0.9999810748540378,
                0.9999991148433863,
                0.9999952149043657,
                0.9999869928668952,
                0.9999930377445833,
                0.9999982396563675,
                0.9999983463108088,
                0.9999982396572068
            ],
            [
                3.72663883989755e-06,
                3.72663883989755e-06,
                0.00012339454556667436,
                6.1441767993788005e-06,
                1.0129988565084915e-05,
                2.2603245673443566e-06,
                3.288749849529972e-06,
                9.422443692574719e-07,
                1.994729483729522e-06,
                3.7266383956509585e-06
            ],
            [
                0.99999976176309,
                0.9999885212359858,
                0.999996910506658,
                0.9999910603015689,
                0.9999993916410359,
                0.9999994631251242,
                0.9999984465026164,
                0.9999967112497594,
                0.9999982396572069,
                0.9999930377420938
            ],
            [
                0.9999898700078299,
                0.9999852610215911,
                0.9999993916410364,
                2.9023123311583482e-06,
                0.999860177911538,
                0.9999952149037998,
                7.338213304363436e-07,
                6.475947982037486e-07,
                2.561283432035425e-06,
                4.4508510499849186e-07
            ],
            [
                0.9999989969855533,
                0.9999972735287552,
                0.9999969105055528,
                0.9999982396559477,
                0.9999964991451705,
                0.9999991684719726,
                0.9999994631250602,
                0.9999986290423033,
                0.9999993524049703,
                0.9999995818811275
            ],
            [
                0.9999995549147891,
                0.9999930377412684,
                0.9999997761971582,
                0.9999998144609646,
                0.9999977396746252,
                0.9999982396563676,
                0.9999974387177901,
                0.9999982396569972,
                0.9999952149055066,
                0.9999910603005041
            ],
            [
                1.994729008151319e-06,
                1.9947292459406333e-06,
                0.9999985406234319,
                1.994729721518893e-06,
                7.338207180898968e-07,
                1.209865539298447e-06,
                8.315278294114555e-07,
                9.422443692574719e-07,
                1.5534981249736758e-06,
                1.3709576971463352e-06
            ],
            [
                8.315281267834927e-07,
                1.0677032518814388e-06,
                6.144172404738491e-06,
                4.450848927637999e-07,
                1.0677027427569065e-06,
                1.3709567165461505e-06,
                5.715003789046955e-07,
                4.222834954801051e-06,
                1.2751901248454963e-07,
                2.3823685319174098e-07
            ],
            [
                2.6995784182140636e-07,
                1.2098656835224664e-06,
                1.4449795205429202e-07,
                8.315282259138311e-07,
                8.764245361752286e-08,
                2.2603242978871282e-06,
                1.3709576971463352e-06,
                6.475949526020042e-07,
                9.422443692574719e-07,
                1.8553907971855875e-07
            ],
            [
                9.422448185510695e-07,
                3.7266410611296085e-06,
                2.7535697667202906e-05,
                1.3709572068422585e-06,
                1.2098656835224664e-06,
                4.539788488687281e-05,
                3.288748673376478e-06,
                5.715004470313855e-07,
                2.4300243631890864e-05,
                6.962254589978262e-06
            ],
            [
                2.2603234895372223e-06,
                2.6995784182140636e-07,
                4.785095635655362e-06,
                3.4663249714612693e-07,
                4.450848927658745e-07,
                1.473898900066424e-05,
                2.561282210740037e-06,
                6.475949526020042e-07,
                1.1478772231232203e-05,
                4.450852111155216e-07
            ],
            [
                3.927860597945825e-07,
                2.699577774585891e-07,
                1.2098653950656417e-06,
                4.2228339479858295e-06,
                6.475949526020042e-07,
                1.0677028700363782e-06,
                4.450851580555361e-07,
                5.715005151606823e-07,
                1.4449807263312446e-07,
                1.7603440527286572e-06
            ],
            [
                3.2887478892504536e-06,
                1.994730197071414e-06,
                2.5612834320214477e-06,
                1.0129987357407137e-05,
                1.2098656835224664e-06,
                2.2603242978778778e-06,
                2.90231094723893e-06,
                1.0677032518785256e-06,
                6.144174601935314e-06,
                7.338208055664991e-07
            ],
            [
                6.962257909842961e-06,
                3.466326211113502e-07,
                8.939699501229642e-06,
                1.2098662604291696e-06,
                1.5534975693933505e-06,
                5.715005832853093e-07,
                1.2098658277451275e-06,
                8.315283250371857e-07,
                2.5612831266165976e-06,
                3.7266397283231055e-06
            ],
            [
                1.444980209564556e-07,
                1.1253516205489029e-07,
                1.1253518888531272e-07,
                1.6373766672973748e-07,
                1.2751899728286965e-07,
                4.691162124067829e-08,
                7.73441946488886e-08,
                7.734416698849138e-08,
                5.315786239218605e-08,
                1.2751901248454963e-07
            ],
            [
                8.315280276626197e-07,
                3.2887506336235617e-06,
                7.889261645269683e-06,
                9.422448185510695e-07,
                4.2228319344021954e-06,
                1.3709567165617364e-06,
                5.715003107767143e-07,
                3.288749457469787e-06,
                1.5534984953510149e-06,
                8.315281267882195e-07
            ],
            [
                0.9999987121046315,
                4.785094494811783e-06,
                1.5534984953552536e-06,
                5.715005832886879e-07,
                9.422443692574719e-07,
                3.288749065423109e-06,
                3.927860597945825e-07,
                2.6995771309523475e-07,
                4.450850519403407e-07,
                3.05902190458764e-07
            ],
            [
                3.466327863983311e-07,
                2.1024336609874897e-07,
                1.1253514863968147e-07,
                6.023569166654288e-08,
                7.734414854823498e-08,
                8.764245361752286e-08,
                1.8553914607237736e-07,
                2.5612834320563895e-06,
                9.931195693628605e-08,
                8.7642558095602e-08
            ],
            [
                8.31527928532683e-07,
                5.82912516497227e-05,
                4.222834954687752e-06,
                1.3709572068422585e-06,
                6.962255419653012e-06,
                1.5534973841705173e-06,
                8.939696304116203e-06,
                2.2603245673155757e-06,
                1.209865539274514e-06,
                2.9023130231176453e-06
            ],
            [
                1.0677032518748838e-06,
                8.31528424162821e-07,
                3.927862002641863e-07,
                6.475947210031623e-07,
                6.475951069985296e-07,
                5.043474081993875e-07,
                7.338209805200689e-07,
                7.338209805224048e-07,
                8.315280276546789e-07,
                1.0677028700363782e-06
            ],
            [
                1.4449803818215767e-07,
                0.9999934595596603,
                0.9999952149055086,
                0.9999930377404366,
                0.9999942280806623,
                1.1253509497883659e-07,
                3.4663253846718004e-07,
                0.9999832985702075,
                0.9999986290427939,
                0.9999921107346014
            ],
            [
                0.9999962733616061,
                0.9999955048184253,
                0.9999994956525919,
                0.999992110740239,
                0.9999982396572071,
                0.9999962733593845,
                0.9999832985702107,
                0.9999957771675648,
                0.9999038975397635,
                0.9999945777823249
            ],
            [
                6.475945666051092e-07,
                1.0129987357407137e-05,
                3.927862470899887e-07,
                5.715007195447234e-07,
                3.927862470899887e-07,
                1.067702870039777e-06,
                3.927862470899887e-07,
                NaN,
                3.9278634073732336e-07,
                2.69957906184239e-07
            ],
            [
                0.999993855825401,
                0.9999985406237797,
                0.9999934595596619,
                0.9999981261241703,
                0.9999983463104145,
                0.999993037742926,
                0.9999949062956078,
                0.9999942280779102,
                3.059022998576899e-07,
                0.9999885212332612
            ],
            [
                1.7603440527334603e-06,
                1.0677024882029858e-06,
                4.222834954801051e-06,
                5.043476486924565e-07,
                1.2098656835252174e-06,
                1.209865539298447e-06,
                4.785094494811783e-06,
                9.422450432030903e-07,
                2.9023116392097746e-06,
                1.994729008151319e-06
            ],
            [
                1.7603434231777837e-06,
                3.466327450765785e-07,
                5.715006514167015e-07,
                7.338212429537553e-07,
                5.043476486915964e-07,
                1.2098662604247682e-06,
                2.902312677060767e-06,
                8.939695238634211e-06,
                1.6701423836262173e-05,
                3.466326211113502e-07
            ],
            [
                3.9278605979534166e-07,
                2.102434162245973e-07,
                2.102434162245973e-07,
                2.10243290909724e-07,
                2.3823693839325527e-07,
                1.637376862489725e-07,
                3.4663249714612693e-07,
                4.4508515805735777e-07,
                8.764247451307293e-08,
                2.382370235933104e-07
            ],
            [
                2.9023109472494878e-06,
                2.1024341622426268e-07,
                5.422218969895357e-06,
                7.889263526409699e-06,
                8.93969843573914e-06,
                1.4738976701652988e-05,
                3.2887506336235617e-06,
                7.889265407327733e-06,
                4.785093924389007e-06,
                3.2887494574832472e-06
            ],
            [
                5.144221366623174e-05,
                5.043472879525233e-07,
                1.2098662604126641e-06,
                1.3709572068422585e-06,
                1.0677032518748838e-06,
                4.450849988811838e-07,
                1.2098655392871682e-06,
                9.4224425692559e-07,
                7.484622727591568e-05,
                1.3709568799919866e-06
            ],
            [
                1.3709573702856596e-06,
                3.7266383956509585e-06,
                2.9023112932296107e-06,
                1.3709576971463352e-06,
                1.0677024882029858e-06,
                2.9023116392097746e-06,
                4.222834451403972e-06,
                1.2098656835252174e-06,
                5.4222183235249605e-06,
                3.059022998576899e-07
            ],
            [
                1.0129987357517693e-05,
                1.300712536408621e-05,
                2.5612819054133693e-06,
                2.699576809143613e-07,
                1.3007134667436886e-05,
                1.209865827752005e-06,
                2.2603248367949354e-06,
                1.3007126914612648e-05,
                8.939697370069891e-06,
                1.994729721518893e-06
            ],
            [
                1.4449807263312446e-07,
                1.444979692800516e-07,
                7.73441946488886e-08,
                1.4449802095666915e-07,
                1.6373774480605869e-07,
                9.931202796993203e-08,
                1.1253508156363576e-07,
                9.931185038635267e-08,
                1.275191036933194e-07,
                1.4449803818215767e-07
            ],
            [
                0.9999987121044775,
                0.999995214905507,
                1.2751904288710323e-07,
                6.023576347299818e-08,
                0.9999869928668906,
                2.699578096393206e-07,
                0.999995214904366,
                0.9999990577552941,
                0.9999957771650467,
                0.9999985406237795
            ],
            [
                7.338213304363436e-07,
                3.9278615344178325e-07,
                2.6995784182140636e-07,
                4.450852111148132e-07,
                6.475945666051092e-07,
                7.338208055664991e-07,
                9.422445939032799e-07,
                2.9023133690821773e-06,
                2.5612819054028872e-06,
                1.370957860576702e-06
            ],
            [
                0.9999978766210321,
                0.9999942280806621,
                0.9999993106387904,
                0.9999994631251883,
                0.9999952149049374,
                0.99999385582394,
                0.9999945777829721,
                0.999998005269566,
                0.999997097688017,
                0.9999986290424671
            ],
            [
                2.260324028443809e-06,
                4.785093924389007e-06,
                7.889261645499288e-06,
                2.9023119851899796e-06,
                7.338211554813555e-07,
                1.994729483729522e-06,
                2.561282821402217e-06,
                2.561283126728994e-06,
                1.994729483729522e-06,
                1.0129987357517693e-05
            ],
            [
                0.9999982396561578,
                0.9999986290426301,
                0.9999996533674202,
                1.0677026154774503e-06,
                0.9999962733620503,
                0.9999986290431208,
                0.9999995818814265,
                2.260324567337161e-06,
                3.466325384661554e-07,
                0.9999987121044777
            ],
            [
                1.0129988564974359e-05,
                4.222834954801051e-06,
                3.7266401726359486e-06,
                5.422220262636381e-06,
                8.315282259117513e-07,
                6.962259569750576e-06,
                3.7266397283908927e-06,
                6.475950298011458e-07,
                0.0007096703848180754,
                0.0001795280091877212
            ],
            [
                7.338207180898968e-07,
                6.47594952603035e-07,
                6.962257079889302e-06,
                1.0677032518700286e-06,
                3.2887494574832472e-06,
                8.31528325040778e-07,
                2.2603245673443566e-06,
                2.9023112932296107e-06,
                6.144175334510455e-06,
                8.315277302857965e-07
            ],
            [
                1.3007128465151102e-05,
                1.3709573702856596e-06,
                3.288748281329893e-06,
                7.889260704968913e-06,
                4.222832941193893e-06,
                3.72663883989755e-06,
                1.1478769494542698e-05,
                5.4222183235249605e-06,
                8.939693107288474e-06,
                5.4222183235249605e-06
            ],
            [
                0.9999993916408186,
                0.9999949062949993,
                0.9999955048189595,
                0.9999975938970881,
                0.9999910603026371,
                0.9999957771650473,
                0.9999852610197999,
                0.9999945777829752,
                0.9999986290423036,
                0.9999977396754338
            ],
            [
                8.93969843573914e-06,
                4.222834954801051e-06,
                7.889262585958025e-06,
                4.785094494811783e-06,
                4.785094494811783e-06,
                7.889263526409699e-06,
                1.0129993395336818e-05,
                4.222834451403972e-06,
                1.3007123813559956e-05,
                4.222834451403972e-06
            ],
            [
                2.1024336609843824e-07,
                0.9999962733598314,
                0.9999952149043747,
                0.9999977396759749,
                0.9999904837505895,
                0.9999925887192537,
                0.9999934595604407,
                0.9999975938968014,
                0.9999969105059228,
                0.9999984465015053
            ],
            [
                0.9999916019239703,
                0.9999970976887088,
                0.9999957771675646,
                0.999988521235993,
                0.9999952149043678,
                0.9999987121043241,
                0.9999978766217918,
                0.9999981261237235,
                0.9999986290429571,
                0.9999977396746252
            ],
            [
                4.450850519409479e-07,
                7.889263526409699e-06,
                2.2603245673443566e-06,
                9.422443692574719e-07,
                2.9023116392097746e-06,
                2.9023116392097746e-06,
                1.7603438428848787e-06,
                2.2603248367949354e-06,
                1.3709570434250617e-06,
                9.422450432030903e-07
            ],
            [
                1.7603436330091044e-06,
                7.338212429537553e-07,
                1.2098652508424818e-06,
                7.338208930391909e-07,
                2.2603245673155757e-06,
                3.2887506336235617e-06,
                1.855391681906175e-07,
                1.6373764721072816e-07,
                8.315284241597959e-07,
                2.90231094723893e-06
            ],
            [
                0.9999991148432811,
                0.9999994631248683,
                0.9999960330131428,
                0.9999993916407459,
                0.9999995549151076,
                0.9999991148432813,
                0.9999982396561585,
                0.9999980052702803,
                0.999999266178845,
                0.9999989322975129
            ],
            [
                0.9999916019299935,
                0.9999962733611677,
                0.9999970976883642,
                0.9999955048178946,
                0.9999984465024319,
                0.9999925887174946,
                0.999993855827605,
                0.9999945777823291,
                0.9999970976873275,
                0.9999945777810417
            ],
            [
                2.2603248367949354e-06,
                1.5534981249736758e-06,
                3.288749849529972e-06,
                9.422450432030903e-07,
                1.209865827752005e-06,
                9.422445939054222e-07,
                1.2098659719788098e-06,
                1.5534984953552536e-06,
                3.2887502415767434e-06,
                6.144177531811707e-06
            ],
            [
                0.9999967112517205,
                0.9999985406237791,
                0.9999978766205259,
                0.9999995818810776,
                0.9999970976866324,
                0.9999981261239469,
                0.9999955048200326,
                0.9999955048178878,
                0.9999952149072195,
                0.9999967112501515
            ],
            [
                1.5534979397740895e-06,
                1.9947297215043796e-06,
                1.209865539295696e-06,
                1.8553910183607374e-07,
                5.715007195447234e-07,
                7.338208930443633e-07,
                3.927862470899887e-07,
                2.2603234895289998e-06,
                9.422442569315887e-07,
                3.927860597935108e-07
            ],
            [
                0.9999852610145252,
                0.9999997126314468,
                0.9999986290421398,
                0.9999992188519489,
                0.9999972735307054,
                0.99999879013374,
                0.999999057755631,
                0.9999981261241702,
                0.9999969105062901,
                0.999998126124617
            ],
            [
                4.450852111148132e-07,
                3.120191881423529e-05,
                2.260325106237323e-06,
                1.275190276859705e-07,
                8.315280276607289e-07,
                2.5612831267202583e-06,
                1.9947297215043796e-06,
                1.553497754577351e-06,
                8.315281267834927e-07,
                2.7535700949523498e-05
            ],
            [
                3.059022998576899e-07,
                2.699577774585891e-07,
                3.927860597945825e-07,
                8.315284241650899e-07,
                5.715003107767143e-07,
                1.7603434231777837e-06,
                3.4663274507713016e-07,
                1.760343213335281e-06,
                2.102434412875379e-07,
                1.3709576971425944e-06
            ],
            [
                2.1024341622426268e-07,
                1.1253513522447425e-07,
                3.726639728370556e-06,
                1.8553907971855875e-07,
                4.450852111148132e-07,
                7.889262585958025e-06,
                6.475950298011458e-07,
                6.475949526020042e-07,
                2.1024331597262577e-07,
                3.466327037548308e-07
            ],
            [
                2.902312331170226e-06,
                3.9278615344178325e-07,
                1.2098656835252174e-06,
                8.939699501416646e-06,
                2.561281294760143e-06,
                5.144223206414209e-05,
                9.422444815814404e-07,
                5.422220909009474e-06,
                2.6995771309523475e-07,
                3.2887502415767434e-06
            ],
            [
                1.9947304348862686e-06,
                2.902312677137316e-06,
                4.785092783519724e-06,
                6.962253760024999e-06,
                6.144173869603344e-06,
                1.3709573702822306e-06,
                2.2603248367949354e-06,
                1.147877359957198e-05,
                3.0590237279032884e-07,
                4.450848927650143e-07
            ],
            [
                0.9999861539971141,
                0.9999972735294057,
                3.7266388398585725e-06,
                0.9999994631248041,
                0.9999978766207793,
                0.9999991148433867,
                0.9999955048168174,
                0.9999869928746471,
                0.9999989969859123,
                0.9999921107393067
            ],
            [
                2.6995784182140636e-07,
                7.889263526345123e-06,
                9.422447062094932e-07,
                3.466325797888292e-07,
                1.0677024882029858e-06,
                1.5534981249697903e-06,
                7.338207180864763e-07,
                6.962253760024999e-06,
                4.450851049941403e-07,
                7.338213304363436e-07
            ],
            [
                6.475950298011458e-07,
                1.444980209564556e-07,
                2.1024341622368903e-07,
                3.0590215399183813e-07,
                4.4508510499849186e-07,
                3.0590215399183813e-07,
                4.450852111148132e-07,
                2.382369667929001e-07,
                2.3823690999290963e-07,
                5.715005832886879e-07
            ],
            [
                4.785093924389007e-06,
                8.31528325040778e-07,
                1.3709575337159875e-06,
                2.260324028443809e-06,
                1.3709572068553509e-06,
                8.93969843573914e-06,
                1.0677026154827912e-06,
                1.3709575337159875e-06,
                6.962257079889302e-06,
                2.561283126728994e-06
            ],
            [
                2.5612822106841303e-06,
                2.430023494002383e-05,
                3.535623806861614e-05,
                5.829126554578343e-05,
                1.4738987242968784e-05,
                2.9023119851635836e-06,
                5.1442225927013303e-05,
                1.994729245917502e-06,
                4.222835458117536e-06,
                3.2887494574518405e-06
            ],
            [
                1.0129990979842057e-05,
                0.0001233946190813656,
                7.484620943415587e-05,
                1.1478770862735993e-05,
                1.1478773599425825e-05,
                4.785092783454444e-06,
                1.3007130015488633e-05,
                2.144495863958007e-05,
                1.1478773599425825e-05,
                2.7535700947019215e-05
            ],
            [
                0.9999667858131945,
                0.9999822214439541,
                0.9999962733602806,
                0.9999843104522015,
                0.9999942280799892,
                0.9999980052695692,
                0.9999988634358852,
                8.315278294072958e-07,
                0.9999985406232594,
                0.9999942280772292
            ],
            [
                1.7603438428740716e-06,
                3.2887482813149375e-06,
                7.889259764445822e-06,
                1.0677032518748838e-06,
                6.144173137126169e-06,
                1.5534979397740895e-06,
                4.222833947932061e-06,
                1.3709576971425944e-06,
                8.315279285351409e-07,
                7.338209805224048e-07
            ],
            [
                3.288749065436569e-06,
                1.209865539298447e-06,
                1.209865539298447e-06,
                3.288749065436569e-06,
                4.7850933539684755e-06,
                1.3709575337159875e-06,
                2.9023109472494878e-06,
                1.7603425837903113e-06,
                1.760342793638743e-06,
                3.288749849529972e-06
            ],
            [
                2.6995774527718623e-07,
                3.927862470899887e-07,
                5.043473480777865e-07,
                3.288749457469787e-06,
                3.927860597945825e-07,
                1.4449796927932878e-07,
                5.04347468323289e-07,
                3.927862470905692e-07,
                3.726639728370556e-06,
                1.637377448057981e-07
            ],
            [
                9.4224425692559e-07,
                5.715005832853093e-07,
                5.715003789017068e-07,
                4.450849458218309e-07,
                1.2098658277451275e-06,
                1.0677024881980089e-06,
                1.5534975693869924e-06,
                3.466325797888292e-07,
                1.0677028700363782e-06,
                9.422448185510695e-07
            ],
            [
                0.9999885212305162,
                0.9999993106390368,
                0.999999653367379,
                0.9999885212359894,
                0.9999810748472581,
                0.999997273529731,
                0.9999972735287552,
                0.999999653367503,
                0.999998346309626,
                0.999998790133884
            ],
            [
                6.475950297971703e-07,
                6.475948754012522e-07,
                1.2098652508391807e-06,
                5.043476486915964e-07,
                3.2887506336086064e-06,
                5.715003107755449e-07,
                4.2228329411708495e-06,
                5.715003789017068e-07,
                7.338213304363436e-07,
                1.760343003481596e-06
            ],
            [
                7.338209805224048e-07,
                7.338212429537553e-07,
                2.699578096393206e-07,
                7.338213304363436e-07,
                3.466327037548308e-07,
                1.7603434231777837e-06,
                3.466327863983311e-07,
                3.927860597945825e-07,
                7.338209805224048e-07,
                1.0677027427600627e-06
            ],
            [
                0.9999885212277811,
                0.9999981261252875,
                0.999986992869995,
                0.9999852610110127,
                0.99999743871779,
                0.9999957771645431,
                0.9999910603068978,
                0.9999969105055532,
                0.9999975938979482,
                0.9999993916409635
            ],
            [
                0.9999980052709925,
                0.9999898700114427,
                0.9999975938985217,
                0.9999982396563681,
                0.9999995549149483,
                0.9999964991464221,
                0.999998239657207,
                0.9999982396559479,
                0.9999985406241276,
                0.9999972735303803
            ],
            [
                9.931186222523604e-08,
                5.043473480678099e-07,
                9.931190958076104e-08,
                6.023569884718319e-08,
                8.7642558095602e-08,
                6.47594566597747e-07,
                7.338212429464139e-07,
                4.450849988798682e-07,
                2.3823702359290413e-07,
                3.46632497145457e-07
            ],
            [
                0.9999964991443372,
                0.9999978766207822,
                0.9999977396757033,
                0.9999916019239835,
                0.9999945777823321,
                0.9999982396574179,
                1.2098659719661556e-06,
                0.9999930377454253,
                0.9999969105066604,
                0.99999671124937
            ],
            [
                0.9999991148429643,
                0.9999978766220444,
                0.9999930377429237,
                0.9999994956525919,
                0.9999999067051277,
                0.9999998642567189,
                0.9999995818813268,
                0.999992588718367,
                0.9999984465015052,
                0.9999967112517195
            ],
            [
                0.9999977396751643,
                0.9999988634357478,
                0.9999987121050918,
                0.999997273529731,
                0.999990483744912,
                0.9999952149066482,
                0.9999977396748944,
                0.9999978766205259,
                0.9999998555019963,
                0.9999955048168169
            ],
            [
                7.338210679979539e-07,
                5.043472879540142e-07,
                1.2098656835224664e-06,
                2.2603248367949354e-06,
                6.144174602077811e-06,
                2.1024326584582131e-07,
                1.0677028700422047e-06,
                1.209865827752005e-06,
                6.47594952603035e-07,
                1.9947304348595095e-06
            ],
            [
                3.059022269250683e-07,
                2.3823685319244518e-07,
                1.7603434231777837e-06,
                1.6373764721072816e-07,
                3.0590226339061185e-07,
                1.0677032518748838e-06,
                3.726639728370556e-06,
                2.9023119851781017e-06,
                3.059022998576899e-07,
                1.300712536408621e-05
            ],
            [
                0.9999921107374162,
                0.999997273530705,
                0.9999756997535258,
                0.9999962733611621,
                0.9999977396759724,
                0.9999938558254022,
                0.9999945777797395,
                0.9999910602994392,
                0.9999967112517197,
                0.9999967112513278
            ],
            [
                5.422220909041528e-06,
                3.7266383956509585e-06,
                8.939699501416646e-06,
                0.9999921107374196,
                7.889263526409699e-06,
                2.561282821402217e-06,
                1.5534984953552536e-06,
                1.0677024882029858e-06,
                1.760343213335281e-06,
                9.422450432030903e-07
            ],
            [
                6.9622595696935874e-06,
                1.8925150497848527e-05,
                1.8925141473978602e-05,
                1.7603434231833873e-06,
                1.0677024882009222e-06,
                5.422218969858371e-06,
                1.9947297215125433e-06,
                7.338210680021253e-07,
                1.3007128464961824e-05,
                4.450851580555361e-07
            ],
            [
                2.699576809143613e-07,
                1.5534984953552536e-06,
                3.9278634073732336e-07,
                5.043474081993875e-07,
                9.931190958076104e-08,
                1.2098653950716937e-06,
                3.059022998576899e-07,
                2.2603251062450327e-06,
                2.5612834320563895e-06,
                3.288749065423109e-06
            ],
            [
                1.3709576971160984e-06,
                5.04347468323289e-07,
                3.927863875584984e-07,
                1.553498310118888e-06,
                2.9023119851635836e-06,
                1.5534973841895917e-06,
                5.715005832853093e-07,
                9.422447062202052e-07,
                1.2098656835224664e-06,
                5.715007195384861e-07
            ],
            [
                7.338209805200689e-07,
                5.715007195431641e-07,
                1.2098656835224664e-06,
                1.2098659719757836e-06,
                5.043476486915964e-07,
                7.338212429537553e-07,
                5.715005832853093e-07,
                7.338209805224048e-07,
                1.3709570434178922e-06,
                1.0677028700266676e-06
            ],
            [
                5.715004470313855e-07,
                7.484626297142789e-05,
                1.855391239544352e-07,
                3.2887482813149375e-06,
                3.2887482813149375e-06,
                1.3709567165530083e-06,
                1.3007125363719486e-05,
                1.9947297215043796e-06,
                1.7603438428740716e-06,
                1.994730672668496e-06
            ],
            [
                2.2603248367949354e-06,
                2.2603248367949354e-06,
                4.785095065232451e-06,
                1.994729721518893e-06,
                3.288748281329893e-06,
                2.9023116392097746e-06,
                5.422217030781934e-06,
                3.7266383956509585e-06,
                4.2228339479858295e-06,
                4.785093924389007e-06
            ],
            [
                3.7266401726173067e-06,
                2.2603253756874524e-06,
                1.8925141473978602e-05,
                0.9999967112513297,
                2.1024326584639497e-07,
                5.715005832886879e-07,
                3.466327450765785e-07,
                9.422444815765128e-07,
                4.450850519403407e-07,
                9.422448185478557e-07
            ],
            [
                3.7266410611465547e-06,
                7.889265407327733e-06,
                3.7266410611465547e-06,
                1.4738985486721259e-05,
                5.715006514176113e-07,
                2.2603242978943238e-06,
                2.2603242978943238e-06,
                2.260324028443809e-06,
                1.9947292459406333e-06,
                1.7603440527334603e-06
            ],
            [
                5.422217030781934e-06,
                0.9999724643188062,
                1.9947304348703948e-06,
                8.481105151274973e-05,
                3.927862002663297e-07,
                4.539787947559951e-05,
                3.9278610661902853e-07,
                3.4663266243308805e-07,
                5.715005832853093e-07,
                4.4508494582405734e-07
            ],
            [
                0.9999992188515764,
                0.9999994631247401,
                0.9999977396765113,
                0.999978555054167,
                0.9999952149072179,
                0.9999989969859121,
                0.9999921107402416,
                0.9999987901346054,
                0.9999975938973742,
                0.9999977396765113
            ],
            [
                1.994729008151319e-06,
                1.7603425837903113e-06,
                3.7266383956509585e-06,
                1.3007126914612648e-05,
                4.222834954801051e-06,
                1.5534981249736758e-06,
                6.144176066943187e-06,
                3.2887506336235617e-06,
                1.209865827752005e-06,
                4.7850933539684755e-06
            ],
            [
                8.315283250371857e-07,
                1.3709567165579959e-06,
                8.315279285351409e-07,
                1.7603438428740716e-06,
                1.0677024881980089e-06,
                1.9947306726358406e-06,
                6.962253759828703e-06,
                1.5534983101549167e-06,
                7.889263525778283e-06,
                4.785095065045315e-06
            ],
            [
                0.9999991148429644,
                0.9999949062956072,
                0.9999960330121965,
                0.9999921107346007,
                0.9999980052702795,
                0.9999974387165691,
                0.9999978766222977,
                0.9999988634361544,
                0.9999995549150542,
                0.9999945777816807
            ],
            [
                0.9999967112501519,
                2.561282210729555e-06,
                0.9999989969854337,
                0.999998346309626,
                0.9999898700102351,
                0.9999978766210322,
                2.2603251061849014e-06,
                0.9999898700114431,
                4.450851580555361e-07,
                0.9999921107374201
            ],
            [
                3.2887498495150166e-06,
                4.4508510499849186e-07,
                4.4508526417298334e-07,
                3.72663883989755e-06,
                9.422442569315887e-07,
                1.4738978458623327e-05,
                8.315279285370317e-07,
                2.6995784182140636e-07,
                3.288749457469787e-06,
                4.785093353940187e-06
            ],
            [
                3.0590237279085045e-07,
                1.4738987243478167e-05,
                4.785093353940187e-06,
                2.260323758987159e-06,
                2.382368531929327e-07,
                6.475947210031623e-07,
                5.04347468323289e-07,
                1.8553905760062447e-07,
                4.2228319344021954e-06,
                5.422220909009474e-06
            ],
            [
                7.889265407327733e-06,
                1.9947292459406333e-06,
                1.0677027427624903e-06,
                5.715005832895975e-07,
                3.2887502415767434e-06,
                2.69957906184239e-07,
                3.2887502415767434e-06,
                3.0590237279032884e-07,
                2.260323758987159e-06,
                2.6995784182140636e-07
            ],
            [
                1.2751904288739315e-07,
                1.6373762769138607e-07,
                1.2751910369310194e-07,
                9.422450432014836e-07,
                1.5534983101602148e-06,
                2.699577774585891e-07,
                2.382368247924618e-07,
                3.927862002654366e-07,
                2.6995784182140636e-07,
                6.475949526020042e-07
            ],
            [
                2.9023116392097746e-06,
                6.144174602077811e-06,
                3.7266383956509585e-06,
                2.561282210740037e-06,
                9.422442569334097e-07,
                1.3709575337159875e-06,
                2.9023109472494878e-06,
                1.3709575337159875e-06,
                9.422443692574719e-07,
                3.2887502415767434e-06
            ],
            [
                7.338212429582604e-07,
                1.760342793638743e-06,
                1.2098655392871682e-06,
                4.450848927650143e-07,
                1.8553910183607374e-07,
                3.059022269250683e-07,
                2.1024336609843824e-07,
                8.31527928532683e-07,
                1.5534981249697903e-06,
                5.715006514167015e-07
            ],
            [
                0.9999962733620522,
                0.999997876620779,
                0.9999952149049386,
                0.9999646437367895,
                3.4663266243308805e-07,
                3.466327863983311e-07,
                3.288750241561788e-06,
                0.9999980052693285,
                0.999998712104478,
                0.9999993106389549
            ],
            [
                4.785093924389007e-06,
                5.422220909041528e-06,
                2.9023109472494878e-06,
                3.7266383956509585e-06,
                3.7266379514061143e-06,
                9.422443692574719e-07,
                1.5534979397829198e-06,
                1.7603440527334603e-06,
                5.715003107767143e-07,
                1.7603425837903113e-06
            ],
            [
                5.422221555414699e-06,
                2.260324028443809e-06,
                4.785094494811783e-06,
                1.7603440527334603e-06,
                5.422220909009474e-06,
                8.315282259151545e-07,
                9.422450432014836e-07,
                2.2603248367949354e-06,
                7.889259764517575e-06,
                5.715003107755449e-07
            ],
            [
                2.2603242978778778e-06,
                3.4663266243308805e-07,
                4.4508526417298334e-07,
                2.6995784182140636e-07,
                8.315281267834927e-07,
                1.2098662604291696e-06,
                7.338211554783522e-07,
                1.2098662604291696e-06,
                1.7603430034743913e-06,
                1.2098656835224664e-06
            ],
            [
                1.3709578605729614e-06,
                1.300712846477255e-05,
                3.0590226339061185e-07,
                2.3823690999290963e-07,
                2.382368815916736e-07,
                0.0003353501911629164,
                3.0590237279032884e-07,
                5.422221555380179e-06,
                0.9999930377462478,
                9.422443692555439e-07
            ],
            [
                8.7642558095602e-08,
                9.931190958076104e-08,
                1.9947301970972664e-06,
                1.1253506814842375e-07,
                2.1444940746307572e-05,
                4.450848927658745e-07,
                3.059021175261338e-07,
                3.9278610661902853e-07,
                5.4222183235249605e-06,
                6.825598028392069e-08
            ],
            [
                1.892515049819277e-05,
                2.9023112932296107e-06,
                2.5612834320563895e-06,
                8.93969843573914e-06,
                2.2603242978943238e-06,
                8.939699501416646e-06,
                4.5397874064161706e-05,
                4.222834451403972e-06,
                2.561281600086738e-06,
                8.939700567094277e-06
            ],
            [
                5.4222176771176554e-06,
                4.785092783454444e-06,
                1.2098652508391807e-06,
                3.726638839833152e-06,
                6.962255419653012e-06,
                1.1478766757049986e-05,
                4.222835458044565e-06,
                1.7603427936335396e-06,
                1.99472900813862e-06,
                2.9023116391675407e-06
            ],
            [
                2.9023116392097746e-06,
                9.422447062270609e-07,
                1.209865827752005e-06,
                2.561282210701601e-06,
                8.939700567094277e-06,
                1.2098659719757836e-06,
                9.422444815792981e-07,
                3.0590237279032884e-07,
                6.475947210031623e-07,
                5.715003107767143e-07
            ],
            [
                2.2603245673443566e-06,
                4.7850933539684755e-06,
                1.9947292459406333e-06,
                2.9023116392097746e-06,
                3.288747889284851e-06,
                4.785094494811783e-06,
                2.2603234895372223e-06,
                3.72663883989755e-06,
                6.144173137170873e-06,
                3.288749849529972e-06
            ],
            [
                7.33821330437595e-07,
                2.5612834320563895e-06,
                5.043472278322555e-07,
                1.209866260432471e-06,
                1.994729721518893e-06,
                2.561282210740037e-06,
                8.315277302857965e-07,
                8.315278294114555e-07,
                7.33821330437595e-07,
                5.043472278322555e-07
            ],
            [
                6.47595107001401e-07,
                1.1478770862882149e-05,
                3.466326211113502e-07,
                2.6995790618469934e-07,
                4.222834451403972e-06,
                1.8553905760062447e-07,
                1.5534981249697903e-06,
                6.475950298011458e-07,
                5.422217677152175e-06,
                6.962257909842961e-06
            ],
            [
                0.9999991684717744,
                0.9999949062937844,
                0.9999969105062897,
                0.999998239657207,
                0.9999998257022045,
                0.9999962733616068,
                0.9999967112493674,
                0.9999993916409635,
                0.999999802494633,
                0.9999977396757026
            ],
            [
                0.9999978766207795,
                7.889262585886274e-06,
                4.4508494582405734e-07,
                6.962254589978262e-06,
                0.9999967112509379,
                6.475949526020042e-07,
                0.9999724642958431,
                1.3709576971379186e-06,
                0.9999942280799824,
                0.9999960330126756
            ],
            [
                1.5534971990126997e-06,
                1.7603434231705793e-06,
                1.7603434231705793e-06,
                1.7603438428740716e-06,
                1.0677028700363782e-06,
                2.5612812947380135e-06,
                4.450848927650143e-07,
                1.2098652508347793e-06,
                5.043475885674441e-07,
                1.0677026154730804e-06
            ],
            [
                0.9999945777823247,
                0.99998987000782,
                0.9999962733616057,
                0.9999925887219014,
                0.9999945777784476,
                0.9999957771645438,
                0.9999852610145252,
                0.9999992661790196,
                0.9999964991464223,
                0.9999756997506137
            ],
            [
                1.444979692800516e-07,
                2.2603253756956754e-06,
                3.059022269250683e-07,
                7.338210680021253e-07,
                4.450850519403407e-07,
                5.043476486924565e-07,
                1.9947301970972664e-06,
                6.475945666063607e-07,
                3.466326211113502e-07,
                8.315282259138311e-07
            ],
            [
                3.288749065436569e-06,
                2.9023112932296107e-06,
                3.2887494574832472e-06,
                8.315284241665078e-07,
                4.785093924389007e-06,
                5.422220909041528e-06,
                3.288749849529972e-06,
                1.3709575337159875e-06,
                3.2887494574832472e-06,
                1.7603438428848787e-06
            ]
        ]
    },
    {
        "q_id": "10122_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999999317440035,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999611089043,
                1.0,
                0.999999943413784,
                1.0
            ],
            [
                0.9999999397642582,
                0.9999999273417836,
                0.9999999530883844,
                1.0,
                0.9999999500628155,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.999999973270557,
                0.9999999634651487,
                0.9999999226558146,
                1.0,
                0.9999998942830359,
                0.9999999732705347,
                1.0,
                0.9999999530883452,
                1.0
            ],
            [
                1.0,
                0.999999922655787,
                1.0,
                0.9999999123574733,
                0.9999997463980729,
                0.9999999468421565,
                0.9999998724809875,
                0.9999999397642437,
                0.9999999397642725,
                0.9999999317439384
            ],
            [
                0.9999999273418009,
                0.9999999559305891,
                0.9999999123575778,
                1.0,
                0.9999998555019791,
                0.9999999176674651,
                0.9999999176674651,
                0.9999999397642939,
                0.9999999358793485,
                1.0
            ],
            [
                1.0,
                0.9999999358794021,
                1.0,
                1.0,
                0.9999999434137233,
                1.0,
                1.0,
                0.9999999434137435,
                1.0,
                1.0
            ],
            [
                0.9999999358793409,
                0.9999999559306049,
                0.9999999226558146,
                0.9999999226558054,
                0.9999999358793715,
                0.9999999273418961,
                1.0,
                0.9999998724809116,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999999559305787,
                1.0,
                0.9999999317439546,
                0.9999999226557501,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999273417923,
                0.9999998024946096,
                0.9999999123574523,
                0.999999912357536,
                0.9999998724809268,
                0.9999998802069731,
                0.9999999317439221,
                0.9999999226558146,
                1.0,
                0.9999999176675338
            ],
            [
                1.0,
                1.0,
                0.9999999468421186,
                1.0,
                0.999999943413757,
                0.9999998461827323,
                0.9999999358793638,
                0.9999999358794021,
                1.0,
                0.9999999500627856
            ],
            [
                1.0,
                0.9999999434137773,
                0.9999999656787365,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999358793792,
                0.9999999500628394
            ],
            [
                0.9999999748900031,
                1.0,
                1.0,
                0.9999999176675436,
                1.0,
                0.9999999559305839,
                1.0,
                1.0,
                1.0,
                0.9999999273418875
            ],
            [
                1.0,
                0.9999999434137975,
                1.0,
                1.0,
                0.9999997126313787,
                0.9999999358794402,
                1.0,
                1.0,
                1.0,
                0.9999999123575882
            ],
            [
                1.0,
                1.0,
                0.999999946842163,
                0.999999917667573,
                0.9999999273418788,
                0.99999994341373,
                1.0,
                1.0,
                1.0,
                0.9999999067050943
            ],
            [
                1.0,
                0.9999999317439058,
                0.9999999500628035,
                1.0,
                1.0,
                0.9999998942830359,
                0.9999999559305943,
                1.0,
                0.9999998942830233,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999998642566866,
                0.9999998642566867,
                0.9999999006881496,
                0.9999999358794173,
                1.0,
                0.9999998461826772,
                0.9999998024946096,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999067051499,
                0.9999999397642294,
                0.9999999397643085,
                0.9999999006881378,
                0.9999999226557316,
                1.0,
                0.9999999358793409,
                0.9999999176675436,
                0.999999887464932
            ],
            [
                0.9999999397642293,
                0.999999931743979,
                1.0,
                1.0,
                1.0,
                0.9999999500628095,
                1.0,
                1.0,
                0.9999999317439384,
                0.999999931743971
            ],
            [
                0.9999999067049831,
                1.0,
                0.9999999434137166,
                0.9999999176675142,
                0.999999931743979,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999434137908
            ],
            [
                0.9999999273417837,
                1.0,
                0.9999999317439872,
                0.9999997617631187,
                0.9999999358794402,
                1.0,
                0.9999999176675829,
                0.9999999226557962,
                0.9999998874648379,
                0.9999999226558146
            ],
            [
                0.9999999123575151,
                0.9999999226557685,
                0.9999998802069588,
                0.9999999530883508,
                0.9999999559306259,
                0.9999999226558238,
                0.9999998461826956,
                0.9999998874648917,
                1.0,
                0.9999999123575568
            ],
            [
                1.0,
                0.9999999434137975,
                0.9999999434137907,
                1.0,
                0.9999999358793792,
                0.9999999358793792,
                0.9999999273418703,
                0.9999999397642868,
                1.0,
                0.9999999067050388
            ],
            [
                1.0,
                1.0,
                0.9999999273417749,
                0.9999999434137975,
                0.9999999226558238,
                0.9999999067050387,
                0.9999999468421503,
                0.9999999468421567,
                0.9999999397643011,
                0.9999999273418789
            ],
            [
                0.9999999006880195,
                1.0,
                0.9999998942830485,
                0.9999999123575777,
                0.9999997897566842,
                0.9999999067050053,
                0.9999999226557317,
                0.9999999006881378,
                0.9999998257021423,
                0.9999999226557501
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999500627857
            ],
            [
                1.0,
                1.0,
                0.9999999358793638,
                1.0,
                1.0,
                0.9999999226557778,
                1.0,
                0.9999999468421883,
                0.9999999634652009,
                1.0
            ],
            [
                0.9999998802069445,
                1.0,
                0.999999931743979,
                0.9999999500628453,
                0.9999999176675829,
                1.0,
                1.0,
                0.9999999176674946,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999999226558146,
                0.9999999273418703,
                1.0,
                1.0,
                0.9999999317440035,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999317439954,
                0.9999999468421946,
                1.0,
                0.999999917667524,
                0.9999999468421567,
                0.9999999273418703,
                0.999999912357442,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999998942830359,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999998461827323,
                0.9999999317440198,
                1.0,
                0.9999999586006542,
                1.0
            ],
            [
                0.9999999176675338,
                0.9999999123574838,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999500628511,
                1.0,
                0.9999999123575047,
                0.9999997617630902
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999358794173,
                0.9999999006880668,
                1.0,
                0.9999999067051499,
                0.9999999586006393,
                0.9999998874648917,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999434137705,
                0.9999999067050387,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999500627798,
                0.9999999677581529,
                1.0,
                0.9999999715466764
            ],
            [
                0.9999999397643156,
                0.9999998362622748,
                1.0,
                0.9999998642566867,
                0.9999998942829099,
                0.9999999176675043,
                0.9999999317439954,
                0.999999931743914,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999176675437,
                0.9999999434137232,
                0.9999999397642366,
                0.9999999226557224,
                0.9999999226557593,
                0.9999999067051388,
                0.9999999226558515,
                0.9999999317440035,
                0.9999999123575674
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999559305786,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999123575987
            ],
            [
                0.9999999226557685,
                1.0,
                0.9999999226558515,
                0.9999999468421756,
                1.0,
                0.9999999358793867,
                0.9999999397642868,
                0.9999999358793944,
                0.9999998362623334,
                0.9999999397642437
            ],
            [
                0.9999999468421883,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999998724808964,
                0.9999999176674848,
                1.0,
                1.0,
                0.9999999006881497
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999397642222,
                0.9999999468421376,
                1.0,
                1.0,
                1.0,
                0.999999917667524,
                0.9999999559305996
            ],
            [
                0.9999999500628036,
                0.9999999397642868,
                0.99999982570208,
                0.9999998642566542,
                1.0,
                1.0,
                1.0,
                0.9999999226557685,
                0.9999999397642796,
                1.0
            ],
            [
                0.9999998144609648,
                0.9999999006881378,
                1.0,
                0.9999999006880312,
                0.9999998555020481,
                0.9999999611088997,
                1.0,
                0.9999999226557131,
                0.999999946842144,
                1.0
            ],
            [
                0.9999999468421059,
                0.9999999006881497,
                0.9999999226557962,
                1.0,
                1.0,
                0.9999999226557962,
                0.9999999123575569,
                1.0,
                1.0,
                0.9999998362622552
            ],
            [
                0.9999999434137705,
                1.0,
                1.0,
                1.0,
                0.9999999611088626,
                0.9999999500628274,
                1.0,
                0.9999999067050165,
                1.0,
                1.0
            ],
            [
                0.9999999226557778,
                1.0,
                0.9999999273418961,
                1.0,
                1.0,
                0.9999999226557685,
                1.0,
                1.0,
                0.9999999226557131,
                0.9999999176675044
            ],
            [
                0.9999998942829351,
                0.9999999468421377,
                0.9999999006880431,
                1.0,
                1.0,
                0.9999999358793332,
                0.9999999468421567,
                0.9999999715466256,
                1.0,
                1.0
            ],
            [
                0.9999999317440197,
                0.9999999530883563,
                1.0,
                0.9999999530884011,
                1.0,
                0.9999999586006542,
                1.0,
                0.9999998461827139,
                0.9999999397642078,
                0.9999999500628036
            ],
            [
                0.999999939764258,
                0.9999999500628453,
                0.9999999317440035,
                1.0,
                1.0,
                0.999999943413811,
                1.0,
                1.0,
                1.0,
                0.9999999317439139
            ],
            [
                0.999999927341853,
                0.9999999006880076,
                1.0,
                0.9999999067051388,
                0.9999999697115624,
                0.9999999226557685,
                1.0,
                0.9999999226557685,
                0.999999939764258,
                0.9999997897567092
            ],
            [
                0.9999998942829602,
                0.9999999468421756,
                0.9999999559305576,
                1.0,
                0.9999999226557132,
                0.999999939764294,
                1.0,
                1.0,
                0.9999999176674456,
                0.9999999715466289
            ],
            [
                1.0,
                0.9999999273418616,
                0.9999995262092167,
                0.9999998874647843,
                0.9999999273418356,
                0.9999999226558146,
                0.9999999176675142,
                0.9999998942829477,
                0.9999999176674357,
                1.0
            ],
            [
                1.0,
                0.9999998257020799,
                0.9999999226558146,
                1.0,
                0.9999999226557501,
                1.0,
                0.9999999226557685,
                0.9999999226557778,
                1.0,
                0.9999999397643012
            ],
            [
                1.0,
                1.0,
                0.9999999500627976,
                1.0,
                1.0,
                1.0,
                0.9999999273418876,
                1.0,
                0.9999999468421122,
                0.9999999397643156
            ],
            [
                0.9999999317439302,
                0.9999998942829602,
                0.999999887464771,
                0.9999999358793332,
                0.9999999434137637,
                0.9999999317439547,
                0.9999998874647575,
                0.9999999317439058,
                0.999999931743914,
                0.9999999500628333
            ],
            [
                0.9999999176675338,
                1.0,
                0.9999999434137705,
                1.0,
                1.0,
                1.0,
                0.9999999226558423,
                0.9999999586006245,
                1.0,
                0.9999999317440198
            ],
            [
                0.9999999123575359,
                0.9999999397642222,
                0.9999999468421567,
                0.9999999434137503,
                0.9999999273418876,
                0.9999999434137705,
                0.9999999697115551,
                0.9999999586006096,
                1.0,
                0.999999943413784
            ],
            [
                0.9999999226558054,
                0.9999998874647977,
                0.9999999273418356,
                0.9999999176675437,
                1.0,
                1.0,
                0.9999999273418443,
                0.9999998257021007,
                0.9999999358794096,
                0.9999998257022046
            ],
            [
                1.0,
                0.9999991148429644,
                0.9999999317439627,
                1.0,
                1.0,
                0.9999998874647441,
                0.9999999123575987,
                0.9999998874647307,
                0.9999999273418183,
                1.0
            ],
            [
                0.9999999273417837,
                1.0,
                0.9999999226557778,
                0.9999999226557593,
                0.9999998724809572,
                0.9999999697115444,
                0.9999999397642437,
                0.9999999611088487,
                1.0,
                0.9999999530883787
            ],
            [
                0.999999935879425,
                1.0,
                0.9999999123575882,
                0.9999999677581298,
                0.9999999397642868,
                1.0,
                1.0,
                1.0,
                0.9999997126314469,
                1.0
            ],
            [
                1.0,
                1.0,
                0.999999931743971,
                1.0,
                1.0,
                1.0,
                0.9999999273418616,
                0.9999999273418616,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999226557225,
                1.0,
                1.0,
                0.9999999586005949
            ],
            [
                1.0,
                0.9999999732705475,
                0.9999997617631184,
                1.0,
                0.9999998555019447,
                0.9999999397642365,
                1.0,
                0.9999999006880431,
                0.9999999317440117,
                0.9999999067051165
            ],
            [
                1.0,
                1.0,
                0.9999999317439384,
                1.0,
                0.9999999317439302,
                1.0,
                1.0,
                1.0,
                0.9999999176675436,
                1.0
            ],
            [
                0.9999999397643083,
                1.0,
                0.9999999006881142,
                0.9999999273418789,
                0.9999999358793638,
                0.9999999358793562,
                0.9999999176675829,
                0.9999999123575464,
                0.9999999317439383,
                0.9999999273418616
            ],
            [
                0.999999894282935,
                0.9999999559306259,
                0.9999998257021838,
                0.9999999468421502,
                0.9999999358793409,
                0.9999998942829477,
                0.9999999317440198,
                0.9999998024945626,
                0.9999999358794174,
                1.0
            ],
            [
                0.9999999176675044,
                0.9999998942830485,
                0.9999999358793638,
                0.9999996940978099,
                0.9999999434137368,
                1.0,
                1.0,
                0.9999999006879838,
                0.9999999358793485,
                0.9999999434137975
            ],
            [
                0.9999999586006245,
                0.9999999123575778,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.999999943413757,
                0.9999999358794479
            ],
            [
                1.0,
                1.0,
                0.9999999226558423,
                1.0,
                1.0,
                0.9999999176675534,
                0.9999999611088858,
                0.9999999317440117,
                0.9999998942829225,
                1.0
            ],
            [
                1.0,
                0.9999999732705507,
                1.0,
                0.9999999273417749,
                1.0,
                1.0,
                0.9999998724810027,
                1.0,
                0.9999999500628334,
                0.9999997463980428
            ],
            [
                1.0,
                1.0,
                0.9999999226557778,
                0.9999999397642294,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999358793485,
                0.9999999006881378
            ],
            [
                1.0,
                0.999999967758103,
                1.0,
                1.0,
                1.0,
                0.9999999677581414,
                0.9999999837877692,
                0.9999999586006146,
                0.9999999397643156,
                0.9999999530883675
            ],
            [
                0.9999999273417662,
                0.9999997300420939,
                1.0,
                1.0,
                1.0,
                0.9999999697115551,
                0.999999825702059,
                1.0,
                0.999999917667524,
                1.0
            ],
            [
                1.0,
                0.999999946842163,
                0.9999999434137907,
                1.0,
                0.9999999804443264,
                0.9999997126315496,
                1.0,
                0.9999998802069445,
                0.9999999226557132,
                0.9999999226557224
            ],
            [
                0.9999999273417749,
                0.999999917667524,
                0.9999999500628572,
                0.9999999434137098,
                0.9999998024945626,
                0.9999999317439546,
                1.0,
                0.9999998642566542,
                0.9999999434138109,
                0.999999880206916
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999176674553,
                0.9999999006880904,
                0.9999999123574523,
                1.0,
                1.0,
                1.0,
                0.9999999067050832
            ],
            [
                1.0,
                0.9999999067051165,
                0.9999998642566381,
                0.9999999123574628,
                0.9999999176675731,
                1.0,
                0.9999999317439221,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999748899852,
                1.0,
                0.999999953088362,
                1.0,
                0.9999999358793485,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999397642868,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999434137975,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999123575046,
                1.0,
                0.9999998555020307,
                0.9999999317439546,
                1.0,
                1.0,
                0.9999999434137435,
                0.9999998724808964,
                0.9999999273418443
            ],
            [
                1.0,
                0.9999999273417749,
                1.0,
                0.999999958600595,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999358794174,
                1.0,
                0.999999939764258,
                1.0,
                1.0,
                0.9999999317439546,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999998724809419,
                0.9999999634651487,
                0.9999999358794097,
                0.9999999559306312,
                0.9999999176675436,
                1.0,
                1.0,
                0.9999999697115948
            ],
            [
                1.0,
                0.9999999226557408,
                1.0,
                0.9999999006880076,
                0.9999998802069731,
                0.99999992265575,
                0.999999927341853,
                0.999999958600659,
                1.0,
                0.9999999468421567
            ],
            [
                1.0,
                0.9999999500628274,
                0.9999999468421883,
                0.9999999434137166,
                0.9999999397642365,
                1.0,
                1.0,
                1.0,
                0.9999999434137368,
                0.9999999176674456
            ],
            [
                0.9999999273418703,
                0.9999999176675535,
                0.999999939764215,
                0.9999999317439221,
                0.9999999273418009,
                1.0,
                1.0,
                1.0,
                0.9999999226558238,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999226557685,
                1.0,
                1.0,
                1.0,
                0.9999999006881023,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999434137368,
                1.0,
                0.9999999468421249,
                0.9999999530883787,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999226558054,
                0.9999997897566341,
                0.9999999317440116,
                0.9999999317439384,
                1.0,
                0.9999999530883564,
                0.9999999317439384,
                0.999999931743914,
                0.9999999317440117,
                0.999999864256622
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999397642724,
                0.9999999559306049,
                1.0,
                1.0,
                0.9999999559306259,
                1.0,
                0.9999999358794326
            ],
            [
                1.0,
                1.0,
                0.9999999697115406,
                0.9999999837877829,
                0.9999999358793792,
                1.0,
                1.0,
                1.0,
                0.999999927341827,
                1.0
            ],
            [
                1.0,
                1.0,
                0.999999917667524,
                0.9999999397642939,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999998874647844,
                0.9999996743686648,
                1.0,
                1.0,
                1.0,
                0.9999999358793561,
                1.0,
                1.0,
                0.9999999006880312
            ],
            [
                1.0,
                0.9999999397642653,
                0.9999999434137233,
                0.9999999317439954,
                1.0,
                0.9999999500628393,
                0.9999999123575359,
                0.9999999764113409,
                1.0,
                0.9999999273418702
            ],
            [
                0.999999939764294,
                1.0,
                1.0,
                0.999999953088334,
                0.9999999397642079,
                1.0,
                0.9999999317439139,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999434137368,
                0.9999999226557409,
                0.9999999317440279,
                0.999999825702163,
                0.9999998362622553,
                1.0,
                1.0,
                0.99999994341373,
                0.9999999006880431,
                1.0
            ],
            [
                6.962255419868303e-06,
                0.9999999656786833,
                0.9999999123575882,
                0.9999996072138936,
                1.0,
                1.0,
                0.9999999468421502,
                0.9999999123575672,
                0.9999999226557131,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999317439708,
                1.0,
                1.0,
                0.9999999226558423,
                0.9999999559305839,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.999999935879425,
                0.9999998461826223,
                1.0,
                1.0,
                0.9999999273418096,
                1.0,
                0.9999999358793792,
                0.9999999434137368,
                1.0,
                0.9999999317439221
            ],
            [
                1.0,
                1.0,
                0.9999996533673794,
                1.0,
                0.999999906705061,
                0.9999999500628214,
                1.0,
                1.0,
                0.9999999634651705,
                0.9999999317439954
            ],
            [
                1.0,
                0.999999939764294,
                0.9999999317440197,
                0.9999999176675044,
                0.9999999006881496,
                0.9999998802069874,
                0.9999999067050832,
                0.9999996310114163,
                1.0,
                0.9999998942829981
            ],
            [
                0.9999999176674945,
                0.9999999358793485,
                0.9999999176675142,
                1.0,
                0.9999999176675142,
                0.9999999006879721,
                1.0,
                0.999999917667475,
                0.9999999317439628,
                0.9999999500628453
            ],
            [
                0.99999994341373,
                1.0,
                0.9999998257021214,
                0.9999999358793333,
                1.0,
                0.9999998024945624,
                1.0,
                1.0,
                0.9999999123574941,
                1.0
            ],
            [
                0.9999999273418875,
                0.9999999434137637,
                0.9999999067051388,
                0.9999998724810027,
                0.9999999358793791,
                1.0,
                1.0,
                0.9999999434138043,
                0.9999998874649185,
                0.9999998144608762
            ],
            [
                0.9999999434138043,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999176675535,
                1.0,
                1.0,
                0.9999999586006294,
                1.0,
                0.9999999123574942,
                0.9999999317439953,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999067049831,
                1.0,
                0.999999935879425,
                1.0,
                1.0,
                0.999999946842182,
                1.0,
                1.0,
                0.9999999176675436
            ],
            [
                1.0,
                0.9999999273418443,
                0.9999999226558054,
                0.9999999123574942,
                1.0,
                0.9999999176675634,
                0.9999998942830737,
                0.9999999273417836,
                0.9999998942829855,
                0.999999927341853
            ],
            [
                1.0,
                0.999999943413784,
                1.0,
                0.9999998024946096,
                0.9999999006880904,
                0.9999997761971318,
                1.0,
                0.9999999317440198,
                1.0,
                0.9999999586006394
            ],
            [
                0.9999999176674357,
                0.999999939764294,
                0.9999999273418095,
                1.0,
                1.0,
                0.9999999067051388,
                0.9999999006880904,
                1.0,
                1.0,
                0.9999999317439221
            ],
            [
                1.0,
                1.0,
                1.0,
                0.999999917667524,
                0.9999999715466663,
                0.9999999634651661,
                1.0,
                0.9999999715466256,
                0.9999999226558054,
                0.9999999468421439
            ],
            [
                1.0,
                1.0,
                0.9999999434138042,
                1.0,
                0.9999999468421947,
                1.0,
                0.9999999500628334,
                0.9999999500628035,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999500628155,
                0.9999999067051054,
                1.0,
                1.0,
                0.9999999358794096,
                0.9999999123574838,
                0.999999939764251,
                0.9999999067049942,
                0.9999999434137705
            ],
            [
                0.9999999397642222,
                1.0,
                0.9999998802069445,
                0.9999998362623529,
                1.0,
                0.999999917667524,
                0.9999999226558146,
                0.999999927341775,
                0.9999998724808964,
                0.9999999468421693
            ],
            [
                0.9999999586006492,
                1.0,
                1.0,
                0.9999999123575674,
                0.9999999273418356,
                0.9999999530883285,
                0.9999999468421567,
                0.9999999067050165,
                0.9999999468421313,
                0.9999999006880194
            ],
            [
                0.9999999434137637,
                1.0,
                0.9999998461827138,
                0.9999999226557593,
                1.0,
                0.9999999677581567,
                0.9999999006881142,
                0.999999931743971,
                0.9999999176675731,
                1.0
            ],
            [
                0.9999999317439059,
                1.0,
                1.0,
                0.999999974890015,
                1.0,
                0.9999999067051277,
                1.0,
                1.0,
                0.9999999176675634,
                0.999999935879425
            ],
            [
                1.0,
                0.9999999559306153,
                1.0,
                1.0,
                0.9999999500628095,
                0.9999999358793639,
                1.0,
                0.99999994341373,
                0.9999999176674357,
                0.999999927341775
            ],
            [
                1.0,
                1.0,
                0.9999999317439872,
                0.9999999273418703,
                1.0,
                1.0,
                0.9999999226557593,
                1.0,
                0.9999998257021214,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999317440116,
                0.9999998362623529,
                0.999999712631447,
                0.9999998942830863,
                0.999999943413784
            ],
            [
                0.999999958600659,
                0.999999917667475,
                1.0,
                1.0,
                0.9999999006880786,
                1.0,
                0.9999999123574628,
                0.9999999226557132,
                1.0,
                0.9999999434137705
            ],
            [
                1.0,
                0.9999999123574629,
                0.9999999067051055,
                1.0,
                0.9999999006880786,
                0.9999999273418443,
                0.9999999273418183,
                0.9999999358793945,
                1.0,
                0.9999999434137503
            ],
            [
                0.999999935879425,
                1.0,
                0.9999999006881378,
                0.9999998724809116,
                1.0,
                0.9999999317440117,
                1.0,
                0.9999999500628393,
                1.0,
                0.9999998642566704
            ],
            [
                0.9999999273418962,
                0.999999887464771,
                1.0,
                0.999999917667475,
                0.9999998874649184,
                0.9999998642566543,
                1.0,
                1.0,
                0.9999999226558515,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999998724808965,
                0.99999994341373,
                1.0,
                1.0,
                0.999999935879425,
                1.0,
                0.9999999176675044,
                0.9999999317439139
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999273418183,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999176675829
            ]
        ]
    },
    {
        "q_id": "9500_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            6,
            7,
            9,
            10,
            11,
            13,
            14,
            15,
            18,
            19,
            20,
            21,
            22,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            33,
            36,
            38,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            59,
            60,
            61,
            62,
            64,
            65,
            66,
            67,
            68,
            71,
            73,
            75,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            89,
            90,
            91,
            93,
            94,
            96,
            97,
            98,
            99,
            102,
            103,
            104,
            105,
            106,
            107,
            109,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            125,
            127
        ],
        "rewards": [
            [
                2.9023133690980155e-06,
                8.315280276626197e-07,
                9.422445939054222e-07,
                4.4508510499849186e-07,
                5.715006514151423e-07,
                2.3823688159291947e-07,
                3.288749065423109e-06,
                3.9278634073732336e-07,
                3.059023363207381e-07,
                3.0590237279032884e-07
            ],
            [
                4.53978524104898e-05,
                2.1024334103352274e-07,
                3.927861066170637e-07,
                3.4663249714451116e-07,
                5.04347348070562e-07,
                4.450849458179853e-07,
                5.043474081993875e-07,
                1.2098659719757836e-06,
                3.059021904559123e-07,
                4.450851580555361e-07
            ],
            [
                1.6701417863559525e-05,
                5.04347528446051e-07,
                8.93969950132721e-06,
                3.288747889284851e-06,
                1.1478768126057254e-05,
                9.422447062270609e-07,
                1.2098659719788098e-06,
                1.0677028700422047e-06,
                NaN,
                1.5534975693979422e-06
            ],
            [
                3.2887506336235617e-06,
                3.72663883989755e-06,
                3.2887502415767434e-06,
                2.5612819054133693e-06,
                6.475950298011458e-07,
                2.5612834320563895e-06,
                3.4663278639892215e-07,
                2.902313023130843e-06,
                NaN,
                3.726637951387472e-06
            ],
            [
                7.338207180898968e-07,
                5.715006514176113e-07,
                NaN,
                6.475946438055299e-07,
                7.338208055664991e-07,
                5.71500719545698e-07,
                7.338211554783522e-07,
                7.338209805240734e-07,
                5.715005832895975e-07,
                1.855391681906175e-07
            ],
            [
                1.3709578605729614e-06,
                1.209865539295696e-06,
                2.561283432035425e-06,
                1.0677032518748838e-06,
                4.222833947960866e-06,
                1.3709567165579959e-06,
                2.561283432005142e-06,
                1.067702870039777e-06,
                6.475948754012522e-07,
                2.9023119851781017e-06
            ],
            [
                2.2603240284371276e-06,
                3.288750241561788e-06,
                1.7603432133296774e-06,
                2.9023119851781017e-06,
                2.9023119851781017e-06,
                2.2603234895289998e-06,
                2.2603240284371276e-06,
                2.561281600076256e-06,
                5.4222209089700225e-06,
                4.785093924362895e-06
            ],
            [
                3.05902263391829e-07,
                7.338211554783522e-07,
                5.043476486924565e-07,
                3.927860597935108e-07,
                1.7603440527222532e-06,
                5.715007195447234e-07,
                8.315280276607289e-07,
                1.8553914607267268e-07,
                4.450852111148132e-07,
                5.715003107767143e-07
            ],
            [
                1.7603430034867993e-06,
                NaN,
                3.726637951387472e-06,
                1.4449800373065699e-07,
                2.561282210740037e-06,
                NaN,
                1.9947306726594253e-06,
                7.338213304316717e-07,
                5.715005832886879e-07,
                1.2098658277451275e-06
            ],
            [
                5.715003107767143e-07,
                3.288748281329893e-06,
                8.939697369980456e-06,
                5.715006514176113e-07,
                3.2887506336235617e-06,
                8.939699501416646e-06,
                7.889260704968913e-06,
                3.726637951387472e-06,
                9.422443692555439e-07,
                1.3709575337159875e-06
            ],
            [
                7.338212429537553e-07,
                2.3823685319244518e-07,
                2.10243290909724e-07,
                5.04347287955046e-07,
                2.6995774527718623e-07,
                7.33821330437595e-07,
                2.6995771309523475e-07,
                2.5612828213934817e-06,
                1.855391239544352e-07,
                2.382369951932796e-07
            ],
            [
                8.315281267861397e-07,
                1.6701429808632785e-05,
                9.422448185510695e-07,
                2.9023119851635836e-06,
                2.561282516066741e-06,
                NaN,
                2.5612812947508257e-06,
                9.422445939032799e-07,
                1.5534975693933505e-06,
                9.422448185478557e-07
            ],
            [
                2.6995790618469934e-07,
                9.422447062270609e-07,
                6.475947982037486e-07,
                2.2603253756874524e-06,
                3.288748281329893e-06,
                1.8925143729575624e-05,
                NaN,
                2.260324567337161e-06,
                4.785094494783494e-06,
                6.1441746020359e-06
            ],
            [
                1.3709575337125585e-06,
                1.5534977545886537e-06,
                7.338208930460318e-07,
                1.0677028700422047e-06,
                2.561281294760143e-06,
                5.715003107767143e-07,
                1.5534981249697903e-06,
                2.2603253756956754e-06,
                2.9023116392097746e-06,
                9.422450432014836e-07
            ],
            [
                1.7603436329978976e-06,
                4.450848927637999e-07,
                1.7603438428800754e-06,
                5.043474081993875e-07,
                3.059022269250683e-07,
                1.9947301970972664e-06,
                7.889264466868659e-06,
                3.2887506336235617e-06,
                7.338213304316717e-07,
                8.315283250371857e-07
            ],
            [
                NaN,
                3.4663278639892215e-07,
                1.0677024881980089e-06,
                1.5534973842076057e-06,
                1.760343633031919e-06,
                9.422444815792981e-07,
                2.2603242978665707e-06,
                2.5612828213934817e-06,
                1.5534979397790343e-06,
                9.422450432014836e-07
            ],
            [
                1.7603434231833873e-06,
                4.450851580469341e-07,
                4.450849988811838e-07,
                5.043475284430694e-07,
                2.699578740011634e-07,
                2.4300237837960777e-05,
                1.2098655392811161e-06,
                1.0677032518814388e-06,
                2.6995771309523475e-07,
                7.338212429582604e-07
            ],
            [
                5.715007195447234e-07,
                3.466325797896173e-07,
                2.2603245673443566e-06,
                2.5612819054133693e-06,
                3.9278605979534166e-07,
                1.9947304348862686e-06,
                6.475947982037486e-07,
                3.05902190458764e-07,
                3.288749457469787e-06,
                5.04347287955046e-07
            ],
            [
                3.9278610661902853e-07,
                1.8925145985895816e-05,
                1.637377448057981e-07,
                3.466326211113502e-07,
                8.315279285351409e-07,
                1.7603430034867993e-06,
                5.043475885674441e-07,
                5.043472879525233e-07,
                8.315281267861397e-07,
                2.69957906184239e-07
            ],
            [
                8.315277302747361e-07,
                2.699577774585891e-07,
                5.043472879504592e-07,
                3.05902190458764e-07,
                3.059023363190688e-07,
                7.88926446679691e-06,
                2.699578740011634e-07,
                2.6995771309523475e-07,
                1.3709572068522336e-06,
                3.466327863961242e-07
            ],
            [
                6.144175334239434e-06,
                2.902311639183378e-06,
                1.5534975693869924e-06,
                9.422444815792981e-07,
                1.7603432133296774e-06,
                4.222833444590791e-06,
                2.902312331081799e-06,
                8.315278294072958e-07,
                1.994729721482609e-06,
                7.338212429562581e-07
            ],
            [
                2.3823702359290413e-07,
                4.785096776468749e-06,
                1.0677026154806063e-06,
                9.422449308774482e-07,
                1.4449795205429202e-07,
                5.422217030707961e-06,
                1.760343213335281e-06,
                2.5612819054133693e-06,
                NaN,
                1.994730197090463e-06
            ],
            [
                5.043475885674441e-07,
                3.7266397283908927e-06,
                1.2098661162056318e-06,
                7.338210679979539e-07,
                5.04347348075149e-07,
                2.2603234895289998e-06,
                7.338209805240734e-07,
                1.2098658277264215e-06,
                4.450848927658745e-07,
                5.04347528440776e-07
            ],
            [
                6.475946438055299e-07,
                NaN,
                2.3823693839325527e-07,
                3.059021175247079e-07,
                9.422445939054222e-07,
                6.475947982037486e-07,
                1.6373764720990908e-07,
                3.466326211113502e-07,
                3.4663274507713016e-07,
                8.315277302857965e-07
            ],
            [
                1.2098659719757836e-06,
                1.9947304348703948e-06,
                1.5534973842030142e-06,
                2.6995771309523475e-07,
                1.5534981249574276e-06,
                9.422443692489024e-07,
                5.422218969895357e-06,
                1.0677032518700286e-06,
                1.7603434231777837e-06,
                1.7603434231705793e-06
            ],
            [
                6.962257079832313e-06,
                NaN,
                2.430024073461624e-05,
                NaN,
                1.3709568799679844e-06,
                1.4738985486506781e-05,
                6.144175334418252e-06,
                5.422220909009474e-06,
                3.2887494574518405e-06,
                6.962257909785973e-06
            ],
            [
                1.5534971990126997e-06,
                1.9947297215125433e-06,
                1.9947292459347367e-06,
                5.422220909009474e-06,
                NaN,
                1.3709572068522336e-06,
                7.889266347715168e-06,
                7.889263526345123e-06,
                NaN,
                1.3709572068522336e-06
            ],
            [
                1.5534971990169383e-06,
                8.939694172957213e-06,
                1.2098659719788098e-06,
                1.1253512180925583e-07,
                4.4508515805735777e-07,
                NaN,
                3.927863875616689e-07,
                1.209865827752005e-06,
                2.9023116392097746e-06,
                NaN
            ],
            [
                2.9023119851781017e-06,
                5.715005832853093e-07,
                1.3709568799679844e-06,
                5.422220909009474e-06,
                2.2603237589676295e-06,
                3.726638395611981e-06,
                6.475945666051092e-07,
                3.2887506336086064e-06,
                2.260324836776948e-06,
                2.902312331125353e-06
            ],
            [
                3.466327037539638e-07,
                9.422448185510695e-07,
                9.422445939032799e-07,
                7.338207180864763e-07,
                1.9947299593014888e-06,
                1.3709567165579959e-06,
                1.2098656835076114e-06,
                2.699578096393206e-07,
                4.4508526417298334e-07,
                8.315277302841894e-07
            ],
            [
                2.2603248367173307e-06,
                1.7603440527046419e-06,
                1.5534981249574276e-06,
                8.93969736955767e-06,
                3.288750241500471e-06,
                3.726638395611981e-06,
                2.90231233114251e-06,
                1.3709567165530083e-06,
                2.902312677137316e-06,
                6.962256249885085e-06
            ],
            [
                1.3709572068522336e-06,
                2.5612834320470717e-06,
                1.1478769494396542e-05,
                5.8291293344700434e-05,
                1.209865539295696e-06,
                1.3709567165579959e-06,
                1.3709567165617364e-06,
                1.0677026154806063e-06,
                1.2098659719757836e-06,
                2.2603237589676295e-06
            ],
            [
                1.2098656835136636e-06,
                3.05902190458764e-07,
                1.8553910183674878e-07,
                1.994730197090463e-06,
                2.1024336609874897e-07,
                8.315277302857965e-07,
                3.05902336324494e-07,
                NaN,
                3.4663257978780455e-07,
                4.4508515805735777e-07
            ],
            [
                1.0129989772412744e-05,
                3.288749457409966e-06,
                1.2098662604247682e-06,
                7.889260704968913e-06,
                1.994730434847717e-06,
                1.994729008145876e-06,
                7.889261645427538e-06,
                9.610241501774589e-05,
                2.2603248367949354e-06,
                1.147877359957198e-05
            ],
            [
                1.3709568799919866e-06,
                3.059022998576899e-07,
                3.2887498495150166e-06,
                2.6995784182140636e-07,
                4.785093924362895e-06,
                NaN,
                NaN,
                1.8553916819032217e-07,
                1.994729483723626e-06,
                NaN
            ],
            [
                8.764254764780641e-08,
                3.4663249714612693e-07,
                3.466326624336003e-07,
                NaN,
                1.637376862489725e-07,
                7.338207180898968e-07,
                2.6995784182140636e-07,
                4.450851049991497e-07,
                3.927863875616689e-07,
                1.4449798650569826e-07
            ],
            [
                5.043476486915964e-07,
                1.2098659719716573e-06,
                5.715005832853093e-07,
                5.043476486915964e-07,
                8.315284241650899e-07,
                1.5534977545886537e-06,
                5.043472879525233e-07,
                1.7603425837791042e-06,
                5.043476486902204e-07,
                8.31527928532683e-07
            ],
            [
                2.9023112932177327e-06,
                5.715005832886879e-07,
                2.5612812947508257e-06,
                5.04347468323289e-07,
                2.2603234895372223e-06,
                1.3709572068522336e-06,
                1.3709576971379186e-06,
                1.3709575337078829e-06,
                3.726639728370556e-06,
                6.144173869558639e-06
            ],
            [
                3.0590237279085045e-07,
                NaN,
                8.31528325040778e-07,
                9.422443692574719e-07,
                1.9947292459347367e-06,
                1.3709573702822306e-06,
                4.450852111148132e-07,
                1.5534983101602148e-06,
                2.382370235933104e-07,
                7.338207180898968e-07
            ],
            [
                1.3709568799592562e-06,
                2.902312677150514e-06,
                1.0677028700422047e-06,
                3.9278615344178325e-07,
                6.475951070002966e-07,
                8.31527928532683e-07,
                2.902312331170226e-06,
                4.785095065232451e-06,
                7.338210679979539e-07,
                2.260325106237323e-06
            ],
            [
                3.4663262110945863e-07,
                NaN,
                6.47595107001401e-07,
                2.6995771309523475e-07,
                9.422447062270609e-07,
                1.2098659719757836e-06,
                NaN,
                1.6373770576776313e-07,
                3.2887506336235617e-06,
                1.2098661162023305e-06
            ],
            [
                4.785096206047877e-06,
                2.1024331597152624e-07,
                5.422220909009474e-06,
                5.043472879540142e-07,
                6.475947210031623e-07,
                1.9947299593078385e-06,
                NaN,
                6.475946438055299e-07,
                2.2603234895372223e-06,
                3.2887502415767434e-06
            ],
            [
                NaN,
                0.9999798543164616,
                5.043473480777865e-07,
                NaN,
                NaN,
                2.430024942462891e-05,
                2.9023112932177327e-06,
                4.785092783454444e-06,
                NaN,
                3.288750241561788e-06
            ],
            [
                8.315281267882195e-07,
                2.9023133690980155e-06,
                5.715005832853093e-07,
                8.315284241665078e-07,
                8.315284241650899e-07,
                3.288749065406658e-06,
                6.144173869558639e-06,
                9.422448185510695e-07,
                8.315283250371857e-07,
                1.2098659719757836e-06
            ],
            [
                NaN,
                9.422442569315887e-07,
                2.5612819054028872e-06,
                3.7266397283908927e-06,
                1.9947299593014888e-06,
                9.422444815726566e-07,
                1.1478764020372226e-05,
                7.88926446679691e-06,
                8.315279285370317e-07,
                4.2228339479858295e-06
            ],
            [
                1.8925141473978602e-05,
                2.260324567337161e-06,
                3.535625071602016e-05,
                2.90231094723893e-06,
                2.561282210740037e-06,
                2.5612831267202583e-06,
                3.288748673360027e-06,
                9.422443692555439e-07,
                6.475949526020042e-07,
                2.2603234895289998e-06
            ],
            [
                NaN,
                1.2098656835224664e-06,
                NaN,
                2.561281600086738e-06,
                6.962255419931625e-06,
                1.7603430034867993e-06,
                NaN,
                4.785092783519724e-06,
                NaN,
                NaN
            ],
            [
                5.715005151606823e-07,
                9.422447062294175e-07,
                4.450852111155216e-07,
                1.5534971990169383e-06,
                8.315281267882195e-07,
                2.430024073461624e-05,
                2.2603253756956754e-06,
                1.994729008145876e-06,
                6.475949526020042e-07,
                4.4508515805735777e-07
            ],
            [
                2.561282210740037e-06,
                5.715005151574337e-07,
                3.4663274507713016e-07,
                4.450848927650143e-07,
                5.715005832895975e-07,
                1.2098653950606901e-06,
                1.2098659719788098e-06,
                2.902312677150514e-06,
                3.927862470899887e-07,
                5.04347528446051e-07
            ],
            [
                3.466325797896173e-07,
                1.0677031245990084e-06,
                2.3823693839325527e-07,
                1.0677029973219343e-06,
                2.3823696679327928e-07,
                6.475951069985296e-07,
                3.059021175261338e-07,
                3.9278615344178325e-07,
                2.1024339116168358e-07,
                1.6373762769138607e-07
            ],
            [
                2.5612831267202583e-06,
                1.5534971990126997e-06,
                4.785093924362895e-06,
                4.222832941193893e-06,
                3.466327863961242e-07,
                1.1478765389368729e-05,
                1.370957370247318e-06,
                4.450848927650143e-07,
                1.1478770862735993e-05,
                4.222834954778007e-06
            ],
            [
                1.2098659719757836e-06,
                1.4738989000422955e-05,
                1.2098662604247682e-06,
                9.422445939054222e-07,
                7.338209805224048e-07,
                6.475949526020042e-07,
                1.3709567165579959e-06,
                1.2098661161927025e-06,
                9.422450431989127e-07,
                6.144176799334096e-06
            ],
            [
                2.260324567337161e-06,
                1.3709567165617364e-06,
                1.3709572068522336e-06,
                9.422450431989127e-07,
                6.962255419931625e-06,
                3.288748281329893e-06,
                6.962254589914941e-06,
                4.785094494750855e-06,
                NaN,
                3.2887506336086064e-06
            ],
            [
                9.422444815628016e-07,
                1.2098652508424818e-06,
                NaN,
                1.0677029973219343e-06,
                5.715003107755449e-07,
                9.422448185534261e-07,
                1.994729483729522e-06,
                1.7603438428660665e-06,
                2.2603253756956754e-06,
                4.450850519403407e-07
            ],
            [
                1.2098652508144226e-06,
                3.2887502415767434e-06,
                1.3709567165617364e-06,
                5.04347528446051e-07,
                2.102434162245973e-07,
                1.0677026154806063e-06,
                NaN,
                2.2603237589542675e-06,
                1.3709567165617364e-06,
                2.699578740032504e-07
            ],
            [
                1.3709576971425944e-06,
                1.1253518888531272e-07,
                5.043476486924565e-07,
                6.962255419931625e-06,
                3.4663274507713016e-07,
                1.637377448057981e-07,
                1.3709568799919866e-06,
                1.8553910183607374e-07,
                1.5534975693933505e-06,
                4.4508505193791187e-07
            ],
            [
                1.370957860567974e-06,
                1.3709567165617364e-06,
                5.043473480777865e-07,
                NaN,
                3.059022998569248e-07,
                3.2887482813149375e-06,
                1.5534981249697903e-06,
                3.927862002625787e-07,
                2.1444940745839484e-05,
                7.338213304363436e-07
            ],
            [
                7.338209805240734e-07,
                6.475949526003845e-07,
                8.315277302841894e-07,
                3.466326211113502e-07,
                2.90231094723893e-06,
                3.9278634073732336e-07,
                8.939693107190907e-06,
                2.902312331125353e-06,
                6.475950297971703e-07,
                1.7603434231777837e-06
            ],
            [
                3.4663253846718004e-07,
                3.9278610661902853e-07,
                1.1253516205427619e-07,
                2.699576809143613e-07,
                3.927863875616689e-07,
                3.466326211113502e-07,
                5.715007195447234e-07,
                5.043472879540142e-07,
                8.315281267800897e-07,
                2.6995774527718623e-07
            ],
            [
                6.475949526003845e-07,
                2.5612812947077304e-06,
                1.3709572068522336e-06,
                3.2887482812745586e-06,
                2.902312677137316e-06,
                2.902312331170226e-06,
                1.9947304348862686e-06,
                1.553497199007048e-06,
                1.2098656835224664e-06,
                5.422220909009474e-06
            ],
            [
                1.5534971990126997e-06,
                5.144223206152219e-05,
                2.9023119851635836e-06,
                8.939695238536645e-06,
                NaN,
                8.939698435657833e-06,
                1.5534981249697903e-06,
                8.939696304213768e-06,
                4.785094494783494e-06,
                1.3007131566015624e-05
            ],
            [
                5.04347348075149e-07,
                2.6995777745711594e-07,
                1.2098659719716573e-06,
                2.3823685319244518e-07,
                1.0677029973192638e-06,
                3.9278605979208185e-07,
                2.1024344128584085e-07,
                7.338213304283347e-07,
                4.450848927650143e-07,
                3.4663253846718004e-07
            ],
            [
                3.2887502415438413e-06,
                1.9947294837154625e-06,
                8.315278294072958e-07,
                1.2098653950656417e-06,
                2.2603242978778778e-06,
                1.0677032518700286e-06,
                6.47594952595231e-07,
                1.2098661161927025e-06,
                5.422218323487975e-06,
                1.2098653950656417e-06
            ],
            [
                4.2228334445370225e-06,
                6.475945666063607e-07,
                3.466327037539638e-07,
                3.726638839833152e-06,
                3.726637951387472e-06,
                9.422448185534261e-07,
                2.1444953527476883e-05,
                1.0677024882009222e-06,
                1.147877359957198e-05,
                3.4663249714612693e-07
            ],
            [
                3.927860597935108e-07,
                2.7535700947920753e-05,
                2.1024331597262577e-07,
                3.059022998576899e-07,
                1.1478768125577027e-05,
                NaN,
                1.670142383595838e-05,
                2.6995771309523475e-07,
                NaN,
                2.5612812947380135e-06
            ],
            [
                6.475947210012481e-07,
                5.043472879525233e-07,
                1.0677024881980089e-06,
                4.450848927637999e-07,
                4.4508526417014975e-07,
                8.315283250371857e-07,
                6.475947210031623e-07,
                6.475949525981759e-07,
                2.1024334103505245e-07,
                1.5534975693869924e-06
            ],
            [
                8.939693107190907e-06,
                1.2098652508391807e-06,
                6.962257909785973e-06,
                7.338207180838067e-07,
                6.47595107001401e-07,
                1.760342793638743e-06,
                1.2098658277451275e-06,
                1.5534975693979422e-06,
                3.288749065423109e-06,
                NaN
            ],
            [
                1.147877359957198e-05,
                5.4222183235249605e-06,
                1.4738987243478167e-05,
                8.315277302841894e-07,
                2.561282210740037e-06,
                3.9278610661902853e-07,
                1.2098662604291696e-06,
                1.7603430034867993e-06,
                1.7603425837903113e-06,
                1.5534973842030142e-06
            ],
            [
                5.04347287955046e-07,
                5.043473480777865e-07,
                5.043474683220276e-07,
                3.927862470899887e-07,
                5.715005832872586e-07,
                5.715003789033962e-07,
                3.72663883989755e-06,
                2.102434412875379e-07,
                8.315278294097538e-07,
                1.3709567165617364e-06
            ],
            [
                7.338212429582604e-07,
                4.785095635655362e-06,
                1.3709576971425944e-06,
                4.785095635655362e-06,
                1.1478764020883773e-05,
                6.144177531767002e-06,
                5.4222183235249605e-06,
                1.3709576971425944e-06,
                2.2603234895289998e-06,
                6.962254589978262e-06
            ],
            [
                2.7535700948722127e-05,
                1.5534979397790343e-06,
                6.475950297971703e-07,
                1.3709572068522336e-06,
                1.0677029973192638e-06,
                3.4663278639892215e-07,
                4.222832941193893e-06,
                8.315283250394546e-07,
                1.3709576971379186e-06,
                4.222831934379152e-06
            ],
            [
                3.726639728370556e-06,
                3.05902263391829e-07,
                4.4508494582405734e-07,
                7.338208055680009e-07,
                0.999876605413428,
                6.475949526020042e-07,
                4.450852111148132e-07,
                5.715004470313855e-07,
                3.466325797896173e-07,
                7.338209805240734e-07
            ],
            [
                2.902313023130843e-06,
                3.927862002641863e-07,
                5.043475885674441e-07,
                5.043474683204221e-07,
                2.1024339116168358e-07,
                2.902312331170226e-06,
                3.059021175261338e-07,
                6.475950297942253e-07,
                6.475948754012522e-07,
                NaN
            ],
            [
                1.2098653950692178e-06,
                NaN,
                1.760343213335281e-06,
                NaN,
                2.2603248367949354e-06,
                5.04347468323289e-07,
                1.5534975693979422e-06,
                NaN,
                3.288748673376478e-06,
                1.2098652508391807e-06
            ],
            [
                1.7603434231833873e-06,
                2.1024339116168358e-07,
                8.939696304116203e-06,
                3.9278615344178325e-07,
                3.05902190458764e-07,
                4.785094494811783e-06,
                4.450848927658745e-07,
                4.4508505193791187e-07,
                7.338209805224048e-07,
                5.715003107767143e-07
            ],
            [
                2.3823690999063455e-07,
                2.1024341622368903e-07,
                5.715005832827105e-07,
                5.043474081993875e-07,
                3.059023727894942e-07,
                2.6995790618350237e-07,
                7.734416698849138e-08,
                1.0677026154827912e-06,
                NaN,
                1.8553910183607374e-07
            ],
            [
                2.9023116392097746e-06,
                2.6995774527718623e-07,
                1.8553905760062447e-07,
                4.450852111148132e-07,
                4.450848927621807e-07,
                1.760342793638743e-06,
                9.422443692574719e-07,
                9.93120161310289e-08,
                2.699576809143613e-07,
                2.6995790618350237e-07
            ],
            [
                8.315278294038928e-07,
                5.715006513952608e-07,
                3.0590215399183813e-07,
                5.043474683204221e-07,
                7.338211554783522e-07,
                3.4663262110803996e-07,
                3.4663274507287414e-07,
                7.338209805200689e-07,
                3.466326624322211e-07,
                1.3709568799679844e-06
            ],
            [
                4.785095635655362e-06,
                4.785095635655362e-06,
                4.222834954801051e-06,
                NaN,
                1.370957860576702e-06,
                6.475946438055299e-07,
                1.3709572068522336e-06,
                3.2887502415767434e-06,
                1.9947297215125433e-06,
                1.7603438428800754e-06
            ],
            [
                2.699578740011634e-07,
                2.2603237589779086e-06,
                5.04347528446051e-07,
                1.3709570434178922e-06,
                1.3709572068522336e-06,
                1.99472900813862e-06,
                7.338211554783522e-07,
                6.475947982002148e-07,
                3.927860597945825e-07,
                1.3709573702722555e-06
            ],
            [
                1.4738989000422955e-05,
                2.902312677137316e-06,
                7.889260704968913e-06,
                2.2603234895176927e-06,
                1.3709567165579959e-06,
                6.475946437966953e-07,
                2.260324028427877e-06,
                1.994730197071414e-06,
                9.422447062202052e-07,
                1.3709568799823232e-06
            ],
            [
                NaN,
                1.9947299592933255e-06,
                4.4508494582405734e-07,
                8.315279285351409e-07,
                1.9947299593078385e-06,
                1.0677027427569065e-06,
                NaN,
                3.288749849498565e-06,
                7.338210680021253e-07,
                5.043473480777865e-07
            ],
            [
                4.450852641737424e-07,
                2.2603234895176927e-06,
                8.315278294072958e-07,
                7.338208930391909e-07,
                NaN,
                8.315281267834927e-07,
                6.475949526020042e-07,
                3.466325797900508e-07,
                1.7603434231833873e-06,
                4.450848927637999e-07
            ],
            [
                1.2098658277451275e-06,
                8.315284241597959e-07,
                5.043474683220276e-07,
                3.466327037539638e-07,
                1.2098662604291696e-06,
                3.0590215399183813e-07,
                1.2751899728286965e-07,
                5.4222183235249605e-06,
                5.422221555414699e-06,
                1.2098662604291696e-06
            ],
            [
                1.6373764721072816e-07,
                1.2098656835224664e-06,
                8.315279285351409e-07,
                1.7603440527286572e-06,
                3.9278605979534166e-07,
                3.466325797896173e-07,
                5.715005832886879e-07,
                1.5534981249697903e-06,
                3.288747889284851e-06,
                2.3823690999290963e-07
            ],
            [
                3.288750241561788e-06,
                7.338207180864763e-07,
                2.260324028427877e-06,
                6.144173137126169e-06,
                NaN,
                3.2887498495150166e-06,
                1.5534973842076057e-06,
                6.144177531767002e-06,
                1.5534973842076057e-06,
                NaN
            ],
            [
                2.3823688159291947e-07,
                1.7603438428800754e-06,
                3.0590237279085045e-07,
                5.715005151606823e-07,
                4.4508510499849186e-07,
                3.059021175261338e-07,
                3.9278610661902853e-07,
                2.102434162245973e-07,
                1.855391239544352e-07,
                5.04347468323289e-07
            ],
            [
                7.889261645427538e-06,
                5.715002426486762e-07,
                2.3823693839290317e-07,
                1.994729721518893e-06,
                6.962255419931625e-06,
                5.043472278322555e-07,
                1.209865539295696e-06,
                1.5534983101602148e-06,
                2.561282210740037e-06,
                7.889264466868659e-06
            ],
            [
                NaN,
                8.939695238634211e-06,
                2.2603248367949354e-06,
                3.288749457469787e-06,
                1.3709575337159875e-06,
                1.7603438428800754e-06,
                2.4300243631890864e-05,
                1.3709572068522336e-06,
                1.5534979397829198e-06,
                NaN
            ]
        ]
    },
    {
        "q_id": "9701_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3709573702822306e-06,
                5.043476486924565e-07,
                5.043473480777865e-07,
                2.699577774585891e-07,
                3.9278634073732336e-07,
                7.338210680021253e-07,
                5.422218969895357e-06,
                5.04347287955046e-07,
                1.209866260432471e-06,
                4.450852111148132e-07
            ],
            [
                1.370957860576702e-06,
                1.012998977264307e-05,
                0.9999993524054338,
                1.1478770862882149e-05,
                0.9999994956524718,
                1.2098661162056318e-06,
                4.785095065232451e-06,
                9.422445939054222e-07,
                2.2603251062450327e-06,
                0.9999997617630617
            ],
            [
                5.715003107715166e-07,
                2.9023133690980155e-06,
                2.260323758987159e-06,
                8.315280276626197e-07,
                1.209865539295696e-06,
                1.0677032518814388e-06,
                3.7266401725935817e-06,
                9.422443692555439e-07,
                1.994730434879465e-06,
                1.1478768125911099e-05
            ],
            [
                1.637377448057981e-07,
                6.825601283086733e-08,
                5.715006514167015e-07,
                3.2887502415767434e-06,
                1.209865827752005e-06,
                2.430025232128576e-05,
                6.47595107001401e-07,
                2.5612831267202583e-06,
                1.3709572068522336e-06,
                4.4508494582405734e-07
            ],
            [
                0.9999996072137062,
                0.9999997617631469,
                0.9999994956524717,
                0.9999997463981032,
                0.9999997300423192,
                0.9999993106387904,
                0.9999997463981334,
                0.9999998642567028,
                0.9999996310114161,
                0.999999653367379
            ],
            [
                5.043473480777865e-07,
                8.315281267882195e-07,
                2.2603242978871282e-06,
                1.6373776432509826e-07,
                2.6995784182140636e-07,
                7.734421308914719e-08,
                5.715005832895975e-07,
                9.422445939054222e-07,
                5.715006514176113e-07,
                9.422443692574719e-07
            ],
            [
                1.7603434231833873e-06,
                9.422450432014836e-07,
                8.315283250371857e-07,
                1.9947304348862686e-06,
                5.715004470313855e-07,
                1.2098656835224664e-06,
                7.338213304363436e-07,
                2.5612819054028872e-06,
                5.715007195447234e-07,
                7.889260704968913e-06
            ],
            [
                0.9999991148433867,
                0.9999988634360191,
                1.3007125363908762e-05,
                0.9999999559305891,
                1.5534975693979422e-06,
                0.9999998461826038,
                0.9999999067050276,
                2.90231094723893e-06,
                6.962256249885085e-06,
                5.4222183235249605e-06
            ],
            [
                7.889265407255982e-06,
                0.9999990577555189,
                2.1444950971601277e-05,
                2.753569766795419e-05,
                0.9999952149060793,
                0.9999993524048931,
                0.9999989969860317,
                0.9999994631250603,
                1.012999581057419e-05,
                0.9999995262093858
            ],
            [
                NaN,
                5.4222183235249605e-06,
                1.6701423836262173e-05,
                5.4222176771176554e-06,
                4.785096776499213e-06,
                6.144174601991196e-06,
                1.8925145985895816e-05,
                1.3709567165530083e-06,
                1.3007126914612648e-05,
                1.5534979397740895e-06
            ],
            [
                3.466325797896173e-07,
                3.4663278639892215e-07,
                3.05902190458764e-07,
                3.4663278639892215e-07,
                8.7642558095602e-08,
                4.4508494582314646e-07,
                4.450848927650143e-07,
                9.422447062294175e-07,
                3.2887502415767434e-06,
                1.3007130015677909e-05
            ],
            [
                0.9999998724808964,
                0.9999992661787576,
                0.9999998642566704,
                0.9999998874648246,
                1.0,
                1.0,
                0.9999999176675142,
                0.9999998724809723,
                0.9999999358794021,
                0.9999999530883675
            ],
            [
                0.9999999176674454,
                0.9999997897565588,
                2.144495864106235e-05,
                0.9999996743688199,
                0.9999998942830862,
                0.9999994956523514,
                0.9999996743686645,
                0.999999428499485,
                0.9999997126314469,
                0.9999995262094422
            ],
            [
                3.9278629391427843e-07,
                1.8553919030776337e-07,
                4.450850519403407e-07,
                9.422443692555439e-07,
                3.927862002663297e-07,
                1.0677029973219343e-06,
                1.0677026154806063e-06,
                1.8553905760062447e-07,
                5.315781803390236e-08,
                3.46632497145457e-07
            ],
            [
                1.6373762769138607e-07,
                1.3709567165579959e-06,
                6.475947210031623e-07,
                2.382369383923073e-07,
                9.931198061405701e-08,
                1.2098662604247682e-06,
                8.315284241650899e-07,
                9.422450431989127e-07,
                1.6373762769138607e-07,
                3.059021175247079e-07
            ],
            [
                0.9999997300422228,
                0.9999995262096119,
                0.9999998144608541,
                0.9999994284996894,
                0.9999996072137063,
                0.9999998144608981,
                0.999999746398073,
                0.9999996743686645,
                0.9999993524051253,
                0.9999998024945624
            ],
            [
                0.9999997617631186,
                0.9999994956523515,
                0.9999998362622943,
                6.023579219579052e-08,
                0.9999998802069587,
                0.999998126124394,
                2.2603245673443566e-06,
                0.9999998874649185,
                0.9999998724809116,
                0.999999927341827
            ],
            [
                4.2228339479858295e-06,
                0.9999986290427946,
                8.939694172957213e-06,
                0.9999994956526524,
                0.9999994631247406,
                0.9999990577556315,
                0.9999981261239488,
                0.9999992188513906,
                0.9999981261246189,
                0.9999993524048936
            ],
            [
                0.9999999067051165,
                0.9999999226558238,
                1.0,
                0.9999999468421313,
                0.999999939764294,
                0.9999999067050054,
                0.9999998362622358,
                0.9999998362623724,
                1.0,
                0.9999998144609646
            ],
            [
                0.9999987121043247,
                0.9999978766212861,
                0.9999983463110069,
                0.9999970976887134,
                0.9999993916408187,
                0.9999996533674617,
                1.1478765389222573e-05,
                0.9999991148428594,
                6.962259569750576e-06,
                0.9999992661789325
            ],
            [
                0.9999998461826771,
                0.9999988634357484,
                0.9999990577550699,
                0.9999997617630049,
                0.9999993524052795,
                0.9999990577556314,
                0.9999989322970032,
                0.9999999123575882,
                0.9999998555019963,
                2.102434162245973e-07
            ],
            [
                1.0677026154806063e-06,
                3.7266406168624155e-06,
                4.222831934379152e-06,
                7.338207180864763e-07,
                6.475948754012522e-07,
                0.9999992661789324,
                3.726638395611981e-06,
                6.962257079705671e-06,
                6.9622587397397306e-06,
                5.422218323487975e-06
            ],
            [
                1.7603434231833873e-06,
                0.9999969105044528,
                0.9999991684721712,
                1.5534975693979422e-06,
                6.475946438055299e-07,
                3.4663274507713016e-07,
                1.2098659719788098e-06,
                3.05902336324494e-07,
                1.0677029973219343e-06,
                1.0677033791612137e-06
            ],
            [
                1.8553914607267268e-07,
                0.9999997300422548,
                1.209865827752005e-06,
                0.9999996072137062,
                1.1478770862882149e-05,
                8.939700567094277e-06,
                5.715006514176113e-07,
                8.939699501416646e-06,
                0.9999998257021214,
                1.3007123813559956e-05
            ],
            [
                8.315277302857965e-07,
                9.931202796993203e-08,
                3.9278605979534166e-07,
                7.338212429594283e-07,
                2.382370235933104e-07,
                4.450852111155216e-07,
                2.699578740032504e-07,
                2.3823685319320354e-07,
                2.1024336609874897e-07,
                3.927862470905692e-07
            ],
            [
                3.9278610661902853e-07,
                0.9996646498964229,
                0.999999057755294,
                2.6995784182140636e-07,
                1.2098661162056318e-06,
                9.610243794422881e-05,
                0.9999970976883623,
                1.3709572068522336e-06,
                7.338209805240734e-07,
                2.382370235933104e-07
            ],
            [
                0.9999981261246175,
                0.9999997617631184,
                0.9999997300423192,
                0.9999998874648515,
                0.9999999176674945,
                0.9999999559305943,
                0.9999975938982352,
                0.9999998802069873,
                0.9999998642567028,
                0.9999996072138467
            ],
            [
                0.9999997463980729,
                0.9999983463102176,
                1.2751902768612997e-07,
                5.715006514176113e-07,
                0.9999997300421581,
                7.338208930460318e-07,
                1.5534983101602148e-06,
                3.927863407379485e-07,
                4.450852111155216e-07,
                2.1024339116168358e-07
            ],
            [
                0.9999988634358842,
                0.9999999397643083,
                0.9999998874648648,
                0.9999993106392014,
                0.9999993916408187,
                0.9999999123574733,
                0.9999991148429646,
                0.9999995262096117,
                0.9999998642566866,
                0.9999993916409636
            ],
            [
                0.9999984465026165,
                3.535625914621054e-05,
                1.147877359957198e-05,
                0.9999916019259781,
                0.9999892166878009,
                0.9999993916409636,
                0.9999996072136126,
                0.9999983463096269,
                0.00010889690936027806,
                0.9999994956524115
            ],
            [
                0.9999993916409636,
                6.47595107001401e-07,
                2.3823693839325527e-07,
                3.466327037553825e-07,
                0.9999995818811774,
                6.962256249935742e-06,
                3.9278620026686556e-07,
                0.9999985406241276,
                1.3709575337159875e-06,
                1.5534983101644536e-06
            ],
            [
                0.9999997300422226,
                0.9999997463981637,
                0.9999998144609424,
                0.9999996072137062,
                0.9999996743687424,
                0.9999997300421261,
                0.9999993916408185,
                0.9999995818812771,
                0.9999998461826956,
                0.9999998024946566
            ],
            [
                0.9999999176675632,
                0.9999993524049705,
                0.9999998024947038,
                0.9999998024947037,
                0.9999991684720722,
                0.9999997126315496,
                0.999999917667524,
                0.9999995818813269,
                0.9999999123575464,
                0.999998629042304
            ],
            [
                0.9999996072137063,
                0.9999998144609203,
                0.9999997617631469,
                0.9999998942829098,
                0.9999997761971583,
                0.9999997761972117,
                0.9999997761971849,
                0.9999994284996215,
                0.9999998555019619,
                0.9999998024947272
            ],
            [
                3.466325797896173e-07,
                1.0677029973219343e-06,
                3.05902263391829e-07,
                2.5612831267202583e-06,
                8.315280276626197e-07,
                2.260323758987159e-06,
                1.9947304348862686e-06,
                0.9999972735303826,
                1.994729483729522e-06,
                3.059022998581767e-07
            ],
            [
                4.4508515805735777e-07,
                7.889266347786918e-06,
                3.9278610661902853e-07,
                3.0590237279085045e-07,
                5.715003107767143e-07,
                0.9999998802069731,
                3.9278610661902853e-07,
                4.4508515805735777e-07,
                1.209865827752005e-06,
                1.4449798650551755e-07
            ],
            [
                7.889261645269683e-06,
                6.144175334468545e-06,
                1.6701421845057263e-05,
                3.7266401726359486e-06,
                1.1478770862882149e-05,
                2.430024073523505e-05,
                2.2603251062450327e-06,
                1.8925143729954285e-05,
                6.144173869603344e-06,
                2.260323758987159e-06
            ],
            [
                0.9999997897567343,
                0.9999994631247403,
                2.3823696679327928e-07,
                0.9999999468421756,
                0.999999894283061,
                0.9999999123575986,
                1.0,
                0.9999952149037987,
                0.9999999586006492,
                0.9999996072137063
            ],
            [
                1.0,
                1.0,
                0.9999999434137637,
                0.9999999317439302,
                1.0,
                0.9999995818813269,
                0.9999999067050609,
                0.9999993106389548,
                0.9999999006879721,
                0.9999999397642868
            ],
            [
                0.9999998724809419,
                8.93969950132721e-06,
                0.9999998642567028,
                5.04347287955046e-07,
                0.9999998362622553,
                0.9999998555019619,
                0.9999998362623138,
                2.102434412875379e-07,
                0.999999114842648,
                0.9999998024945624
            ],
            [
                6.144176799334096e-06,
                1.0129989772412744e-05,
                1.0129989772412744e-05,
                NaN,
                3.288747889229516e-06,
                2.430023204460668e-05,
                3.726638395611981e-06,
                1.0677028700363782e-06,
                6.9622579096593295e-06,
                1.4738981972082061e-05
            ],
            [
                0.9999977396765138,
                0.999999310639037,
                0.9999990577552945,
                0.9999998461826956,
                0.9999996743688586,
                0.9999998642566219,
                0.9999998724809267,
                0.9999998555019447,
                0.9999998257021213,
                0.9999998144608319
            ],
            [
                0.9999999317440035,
                0.9999997300421261,
                0.9999997761970782,
                0.9999999226557685,
                0.9999996310115039,
                0.999999554914736,
                0.9999998802069731,
                0.9999999067050387,
                0.9999997617630617,
                0.9999994631251243
            ],
            [
                1.2098652508391807e-06,
                5.715003107755449e-07,
                3.0590237279085045e-07,
                3.0590237279032884e-07,
                3.9278610661902853e-07,
                9.422445939032799e-07,
                1.0677027427600627e-06,
                3.4663249714612693e-07,
                1.8553916819032217e-07,
                6.475947210046347e-07
            ],
            [
                0.9999999123575359,
                0.9999995818813269,
                0.9999995262093857,
                0.9999996743688198,
                0.99999926617867,
                0.9999996072137062,
                0.9999998874648915,
                0.9999998724808964,
                0.999999607213753,
                0.9999992661789323
            ],
            [
                0.9999981261241706,
                0.9999994631251884,
                0.9999990577554069,
                0.9999977396748959,
                0.9999987901346056,
                1.6701421843720577e-05,
                0.9999861539888927,
                2.9023130230846496e-06,
                5.715003107755449e-07,
                2.1444953527476883e-05
            ],
            [
                5.04347528446051e-07,
                4.2228339479858295e-06,
                3.466327037553825e-07,
                7.338213304363436e-07,
                2.2603251062450327e-06,
                3.9278629391427843e-07,
                1.2751901248454963e-07,
                1.8553919030858602e-07,
                8.315279285351409e-07,
                2.699576809143613e-07
            ],
            [
                0.9999999067050499,
                0.999999939764215,
                0.9999996940977367,
                0.9999995818813766,
                0.9999999273418269,
                0.9999998461827139,
                0.999999943413757,
                0.999999887464744,
                0.9999999397642508,
                0.9999997463981031
            ],
            [
                0.999999352405202,
                0.9999998461826038,
                0.9999999317439873,
                0.9999995262094986,
                0.9999930377445863,
                0.9999982396559485,
                0.9999934595635596,
                1.6701425827133152e-05,
                0.9999998874648112,
                0.999999674368781
            ],
            [
                1.994729483729522e-06,
                5.715002426486762e-07,
                2.1024336609874897e-07,
                5.715006514176113e-07,
                7.338208055680009e-07,
                2.382370235933104e-07,
                3.059022998581767e-07,
                2.6995790618469934e-07,
                2.3823682479292225e-07,
                1.855391681906175e-07
            ],
            [
                0.999999789756609,
                0.9999991148433871,
                0.9999992188519492,
                0.9999990577549581,
                0.999999168471973,
                0.9999998144608098,
                0.999999825702059,
                0.9999996743688587,
                0.9999990577555193,
                0.9999996743687036
            ],
            [
                6.475947982037486e-07,
                2.6995784182140636e-07,
                3.466325797888292e-07,
                2.382370235933104e-07,
                3.535626336072768e-05,
                0.9999992188513905,
                6.475949526020042e-07,
                1.209866260432471e-06,
                2.260323758987159e-06,
                4.450852641737424e-07
            ],
            [
                1.3709568799919866e-06,
                2.2603245673443566e-06,
                1.0129987357407137e-05,
                3.288749849529972e-06,
                8.315284241650899e-07,
                2.561281600086738e-06,
                1.670141985446017e-05,
                3.288750241561788e-06,
                3.059022998581767e-07,
                2.2603240284371276e-06
            ],
            [
                2.102434412875379e-07,
                4.785093924362895e-06,
                1.3709576971463352e-06,
                9.422450432014836e-07,
                1.2751901248454963e-07,
                5.043474683240344e-07,
                4.4508515805735777e-07,
                6.475947982037486e-07,
                5.715005832895975e-07,
                3.4663249714612693e-07
            ],
            [
                0.9999998362623138,
                0.9999998642567351,
                0.9999999358793485,
                0.999999802494586,
                0.9999999468421377,
                0.999999802494633,
                0.9999988634361545,
                1.0,
                0.9999998874647843,
                0.9999999358793944
            ],
            [
                1.855391239547094e-07,
                2.102434412875379e-07,
                5.043476486924565e-07,
                1.1478768126057254e-05,
                3.4663274507713016e-07,
                3.4663249714612693e-07,
                2.6995790618469934e-07,
                1.0677028700422047e-06,
                3.9278605979534166e-07,
                1.27519088491875e-07
            ],
            [
                0.9999997300422548,
                0.9999998461827139,
                0.9999997617630333,
                0.9999997300421261,
                0.9999998362623334,
                0.9999996072136594,
                0.9999997897565838,
                0.9999994284996894,
                0.9999996533673378,
                0.9999995549148951
            ],
            [
                1.209866260432471e-06,
                3.4663278639892215e-07,
                4.2228319344021954e-06,
                6.475946438055299e-07,
                6.475946438042047e-07,
                0.9999993916408186,
                1.7603425837903113e-06,
                9.422445939054222e-07,
                2.6995774527718623e-07,
                7.338212429582604e-07
            ],
            [
                0.9999997761970248,
                0.9999992188519493,
                1.0,
                0.999999917667475,
                0.9999998802068873,
                1.0,
                0.999999953088334,
                0.9999982396567876,
                1.0,
                0.9999999500627976
            ],
            [
                7.338207180898968e-07,
                8.315277302857965e-07,
                5.04347287955046e-07,
                6.475945666063607e-07,
                3.7266383956509585e-06,
                3.927863875616689e-07,
                2.561283432035425e-06,
                8.315277302841894e-07,
                1.6373766672973748e-07,
                1.0129995810463632e-05
            ],
            [
                0.9999998257020799,
                0.9999986290426303,
                0.999999825702059,
                0.9999998942828973,
                0.9999997761971049,
                0.9999996743687811,
                0.9999996940978096,
                0.9999989969854339,
                0.9999998942830106,
                0.9999994284994851
            ],
            [
                0.9999993524054339,
                0.9999980052698044,
                0.9999991148431753,
                0.9999991684715765,
                0.9999975938968031,
                0.9999980052707554,
                0.9999987901338846,
                1.0129987357287368e-05,
                1.553497754577351e-06,
                0.9999993106387085
            ],
            [
                0.9999997300421261,
                5.043472278322555e-07,
                7.889265407327733e-06,
                0.9999998724809115,
                0.9999921107393084,
                5.422221555414699e-06,
                0.9999999358793485,
                0.9999989969861512,
                1.9947301970972664e-06,
                0.9999996533674204
            ],
            [
                0.9999990577552941,
                0.999995504817891,
                0.9999988634366962,
                0.0010322308520079393,
                0.9999995262092728,
                2.4300252321904572e-05,
                0.9999987901347501,
                0.999999218851856,
                0.9999995262096116,
                0.9999994956525919
            ],
            [
                2.260324836787226e-06,
                0.9999983463104148,
                0.999999825702059,
                1.3709573702822306e-06,
                0.9999996072137063,
                0.9999996310114598,
                0.9999999067050943,
                0.9999998555019446,
                0.9999995262094422,
                8.939696304311336e-06
            ],
            [
                0.9999999123574419,
                0.9999995262093858,
                0.9999998461826038,
                1.0,
                0.9999998942829603,
                0.9999998257020798,
                0.9999998362622747,
                0.9999999468421377,
                1.994730672675753e-06,
                0.9999989969862711
            ],
            [
                8.315279285370317e-07,
                5.715002426460124e-07,
                0.9999999067050054,
                0.999999674368781,
                5.043476486915964e-07,
                1.9947292459347367e-06,
                3.466326211113502e-07,
                3.9278605979534166e-07,
                4.450852641737424e-07,
                5.715003789046955e-07
            ],
            [
                5.715002426486762e-07,
                7.338208055680009e-07,
                7.338209805240734e-07,
                1.3709568799919866e-06,
                6.47594952603035e-07,
                7.338208055680009e-07,
                1.3709575337159875e-06,
                3.059021175261338e-07,
                1.760343213335281e-06,
                1.0677028700422047e-06
            ],
            [
                2.6995790618469934e-07,
                2.699578096403948e-07,
                3.466327037553825e-07,
                2.102434412875379e-07,
                1.4449800373118268e-07,
                1.6373764721072816e-07,
                1.275190428875671e-07,
                1.4449798650551755e-07,
                2.6995784182183607e-07,
                9.422448185534261e-07
            ],
            [
                0.999999607213753,
                0.9999999123575882,
                0.9999997126314127,
                0.999999931743971,
                0.9999999067050943,
                0.9999987901338855,
                0.9999980052705183,
                0.9999999358793714,
                0.9999995549151076,
                0.9999998257021421
            ],
            [
                3.726641061085547e-06,
                1.855391239547094e-07,
                1.855391239547094e-07,
                1.275190124846946e-07,
                4.450848927658745e-07,
                2.6995771309523475e-07,
                2.1024331597262577e-07,
                1.6373770576776313e-07,
                1.275191036933194e-07,
                1.637377448057981e-07
            ],
            [
                0.0001088969223388039,
                3.288748281329893e-06,
                1.760343213335281e-06,
                3.927862002663297e-07,
                1.3709576971463352e-06,
                1.2098659719788098e-06,
                4.785095635655362e-06,
                3.466326211113502e-07,
                5.71500719545698e-07,
                1.0677026154806063e-06
            ],
            [
                5.043472278322555e-07,
                1.2098661162056318e-06,
                9.422448185534261e-07,
                0.9999999226557224,
                0.9999995549148951,
                3.05902263391829e-07,
                0.9999995262093858,
                9.422448185510695e-07,
                1.3709567165617364e-06,
                0.9999832985702142
            ],
            [
                8.315277302857965e-07,
                3.9278610661902853e-07,
                5.715006514167015e-07,
                5.04347468323289e-07,
                1.5534971990169383e-06,
                1.209865827752005e-06,
                6.475947210031623e-07,
                3.9278629391427843e-07,
                3.2887502415767434e-06,
                4.450850519403407e-07
            ],
            [
                0.3775406687981454,
                2.5612819054028872e-06,
                2.2603242978665707e-06,
                8.315281267800897e-07,
                6.9622579096593295e-06,
                3.7266410611296085e-06,
                2.260325106237323e-06,
                3.726639728370556e-06,
                8.315278294072958e-07,
                2.260324836776948e-06
            ],
            [
                6.144172404738491e-06,
                8.939693107288474e-06,
                0.9999916019279822,
                3.120192625482384e-05,
                0.9999996743687034,
                2.2603245673443566e-06,
                5.422217030781934e-06,
                0.9999996072136594,
                0.9999998362622943,
                3.288749849529972e-06
            ],
            [
                0.9999996310115482,
                1.9947301970972664e-06,
                5.043474081993875e-07,
                0.9999998724809267,
                1.9947299593078385e-06,
                1.0129994602895546e-05,
                2.2603248367949354e-06,
                2.699576809143613e-07,
                0.9999989969855538,
                0.9999997617630333
            ],
            [
                1.209865827752005e-06,
                3.9278605979208185e-07,
                3.7266401726173067e-06,
                1.994729721518893e-06,
                8.315279285351409e-07,
                3.726638839806038e-06,
                0.9999949062962158,
                1.0677032518785256e-06,
                4.450849988811838e-07,
                6.475947210012481e-07
            ],
            [
                3.288747889284851e-06,
                1.3709576971463352e-06,
                5.715003789046955e-07,
                1.2098661162056318e-06,
                6.47595107001401e-07,
                1.5534971990169383e-06,
                9.422447062294175e-07,
                3.9278605979534166e-07,
                8.315278294114555e-07,
                3.2887506336235617e-06
            ],
            [
                0.9999904837483236,
                0.9999998362623334,
                0.9999987901346054,
                0.999998239657417,
                0.9999999123575359,
                0.9999999123575046,
                0.9999998802069587,
                1.6701421844753466e-05,
                0.999999712631344,
                0.9999997300422547
            ],
            [
                1.3709568799919866e-06,
                0.9999998724809572,
                1.7603438428740716e-06,
                1.3007125363908762e-05,
                2.102434412875379e-07,
                8.315278294114555e-07,
                4.4508494582405734e-07,
                0.9999892166890789,
                1.8925155009767892e-05,
                1.0677026154806063e-06
            ],
            [
                0.9999989969855544,
                0.999999168472072,
                0.9999993916406735,
                0.9999994956523516,
                0.9999997300422869,
                0.9999984465016909,
                0.99999911484307,
                0.9999995549148952,
                0.9999985406237805,
                0.9999998874647306
            ],
            [
                5.715005832886879e-07,
                2.699576809143613e-07,
                2.3823690999323465e-07,
                2.699577774585891e-07,
                3.927863407379485e-07,
                2.1024336609874897e-07,
                2.3823696679327928e-07,
                6.9622595696935874e-06,
                2.1024336609874897e-07,
                3.466327037553825e-07
            ],
            [
                2.5612819054133693e-06,
                1.2098661162056318e-06,
                4.4508505193932864e-07,
                1.3709576971425944e-06,
                9.422448185534261e-07,
                5.422220909009474e-06,
                1.0129988564716393e-05,
                7.338209805240734e-07,
                9.422449308774482e-07,
                6.475946438055299e-07
            ],
            [
                0.9999996533674617,
                2.144495608424996e-05,
                1.3007128464961824e-05,
                0.9999992661788448,
                0.9999991684719727,
                2.430023204460668e-05,
                0.9999898700054167,
                0.9999993916409635,
                5.1442201405453086e-05,
                0.9999960330136162
            ],
            [
                NaN,
                4.222832437798974e-06,
                2.9023119851781017e-06,
                1.0677029973219343e-06,
                5.422217677152175e-06,
                8.939694172656384e-06,
                1.3709568799919866e-06,
                1.3709575337159875e-06,
                1.9947304348862686e-06,
                1.2098661162056318e-06
            ],
            [
                0.9999999006880195,
                1.0,
                0.9999999559306049,
                0.9999999317440197,
                0.999999631011372,
                0.9999999067051165,
                0.9999998802069302,
                0.9999999067050165,
                1.0,
                0.9999999586006492
            ],
            [
                0.9999996072136593,
                0.9999999273418183,
                0.9999996310115479,
                0.9999997126313098,
                0.9999998724809723,
                0.9999997897565838,
                0.9999998461827322,
                0.9999998257022045,
                0.9999998144608983,
                0.9999997897565838
            ],
            [
                0.9999999176675338,
                0.9999999586006294,
                0.9999991148428589,
                0.9999987121044783,
                5.422218969895357e-06,
                0.9999994284992807,
                0.9999999226557685,
                0.9999892166852244,
                0.9999997897565587,
                0.9999996533672963
            ],
            [
                5.043474683240344e-07,
                2.699578096403948e-07,
                5.043472278322555e-07,
                5.715006514176113e-07,
                3.05902263391829e-07,
                4.450848927658745e-07,
                7.338212429582604e-07,
                2.561281600086738e-06,
                5.043476486924565e-07,
                5.043472278322555e-07
            ],
            [
                7.889261645427538e-06,
                8.315281267882195e-07,
                0.9999994956524116,
                0.9999995262093857,
                0.9999997300421904,
                0.9999997761970781,
                0.9999996072138935,
                0.9999925887192572,
                0.9999877809283855,
                0.9999987901337402
            ],
            [
                1.067703124601679e-06,
                5.715002426486762e-07,
                5.043476486915964e-07,
                2.2603251062450327e-06,
                3.059022998576899e-07,
                1.0677033791612137e-06,
                5.715007195447234e-07,
                2.561281294760143e-06,
                1.0677027427600627e-06,
                4.450852641737424e-07
            ],
            [
                0.9999995549150542,
                5.422220909009474e-06,
                0.9999983463100206,
                0.9999998802069731,
                3.726639284144195e-06,
                5.71500719545698e-07,
                9.422447062294175e-07,
                6.825609419848033e-08,
                4.450850519403407e-07,
                2.102434412875379e-07
            ],
            [
                2.699578096403948e-07,
                2.260323758987159e-06,
                6.475945666063607e-07,
                2.1024336609874897e-07,
                2.2603242978871282e-06,
                4.4508494582405734e-07,
                7.338208055680009e-07,
                5.715003107767143e-07,
                1.3709567165617364e-06,
                2.699576809143613e-07
            ],
            [
                0.9999999358793944,
                0.9999997617631469,
                0.9999998362623137,
                0.9999998362623529,
                0.9999992661789324,
                0.999999631011592,
                0.9999998257021214,
                0.9999998555019619,
                0.999999927341827,
                0.9999998642566381
            ],
            [
                3.120191881616493e-05,
                2.382369951932796e-07,
                1.2098659719757836e-06,
                6.475949526020042e-07,
                0.9999995262095552,
                2.382369667929001e-07,
                1.2751899728311609e-07,
                8.315284241650899e-07,
                4.450852111148132e-07,
                2.260323758987159e-06
            ],
            [
                0.999999887464771,
                0.9999999226557869,
                0.999999900688055,
                0.9999993916406734,
                0.9999998257020798,
                0.9999999176674651,
                0.9999994631247402,
                0.9999999067050387,
                0.9999999358794174,
                0.9999997617630333
            ],
            [
                8.939695238634211e-06,
                0.9999989322970033,
                1.3709576971463352e-06,
                0.9999969105044516,
                3.288748281329893e-06,
                0.9999930377445908,
                0.9999877809240456,
                4.222834451403972e-06,
                0.9999993916408186,
                8.939700567094277e-06
            ],
            [
                0.999999428499417,
                0.9999998942830611,
                0.999999730042287,
                0.9999998724810027,
                0.9999994284993489,
                0.9999998942830485,
                0.999999761763005,
                0.999997593898237,
                0.9999999176675632,
                0.9999992661791951
            ],
            [
                2.5612828213934817e-06,
                7.338209805240734e-07,
                4.22283545819819e-06,
                6.962259569750576e-06,
                8.315278294114555e-07,
                1.5534973842076057e-06,
                9.422447062294175e-07,
                5.422220262636381e-06,
                0.9999981261252889,
                4.450852641737424e-07
            ],
            [
                6.475946438055299e-07,
                3.05902190458764e-07,
                8.315280276626197e-07,
                1.760342793638743e-06,
                1.760343213335281e-06,
                5.043473480777865e-07,
                1.3709575337159875e-06,
                1.5534983101602148e-06,
                2.902312677150514e-06,
                0.9999993524053565
            ],
            [
                1.209865539295696e-06,
                1.012999218776902e-05,
                2.260324567337161e-06,
                3.288749065423109e-06,
                1.6373774480605869e-07,
                1.0129988564974359e-05,
                5.422220262636381e-06,
                1.4449800373118268e-07,
                0.9999992661792823,
                1.3709567165617364e-06
            ],
            [
                0.9999986290431209,
                0.9999980052700419,
                0.9999993106386261,
                4.785093924389007e-06,
                4.53978902983119e-05,
                0.9999988634358834,
                4.2228319344021954e-06,
                1.6701421845361053e-05,
                1.3007133116732079e-05,
                0.9999994284995531
            ],
            [
                0.9999995818812273,
                0.99999911484307,
                0.9999994631249324,
                0.9999997126313098,
                0.9999997300423191,
                0.9999994284997576,
                0.9999993106387903,
                0.9999993106391192,
                0.9999989322968765,
                0.9999993524048933
            ],
            [
                1.3007133116732079e-05,
                3.726639284144195e-06,
                8.315278294114555e-07,
                0.9999975938979487,
                0.9999955048194975,
                7.338208930460318e-07,
                3.53562422882756e-05,
                5.715002426486762e-07,
                4.785095065232451e-06,
                9.422445939054222e-07
            ],
            [
                0.9999997300423191,
                0.9999993524054337,
                0.9999996072138467,
                0.9999996072139404,
                0.9999998144608319,
                0.9999998024945624,
                0.999999607213753,
                0.9999997463982242,
                0.9999997761971049,
                0.9999998555019963
            ],
            [
                0.9999998362623723,
                0.9999999006881141,
                0.9999998555019619,
                0.9999998724809875,
                0.9999998874649184,
                0.9999998802069302,
                0.9999996310114599,
                0.9999997126314126,
                0.9999999226558054,
                0.9999998555019963
            ],
            [
                0.9999994284997575,
                0.9999998461826588,
                0.9999977396754337,
                0.9999997761970781,
                0.9999998257022045,
                0.9999996743688975,
                0.999999906705061,
                1.0,
                0.9999999176675829,
                0.9999992188512973
            ],
            [
                0.9999989969855534,
                4.0063696969564425e-05,
                2.902312677150514e-06,
                0.9999991684718736,
                1.0677033791612137e-06,
                1.3709575337159875e-06,
                2.5612819054133693e-06,
                1.670142980893658e-05,
                0.9999990577555188,
                6.962257909842961e-06
            ],
            [
                0.9999999123575987,
                2.260325106237323e-06,
                4.222833444590791e-06,
                7.338209805240734e-07,
                5.715003789046955e-07,
                0.9999997897565588,
                7.338208930460318e-07,
                6.1441746020359e-06,
                0.9999999067049942,
                0.9999998257021213
            ],
            [
                1.0,
                0.9999999123575464,
                1.0,
                0.9999974387187077,
                0.9999999358794479,
                0.9999999226558238,
                0.9999999123575987,
                0.9999999317439464,
                0.9999980052709941,
                0.9999999500628215
            ],
            [
                5.043475885696228e-07,
                1.27519088491875e-07,
                2.5612828213934817e-06,
                5.715006514176113e-07,
                2.3823696679327928e-07,
                3.466326211113502e-07,
                2.1024339116168358e-07,
                2.1444953528413058e-05,
                1.6373764721072816e-07,
                2.3823693839325527e-07
            ],
            [
                1.1253526937656726e-07,
                1.8553916819032217e-07,
                2.1024331597262577e-07,
                1.4449805540740185e-07,
                1.4449795205429202e-07,
                1.4449805540740185e-07,
                9.931198061405701e-08,
                1.8553916819032217e-07,
                1.1253509497835043e-07,
                8.315277302841894e-07
            ],
            [
                1.012998977264307e-05,
                2.561281294760143e-06,
                1.300712536408621e-05,
                6.962255419931625e-06,
                1.5534984953552536e-06,
                5.422220262636381e-06,
                6.962258739796719e-06,
                5.422220262636381e-06,
                0.9999991148430701,
                5.715005151606823e-07
            ],
            [
                0.9999998802069873,
                0.9999998802069731,
                0.9999998724809571,
                0.9999990577549572,
                0.9999998942830485,
                0.9999999123575046,
                0.999999266179195,
                0.9999999397642437,
                1.0,
                0.9999998802068873
            ],
            [
                0.9999990577549573,
                0.9999995262093857,
                0.9999989969862711,
                0.9999999500627916,
                0.9999998257020799,
                0.9999999358793944,
                1.0,
                0.9999990577557434,
                0.99999926617867,
                0.9999997617629766
            ],
            [
                2.90231094723893e-06,
                0.0003353501112555357,
                2.561282210740037e-06,
                1.5534973842076057e-06,
                7.889263526409699e-06,
                1.1478764021029928e-05,
                0.9999985406236066,
                1.5534973842076057e-06,
                0.9999986290423037,
                2.2603234895372223e-06
            ],
            [
                2.699578096393206e-07,
                3.4663249714451116e-07,
                1.275190884913241e-07,
                3.4663249714612693e-07,
                5.043474081993875e-07,
                1.8553910183607374e-07,
                6.475949526020042e-07,
                1.5534984953453635e-06,
                3.4663274507713016e-07,
                3.927862002663297e-07
            ],
            [
                1.8925145985895816e-05,
                0.00010889690934918666,
                0.9999991148433867,
                0.9999990577552943,
                1.3007123813382511e-05,
                5.043473480777865e-07,
                0.9999993106388726,
                6.9622595696935874e-06,
                0.9999996533674617,
                0.9999892166890845
            ],
            [
                5.043476486924565e-07,
                8.315284241650899e-07,
                7.338208055680009e-07,
                3.2887502415767434e-06,
                1.209865539295696e-06,
                9.422444815814404e-07,
                5.715002426486762e-07,
                7.338208930460318e-07,
                5.715006514176113e-07,
                6.475946438055299e-07
            ],
            [
                1.5534975693979422e-06,
                7.338209805240734e-07,
                1.9947299593078385e-06,
                2.6995790618469934e-07,
                6.144172404738491e-06,
                3.288748281329893e-06,
                5.4222176771176554e-06,
                5.422221555340727e-06,
                0.9999994956524119,
                1.0129995810463632e-05
            ],
            [
                3.72663883989755e-06,
                7.889266347786918e-06,
                0.9999992661788449,
                1.3709567165617364e-06,
                6.475946438055299e-07,
                0.9999997617630333,
                8.315277302857965e-07,
                1.0677027427624903e-06,
                1.2098652508424818e-06,
                0.9999996310113721
            ],
            [
                1.9947304348862686e-06,
                0.9999991148426479,
                0.9999999468421249,
                0.9999998555020135,
                0.9999989969856731,
                0.9999996310115039,
                0.9999995262092729,
                0.9999996072138467,
                1.0,
                0.9999989969856731
            ]
        ]
    },
    {
        "q_id": "9699_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            12,
            14,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            72,
            73,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999988634361552,
                0.9999997463981637,
                0.9999994956527726,
                0.9999991148431757,
                0.9999988634366967,
                0.9999981261250663,
                0.9999989969861518,
                0.9999980052709964,
                0.9999993916411088,
                0.9999984465015074
            ],
            [
                2.561281600086738e-06,
                4.450848927658745e-07,
                6.475947982037486e-07,
                1.7603438428800754e-06,
                1.3007125363908762e-05,
                6.475949526020042e-07,
                0.9999898700102774,
                7.889266347786918e-06,
                2.561281294760143e-06,
                1.4449805540740185e-07
            ],
            [
                6.9622587397397306e-06,
                3.535624650150453e-05,
                2.902312677137316e-06,
                3.535625914492432e-05,
                0.999966785797566,
                0.9999967112501625,
                4.539786865090791e-05,
                2.9023130230846496e-06,
                0.9999938558224899,
                0.00012339460442007728
            ],
            [
                0.9999989322968769,
                0.9999996310114162,
                0.9999989322971312,
                0.9999990577556312,
                0.9999994956524721,
                0.9999992661788452,
                0.9999972735297353,
                0.9999945777823337,
                1.7603440527286572e-06,
                0.9999989969859128
            ],
            [
                1.6701425827133152e-05,
                0.9999993524051254,
                0.9999984465022469,
                0.9999993106391194,
                0.9999992661789325,
                0.00010889690934918666,
                0.9999972735297337,
                0.9999910603037351,
                0.9999970976883654,
                0.9999980052700435
            ],
            [
                0.9999986290424682,
                0.9999987121047877,
                0.9999097196154983,
                0.99999823965658,
                0.9999989969859135,
                0.9999993916408186,
                0.9999910603005335,
                0.9999977396762447,
                0.9999989969857929,
                0.9999986290426316
            ],
            [
                2.5612819054133693e-06,
                1.0129988565084915e-05,
                2.4300252321904572e-05,
                2.1444943302181958e-05,
                4.539785241676547e-05,
                2.902313369111213e-06,
                2.5612828213934817e-06,
                3.927862470899887e-07,
                1.0677027427600627e-06,
                2.5612812947508257e-06
            ],
            [
                1.994729483729522e-06,
                2.9023119851899796e-06,
                5.422218969895357e-06,
                8.315277302857965e-07,
                5.422220909009474e-06,
                1.209866260432471e-06,
                8.315279285370317e-07,
                1.9947299593078385e-06,
                5.71500719545698e-07,
                1.3709567165617364e-06
            ],
            [
                0.9999980052709956,
                0.9999991684715768,
                0.9999967112517234,
                2.1444940745371397e-05,
                0.9999516743450894,
                3.288749065423109e-06,
                8.93969950132721e-06,
                0.9999957771645467,
                0.999998629043122,
                0.9999967112493722
            ],
            [
                0.9999960330145683,
                0.9999960330122072,
                NaN,
                0.9997040429414764,
                1.4738987242968784e-05,
                1.0,
                0.9999969105048261,
                0.9999810748564198,
                0.9999898700054324,
                0.9999832985842227
            ],
            [
                2.2603242978943238e-06,
                3.535626757653154e-05,
                2.561281600086738e-06,
                5.144221980317192e-05,
                2.561281600086738e-06,
                3.53562422882756e-05,
                6.962257079889302e-06,
                NaN,
                3.059022269250683e-07,
                9.610243795331803e-05
            ],
            [
                5.04347528446051e-07,
                0.9999339478558297,
                0.9999916019309859,
                1.994730434879465e-06,
                6.605212895289091e-05,
                1.0129989772412744e-05,
                0.99999773967571,
                0.9999916019299935,
                0.9999916019269985,
                0.9999952149049457
            ],
            [
                1.7603434231833873e-06,
                0.9999987121044781,
                0.9999988634360202,
                0.9999996310113282,
                1.670142980920999e-05,
                0.9999989322968762,
                1.012998977264307e-05,
                0.9999952149043733,
                6.962258739796719e-06,
                0.9999975938973764
            ],
            [
                1.0129988565084915e-05,
                NaN,
                1.9947304348862686e-06,
                4.785093353940187e-06,
                3.2887506336235617e-06,
                2.902312677137316e-06,
                NaN,
                4.785095635655362e-06,
                0.0,
                3.059022998576899e-07
            ],
            [
                2.10243290909724e-07,
                3.288748281329893e-06,
                4.450850519403407e-07,
                3.927862002654366e-07,
                0.9999945777784554,
                3.059021175261338e-07,
                8.315281267882195e-07,
                9.931194509740267e-08,
                0.9999993916407459,
                1.855391239539711e-07
            ],
            [
                8.939700566907275e-06,
                2.2603251062450327e-06,
                1.8553905760062447e-07,
                9.422448185534261e-07,
                9.422443692555439e-07,
                4.222833444590791e-06,
                5.422220262599396e-06,
                6.962255419868303e-06,
                1.3709573702822306e-06,
                3.120190393794438e-05
            ],
            [
                2.2603240284371276e-06,
                3.288747889284851e-06,
                7.889263526345123e-06,
                1.5534981249697903e-06,
                3.7266410611296085e-06,
                9.422442569315887e-07,
                2.260324836787226e-06,
                1.0677027427600627e-06,
                2.5612819054028872e-06,
                2.561282516066741e-06
            ],
            [
                3.927863407379485e-07,
                6.144172404738491e-06,
                1.275190428875671e-07,
                NaN,
                3.0590237279085045e-07,
                7.338208055664991e-07,
                6.475947982037486e-07,
                0.9999989322971304,
                1.994729483729522e-06,
                2.2603248367949354e-06
            ],
            [
                2.902312677150514e-06,
                2.260323758987159e-06,
                1.7603434231833873e-06,
                1.067703124601679e-06,
                2.2603251062450327e-06,
                2.902312677150514e-06,
                2.7535700949523498e-05,
                9.422447062294175e-07,
                2.2603245673443566e-06,
                3.7266397283908927e-06
            ],
            [
                1.4449805540763184e-07,
                2.561281294760143e-06,
                1.8553914607267268e-07,
                7.338208930460318e-07,
                1.067703124601679e-06,
                1.994729721518893e-06,
                2.5612834320563895e-06,
                2.9023116392097746e-06,
                3.726639284144195e-06,
                2.1024339116168358e-07
            ],
            [
                2.9023109472244114e-06,
                6.144176799334096e-06,
                1.3709575337125585e-06,
                1.3709567165617364e-06,
                8.315282259138311e-07,
                2.902312677150514e-06,
                1.2098652508391807e-06,
                3.059021175255426e-07,
                5.715005151606823e-07,
                2.902313369111213e-06
            ],
            [
                8.48110818169142e-05,
                1.0677026154806063e-06,
                1.0677027427600627e-06,
                1.3709576971425944e-06,
                6.962254589914941e-06,
                7.338209805224048e-07,
                1.7603425837855082e-06,
                1.4738980215111302e-05,
                6.475947210046347e-07,
                2.5612828213934817e-06
            ],
            [
                1.4449798650569826e-07,
                5.315789407685159e-08,
                1.1253516205489029e-07,
                8.764241182641775e-08,
                1.4449795205429202e-07,
                1.1253509497883659e-07,
                5.315781803390236e-08,
                1.5534981249697903e-06,
                1.2098656835224664e-06,
                4.139934092760465e-08
            ],
            [
                1.99472900813862e-06,
                2.260324567337161e-06,
                0.0001795279663064015,
                4.222835458175145e-06,
                1.3709572068478697e-06,
                5.4222176771176554e-06,
                0.16451646904109266,
                0.9740426446859761,
                1.209865683518615e-06,
                0.9989677688745331
            ],
            [
                6.1441746020359e-06,
                1.1478768126057254e-05,
                0.9999667857895705,
                0.999994228077927,
                1.30071315662049e-05,
                4.222833444590791e-06,
                7.889261645427538e-06,
                0.999990483746084,
                0.9999962733593954,
                1.0129992187658463e-05
            ],
            [
                1.994729483729522e-06,
                1.994729721518893e-06,
                5.422217677152175e-06,
                9.422445939054222e-07,
                8.315279285370317e-07,
                2.561281294760143e-06,
                3.7266383956509585e-06,
                2.561281294760143e-06,
                9.422443692574719e-07,
                3.72663883989755e-06
            ],
            [
                4.785093924330255e-06,
                3.2887478892683997e-06,
                2.6995784182140636e-07,
                3.466327037539638e-07,
                4.450848927650143e-07,
                6.475950297993789e-07,
                1.3709568799879344e-06,
                3.059022998576899e-07,
                8.315279285351409e-07,
                2.1024336609843824e-07
            ],
            [
                6.1441767993788005e-06,
                5.71500515161527e-07,
                1.4449798650569826e-07,
                7.338210680032098e-07,
                3.535624650407695e-05,
                1.7603425837903113e-06,
                1.7603438428848787e-06,
                2.3823685319320354e-07,
                1.2751902768612997e-07,
                6.475950298021765e-07
            ],
            [
                6.475947210046347e-07,
                9.422442569315887e-07,
                4.222833444590791e-06,
                5.715003789046955e-07,
                5.04347468323289e-07,
                1.6373774480605869e-07,
                NaN,
                3.9278605979534166e-07,
                1.370957860576702e-06,
                1.9947301970972664e-06
            ],
            [
                0.9999877809254656,
                0.999998996985674,
                0.9999994956527722,
                4.78509278348926e-06,
                0.9999957771655558,
                0.9999988634364255,
                0.9999977396751644,
                0.9999993524052793,
                0.9999992661788449,
                0.9999992188512972
            ],
            [
                0.9999967112521168,
                0.9999989969860325,
                0.9999969105066611,
                0.9999989969855538,
                1.3007128464961824e-05,
                0.9999995549150015,
                1.8925157266089433e-05,
                0.9999967112501582,
                0.9999970976880187,
                0.9999970976890582
            ],
            [
                0.9999991148429646,
                0.9999996072137999,
                0.9999990577550696,
                0.9999994284997576,
                0.9999996940978826,
                0.999999526209499,
                0.9999992661791945,
                0.9999989322971304,
                0.9999994284996213,
                0.9999995818813271
            ],
            [
                0.9999997617630333,
                0.99999834631081,
                0.9999993106387088,
                0.9999869928700894,
                0.9999987121041715,
                0.9999975938982378,
                0.9999957771670716,
                0.9999985406239553,
                0.9999989969857929,
                0.9999981261246192
            ],
            [
                0.9999984465018756,
                0.999996910505925,
                0.9999741325690248,
                0.9999985406230838,
                0.9999949062937888,
                0.9999861539905115,
                8.939696303758459e-06,
                3.05902263391829e-07,
                0.9999975938970905,
                0.014063626423394072
            ],
            [
                0.9999785550594904,
                2.144494585801764e-05,
                0.9999885212264501,
                1.4738981972564636e-05,
                NaN,
                1.1478770862735993e-05,
                NaN,
                NaN,
                5.422220909009474e-06,
                3.288749065423109e-06
            ],
            [
                3.288747889284851e-06,
                5.422220262636381e-06,
                2.5612834320563895e-06,
                3.466327037553825e-07,
                1.9947304348862686e-06,
                2.5612812947508257e-06,
                2.561283126728994e-06,
                3.288748281329893e-06,
                2.5612819054133693e-06,
                NaN
            ],
            [
                0.9999995818811774,
                7.889262585958025e-06,
                9.422447062294175e-07,
                1.6701421845361053e-05,
                3.2887506336235617e-06,
                2.7535694385633984e-05,
                3.535625493182252e-05,
                1.994729483729522e-06,
                0.9999982396559496,
                0.9999970976880208
            ],
            [
                4.785093353940187e-06,
                6.47595107001401e-07,
                7.338208930460318e-07,
                3.726639284144195e-06,
                1.5534971990169383e-06,
                0.9999877809269345,
                1.067703124601679e-06,
                1.2098652508424818e-06,
                1.5534977545886537e-06,
                1.5534981249697903e-06
            ],
            [
                1.9947297215043796e-06,
                2.753568453712307e-05,
                1.012999097997104e-05,
                2.5612812947380135e-06,
                2.4300234940642642e-05,
                3.120190765625026e-05,
                1.147877359926923e-05,
                2.9023116391675407e-06,
                1.89251527534122e-05,
                5.1442195268327955e-05
            ],
            [
                5.422218323487975e-06,
                0.9999980052700451,
                NaN,
                8.481106161413668e-05,
                4.539786865090791e-05,
                0.9999934595627872,
                1.147877359957198e-05,
                0.999925153746405,
                0.9999892166839571,
                0.00013982205753511605
            ],
            [
                2.561281905390075e-06,
                1.8553914607237736e-07,
                8.315279285351409e-07,
                9.422443692555439e-07,
                5.043475284447896e-07,
                3.46632497145457e-07,
                8.315283250371857e-07,
                2.5612828213818346e-06,
                9.422450431989127e-07,
                8.315282259089153e-07
            ],
            [
                0.999951674362478,
                0.9999989969861514,
                0.9999852610129184,
                0.9999949062950148,
                0.9999987121044788,
                0.9999983463096281,
                0.9999991148428597,
                0.9999978766220496,
                0.9999994284992807,
                0.9999957771655609
            ],
            [
                1.0129989772532511e-05,
                3.535626757524533e-05,
                0.999995777166064,
                1.6701423836262173e-05,
                7.484624512911504e-05,
                2.5612828213934817e-06,
                1.6701421845057263e-05,
                1.3007126914435202e-05,
                3.535626757524533e-05,
                1.3007133116732079e-05
            ],
            [
                7.33821330437595e-07,
                2.561281294760143e-06,
                3.2887506336235617e-06,
                1.7603430034867993e-06,
                8.315281267882195e-07,
                2.9023116391978967e-06,
                1.209865539295696e-06,
                5.422217030781934e-06,
                1.3709567165617364e-06,
                0.9999996072136594
            ],
            [
                6.475945666051092e-07,
                2.382369383923073e-07,
                2.6995771309523475e-07,
                8.315279285351409e-07,
                2.699578096393206e-07,
                6.475947210012481e-07,
                7.338209805224048e-07,
                1.2098659719757836e-06,
                3.288749065406658e-06,
                7.338212429537553e-07
            ],
            [
                0.9999869928685006,
                0.999999352405048,
                8.939696304311336e-06,
                0.9999916019280256,
                0.9999986290426326,
                0.9999993524052027,
                0.9999960330122051,
                0.999195914056327,
                0.9999955048162901,
                0.9999987121047856
            ],
            [
                3.1201907657271834e-05,
                5.8291272493815044e-05,
                2.144495097113319e-05,
                NaN,
                1.3007128464961824e-05,
                3.120190765625026e-05,
                5.829127944524028e-05,
                6.1441724046434924e-06,
                7.889262585886274e-06,
                8.939696304213768e-06
            ],
            [
                NaN,
                4.222831934352267e-06,
                2.9023112931688987e-06,
                8.939695238536645e-06,
                8.93969950132721e-06,
                1.3007134667070165e-05,
                3.2887482813149375e-06,
                1.5534975693792215e-06,
                1.0677024882009222e-06,
                1.8925145985895816e-05
            ],
            [
                0.9999985406234326,
                0.9999983463102203,
                0.9999974387174885,
                0.9999977396759745,
                0.9999962733602865,
                0.9999962733602835,
                0.9999983463096306,
                0.9999980052700455,
                0.9999978766210353,
                0.9999962733611698
            ],
            [
                2.1444943302181958e-05,
                4.222834954801051e-06,
                5.715003789046955e-07,
                5.422220262636381e-06,
                2.699578740032504e-07,
                NaN,
                5.422220909009474e-06,
                5.715005832886879e-07,
                6.1441746020359e-06,
                8.315277302841894e-07
            ],
            [
                3.4663253846718004e-07,
                8.939696304213768e-06,
                2.430023204460668e-05,
                8.939694172867777e-06,
                1.5534973842076057e-06,
                1.670141786325573e-05,
                3.726638395634011e-06,
                4.4508510499849186e-07,
                1.8925155009767892e-05,
                1.4738980215111302e-05
            ],
            [
                2.144494585747154e-05,
                4.785093924362895e-06,
                1.5534981249574276e-06,
                2.4300243631272052e-05,
                NaN,
                6.9622587396067566e-06,
                1.012999460278499e-05,
                2.902311985146426e-06,
                1.4738987242968784e-05,
                6.9622595696935874e-06
            ],
            [
                1.1253520230052635e-07,
                1.3709568799919866e-06,
                5.715002426475718e-07,
                7.338212429582604e-07,
                1.2098658277451275e-06,
                7.338209805240734e-07,
                2.902311639183378e-06,
                9.422443692555439e-07,
                5.715007195431641e-07,
                1.760343213335281e-06
            ],
            [
                1.1253524254650944e-07,
                5.71500719545698e-07,
                2.9023119851899796e-06,
                5.422217030781934e-06,
                1.5534983101644536e-06,
                1.994729008145876e-06,
                NaN,
                2.2603245673443566e-06,
                1.7603425837903113e-06,
                2.1024341622426268e-07
            ],
            [
                7.338212429594283e-07,
                5.043475284468537e-07,
                2.561282210740037e-06,
                8.76424013786396e-08,
                7.33821330437595e-07,
                6.47595107001401e-07,
                1.8553910183674878e-07,
                6.825608606172863e-08,
                5.71500515161527e-07,
                1.3709576971463352e-06
            ],
            [
                2.1444945858485726e-05,
                1.2098659719757836e-06,
                5.422217677152175e-06,
                1.3007123813559956e-05,
                1.4738985486506781e-05,
                8.939695238634211e-06,
                1.4738983729535602e-05,
                4.0063701745046735e-05,
                2.4300249425247723e-05,
                7.889265407255982e-06
            ],
            [
                6.962255419931625e-06,
                NaN,
                2.4300234940642642e-05,
                1.994730672675753e-06,
                6.144173869558639e-06,
                1.7603430034867993e-06,
                3.120190393794438e-05,
                1.4738989000422955e-05,
                4.785095065232451e-06,
                2.9023119851781017e-06
            ],
            [
                2.2603234895372223e-06,
                0.9999967112513359,
                0.9999798543116533,
                1.0677028700422047e-06,
                0.999997438717796,
                0.9999960330145656,
                0.9999982396563687,
                0.9999986290423044,
                5.144223206414209e-05,
                7.889266347786918e-06
            ],
            [
                0.999088948841627,
                4.785093924330255e-06,
                0.004609572160144765,
                NaN,
                0.9999904837517763,
                0.9999843104540868,
                0.9998601778801656,
                6.9622537599680095e-06,
                NaN,
                NaN
            ],
            [
                8.315281267882195e-07,
                2.699576809143613e-07,
                2.699578740032504e-07,
                2.6995784182140636e-07,
                2.382369667929001e-07,
                2.1024341622426268e-07,
                3.0590237279032884e-07,
                1.275191036933194e-07,
                1.6373774480605869e-07,
                2.3823688159291947e-07
            ],
            [
                2.2603234895372223e-06,
                6.1441746020359e-06,
                2.902312331170226e-06,
                3.535624228698939e-05,
                NaN,
                3.2887502415767434e-06,
                7.88926446679691e-06,
                4.006368264282944e-05,
                NaN,
                7.889265407255982e-06
            ],
            [
                0.9999996310113721,
                0.9999996940976639,
                0.9999756997564291,
                0.9999994956525922,
                0.9999996533672966,
                0.9999988634362912,
                0.9999997300422871,
                0.9999996940977368,
                1.8925148241872038e-05,
                1.760343213335281e-06
            ],
            [
                0.9999989969857939,
                0.9999977396746286,
                0.9999980052698066,
                NaN,
                0.9999995549149487,
                0.999998932297386,
                0.9999934595604557,
                0.9999986290432865,
                1.760343213335281e-06,
                0.9999785550414813
            ],
            [
                0.9999934595651305,
                0.9999969105062997,
                0.9999982396563684,
                0.999997876621544,
                0.9999974387165783,
                0.9999957771680774,
                0.9999974387177979,
                0.9999960330122085,
                0.9999949062937992,
                0.9999991684718739
            ],
            [
                0.0002959571355140204,
                8.939700567004841e-06,
                0.9988304898008994,
                1.8925148241493373e-05,
                0.9859363715491752,
                0.0010322309701306972,
                1.3007125363908762e-05,
                4.785093353940187e-06,
                4.785093924330255e-06,
                0.9924227599402229
            ],
            [
                0.999997739675435,
                0.9999952149060898,
                0.9999942280792958,
                0.9999869928669302,
                0.9999985406230842,
                0.9999970976876741,
                0.9999980052702823,
                0.9999623635576401,
                0.9997388097565436,
                0.9999925887227968
            ],
            [
                6.96225873967641e-06,
                4.539785782390681e-05,
                1.8925148241493373e-05,
                1.6701427817427163e-05,
                4.006369219233375e-05,
                NaN,
                8.939696304311336e-06,
                6.144176799283803e-06,
                0.9999038976089673,
                0.99883048950213
            ],
            [
                9.422447062270609e-07,
                1.4449798650518898e-07,
                8.939694172867777e-06,
                0.9999957771645477,
                2.2603253756874524e-06,
                3.466325797888292e-07,
                1.3709576971463352e-06,
                1.5534975693933505e-06,
                1.1253518888531272e-07,
                2.699577774585891e-07
            ],
            [
                0.9999996310114604,
                0.9999997463982241,
                0.9999988634366972,
                0.999999607213753,
                0.999978555059347,
                0.9999993916410367,
                0.9999991684719735,
                0.99999931063912,
                0.9999980052709947,
                0.9999945777791137
            ],
            [
                6.962255419931625e-06,
                9.422443692574719e-07,
                NaN,
                6.144172404738491e-06,
                3.2887506336235617e-06,
                1.7603425837903113e-06,
                5.043474683240344e-07,
                3.927863407379485e-07,
                4.4508515805735777e-07,
                2.1024336609874897e-07
            ],
            [
                2.144495608424996e-05,
                7.889265407255982e-06,
                0.9999990577556319,
                3.466325797896173e-07,
                7.889263526345123e-06,
                2.1444953527944967e-05,
                3.535624650279074e-05,
                4.785094494783494e-06,
                0.9999955048178975,
                3.927863875616689e-07
            ],
            [
                3.7266397283908927e-06,
                3.2887506336235617e-06,
                1.4738976701652988e-05,
                2.7535691103314177e-05,
                5.422217030781934e-06,
                2.2603253756956754e-06,
                9.422448185478557e-07,
                0.0004878572383017746,
                2.4300234941880266e-05,
                3.2887494574518405e-06
            ],
            [
                0.9999985406243022,
                4.785095635655362e-06,
                5.422218969895357e-06,
                0.9999980052693305,
                0.9999810748428052,
                2.5612828213934817e-06,
                0.9999983463110083,
                1.3709575337159875e-06,
                0.9999989969856736,
                0.9999251537729239
            ],
            [
                0.9999974387177926,
                0.9999980052709952,
                0.9999985406237808,
                0.9999991148430707,
                0.9999994284994174,
                0.9999938558246816,
                0.999994577780394,
                0.9999984465018766,
                0.9999969105048193,
                0.9999972735307081
            ],
            [
                0.999996910504089,
                1.8925141473599938e-05,
                4.539787406217992e-05,
                0.9999949062968346,
                0.9999984465028027,
                1.4738981972323349e-05,
                0.9999910603069249,
                0.0001233945749933723,
                0.00012339453086050964,
                0.9999989322972592
            ],
            [
                1.7603438428740716e-06,
                7.889265407255982e-06,
                2.4300252321904572e-05,
                2.144494841482881e-05,
                1.9947297215125433e-06,
                2.561283432035425e-06,
                1.30071315662049e-05,
                7.88926070489716e-06,
                NaN,
                6.14417753171671e-06
            ],
            [
                5.8291272497207844e-05,
                9.4224425692559e-07,
                1.7603430034655858e-06,
                3.726638839878908e-06,
                1.1478768125911099e-05,
                1.0129992187658463e-05,
                6.962257079775324e-06,
                3.2887478892683997e-06,
                0.0006263340328472375,
                1.1478768125577027e-05
            ],
            [
                4.4508494582405734e-07,
                5.715003107767143e-07,
                2.6995774527718623e-07,
                3.0590237279085045e-07,
                2.6995774527718623e-07,
                3.05902336324494e-07,
                1.5534984953552536e-06,
                3.4663274507713016e-07,
                2.6995784182183607e-07,
                1.4449805540763184e-07
            ],
            [
                6.144173137170873e-06,
                6.144172404738491e-06,
                2.90231094723893e-06,
                1.3007126914612648e-05,
                5.715005832886879e-07,
                3.2887498495150166e-06,
                2.5612834320470717e-06,
                8.939696304311336e-06,
                8.939696304311336e-06,
                3.7266410611296085e-06
            ],
            [
                7.338209805224048e-07,
                2.5612834320563895e-06,
                1.4449807263312446e-07,
                2.2603248367949354e-06,
                2.382370235933104e-07,
                1.0677033791612137e-06,
                3.466326624336003e-07,
                2.902312677150514e-06,
                1.5534973842076057e-06,
                9.422442569315887e-07
            ],
            [
                2.699578740032504e-07,
                5.715006514167015e-07,
                1.2098653950692178e-06,
                2.6995774527718623e-07,
                2.6995774527718623e-07,
                8.315284241650899e-07,
                8.315277302841894e-07,
                2.2603234895372223e-06,
                1.370957860576702e-06,
                1.6373764721072816e-07
            ],
            [
                2.5612834320563895e-06,
                9.422448185534261e-07,
                6.144175334510455e-06,
                3.288749849529972e-06,
                1.760342793638743e-06,
                6.1441746020359e-06,
                NaN,
                4.4508515805735777e-07,
                1.067703124601679e-06,
                7.338210680021253e-07
            ],
            [
                2.2603242978871282e-06,
                5.715005151606823e-07,
                5.04347287955046e-07,
                1.0677027427600627e-06,
                3.4663266243308805e-07,
                5.04347287955046e-07,
                9.422442569315887e-07,
                3.927862002663297e-07,
                5.715005832886879e-07,
                1.2751905808881762e-07
            ],
            [
                0.9999982396567879,
                0.99999921885167,
                0.9999962733598364,
                0.9999991148429651,
                0.9999978766215398,
                0.9999995262095553,
                0.9999983463102192,
                0.999999218851577,
                0.9999991684715771,
                0.9999993524054342
            ],
            [
                5.715007195431641e-07,
                8.315281267834927e-07,
                4.450848927650143e-07,
                6.475947210031623e-07,
                4.450849458218309e-07,
                3.9278610661545617e-07,
                3.466327863983311e-07,
                6.475947210031623e-07,
                1.7603438428800754e-06,
                4.450849988811838e-07
            ],
            [
                0.9999985406239535,
                0.9999989322971308,
                0.9999992188513908,
                0.9999994631250604,
                0.9999992188512973,
                0.9999949062925767,
                0.999999631011636,
                0.9999151889591551,
                0.9999988634361545,
                0.9999997761970516
            ],
            [
                6.9622587397397306e-06,
                1.4738976701411704e-05,
                1.5534979397740895e-06,
                2.753569110256289e-05,
                4.006370174344354e-05,
                4.0063711294555596e-05,
                0.0001795279663064015,
                4.5397852414783676e-05,
                4.539787947345257e-05,
                0.00010889696126329929
            ],
            [
                1.994729721518893e-06,
                3.72663883989755e-06,
                2.561281600076256e-06,
                1.3709575337159875e-06,
                3.288748673376478e-06,
                1.7603425837903113e-06,
                3.726639284144195e-06,
                1.5534975693979422e-06,
                3.2887494574832472e-06,
                3.4663278639892215e-07
            ],
            [
                0.9999987121044781,
                0.9999982396572099,
                0.9999996072139405,
                0.9999994956525321,
                0.9999996072139407,
                0.9999977396757059,
                0.9999992661787579,
                0.9999987121044789,
                0.9999983463096273,
                0.9999984465015067
            ],
            [
                1.4738976701652988e-05,
                8.939694172957213e-06,
                2.430024652854702e-05,
                4.222834451403972e-06,
                1.3007126914612648e-05,
                5.422220909009474e-06,
                NaN,
                7.889265407327733e-06,
                0.9999981261252886,
                5.1442225934873024e-05
            ],
            [
                0.9999989322973851,
                4.785094494811783e-06,
                0.9999980052695672,
                0.9999892166878108,
                1.1478770862882149e-05,
                2.5612834320563895e-06,
                2.1444943302650045e-05,
                4.222834451403972e-06,
                1.5534983101644536e-06,
                1.0129987357517693e-05
            ],
            [
                0.9999997126313098,
                0.9999983463096269,
                0.9999995262092729,
                0.9999992661792826,
                6.144173137170873e-06,
                0.9999996310116358,
                0.9999989322975127,
                0.9999974387187117,
                0.9999984465028025,
                NaN
            ],
            [
                0.9999916019269843,
                0.9999945777829765,
                2.430024942462891e-05,
                4.785096206076165e-06,
                3.120191509592808e-05,
                2.144495864059426e-05,
                4.006368741670684e-05,
                7.484620050755993e-05,
                6.962254589914941e-06,
                6.962256249821764e-06
            ],
            [
                0.9999996743687035,
                0.9999993916411815,
                0.9999993916411812,
                0.9999996310114162,
                0.9999994956527123,
                0.9999996310113283,
                0.9999852610198264,
                0.9999994631247409,
                0.999999802494633,
                0.9999989969855538
            ],
            [
                1.0677027427624903e-06,
                4.2228319344021954e-06,
                1.3709575337159875e-06,
                2.9023116392097746e-06,
                3.927863875616689e-07,
                5.04347287955046e-07,
                6.475950298021765e-07,
                7.338207180898968e-07,
                3.4663249714612693e-07,
                1.0677029973219343e-06
            ],
            [
                0.9999962733620538,
                1.0129994602895546e-05,
                2.753568782024347e-05,
                3.288748281329893e-06,
                1.0129988564974359e-05,
                5.144221979793211e-05,
                3.288749065423109e-06,
                3.726638839878908e-06,
                4.2228339479858295e-06,
                4.785096206076165e-06
            ],
            [
                2.2603234895289998e-06,
                6.475947210031623e-07,
                5.715002426486762e-07,
                8.939700567094277e-06,
                1.4449795205429202e-07,
                3.0590237279032884e-07,
                1.6373770576776313e-07,
                3.726639728370556e-06,
                1.0677027427600627e-06,
                1.7603438428740716e-06
            ],
            [
                0.9999960330140972,
                0.9999910603069342,
                NaN,
                1.0129988564974359e-05,
                0.999995504818972,
                6.605215256765022e-05,
                5.422220262636381e-06,
                0.9999970976873305,
                0.999992588717493,
                1.8925143729954285e-05
            ],
            [
                1.9947292459347367e-06,
                1.5534979397740895e-06,
                2.90231094723893e-06,
                5.422217030747413e-06,
                3.288749065423109e-06,
                1.30071315662049e-05,
                3.288749065423109e-06,
                1.0129987357287368e-05,
                2.144495608378187e-05,
                0.00013982210754460409
            ],
            [
                7.338208055664991e-07,
                3.7266406168827523e-06,
                6.475948754012522e-07,
                1.5534981249697903e-06,
                2.561281600076256e-06,
                1.2098659719757836e-06,
                1.1478770862735993e-05,
                4.222834451355964e-06,
                1.2098659719757836e-06,
                1.3007134667259441e-05
            ],
            [
                3.288749065423109e-06,
                7.338212429582604e-07,
                5.715006514167015e-07,
                1.0677027427600627e-06,
                9.422443692555439e-07,
                1.5534984953510149e-06,
                1.7603438428800754e-06,
                3.466325797896173e-07,
                3.466327450765785e-07,
                4.450852111148132e-07
            ],
            [
                1.670142980893658e-05,
                3.535626335944147e-05,
                2.2603237589779086e-06,
                1.8925143729575624e-05,
                1.3709568799879344e-06,
                3.2887478892504536e-06,
                1.3007125363719486e-05,
                2.260324028427877e-06,
                1.7603425837791042e-06,
                2.2603234895289998e-06
            ],
            [
                7.338208930460318e-07,
                0.9999203269633278,
                1.760342793638743e-06,
                1.7603425837903113e-06,
                8.315278294114555e-07,
                0.9999599363231703,
                1.3709568799919866e-06,
                1.637376862489725e-07,
                2.2603248367949354e-06,
                1.6373772528704005e-07
            ],
            [
                0.9999991684716758,
                0.9999995262093294,
                0.9999998144609645,
                0.9999981261243951,
                0.9999993916407459,
                0.9999994956527725,
                NaN,
                0.9999991684719729,
                0.9999417087350428,
                0.9999992661791075
            ],
            [
                3.288750241561788e-06,
                2.2603234895372223e-06,
                4.222833444590791e-06,
                6.144177531767002e-06,
                6.144173869603344e-06,
                6.9622537599680095e-06,
                2.7535704231844484e-05,
                1.760343633031919e-06,
                5.422217030747413e-06,
                1.994729008145876e-06
            ],
            [
                0.999996033015046,
                8.939697369980456e-06,
                4.53978632394714e-05,
                4.785092783519724e-06,
                NaN,
                1.994729483723626e-06,
                5.829127945202588e-05,
                1.7603425837855082e-06,
                3.120191881616493e-05,
                0.9999970976880197
            ],
            [
                0.9999995549148425,
                0.9999988634364261,
                0.9999996940978827,
                0.999999730042094,
                0.9999996310115481,
                6.475947210046347e-07,
                1.892515049819277e-05,
                0.9999997126314811,
                0.9999994284994171,
                0.9999997300422548
            ],
            [
                3.120191137659974e-05,
                1.0129993395336818e-05,
                4.2228329411708495e-06,
                1.3007133116542802e-05,
                0.00017952805188098652,
                1.3007126914435202e-05,
                4.006371129615879e-05,
                0.0007096705554652252,
                8.481106162154104e-05,
                1.670142582682936e-05
            ],
            [
                3.4663262110945863e-07,
                8.315277302841894e-07,
                7.338211554783522e-07,
                1.0677032518785256e-06,
                1.0677027427600627e-06,
                3.4663266243308805e-07,
                9.422448185510695e-07,
                1.855391239544352e-07,
                3.7266406168624155e-06,
                1.3709573702822306e-06
            ],
            [
                0.9999955048200458,
                0.9999485577868865,
                0.9999798543045293,
                0.9999785550517172,
                0.9999960330126727,
                1.7603440527286572e-06,
                0.9999984465028031,
                0.9999843104559444,
                0.9999972735284345,
                5.422220909009474e-06
            ],
            [
                0.9999964991460082,
                6.475949526020042e-07,
                3.7266410611296085e-06,
                4.785095635655362e-06,
                1.994729483723626e-06,
                1.209866260432471e-06,
                9.422444815814404e-07,
                6.475947210046347e-07,
                3.0590237279085045e-07,
                0.9999987901347502
            ],
            [
                2.9023119851899796e-06,
                1.760343213335281e-06,
                5.422217030781934e-06,
                7.889264466868659e-06,
                2.2603248367949354e-06,
                3.2887506336235617e-06,
                1.4449807263312446e-07,
                4.785094494811783e-06,
                9.422443692574719e-07,
                4.785093924389007e-06
            ],
            [
                1.3709573702778664e-06,
                1.0677028700363782e-06,
                1.0129989772274546e-05,
                6.962254589781966e-06,
                1.0677028700363782e-06,
                3.7266410611296085e-06,
                4.450848927637999e-07,
                2.561283432005142e-06,
                3.7266401725681614e-06,
                8.315278294072958e-07
            ],
            [
                5.715003789046955e-07,
                2.5612831267202583e-06,
                6.9622595696935874e-06,
                2.9023119851781017e-06,
                3.059021175261338e-07,
                6.475949526020042e-07,
                8.315281267882195e-07,
                5.043473480777865e-07,
                2.382369667929001e-07,
                6.9622595696935874e-06
            ],
            [
                0.9999994956527128,
                0.9999994284994858,
                0.9999993916409641,
                0.9999978766223021,
                0.9999960330131474,
                0.9999996072139407,
                0.9999981261252907,
                0.9999898700102745,
                0.9999986290423049,
                0.9999994631249965
            ]
        ]
    },
    {
        "q_id": "9654_mmlu_physics",
        "cot_ids": [
            2,
            3,
            5,
            6,
            9,
            12,
            19,
            20,
            23,
            24,
            25,
            28,
            30,
            32,
            33,
            37,
            40,
            44,
            46,
            48,
            49,
            51,
            52,
            54,
            55,
            58,
            59,
            61,
            63,
            65,
            66,
            67,
            68,
            72,
            73,
            74,
            75,
            76,
            77,
            80,
            81,
            83,
            85,
            86,
            87,
            88,
            89,
            93,
            94,
            95,
            96,
            97,
            99,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            110,
            112,
            115,
            116,
            117,
            118,
            119,
            124,
            125,
            126
        ],
        "rewards": [
            [
                1.9947292459265734e-06,
                3.7266406168624155e-06,
                1.8925155009767892e-05,
                2.4300246526646385e-05,
                2.4300237837960777e-05,
                6.14417753171671e-06,
                2.5612819054028872e-06,
                1.4738980215111302e-05,
                3.12019150949065e-05,
                6.144172404693786e-06
            ],
            [
                3.927862002663297e-07,
                2.6995790618350237e-07,
                2.5612819054028872e-06,
                1.2098655392871682e-06,
                5.715005832827105e-07,
                2.1024329090867228e-07,
                3.0590226339061185e-07,
                2.1024336609843824e-07,
                2.5612819053586272e-06,
                1.3709572068354007e-06
            ],
            [
                1.855391239544352e-07,
                1.444980209564556e-07,
                2.1024341622426268e-07,
                1.2751904288739315e-07,
                1.27519058086875e-07,
                1.855391681898159e-07,
                1.1253521571574156e-07,
                5.144221980055201e-05,
                2.699576809143613e-07,
                2.1024331597262577e-07
            ],
            [
                1.0677028700363782e-06,
                7.338208930391909e-07,
                7.338212429537553e-07,
                7.338207180864763e-07,
                5.043475885674441e-07,
                7.338212429504183e-07,
                1.0677027427600627e-06,
                1.7603425837791042e-06,
                1.7603434231777837e-06,
                3.535625071730638e-05
            ],
            [
                4.0063706517323215e-05,
                4.222832941111319e-06,
                3.288750633569722e-06,
                2.260324297853209e-06,
                1.9947290081177566e-06,
                6.144176799227922e-06,
                1.553498124964492e-06,
                3.7266401725935817e-06,
                1.4738985486265496e-05,
                6.144172404587612e-06
            ],
            [
                1.3007131566015624e-05,
                3.1201922533564516e-05,
                1.670141587174774e-05,
                1.1478764020883773e-05,
                6.962257909785973e-06,
                6.144176066795103e-06,
                2.7535704229340197e-05,
                3.288750633569722e-06,
                1.1478766757561534e-05,
                1.1478772230929451e-05
            ],
            [
                3.9278615343901467e-07,
                6.475946437996402e-07,
                4.450851049959619e-07,
                2.9023123311583482e-06,
                1.994729721482609e-06,
                2.2603237589676295e-06,
                1.209865827740176e-06,
                3.9278615344178325e-07,
                1.5534981249574276e-06,
                8.315282259117513e-07
            ],
            [
                1.1478768125911099e-05,
                1.3007134667259441e-05,
                5.422217030707961e-06,
                4.222833947932061e-06,
                4.222833947820683e-06,
                1.1478772230762415e-05,
                1.1478772230929451e-05,
                7.889261645355786e-06,
                4.0063711294555596e-05,
                1.0129989772412744e-05
            ],
            [
                1.994730434847717e-06,
                6.962254589914941e-06,
                5.422220262505697e-06,
                4.222832437677995e-06,
                4.785092783454444e-06,
                1.89251482406672e-05,
                2.9023112931688987e-06,
                2.2603245673155757e-06,
                5.422220908703723e-06,
                4.785092783371756e-06
            ],
            [
                1.1478764021029928e-05,
                0.00023050663325510615,
                1.3007123813382511e-05,
                2.9023112932177327e-06,
                1.9947299593014888e-06,
                6.962259569750576e-06,
                1.0129992187658463e-05,
                6.144175334418252e-06,
                2.1444950970626095e-05,
                2.2603253756874524e-06
            ],
            [
                5.043474081993875e-07,
                2.5612812947380135e-06,
                1.3709567165530083e-06,
                1.0677024881980089e-06,
                4.785092783519724e-06,
                1.0677032518748838e-06,
                9.422445939032799e-07,
                9.422448185510695e-07,
                1.7603432133296774e-06,
                1.7603434231833873e-06
            ],
            [
                1.1478768125911099e-05,
                3.288749065406658e-06,
                1.6701419854156377e-05,
                1.0129995810343862e-05,
                2.9023119851781017e-06,
                5.043476486902204e-07,
                1.1478764020883773e-05,
                1.3709572068478697e-06,
                2.561283432035425e-06,
                3.7266406168403854e-06
            ],
            [
                1.1478773599102191e-05,
                2.260324297853209e-06,
                2.5612825160271407e-06,
                8.939694172656384e-06,
                4.0063696967815485e-05,
                4.785095635592258e-06,
                7.88926164518358e-06,
                2.144494585747154e-05,
                1.5534973841895917e-06,
                3.2887502415243994e-06
            ],
            [
                3.0590215399183813e-07,
                7.338209805200689e-07,
                1.5534975693933505e-06,
                2.1024331597262577e-07,
                2.69957906184239e-07,
                2.1024331597262577e-07,
                1.1253516205489029e-07,
                2.3823685319244518e-07,
                1.275190732904469e-07,
                2.69957906184239e-07
            ],
            [
                4.785092783519724e-06,
                1.5534971990126997e-06,
                7.889263526266196e-06,
                1.3709572068522336e-06,
                1.994730434879465e-06,
                5.422220262555012e-06,
                1.3709570434178922e-06,
                5.4222176771176554e-06,
                3.726639728370556e-06,
                7.889265407255982e-06
            ],
            [
                2.699578740032504e-07,
                3.466325384678894e-07,
                2.3823702359290413e-07,
                1.637377057680051e-07,
                1.855391681906175e-07,
                2.1024334103581732e-07,
                3.927863875616689e-07,
                2.1024336609874897e-07,
                2.3823688159291947e-07,
                3.9278634073732336e-07
            ],
            [
                5.715002426410745e-07,
                3.927860597935108e-07,
                3.0590226339061185e-07,
                1.2098659719757836e-06,
                1.0677026154730804e-06,
                5.715005832827105e-07,
                1.0677033791437343e-06,
                1.994730434847717e-06,
                7.338208930391909e-07,
                1.3709567165461505e-06
            ],
            [
                8.939696304213768e-06,
                3.726641061058432e-06,
                1.1478766757718129e-05,
                7.889260704818233e-06,
                1.2098655392871682e-06,
                1.0129989772532511e-05,
                1.7603432133136672e-06,
                6.962257079629686e-06,
                5.422217677028889e-06,
                6.144176066795103e-06
            ],
            [
                9.422447062294175e-07,
                1.3709567165530083e-06,
                7.889259764445822e-06,
                7.889265407255982e-06,
                1.0129994602895546e-05,
                1.7603438428800754e-06,
                3.726638395634011e-06,
                6.144173137170873e-06,
                7.889266347786918e-06,
                9.422450431989127e-07
            ],
            [
                6.9622587397397306e-06,
                1.0129995810463632e-05,
                1.553497754577351e-06,
                2.260325106237323e-06,
                6.962257079832313e-06,
                3.726638839878908e-06,
                4.785095635624897e-06,
                8.939699501229642e-06,
                2.2603237589779086e-06,
                8.315282259117513e-07
            ],
            [
                1.0677031245905116e-06,
                9.422442569290178e-07,
                4.4508526417298334e-07,
                7.338209805224048e-07,
                1.0677032518748838e-06,
                6.475947210012481e-07,
                6.475947210012481e-07,
                3.9278615344178325e-07,
                2.699578096393206e-07,
                5.715007195431641e-07
            ],
            [
                3.2887498495150166e-06,
                1.7603438428740716e-06,
                7.338212429582604e-07,
                4.2228329411708495e-06,
                1.0677031245990084e-06,
                8.315281267882195e-07,
                6.475946438042047e-07,
                1.9947299593014888e-06,
                4.785095065171522e-06,
                1.209865539295696e-06
            ],
            [
                1.2098662604247682e-06,
                1.2098659719716573e-06,
                6.475947210012481e-07,
                1.2098658277451275e-06,
                2.5612831267202583e-06,
                6.962253759904688e-06,
                1.0677026154806063e-06,
                1.553497199007048e-06,
                9.422448185510695e-07,
                8.315283250371857e-07
            ],
            [
                2.3823693839290317e-07,
                3.927860597945825e-07,
                1.0129987357407137e-05,
                1.9947292459347367e-06,
                3.9278615344178325e-07,
                2.6995774527718623e-07,
                3.0590226339061185e-07,
                1.2751901248454963e-07,
                2.561282210729555e-06,
                9.931198061405701e-08
            ],
            [
                1.2751904288739315e-07,
                9.422450431989127e-07,
                1.2098659719757836e-06,
                4.4508510499849186e-07,
                2.6995784182140636e-07,
                1.6373776432509826e-07,
                5.043474081993875e-07,
                2.10243290909724e-07,
                2.102434412875379e-07,
                5.715003789046955e-07
            ],
            [
                7.889265407090955e-06,
                1.4738985485997396e-05,
                6.962257079775324e-06,
                3.288748673360027e-06,
                6.962257079775324e-06,
                1.3709570434122812e-06,
                1.553497754583709e-06,
                1.99472900813862e-06,
                2.260324836787226e-06,
                6.1441760667392215e-06
            ],
            [
                7.338210680021253e-07,
                1.012999098021058e-05,
                5.4222209089700225e-06,
                4.0063701745046735e-05,
                1.3007125363719486e-05,
                3.726638395634011e-06,
                3.2887506335906595e-06,
                5.043476486915964e-07,
                6.144177531599359e-06,
                1.994730434879465e-06
            ],
            [
                2.699578096393206e-07,
                2.699578096393206e-07,
                1.4449795205429202e-07,
                1.855391681898159e-07,
                1.6373764721072816e-07,
                9.931190958026426e-08,
                3.9278615344178325e-07,
                1.4449805540700758e-07,
                1.2751904288710323e-07,
                1.1253518888531272e-07
            ],
            [
                0.9999599362935793,
                0.9998601779116947,
                0.9999930377404419,
                0.9999546021206986,
                0.9999785550567524,
                0.9999869928762173,
                0.999959936298381,
                0.9999485577803418,
                0.9999771720083428,
                0.999991060300515
            ],
            [
                1.6701421845057263e-05,
                2.1444948413814623e-05,
                2.7535681252300143e-05,
                0.0021827166360125373,
                0.00012339457491796526,
                3.1201926253802263e-05,
                1.3007131566015624e-05,
                0.0002959571002522352,
                4.222832437798974e-06,
                9.61024493798551e-05
            ],
            [
                4.450848927650143e-07,
                3.726638839878908e-06,
                2.382370235922541e-07,
                1.2751907329024393e-07,
                8.315277302841894e-07,
                2.382368247924618e-07,
                3.0590215399183813e-07,
                1.4449805540740185e-07,
                2.9023123311583482e-06,
                1.2098652508424818e-06
            ],
            [
                1.067702870039777e-06,
                1.0677029973158649e-06,
                1.553497754577351e-06,
                1.3709572068422585e-06,
                7.338210680002898e-07,
                4.222834451382849e-06,
                2.9023133690980155e-06,
                1.209865539274514e-06,
                1.9947301970813926e-06,
                2.2603234895176927e-06
            ],
            [
                8.315284241560147e-07,
                1.3709568799760888e-06,
                1.7603432133136672e-06,
                3.726639728370556e-06,
                3.927860597945825e-07,
                5.04347468309184e-07,
                8.315284241597959e-07,
                3.726638839878908e-06,
                6.475949525878687e-07,
                8.315278294072958e-07
            ],
            [
                1.5534981249697903e-06,
                1.2098653950656417e-06,
                6.962257079775324e-06,
                4.2228339479858295e-06,
                5.71500515159253e-07,
                1.0129993395217047e-05,
                2.90231094723893e-06,
                6.9622595696935874e-06,
                6.962256249885085e-06,
                1.0677032518785256e-06
            ],
            [
                2.902312677137316e-06,
                4.785092783519724e-06,
                8.939700566907275e-06,
                6.962257909785973e-06,
                1.3007128464961824e-05,
                3.2887494574518405e-06,
                5.043475885674441e-07,
                1.4738980215352592e-05,
                1.3709572068422585e-06,
                9.422447062270609e-07
            ],
            [
                3.288750241561788e-06,
                1.3709576971316842e-06,
                1.9947297215125433e-06,
                1.3709567165617364e-06,
                2.2603240284371276e-06,
                6.475947210031623e-07,
                1.2098658277451275e-06,
                4.22283545819819e-06,
                4.785096206076165e-06,
                3.726638839878908e-06
            ],
            [
                5.043472879540142e-07,
                1.0677026154806063e-06,
                5.715003107767143e-07,
                6.475950298011458e-07,
                1.994730434879465e-06,
                4.450848927621807e-07,
                3.9278615344178325e-07,
                3.927862002663297e-07,
                2.699578740032504e-07,
                9.422448185510695e-07
            ],
            [
                1.4738987242700688e-05,
                1.892515049702235e-05,
                1.6701429807630274e-05,
                6.144175334418252e-06,
                3.2887502415438413e-06,
                5.422217030747413e-06,
                1.3007131565613412e-05,
                1.300712846477255e-05,
                4.222833444429485e-06,
                6.144175334367959e-06
            ],
            [
                4.785094494783494e-06,
                1.670142582682936e-05,
                5.715006514151423e-07,
                2.2603234895176927e-06,
                1.670142980893658e-05,
                4.222831934379152e-06,
                2.260324836776948e-06,
                2.9023109472244114e-06,
                6.962257909785973e-06,
                4.785094494750855e-06
            ],
            [
                3.2887506336086064e-06,
                9.422450431989127e-07,
                3.7266406168827523e-06,
                1.0677032518748838e-06,
                1.6701427818034747e-05,
                6.475950298011458e-07,
                2.2603234895289998e-06,
                1.5534975693869924e-06,
                3.288749065406658e-06,
                1.0677028700320085e-06
            ],
            [
                9.422444815765128e-07,
                1.9947306726358406e-06,
                9.422447062202052e-07,
                8.939698434820389e-06,
                1.2098658277451275e-06,
                2.260325375664839e-06,
                2.260325375664839e-06,
                2.5612828213818346e-06,
                1.5534981249496567e-06,
                5.715006514151423e-07
            ],
            [
                2.7535697666401535e-05,
                1.9947304348703948e-06,
                2.1444943301674863e-05,
                1.1478765389222573e-05,
                2.2603242978665707e-06,
                2.9023112931688987e-06,
                0.9999599363079026,
                1.5534984953453635e-06,
                6.144177531767002e-06,
                2.902310947208574e-06
            ],
            [
                5.043472879540142e-07,
                8.315277302857965e-07,
                1.3709576971463352e-06,
                7.734414854823498e-08,
                3.0590233632400716e-07,
                1.0677032518785256e-06,
                5.715005832886879e-07,
                1.7603434231833873e-06,
                1.994730672675753e-06,
                6.144173137170873e-06
            ],
            [
                6.144176799334096e-06,
                3.288748673360027e-06,
                2.260323758987159e-06,
                1.3709570434178922e-06,
                1.8925143729575624e-05,
                1.0677032518748838e-06,
                7.338211554783522e-07,
                3.2887478892683997e-06,
                5.422221555340727e-06,
                2.5612825160562587e-06
            ],
            [
                8.939695238536645e-06,
                1.6701421844419295e-05,
                1.5534983101393749e-06,
                3.726638395611981e-06,
                2.9023126771227976e-06,
                7.889263526345123e-06,
                2.2603242978665707e-06,
                3.7266401725935817e-06,
                2.5612822107167428e-06,
                1.3709567165530083e-06
            ],
            [
                5.043476486924565e-07,
                2.3823688159291947e-07,
                2.382369667929001e-07,
                1.3709568799919866e-06,
                7.338212429582604e-07,
                2.1024336609843824e-07,
                3.9278634073732336e-07,
                2.3823702359290413e-07,
                1.1253514863968147e-07,
                2.1024331597262577e-07
            ],
            [
                3.288748673360027e-06,
                4.785094494750855e-06,
                6.144173869558639e-06,
                2.2603242978871282e-06,
                8.315280276626197e-07,
                1.3709567165617364e-06,
                7.734428685047173e-08,
                1.0677026154806063e-06,
                9.422447062270609e-07,
                6.144174601991196e-06
            ],
            [
                5.4222183235249605e-06,
                9.4224425692559e-07,
                3.927862939136532e-07,
                4.450848927650143e-07,
                6.1441731370702875e-06,
                3.726638395611981e-06,
                2.2603240284371276e-06,
                1.7603438428740716e-06,
                3.2887494574518405e-06,
                8.315282259138311e-07
            ],
            [
                1.7603434231777837e-06,
                1.3709573702647743e-06,
                3.726639728348526e-06,
                7.338212429537553e-07,
                3.2887482812506295e-06,
                4.785095635592258e-06,
                2.561283432035425e-06,
                6.144172404587612e-06,
                4.222834451355964e-06,
                2.9023112932045342e-06
            ],
            [
                1.6701421845361053e-05,
                4.78509563546605e-06,
                7.889264466115267e-06,
                1.3007125363908762e-05,
                7.88926634755014e-06,
                2.260324297853209e-06,
                3.288749457432399e-06,
                1.9947304348595095e-06,
                4.785095635592258e-06,
                3.1201900215552636e-05
            ],
            [
                3.46632497145457e-07,
                6.825600469412533e-08,
                2.3823693839290317e-07,
                2.6995784182140636e-07,
                1.637377448057981e-07,
                5.043475885674441e-07,
                1.2751899728311609e-07,
                2.6995774527718623e-07,
                1.8553919030858602e-07,
                3.059022998576899e-07
            ],
            [
                3.927862470899887e-07,
                5.71500515159253e-07,
                4.4508526417298334e-07,
                7.338209805200689e-07,
                9.422448185478557e-07,
                8.315281267882195e-07,
                1.2098653950656417e-06,
                6.475947210031623e-07,
                1.3709567165530083e-06,
                3.927860597945825e-07
            ],
            [
                4.7850939242083995e-06,
                1.9947290081286418e-06,
                6.962259569560613e-06,
                1.9947290081286418e-06,
                2.5612822107167428e-06,
                3.726641061085547e-06,
                2.902313023063532e-06,
                5.422220908925639e-06,
                1.3007125362820425e-05,
                2.902311985146426e-06
            ],
            [
                7.338212429582604e-07,
                8.315281267861397e-07,
                5.715003789017068e-07,
                3.4663262110945863e-07,
                5.715007195447234e-07,
                5.043472879525233e-07,
                9.422442569208767e-07,
                8.315281267882195e-07,
                5.043472879525233e-07,
                5.715003107767143e-07
            ],
            [
                3.2887494574518405e-06,
                3.726638395611981e-06,
                2.9023112932045342e-06,
                1.0129995810463632e-05,
                5.4222183234485234e-06,
                2.9023116391978967e-06,
                1.3007131566015624e-05,
                6.144173869502757e-06,
                1.3709572068354007e-06,
                3.2887506336086064e-06
            ],
            [
                2.144495608424996e-05,
                7.338212429504183e-07,
                3.288749849498565e-06,
                3.2887506336086064e-06,
                4.785095635592258e-06,
                2.561283432035425e-06,
                7.338209805200689e-07,
                4.450852111135988e-07,
                5.4222209089700225e-06,
                9.422444815765128e-07
            ],
            [
                9.610242647154786e-05,
                1.8925143729575624e-05,
                1.0129994602656007e-05,
                6.144177531767002e-06,
                2.260324297853209e-06,
                3.535625071602016e-05,
                5.422220908925639e-06,
                4.785093353909723e-06,
                1.3709576971425944e-06,
                7.889259764359722e-06
            ],
            [
                3.059022998576899e-07,
                3.726639728370556e-06,
                4.450849988811838e-07,
                5.715004470313855e-07,
                6.475947210012481e-07,
                9.422447062202052e-07,
                1.2098653950656417e-06,
                5.043472879540142e-07,
                2.3823699519290042e-07,
                4.450852111148132e-07
            ],
            [
                7.338209805240734e-07,
                1.994730434847717e-06,
                2.3823693839290317e-07,
                8.315278294097538e-07,
                1.0677029973192638e-06,
                1.7603438428800754e-06,
                7.338211554783522e-07,
                5.715003107738556e-07,
                1.0677028700203557e-06,
                8.315283250371857e-07
            ],
            [
                1.8925150497848527e-05,
                0.00013982204087139387,
                6.144174601935314e-06,
                0.43782349911420193,
                3.120191137659974e-05,
                2.5612831267086116e-06,
                1.2098661161982042e-06,
                7.889263526180094e-06,
                1.4738989000422955e-05,
                3.726641061027928e-06
            ],
            [
                1.1478772230929451e-05,
                6.962256249758443e-06,
                4.222835458148261e-06,
                1.994730434879465e-06,
                0.9996646497417206,
                1.4738978458382043e-05,
                4.785093924362895e-06,
                2.561281905376098e-06,
                1.8925150497435443e-05,
                1.1478773599425825e-05
            ],
            [
                1.1478765389065974e-05,
                3.726641061085547e-06,
                1.4738976701411704e-05,
                3.726639284125553e-06,
                6.962257909722651e-06,
                0.0003799845309913699,
                3.120190393794438e-05,
                1.1478765389222573e-05,
                3.288749457409966e-06,
                1.0129989772412744e-05
            ],
            [
                2.6995774527577444e-07,
                5.04347528446051e-07,
                1.0677031245990084e-06,
                5.715004470313855e-07,
                2.382370235922541e-07,
                2.6995771309523475e-07,
                2.699578740032504e-07,
                3.9278634073732336e-07,
                3.927862939126708e-07,
                1.855391239544352e-07
            ],
            [
                8.315278294072958e-07,
                4.450852111148132e-07,
                1.0677026154730804e-06,
                1.7603434231777837e-06,
                6.475947210012481e-07,
                1.0677027427600627e-06,
                1.5534975693869924e-06,
                6.144177531532303e-06,
                8.315279285351409e-07,
                8.315281267861397e-07
            ],
            [
                6.144175334468545e-06,
                2.561282210740037e-06,
                2.9023133690980155e-06,
                2.5612834320470717e-06,
                2.561283432035425e-06,
                1.3709572068478697e-06,
                1.5534983101602148e-06,
                2.2603234895289998e-06,
                1.3709570434122812e-06,
                3.726639284125553e-06
            ],
            [
                0.9999516743507113,
                3.2887498495150166e-06,
                1.5534981249697903e-06,
                1.0677031245905116e-06,
                4.785096776468749e-06,
                3.288747889229516e-06,
                1.0677031245905116e-06,
                5.04347528446051e-07,
                2.5612828213818346e-06,
                1.0677028700363782e-06
            ],
            [
                3.466325797888292e-07,
                4.450852111155216e-07,
                2.1024341622426268e-07,
                2.3823699519290042e-07,
                2.699577774585891e-07,
                1.8553910183607374e-07,
                7.338213304363436e-07,
                2.382368531929327e-07,
                3.466327037539638e-07,
                3.0590226339061185e-07
            ],
            [
                3.288748281295496e-06,
                5.4222183234485234e-06,
                1.0677028700363782e-06,
                2.4300234941261454e-05,
                3.2887506336086064e-06,
                8.315281267834927e-07,
                9.422447062202052e-07,
                1.2098662604247682e-06,
                1.0129994602222992e-05,
                6.144172404693786e-06
            ],
            [
                1.3709573702822306e-06,
                2.5612831267202583e-06,
                1.0677027427600627e-06,
                5.043476486924565e-07,
                2.2603237589779086e-06,
                5.14422075345321e-05,
                1.3709568799879344e-06,
                4.450851580566494e-07,
                9.422448185534261e-07,
                4.450851580566494e-07
            ],
            [
                8.315282259089153e-07,
                4.006368741670684e-05,
                7.889265407090955e-06,
                2.7535697667202906e-05,
                8.939700567004841e-06,
                6.605217618626244e-05,
                3.1201922533564516e-05,
                3.288748281329893e-06,
                2.1444948414321717e-05,
                2.430023204129162e-05
            ]
        ]
    },
    {
        "q_id": "9614_mmlu_physics",
        "cot_ids": [
            2,
            4,
            5,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            17,
            18,
            19,
            20,
            23,
            25,
            27,
            29,
            31,
            32,
            33,
            34,
            35,
            37,
            39,
            40,
            41,
            43,
            44,
            45,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            59,
            60,
            61,
            64,
            65,
            66,
            68,
            69,
            70,
            71,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            84,
            85,
            87,
            89,
            90,
            93,
            97,
            98,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            108,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                6.962257079705671e-06,
                6.475947982037486e-07,
                1.2098659719716573e-06,
                NaN,
                7.889261645427538e-06,
                3.120190021657421e-05,
                4.2228319344021954e-06,
                4.222832941193893e-06,
                8.939693106987645e-06,
                1.1478769494396542e-05
            ],
            [
                0.9999945777816883,
                0.9999972735307071,
                0.9999975938965152,
                2.382370235933104e-07,
                0.9999916019309782,
                0.9999974387165713,
                0.9999952149060859,
                0.9999960330126736,
                0.9999972735303828,
                7.338208055664991e-07
            ],
            [
                0.9999988634361553,
                0.9999832985763039,
                0.9999934595596741,
                0.9999934595612257,
                0.9999957771675754,
                5.422220909009474e-06,
                0.9999938558239445,
                0.9999957771675766,
                0.9999987121044784,
                1.8925152753790864e-05
            ],
            [
                2.2603248367949354e-06,
                3.2887502415767434e-06,
                2.902312331170226e-06,
                1.5534971990126997e-06,
                3.288748281329893e-06,
                1.3007130015677909e-05,
                3.72663883989755e-06,
                1.4738989000422955e-05,
                6.144177531811707e-06,
                1.9947301970972664e-06
            ],
            [
                0.9992903297137148,
                2.561282516066741e-06,
                1.3709573702822306e-06,
                4.785095635624897e-06,
                5.043473480777865e-07,
                1.3709570434219446e-06,
                5.4222176771176554e-06,
                1.3709570434219446e-06,
                1.0129992187658463e-05,
                0.0001233945896995423
            ],
            [
                3.059022998576899e-07,
                2.5612834320470717e-06,
                3.2887506336086064e-06,
                2.5612828213690224e-06,
                2.6995790618469934e-07,
                1.1478768126057254e-05,
                5.422217030747413e-06,
                NaN,
                4.4508510499849186e-07,
                7.338208930460318e-07
            ],
            [
                6.144177531811707e-06,
                4.785094494811783e-06,
                4.4508494582405734e-07,
                3.288747889284851e-06,
                6.144173137170873e-06,
                5.715002426486762e-07,
                2.561281600086738e-06,
                1.5534973842076057e-06,
                2.5612819054133693e-06,
                4.4508494582405734e-07
            ],
            [
                1.0677032518814388e-06,
                2.6995784182140636e-07,
                2.902312677150514e-06,
                2.5612819054028872e-06,
                1.147877359957198e-05,
                0.9999516743795418,
                1.2098658277451275e-06,
                2.1444945858485726e-05,
                5.04347528446051e-07,
                3.05902336324494e-07
            ],
            [
                3.7266401726359486e-06,
                6.962257909722651e-06,
                2.5612828213934817e-06,
                1.8925143729954285e-05,
                1.6701427817730953e-05,
                3.2887506336086064e-06,
                6.962256249885085e-06,
                3.726638839878908e-06,
                1.1478768125911099e-05,
                1.3007134667070165e-05
            ],
            [
                0.9999151889703357,
                8.315281267882195e-07,
                1.6701415872659116e-05,
                2.561281600076256e-06,
                1.3709575337159875e-06,
                1.2098655392921197e-06,
                4.006369697116762e-05,
                0.0001584361604033022,
                0.9999038975862135,
                2.9023112932296107e-06
            ],
            [
                5.043472879525233e-07,
                1.5534975693979422e-06,
                2.902311639183378e-06,
                1.30071315662049e-05,
                NaN,
                1.0677032518748838e-06,
                1.5534971990126997e-06,
                5.043472879540142e-07,
                1.209866260432471e-06,
                1.30071315662049e-05
            ],
            [
                1.7603440527222532e-06,
                5.043475284430694e-07,
                2.2603251062147097e-06,
                9.422450432014836e-07,
                3.4663249714612693e-07,
                1.2098652508424818e-06,
                1.2098661162056318e-06,
                1.0677027427525368e-06,
                NaN,
                6.47595107001401e-07
            ],
            [
                9.422443692574719e-07,
                3.466325797896173e-07,
                1.2098655392921197e-06,
                NaN,
                2.2603251062450327e-06,
                6.475947210046347e-07,
                3.466327037553825e-07,
                1.0677028700422047e-06,
                NaN,
                2.2603248367949354e-06
            ],
            [
                1.209865539295696e-06,
                8.31528325040778e-07,
                1.1478768126057254e-05,
                4.7850933539684755e-06,
                1.209865827752005e-06,
                6.475945666063607e-07,
                1.1478770862882149e-05,
                7.338207180884785e-07,
                NaN,
                3.466326624336003e-07
            ],
            [
                7.338207180898968e-07,
                2.9023119851899796e-06,
                7.338212429582604e-07,
                2.260324836787226e-06,
                NaN,
                3.05902190458764e-07,
                3.288749065436569e-06,
                6.475947210046347e-07,
                7.338207180898968e-07,
                1.8925141473978602e-05
            ],
            [
                1.2098659719716573e-06,
                1.0677033791612137e-06,
                1.2098659719757836e-06,
                4.4508505193932864e-07,
                3.466325384661554e-07,
                1.760342793638743e-06,
                4.222833444590791e-06,
                2.9023119851899796e-06,
                2.382370235933104e-07,
                3.7266410611296085e-06
            ],
            [
                2.3823693839325527e-07,
                5.715006514167015e-07,
                2.382369951932796e-07,
                8.315281267882195e-07,
                4.006371129776199e-05,
                3.288747889284851e-06,
                0.9999339478481513,
                3.927862002663297e-07,
                0.0001398220742354593,
                0.9999985406241285
            ],
            [
                2.9023112932177327e-06,
                4.0063677865600476e-05,
                1.1253518888531272e-07,
                5.71500719545698e-07,
                1.994729721482609e-06,
                NaN,
                2.2603234895372223e-06,
                8.315277302857965e-07,
                NaN,
                1.2098658277451275e-06
            ],
            [
                1.2098652508424818e-06,
                6.47595107001401e-07,
                7.338208930460318e-07,
                5.4222183235249605e-06,
                2.2603253756956754e-06,
                2.902313369111213e-06,
                3.059022998576899e-07,
                8.315279285370317e-07,
                3.2887482813149375e-06,
                6.475945666063607e-07
            ],
            [
                0.9999975938973766,
                0.9999962733611709,
                1.3709575337159875e-06,
                0.9999942280792995,
                0.9999977396757054,
                4.4508510499849186e-07,
                0.9999964991460119,
                0.9999955048179001,
                0.9999967112497685,
                7.338210680021253e-07
            ],
            [
                5.715002426475718e-07,
                1.5534984953510149e-06,
                2.561283432005142e-06,
                7.338212429582604e-07,
                2.699578096403948e-07,
                3.05902190458764e-07,
                1.5534983101602148e-06,
                4.2228339479858295e-06,
                9.422442569315887e-07,
                1.2098659719757836e-06
            ],
            [
                4.006368741670684e-05,
                1.6701427818034747e-05,
                1.3007125363908762e-05,
                1.892515501014656e-05,
                2.561282210740037e-06,
                NaN,
                1.3709578605729614e-06,
                4.785095635592258e-06,
                9.422449308716635e-07,
                5.043475885696228e-07
            ],
            [
                3.7266406168624155e-06,
                1.0677029973192638e-06,
                1.1478770862882149e-05,
                6.144172404738491e-06,
                NaN,
                0.9999960330145675,
                1.6701421845057263e-05,
                3.9278615344178325e-07,
                NaN,
                9.422448185478557e-07
            ],
            [
                2.5612819054133693e-06,
                1.6701417863559525e-05,
                0.9999667857895845,
                8.315277302857965e-07,
                NaN,
                7.889259764517575e-06,
                6.47595107001401e-07,
                4.2228319344021954e-06,
                7.889264466868659e-06,
                3.726637951387472e-06
            ],
            [
                1.3709567165579959e-06,
                2.561282516066741e-06,
                1.5534971990126997e-06,
                3.2887490653872164e-06,
                1.5534975693979422e-06,
                9.422445939032799e-07,
                3.7266406168624155e-06,
                1.3709570434178922e-06,
                1.3007133116732079e-05,
                6.962257909785973e-06
            ],
            [
                3.9278634073732336e-07,
                1.9947299593078385e-06,
                NaN,
                1.9947304348862686e-06,
                NaN,
                7.338213304363436e-07,
                3.9278634073732336e-07,
                9.422444815792981e-07,
                4.4508510499849186e-07,
                3.4663249714612693e-07
            ],
            [
                3.4663249714451116e-07,
                6.144172404693786e-06,
                7.338212429537553e-07,
                6.47594798194325e-07,
                1.0677032518785256e-06,
                1.2098662604126641e-06,
                9.422443692489024e-07,
                8.315279285351409e-07,
                6.144175334418252e-06,
                1.3709568799919866e-06
            ],
            [
                8.315281267882195e-07,
                9.422445939032799e-07,
                1.3709567165617364e-06,
                1.7603434231833873e-06,
                6.475949526020042e-07,
                3.4663278639892215e-07,
                2.561282210740037e-06,
                7.338213304363436e-07,
                1.7603430034867993e-06,
                1.994730672675753e-06
            ],
            [
                7.338207180898968e-07,
                5.144221980317192e-05,
                0.9999975938968013,
                1.0677026154827912e-06,
                1.0677028700422047e-06,
                5.715002426486762e-07,
                1.994729483729522e-06,
                4.006370652227855e-05,
                1.7603425837903113e-06,
                3.7266397283908927e-06
            ],
            [
                2.2603251062450327e-06,
                NaN,
                1.209865539295696e-06,
                2.9023116392097746e-06,
                1.2098652508424818e-06,
                1.9947292459347367e-06,
                1.994729008151319e-06,
                2.2603242978943238e-06,
                3.2887502415767434e-06,
                4.222834451403972e-06
            ],
            [
                9.610246083366117e-05,
                1.5534979397790343e-06,
                4.78509278348926e-06,
                1.3007134667070165e-05,
                6.144177531767002e-06,
                1.5534975693869924e-06,
                1.994730672668496e-06,
                1.0129987357158383e-05,
                1.6701419854156377e-05,
                7.889263526180094e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                8.939693107190907e-06,
                3.288748673376478e-06,
                1.370957860576702e-06,
                5.043472879540142e-07,
                0.9999646437379232,
                7.889259764359722e-06,
                2.9023112932045342e-06
            ],
            [
                1.275189972832538e-07,
                2.561282821402217e-06,
                1.2098653950716937e-06,
                8.31528325040778e-07,
                3.9278629391427843e-07,
                3.466327450765785e-07,
                1.0677024882029858e-06,
                5.043474683240344e-07,
                1.0677026154827912e-06,
                1.1253522913127183e-07
            ],
            [
                6.144177531811707e-06,
                2.260324028443809e-06,
                0.0010322308488868097,
                5.043472278322555e-07,
                0.9999987121049395,
                0.9999339478485598,
                6.144175334468545e-06,
                0.9999687980889085,
                6.962259569750576e-06,
                7.338209805240734e-07
            ],
            [
                8.315281267861397e-07,
                1.3007134667259441e-05,
                1.994730197090463e-06,
                4.785095065204162e-06,
                8.315281267834927e-07,
                9.422442569315887e-07,
                6.9622595696935874e-06,
                4.785093924362895e-06,
                0.0003353501511018999,
                5.715002426475718e-07
            ],
            [
                NaN,
                NaN,
                7.889262585958025e-06,
                1.3007133116542802e-05,
                5.4222183234485234e-06,
                0.9999516743627817,
                3.2887502415767434e-06,
                0.00017952803042334226,
                2.2603242978871282e-06,
                0.9999832985859897
            ],
            [
                NaN,
                2.3823696679327928e-07,
                2.260323758987159e-06,
                3.927862002663297e-07,
                1.3709570434219446e-06,
                8.939693107288474e-06,
                5.04347287955046e-07,
                7.338208930460318e-07,
                1.0677031245990084e-06,
                2.2603242978871282e-06
            ],
            [
                2.2603251062450327e-06,
                0.9999516743394623,
                1.0677029973219343e-06,
                0.9999977396765122,
                3.288749065423109e-06,
                6.475946438055299e-07,
                0.999991060304775,
                2.902313369111213e-06,
                2.699576809143613e-07,
                0.9999949062925805
            ],
            [
                1.994729008145876e-06,
                2.9023112932177327e-06,
                2.9023119851899796e-06,
                5.4222183235249605e-06,
                3.9278629391427843e-07,
                8.315277302857965e-07,
                3.288748281329893e-06,
                1.3709570434219446e-06,
                5.04347528446051e-07,
                5.04347468323289e-07
            ],
            [
                2.5612819054133693e-06,
                0.9999898700078498,
                0.9998766054702402,
                5.8291251656508296e-05,
                0.9999962733607218,
                4.222831934379152e-06,
                2.382369667929001e-07,
                0.9999949062968296,
                0.00043055714347597695,
                0.9999925887166193
            ],
            [
                4.222832437798974e-06,
                NaN,
                0.9999810748563914,
                8.939695238536645e-06,
                1.8925148242250705e-05,
                1.3007130015677909e-05,
                NaN,
                5.4222176771176554e-06,
                0.9999646437326103,
                0.9999945777810366
            ],
            [
                0.00029595699421718763,
                1.0129988564974359e-05,
                3.288747889284851e-06,
                1.067703124601679e-06,
                4.785093353940187e-06,
                5.04347287955046e-07,
                6.605217619491253e-05,
                1.4738985486506781e-05,
                1.067703124601679e-06,
                6.144173137170873e-06
            ],
            [
                6.475945666063607e-07,
                5.715006514176113e-07,
                1.670141786325573e-05,
                9.422444815765128e-07,
                3.288747889284851e-06,
                3.2887482813149375e-06,
                1.553498124964492e-06,
                1.0677032518700286e-06,
                7.338213304363436e-07,
                8.939696304311336e-06
            ],
            [
                6.962255419804982e-06,
                6.144175334468545e-06,
                4.222833947960866e-06,
                1.760343633031919e-06,
                3.726639284050988e-06,
                7.889262585886274e-06,
                NaN,
                1.1478766757561534e-05,
                4.785092783415276e-06,
                0.00020342702201785152
            ],
            [
                1.3709572068522336e-06,
                NaN,
                6.962254589978262e-06,
                2.9023116391978967e-06,
                6.1441767993788005e-06,
                2.9023119851899796e-06,
                1.2098656835136636e-06,
                3.059021904571643e-07,
                2.699578740032504e-07,
                7.338208930443633e-07
            ],
            [
                6.962257909842961e-06,
                0.00012339457500953096,
                2.4300249425822333e-05,
                3.288749849529972e-06,
                NaN,
                2.753569766795419e-05,
                1.3709576971463352e-06,
                1.5534981249697903e-06,
                1.3007126914612648e-05,
                3.7266383956509585e-06
            ],
            [
                1.760343633031919e-06,
                8.315277302857965e-07,
                4.4508515805735777e-07,
                2.2603251062450327e-06,
                1.760343213335281e-06,
                1.3709575337159875e-06,
                3.9278605979534166e-07,
                3.4663274507713016e-07,
                3.72663883989755e-06,
                3.466327037553825e-07
            ],
            [
                7.338210680021253e-07,
                4.006369219393695e-05,
                7.338211554783522e-07,
                7.889262585814522e-06,
                8.939699501229642e-06,
                3.288749457469787e-06,
                4.222834451355964e-06,
                1.7603434231833873e-06,
                NaN,
                1.892515501014656e-05
            ],
            [
                6.144173869603344e-06,
                NaN,
                2.2603242978778778e-06,
                2.9023119851781017e-06,
                2.9023116391978967e-06,
                1.0677029973219343e-06,
                3.288747889284851e-06,
                4.5397857828200684e-05,
                1.067703379154416e-06,
                8.315279285351409e-07
            ],
            [
                1.6373770576776313e-07,
                7.338208930460318e-07,
                8.939700567094277e-06,
                3.288749065423109e-06,
                0.9999977396759736,
                5.043475885696228e-07,
                0.9999989322975126,
                1.0677026154827912e-06,
                0.9999982396563677,
                2.1024336609874897e-07
            ],
            [
                4.78509278348926e-06,
                2.2603234895289998e-06,
                2.9023112932177327e-06,
                1.7603436330259153e-06,
                1.3709572068522336e-06,
                1.994730672668496e-06,
                1.9947297215125433e-06,
                2.2603242978871282e-06,
                1.9947304348862686e-06,
                1.0
            ],
            [
                1.760343213335281e-06,
                NaN,
                7.338207180898968e-07,
                5.043475284468537e-07,
                1.9947304348862686e-06,
                1.1478764021029928e-05,
                1.1478764021029928e-05,
                3.288747889284851e-06,
                6.47595107001401e-07,
                2.6995784182183607e-07
            ],
            [
                2.9023112932296107e-06,
                9.93120161310289e-08,
                NaN,
                3.059022269254856e-07,
                1.4449796928021588e-07,
                1.7603425837903113e-06,
                6.962257909842961e-06,
                1.5534983101644536e-06,
                1.0677032518814388e-06,
                1.067703124601679e-06
            ],
            [
                8.315281267882195e-07,
                8.315280276626197e-07,
                1.9947301970972664e-06,
                3.9278629391427843e-07,
                4.450852641737424e-07,
                7.338208930460318e-07,
                1.855391239547094e-07,
                5.715005832895975e-07,
                1.994729721518893e-06,
                1.0677029973219343e-06
            ],
            [
                2.902313369111213e-06,
                5.422220262636381e-06,
                NaN,
                8.315277302857965e-07,
                3.9278629391427843e-07,
                1.209866260432471e-06,
                4.7850933539684755e-06,
                4.450848927658745e-07,
                6.475947210046347e-07,
                6.475949526020042e-07
            ],
            [
                0.9999957771655572,
                0.9999974387184031,
                0.999996711250549,
                0.9999984465022468,
                1.7603425837903113e-06,
                4.22283545819819e-06,
                3.927862002663297e-07,
                1.0677029973158649e-06,
                1.0677027427525368e-06,
                2.102434162245973e-07
            ],
            [
                0.001169510291981473,
                5.422220262636381e-06,
                NaN,
                3.7266401726173067e-06,
                2.561282210740037e-06,
                NaN,
                NaN,
                2.561282210740037e-06,
                2.2603248367949354e-06,
                4.785095065132354e-06
            ],
            [
                1.1478768126057254e-05,
                4.785096206076165e-06,
                4.785096776499213e-06,
                1.2098659719757836e-06,
                1.2098661162056318e-06,
                4.006368741670684e-05,
                1.7603440527286572e-06,
                0.00023050679810176722,
                1.2098656835224664e-06,
                6.47595107001401e-07
            ],
            [
                2.6995790618469934e-07,
                1.3709576971463352e-06,
                1.3709572068522336e-06,
                2.902313369111213e-06,
                1.5534973841895917e-06,
                3.7266379513434106e-06,
                1.5534983101393749e-06,
                1.9947301970972664e-06,
                7.338213304363436e-07,
                1.7603434231777837e-06
            ],
            [
                1.30071315662049e-05,
                4.222834451355964e-06,
                1.5534981249697903e-06,
                6.475947982037486e-07,
                3.9278634073732336e-07,
                8.315277302857965e-07,
                1.0129988565084915e-05,
                3.288748281329893e-06,
                8.939697369980456e-06,
                NaN
            ],
            [
                5.715003789033962e-07,
                1.2098662604291696e-06,
                9.422448185478557e-07,
                7.338211554725124e-07,
                2.1024341622426268e-07,
                3.927861066170637e-07,
                3.0590226339061185e-07,
                5.043474081993875e-07,
                6.475947210012481e-07,
                1.8553916819032217e-07
            ],
            [
                1.994729721518893e-06,
                6.47594952603035e-07,
                3.9278610661902853e-07,
                3.927862470905692e-07,
                7.889263525778283e-06,
                1.0129987357517693e-05,
                6.475950298021765e-07,
                9.422450432030903e-07,
                1.300712536408621e-05,
                2.5612834320470717e-06
            ],
            [
                8.481106160734935e-05,
                5.715003107767143e-07,
                3.288748281329893e-06,
                4.785094494811783e-06,
                9.422443692574719e-07,
                2.9023112932177327e-06,
                4.785095635655362e-06,
                1.0677024882009222e-06,
                1.994730197090463e-06,
                2.7535697667202906e-05
            ],
            [
                2.902312331170226e-06,
                0.9999983463106126,
                3.535626335944147e-05,
                2.5612819054133693e-06,
                1.3007130015677909e-05,
                5.422218969895357e-06,
                0.9999978766210351,
                6.144173869603344e-06,
                2.753569110256289e-05,
                1.7603425837855082e-06
            ],
            [
                3.0590215399281185e-07,
                0.9999987901347502,
                2.1024331597262577e-07,
                1.0677024882009222e-06,
                7.338209805240734e-07,
                3.9278634073732336e-07,
                1.5534981249697903e-06,
                5.715002426475718e-07,
                1.0677033791612137e-06,
                2.5612834320563895e-06
            ],
            [
                1.9947301970972664e-06,
                9.422448185510695e-07,
                1.2098662604247682e-06,
                1.6373768624837685e-07,
                3.726639284144195e-06,
                NaN,
                1.067703124601679e-06,
                9.422444815814404e-07,
                3.4663249714612693e-07,
                1.994729008145876e-06
            ],
            [
                2.2603234895372223e-06,
                1.3709567165617364e-06,
                5.04347468323289e-07,
                3.7266401726359486e-06,
                1.5534971990169383e-06,
                4.2228319344021954e-06,
                1.5534973842076057e-06,
                8.939696304311336e-06,
                2.9023119851899796e-06,
                1.0677024882009222e-06
            ],
            [
                4.222833444590791e-06,
                NaN,
                4.450848927658745e-07,
                9.422444815814404e-07,
                3.2887498495150166e-06,
                5.715005832886879e-07,
                0.9988304897436477,
                7.338207180864763e-07,
                3.927862939126708e-07,
                7.338208055664991e-07
            ],
            [
                4.450850519409479e-07,
                4.222834451403972e-06,
                1.5534984953552536e-06,
                7.889264466868659e-06,
                1.9947301970972664e-06,
                1.5534971990169383e-06,
                1.209865827752005e-06,
                NaN,
                2.902312331170226e-06,
                1.5534975693979422e-06
            ],
            [
                4.785092783319532e-06,
                2.1444948414321717e-05,
                2.1444958640087166e-05,
                4.222833947932061e-06,
                2.4300240732671408e-05,
                1.3007128464346676e-05,
                1.5534979397740895e-06,
                3.7266388398585725e-06,
                1.3007125363908762e-05,
                NaN
            ],
            [
                7.889263526266196e-06,
                3.2887506336086064e-06,
                6.962254589851619e-06,
                3.288749457469787e-06,
                5.4222215550004564e-06,
                4.2228319344021954e-06,
                1.6701421844085127e-05,
                4.785095065204162e-06,
                9.422444815726566e-07,
                4.5397879467176906e-05
            ],
            [
                2.2603253756956754e-06,
                1.2098662603862553e-06,
                2.90231094723893e-06,
                1.7603425837903113e-06,
                1.994729008151319e-06,
                4.222834451403972e-06,
                6.962257909842961e-06,
                2.561282516066741e-06,
                2.699576809143613e-07,
                1.370957860576702e-06
            ],
            [
                5.422220908925639e-06,
                3.726638839878908e-06,
                NaN,
                3.120192625482384e-05,
                1.6701427817730953e-05,
                2.1444945856964448e-05,
                4.222834451169694e-06,
                2.9023112931688987e-06,
                3.726641061085547e-06,
                7.889264466639056e-06
            ],
            [
                1.0677029973219343e-06,
                1.5534971990169383e-06,
                5.04347287955046e-07,
                4.450852641737424e-07,
                1.5534973842076057e-06,
                5.043475885696228e-07,
                2.561281600086738e-06,
                3.927863407379485e-07,
                2.561281294760143e-06,
                5.715006514176113e-07
            ],
            [
                4.006369219233375e-05,
                6.962257079832313e-06,
                1.9947294837154625e-06,
                2.2603234895289998e-06,
                8.93969950132721e-06,
                1.7603438428800754e-06,
                6.475950298011458e-07,
                8.93969950132721e-06,
                2.2603253756956754e-06,
                1.6701421845057263e-05
            ],
            [
                0.9999969105062934,
                8.315279285351409e-07,
                1.5534983101644536e-06,
                0.999993459562011,
                0.9999938558254143,
                2.1444943302650045e-05,
                2.2603242978871282e-06,
                5.043473480777865e-07,
                7.338207180898968e-07,
                6.962256249885085e-06
            ],
            [
                9.610246085253877e-05,
                NaN,
                9.422442569315887e-07,
                1.994729721518893e-06,
                1.2098659719788098e-06,
                9.422450432014836e-07,
                2.561281294760143e-06,
                8.315280276626197e-07,
                5.422221555414699e-06,
                5.422217030747413e-06
            ],
            [
                1.994730197090463e-06,
                3.927862002663297e-07,
                2.5612828213818346e-06,
                NaN,
                1.2098653950656417e-06,
                5.043476486915964e-07,
                4.785095065232451e-06,
                1.4738978458140753e-05,
                9.422447062294175e-07,
                1.0677028700363782e-06
            ],
            [
                3.2887498495150166e-06,
                NaN,
                6.475947210012481e-07,
                NaN,
                1.4738976701411704e-05,
                8.315280276546789e-07,
                1.2098653950656417e-06,
                1.99472900813862e-06,
                2.5612831267202583e-06,
                1.5534975693869924e-06
            ],
            [
                0.00015843625480754269,
                5.043476486924565e-07,
                2.90231094723893e-06,
                3.7266397283908927e-06,
                1.3709575337125585e-06,
                0.00015843629259415065,
                2.4300243631890864e-05,
                1.8925148241872038e-05,
                NaN,
                0.9999980052695702
            ],
            [
                1.7603425837903113e-06,
                5.043476486915964e-07,
                3.466326624336003e-07,
                3.7266383956509585e-06,
                2.2603251062450327e-06,
                5.043472278322555e-07,
                2.561283432035425e-06,
                4.4508494582405734e-07,
                6.47594952603035e-07,
                1.994729721518893e-06
            ],
            [
                6.475948754028718e-07,
                6.144175334468545e-06,
                7.889259764517575e-06,
                NaN,
                NaN,
                2.2603253756874524e-06,
                9.422444815814404e-07,
                6.475946438055299e-07,
                4.785094494783494e-06,
                1.5534973842076057e-06
            ],
            [
                1.9947292459347367e-06,
                4.4508494582405734e-07,
                2.902313369111213e-06,
                3.059022998576899e-07,
                3.7266410611465547e-06,
                5.715005151606823e-07,
                1.3709576971425944e-06,
                4.4508526417298334e-07,
                1.7603440527286572e-06,
                5.043472278322555e-07
            ],
            [
                4.222832437798974e-06,
                1.5534977545886537e-06,
                1.994729483723626e-06,
                1.209866260432471e-06,
                7.338208055664991e-07,
                3.288749457469787e-06,
                7.338213304363436e-07,
                2.102434412875379e-07,
                8.315278294072958e-07,
                3.927860597945825e-07
            ],
            [
                2.5612828213934817e-06,
                NaN,
                NaN,
                3.288749457469787e-06,
                2.2603242978871282e-06,
                1.9947297215125433e-06,
                NaN,
                1.9947297215125433e-06,
                1.9947292459347367e-06,
                0.00017952792332844784
            ],
            [
                1.0677027427600627e-06,
                1.4449798650551755e-07,
                0.9953904288825183,
                7.889260704968913e-06,
                3.05902336324494e-07,
                3.4663274507713016e-07,
                3.7266383956509585e-06,
                5.715002426486762e-07,
                1.9947301970972664e-06,
                2.5612834320563895e-06
            ],
            [
                3.9278629391427843e-07,
                NaN,
                1.9947292459406333e-06,
                NaN,
                7.338208055680009e-07,
                4.4508515805735777e-07,
                3.9278610661902853e-07,
                1.5534979397829198e-06,
                6.475946438055299e-07,
                3.927863407379485e-07
            ],
            [
                6.144174602077811e-06,
                3.059022269254856e-07,
                7.338212429594283e-07,
                3.726639284144195e-06,
                1.7603438428848787e-06,
                2.1024336609843824e-07,
                1.0677028700422047e-06,
                2.5612834320563895e-06,
                1.5534981249736758e-06,
                1.994729008151319e-06
            ],
            [
                0.9999771720056514,
                1.2098653950692178e-06,
                3.0590237279032884e-07,
                0.999989870006626,
                6.475947982037486e-07,
                4.450852111148132e-07,
                0.9999925887166164,
                1.4738983729750081e-05,
                1.3709570434178922e-06,
                2.902312677150514e-06
            ],
            [
                0.9999934595651283,
                5.043475885696228e-07,
                0.9999969105040853,
                3.7266383956509585e-06,
                4.539786324145319e-05,
                1.370957860576702e-06,
                1.892514598627448e-05,
                3.288747889284851e-06,
                0.9999904837494573,
                0.9999981261239482
            ],
            [
                8.315277302857965e-07,
                2.5612819054133693e-06,
                4.785093353940187e-06,
                0.9999964991464276,
                0.9999974387168757,
                6.962255419931625e-06,
                5.715002426486762e-07,
                1.5534984953552536e-06,
                9.422443692574719e-07,
                1.994729483729522e-06
            ]
        ]
    },
    {
        "q_id": "9978_mmlu_physics",
        "cot_ids": [
            0,
            3,
            4,
            8,
            10,
            12,
            16,
            17,
            18,
            20,
            23,
            24,
            26,
            27,
            31,
            32,
            33,
            34,
            38,
            41,
            45,
            46,
            50,
            51,
            53,
            54,
            55,
            58,
            59,
            63,
            64,
            65,
            66,
            70,
            71,
            73,
            74,
            75,
            79,
            81,
            84,
            90,
            91,
            95,
            96,
            97,
            101,
            103,
            104,
            105,
            106,
            108,
            109,
            111,
            112,
            116,
            119,
            120,
            127
        ],
        "rewards": [
            [
                2.5612822107167428e-06,
                2.1444953526969788e-05,
                8.939693107190907e-06,
                4.222833947932061e-06,
                6.605216831803618e-05,
                6.962257909785973e-06,
                2.561282516066741e-06,
                NaN,
                1.4738976700929127e-05,
                6.962257909785973e-06
            ],
            [
                8.939694172867777e-06,
                3.535625914492432e-05,
                1.5534983101478522e-06,
                6.14417753171671e-06,
                2.5612834320214477e-06,
                4.785092783371756e-06,
                3.7266379513434106e-06,
                6.475951069961737e-07,
                1.0677029973192638e-06,
                6.144176066850984e-06
            ],
            [
                NaN,
                1.0129988564974359e-05,
                6.144175334418252e-06,
                6.475947210012481e-07,
                NaN,
                NaN,
                6.1441731370702875e-06,
                3.726639284050988e-06,
                NaN,
                NaN
            ],
            [
                3.059023727894942e-07,
                1.3709576971379186e-06,
                7.3382080556433e-07,
                4.450848927650143e-07,
                NaN,
                6.475950298011458e-07,
                1.9947292459265734e-06,
                5.715003107755449e-07,
                1.2098652508424818e-06,
                NaN
            ],
            [
                6.9622595696935874e-06,
                7.338207180864763e-07,
                2.2603234895176927e-06,
                NaN,
                2.5612819054028872e-06,
                1.3709576971425944e-06,
                2.902312677137316e-06,
                1.0129990980100021e-05,
                1.3709575337125585e-06,
                8.939698435560267e-06
            ],
            [
                1.6701425826525565e-05,
                1.3007131566015624e-05,
                7.889266347715168e-06,
                NaN,
                1.4738987243236881e-05,
                8.315281267861397e-07,
                3.2887490653872164e-06,
                6.144177531811707e-06,
                NaN,
                9.422442569315887e-07
            ],
            [
                1.7603436330259153e-06,
                NaN,
                1.5534981249697903e-06,
                6.475950297971703e-07,
                1.0677032518748838e-06,
                6.475945666051092e-07,
                8.315283250394546e-07,
                5.04347287955046e-07,
                NaN,
                NaN
            ],
            [
                1.2098659719757836e-06,
                4.2228324377740105e-06,
                9.422443692446175e-07,
                2.2603237589542675e-06,
                9.422445939002803e-07,
                1.7603436330179102e-06,
                4.785092783519724e-06,
                1.3709576971316842e-06,
                1.9947297215125433e-06,
                1.5534981249697903e-06
            ],
            [
                3.927862470899887e-07,
                1.7603436330259153e-06,
                1.9947299593014888e-06,
                1.994730197090463e-06,
                2.9023109472244114e-06,
                NaN,
                5.422217030747413e-06,
                4.222834451382849e-06,
                NaN,
                2.9023133690821773e-06
            ],
            [
                5.422217030747413e-06,
                3.288748673319648e-06,
                6.475950298011458e-07,
                3.726641061109272e-06,
                2.5612834320470717e-06,
                2.2603251062450327e-06,
                6.144176799334096e-06,
                NaN,
                3.12019225345861e-05,
                8.315278294072958e-07
            ],
            [
                NaN,
                1.3709576971425944e-06,
                1.2098658277489788e-06,
                NaN,
                6.475947210031623e-07,
                NaN,
                6.475949526020042e-07,
                4.785094494783494e-06,
                NaN,
                1.2098662604291696e-06
            ],
            [
                1.3709568799919866e-06,
                6.475951069961737e-07,
                6.475947210046347e-07,
                6.475947210012481e-07,
                5.043476486924565e-07,
                9.422447062094932e-07,
                1.3709573702722555e-06,
                4.222834451355964e-06,
                1.994730434879465e-06,
                6.475948754028718e-07
            ],
            [
                NaN,
                8.939696304213768e-06,
                1.5534975693979422e-06,
                1.6701421845057263e-05,
                4.2228349547223175e-06,
                5.04347528446051e-07,
                1.5534973842076057e-06,
                4.4508510499849186e-07,
                1.2098653950656417e-06,
                5.71500515159253e-07
            ],
            [
                7.484624511223438e-05,
                1.1478768125911099e-05,
                4.785094494783494e-06,
                2.2603245673155757e-06,
                1.209865539274514e-06,
                6.144176066795103e-06,
                3.726639283901856e-06,
                1.3007133116542802e-05,
                8.939694172656384e-06,
                4.222834954687752e-06
            ],
            [
                1.3709572068272963e-06,
                NaN,
                2.260323758987159e-06,
                2.9023126771227976e-06,
                1.9947301970813926e-06,
                1.7603438428660665e-06,
                NaN,
                1.99473067264854e-06,
                1.7603436330091044e-06,
                1.7603440527222532e-06
            ],
            [
                8.315284241650899e-07,
                0.00010889694826100151,
                1.067703124601679e-06,
                4.006370174184034e-05,
                1.0129989772412744e-05,
                1.0129987357158383e-05,
                1.3709570434178922e-06,
                3.288748673295719e-06,
                3.2887502415767434e-06,
                7.338208055664991e-07
            ],
            [
                NaN,
                1.3709567165579959e-06,
                5.422220262636381e-06,
                1.3709567165579959e-06,
                NaN,
                1.7603430034867993e-06,
                6.1441746020359e-06,
                1.3007126914245925e-05,
                1.3007123813382511e-05,
                NaN
            ],
            [
                1.6373774480605869e-07,
                9.422443692555439e-07,
                5.043472879540142e-07,
                1.3709576971425944e-06,
                8.315283250394546e-07,
                5.04347528446051e-07,
                7.338212429504183e-07,
                5.715003789046955e-07,
                5.04347468323289e-07,
                NaN
            ],
            [
                2.4300237837960777e-05,
                NaN,
                7.889266347715168e-06,
                NaN,
                8.939698435657833e-06,
                5.422217030707961e-06,
                NaN,
                2.7535694384081332e-05,
                0.0011695101476964214,
                NaN
            ],
            [
                6.962254589914941e-06,
                2.9023123311583482e-06,
                1.553498124964492e-06,
                6.14417753171671e-06,
                1.7603430034743913e-06,
                NaN,
                2.260324836787226e-06,
                3.466326211113502e-07,
                7.338207180864763e-07,
                1.760344052714248e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                5.715005832827105e-07,
                NaN,
                1.209865539295696e-06,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                9.422450432014836e-07,
                2.2603234895176927e-06,
                NaN,
                3.726639284125553e-06,
                4.785092783519724e-06,
                NaN,
                1.670141786325573e-05,
                6.60521446989462e-05,
                1.5534975693869924e-06,
                2.9023109472244114e-06
            ],
            [
                2.2603237589779086e-06,
                NaN,
                3.120190393794438e-05,
                1.3709572068478697e-06,
                3.2887502415243994e-06,
                3.288748673265808e-06,
                2.5612812947380135e-06,
                2.144495097113319e-05,
                2.902311985146426e-06,
                1.7603434231777837e-06
            ],
            [
                4.222832437677995e-06,
                4.785094494783494e-06,
                2.5612812947508257e-06,
                1.994729483705484e-06,
                2.7535700949523498e-05,
                3.726641061027928e-06,
                NaN,
                2.902310947208574e-06,
                NaN,
                2.1444940745371397e-05
            ],
            [
                NaN,
                3.288749065423109e-06,
                1.5534975693869924e-06,
                1.7603427936263351e-06,
                1.3709570434178922e-06,
                NaN,
                1.5534981249697903e-06,
                2.5612812947508257e-06,
                4.222833444590791e-06,
                2.9023112932177327e-06
            ],
            [
                3.288749457432399e-06,
                NaN,
                7.338209805200689e-07,
                5.04347287955046e-07,
                NaN,
                0.0,
                3.927862470899887e-07,
                NaN,
                1.0677029973219343e-06,
                3.288748281295496e-06
            ],
            [
                NaN,
                NaN,
                2.2603237589779086e-06,
                9.422445939032799e-07,
                NaN,
                3.2887478892683997e-06,
                1.3709567165617364e-06,
                5.422220908116881e-06,
                1.553498124964492e-06,
                1.9947304348703948e-06
            ],
            [
                NaN,
                NaN,
                1.994730197090463e-06,
                4.222831934379152e-06,
                1.8925143729575624e-05,
                1.1478766757718129e-05,
                1.8925143729162536e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                1.3709575336947905e-06,
                1.7603434231777837e-06,
                1.2098659719757836e-06,
                1.994729245917502e-06,
                8.315278294072958e-07,
                3.7266401725681614e-06,
                1.5534983101393749e-06,
                4.785093353909723e-06,
                2.9023116391675407e-06,
                3.726641061109272e-06
            ],
            [
                3.726638395634011e-06,
                2.9023109472244114e-06,
                NaN,
                2.9023130231176453e-06,
                2.90231094723893e-06,
                2.5612828213934817e-06,
                3.7266401726173067e-06,
                4.222832941142044e-06,
                1.760343003481596e-06,
                1.5534975693869924e-06
            ],
            [
                1.3709567165617364e-06,
                4.222832941193893e-06,
                3.726639728370556e-06,
                1.3709570434178922e-06,
                5.422220262636381e-06,
                1.0677032518785256e-06,
                NaN,
                1.7603438428740716e-06,
                1.2098656835224664e-06,
                3.726638395634011e-06
            ],
            [
                NaN,
                NaN,
                2.561281600086738e-06,
                1.5534984953510149e-06,
                NaN,
                1.8925155009354808e-05,
                7.889265407255982e-06,
                1.300712846477255e-05,
                NaN,
                1.8925141473599938e-05
            ],
            [
                8.315283250394546e-07,
                9.422443692555439e-07,
                2.5612828213690224e-06,
                NaN,
                4.450850519403407e-07,
                2.699576809143613e-07,
                1.994729008145876e-06,
                2.9023116391978967e-06,
                1.3709573702822306e-06,
                3.288748673360027e-06
            ],
            [
                2.902310947190096e-06,
                1.473898899908247e-05,
                7.889265407090955e-06,
                1.4738989000181669e-05,
                5.422218323349895e-06,
                2.5612825160562587e-06,
                NaN,
                8.939699501229642e-06,
                1.7603427936263351e-06,
                1.9947297215043796e-06
            ],
            [
                4.222832437747125e-06,
                5.422221555340727e-06,
                7.338209805224048e-07,
                4.222834451382849e-06,
                1.6701429808632785e-05,
                NaN,
                1.2098656835224664e-06,
                7.484623620850474e-05,
                NaN,
                1.5534983101602148e-06
            ],
            [
                4.222834954778007e-06,
                1.1478769494250387e-05,
                7.889260704818233e-06,
                2.144494585747154e-05,
                NaN,
                NaN,
                8.939693107190907e-06,
                7.889263526093993e-06,
                2.7535700949523498e-05,
                7.889259764273619e-06
            ],
            [
                5.422218323399208e-06,
                NaN,
                4.785092783454444e-06,
                6.14417753171671e-06,
                2.902310947208574e-06,
                2.5612831267202583e-06,
                NaN,
                7.889264466445326e-06,
                NaN,
                1.99472924590571e-06
            ],
            [
                6.475947210031623e-07,
                9.422442569315887e-07,
                1.300712846477255e-05,
                3.7266397283908927e-06,
                1.7603434231705793e-06,
                8.939699501229642e-06,
                2.2603253756874524e-06,
                NaN,
                NaN,
                9.422445939002803e-07
            ],
            [
                3.726639728370556e-06,
                3.9278605979534166e-07,
                5.043472879540142e-07,
                NaN,
                NaN,
                NaN,
                2.102433660979124e-07,
                6.144176799334096e-06,
                1.5534973842076057e-06,
                4.2228319344021954e-06
            ],
            [
                NaN,
                NaN,
                5.715002426460124e-07,
                0.0,
                9.422442569315887e-07,
                8.315280276626197e-07,
                1.8553914607267268e-07,
                1.9947306726594253e-06,
                7.33821330437595e-07,
                1.7603427936335396e-06
            ],
            [
                5.422218969858371e-06,
                1.7603434231777837e-06,
                6.475947210012481e-07,
                9.422444815792981e-07,
                1.5534973842030142e-06,
                5.715003107755449e-07,
                1.9947299593014888e-06,
                1.994729245917502e-06,
                1.9947304348703948e-06,
                NaN
            ],
            [
                1.9947297215043796e-06,
                1.4738983729294318e-05,
                NaN,
                NaN,
                2.144495608378187e-05,
                5.715003107767143e-07,
                8.939696304213768e-06,
                7.889259764359722e-06,
                3.726638839833152e-06,
                1.892514598551715e-05
            ],
            [
                1.760343213335281e-06,
                NaN,
                NaN,
                1.9947299593014888e-06,
                NaN,
                3.726639284050988e-06,
                1.7603427936263351e-06,
                7.338209805224048e-07,
                3.288749457469787e-06,
                2.260325106237323e-06
            ],
            [
                9.4224425692559e-07,
                1.3709578605455302e-06,
                2.5612825160271407e-06,
                4.222834954687752e-06,
                3.7266383954560706e-06,
                1.012999097997104e-05,
                4.222834451254188e-06,
                6.144172404520556e-06,
                5.422218969818919e-06,
                4.785096776303374e-06
            ],
            [
                3.726639284125553e-06,
                1.9947297215125433e-06,
                NaN,
                6.962256249885085e-06,
                1.9947292459265734e-06,
                1.7603432133296774e-06,
                2.9023126771227976e-06,
                6.962255419804982e-06,
                1.1478768126057254e-05,
                7.338209805200689e-07
            ],
            [
                3.2887494574518405e-06,
                2.144495864059426e-05,
                NaN,
                6.1441724046434924e-06,
                NaN,
                1.1478764020883773e-05,
                3.2887498495150166e-06,
                5.422218969769604e-06,
                1.4738987242968784e-05,
                8.939698435560267e-06
            ],
            [
                7.338212429582604e-07,
                1.3709578605617394e-06,
                1.0677032518814388e-06,
                2.3823696679327928e-07,
                8.315281267882195e-07,
                5.715005832886879e-07,
                5.04347287955046e-07,
                3.927862939136532e-07,
                3.466325797888292e-07,
                7.338210680021253e-07
            ],
            [
                7.338213304363436e-07,
                6.475945666051092e-07,
                1.0677033791612137e-06,
                1.0677032518700286e-06,
                NaN,
                1.3709570434178922e-06,
                2.260325375615501e-06,
                5.4222176771176554e-06,
                2.9023109471689794e-06,
                6.475945666051092e-07
            ],
            [
                1.3709570434122812e-06,
                2.5612828213352452e-06,
                1.209865827740176e-06,
                2.260323489490968e-06,
                1.7603427936263351e-06,
                3.288748281295496e-06,
                1.9947299592570416e-06,
                2.2603242978377903e-06,
                2.260324297853209e-06,
                2.4300243631272052e-05
            ],
            [
                3.466327037548308e-07,
                4.785093924362895e-06,
                1.9947297215125433e-06,
                5.715007195447234e-07,
                1.3709570434122812e-06,
                4.785095635624897e-06,
                NaN,
                1.209865827740176e-06,
                8.315281267861397e-07,
                4.450852641737424e-07
            ],
            [
                2.260324028427877e-06,
                6.475945666051092e-07,
                7.338213304363436e-07,
                1.994730672668496e-06,
                1.994730672668496e-06,
                6.144176066901277e-06,
                6.1441724046434924e-06,
                NaN,
                1.5534979397677313e-06,
                1.0677027427600627e-06
            ],
            [
                1.0129993395336818e-05,
                8.93969950132721e-06,
                NaN,
                1.5534984953510149e-06,
                6.9622587397397306e-06,
                2.9023112932177327e-06,
                4.4508499888219586e-07,
                2.561283432035425e-06,
                5.422221555380179e-06,
                3.726639284125553e-06
            ],
            [
                NaN,
                7.889260704818233e-06,
                NaN,
                1.0677026154806063e-06,
                1.3709570433979422e-06,
                NaN,
                9.422447062270609e-07,
                1.0129992187658463e-05,
                8.315281267861397e-07,
                8.315281267800897e-07
            ],
            [
                NaN,
                2.4300234940642642e-05,
                9.422450431989127e-07,
                3.7266388398585725e-06,
                1.1478773599425825e-05,
                1.3007123812554424e-05,
                6.144175334418252e-06,
                1.4738985486265496e-05,
                3.726638395611981e-06,
                1.1478770862255766e-05
            ],
            [
                8.315283250371857e-07,
                7.338209805240734e-07,
                1.2098653950692178e-06,
                1.3709572068422585e-06,
                5.715005151606823e-07,
                1.3709568799823232e-06,
                5.422217030707961e-06,
                4.450848927650143e-07,
                1.7603425837791042e-06,
                1.994729008145876e-06
            ],
            [
                6.144177531767002e-06,
                1.0129989771823107e-05,
                7.88926164518358e-06,
                7.889262585814522e-06,
                8.315281267834927e-07,
                4.2228334445370225e-06,
                4.2228324377740105e-06,
                3.288749457469787e-06,
                1.5534979397790343e-06,
                1.3007126914245925e-05
            ],
            [
                1.2098659719757836e-06,
                NaN,
                1.760344052714248e-06,
                5.4222209089700225e-06,
                4.222832941034507e-06,
                1.7603427936263351e-06,
                3.726638395611981e-06,
                1.9947292459265734e-06,
                4.222832941142044e-06,
                1.2098656835224664e-06
            ],
            [
                5.422217677028889e-06,
                3.726639728348526e-06,
                2.902311985146426e-06,
                2.9023119851781017e-06,
                2.9023116391978967e-06,
                NaN,
                9.422443692446175e-07,
                1.0677032518785256e-06,
                2.561282515988704e-06,
                1.7603438428460541e-06
            ],
            [
                3.466325797896173e-07,
                8.315283250394546e-07,
                4.222834954778007e-06,
                3.927862002641863e-07,
                1.2098662604291696e-06,
                1.6373776432509826e-07,
                3.4663253846718004e-07,
                NaN,
                1.2098653950656417e-06,
                1.7603438428740716e-06
            ]
        ]
    },
    {
        "q_id": "9205_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                8.315282259089153e-07,
                3.0590215399183813e-07,
                3.4663266243308805e-07,
                1.3709575337016483e-06,
                4.222834954778007e-06,
                NaN,
                4.450849458218309e-07,
                1.2098658277489788e-06,
                1.2098659719661556e-06,
                1.9947297215125433e-06
            ],
            [
                5.715007195431641e-07,
                3.05902190458764e-07,
                6.475951069985296e-07,
                1.4738981972564636e-05,
                2.2603251062450327e-06,
                0.9999990577551819,
                5.829125165990109e-05,
                6.962257909785973e-06,
                1.209865539295696e-06,
                1.2098656835252174e-06
            ],
            [
                1.7603430034867993e-06,
                1.209865539295696e-06,
                2.2603253756956754e-06,
                3.7266383956509585e-06,
                2.561281294760143e-06,
                1.994729008151319e-06,
                9.422445939054222e-07,
                7.338211554801876e-07,
                5.043476486924565e-07,
                1.760342793638743e-06
            ],
            [
                2.902313369111213e-06,
                5.422218969818919e-06,
                2.2603234895372223e-06,
                1.7603432133136672e-06,
                1.5534981249496567e-06,
                2.2603242978778778e-06,
                2.5612812947380135e-06,
                1.2098659719757836e-06,
                2.561283126679493e-06,
                7.338208930391909e-07
            ],
            [
                1.7603430034439723e-06,
                2.2603234894745224e-06,
                1.5534975693347152e-06,
                3.288750633488963e-06,
                8.315282258956806e-07,
                3.2887502414436403e-06,
                1.7603427936183298e-06,
                1.5534984953199313e-06,
                1.067702870039777e-06,
                1.994729483694599e-06
            ],
            [
                1.0677024882009222e-06,
                6.475950298011458e-07,
                3.2887486732000038e-06,
                2.5612831265909735e-06,
                2.2603251062013478e-06,
                1.3709567165386693e-06,
                8.315280276607289e-07,
                1.7603440526806268e-06,
                1.553498124964492e-06,
                2.260323758939877e-06
            ],
            [
                1.2098653950656417e-06,
                2.561283432035425e-06,
                7.338211554783522e-07,
                8.939693107190907e-06,
                1.3007128464961824e-05,
                8.315283250371857e-07,
                5.422220262599396e-06,
                4.785095635624897e-06,
                1.3709573702822306e-06,
                1.3709573702822306e-06
            ],
            [
                1.1253517547010071e-07,
                5.715006514151423e-07,
                1.6373764721039308e-07,
                2.69957906184239e-07,
                1.6373776432509826e-07,
                3.927862939113312e-07,
                1.6373774480605869e-07,
                4.4508499888219586e-07,
                2.3823702359290413e-07,
                2.6995790618469934e-07
            ],
            [
                0.9999892166852525,
                0.9999925887192601,
                1.994729483729522e-06,
                0.9999898700066352,
                0.9999251537641003,
                0.9999952149060821,
                0.9999916019279871,
                0.7981867777396212,
                0.9998911030402253,
                0.9999852610180436
            ],
            [
                0.9999925887166033,
                1.3709576971425944e-06,
                0.9999869928700016,
                0.9999988634358838,
                0.9999942280779168,
                0.999994228081357,
                7.338212429594283e-07,
                0.999994228079286,
                5.043476486924565e-07,
                4.785096206076165e-06
            ],
            [
                2.2603251062450327e-06,
                0.9999832985841555,
                1.5534971990126997e-06,
                1.5534975693979422e-06,
                1.5534977545886537e-06,
                4.4508494582405734e-07,
                2.144494841482881e-05,
                0.9999417087348003,
                2.5612828213934817e-06,
                6.144172404738491e-06
            ],
            [
                8.315279285351409e-07,
                1.3709570434219446e-06,
                0.9999785550439478,
                0.9999898700054198,
                9.422449308774482e-07,
                0.9999877809210914,
                1.3007123813382511e-05,
                5.043476486902204e-07,
                7.338213304363436e-07,
                2.6995784182140636e-07
            ],
            [
                9.422443692574719e-07,
                1.5534973842076057e-06,
                8.315277302841894e-07,
                0.999993855826142,
                0.9999892166839625,
                0.9999993524054337,
                0.9999970976883631,
                0.999996033013145,
                0.9999988634357478,
                1.5534979397790343e-06
            ],
            [
                0.9999990577549571,
                0.9998415637652246,
                2.1024339116168358e-07,
                1.1253525596174225e-07,
                3.4663266243111764e-07,
                3.288747889284851e-06,
                0.9999960330150329,
                0.9995694430157853,
                3.059022269250683e-07,
                0.9999962733589399
            ],
            [
                3.927862939126708e-07,
                5.422219616228845e-06,
                1.8553910183607374e-07,
                3.288749849498565e-06,
                3.927860597945825e-07,
                3.9278615344178325e-07,
                3.466327037539638e-07,
                6.144176799334096e-06,
                1.2098659719601033e-06,
                8.315281267834927e-07
            ],
            [
                6.475946437996402e-07,
                1.4449805540740185e-07,
                2.102433410343832e-07,
                2.3823699519143784e-07,
                3.059023727894942e-07,
                1.6373768624837685e-07,
                2.3823702359138736e-07,
                3.9278634073732336e-07,
                2.382369383923073e-07,
                3.059022269250683e-07
            ],
            [
                4.539786865090791e-05,
                6.475945666063607e-07,
                4.785093924389007e-06,
                3.7266410611296085e-06,
                1.3709575337159875e-06,
                1.209865539298447e-06,
                5.715002426486762e-07,
                1.9947292459347367e-06,
                8.315280276626197e-07,
                3.288748281329893e-06
            ],
            [
                3.726639728348526e-06,
                5.422220909009474e-06,
                2.260325375664839e-06,
                1.209865539295696e-06,
                5.715003789033962e-07,
                3.726637951367137e-06,
                2.561282210729555e-06,
                7.889259764445822e-06,
                1.7603434231505666e-06,
                4.785095635624897e-06
            ],
            [
                4.4508510499849186e-07,
                3.288750241500471e-06,
                2.3823685319244518e-07,
                1.7603432133296774e-06,
                8.939694172867777e-06,
                2.2603240284371276e-06,
                3.927862470899887e-07,
                1.3709570434122812e-06,
                1.0677029973192638e-06,
                5.043476486915964e-07
            ],
            [
                5.043475885674441e-07,
                5.043476486915964e-07,
                2.5612828213934817e-06,
                1.2098656835224664e-06,
                8.315283250371857e-07,
                2.1024341622426268e-07,
                4.4508494582405734e-07,
                1.5534981249697903e-06,
                9.4224425692559e-07,
                2.3823702359290413e-07
            ],
            [
                2.5612834320563895e-06,
                7.338208930460318e-07,
                7.889262585958025e-06,
                4.222833948008874e-06,
                1.0677027427624903e-06,
                8.315280276626197e-07,
                6.144177531811707e-06,
                1.7603440527334603e-06,
                9.422447062294175e-07,
                1.3709576971463352e-06
            ],
            [
                6.475945666033422e-07,
                3.927862002654366e-07,
                1.5534984953510149e-06,
                8.315282259089153e-07,
                5.715002426486762e-07,
                8.315279285351409e-07,
                1.3709576971425944e-06,
                3.2887498495150166e-06,
                3.927861534406222e-07,
                1.2098656835224664e-06
            ],
            [
                4.222832437798974e-06,
                2.6995790618469934e-07,
                3.927862002663297e-07,
                3.059021175261338e-07,
                5.043476486915964e-07,
                3.4663249714612693e-07,
                5.043475885696228e-07,
                2.1024339116168358e-07,
                1.27519088491875e-07,
                3.059021904571643e-07
            ],
            [
                4.450852641737424e-07,
                1.5534983101644536e-06,
                1.5534973842076057e-06,
                6.47595107001401e-07,
                2.902312677150514e-06,
                9.422444815814404e-07,
                1.3709575337159875e-06,
                1.760342793638743e-06,
                9.422444815814404e-07,
                5.043475885696228e-07
            ],
            [
                1.3709578605729614e-06,
                3.7266406168827523e-06,
                4.222832941193893e-06,
                3.288750241561788e-06,
                2.5612819054133693e-06,
                1.3709578605729614e-06,
                2.561282516066741e-06,
                1.0677032518814388e-06,
                1.5534973842030142e-06,
                4.785095635655362e-06
            ],
            [
                6.475945666063607e-07,
                8.315277302841894e-07,
                4.4508494582405734e-07,
                1.3709567165579959e-06,
                6.475946438055299e-07,
                2.699578096403948e-07,
                9.422443692574719e-07,
                3.9278610661902853e-07,
                8.939700567094277e-06,
                5.043474683240344e-07
            ],
            [
                1.5534979397740895e-06,
                1.5534975693933505e-06,
                4.450851580555361e-07,
                1.5534979397740895e-06,
                3.726639728370556e-06,
                1.3709568799823232e-06,
                2.2603234895176927e-06,
                3.7266406168624155e-06,
                4.785094494716039e-06,
                1.1478769494396542e-05
            ],
            [
                1.27519088491875e-07,
                1.0677027427624903e-06,
                2.9023116392097746e-06,
                2.2603237589779086e-06,
                1.3709575337159875e-06,
                1.3709575337159875e-06,
                1.275191036933194e-07,
                2.2603248367949354e-06,
                3.726639284144195e-06,
                3.466325384678894e-07
            ],
            [
                1.4449802095609418e-07,
                2.1024341622426268e-07,
                3.9278629391427843e-07,
                1.5534979397790343e-06,
                3.0590215399183813e-07,
                1.6373776432509826e-07,
                1.1253517547010071e-07,
                1.2751910369343538e-07,
                6.475945666063607e-07,
                3.059022998576899e-07
            ],
            [
                0.9999978766210328,
                0.9999955048178903,
                0.9999967112517204,
                0.9999885212291505,
                0.999995214905509,
                0.9999969105062912,
                0.9999955048200326,
                6.144177531811707e-06,
                0.9999969105051855,
                0.9999986290432845
            ],
            [
                0.9999969105048206,
                0.9999985406243025,
                0.9999972735300571,
                0.9999972735297337,
                0.9999945777791,
                0.9998766053837823,
                0.9999986290429577,
                6.144173137170873e-06,
                0.999948557780893,
                0.9998204720566296
            ],
            [
                7.338208055680009e-07,
                4.450852111155216e-07,
                2.6995784182183607e-07,
                1.7603440527286572e-06,
                1.5534975693792215e-06,
                5.71500515159253e-07,
                1.275190428875671e-07,
                3.466325384678894e-07,
                7.338208055680009e-07,
                2.699578096403948e-07
            ],
            [
                4.450848927658745e-07,
                1.5534983101602148e-06,
                1.994729483729522e-06,
                0.9999970976880159,
                4.4508494582405734e-07,
                0.999996910505922,
                2.1024339116168358e-07,
                3.05902336324494e-07,
                7.338212429594283e-07,
                8.315281267882195e-07
            ],
            [
                6.475951069932288e-07,
                1.2098659719601033e-06,
                5.043474683156057e-07,
                1.5534973842030142e-06,
                9.422445938917108e-07,
                2.5612825160271407e-06,
                3.927862939126708e-07,
                6.475945665900901e-07,
                3.059022998569248e-07,
                0.9999934595643445
            ],
            [
                3.9278610661822475e-07,
                3.927862002654366e-07,
                2.1024339116082313e-07,
                7.338213304363436e-07,
                4.450852641717689e-07,
                3.466327450756327e-07,
                2.382369383923073e-07,
                1.4449807263287805e-07,
                2.1024334103553052e-07,
                4.450852111120808e-07
            ],
            [
                1.994730434879465e-06,
                4.222833947960866e-06,
                4.785093924362895e-06,
                3.9278605979534166e-07,
                7.338213304283347e-07,
                9.422442569315887e-07,
                1.2098662604291696e-06,
                1.7603430034743913e-06,
                3.2887506336086064e-06,
                3.288749065423109e-06
            ],
            [
                6.47595107001401e-07,
                1.855391239547094e-07,
                3.288749457469787e-06,
                3.288747889284851e-06,
                6.475950298011458e-07,
                1.7603430034867993e-06,
                3.9278610661902853e-07,
                2.382369951932796e-07,
                2.5612819054133693e-06,
                2.6995784182183607e-07
            ],
            [
                1.3709575337159875e-06,
                1.275190276859705e-07,
                5.715006514176113e-07,
                6.962256249821764e-06,
                2.902312331170226e-06,
                3.05902263391829e-07,
                1.0677028700422047e-06,
                1.275190580890061e-07,
                9.931199245322124e-08,
                2.2603248367949354e-06
            ],
            [
                2.382370235933104e-07,
                2.6995784182140636e-07,
                3.7266410611296085e-06,
                2.561281600076256e-06,
                2.3823682479292225e-07,
                1.7603427936335396e-06,
                1.9947292459347367e-06,
                2.69957906184239e-07,
                2.69957906184239e-07,
                2.1024331597262577e-07
            ],
            [
                1.5534984953552536e-06,
                0.9999977396746255,
                6.475949526020042e-07,
                3.2887494574518405e-06,
                0.999995777168069,
                0.9999885212291584,
                9.422443692555439e-07,
                4.4508515805735777e-07,
                1.9947304348862686e-06,
                0.9999296881249302
            ],
            [
                5.043472879525233e-07,
                3.059022998576899e-07,
                8.315284241597959e-07,
                2.3823685319244518e-07,
                2.1024344128660572e-07,
                4.4508494582314646e-07,
                1.3709570434122812e-06,
                2.102434412871794e-07,
                3.927862939126708e-07,
                4.450849458218309e-07
            ],
            [
                3.927860597945825e-07,
                5.043474081993875e-07,
                1.0677028700422047e-06,
                5.043474683220276e-07,
                5.715005832872586e-07,
                8.315278294114555e-07,
                2.699576809143613e-07,
                2.382369667929001e-07,
                1.0677029973158649e-06,
                8.315281267882195e-07
            ],
            [
                0.99990971959009,
                1.670141786325573e-05,
                5.715006514167015e-07,
                2.75356812556058e-05,
                7.889263526345123e-06,
                2.430023204460668e-05,
                7.338209805224048e-07,
                1.3007133116732079e-05,
                5.043475885674441e-07,
                4.222834451382849e-06
            ],
            [
                8.764245361752286e-08,
                0.9999964991439187,
                1.760342793638743e-06,
                0.9999798543043987,
                0.9999992661791072,
                0.9999949062962166,
                5.715003789046955e-07,
                0.9999960330121953,
                2.561282210740037e-06,
                0.9999898700126617
            ],
            [
                0.999995777164545,
                0.9999957771650514,
                0.999999310638955,
                0.9999972735303816,
                0.9999967112521143,
                2.699578740032504e-07,
                1.0677028700422047e-06,
                0.9999980052695667,
                5.715003789046955e-07,
                0.9999934595620057
            ],
            [
                9.4224425692559e-07,
                1.2098653950606901e-06,
                1.2098653950480359e-06,
                3.535626757524533e-05,
                3.2887506334560605e-06,
                5.043475885674441e-07,
                1.3709568799919866e-06,
                2.902311639183378e-06,
                0.9999904837471966,
                1.0677027427471959e-06
            ],
            [
                0.9999964991464224,
                0.9999949062931783,
                0.9999964991451707,
                0.9999962733616068,
                0.9999969105062906,
                4.450848927637999e-07,
                1.3709568799823232e-06,
                3.0590237279032884e-07,
                0.9999969105055536,
                0.9999945777816823
            ],
            [
                5.043476486915964e-07,
                3.4663249714451116e-07,
                5.71500515159253e-07,
                3.9278610661545617e-07,
                6.475945666051092e-07,
                4.450848927650143e-07,
                3.4663249714451116e-07,
                2.3823690999323465e-07,
                1.855391681891831e-07,
                1.8553903548231313e-07
            ],
            [
                0.9999546021369493,
                2.561281294760143e-06,
                0.9999724642991211,
                0.9999599362887583,
                1.994730672675753e-06,
                2.260323758987159e-06,
                1.9947301970972664e-06,
                6.144175334468545e-06,
                6.475950298011458e-07,
                0.9999485578048909
            ],
            [
                3.466327863983311e-07,
                3.059022998576899e-07,
                4.4508510499737865e-07,
                8.315279285351409e-07,
                8.315284241650899e-07,
                5.715005832886879e-07,
                5.715004470272272e-07,
                6.475948754012522e-07,
                3.466327863983311e-07,
                5.715005832872586e-07
            ],
            [
                1.5534973841895917e-06,
                1.9947297214544894e-06,
                5.715005832853093e-07,
                2.9023116391675407e-06,
                6.475945666051092e-07,
                4.785095635624897e-06,
                0.9999885212305433,
                9.422444815765128e-07,
                0.9999869928731581,
                3.0590219045914655e-07
            ],
            [
                7.338208930443633e-07,
                2.3823690999290963e-07,
                3.466327450765785e-07,
                3.4663266243308805e-07,
                1.8553910183674878e-07,
                2.5612828213934817e-06,
                1.9947301970813926e-06,
                3.7266383956509585e-06,
                8.315280276626197e-07,
                1.3709575337078829e-06
            ],
            [
                1.5534971990169383e-06,
                2.3823690999323465e-07,
                1.6373764721091427e-07,
                0.9999938558261355,
                1.9947299593078385e-06,
                5.715002426475718e-07,
                1.2098661162056318e-06,
                0.9999970976876705,
                4.4508515805735777e-07,
                0.9999974387174859
            ],
            [
                1.7603427935967163e-06,
                1.7603436330091044e-06,
                0.9999756997680972,
                4.5397852414783676e-05,
                0.9999706884650926,
                1.5534979397592542e-06,
                5.715003107755449e-07,
                1.994729721482609e-06,
                2.5612828213818346e-06,
                1.3709576971242028e-06
            ],
            [
                2.6995777745711594e-07,
                2.382369667929001e-07,
                2.3823702359290413e-07,
                1.637377057680051e-07,
                9.931193325852072e-08,
                1.8553907971855875e-07,
                3.059021175247079e-07,
                1.4449798650551755e-07,
                1.637377448057981e-07,
                2.1024341622426268e-07
            ],
            [
                6.962256249885085e-06,
                2.902312331170226e-06,
                4.785095635655362e-06,
                1.7603440527286572e-06,
                2.902312677150514e-06,
                1.9947299593078385e-06,
                1.9947299593014888e-06,
                1.5534973842030142e-06,
                2.2603242978778778e-06,
                1.7603434231833873e-06
            ],
            [
                0.9999339478478619,
                5.043475885674441e-07,
                0.9999942280786006,
                2.2603242978778778e-06,
                0.999979854299605,
                5.043475885674441e-07,
                9.4224425692559e-07,
                3.288749457469787e-06,
                3.7266406168624155e-06,
                1.7603438428740716e-06
            ],
            [
                6.475950298011458e-07,
                1.855391239547094e-07,
                3.059021175255426e-07,
                1.8553910183674878e-07,
                3.927862470890063e-07,
                1.0677026154774503e-06,
                6.475945666051092e-07,
                2.6995768091383957e-07,
                1.0677027427600627e-06,
                4.4508494582405734e-07
            ],
            [
                0.9999987121050921,
                0.9999982396559485,
                0.999996711250936,
                0.9999969105059225,
                0.9999898700114443,
                0.9999952149032261,
                0.9999985406232579,
                0.9999785550490706,
                0.9999980052707551,
                0.9999898700126566
            ],
            [
                5.715003789046955e-07,
                6.47595107001401e-07,
                3.9278615344178325e-07,
                1.370957860576702e-06,
                3.059022998581767e-07,
                9.422445939054222e-07,
                4.450850519403407e-07,
                5.715007195431641e-07,
                5.043475885696228e-07,
                6.475947210031623e-07
            ],
            [
                6.14417753171671e-06,
                0.9999994284993488,
                0.9999151889386246,
                0.999972464315524,
                0.9999945777790956,
                0.999993855825402,
                0.9999970976866334,
                6.144172404738491e-06,
                0.9999996940976638,
                0.9999955048173538
            ],
            [
                8.76424013786396e-08,
                3.4663253846718004e-07,
                3.9278634073732336e-07,
                5.715007195431641e-07,
                3.927862470899887e-07,
                1.275190732904469e-07,
                6.825602910433871e-08,
                7.734418542875216e-08,
                2.6995774527657245e-07,
                3.466325797900508e-07
            ],
            [
                0.9999955048178935,
                4.450852111155216e-07,
                6.144177531767002e-06,
                1.4449803818215767e-07,
                3.4663262110945863e-07,
                0.9999810748541256,
                2.2603237589779086e-06,
                0.9998601779296259,
                1.2098655392921197e-06,
                3.0590219045914655e-07
            ],
            [
                3.9278610661902853e-07,
                2.2603248367949354e-06,
                4.222834451403972e-06,
                1.7603425837903113e-06,
                1.5534984953552536e-06,
                1.7603438428800754e-06,
                1.0677029973219343e-06,
                2.2603248367949354e-06,
                7.338207180898968e-07,
                3.288747889284851e-06
            ],
            [
                2.382368531929327e-07,
                1.1253514863968147e-07,
                4.4508494582405734e-07,
                7.338208930460318e-07,
                8.315283250371857e-07,
                1.1253526937697666e-07,
                1.275190124846946e-07,
                2.699578096393206e-07,
                2.3823688159291947e-07,
                7.338210680002898e-07
            ],
            [
                5.043472278322555e-07,
                2.5612831267202583e-06,
                1.2098652508391807e-06,
                1.760342793638743e-06,
                9.422445939002803e-07,
                1.3007123813382511e-05,
                1.0677032518814388e-06,
                6.475945666033422e-07,
                0.9999885212332632,
                1.5534979397790343e-06
            ],
            [
                2.1024326584582131e-07,
                1.4449803818215767e-07,
                1.855391239547094e-07,
                1.6373770576776313e-07,
                1.855391239547094e-07,
                1.6373762769138607e-07,
                8.764244316973974e-08,
                2.6995784182140636e-07,
                1.6373772528704005e-07,
                1.444980209564556e-07
            ],
            [
                0.9997040428709614,
                6.962257909785973e-06,
                1.760342793638743e-06,
                0.9999960330140888,
                2.2603234895372223e-06,
                4.22283545819819e-06,
                3.466325797896173e-07,
                2.9023116392097746e-06,
                0.9999810748472974,
                2.699578096403948e-07
            ],
            [
                0.9999962733616085,
                0.9999974387177918,
                1.1253512180925583e-07,
                0.9999982396567882,
                1.2751902768612997e-07,
                1.4449803818215767e-07,
                2.3823682479292225e-07,
                0.999999266179195,
                0.9999930377429298,
                0.9999904837483209
            ],
            [
                6.475948754012522e-07,
                3.9278605979208185e-07,
                6.475947210012481e-07,
                5.715007195384861e-07,
                9.422444815765128e-07,
                6.475951069932288e-07,
                5.043472278280699e-07,
                5.043474683156057e-07,
                6.475945666009864e-07,
                5.043473480730849e-07
            ],
            [
                2.90231094723893e-06,
                2.5612828213818346e-06,
                1.1478765389368729e-05,
                1.3007133116732079e-05,
                1.9947297215125433e-06,
                1.2098656835224664e-06,
                1.5534971990126997e-06,
                2.902313023130843e-06,
                6.144177531811707e-06,
                6.475947210031623e-07
            ],
            [
                6.475950298021765e-07,
                2.2603251062450327e-06,
                5.715006514176113e-07,
                8.31528325040778e-07,
                0.9999925887192572,
                1.5534971990169383e-06,
                1.994729721518893e-06,
                1.209865827752005e-06,
                6.47594875403829e-07,
                9.422445939054222e-07
            ],
            [
                1.892515501014656e-05,
                0.9999861539888579,
                0.9999967112517196,
                1.7603440527334603e-06,
                0.9999970976887095,
                0.9999898700078294,
                0.9999978766217915,
                0.9999972735290806,
                0.9999960330155081,
                3.120191137659974e-05
            ],
            [
                9.422444815814404e-07,
                5.715003107767143e-07,
                1.275190276859705e-07,
                5.715003107755449e-07,
                6.475945666063607e-07,
                9.422442569334097e-07,
                2.699576809143613e-07,
                9.931194509740267e-08,
                1.1253524254650944e-07,
                1.0677029973158649e-06
            ],
            [
                1.209865827752005e-06,
                3.9278629391427843e-07,
                9.422443692574719e-07,
                5.043475885696228e-07,
                4.450851049991497e-07,
                3.72663883989755e-06,
                3.7266383956509585e-06,
                1.3709576971463352e-06,
                9.422444815814404e-07,
                1.994729721518893e-06
            ],
            [
                3.9278629391427843e-07,
                8.315281267882195e-07,
                7.338210680021253e-07,
                3.9278629391427843e-07,
                5.715003107767143e-07,
                1.4449803818215767e-07,
                7.338207180898968e-07,
                1.0129987357517693e-05,
                4.785093924389007e-06,
                8.315281267882195e-07
            ],
            [
                2.9023119851899796e-06,
                2.2603248367949354e-06,
                8.315284241650899e-07,
                0.9999417087069827,
                1.3709575337159875e-06,
                0.9999251537463113,
                2.9023119851899796e-06,
                4.222833444590791e-06,
                5.715002426486762e-07,
                7.338212429594283e-07
            ],
            [
                1.2098661162056318e-06,
                1.5534973842076057e-06,
                0.9999945777829723,
                0.9999687980776268,
                2.561281600086738e-06,
                7.338207180898968e-07,
                7.338208055680009e-07,
                8.315278294114555e-07,
                1.5534971990169383e-06,
                3.927863875616689e-07
            ],
            [
                1.0677027427600627e-06,
                2.69957906184239e-07,
                3.46632497145457e-07,
                1.209865539295696e-06,
                1.8553919030776337e-07,
                8.939698435657833e-06,
                0.9999930377412665,
                8.315279285351409e-07,
                5.422219616265831e-06,
                3.927862939126708e-07
            ],
            [
                3.9278610661902853e-07,
                1.9947292459406333e-06,
                3.288749849529972e-06,
                2.2603253756956754e-06,
                1.275190428875671e-07,
                0.9999646437367669,
                1.892514598627448e-05,
                6.475945666063607e-07,
                2.3823693839325527e-07,
                1.1253524254650944e-07
            ],
            [
                1.3709572068422585e-06,
                8.764249540862797e-08,
                2.1024326584582131e-07,
                2.6995774527657245e-07,
                1.6373774480605869e-07,
                4.4508505193932864e-07,
                2.3823685319244518e-07,
                2.6995774527718623e-07,
                6.475949526020042e-07,
                1.637377448057981e-07
            ],
            [
                1.0677024881887838e-06,
                6.475948753991907e-07,
                1.0677027427525368e-06,
                1.2098656835136636e-06,
                6.144174601935314e-06,
                5.422217030614265e-06,
                1.5534971990126997e-06,
                8.315283250305684e-07,
                5.715005151574337e-07,
                1.209865827740176e-06
            ],
            [
                2.2603245673443566e-06,
                1.8553916819032217e-07,
                2.260324567302214e-06,
                3.2887494574832472e-06,
                6.475949526020042e-07,
                2.902313369111213e-06,
                4.450851580540182e-07,
                1.0677027427624903e-06,
                3.2887502415767434e-06,
                2.561282821402217e-06
            ],
            [
                6.144172404738491e-06,
                NaN,
                0.9999599363223418,
                0.9999980052695668,
                6.144175334468545e-06,
                0.9999861539921737,
                0.9999952149032275,
                0.999987780928377,
                4.785095635655362e-06,
                0.9999916019279771
            ],
            [
                0.9999960330150361,
                4.222831934379152e-06,
                5.422218969858371e-06,
                1.0677032518785256e-06,
                3.726639284125553e-06,
                4.222834954778007e-06,
                2.5612812947508257e-06,
                0.9999038975978253,
                6.9622537599680095e-06,
                3.2887478892683997e-06
            ],
            [
                5.8291293348093234e-05,
                0.9999921107364859,
                9.422445939002803e-07,
                5.422220262636381e-06,
                2.902313369111213e-06,
                6.144172404693786e-06,
                1.7603427936263351e-06,
                8.93969950132721e-06,
                5.422220909009474e-06,
                4.222834451355964e-06
            ],
            [
                1.0677029973219343e-06,
                3.7266383956509585e-06,
                1.3709573702856596e-06,
                1.5534983101644536e-06,
                2.2603248367949354e-06,
                1.209865827752005e-06,
                1.067703124601679e-06,
                1.067703124601679e-06,
                6.962257909842961e-06,
                1.994730672675753e-06
            ],
            [
                1.760342793638743e-06,
                4.785093924389007e-06,
                1.994729483729522e-06,
                4.785094494811783e-06,
                3.7266383956509585e-06,
                6.962257079889302e-06,
                3.72663883989755e-06,
                1.4738980215593877e-05,
                5.422218969895357e-06,
                1.067703124601679e-06
            ],
            [
                0.999998346310809,
                2.382369951932796e-07,
                1.2751910369275402e-07,
                2.1024336609874897e-07,
                2.6995774527718623e-07,
                0.9999852610180593,
                2.102434412875379e-07,
                4.450848927658745e-07,
                8.315277302841894e-07,
                3.466325384678894e-07
            ],
            [
                2.2603237589779086e-06,
                2.9023112932177327e-06,
                5.715005832886879e-07,
                1.5534981249697903e-06,
                8.315283250343497e-07,
                3.9278610661902853e-07,
                1.7603427936263351e-06,
                1.0677026154806063e-06,
                4.450852111155216e-07,
                2.9023116391978967e-06
            ],
            [
                0.9999885212277811,
                0.9999852610180556,
                0.9999921107402404,
                2.699577774585891e-07,
                1.4449798650551755e-07,
                0.9999417087419311,
                5.043475885674441e-07,
                0.999968798092416,
                0.999954602115403,
                0.9998911030398118
            ],
            [
                8.315280276580819e-07,
                0.9999599363223503,
                0.99998852123326,
                0.9999925887227917,
                0.9999949062962158,
                0.9996646499930338,
                4.006370652067535e-05,
                0.9999975938965159,
                0.9999925887192559,
                3.4663262111182307e-07
            ],
            [
                3.7266401726359486e-06,
                7.889266347786918e-06,
                5.043476486902204e-07,
                0.9999960330126736,
                0.9999910603069206,
                2.5612831267202583e-06,
                8.315279285370317e-07,
                0.9999339478401893,
                6.962257909785973e-06,
                0.9999991148433868
            ],
            [
                5.715002426460124e-07,
                3.059023363231725e-07,
                3.927862002654366e-07,
                1.5534975693869924e-06,
                3.4663257978780455e-07,
                6.475951069985296e-07,
                2.1024326584639497e-07,
                2.6995774527718623e-07,
                8.315281267834927e-07,
                3.46632497145457e-07
            ],
            [
                7.338211554783522e-07,
                1.0677024881980089e-06,
                7.338209805224048e-07,
                8.315281267861397e-07,
                6.475945666051092e-07,
                2.69957906184239e-07,
                4.4508494582405734e-07,
                6.475947982002148e-07,
                7.338210679979539e-07,
                5.043472278280699e-07
            ],
            [
                0.9999952149072211,
                4.450852111155216e-07,
                3.4663274507713016e-07,
                5.043475284468537e-07,
                0.9999485577926047,
                0.9999987901341728,
                1.6373774480605869e-07,
                0.9999546021097849,
                4.4508515805735777e-07,
                0.9999977396754336
            ],
            [
                1.9947301970972664e-06,
                7.338208055664991e-07,
                3.9278629391427843e-07,
                1.3709572068522336e-06,
                4.450852641737424e-07,
                2.2603248367949354e-06,
                7.338212429582604e-07,
                4.450852111155216e-07,
                7.338209805224048e-07,
                8.315278294114555e-07
            ],
            [
                0.9999771720028822,
                3.927863407379485e-07,
                0.9999687980924614,
                0.9999952149032281,
                5.3157900413760374e-08,
                8.764247451307293e-08,
                0.9999982396572071,
                0.9999955048194972,
                0.9999969105040808,
                0.9999942280799738
            ],
            [
                4.4508494582405734e-07,
                8.315278294114555e-07,
                1.0677028700422047e-06,
                2.382369667929001e-07,
                9.931189774187203e-08,
                9.931187406410953e-08,
                3.466327450765785e-07,
                0.9999934595620011,
                5.043472879540142e-07,
                3.0590237279085045e-07
            ],
            [
                0.9999339478247182,
                0.9999952149060812,
                0.9999996310114599,
                0.9999930377429278,
                0.999994577779098,
                0.9999988634357477,
                0.9999957771680713,
                0.9999843104503124,
                0.9999930377421011,
                0.9999984465028027
            ],
            [
                7.338209805200689e-07,
                1.2098655392871682e-06,
                7.338209805200689e-07,
                1.3007134667259441e-05,
                6.475947210012481e-07,
                1.9947297215043796e-06,
                3.288748281295496e-06,
                6.1441746020359e-06,
                3.7266406168403854e-06,
                2.260324028427877e-06
            ],
            [
                0.9999925887174972,
                0.9999904837483358,
                0.9999952149049454,
                0.9999987901343188,
                0.9999904837494601,
                0.9999573525475417,
                8.315278294097538e-07,
                0.9999623635486496,
                0.9999992661789328,
                0.9999955048189649
            ],
            [
                3.927863407379485e-07,
                6.1441767993788005e-06,
                1.5534984953552536e-06,
                2.561281294760143e-06,
                4.222834451403972e-06,
                2.561281294760143e-06,
                1.3709576971463352e-06,
                2.561281600086738e-06,
                2.7535700950274782e-05,
                3.2887506336235617e-06
            ],
            [
                1.3709576971242028e-06,
                6.475950298011458e-07,
                1.3709570434122812e-06,
                1.2098656835136636e-06,
                2.2603251062147097e-06,
                1.7603438428740716e-06,
                9.422448185435711e-07,
                1.9947299593014888e-06,
                5.043476486883855e-07,
                2.260324028427877e-06
            ],
            [
                1.3709575337078829e-06,
                5.715003788993679e-07,
                3.927862470861484e-07,
                8.315281267834927e-07,
                3.9278605979208185e-07,
                4.4508521110499674e-07,
                4.450848927650143e-07,
                7.338212429537553e-07,
                2.2603242978778778e-06,
                7.338212429537553e-07
            ],
            [
                2.6995768091310296e-07,
                1.275190124842887e-07,
                2.1024339116168358e-07,
                2.699578740032504e-07,
                1.6373776432481905e-07,
                1.855391681898159e-07,
                3.466327037539638e-07,
                3.059022998558814e-07,
                6.023568448589658e-08,
                4.450852111148132e-07
            ],
            [
                3.288749849529972e-06,
                3.4663266243308805e-07,
                2.2603251062450327e-06,
                7.338208930460318e-07,
                8.764254764780641e-08,
                5.043472278322555e-07,
                0.00033535003135793073,
                7.88926070489716e-06,
                9.422447062294175e-07,
                5.71500719545698e-07
            ],
            [
                0.9999925887201414,
                1.2098656835252174e-06,
                1.2098661161927025e-06,
                0.9999687980737968,
                1.2098652508347793e-06,
                3.927863407379485e-07,
                1.7603425837903113e-06,
                7.338210679949506e-07,
                9.4224425692559e-07,
                4.450852111155216e-07
            ],
            [
                2.2603253756874524e-06,
                0.9999516743451462,
                0.9999964991451706,
                0.9999989969855538,
                1.3709572068522336e-06,
                0.9999995262093293,
                0.9998601779441758,
                0.9990889488957215,
                0.9999916019269801,
                0.9999949062925721
            ],
            [
                1.2098662604291696e-06,
                5.422220262599396e-06,
                3.4663262110803996e-07,
                5.04347528446051e-07,
                4.785096206013061e-06,
                2.260324836787226e-06,
                2.260323758987159e-06,
                2.260324836787226e-06,
                2.5612828213934817e-06,
                5.422219616265831e-06
            ],
            [
                4.450848927650143e-07,
                1.994729721518893e-06,
                0.9999974387165709,
                3.288747889284851e-06,
                2.699578740011634e-07,
                6.962253760024999e-06,
                5.043475885674441e-07,
                0.9999910603037129,
                3.059022998576899e-07,
                9.422447062294175e-07
            ],
            [
                1.0677031245905116e-06,
                3.927860597945825e-07,
                3.059022269250683e-07,
                5.715003789033962e-07,
                1.6373772528704005e-07,
                6.475949525981759e-07,
                4.4508526417298334e-07,
                1.2098653950656417e-06,
                7.338207180864763e-07,
                9.422449308748773e-07
            ],
            [
                5.715006514176113e-07,
                1.4449798650551755e-07,
                1.637377057680051e-07,
                1.6373772528704005e-07,
                2.382369383923073e-07,
                8.764242227418718e-08,
                1.444979692800516e-07,
                5.4222176771176554e-06,
                1.4449795205429202e-07,
                9.931190958076104e-08
            ],
            [
                6.144177531811707e-06,
                7.889262585814522e-06,
                6.962256249885085e-06,
                3.288749457469787e-06,
                2.430023204460668e-05,
                1.0129988564974359e-05,
                1.5534979397740895e-06,
                5.829127945202588e-05,
                7.889263526345123e-06,
                1.1478765389222573e-05
            ],
            [
                1.0677024881980089e-06,
                1.3709567165617364e-06,
                4.2228329411708495e-06,
                1.2098662604291696e-06,
                1.553497754577351e-06,
                1.0677029973158649e-06,
                2.3823690999290963e-07,
                8.315277302841894e-07,
                1.2098656835224664e-06,
                1.3709567165617364e-06
            ],
            [
                4.450852111135988e-07,
                1.760342793638743e-06,
                6.962257909785973e-06,
                9.422450432014836e-07,
                7.88926446679691e-06,
                1.5534975693933505e-06,
                8.315281267882195e-07,
                3.927862939126708e-07,
                1.5534971990126997e-06,
                3.2887486733420804e-06
            ],
            [
                0.9999724643057415,
                0.9999964991464257,
                0.9999916019249692,
                2.2603251062450327e-06,
                1.8925150497435443e-05,
                0.9999982396572071,
                8.939698435657833e-06,
                1.5534977545886537e-06,
                1.0677029973192638e-06,
                0.9999861539954689
            ],
            [
                1.2751899728286965e-07,
                1.8553903548231313e-07,
                1.3709567165617364e-06,
                2.1024341622426268e-07,
                8.315279285370317e-07,
                1.1253516205489029e-07,
                7.338209805240734e-07,
                5.715005832895975e-07,
                0.9999339478795896,
                1.27519088491875e-07
            ],
            [
                2.561282210729555e-06,
                5.043475885674441e-07,
                7.338209805200689e-07,
                2.260325375677174e-06,
                7.338211554725124e-07,
                2.7535681250497054e-05,
                2.561283432005142e-06,
                5.04347528446051e-07,
                1.0677029973056687e-06,
                5.715005832853093e-07
            ],
            [
                1.3709575337159875e-06,
                6.475945666051092e-07,
                4.2228319344021954e-06,
                1.994729721518893e-06,
                9.422443692574719e-07,
                6.475950298021765e-07,
                1.760342793638743e-06,
                5.715002426460124e-07,
                7.338207180898968e-07,
                5.715002426486762e-07
            ],
            [
                1.3709573702822306e-06,
                3.059022269250683e-07,
                8.315279285351409e-07,
                4.0063711294555596e-05,
                3.0590237279032884e-07,
                2.69957906184239e-07,
                1.012999097997104e-05,
                3.726637951367137e-06,
                7.338209805170655e-07,
                1.0677032518785256e-06
            ],
            [
                0.9999916019269801,
                3.466325797888292e-07,
                3.46632497145457e-07,
                8.764247451307293e-08,
                2.3823682479181176e-07,
                9.931187406410953e-08,
                5.043474081993875e-07,
                1.4449805540700758e-07,
                8.31527928532683e-07,
                1.4449796927932878e-07
            ],
            [
                0.9999957771670624,
                6.1441767993788005e-06,
                0.999996033014561,
                2.1024336609843824e-07,
                1.1253512180925583e-07,
                2.7535704232595768e-05,
                3.288748281329893e-06,
                0.999995504816282,
                1.6701421845361053e-05,
                1.0129993395336818e-05
            ],
            [
                5.04347528446051e-07,
                2.3823690999323465e-07,
                2.10243290909963e-07,
                3.059022269250683e-07,
                2.3823688159291947e-07,
                0.9999993524054338,
                1.760343213335281e-06,
                4.4508515805735777e-07,
                3.927860597945825e-07,
                4.450852111148132e-07
            ],
            [
                1.994729721518893e-06,
                0.9999904837494645,
                0.999964643732562,
                7.889261645427538e-06,
                1.994729483729522e-06,
                4.222834954801051e-06,
                8.939697369980456e-06,
                4.785095635655362e-06,
                2.5612822106421996e-06,
                7.338209805224048e-07
            ],
            [
                2.699576809143613e-07,
                9.422444815814404e-07,
                3.466327450765785e-07,
                1.3709572068522336e-06,
                1.2098656835224664e-06,
                9.931189774187203e-08,
                3.466325384661554e-07,
                3.927863875616689e-07,
                1.8553914607237736e-07,
                3.9278634073732336e-07
            ]
        ]
    },
    {
        "q_id": "9049_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999994956525919,
                2.9023119851899796e-06,
                1.994729483729522e-06,
                9.422443692574719e-07,
                1.9947304348862686e-06,
                1.0129987357517693e-05,
                5.422221555414699e-06,
                2.561283126728994e-06,
                2.5612834320563895e-06,
                0.9999989969854338
            ],
            [
                0.9999984465022458,
                8.315279285370317e-07,
                0.9999977396748948,
                2.2603240284371276e-06,
                0.9999904837471802,
                9.422442569315887e-07,
                0.9999942280792865,
                0.999998239657417,
                5.043473480777865e-07,
                0.9999646437409275
            ],
            [
                0.9999869928699899,
                4.785095065232451e-06,
                8.939693107190907e-06,
                0.999991060302633,
                0.9999945777784474,
                3.7266410611296085e-06,
                8.939699501416646e-06,
                0.999941708748561,
                0.9999957771665566,
                0.9999984465028015
            ],
            [
                0.9999832985821608,
                0.9999687980775283,
                0.999992588716602,
                3.9278605979534166e-07,
                0.9999852610180429,
                5.71500378896509e-07,
                0.9999485577927548,
                0.9999785550439455,
                0.9999546021476804,
                0.9997040430191297
            ],
            [
                0.9999977396754335,
                0.9999921107383618,
                0.9999977396746255,
                0.9999983463100203,
                2.3823690999160957e-07,
                0.9999987901344612,
                0.999999939764294,
                0.9999910602994384,
                0.999995777166054,
                0.999992110735539
            ],
            [
                0.9999982396574166,
                1.3709568799919866e-06,
                0.9999832985701962,
                0.9999967112505433,
                0.999997438718095,
                0.9999987121049383,
                0.9999885212291435,
                0.9999970976887075,
                0.9999999273418875,
                1.209865827752005e-06
            ],
            [
                0.9999810748427502,
                4.4508515805735777e-07,
                8.93969950132721e-06,
                0.9999785550567181,
                2.382369951932796e-07,
                0.9999964991455879,
                1.209865827752005e-06,
                1.1253508156363576e-07,
                1.8553910183674878e-07,
                0.9999987121050916
            ],
            [
                4.4508510499849186e-07,
                1.3709576971463352e-06,
                1.275190732904469e-07,
                2.102434412875379e-07,
                0.9999885212359879,
                2.69957906184239e-07,
                1.4449805540740185e-07,
                2.102434162245973e-07,
                0.9999921107374191,
                0.9999810748517747
            ],
            [
                0.9999962733598282,
                0.999991060304767,
                0.9999982396569971,
                9.422450432030903e-07,
                0.9999993524054336,
                0.9999724642990933,
                0.9999957771660535,
                0.9999992661789321,
                3.288747889284851e-06,
                0.9999987901341725
            ],
            [
                2.1444953526969788e-05,
                3.7266406167827664e-06,
                3.7266397283231055e-06,
                4.222834451355964e-06,
                1.6701421845057263e-05,
                2.1444945858485726e-05,
                7.889265407090955e-06,
                3.9278610661902853e-07,
                2.430024942462891e-05,
                0.9998204719933432
            ],
            [
                1.0677028700422047e-06,
                0.9999339478555562,
                0.9999991148431753,
                0.9999921107383615,
                0.9999417087067719,
                0.9999987121047847,
                1.760343213335281e-06,
                1.3709575337159875e-06,
                0.9999982396572069,
                1.5534971990169383e-06
            ],
            [
                8.31528325040778e-07,
                0.9999952149043678,
                1.209865539298447e-06,
                1.5534983101644536e-06,
                0.9999646437493461,
                3.288749849529972e-06,
                0.999986992869992,
                3.9278620026686556e-07,
                0.9999724643187952,
                1.209865827752005e-06
            ],
            [
                0.9999952149072182,
                0.9999417087137769,
                2.1444940746307572e-05,
                0.9999930377437523,
                5.043474683240344e-07,
                4.222834954801051e-06,
                1.3709575337159875e-06,
                2.561281294760143e-06,
                1.4449805540740185e-07,
                1.1478770862882149e-05
            ],
            [
                0.9999993524052792,
                0.9999942280779106,
                9.422449308774482e-07,
                2.6995768091310296e-07,
                2.2603253756956754e-06,
                1.8553905760024476e-07,
                3.927862002663297e-07,
                0.9999977396765116,
                0.9999982396559483,
                0.9999975938973745
            ],
            [
                0.9999997463980124,
                0.9999986290427936,
                0.9999983463110063,
                0.9999996743686257,
                0.999998005270517,
                0.9999972735290805,
                0.999999391641036,
                0.9999999468421567,
                0.9999988634364252,
                0.9999983463108088
            ],
            [
                5.422217677152175e-06,
                NaN,
                0.9999962733616056,
                0.9999945777803864,
                3.7266383956509585e-06,
                0.9999785550541569,
                0.9999982396569972,
                9.422444815814404e-07,
                0.9999898700114392,
                0.0006263341085583501
            ],
            [
                0.9999970976869775,
                2.902312677150514e-06,
                0.9999938558275977,
                0.9999975938970876,
                0.9999984465016901,
                0.9999991148429642,
                2.9023116392097746e-06,
                0.9996646499717837,
                3.726639284144195e-06,
                3.059021175261338e-07
            ],
            [
                0.9999964991468394,
                0.9999993916406733,
                0.9999982396565773,
                2.102433410343832e-07,
                0.9999988634364251,
                0.9999989322971303,
                0.9999921107402402,
                0.9999785550490641,
                0.9999930377445841,
                0.9999957771675636
            ],
            [
                0.9999785550464871,
                0.9999910603058315,
                0.9999988634357478,
                1.9947301970972664e-06,
                0.9999989322966211,
                1.012999098021058e-05,
                0.9999952149043673,
                0.9999921107345956,
                0.9999952149072182,
                7.889266347786918e-06
            ],
            [
                NaN,
                0.9999984465016905,
                0.9999975938982347,
                1.147877359957198e-05,
                0.9999930377412639,
                1.012998977264307e-05,
                0.9999869928699966,
                1.147876812620341e-05,
                0.9999984465015053,
                0.9999843104503016
            ],
            [
                1.8553916819032217e-07,
                0.9999991684719726,
                4.785094494811783e-06,
                0.999998126124617,
                0.9999485577680165,
                0.9999974387184005,
                0.9999910603005021,
                3.7266383956509585e-06,
                0.9999785550541638,
                1.3007134667259441e-05
            ],
            [
                4.7850933539684755e-06,
                0.9999991684719727,
                4.222834954801051e-06,
                0.9999810748540359,
                9.422447062294175e-07,
                0.00015843627366396256,
                0.999978555043942,
                2.2603248367949354e-06,
                1.994729483729522e-06,
                0.9999975938982347
            ],
            [
                0.999998863435748,
                0.9999962733616065,
                0.9999930377420924,
                0.9999930377429255,
                0.9999869928761975,
                0.9999982396567874,
                0.9999916019289753,
                0.9999955048168169,
                0.9999546021152388,
                0.999989870004203
            ],
            [
                0.9999969105062899,
                0.999998126125287,
                0.9999974387177905,
                0.999998239656787,
                0.9999995262094987,
                0.9999945777823268,
                0.9999724642958031,
                6.962257909842961e-06,
                0.9999962733598287,
                0.9999921107383576
            ],
            [
                0.999998346309626,
                0.9999756997505924,
                9.931195693628605e-08,
                6.962258739796719e-06,
                6.144175334510455e-06,
                1.5534971990169383e-06,
                6.144176066795103e-06,
                6.475945666063607e-07,
                5.422217030781934e-06,
                0.9999417087067766
            ],
            [
                0.9999988634360187,
                0.9999997126313098,
                0.9999995818811773,
                0.9999993524049704,
                0.999997097688016,
                0.9999992188513904,
                0.9999995549148951,
                0.999998005269804,
                0.9999995818811275,
                0.9999970976890538
            ],
            [
                0.9999975938985216,
                6.144176066943187e-06,
                2.2603253756874524e-06,
                1.4738976701652988e-05,
                0.9999546021097657,
                1.012999581057419e-05,
                1.994729008151319e-06,
                1.5534984953552536e-06,
                1.0677024882029858e-06,
                6.962258739796719e-06
            ],
            [
                1.1478772231086046e-05,
                1.5534983101644536e-06,
                1.994729959270648e-06,
                6.47595107001401e-07,
                1.5534984953552536e-06,
                0.9999885212277796,
                5.043474683240344e-07,
                1.994729008151319e-06,
                1.6701427816728442e-05,
                1.0677029973219343e-06
            ],
            [
                1.4738985486506781e-05,
                0.99999976176309,
                1.7603438428660665e-06,
                0.9999991684716751,
                0.9999930377429231,
                4.785093353787868e-06,
                0.999981074845007,
                2.382368247924618e-07,
                5.043472278312808e-07,
                2.699577774585891e-07
            ],
            [
                0.9999957771675634,
                4.785096776468749e-06,
                1.209865539298447e-06,
                4.222834954801051e-06,
                2.2603248367949354e-06,
                2.5612834320563895e-06,
                5.715002426486762e-07,
                1.7603440527334603e-06,
                6.144177531811707e-06,
                2.5612834320563895e-06
            ],
            [
                0.9999990577557435,
                0.999999607213753,
                0.9999994284992806,
                0.9999991148427534,
                0.9999995549150013,
                0.999999057754957,
                0.9999934595627792,
                0.9999994956523515,
                0.999993855825401,
                0.9999992661790198
            ],
            [
                0.9999930377437531,
                0.9999921107383586,
                1.9947299593078385e-06,
                0.9999991148432809,
                0.9999977396748944,
                0.9999987121046311,
                0.9999993524054335,
                6.475945666051092e-07,
                0.9999962733607166,
                0.9999992661792821
            ],
            [
                0.999997739675433,
                0.9999960330150327,
                0.999915188969151,
                3.7266397283908927e-06,
                0.9991959139563873,
                0.9999969105044489,
                0.9999975938976617,
                0.9999983463104146,
                0.9999852610110085,
                0.9999993106387081
            ],
            [
                0.9999785550541559,
                2.2603248367949354e-06,
                2.561282821402217e-06,
                1.5534983101644536e-06,
                0.9999646437451097,
                3.7266383956509585e-06,
                1.670142980893658e-05,
                1.3709575337159875e-06,
                2.561283126728994e-06,
                1.5534981249736758e-06
            ],
            [
                0.9999985406239535,
                0.9999992188512972,
                0.9999991684720717,
                0.9999981261246177,
                6.962254589978262e-06,
                0.9999852610162787,
                4.785096206076165e-06,
                0.9999994284992808,
                0.9999996310114159,
                0.9999992661791947
            ],
            [
                0.9999994956524116,
                0.9999992188513902,
                0.9999982396559479,
                0.9999975938976615,
                0.9999987901337398,
                0.9999967112497602,
                0.9999996743686645,
                0.9999985406232577,
                0.9999998461826405,
                0.9999977396765115
            ],
            [
                1.5534981249697903e-06,
                8.31528325040778e-07,
                1.1253506814842375e-07,
                0.9999251537551382,
                0.9999991148431754,
                0.9999810748585407,
                3.4663262111182307e-07,
                0.9999952149043662,
                0.9999962733616055,
                0.9999982396559478
            ],
            [
                3.927863875616689e-07,
                3.059022998576899e-07,
                2.3823688159291947e-07,
                1.760342793638743e-06,
                0.9999417087557236,
                3.927862002663297e-07,
                3.4663274507713016e-07,
                1.209865827752005e-06,
                1.370957860576702e-06,
                4.785094494811783e-06
            ],
            [
                0.9999885212264068,
                0.9999988634360186,
                0.9999977396765115,
                0.9999921107345968,
                0.999981074851779,
                2.5612834320470717e-06,
                0.9999993524052793,
                0.9999983463110057,
                0.9999975938968013,
                0.9999983463100206
            ],
            [
                6.475951069932288e-07,
                3.466325797896173e-07,
                0.9999982396574169,
                0.9999993524052792,
                0.9999997897565838,
                0.9999949062956072,
                0.9999962733611618,
                0.9999992661789322,
                0.9999991148431755,
                0.9999990577550695
            ],
            [
                0.999998239657417,
                0.9999980052705171,
                0.9999989969857924,
                1.0677029973219343e-06,
                0.9999980052700415,
                0.999998005269328,
                0.9999964991443355,
                1.2751899728286965e-07,
                0.9999995549148951,
                0.9999988634358831
            ],
            [
                0.9999989969857925,
                0.9999989969854339,
                0.9999985406230839,
                0.9999546021476836,
                0.9999952149037975,
                0.9999960330140877,
                2.6995790618350237e-07,
                0.9999832985801779,
                0.9999885212318943,
                0.9999977396754333
            ],
            [
                0.9999921107355375,
                0.9999991148429643,
                0.9999992188512972,
                0.9999986290431204,
                0.999986992873094,
                0.9999983463108088,
                0.999995214904366,
                0.9999957771660537,
                0.9999975938979478,
                0.9999967112493678
            ],
            [
                1.0677029973219343e-06,
                0.999991060305834,
                0.9999987901338838,
                0.9999987121047847,
                8.315280276626197e-07,
                1.0677028700422047e-06,
                0.9999985406237796,
                1.3709575337159875e-06,
                8.315278294114555e-07,
                0.9999921107355363
            ],
            [
                8.3152792852928e-07,
                0.9999756997477076,
                0.9999984465018757,
                0.9999972735300555,
                0.9999981261252874,
                0.9999952149043662,
                0.9999934595604394,
                0.9999995549151074,
                8.315284241665078e-07,
                0.9999938558254029
            ],
            [
                0.9999964991468402,
                0.9999989969859121,
                0.999998446502246,
                0.999997739675973,
                0.9999992661791073,
                0.9999949062925744,
                0.9999960330140877,
                1.0677026154806063e-06,
                0.9999832985801701,
                0.999999391640891
            ],
            [
                0.9999998942830737,
                1.994729721518893e-06,
                3.466327037553825e-07,
                0.9999921107364772,
                0.9999997300421904,
                1.209865827752005e-06,
                1.3709570434250617e-06,
                6.144175334418252e-06,
                0.9999921107392977,
                1.3709575337159875e-06
            ],
            [
                3.059022269250683e-07,
                2.699576809143613e-07,
                0.9999960330155068,
                3.466326211113502e-07,
                0.9999980052698042,
                0.9999972735294058,
                2.382368531929327e-07,
                4.450852111155216e-07,
                9.422447062294175e-07,
                2.2603245673443566e-06
            ],
            [
                1.067703124601679e-06,
                2.260323758987159e-06,
                9.422448185435711e-07,
                2.382370235922541e-07,
                1.6373774480535133e-07,
                0.999997438717485,
                6.475947209985977e-07,
                7.338210679979539e-07,
                1.8553916819032217e-07,
                1.2751905808881762e-07
            ],
            [
                1.7603430034867993e-06,
                0.9999992661791947,
                5.715004470295662e-07,
                0.999998346309823,
                0.9999975938968018,
                2.2603242978943238e-06,
                0.9999989322970029,
                0.999997438718096,
                0.9999997463981636,
                0.9999975938968007
            ],
            [
                3.72663883989755e-06,
                0.9999990577555189,
                0.9999687980998273,
                1.760342793638743e-06,
                3.7266397283908927e-06,
                NaN,
                0.9999983463102174,
                2.9023116392097746e-06,
                0.999954602115177,
                0.9999910603068982
            ],
            [
                0.9999970976887079,
                0.9999990577555187,
                0.9999952149043655,
                0.9999985406234313,
                0.999998863435748,
                0.999998932297512,
                0.9999869928668915,
                0.9999988634366962,
                0.9999885212332484,
                0.9999993916408909
            ],
            [
                1.3709575337159875e-06,
                3.7266397283908927e-06,
                1.8925143729954285e-05,
                0.999972464318785,
                3.2887502415767434e-06,
                0.999997097688362,
                0.9999898700078178,
                0.9999810748472743,
                0.9999885212359866,
                0.9999898700126498
            ],
            [
                4.450851049991497e-07,
                0.9999885212264061,
                0.9999898700114389,
                NaN,
                4.450852641717689e-07,
                5.422217677152175e-06,
                0.9999984465026162,
                0.9999898700041936,
                5.422221555414699e-06,
                5.043472278322555e-07
            ],
            [
                3.726637951387472e-06,
                6.47595107001401e-07,
                6.47595107001401e-07,
                2.5612831266946347e-06,
                7.338208055680009e-07,
                0.999968798073805,
                0.999985261012779,
                0.9999599362888338,
                7.338210680021253e-07,
                3.9278634073732336e-07
            ],
            [
                0.9999985406241272,
                0.9999997463980729,
                0.9999991148426478,
                1.6373776432481905e-07,
                0.9999984465015052,
                0.9999995262093292,
                0.9999986290426301,
                0.9999990577551816,
                0.9999785550464919,
                2.1024344128584085e-07
            ],
            [
                0.9999938558224699,
                0.9999982396572066,
                0.999983298582147,
                0.9999982396565771,
                1.0129987357517693e-05,
                0.999972464305641,
                1.6701417863559525e-05,
                2.9023119851899796e-06,
                1.3007123813559956e-05,
                6.962256249935742e-06
            ],
            [
                1.1253512180925583e-07,
                0.9999962733593843,
                0.9999990577556311,
                0.9999991684719725,
                0.9999992188514834,
                0.9999952149032274,
                0.9999992188516695,
                0.9999852610127639,
                0.9999945777829703,
                0.9999981261237233
            ],
            [
                0.9999952149032257,
                6.962256249935742e-06,
                7.889262585958025e-06,
                2.1024331597262577e-07,
                1.5534971990169383e-06,
                0.999998932297512,
                2.9023112932296107e-06,
                0.0003353501513165474,
                1.8925148242250705e-05,
                0.9999885212346187
            ],
            [
                0.9999960330126691,
                0.9999978766207793,
                0.999999391641181,
                0.9999981261250638,
                6.475946438055299e-07,
                0.9999967112513289,
                0.9999975938976613,
                8.315282259138311e-07,
                0.9999964991468394,
                0.999999057755294
            ],
            [
                2.6995784182140636e-07,
                1.275190276859705e-07,
                0.9999910603047688,
                1.4449802095666915e-07,
                0.9999785550567315,
                2.382370235933104e-07,
                3.05902336324494e-07,
                0.9999546021207343,
                0.9999985406236056,
                2.382370235933104e-07
            ],
            [
                0.9999962733616065,
                0.9999975938985219,
                0.9999982396574166,
                0.9999992188516698,
                0.9999972735290811,
                0.9999974387174846,
                0.9999993916409634,
                0.9999986290427937,
                0.999998126123947,
                0.9999985406234315
            ],
            [
                3.288749849529972e-06,
                0.9999962733602733,
                0.999964643736683,
                9.422448185534261e-07,
                1.3709573702856596e-06,
                4.222834954801051e-06,
                7.33821330437595e-07,
                5.422221555414699e-06,
                0.9999995262094422,
                0.9999975938979483
            ],
            [
                0.9999957771670611,
                4.785093924389007e-06,
                1.5534975693979422e-06,
                5.422217677152175e-06,
                4.785092783545836e-06,
                0.9999981261246169,
                0.999993855825401,
                1.9947292459406333e-06,
                0.9999957771660544,
                0.999993037740435
            ],
            [
                0.9999898700041964,
                2.260325375664839e-06,
                0.9999978766205254,
                0.9999869928668941,
                3.2887494574518405e-06,
                2.144494841482881e-05,
                0.99999879013374,
                0.9999987121046313,
                1.3709575337159875e-06,
                5.422217677152175e-06
            ],
            [
                NaN,
                0.9999810748540305,
                1.3709570434250617e-06,
                0.9999910603047667,
                0.9999945777790926,
                0.9999687980923834,
                0.9999785550439337,
                2.7535687820994754e-05,
                9.422449308789479e-07,
                0.999972464315495
            ],
            [
                0.9999885212332488,
                2.9023119851781017e-06,
                4.450848927658745e-07,
                0.999704042831885,
                4.450848927650143e-07,
                0.9999869928761926,
                2.5612831267086116e-06,
                1.2098661162023305e-06,
                0.9999885212318796,
                0.9999952149043658
            ],
            [
                0.9999993524049705,
                0.9999885212332509,
                0.9999952149043673,
                0.9999982396572067,
                5.422221555414699e-06,
                6.475947210046347e-07,
                1.5534983101644536e-06,
                1.994729483729522e-06,
                8.31527928532683e-07,
                2.5612825160096693e-06
            ],
            [
                0.9999417087067525,
                3.9278629391427843e-07,
                1.0129988565084915e-05,
                1.9947299593078385e-06,
                0.9999983463108086,
                0.9999991148433864,
                0.9999988634361542,
                0.999999352405202,
                0.9999756997564013,
                7.338211554813555e-07
            ],
            [
                0.9999869928746586,
                0.999994577779095,
                0.9999952149043668,
                0.9999898700066139,
                0.9999949062968215,
                0.9999724642991075,
                0.9999832985821696,
                0.9999339478791954,
                0.999993037744588,
                0.9999885212264128
            ],
            [
                0.9999990577555188,
                0.999997739675164,
                0.9999987901344611,
                1.0677028700422047e-06,
                0.9999977396754337,
                0.9999970976866321,
                0.9999989969857926,
                0.9999996533672136,
                0.9999987121052454,
                NaN
            ],
            [
                0.9999724643023589,
                0.999989870010234,
                1.6373762769138607e-07,
                1.067703124601679e-06,
                6.144175334510455e-06,
                6.144175334510455e-06,
                0.9999949062931778,
                0.9999910603015684,
                0.9999964991451693,
                7.889265407327733e-06
            ],
            [
                0.9998766054548085,
                0.9999810748495133,
                1.5534984953552536e-06,
                7.338208930460318e-07,
                0.00017952790218948365,
                4.222834451403972e-06,
                1.3007123813559956e-05,
                4.785095065232451e-06,
                1.7603440527334603e-06,
                0.9999962733593842
            ],
            [
                7.889265407327733e-06,
                0.9999962733611631,
                9.422444815814404e-07,
                0.9999925887192552,
                0.999997593898522,
                0.9999972735300561,
                0.9999980052700419,
                0.9999960330131408,
                0.9998415638239445,
                4.450851580555361e-07
            ],
            [
                1.3709572068553509e-06,
                7.889262585886274e-06,
                2.561281294760143e-06,
                0.9999952149060776,
                3.2887506336235617e-06,
                0.9999910603068967,
                0.99998987000661,
                1.3007134667259441e-05,
                2.2603234895372223e-06,
                6.47594952603035e-07
            ],
            [
                6.962259569750576e-06,
                6.962257909842961e-06,
                2.561283126728994e-06,
                2.43002523073625e-05,
                0.9999938558268671,
                0.999989870006613,
                3.927860597945825e-07,
                8.939700566907275e-06,
                2.5612812947240366e-06,
                0.9999785550541627
            ],
            [
                0.999999607213753,
                0.9999985406230837,
                0.9999989969857928,
                0.999998126125064,
                7.889266347786918e-06,
                0.9999942280799743,
                0.9999945777823263,
                0.9999938558239365,
                0.9999993106387081,
                0.9999898700102333
            ],
            [
                2.3823690999323465e-07,
                1.5534971990169383e-06,
                3.7266379514061143e-06,
                0.9999885212332477,
                1.892515501014656e-05,
                2.5612834320563895e-06,
                8.93969950132721e-06,
                6.47595107001401e-07,
                NaN,
                0.9999921107355365
            ],
            [
                0.9999994631248682,
                0.9999987121046312,
                0.9999151889386432,
                2.3823690999290963e-07,
                7.338207180898968e-07,
                8.764242227418718e-08,
                0.9999970976876699,
                0.9998601778600699,
                1.012999218776902e-05,
                0.9999724642958198
            ],
            [
                0.9999987121049384,
                0.9999998144608981,
                0.9999983463102174,
                0.9999992661791947,
                0.9999974387184012,
                0.9999996940976638,
                0.9999997126313098,
                0.9999996743686645,
                0.999999712631344,
                0.9999988634362897
            ],
            [
                3.7266410611465547e-06,
                2.561282210740037e-06,
                7.889259764517575e-06,
                1.2098656835252174e-06,
                1.0677026154806063e-06,
                1.8553919030858602e-07,
                1.6373770576776313e-07,
                0.999986992876197,
                4.4508515805735777e-07,
                1.3709576971463352e-06
            ],
            [
                0.9999885212332492,
                0.9999869928653384,
                0.9999898700090281,
                0.9999986290423032,
                1.4738983729535602e-05,
                0.9999962733620499,
                0.00013982204091004735,
                0.9999992661791071,
                0.9999930377404351,
                0.9999756997650822
            ],
            [
                3.7266383956509585e-06,
                1.2098653950716937e-06,
                0.999998629042957,
                0.999999391641036,
                1.0677026154827912e-06,
                1.760342793638743e-06,
                0.999999554914789,
                2.9023119851899796e-06,
                1.994729483723626e-06,
                1.5534984953552536e-06
            ],
            [
                0.9999957771665583,
                0.9999756997477143,
                0.999996910504817,
                1.7603440526806268e-06,
                0.9999975938968005,
                0.9999972735300554,
                0.9999977396765113,
                0.9999970976876704,
                0.9999892166890761,
                0.9999989322972576
            ],
            [
                4.222834954801051e-06,
                0.9999995549151074,
                1.2098662604126641e-06,
                0.9999974387177899,
                1.275190124842887e-07,
                7.889263526409699e-06,
                1.0677033791291683e-06,
                4.22283545795623e-06,
                1.3709575337078829e-06,
                8.939695238089467e-06
            ],
            [
                0.99999916847227,
                0.9999984465018757,
                0.9999964991464222,
                0.9999989969862707,
                0.9999987121044777,
                0.9999981261237241,
                0.9999977396748948,
                0.9999980052698044,
                0.9999978766210321,
                0.9999983463098234
            ],
            [
                0.9999546021206736,
                9.422450432030903e-07,
                1.760342793638743e-06,
                2.5612834320563895e-06,
                2.9023109472494878e-06,
                0.9999885212346183,
                2.9023109472494878e-06,
                9.422442569334097e-07,
                1.5534981249736758e-06,
                0.9999984465028018
            ],
            [
                0.9999962733589404,
                3.120192625482384e-05,
                0.9999898700054024,
                5.422218969895357e-06,
                0.9999987121041706,
                0.999998446502431,
                0.9999990577554062,
                0.9999987901346054,
                0.9999938558261338,
                0.9999992661788446
            ],
            [
                0.9999925887201349,
                3.46632497145457e-07,
                0.9999984465022459,
                0.9999987121049382,
                1.3709572068553509e-06,
                4.450851580540182e-07,
                9.422450431954847e-07,
                0.9999996743688586,
                2.3823702359290413e-07,
                2.1024326584639497e-07
            ],
            [
                0.9999952149060787,
                0.9999977396759733,
                1.7603434231833873e-06,
                0.9999955048173551,
                0.9999916019279724,
                0.9999904837437784,
                0.9999967112493686,
                0.9999945777797401,
                0.9999980052707549,
                0.9999972735287564
            ],
            [
                0.9999945777784494,
                0.9999989969862709,
                0.999997593898236,
                0.999972464302454,
                0.9999957771660541,
                0.9999991148433867,
                0.9999989969862707,
                0.9999992661786699,
                0.999995777166053,
                0.9999993106387081
            ],
            [
                9.422442569334097e-07,
                3.288749457469787e-06,
                0.9999962733620511,
                0.9999974387177901,
                0.9999832985761808,
                3.9278629391427843e-07,
                3.7266383956509585e-06,
                0.9999974387184009,
                1.275189972832538e-07,
                7.889263526409699e-06
            ],
            [
                0.999999674368781,
                0.9999975938985217,
                0.9999969105066583,
                0.9999996072137062,
                0.9999982396567874,
                0.9999985406230836,
                0.9999995262093292,
                0.999999352405202,
                0.9999995549149482,
                0.9999998461826222
            ],
            [
                0.999998005270517,
                0.9999832985702019,
                0.9999957771670612,
                NaN,
                2.561283126728994e-06,
                0.9999987901341727,
                0.9999962733620503,
                2.902312331170226e-06,
                0.9999981261237235,
                0.9999945777803854
            ],
            [
                2.9023133690188264e-06,
                0.9999952149049369,
                0.9999991684718734,
                1.209865827740176e-06,
                1.1253520230052635e-07,
                0.9999972735294057,
                8.764242227380856e-08,
                0.9999687980886737,
                1.7603438428848787e-06,
                0.9999785550541844
            ],
            [
                2.9023112932296107e-06,
                1.444980209564556e-07,
                1.0129987357517693e-05,
                1.6373766672973748e-07,
                0.9999930377462417,
                1.855391681906175e-07,
                4.4508510499737865e-07,
                0.999993037742093,
                6.962258739796719e-06,
                2.5612819054028872e-06
            ],
            [
                2.430024073523505e-05,
                1.473898900066424e-05,
                2.4300234941880266e-05,
                0.00013982202420767366,
                1.473898900066424e-05,
                6.962259569750576e-06,
                0.9999949062937857,
                0.9999962733616059,
                2.144495864059426e-05,
                2.902312677137316e-06
            ],
            [
                5.043476486924565e-07,
                0.999981074849529,
                5.043472278322555e-07,
                5.715005151606823e-07,
                3.927862002663297e-07,
                0.9999151889691188,
                0.9999646437325524,
                0.9999898700041956,
                1.7603425837903113e-06,
                8.315279285370317e-07
            ],
            [
                5.422221555414699e-06,
                0.9999910603026334,
                5.422217030781934e-06,
                1.5534975693979422e-06,
                5.422217677152175e-06,
                0.9999945777816779,
                0.9999952149049358,
                1.0677028700422047e-06,
                1.0677027427624903e-06,
                NaN
            ],
            [
                0.9999970976890532,
                0.9999993916411084,
                0.9999970976866319,
                0.999993037746244,
                0.999999746398224,
                0.9999990577551816,
                0.9999964991464215,
                0.9999987121052452,
                0.9999898700114386,
                0.9999991148430699
            ],
            [
                0.9999810748427519,
                1.444980726324838e-07,
                0.999995214907219,
                0.99998107485629,
                0.999933947831953,
                0.999968798073803,
                2.2603248367949354e-06,
                0.9998204720780611,
                0.999996033013614,
                0.9999952149066474
            ],
            [
                2.382368815932174e-07,
                0.99999709768767,
                7.338207180898968e-07,
                1.3709575337159875e-06,
                0.99998329857419,
                2.9023109472494878e-06,
                0.9999967112493685,
                8.31528325040778e-07,
                0.9999898700114399,
                0.9999989969855534
            ],
            [
                1.275190124842887e-07,
                2.1024334103505245e-07,
                0.9999972735307063,
                2.382369383923073e-07,
                0.9999885212264145,
                1.0677029973158649e-06,
                0.9999982396569973,
                0.999995777166055,
                0.9999934595627777,
                0.9999955048200314
            ],
            [
                2.9023116392097746e-06,
                2.9023109472244114e-06,
                0.999997593898235,
                7.889263526409699e-06,
                1.76034363298589e-06,
                1.3007126913346863e-05,
                0.9999974387180958,
                1.0129989770441144e-05,
                0.9999810748427554,
                1.1478773599102191e-05
            ],
            [
                3.7266383956509585e-06,
                5.715006514176113e-07,
                0.9999898700078175,
                0.9999970976876701,
                4.450852111155216e-07,
                0.999991060306896,
                0.9999930377429234,
                1.275191036933194e-07,
                1.3709576971463352e-06,
                3.4663274507713016e-07
            ],
            [
                0.9999938558232058,
                1.3709575337159875e-06,
                0.9999984465026164,
                0.9999988634364252,
                0.999999391641036,
                0.9999977396746262,
                0.9999945777784488,
                3.9278620026686556e-07,
                0.9999995818810776,
                3.466327037553825e-07
            ],
            [
                0.9999972735290804,
                0.9999996072138935,
                0.9999987121041706,
                0.9999992661786699,
                0.9999997463981032,
                0.999999057755631,
                0.9999990577555187,
                0.9999989969855534,
                0.9999995549149482,
                0.9999994284996212
            ],
            [
                0.9999994631251883,
                0.9999756997621945,
                5.4222183235249605e-06,
                0.9999910603068967,
                3.2887506336235617e-06,
                1.5534981249736758e-06,
                0.9999982396559476,
                0.9999995549147359,
                0.9999980052695656,
                0.9999646437408953
            ],
            [
                0.9999995818814265,
                0.9999977396748949,
                0.9999938558268658,
                0.9999974387177905,
                0.9999938558232041,
                0.9999993916411085,
                0.9999991684719726,
                0.9999964991443359,
                4.222834451403972e-06,
                0.9999992188515765
            ],
            [
                0.9999942280779156,
                0.9999942280779197,
                0.9999877809181846,
                1.5534973842076057e-06,
                2.2603251062450327e-06,
                0.9999942280813527,
                0.9999988634358836,
                0.9999938558254045,
                0.9999832985841615,
                0.999989870007831
            ],
            [
                8.764249540862797e-08,
                0.00010889694829665246,
                0.9999994284995531,
                3.466327037553825e-07,
                2.5612828213818346e-06,
                3.9278615344178325e-07,
                4.785094494811783e-06,
                1.0677027427624903e-06,
                0.999994577782325,
                3.2887506336235617e-06
            ],
            [
                0.9999985406241272,
                0.9999949062962147,
                0.9999987121046316,
                0.999996499145589,
                0.9999984465018757,
                0.999998005270517,
                0.9999982396567876,
                0.9999955048200324,
                0.9999949062956077,
                0.9999949062925716
            ],
            [
                0.9999989322971304,
                1.209866260432471e-06,
                0.999981074849517,
                2.2603251062450327e-06,
                0.999999114843281,
                2.902312331170226e-06,
                1.9947301970972664e-06,
                0.9999964991468391,
                0.9999977396754333,
                0.9999981261243934
            ],
            [
                8.315281267834927e-07,
                6.475947982037486e-07,
                0.9999957771670611,
                8.315282259089153e-07,
                9.422442569334097e-07,
                2.902312677150514e-06,
                7.338210679979539e-07,
                1.7603425837855082e-06,
                4.785092783519724e-06,
                1.3709573702856596e-06
            ],
            [
                2.5612834320563895e-06,
                8.315280276626197e-07,
                2.9023119851899796e-06,
                7.338208930460318e-07,
                2.9023109472244114e-06,
                9.422447062294175e-07,
                8.315282259138311e-07,
                1.1478772231232203e-05,
                2.10243290909963e-07,
                1.3007134667259441e-05
            ],
            [
                4.22283545819819e-06,
                3.7266406168827523e-06,
                4.222832437798974e-06,
                1.3709568799919866e-06,
                NaN,
                4.785096206076165e-06,
                6.475951069985296e-07,
                NaN,
                1.8925145985895816e-05,
                1.3709575337159875e-06
            ],
            [
                7.889263526409699e-06,
                0.9999970976876704,
                9.422449308789479e-07,
                5.715005832895975e-07,
                2.9023119851899796e-06,
                1.0677026154827912e-06,
                3.059022269254856e-07,
                NaN,
                0.9999756997650872,
                2.2603248367949354e-06
            ],
            [
                0.9999957771680671,
                0.9999957771645448,
                0.9999996940978096,
                0.9999993916411085,
                0.9999930377462447,
                0.9999916019309782,
                0.9999934595651216,
                0.9999925887183683,
                0.9999921107336581,
                0.9999993106386259
            ],
            [
                0.9999983463106117,
                1.012999218776902e-05,
                0.991422515275318,
                0.999995504820032,
                0.9999955048184241,
                3.288749849529972e-06,
                0.9999987121052454,
                2.561281600086738e-06,
                0.9999991148431754,
                0.9999974387174846
            ],
            [
                1.6373774480605869e-07,
                0.9999810748427493,
                3.927862002663297e-07,
                2.3823702359290413e-07,
                0.9999810748450022,
                2.1024339116082313e-07,
                0.9999987121052454,
                3.466326624336003e-07,
                3.05902263391829e-07,
                9.422443692555439e-07
            ],
            [
                5.71500719545698e-07,
                6.475945666063607e-07,
                0.9999910603015708,
                7.338207180898968e-07,
                0.9999938558275983,
                0.9999417087068746,
                0.9999930377454136,
                0.9999977396765113,
                0.9999930377420948,
                0.9999810748495205
            ],
            [
                1.5534975693979422e-06,
                1.3007128465151102e-05,
                0.9999987901341726,
                0.9999962733589398,
                0.9999978766215383,
                0.9999869928668946,
                0.9999990577549571,
                5.715004470326849e-07,
                3.466325797896173e-07,
                1.8553905760062447e-07
            ],
            [
                8.315284241665078e-07,
                4.22283545819819e-06,
                0.9999985406230839,
                0.9999991148433867,
                5.715003789046955e-07,
                0.9999974387171802,
                5.715005151606823e-07,
                0.9999852610180443,
                0.9999987121047849,
                0.9999921107346007
            ],
            [
                0.9999986290424672,
                6.475950298011458e-07,
                4.450848927658745e-07,
                0.9999969105040811,
                7.889261645355786e-06,
                0.9999991684717743,
                5.715005832886879e-07,
                0.9999984465024311,
                0.9999994284992806,
                0.9999993106388726
            ],
            [
                4.4508499888219586e-07,
                0.9997388097275813,
                7.338207180898968e-07,
                0.9999724643056498,
                1.3709567165386693e-06,
                2.3823690999323465e-07,
                1.0677032518814388e-06,
                4.222833947820683e-06,
                1.8553914607267268e-07,
                5.043475885696228e-07
            ],
            [
                2.10243290909724e-07,
                1.1253521571574156e-07,
                2.9023116392097746e-06,
                6.825608606148807e-08,
                3.466325384661554e-07,
                1.444980726324838e-07,
                3.466325384661554e-07,
                2.102433410343832e-07,
                3.466326624322211e-07,
                3.466327037548308e-07
            ],
            [
                5.043472278280699e-07,
                1.2098656835224664e-06,
                8.315283250371857e-07,
                8.315284241650899e-07,
                1.7603425837903113e-06,
                5.043474683204221e-07,
                7.338207180864763e-07,
                1.3709567165579959e-06,
                2.902312331170226e-06,
                4.450848927650143e-07
            ],
            [
                0.9999898700126507,
                8.315277302857965e-07,
                0.9999991684721709,
                0.9999942280813496,
                0.9999986290429571,
                2.561282821402217e-06,
                1.994729721518893e-06,
                0.9999978766217915,
                3.726639284144195e-06,
                1.994729721518893e-06
            ]
        ]
    },
    {
        "q_id": "9154_mmlu_physics",
        "cot_ids": [
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            17,
            18,
            20,
            22,
            23,
            24,
            25,
            26,
            27,
            29,
            31,
            34,
            35,
            36,
            38,
            41,
            42,
            45,
            46,
            48,
            49,
            50,
            51,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            81,
            84,
            86,
            87,
            88,
            89,
            90,
            91,
            94,
            95,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            125,
            127
        ],
        "rewards": [
            [
                1.0677029973192638e-06,
                2.260325106237323e-06,
                7.889259764445822e-06,
                5.422217030707961e-06,
                1.0677032518785256e-06,
                1.0677029973158649e-06,
                NaN,
                1.3709567165579959e-06,
                1.2098662604291696e-06,
                9.422448185510695e-07
            ],
            [
                1.1478769494396542e-05,
                3.2887482813149375e-06,
                5.715003788993679e-07,
                1.370957860576702e-06,
                8.939699501229642e-06,
                1.0129989772412744e-05,
                1.0677027427525368e-06,
                5.043476486902204e-07,
                2.260325106237323e-06,
                1.2098661162056318e-06
            ],
            [
                3.288750241561788e-06,
                5.422218969858371e-06,
                7.889261645090304e-06,
                1.4738976701411704e-05,
                3.2887494574518405e-06,
                6.144176066850984e-06,
                4.785096206013061e-06,
                3.726639728348526e-06,
                4.785096776468749e-06,
                4.222833947960866e-06
            ],
            [
                1.994729483723626e-06,
                8.315279285351409e-07,
                3.466326211113502e-07,
                5.715003789046955e-07,
                3.2887502415767434e-06,
                7.338212429582604e-07,
                2.561281600086738e-06,
                7.338213304363436e-07,
                3.726639284125553e-06,
                2.9023116391978967e-06
            ],
            [
                3.0590237279085045e-07,
                9.422442569315887e-07,
                1.8553905760062447e-07,
                1.8553905760062447e-07,
                1.8553910183674878e-07,
                2.260325106237323e-06,
                1.275190428875671e-07,
                3.288748281329893e-06,
                1.5534984953552536e-06,
                6.47595107001401e-07
            ],
            [
                2.5612828213934817e-06,
                9.422448185534261e-07,
                3.4663278639892215e-07,
                3.4663278639892215e-07,
                5.4222183235249605e-06,
                5.04347287955046e-07,
                4.4508526417298334e-07,
                1.7603434231833873e-06,
                4.450848927658745e-07,
                6.475950298011458e-07
            ],
            [
                5.043476486915964e-07,
                4.4508494582405734e-07,
                5.715007195447234e-07,
                NaN,
                7.338209805224048e-07,
                NaN,
                2.1024336609874897e-07,
                6.475945666063607e-07,
                7.338208930391909e-07,
                9.931186222523604e-08
            ],
            [
                4.4508494582314646e-07,
                7.338211554801876e-07,
                9.422450432014836e-07,
                1.5534984953510149e-06,
                1.3709567165617364e-06,
                3.927862470899887e-07,
                2.902311985146426e-06,
                1.3709572068522336e-06,
                3.288748673376478e-06,
                1.3709567165617364e-06
            ],
            [
                0.9999982396572088,
                8.315279285351409e-07,
                1.5534981249697903e-06,
                1.0677026154806063e-06,
                4.0063696969564425e-05,
                1.9947299592824403e-06,
                0.9999989969856734,
                0.9999986290429578,
                4.539787406217992e-05,
                4.78509278348926e-06
            ],
            [
                NaN,
                1.6373770576776313e-07,
                3.466327863983311e-07,
                1.0677026154806063e-06,
                2.382370235933104e-07,
                1.6373776432481905e-07,
                3.0590237279032884e-07,
                2.3823693839325527e-07,
                3.927863875616689e-07,
                1.8553919030708836e-07
            ],
            [
                1.0677032518748838e-06,
                2.561282210729555e-06,
                4.222831934379152e-06,
                6.962254589781966e-06,
                5.422217677078203e-06,
                2.902312677137316e-06,
                1.0677033791612137e-06,
                1.3007130015299356e-05,
                2.260324028427877e-06,
                NaN
            ],
            [
                1.7603434231777837e-06,
                2.6995784182073116e-07,
                2.9023130231176453e-06,
                1.8925141473978602e-05,
                2.2603242978778778e-06,
                1.4738980215593877e-05,
                1.7603425837606927e-06,
                2.4300252321904572e-05,
                7.889259764517575e-06,
                1.553498495338299e-06
            ],
            [
                6.475950298011458e-07,
                6.144173869446876e-06,
                3.288748673376478e-06,
                2.2603242978871282e-06,
                7.889263526409699e-06,
                1.3709573702722555e-06,
                2.69957906184239e-07,
                8.315279285370317e-07,
                4.5397857828200684e-05,
                8.315282259089153e-07
            ],
            [
                1.0677027427600627e-06,
                0.9999977396762441,
                0.9999885212360257,
                0.9999969105051901,
                0.999999266178933,
                1.9947292459347367e-06,
                2.2603237589779086e-06,
                0.9999995818812274,
                0.999996499146429,
                0.9999987121046318
            ],
            [
                7.338211554758494e-07,
                1.9947290081286418e-06,
                1.2098655392871682e-06,
                6.962259569630266e-06,
                4.785094494750855e-06,
                3.2887502415438413e-06,
                NaN,
                7.889259764517575e-06,
                1.994729008145876e-06,
                8.315278294072958e-07
            ],
            [
                4.22283545819819e-06,
                1.760343213335281e-06,
                5.715005832895975e-07,
                5.043473480777865e-07,
                2.6995790618469934e-07,
                1.300712536408621e-05,
                4.785096776499213e-06,
                1.3709576971463352e-06,
                4.785095065232451e-06,
                NaN
            ],
            [
                0.9999417087082483,
                1.994730672675753e-06,
                3.12019039369228e-05,
                1.3709573702778664e-06,
                9.422443692527585e-07,
                1.5534979397677313e-06,
                0.9999989322968765,
                9.422445939054222e-07,
                5.422217030707961e-06,
                1.8925148241493373e-05
            ],
            [
                3.72663883989755e-06,
                NaN,
                3.72663883989755e-06,
                0.9995694428644402,
                5.422218969895357e-06,
                NaN,
                3.120191881616493e-05,
                9.422445939032799e-07,
                0.9998911030659986,
                5.715002426475718e-07
            ],
            [
                5.715006514176113e-07,
                5.043476486924565e-07,
                1.7603430034867993e-06,
                4.4508494582314646e-07,
                4.785092783519724e-06,
                1.012998977264307e-05,
                4.785094494811783e-06,
                5.715006514176113e-07,
                1.209865827752005e-06,
                3.288747889284851e-06
            ],
            [
                4.2228334445658276e-06,
                4.2228334445370225e-06,
                3.120192625175911e-05,
                6.144176799227922e-06,
                8.939699501229642e-06,
                8.93969950101825e-06,
                8.315283250371857e-07,
                9.422450431989127e-07,
                4.785094494716039e-06,
                3.726639728348526e-06
            ],
            [
                1.3007126914435202e-05,
                1.0677029973219343e-06,
                NaN,
                3.7266379513434106e-06,
                4.785095635655362e-06,
                7.338211554783522e-07,
                7.889266347636241e-06,
                2.561282210729555e-06,
                3.7266397283908927e-06,
                1.553497754577351e-06
            ],
            [
                1.855391239547094e-07,
                9.422448185534261e-07,
                2.3823682479292225e-07,
                9.422443692555439e-07,
                3.9278634073732336e-07,
                9.422448185534261e-07,
                6.475949526020042e-07,
                6.475948754012522e-07,
                3.4663278639892215e-07,
                5.715002426486762e-07
            ],
            [
                4.222833444590791e-06,
                8.939699501416646e-06,
                6.605213682591808e-05,
                1.760342793638743e-06,
                6.962259569750576e-06,
                5.422217030781934e-06,
                7.88926446679691e-06,
                6.962254589978262e-06,
                1.0677024882009222e-06,
                3.927863875616689e-07
            ],
            [
                1.0677028700363782e-06,
                4.2228334445658276e-06,
                5.04347528446051e-07,
                1.9947304348862686e-06,
                8.93969950132721e-06,
                1.5534984953510149e-06,
                4.222833444590791e-06,
                1.3709572068522336e-06,
                5.715005832886879e-07,
                1.994729483723626e-06
            ],
            [
                3.726639728370556e-06,
                3.726638839878908e-06,
                5.144223206414209e-05,
                5.422220262555012e-06,
                3.7266401726173067e-06,
                7.889264466725156e-06,
                7.484620944504663e-05,
                2.9023116391978967e-06,
                3.535625493182252e-05,
                5.422217030747413e-06
            ],
            [
                5.422220262505697e-06,
                1.0677024881980089e-06,
                3.726637951387472e-06,
                6.475951069985296e-07,
                2.2603242978871282e-06,
                1.3709567165579959e-06,
                9.422442569315887e-07,
                8.315283250371857e-07,
                5.043474081993875e-07,
                1.2098653950656417e-06
            ],
            [
                1.5534984953552536e-06,
                1.209865827752005e-06,
                1.2098656835252174e-06,
                2.2603253756956754e-06,
                1.760343213335281e-06,
                NaN,
                1.7603438428848787e-06,
                NaN,
                NaN,
                1.9947299593078385e-06
            ],
            [
                4.4508499888219586e-07,
                5.71500719545698e-07,
                2.699578096403948e-07,
                9.422450432030903e-07,
                1.3709568799919866e-06,
                NaN,
                1.209865827752005e-06,
                3.466325384678894e-07,
                2.3823682479292225e-07,
                8.315278294114555e-07
            ],
            [
                8.315281267861397e-07,
                8.315277302788957e-07,
                3.4663262110945863e-07,
                3.927862470899887e-07,
                4.4508494582314646e-07,
                2.1024326584639497e-07,
                4.450852111148132e-07,
                6.475947210031623e-07,
                3.0590237279032884e-07,
                4.450849458218309e-07
            ],
            [
                9.422448185510695e-07,
                9.422449308748773e-07,
                2.561282210701601e-06,
                3.466325797888292e-07,
                1.7603436330259153e-06,
                2.902311639183378e-06,
                6.962256249885085e-06,
                0.0,
                1.3709570434178922e-06,
                1.2098655392921197e-06
            ],
            [
                1.6701425827133152e-05,
                1.3709573702822306e-06,
                2.2603248367949354e-06,
                1.7603436330179102e-06,
                3.288749457469787e-06,
                NaN,
                1.7603438428800754e-06,
                3.726639284125553e-06,
                4.222832941193893e-06,
                4.222832941193893e-06
            ],
            [
                NaN,
                4.222833947820683e-06,
                1.8925157265710765e-05,
                1.1478772231232203e-05,
                1.8925157265710765e-05,
                4.785094494783494e-06,
                3.5356238069902345e-05,
                1.3709573702778664e-06,
                NaN,
                0.0002611902786047698
            ],
            [
                0.9999993106387086,
                1.994729483723626e-06,
                0.9999960330126718,
                5.04347528446051e-07,
                0.9999970976873256,
                0.9999992661791953,
                0.9999988634364266,
                6.475945666033422e-07,
                0.9999964991468424,
                0.9999904837449305
            ],
            [
                2.2603253756956754e-06,
                6.144173869603344e-06,
                3.535625493182252e-05,
                1.5534983101602148e-06,
                5.715003789046955e-07,
                6.475951069985296e-07,
                1.067702870039777e-06,
                6.475945666051092e-07,
                9.422445939032799e-07,
                3.4663278639892215e-07
            ],
            [
                2.2603234894745224e-06,
                2.1444940745839484e-05,
                1.7603434231777837e-06,
                5.422220262555012e-06,
                2.9023119851781017e-06,
                7.889264466725156e-06,
                3.0590237279032884e-07,
                1.0129989772532511e-05,
                4.222833444590791e-06,
                3.120190393794438e-05
            ],
            [
                5.422219616265831e-06,
                3.9278634073732336e-07,
                5.715003107767143e-07,
                3.0590237279085045e-07,
                1.3709572068522336e-06,
                2.1024341622426268e-07,
                5.422219616265831e-06,
                7.338208055664991e-07,
                7.338208055664991e-07,
                3.0590237279032884e-07
            ],
            [
                6.1441731370702875e-06,
                0.00043055704046654985,
                7.484624512366966e-05,
                5.422220908876325e-06,
                1.3709568799823232e-06,
                1.067702870039777e-06,
                2.5612819054028872e-06,
                5.422217030614265e-06,
                6.962255419804982e-06,
                1.147876812538911e-05
            ],
            [
                4.006367786399728e-05,
                2.430024073461624e-05,
                2.9023109472244114e-06,
                6.144173869603344e-06,
                2.7535694384882703e-05,
                5.8291258601145456e-05,
                1.8925141473978602e-05,
                4.539787406217992e-05,
                2.4300243630653244e-05,
                4.785096776468749e-06
            ],
            [
                1.147876812574406e-05,
                1.1478765389222573e-05,
                6.144176799283803e-06,
                1.209865539295696e-06,
                1.0677032518785256e-06,
                4.2228324377740105e-06,
                6.144173137126169e-06,
                1.2098653950656417e-06,
                1.7603438428740716e-06,
                2.5612831266946347e-06
            ],
            [
                9.422443692555439e-07,
                0.9999984465028021,
                8.315281267861397e-07,
                4.450852111155216e-07,
                3.466325797888292e-07,
                1.6373764721039308e-07,
                2.1024334103581732e-07,
                3.7266410611296085e-06,
                7.338209805240734e-07,
                3.466327863983311e-07
            ],
            [
                NaN,
                1.994730672675753e-06,
                1.994729483729522e-06,
                3.726639284144195e-06,
                8.315278294072958e-07,
                NaN,
                4.2228334445658276e-06,
                4.785092783519724e-06,
                1.994729721518893e-06,
                2.5612819054133693e-06
            ],
            [
                8.939693106873817e-06,
                5.422220908876325e-06,
                4.78509392429544e-06,
                8.939695238536645e-06,
                1.9947292459265734e-06,
                7.889265407090955e-06,
                6.144176799099397e-06,
                0.0001398220575147721,
                1.3709573702647743e-06,
                2.260325375664839e-06
            ],
            [
                6.144177531767002e-06,
                1.994729245917502e-06,
                1.3007123813382511e-05,
                1.0677026154730804e-06,
                1.5534981249574276e-06,
                2.9023126771227976e-06,
                2.260324836776948e-06,
                4.785093924362895e-06,
                1.3007125363057018e-05,
                2.5612834320214477e-06
            ],
            [
                7.338207180864763e-07,
                9.422448185478557e-07,
                1.3709570434178922e-06,
                1.2098662604291696e-06,
                1.0677024881980089e-06,
                NaN,
                6.475947982022763e-07,
                1.2098659719757836e-06,
                1.760343003481596e-06,
                1.2098653950656417e-06
            ],
            [
                1.2098653950656417e-06,
                1.2098662604247682e-06,
                1.9947306726594253e-06,
                5.715006514151423e-07,
                2.561281905390075e-06,
                4.539787405128009e-05,
                2.561281600076256e-06,
                3.726639728370556e-06,
                1.5534975693933505e-06,
                6.9622587397397306e-06
            ],
            [
                1.760343213335281e-06,
                6.475947210046347e-07,
                2.3823690999063455e-07,
                5.715003107767143e-07,
                6.475947210031623e-07,
                6.475951069985296e-07,
                3.4663249714325014e-07,
                7.338208055680009e-07,
                4.4508510499737865e-07,
                7.338208930443633e-07
            ],
            [
                1.6373774480605869e-07,
                3.2887498495150166e-06,
                5.043473480777865e-07,
                2.6995768091383957e-07,
                2.3823702359290413e-07,
                2.382370235933104e-07,
                4.450848927658745e-07,
                1.6373776432481905e-07,
                1.6373776432509826e-07,
                2.382370235933104e-07
            ],
            [
                4.0063696969564425e-05,
                3.288749065406658e-06,
                4.785095635655362e-06,
                3.535624649610246e-05,
                1.0677026154806063e-06,
                NaN,
                1.0677027427600627e-06,
                2.561282516066741e-06,
                4.785093924362895e-06,
                7.889265407327733e-06
            ],
            [
                9.422450431989127e-07,
                7.889263526345123e-06,
                6.475948754012522e-07,
                1.9947292459347367e-06,
                2.2603253756956754e-06,
                1.0677028700363782e-06,
                3.288748281329893e-06,
                2.5612812947508257e-06,
                1.0677032518748838e-06,
                1.2098662604291696e-06
            ],
            [
                2.2603253756956754e-06,
                1.8553919030858602e-07,
                3.9278629391427843e-07,
                1.4449805540763184e-07,
                3.059022269250683e-07,
                2.102434412875379e-07,
                6.475947210046347e-07,
                1.8553919030858602e-07,
                1.1253506814842375e-07,
                2.1024339116168358e-07
            ],
            [
                6.9622587397397306e-06,
                3.535626336072768e-05,
                NaN,
                1.3007133116542802e-05,
                1.6701427818034747e-05,
                6.144173137170873e-06,
                1.3709572068522336e-06,
                1.670141786325573e-05,
                6.962253759904688e-06,
                1.4738978458382043e-05
            ],
            [
                2.902312331170226e-06,
                6.475950298011458e-07,
                4.222832437798974e-06,
                5.04347468323289e-07,
                7.338209805240734e-07,
                1.0677027427600627e-06,
                1.5534979397790343e-06,
                9.422443692555439e-07,
                1.209865539295696e-06,
                6.475948754028718e-07
            ],
            [
                2.144495608424996e-05,
                1.3007131565613412e-05,
                6.605214469462115e-05,
                1.209865683518615e-06,
                6.962257909722651e-06,
                8.939694172770212e-06,
                1.8925141473186853e-05,
                2.2603237589779086e-06,
                4.785094494750855e-06,
                0.00012339463381806274
            ],
            [
                1.994729008151319e-06,
                5.04347468323289e-07,
                7.338207180898968e-07,
                1.994729483729522e-06,
                1.3709575337159875e-06,
                1.0677027427624903e-06,
                1.5534984953510149e-06,
                6.47594952603035e-07,
                2.9023133690980155e-06,
                2.699578096403948e-07
            ],
            [
                8.93969950132721e-06,
                NaN,
                2.902313369111213e-06,
                2.260323758987159e-06,
                4.0063677865600476e-05,
                1.209865539295696e-06,
                2.561281294760143e-06,
                2.2603234895372223e-06,
                7.338209805240734e-07,
                2.902312331170226e-06
            ],
            [
                4.450852111148132e-07,
                6.47594566597747e-07,
                3.927862002606139e-07,
                4.450851580540182e-07,
                7.338213304316717e-07,
                2.6995784182073116e-07,
                1.7603425837791042e-06,
                9.422443692489024e-07,
                3.9278634073732336e-07,
                1.0677027427525368e-06
            ],
            [
                2.9023119851781017e-06,
                4.450852111148132e-07,
                9.422445939032799e-07,
                NaN,
                2.2603242978871282e-06,
                0.0031726822408839183,
                5.71500515159253e-07,
                2.1444948414321717e-05,
                1.7603430034867993e-06,
                1.8925145985895816e-05
            ],
            [
                1.670142383595838e-05,
                1.0677032518814388e-06,
                1.760343213335281e-06,
                2.902312331170226e-06,
                9.422448185534261e-07,
                5.043476486902204e-07,
                NaN,
                2.2603234895372223e-06,
                4.2228319344021954e-06,
                1.6701421844753466e-05
            ],
            [
                8.315279285351409e-07,
                1.7603440527286572e-06,
                5.715005832886879e-07,
                1.3709573702722555e-06,
                6.475945666051092e-07,
                9.422445939002803e-07,
                7.889260704732132e-06,
                1.5534971990126997e-06,
                2.2603242978778778e-06,
                9.422448185510695e-07
            ],
            [
                5.715004470326849e-07,
                1.9947304348862686e-06,
                1.8553914607267268e-07,
                4.450852111155216e-07,
                6.475947982037486e-07,
                1.994729008145876e-06,
                1.8553907971855875e-07,
                2.2603242978871282e-06,
                1.0129994602895546e-05,
                2.699578096403948e-07
            ],
            [
                2.9023133690637e-06,
                1.6701423835320418e-05,
                5.422217030614265e-06,
                3.726641061027928e-06,
                6.9622587396067566e-06,
                1.0129987357020188e-05,
                4.785094494672519e-06,
                1.0129993395088066e-05,
                2.902312677137316e-06,
                3.7266379513162962e-06
            ],
            [
                1.0677029973192638e-06,
                6.962256249885085e-06,
                NaN,
                2.902312677150514e-06,
                4.785095065232451e-06,
                3.466325797896173e-07,
                7.338207180898968e-07,
                7.338208930460318e-07,
                NaN,
                8.315283250394546e-07
            ],
            [
                7.338209805224048e-07,
                3.466327037539638e-07,
                7.338208055664991e-07,
                1.760343213335281e-06,
                3.7266397283908927e-06,
                3.2887498495150166e-06,
                1.3709568799879344e-06,
                8.315284241650899e-07,
                1.5534984953510149e-06,
                2.2603234895289998e-06
            ],
            [
                2.9023119851781017e-06,
                1.0677029973158649e-06,
                3.059022269250683e-07,
                5.715003789033962e-07,
                2.3823690999290963e-07,
                2.1024329090929374e-07,
                3.9278610661902853e-07,
                4.4508510499737865e-07,
                3.927860597935108e-07,
                3.288749457469787e-06
            ],
            [
                1.9947297215043796e-06,
                5.422218323487975e-06,
                5.043472879525233e-07,
                1.0677028700363782e-06,
                1.553497754577351e-06,
                2.2603234895289998e-06,
                2.260324836787226e-06,
                9.422448185510695e-07,
                1.2098659719757836e-06,
                1.5534984953510149e-06
            ],
            [
                2.2603240284371276e-06,
                1.2098652508424818e-06,
                1.7603440527286572e-06,
                5.422220909009474e-06,
                5.715003107767143e-07,
                9.422448185510695e-07,
                7.338213304363436e-07,
                6.475950298011458e-07,
                9.422443692555439e-07,
                3.288748673360027e-06
            ],
            [
                2.260325375677174e-06,
                8.315278294097538e-07,
                5.715004470313855e-07,
                3.927861534406222e-07,
                1.994729008145876e-06,
                7.88926446679691e-06,
                2.260324028427877e-06,
                9.422442569315887e-07,
                1.3709567165579959e-06,
                1.2098653950692178e-06
            ],
            [
                5.422218323399208e-06,
                1.3007128465151102e-05,
                0.0001398220742354593,
                6.962258739796719e-06,
                3.288748673319648e-06,
                1.4738981972564636e-05,
                7.88926446679691e-06,
                2.4300237838535383e-05,
                1.670141985446017e-05,
                NaN
            ],
            [
                9.931200429212718e-08,
                1.1253506814842375e-07,
                8.764244316973974e-08,
                4.785095065204162e-06,
                8.764241182641775e-08,
                5.315786239218605e-08,
                6.825608606172863e-08,
                2.6995784182183607e-07,
                9.931185038635267e-08,
                7.734414854823498e-08
            ],
            [
                1.2098653950551882e-06,
                7.338211554725124e-07,
                4.450848927637999e-07,
                1.370956716529941e-06,
                1.994729483705484e-06,
                1.5534975693933505e-06,
                1.9947304348595095e-06,
                5.715005832798517e-07,
                2.9023109472244114e-06,
                3.927863875584984e-07
            ],
            [
                2.382370235933104e-07,
                2.6995790618469934e-07,
                3.0590237279085045e-07,
                2.1024336609843824e-07,
                2.382369383923073e-07,
                2.382370235933104e-07,
                5.043475885696228e-07,
                6.475947210046347e-07,
                3.927863875616689e-07,
                9.931187406410953e-08
            ],
            [
                3.726637951367137e-06,
                1.7603434231777837e-06,
                8.315283250371857e-07,
                7.338211554783522e-07,
                2.260324567337161e-06,
                9.422448185510695e-07,
                4.0063711294555596e-05,
                8.315279285351409e-07,
                1.6701427817427163e-05,
                3.288747889229516e-06
            ],
            [
                4.785094494811783e-06,
                2.5612834320470717e-06,
                3.7266410611296085e-06,
                3.288749065423109e-06,
                3.726638395634011e-06,
                2.4300252321904572e-05,
                6.144176066901277e-06,
                2.902312677137316e-06,
                3.726639728370556e-06,
                4.539789029616496e-05
            ],
            [
                1.3007128464961824e-05,
                7.889264466725156e-06,
                2.2603234895289998e-06,
                6.962255419868303e-06,
                1.1478772230929451e-05,
                1.3709576971425944e-06,
                1.0129989772412744e-05,
                1.2098655392871682e-06,
                1.6701423835320418e-05,
                1.3709575337078829e-06
            ],
            [
                6.475951069985296e-07,
                1.5534971990126997e-06,
                7.338212429562581e-07,
                4.222834954778007e-06,
                4.450848927637999e-07,
                5.715003789033962e-07,
                1.9947299593014888e-06,
                1.0677024881980089e-06,
                1.7603440527222532e-06,
                2.5612831267086116e-06
            ],
            [
                2.561281600086738e-06,
                3.9278624708775595e-07,
                2.902312677137316e-06,
                5.715003789033962e-07,
                1.0677029973158649e-06,
                1.3709567165617364e-06,
                3.4663253846316044e-07,
                5.043474081993875e-07,
                NaN,
                1.2098652508391807e-06
            ],
            [
                1.994729483694599e-06,
                0.0001584362925687936,
                2.5612812947508257e-06,
                1.760342793583908e-06,
                2.5612812947240366e-06,
                4.2228339479858295e-06,
                7.338210679979539e-07,
                7.889264466639056e-06,
                NaN,
                NaN
            ],
            [
                7.338209805224048e-07,
                3.288750241500471e-06,
                5.043472278322555e-07,
                6.475947210031623e-07,
                1.7603432133296774e-06,
                3.2887478892683997e-06,
                3.9278605979534166e-07,
                5.422219616265831e-06,
                2.5612831267086116e-06,
                NaN
            ],
            [
                7.338208055680009e-07,
                1.7603430034867993e-06,
                2.902313369111213e-06,
                1.5534975693979422e-06,
                1.3709570434178922e-06,
                4.222831934379152e-06,
                3.466326211113502e-07,
                1.2098659719757836e-06,
                9.422444815814404e-07,
                7.889259764517575e-06
            ],
            [
                1.8553910183607374e-07,
                7.338209805240734e-07,
                2.1024334103581732e-07,
                8.764241182605906e-08,
                1.4449807263312446e-07,
                2.10243290909724e-07,
                1.1253513522447425e-07,
                2.69957906184239e-07,
                9.931198061405701e-08,
                1.4449798650551755e-07
            ],
            [
                2.102434162245973e-07,
                2.1024336609874897e-07,
                1.1253508156363576e-07,
                1.2751904288710323e-07,
                2.382369667929001e-07,
                5.04347528446051e-07,
                3.059022269250683e-07,
                2.102434162245973e-07,
                6.475946438055299e-07,
                1.6373764721072816e-07
            ],
            [
                1.1478770862882149e-05,
                1.5534971990126997e-06,
                3.927860597945825e-07,
                2.699577774585891e-07,
                1.994730434879465e-06,
                1.9947301970972664e-06,
                2.9023133690980155e-06,
                5.4222183235249605e-06,
                1.5534983101644536e-06,
                2.6995784182183607e-07
            ],
            [
                8.315279285351409e-07,
                5.715003789046955e-07,
                6.475947982037486e-07,
                3.7266397283908927e-06,
                2.902312677137316e-06,
                1.0677032518785256e-06,
                5.715005151606823e-07,
                1.4738985486506781e-05,
                1.0677026154806063e-06,
                1.2098661162023305e-06
            ],
            [
                1.3007134667259441e-05,
                1.3007125363908762e-05,
                1.4738983729535602e-05,
                1.2098652508391807e-06,
                3.120190393794438e-05,
                7.338212429582604e-07,
                6.144172404693786e-06,
                1.670141786325573e-05,
                1.5534983101602148e-06,
                2.5612828213934817e-06
            ],
            [
                4.222834451382849e-06,
                7.889259764517575e-06,
                5.4222176771176554e-06,
                2.5612828213934817e-06,
                2.5612819054028872e-06,
                9.422445939054222e-07,
                1.1478766757718129e-05,
                1.3007130015488633e-05,
                2.5612831267202583e-06,
                2.1444953527944967e-05
            ],
            [
                1.2098659719757836e-06,
                3.05902190458764e-07,
                2.699578096393206e-07,
                9.931190958076104e-08,
                1.2098656835224664e-06,
                3.927863875616689e-07,
                3.466326211113502e-07,
                2.699578740032504e-07,
                2.6995784182140636e-07,
                3.0590237279032884e-07
            ],
            [
                1.9947297215043796e-06,
                2.5612828213352452e-06,
                5.043472879540142e-07,
                2.2603245673279107e-06,
                1.3709572068422585e-06,
                1.3709568799823232e-06,
                1.3709573702778664e-06,
                8.315279285351409e-07,
                4.222831934352267e-06,
                3.726641061085547e-06
            ],
            [
                2.2603237589676295e-06,
                1.2098655392921197e-06,
                1.7603440527286572e-06,
                1.2098656835224664e-06,
                8.939694172867777e-06,
                NaN,
                NaN,
                2.2603234895176927e-06,
                3.7266406168624155e-06,
                2.260324567337161e-06
            ],
            [
                3.7266397283908927e-06,
                3.726637951367137e-06,
                6.144177531767002e-06,
                1.0677027427600627e-06,
                1.1478769494396542e-05,
                9.422448185388577e-07,
                1.2098662604291696e-06,
                2.2603234895176927e-06,
                1.9947297215125433e-06,
                8.939696304311336e-06
            ],
            [
                2.561283432005142e-06,
                2.5612828213690224e-06,
                1.0677029973158649e-06,
                9.422445939054222e-07,
                6.1441724046434924e-06,
                9.422444815628016e-07,
                1.5534975693869924e-06,
                2.5612831267086116e-06,
                1.1478770862735993e-05,
                1.0129989772412744e-05
            ],
            [
                9.422444815792981e-07,
                1.0677033791612137e-06,
                6.475951069985296e-07,
                5.715003789033962e-07,
                1.0677026154730804e-06,
                3.726638395634011e-06,
                1.553497754583709e-06,
                6.475950297971703e-07,
                4.450849988811838e-07,
                1.3709576971379186e-06
            ],
            [
                1.5534981249697903e-06,
                2.6995771309523475e-07,
                9.422450432014836e-07,
                2.561281294760143e-06,
                9.422445939054222e-07,
                2.561281600086738e-06,
                1.012998977264307e-05,
                1.8925155008941717e-05,
                8.315279285370317e-07,
                1.2098658277451275e-06
            ]
        ]
    },
    {
        "q_id": "9771_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            104,
            105,
            106,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                9.422447062294175e-07,
                8.939696304311336e-06,
                7.338207180898968e-07,
                9.422443692574719e-07,
                6.60521604406802e-05,
                4.222834451403972e-06,
                1.5534971990126997e-06,
                4.2228319344021954e-06,
                3.7266397283908927e-06,
                0.9999969105044498
            ],
            [
                8.939695238634211e-06,
                2.9023130231176453e-06,
                3.726637951387472e-06,
                1.670142980920999e-05,
                5.715003789046955e-07,
                2.902312331170226e-06,
                7.338210679979539e-07,
                1.760343213335281e-06,
                3.288748673376478e-06,
                1.0129987357517693e-05
            ],
            [
                3.7266406168827523e-06,
                1.4738989000422955e-05,
                2.5612831267202583e-06,
                2.1444943302181958e-05,
                5.422220262636381e-06,
                8.939698435657833e-06,
                1.1478769494396542e-05,
                NaN,
                4.785093353940187e-06,
                1.1478770862735993e-05
            ],
            [
                1.670142980920999e-05,
                NaN,
                2.9023119851899796e-06,
                5.422220262636381e-06,
                2.561281600086738e-06,
                1.0129988564974359e-05,
                2.9023112932177327e-06,
                7.889261645427538e-06,
                1.147876812620341e-05,
                2.2603253756956754e-06
            ],
            [
                9.422447062294175e-07,
                NaN,
                1.4738978458382043e-05,
                NaN,
                4.222833444590791e-06,
                2.260323758987159e-06,
                1.0677028700363782e-06,
                NaN,
                2.4300246526646385e-05,
                2.260324028427877e-06
            ],
            [
                6.47594952603035e-07,
                3.1201903922734266e-05,
                5.715005832886879e-07,
                7.338213304316717e-07,
                8.315283250394546e-07,
                NaN,
                1.370957860567974e-06,
                NaN,
                2.9023119851899796e-06,
                6.962255419982281e-06
            ],
            [
                1.5534981249574276e-06,
                1.2098655392871682e-06,
                3.7266388398585725e-06,
                4.7850967763512445e-06,
                1.3709567165530083e-06,
                2.9023112931688987e-06,
                5.422218323093458e-06,
                7.889262585728421e-06,
                2.9023133690425823e-06,
                1.3709578605617394e-06
            ],
            [
                NaN,
                4.539786864876098e-05,
                6.144175334468545e-06,
                8.315280276626197e-07,
                1.9947299593078385e-06,
                3.7266397283908927e-06,
                NaN,
                1.7603438428800754e-06,
                4.785093353940187e-06,
                1.0677029973219343e-06
            ],
            [
                0.9999151889184854,
                0.9999945777784656,
                0.9999339478637483,
                0.9999251538001105,
                0.0758581784543034,
                NaN,
                0.9999982396561594,
                0.9999957771655538,
                NaN,
                4.539787406217992e-05
            ],
            [
                5.043473480777865e-07,
                0.9999974387174854,
                0.9999921107346067,
                0.9999985406239533,
                0.999999391641036,
                0.9999981261243939,
                0.9999861539905396,
                2.2603242978871282e-06,
                0.9999975938976611,
                0.9999993524049704
            ],
            [
                1.3709567165579959e-06,
                8.939693107190907e-06,
                9.422450431989127e-07,
                4.785093353909723e-06,
                8.939694172867777e-06,
                3.7266406168624155e-06,
                1.7603434231777837e-06,
                7.889263526345123e-06,
                1.209865539295696e-06,
                9.422450431989127e-07
            ],
            [
                1.7603430034867993e-06,
                9.422447062270609e-07,
                1.2098659719757836e-06,
                6.144177531811707e-06,
                1.994729721518893e-06,
                1.3709576971463352e-06,
                2.90231094723893e-06,
                1.5534977545886537e-06,
                7.338208930460318e-07,
                5.4222183235249605e-06
            ],
            [
                4.222832437798974e-06,
                NaN,
                2.699576809143613e-07,
                0.9999991148433864,
                1.5534975693979422e-06,
                1.0677029973219343e-06,
                2.902312677150514e-06,
                6.962253760024999e-06,
                5.422219616265831e-06,
                0.9999877809211066
            ],
            [
                1.1478765389368729e-05,
                1.1478766757718129e-05,
                2.4300252321904572e-05,
                7.88926070489716e-06,
                1.4738980215593877e-05,
                3.120190765829341e-05,
                NaN,
                9.422450432014836e-07,
                7.88926446679691e-06,
                4.785096206047877e-06
            ],
            [
                3.726638839878908e-06,
                5.715006514176113e-07,
                2.561281600076256e-06,
                1.8553905760062447e-07,
                NaN,
                6.962255419931625e-06,
                9.422448185534261e-07,
                2.2603253756956754e-06,
                1.0677027427600627e-06,
                6.475946438055299e-07
            ],
            [
                3.72663883989755e-06,
                0.9999516743449705,
                7.484620052444058e-05,
                7.338212429537553e-07,
                1.2098659719757836e-06,
                6.475945666051092e-07,
                7.889260704968913e-06,
                1.3709576971425944e-06,
                NaN,
                4.5397852414783676e-05
            ],
            [
                1.7603434231833873e-06,
                9.422448185534261e-07,
                NaN,
                6.475945666063607e-07,
                NaN,
                2.902312331170226e-06,
                4.450852111155216e-07,
                NaN,
                8.315279285370317e-07,
                9.422445939054222e-07
            ],
            [
                3.288749065406658e-06,
                6.144173869502757e-06,
                2.5612812947380135e-06,
                7.338208055680009e-07,
                5.829125860453825e-05,
                4.539789029616496e-05,
                2.753568453712307e-05,
                4.785092783454444e-06,
                2.260325106237323e-06,
                8.939700566907275e-06
            ],
            [
                1.7603436330259153e-06,
                4.539789029616496e-05,
                2.2603240283888175e-06,
                4.785094494672519e-06,
                1.300712691403299e-05,
                2.902310947190096e-06,
                4.5397852414783676e-05,
                2.4300243630653244e-05,
                1.4738987242968784e-05,
                6.962253759828703e-06
            ],
            [
                1.370957860576702e-06,
                1.5534973842076057e-06,
                5.043475885696228e-07,
                NaN,
                3.7266397283908927e-06,
                1.0677027427624903e-06,
                3.72663883989755e-06,
                5.715002426486762e-07,
                5.715002426486762e-07,
                1.5534984953552536e-06
            ],
            [
                2.2603251062450327e-06,
                7.338212429594283e-07,
                NaN,
                NaN,
                1.7603425837903113e-06,
                NaN,
                1.1478766757853845e-05,
                1.760342793638743e-06,
                4.222834954801051e-06,
                NaN
            ],
            [
                1.209866260432471e-06,
                5.4222183235249605e-06,
                1.9947301970972664e-06,
                6.475945666063607e-07,
                1.5534979397740895e-06,
                9.422447062294175e-07,
                6.475949526020042e-07,
                1.3709568799919866e-06,
                5.715003107755449e-07,
                6.475950298011458e-07
            ],
            [
                NaN,
                8.939696304311336e-06,
                1.3709573702822306e-06,
                1.2098662604247682e-06,
                1.5534979397740895e-06,
                NaN,
                NaN,
                1.067703124601679e-06,
                NaN,
                NaN
            ],
            [
                1.0677027427624903e-06,
                9.422447062294175e-07,
                1.147877359957198e-05,
                1.8925155009767892e-05,
                2.5612828213934817e-06,
                5.422218969818919e-06,
                1.3007126914435202e-05,
                8.939693107288474e-06,
                7.484620052444058e-05,
                2.9023116392097746e-06
            ],
            [
                4.222834954801051e-06,
                1.994730434879465e-06,
                1.2098662604247682e-06,
                4.785095635655362e-06,
                1.3709575337078829e-06,
                NaN,
                8.93969950132721e-06,
                1.9947304348862686e-06,
                1.1478765389368729e-05,
                8.939697369882888e-06
            ],
            [
                1.2098662604291696e-06,
                3.2887506336086064e-06,
                2.5612819054133693e-06,
                4.222833444590791e-06,
                1.7603434231705793e-06,
                5.715002426486762e-07,
                1.1478765389065974e-05,
                2.5612812947380135e-06,
                3.7266410611296085e-06,
                5.422218323487975e-06
            ],
            [
                1.0129994602895546e-05,
                1.7603430034867993e-06,
                NaN,
                5.4222183235249605e-06,
                4.22283545819819e-06,
                1.994729721518893e-06,
                0.9999916019279802,
                3.7266397283908927e-06,
                NaN,
                4.539786324145319e-05
            ],
            [
                1.9947292459347367e-06,
                2.2603253756956754e-06,
                2.5612819054133693e-06,
                7.889266347786918e-06,
                1.3007128465151102e-05,
                7.889265407327733e-06,
                1.2098652508424818e-06,
                4.222833444590791e-06,
                1.6701421845361053e-05,
                NaN
            ],
            [
                1.0129989772532511e-05,
                2.144494841482881e-05,
                3.7266410611296085e-06,
                1.670142383595838e-05,
                5.829127250060064e-05,
                2.561281600076256e-06,
                1.6701419854156377e-05,
                1.3007126914435202e-05,
                NaN,
                2.4300232043987867e-05
            ],
            [
                2.5612819054028872e-06,
                9.422448185478557e-07,
                7.889262585886274e-06,
                3.288750241561788e-06,
                1.8925145985895816e-05,
                1.3709576971379186e-06,
                1.1478765389368729e-05,
                7.88926446679691e-06,
                1.9947292459265734e-06,
                NaN
            ],
            [
                6.962257909722651e-06,
                1.5534971990126997e-06,
                6.144172404693786e-06,
                3.7266388398585725e-06,
                4.785093924362895e-06,
                4.222834451382849e-06,
                1.8925141473978602e-05,
                1.4738985486265496e-05,
                8.481108182431855e-05,
                7.889261645355786e-06
            ],
            [
                0.00013982212424495333,
                9.610244940712274e-05,
                0.001032231059202948,
                1.012999581057419e-05,
                1.1478769494542698e-05,
                6.605213682591808e-05,
                3.120192625482384e-05,
                2.260324028443809e-06,
                0.9999987121043243,
                2.902312331170226e-06
            ],
            [
                6.962259569750576e-06,
                2.5612834320563895e-06,
                NaN,
                6.144172404738491e-06,
                6.962253760024999e-06,
                4.222834954801051e-06,
                1.994729008145876e-06,
                3.2887482813149375e-06,
                1.5534975693979422e-06,
                3.9278610661902853e-07
            ],
            [
                3.7266388398585725e-06,
                7.889261645355786e-06,
                4.222834451327159e-06,
                8.481108183851022e-05,
                1.0129988564974359e-05,
                1.7603436330259153e-06,
                6.144173869558639e-06,
                1.0129995810463632e-05,
                3.288747889284851e-06,
                NaN
            ],
            [
                2.1024339116168358e-07,
                6.144176799283803e-06,
                4.4508510499849186e-07,
                1.6701425827133152e-05,
                2.3823693839325527e-07,
                3.466326624336003e-07,
                NaN,
                3.059022998581767e-07,
                5.715003107755449e-07,
                2.1024334103581732e-07
            ],
            [
                2.2603234895372223e-06,
                NaN,
                3.53562422882756e-05,
                NaN,
                NaN,
                1.2098659719788098e-06,
                2.144494841482881e-05,
                6.144172404738491e-06,
                NaN,
                2.561281294760143e-06
            ],
            [
                1.9947297215125433e-06,
                8.315283250394546e-07,
                6.1441746020359e-06,
                NaN,
                3.120191881525687e-05,
                0.9998911030546774,
                2.1444950971601277e-05,
                0.9999952149043763,
                NaN,
                1.6701427817730953e-05
            ],
            [
                0.9999546021163879,
                3.4663278639892215e-07,
                3.288748673360027e-06,
                1.3709570434178922e-06,
                NaN,
                1.4738987243478167e-05,
                1.3709567165579959e-06,
                6.144176799334096e-06,
                NaN,
                2.9023123311583482e-06
            ],
            [
                3.288750241561788e-06,
                3.288749457432399e-06,
                7.88926070489716e-06,
                6.1441746018123775e-06,
                2.144494585747154e-05,
                4.222835458175145e-06,
                NaN,
                7.88926070489716e-06,
                NaN,
                4.2228319344021954e-06
            ],
            [
                5.715006514151423e-07,
                5.04347468323289e-07,
                6.475950298021765e-07,
                6.475947210046347e-07,
                3.288749849529972e-06,
                2.5612834320563895e-06,
                1.5534983101644536e-06,
                4.4508515805735777e-07,
                8.315279285351409e-07,
                6.475949526020042e-07
            ],
            [
                1.3709568799919866e-06,
                1.3709573702822306e-06,
                1.3709576971463352e-06,
                2.260324836787226e-06,
                5.144219527356777e-05,
                4.222833444590791e-06,
                5.715003789046955e-07,
                5.829125165990109e-05,
                1.012999098021058e-05,
                3.726641061109272e-06
            ],
            [
                7.33821330437595e-07,
                2.2603248367949354e-06,
                4.222834451403972e-06,
                3.059022998581767e-07,
                3.0590237279085045e-07,
                6.475946438055299e-07,
                7.338207180898968e-07,
                1.2098659719788098e-06,
                5.043476486924565e-07,
                9.422447062294175e-07
            ],
            [
                1.2098659719757836e-06,
                5.043475885696228e-07,
                8.315278294114555e-07,
                4.222834451403972e-06,
                5.04347468323289e-07,
                8.939695238634211e-06,
                1.5534984953510149e-06,
                2.144495864106235e-05,
                3.7266401726359486e-06,
                1.3709575337159875e-06
            ],
            [
                7.338208055664991e-07,
                2.9023119851781017e-06,
                3.9278634073732336e-07,
                1.3709570434219446e-06,
                8.315281267861397e-07,
                3.466327037539638e-07,
                6.475951069985296e-07,
                7.338208930443633e-07,
                1.2098652508424818e-06,
                3.2887506335906595e-06
            ],
            [
                1.9947299593078385e-06,
                NaN,
                1.4738981972564636e-05,
                NaN,
                6.962258739796719e-06,
                8.31528325040778e-07,
                NaN,
                5.4222183235249605e-06,
                2.561283126728994e-06,
                1.0129988565084915e-05
            ],
            [
                9.422442569334097e-07,
                1.4738978458140753e-05,
                1.7603430034867993e-06,
                1.3709572068522336e-06,
                NaN,
                NaN,
                1.1478766757718129e-05,
                4.785096206076165e-06,
                6.962259569750576e-06,
                NaN
            ],
            [
                1.7603425837855082e-06,
                8.315278294038928e-07,
                1.209865539295696e-06,
                4.222833444590791e-06,
                7.338208055664991e-07,
                1.994730434879465e-06,
                NaN,
                2.260325106237323e-06,
                1.994729483723626e-06,
                8.315278294038928e-07
            ],
            [
                6.962257909842961e-06,
                4.450850519403407e-07,
                5.715005832886879e-07,
                5.043476486915964e-07,
                NaN,
                1.3709576971425944e-06,
                2.2603253756956754e-06,
                7.889263526409699e-06,
                0.0001398221242266438,
                1.0677032518785256e-06
            ],
            [
                1.7603438428800754e-06,
                9.422447062294175e-07,
                2.753568782024347e-05,
                1.2098659719716573e-06,
                8.939693107190907e-06,
                1.0129995810463632e-05,
                5.715003789046955e-07,
                1.4738985486265496e-05,
                1.3709573702822306e-06,
                6.144172404693786e-06
            ],
            [
                3.2887494574832472e-06,
                5.04347287955046e-07,
                5.043475284468537e-07,
                NaN,
                3.288750241561788e-06,
                7.889264466868659e-06,
                1.3709575337159875e-06,
                7.889265407255982e-06,
                3.288748673360027e-06,
                5.043476486924565e-07
            ],
            [
                5.422217677152175e-06,
                5.829127944863308e-05,
                5.422221555380179e-06,
                8.481108183851022e-05,
                4.53978632394714e-05,
                2.2603242978871282e-06,
                7.484623620251482e-05,
                4.2228319344021954e-06,
                0.00013982202424632715,
                4.006371129615879e-05
            ],
            [
                3.120191881423529e-05,
                1.9947299593014888e-06,
                1.7603425837702984e-06,
                1.1478768126057254e-05,
                5.144220140264605e-05,
                1.8925157265332104e-05,
                3.288749457469787e-06,
                2.90231094723893e-06,
                2.5612812947380135e-06,
                4.785095635624897e-06
            ],
            [
                9.422443692574719e-07,
                8.481107172971651e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                5.144221366623174e-05,
                2.5612825160562587e-06,
                5.043476486915964e-07,
                5.422220262555012e-06
            ],
            [
                NaN,
                2.561281294760143e-06,
                3.288750241561788e-06,
                1.7603434231777837e-06,
                3.288748281295496e-06,
                4.785094494783494e-06,
                5.422217677078203e-06,
                7.338210680021253e-07,
                1.0677032518814388e-06,
                5.829126555256903e-05
            ],
            [
                1.7603425837855082e-06,
                2.699578740032504e-07,
                1.9947299593078385e-06,
                NaN,
                NaN,
                3.288748281329893e-06,
                NaN,
                4.222834954801051e-06,
                1.994730672675753e-06,
                6.962259569750576e-06
            ],
            [
                4.0063687409856826e-05,
                NaN,
                5.043476486915964e-07,
                1.3709572068478697e-06,
                5.829126555256903e-05,
                1.2098653950656417e-06,
                1.2098662604291696e-06,
                3.2887506335906595e-06,
                1.76034300345598e-06,
                NaN
            ],
            [
                9.931202796993203e-08,
                1.855390576008354e-07,
                3.927863407379485e-07,
                3.0590219045914655e-07,
                1.8553914607267268e-07,
                5.71500515161527e-07,
                2.699576809143613e-07,
                1.4449802095666915e-07,
                9.93120161310289e-08,
                3.4663262111182307e-07
            ],
            [
                NaN,
                NaN,
                3.288748673376478e-06,
                NaN,
                3.288749065436569e-06,
                7.338209805240734e-07,
                1.9947301970972664e-06,
                4.785092783519724e-06,
                5.422220262636381e-06,
                1.9947304348862686e-06
            ],
            [
                7.889265407327733e-06,
                6.962255419931625e-06,
                4.539787947559951e-05,
                5.04347287955046e-07,
                1.8925141473978602e-05,
                1.209866260432471e-06,
                3.2887498495150166e-06,
                NaN,
                1.6701421845361053e-05,
                1.2098661162056318e-06
            ],
            [
                1.9947292459347367e-06,
                8.315279285351409e-07,
                2.902312677150514e-06,
                3.288747889284851e-06,
                8.939694172957213e-06,
                2.902312677150514e-06,
                1.6701423836262173e-05,
                1.370957860576702e-06,
                4.222835458175145e-06,
                1.5534973842076057e-06
            ],
            [
                4.785095635655362e-06,
                2.75356812556058e-05,
                4.2228334445658276e-06,
                1.0129988564845378e-05,
                4.0063677865600476e-05,
                7.889263526345123e-06,
                5.829124470847917e-05,
                1.2098656835224664e-06,
                6.962253760024999e-06,
                1.1478772231232203e-05
            ],
            [
                5.715002426486762e-07,
                2.5612834320563895e-06,
                1.0677029973192638e-06,
                8.315279285370317e-07,
                1.8925155009767892e-05,
                1.9947292459347367e-06,
                2.5612828213934817e-06,
                5.422218323487975e-06,
                1.4738983729294318e-05,
                1.5534973842076057e-06
            ],
            [
                0.9999981261243948,
                1.3709572068422585e-06,
                1.994729483723626e-06,
                NaN,
                0.9999955048168252,
                0.9999957771665655,
                0.9999989322968763,
                1.4738983729535602e-05,
                0.9999988634364257,
                0.9999949062943969
            ],
            [
                8.315279285351409e-07,
                2.1024339116168358e-07,
                4.2228319344021954e-06,
                1.7603427936335396e-06,
                1.5534979397592542e-06,
                NaN,
                6.475946438055299e-07,
                4.785094494750855e-06,
                6.475945666063607e-07,
                2.902312331170226e-06
            ],
            [
                1.3709568799919866e-06,
                6.47595107001401e-07,
                4.450851049991497e-07,
                5.043473480777865e-07,
                7.33821330437595e-07,
                5.71500719545698e-07,
                6.47595107001401e-07,
                1.760343213335281e-06,
                7.338208055680009e-07,
                1.994729483729522e-06
            ],
            [
                1.1478768125911099e-05,
                1.3007126914435202e-05,
                4.5397857828200684e-05,
                3.726641061109272e-06,
                6.144175334468545e-06,
                6.9622537599680095e-06,
                1.7603438428800754e-06,
                6.605213682591808e-05,
                4.2228339479858295e-06,
                1.4738985486265496e-05
            ],
            [
                6.475947210046347e-07,
                1.0677029973219343e-06,
                1.2098662604291696e-06,
                1.7603434231833873e-06,
                1.0677028700422047e-06,
                6.962258739796719e-06,
                6.475947982037486e-07,
                NaN,
                NaN,
                3.466327037553825e-07
            ],
            [
                NaN,
                NaN,
                3.726638395634011e-06,
                1.3007133116542802e-05,
                NaN,
                1.2098656835224664e-06,
                3.726639728370556e-06,
                1.1478766757561534e-05,
                2.902313369111213e-06,
                6.962257079832313e-06
            ],
            [
                2.3823693839325527e-07,
                1.0677026154806063e-06,
                5.4222176771176554e-06,
                8.315282259138311e-07,
                1.0677027427624903e-06,
                3.726639284144195e-06,
                1.6373772528704005e-07,
                1.2098656835224664e-06,
                1.3007133116542802e-05,
                1.2751899728311609e-07
            ],
            [
                4.539785241676547e-05,
                1.3007126914612648e-05,
                9.422448185510695e-07,
                NaN,
                1.760343213335281e-06,
                5.422220909009474e-06,
                NaN,
                7.889265407327733e-06,
                8.315278294114555e-07,
                NaN
            ],
            [
                1.4449798650569826e-07,
                3.059022269254856e-07,
                1.4449805540763184e-07,
                9.931186222523604e-08,
                1.4449800373118268e-07,
                3.466325797896173e-07,
                8.764254764780641e-08,
                1.637377057680051e-07,
                2.382368531929327e-07,
                1.637377057680051e-07
            ],
            [
                1.1478766757718129e-05,
                3.535625914749675e-05,
                NaN,
                1.0129993395336818e-05,
                4.539785241874725e-05,
                NaN,
                NaN,
                1.8925141473978602e-05,
                NaN,
                9.422444815814404e-07
            ],
            [
                NaN,
                3.927863875616689e-07,
                9.422449308748773e-07,
                5.043472879525233e-07,
                7.338210680021253e-07,
                1.3709567165617364e-06,
                1.5534979397592542e-06,
                5.715003107767143e-07,
                NaN,
                1.0677029973192638e-06
            ],
            [
                2.5612828213690224e-06,
                2.5612819054028872e-06,
                1.0129995810463632e-05,
                NaN,
                NaN,
                6.144172404738491e-06,
                1.3709572068522336e-06,
                0.0002034270463816966,
                1.994730672675753e-06,
                5.422220262636381e-06
            ],
            [
                6.962257079889302e-06,
                2.561281905390075e-06,
                8.939700567094277e-06,
                6.1441767993788005e-06,
                6.1441767993788005e-06,
                4.785093353940187e-06,
                1.2098652508424818e-06,
                NaN,
                NaN,
                4.2228319344021954e-06
            ],
            [
                2.5612819054028872e-06,
                1.0129988565084915e-05,
                2.5612825160562587e-06,
                NaN,
                3.7266410611296085e-06,
                3.2887502415767434e-06,
                5.043472278322555e-07,
                2.2603251062450327e-06,
                6.1441767993788005e-06,
                7.338209805240734e-07
            ],
            [
                3.059021175261338e-07,
                1.2098659719757836e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.902312677137316e-06,
                NaN,
                NaN
            ],
            [
                6.475947210031623e-07,
                1.3007123813193233e-05,
                4.539787406003298e-05,
                6.60521604406802e-05,
                2.1444956082767684e-05,
                6.144172404693786e-06,
                4.5397852414783676e-05,
                1.4738985486506781e-05,
                3.7266401726173067e-06,
                1.3007126914435202e-05
            ],
            [
                1.209865683518615e-06,
                3.726639284103523e-06,
                NaN,
                2.7535681254804434e-05,
                NaN,
                3.2887506336235617e-06,
                NaN,
                1.3007130015488633e-05,
                NaN,
                NaN
            ],
            [
                6.962258739796719e-06,
                NaN,
                3.288748281295496e-06,
                5.715006514176113e-07,
                4.22283545819819e-06,
                2.561281600086738e-06,
                1.5534973842076057e-06,
                6.962259569750576e-06,
                3.466325797896173e-07,
                6.47595107001401e-07
            ],
            [
                1.2098656835224664e-06,
                1.2098661162056318e-06,
                0.9999992661791954,
                3.7266410611296085e-06,
                1.2098652508424818e-06,
                8.315278294114555e-07,
                NaN,
                NaN,
                8.939695238536645e-06,
                3.288749849529972e-06
            ],
            [
                1.760343003481596e-06,
                1.370957860576702e-06,
                3.466327037553825e-07,
                1.7603438428740716e-06,
                1.3709568799919866e-06,
                1.0677032518785256e-06,
                5.422218969858371e-06,
                1.7603427936183298e-06,
                1.2098659719757836e-06,
                2.260324567337161e-06
            ],
            [
                4.2228319344021954e-06,
                2.561281600076256e-06,
                3.726637951387472e-06,
                1.8925141473978602e-05,
                6.962255419931625e-06,
                NaN,
                1.1478770862882149e-05,
                6.475950298011458e-07,
                4.0063696967815485e-05,
                4.785092783519724e-06
            ],
            [
                1.4449802095666915e-07,
                6.475949526020042e-07,
                2.382368531929327e-07,
                1.8553910183674878e-07,
                8.315278294114555e-07,
                2.3823702359290413e-07,
                7.338212429594283e-07,
                1.3709575337159875e-06,
                5.043472278322555e-07,
                3.4663274507713016e-07
            ],
            [
                1.4738978458382043e-05,
                6.144175334418252e-06,
                1.2098662604247682e-06,
                8.939700566907275e-06,
                4.785095065171522e-06,
                4.006369696446335e-05,
                NaN,
                1.6701415872385704e-05,
                NaN,
                1.3007134667070165e-05
            ],
            [
                NaN,
                4.222832437798974e-06,
                NaN,
                8.315283250343497e-07,
                4.222834451403972e-06,
                1.7603425837903113e-06,
                1.2098659719788098e-06,
                7.338208930443633e-07,
                NaN,
                NaN
            ],
            [
                1.2098656835224664e-06,
                NaN,
                2.4300232045225487e-05,
                1.067703124601679e-06,
                1.9947297215125433e-06,
                1.0677032518814388e-06,
                1.6701421845361053e-05,
                3.288750241561788e-06,
                1.3709572068522336e-06,
                1.7603430034867993e-06
            ],
            [
                5.043473480777865e-07,
                9.422449308789479e-07,
                1.2098659719788098e-06,
                5.422217030781934e-06,
                4.785095065232451e-06,
                1.7603425837903113e-06,
                NaN,
                4.4508510499849186e-07,
                7.338208055680009e-07,
                2.561283126728994e-06
            ],
            [
                6.475947982037486e-07,
                2.90231094723893e-06,
                3.7266401726359486e-06,
                5.715006514176113e-07,
                1.370957860576702e-06,
                3.7266397283908927e-06,
                1.8925152754169532e-05,
                4.222833444590791e-06,
                3.288750241561788e-06,
                NaN
            ],
            [
                5.043475885696228e-07,
                3.7266410611465547e-06,
                1.7603425837903113e-06,
                5.715003789046955e-07,
                5.715002426486762e-07,
                6.47595107001401e-07,
                5.043474683240344e-07,
                3.726638395611981e-06,
                1.1478770862067849e-05,
                3.7266379514061143e-06
            ],
            [
                4.222834954778007e-06,
                2.2603248367949354e-06,
                6.962254589978262e-06,
                1.9947292459347367e-06,
                2.753568453792444e-05,
                7.889265407327733e-06,
                1.892515049819277e-05,
                1.8925148241872038e-05,
                1.5534975693979422e-06,
                4.539785241676547e-05
            ],
            [
                NaN,
                2.260325375615501e-06,
                1.7603438428460541e-06,
                5.715005832886879e-07,
                NaN,
                1.994729721482609e-06,
                NaN,
                3.120191137659974e-05,
                5.043474081993875e-07,
                2.430024073523505e-05
            ],
            [
                0.9999994631249962,
                4.139939521470304e-08,
                2.10243290909963e-07,
                1.275190732904469e-07,
                NaN,
                0.9999977396757028,
                3.726637951387472e-06,
                0.9999996940978096,
                NaN,
                1.2098659719788098e-06
            ],
            [
                7.889261645427538e-06,
                NaN,
                4.222831934379152e-06,
                2.561281600076256e-06,
                NaN,
                4.4508510499849186e-07,
                1.0677027427624903e-06,
                1.2098656835224664e-06,
                2.2603253756956754e-06,
                2.3823696679327928e-07
            ],
            [
                1.3709572068553509e-06,
                1.760342793638743e-06,
                0.9999982396567882,
                4.450851049991497e-07,
                4.785094494811783e-06,
                NaN,
                4.222833444611915e-06,
                0.999954602120703,
                0.9999986290426303,
                5.715006514176113e-07
            ],
            [
                5.043476486924565e-07,
                1.2098659719788098e-06,
                1.2098659719788098e-06,
                1.5534975693979422e-06,
                8.315279285351409e-07,
                NaN,
                6.475949526020042e-07,
                NaN,
                1.3709576971463352e-06,
                5.715002426486762e-07
            ],
            [
                1.8925148242250705e-05,
                0.9999756997593048,
                0.9999945777790993,
                7.889259764517575e-06,
                6.475950298011458e-07,
                NaN,
                1.5534973842030142e-06,
                0.9999599362983611,
                8.93969843573914e-06,
                1.2098653950692178e-06
            ],
            [
                1.9947297215125433e-06,
                1.3007128465151102e-05,
                2.5612834320563895e-06,
                2.561282210740037e-06,
                1.5534984953552536e-06,
                9.422445939002803e-07,
                6.47595107001401e-07,
                2.2603253756956754e-06,
                1.7603430034867993e-06,
                NaN
            ],
            [
                9.422450432014836e-07,
                NaN,
                NaN,
                1.7603430034867993e-06,
                2.902312331170226e-06,
                NaN,
                8.315277302841894e-07,
                NaN,
                NaN,
                NaN
            ],
            [
                4.785096206076165e-06,
                1.9947299593078385e-06,
                2.2603245673443566e-06,
                6.475947982037486e-07,
                NaN,
                7.484622729279634e-05,
                NaN,
                NaN,
                1.9947297215125433e-06,
                NaN
            ],
            [
                2.2603234895289998e-06,
                1.5534973842076057e-06,
                1.994729483729522e-06,
                1.5534977545886537e-06,
                NaN,
                2.2603248367949354e-06,
                6.144172404693786e-06,
                1.7603440527222532e-06,
                7.338208055664991e-07,
                2.2603245673279107e-06
            ],
            [
                5.043473480766399e-07,
                1.5534971990126997e-06,
                2.260324567337161e-06,
                1.0677026154806063e-06,
                2.561281600086738e-06,
                1.994729483729522e-06,
                1.3007134667259441e-05,
                1.0677032518785256e-06,
                NaN,
                6.475950298011458e-07
            ],
            [
                8.315284241650899e-07,
                1.3709570434178922e-06,
                0.00012339454548947193,
                4.222833444590791e-06,
                5.422221555340727e-06,
                1.5534981249697903e-06,
                2.561283432035425e-06,
                NaN,
                6.1441724046434924e-06,
                2.561283432035425e-06
            ],
            [
                3.7266401726359486e-06,
                9.422450432030903e-07,
                1.9947304348862686e-06,
                2.5612819054133693e-06,
                3.2887506336086064e-06,
                1.5534983101644536e-06,
                2.902313023130843e-06,
                3.726639284144195e-06,
                1.760343213335281e-06,
                3.72663883989755e-06
            ],
            [
                7.338208055680009e-07,
                3.2887502415767434e-06,
                NaN,
                7.338207180898968e-07,
                5.043475885696228e-07,
                2.9023119851635836e-06,
                1.855391681906175e-07,
                1.9947304348862686e-06,
                7.338207180898968e-07,
                2.561282210740037e-06
            ],
            [
                2.1444945858485726e-05,
                0.00012339457494848715,
                2.5612819054028872e-06,
                NaN,
                2.9023112932045342e-06,
                4.785095065232451e-06,
                1.8925143729954285e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                2.260325106237323e-06,
                2.9023112932177327e-06,
                2.90231094723893e-06,
                3.726638839878908e-06,
                6.9622537599680095e-06,
                1.1478764020883773e-05,
                8.939698435657833e-06,
                2.9023109472244114e-06,
                3.7266406168827523e-06,
                6.962256249885085e-06
            ],
            [
                8.315279285351409e-07,
                1.0129993395336818e-05,
                1.2098659719757836e-06,
                1.553497754583709e-06,
                6.475949525981759e-07,
                9.422448185510695e-07,
                7.48462540557163e-05,
                1.7603425837791042e-06,
                6.475945666051092e-07,
                1.2098658277451275e-06
            ],
            [
                4.006370174184034e-05,
                3.288749457469787e-06,
                6.962253759828703e-06,
                2.5612819054133693e-06,
                1.994730197090463e-06,
                7.889265407177056e-06,
                NaN,
                8.939696304311336e-06,
                1.067702870039777e-06,
                2.5612828213934817e-06
            ],
            [
                8.939698435560267e-06,
                7.33821330437595e-07,
                7.338213304363436e-07,
                6.9622579095833456e-06,
                2.9023112932177327e-06,
                6.475949526020042e-07,
                1.3709572068522336e-06,
                7.889261645355786e-06,
                2.561283432035425e-06,
                4.785093924362895e-06
            ],
            [
                1.9947301970972664e-06,
                2.699577774589574e-07,
                NaN,
                2.260324028443809e-06,
                2.5612834320563895e-06,
                2.5612834320563895e-06,
                NaN,
                9.422445939054222e-07,
                1.444979692800516e-07,
                1.9947299593078385e-06
            ],
            [
                1.209865539295696e-06,
                5.043472879540142e-07,
                8.315277302841894e-07,
                5.715003789033962e-07,
                2.260324567337161e-06,
                8.315280276626197e-07,
                1.2098659719757836e-06,
                9.422442569315887e-07,
                1.5534981249697903e-06,
                NaN
            ],
            [
                0.9999485577819343,
                7.889262585886274e-06,
                4.222834451382849e-06,
                3.535624650279074e-05,
                0.9999972735294118,
                7.889265407255982e-06,
                NaN,
                1.4738978458623327e-05,
                2.2603253756956754e-06,
                0.9999921107402883
            ],
            [
                1.3007134667259441e-05,
                1.9947304348862686e-06,
                4.7850933539684755e-06,
                2.2603248367949354e-06,
                5.043474081993875e-07,
                4.222832437798974e-06,
                5.4222183235249605e-06,
                4.785095635655362e-06,
                7.889260704968913e-06,
                8.315284241650899e-07
            ],
            [
                1.0677029973192638e-06,
                3.7266397283908927e-06,
                1.3007128464961824e-05,
                7.889263526345123e-06,
                6.962258739796719e-06,
                NaN,
                4.785096206076165e-06,
                4.2228339479858295e-06,
                1.4738985486506781e-05,
                1.9947292459347367e-06
            ]
        ]
    },
    {
        "q_id": "10302_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            14,
            15,
            18,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            29,
            31,
            33,
            34,
            35,
            36,
            37,
            38,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            67,
            68,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            81,
            82,
            83,
            84,
            86,
            87,
            89,
            91,
            95,
            96,
            97,
            99,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            127
        ],
        "rewards": [
            [
                2.1024334103505245e-07,
                2.382369383923073e-07,
                4.450852111148132e-07,
                4.450848927650143e-07,
                1.8553903548231313e-07,
                1.6373770576776313e-07,
                3.466325384678894e-07,
                5.71500515159253e-07,
                3.9278610661902853e-07,
                5.715005151606823e-07
            ],
            [
                2.260324567337161e-06,
                1.5534975693869924e-06,
                1.5534975693933505e-06,
                2.90231094723893e-06,
                1.2098653950656417e-06,
                2.1024329090867228e-07,
                1.067702615468225e-06,
                1.5534983101602148e-06,
                1.7603430034867993e-06,
                6.475948754012522e-07
            ],
            [
                NaN,
                1.1253512180925583e-07,
                0.9999546021477018,
                1.0677024882009222e-06,
                1.2751907329024393e-07,
                2.5612828213818346e-06,
                3.466327450744504e-07,
                2.1024334103581732e-07,
                3.466326211113502e-07,
                1.8553907971879076e-07
            ],
            [
                9.422444815792981e-07,
                8.315281267882195e-07,
                7.338212429582604e-07,
                9.422445939032799e-07,
                4.785095065232451e-06,
                1.7603440527286572e-06,
                3.726639284144195e-06,
                9.422445939054222e-07,
                NaN,
                2.2603245673443566e-06
            ],
            [
                3.2887506336235617e-06,
                NaN,
                1.760343213335281e-06,
                2.9023116392097746e-06,
                3.927862002663297e-07,
                NaN,
                6.9622595696935874e-06,
                3.7266397283908927e-06,
                6.962259569750576e-06,
                2.2603248367949354e-06
            ],
            [
                6.825604537781398e-08,
                2.6995771309523475e-07,
                3.466327037548308e-07,
                1.8553914607267268e-07,
                1.2751904288739315e-07,
                2.1024336609874897e-07,
                2.699576809143613e-07,
                7.338207180864763e-07,
                2.1024331597262577e-07,
                5.043476486915964e-07
            ],
            [
                1.6373766672973748e-07,
                5.315784971839039e-08,
                1.2751901248454963e-07,
                1.275190732904469e-07,
                8.764245361752286e-08,
                3.46632497145457e-07,
                6.825598028392069e-08,
                1.6373772528704005e-07,
                6.825600469412533e-08,
                1.637376862489725e-07
            ],
            [
                1.0677026154806063e-06,
                5.4222183235249605e-06,
                3.7266410611296085e-06,
                7.338212429582604e-07,
                1.994730672675753e-06,
                5.04347528446051e-07,
                1.8925143729954285e-05,
                1.5534975693979422e-06,
                9.422450431989127e-07,
                1.0677028700363782e-06
            ],
            [
                3.927862002641863e-07,
                5.043472879540142e-07,
                5.043475885674441e-07,
                5.715005832886879e-07,
                9.422448185510695e-07,
                8.315277302841894e-07,
                3.9278634073732336e-07,
                2.699577774585891e-07,
                6.475947210031623e-07,
                1.3709572068478697e-06
            ],
            [
                1.4449800373118268e-07,
                1.6373774480605869e-07,
                8.7642516304188e-08,
                1.2751899728311609e-07,
                1.1253513522447425e-07,
                2.1024334103505245e-07,
                9.931195693628605e-08,
                1.8553910183607374e-07,
                1.6373764720990908e-07,
                1.4449795205429202e-07
            ],
            [
                4.222833947960866e-06,
                0.0004305570403788716,
                2.2603245673279107e-06,
                1.9947297215125433e-06,
                NaN,
                1.670142383595838e-05,
                1.2098658277451275e-06,
                NaN,
                1.012998977213635e-05,
                NaN
            ],
            [
                1.4738978458382043e-05,
                2.2603234895289998e-06,
                7.889260704968913e-06,
                1.209865539295696e-06,
                4.222832941193893e-06,
                0.9997694932935338,
                0.9999417087419481,
                3.72663883989755e-06,
                0.9999417087139718,
                6.962255419931625e-06
            ],
            [
                0.999999352405048,
                0.9999991148433874,
                0.9999996940978828,
                4.450848927650143e-07,
                0.9999987121046322,
                0.9999975938970929,
                0.9999995818811278,
                0.9999993106389554,
                0.999998790134462,
                0.9999991148432816
            ],
            [
                3.4663262110945863e-07,
                2.10243290909724e-07,
                1.6373764720990908e-07,
                9.931190958076104e-08,
                2.1024326584639497e-07,
                1.2751904288739315e-07,
                2.102434412875379e-07,
                1.4449795205429202e-07,
                1.8553914607267268e-07,
                2.699577774585891e-07
            ],
            [
                2.102434412875379e-07,
                1.5534983101602148e-06,
                2.382369383923073e-07,
                1.370957860576702e-06,
                1.553498124964492e-06,
                1.9947301970972664e-06,
                2.1024326584639497e-07,
                1.7603430034743913e-06,
                1.4449805540740185e-07,
                1.855391681906175e-07
            ],
            [
                6.9622595696935874e-06,
                1.994730672668496e-06,
                4.222831934352267e-06,
                1.9947297215043796e-06,
                3.7266406168624155e-06,
                8.939694172867777e-06,
                1.9947304348703948e-06,
                6.962256249885085e-06,
                1.1478764020883773e-05,
                5.422220908925639e-06
            ],
            [
                2.6995790618469934e-07,
                1.4449805540763184e-07,
                1.6373776432509826e-07,
                9.422445939054222e-07,
                3.466326624336003e-07,
                2.699577774589574e-07,
                1.760343213335281e-06,
                1.2751901248454963e-07,
                3.72663883989755e-06,
                2.561283126728994e-06
            ],
            [
                1.209865539295696e-06,
                8.939697369882888e-06,
                1.5534975693979422e-06,
                2.9023119851899796e-06,
                4.450848927650143e-07,
                3.466327037539638e-07,
                1.9947301970972664e-06,
                4.4508505193932864e-07,
                2.902312331170226e-06,
                2.5612831267202583e-06
            ],
            [
                3.7266406168624155e-06,
                4.006371129615879e-05,
                1.209865250822125e-06,
                5.715006514105942e-07,
                6.475947210031623e-07,
                3.7266392840781026e-06,
                2.1444953527476883e-05,
                9.422444815765128e-07,
                1.9947304348703948e-06,
                2.561281600049467e-06
            ],
            [
                2.9023112931873767e-06,
                2.3823688159069855e-07,
                2.2603242978778778e-06,
                5.71500378896509e-07,
                5.715002426486762e-07,
                2.1024329090867228e-07,
                1.7603432133136672e-06,
                1.3709567165579959e-06,
                3.059021904571643e-07,
                9.422450432014836e-07
            ],
            [
                2.1024344128660572e-07,
                3.927863407379485e-07,
                3.927863407379485e-07,
                6.47595107001401e-07,
                1.5534973842076057e-06,
                1.6373766672994222e-07,
                5.043476486924565e-07,
                7.33821330437595e-07,
                1.0677026154827912e-06,
                9.422445939054222e-07
            ],
            [
                6.475949526020042e-07,
                8.481101107142626e-05,
                5.4222183235249605e-06,
                3.535625493182252e-05,
                1.4738987243478167e-05,
                2.9023112932177327e-06,
                6.1441767993788005e-06,
                1.0129993395336818e-05,
                3.120190393794438e-05,
                3.535625071730638e-05
            ],
            [
                1.7603438428740716e-06,
                0.9999599362936495,
                NaN,
                2.753568453712307e-05,
                3.2887482813149375e-06,
                1.0677029973219343e-06,
                4.222832941193893e-06,
                0.9999869928715556,
                0.9995694428706527,
                5.715006514176113e-07
            ],
            [
                3.726638839878908e-06,
                3.2887502415243994e-06,
                7.338212429504183e-07,
                1.7603430034439723e-06,
                4.222835458117536e-06,
                7.889260704732132e-06,
                8.315279285205827e-07,
                1.5534971989809095e-06,
                6.144175334367959e-06,
                3.726638839806038e-06
            ],
            [
                4.78509278348926e-06,
                1.3709572068422585e-06,
                2.5612822107167428e-06,
                7.338212429537553e-07,
                1.0677032518748838e-06,
                3.4663257978780455e-07,
                1.7603434231505666e-06,
                1.0677032518748838e-06,
                1.5534973841895917e-06,
                6.475951069985296e-07
            ],
            [
                2.5612819054028872e-06,
                1.2098661161927025e-06,
                5.715005151550947e-07,
                1.0677028700363782e-06,
                5.71500242637956e-07,
                9.4224425692559e-07,
                7.889261645355786e-06,
                2.260324028427877e-06,
                5.715005151574337e-07,
                9.422442569208767e-07
            ],
            [
                1.444979692800516e-07,
                2.6995790618469934e-07,
                7.338209805224048e-07,
                8.315279285351409e-07,
                1.444979692800516e-07,
                3.927863875616689e-07,
                1.1253516205489029e-07,
                5.043476486915964e-07,
                1.4738985485997396e-05,
                4.222834954778007e-06
            ],
            [
                5.715003107767143e-07,
                NaN,
                NaN,
                5.715002426486762e-07,
                1.8553910183674878e-07,
                9.422443692574719e-07,
                3.9278605979534166e-07,
                NaN,
                1.7603438428800754e-06,
                6.475947982037486e-07
            ],
            [
                4.222831934379152e-06,
                1.7603427936335396e-06,
                1.2098652508424818e-06,
                4.222833444590791e-06,
                3.726639284144195e-06,
                1.3709575337078829e-06,
                4.222832941193893e-06,
                1.7603427936263351e-06,
                1.5534973842076057e-06,
                4.222833444590791e-06
            ],
            [
                9.422448185534261e-07,
                1.9947304348862686e-06,
                NaN,
                NaN,
                6.144177531811707e-06,
                1.067702870039777e-06,
                3.466326624336003e-07,
                NaN,
                1.5534973842076057e-06,
                NaN
            ],
            [
                1.5534975693933505e-06,
                7.338213304363436e-07,
                1.2098661161927025e-06,
                1.760344052714248e-06,
                1.8553912395338048e-07,
                1.7603440527222532e-06,
                9.4224425692559e-07,
                1.5534975693869924e-06,
                8.315283250371857e-07,
                1.5534979397740895e-06
            ],
            [
                8.315283250371857e-07,
                5.715002426439334e-07,
                5.04347468323289e-07,
                5.71500515159253e-07,
                5.715005832853093e-07,
                4.4508515805199415e-07,
                9.422448185510695e-07,
                3.927862002625787e-07,
                5.715007195431641e-07,
                6.475950298011458e-07
            ],
            [
                3.4663262111182307e-07,
                3.05902190458764e-07,
                0.9999546021153471,
                NaN,
                1.0677027427624903e-06,
                NaN,
                1.3709573702822306e-06,
                1.8553919030776337e-07,
                1.6373764721072816e-07,
                2.5612819054133693e-06
            ],
            [
                3.9278615344178325e-07,
                3.466327863983311e-07,
                3.927860597945825e-07,
                4.450848927637999e-07,
                5.043475885674441e-07,
                2.699577452746696e-07,
                2.382368247924618e-07,
                5.71500242637956e-07,
                5.715007195353674e-07,
                3.059021904571643e-07
            ],
            [
                8.764254764780641e-08,
                2.10243290909724e-07,
                1.2751904288710323e-07,
                1.8553914607267268e-07,
                1.1253525596174225e-07,
                1.9947301970972664e-06,
                NaN,
                6.825609419848033e-08,
                5.715004470326849e-07,
                3.466326624336003e-07
            ],
            [
                8.315283250371857e-07,
                2.1024326584639497e-07,
                2.2603234895289998e-06,
                9.422444815765128e-07,
                2.9023119851781017e-06,
                1.0677024881980089e-06,
                1.0677027427600627e-06,
                1.209865539295696e-06,
                3.0590226339061185e-07,
                9.422445939032799e-07
            ],
            [
                8.315281267882195e-07,
                2.561281600086738e-06,
                4.785093353909723e-06,
                1.3709576971425944e-06,
                2.2603234895372223e-06,
                1.7603425837855082e-06,
                3.05902190458764e-07,
                5.715003789017068e-07,
                NaN,
                9.422442569315887e-07
            ],
            [
                5.043473480777865e-07,
                0.9999982396572074,
                3.0590237279085045e-07,
                0.9999995818812273,
                0.9999646437536087,
                0.9999970976887091,
                1.0677029973219343e-06,
                0.999997876621539,
                0.9999785550567378,
                6.475947982037486e-07
            ],
            [
                0.9999988634360192,
                0.9999993524053566,
                0.9999988634358843,
                0.9999952149043763,
                0.9999962733607208,
                0.9999995818813767,
                0.9999955048173584,
                0.9999980052693291,
                1.8553907971855875e-07,
                0.999998126123948
            ],
            [
                9.4224425692559e-07,
                5.043474683204221e-07,
                8.315277302841894e-07,
                9.422448185510695e-07,
                4.4508526417014975e-07,
                4.450849988758202e-07,
                6.475948754012522e-07,
                3.4663278639265633e-07,
                1.0677031245905116e-06,
                5.04347588554027e-07
            ],
            [
                3.4663249714612693e-07,
                7.338209805224048e-07,
                1.855391239547094e-07,
                1.27519088491875e-07,
                5.043474081993875e-07,
                1.3709567165617364e-06,
                3.466327037553825e-07,
                1.5534981249697903e-06,
                3.4663253846718004e-07,
                8.315281267861397e-07
            ],
            [
                8.764244316973974e-08,
                5.3157837044597743e-08,
                7.734415776836702e-08,
                1.4449805540740185e-07,
                1.8553919030858602e-07,
                1.6373766672973748e-07,
                5.3157887739943563e-08,
                7.734423152941018e-08,
                2.6995784182140636e-07,
                1.4449805540740185e-07
            ],
            [
                3.0590237279032884e-07,
                2.9023112931688987e-06,
                6.144174601935314e-06,
                1.275190428875671e-07,
                7.734416698849138e-08,
                3.466327037548308e-07,
                1.4449798650551755e-07,
                5.4222176771176554e-06,
                1.1478769493331685e-05,
                1.6373766672973748e-07
            ],
            [
                3.927862002663297e-07,
                0.9999983463110065,
                NaN,
                1.6373764721072816e-07,
                4.450850519403407e-07,
                1.8553910183674878e-07,
                0.9999949062943951,
                2.2603234895289998e-06,
                9.93120161310289e-08,
                4.450852641737424e-07
            ],
            [
                2.6995790618252024e-07,
                1.6373774480535133e-07,
                NaN,
                2.3823699519143784e-07,
                3.466327037548308e-07,
                2.1024326584639497e-07,
                2.3823699519290042e-07,
                5.71500515159253e-07,
                3.4663274507098256e-07,
                1.6373774480535133e-07
            ],
            [
                4.2228339479858295e-06,
                NaN,
                3.288750241561788e-06,
                2.9023119851781017e-06,
                4.785094494783494e-06,
                1.2098662604247682e-06,
                5.715005151606823e-07,
                1.99472900813862e-06,
                NaN,
                2.5612812947508257e-06
            ],
            [
                5.715005832827105e-07,
                8.315278294072958e-07,
                3.059023727894942e-07,
                5.043474683204221e-07,
                4.450848927637999e-07,
                1.7603425837855082e-06,
                2.1024329090781183e-07,
                6.475951069896949e-07,
                7.338211554783522e-07,
                5.715003107738556e-07
            ],
            [
                1.8553919030858602e-07,
                9.422445939032799e-07,
                5.04347468323289e-07,
                5.71500515161527e-07,
                5.715003789046955e-07,
                NaN,
                NaN,
                NaN,
                5.043473480777865e-07,
                8.315278294072958e-07
            ],
            [
                1.2098659719601033e-06,
                2.3823685319244518e-07,
                4.222832437798974e-06,
                1.8553905759893702e-07,
                2.3823693839290317e-07,
                2.5612828213934817e-06,
                1.3709573702722555e-06,
                3.059022998576899e-07,
                1.8553905759969634e-07,
                1.275190580884987e-07
            ],
            [
                1.1478764020883773e-05,
                7.338211554783522e-07,
                9.422447062202052e-07,
                1.553497754476329e-06,
                1.5534981249496567e-06,
                6.144174601935314e-06,
                3.927862002582919e-07,
                4.450849458179853e-07,
                5.715005832762133e-07,
                0.9999741325568036
            ],
            [
                9.422447062294175e-07,
                2.2603242978871282e-06,
                NaN,
                7.338208930460318e-07,
                7.338213304363436e-07,
                6.144172404738491e-06,
                1.5534973842076057e-06,
                NaN,
                2.1024334103505245e-07,
                2.382369951932796e-07
            ],
            [
                6.144172404693786e-06,
                2.9023133690980155e-06,
                7.338209805133949e-07,
                2.561282210740037e-06,
                8.315280276607289e-07,
                1.7603440527046419e-06,
                1.3709572068522336e-06,
                4.4508510499849186e-07,
                8.315280276546789e-07,
                1.760344052714248e-06
            ],
            [
                0.9999546021098682,
                0.9999955048178879,
                1.4449798650476187e-07,
                0.9999599363127246,
                1.5534977545886537e-06,
                0.9999967112501523,
                4.222833444590791e-06,
                0.999996711252114,
                0.9999980052707558,
                0.9999938558224744
            ],
            [
                2.9023133690980155e-06,
                7.48462005189952e-05,
                1.0129989772532511e-05,
                1.7603436330259153e-06,
                1.994729483723626e-06,
                1.3007126914612648e-05,
                1.3709576971463352e-06,
                1.994729008145876e-06,
                NaN,
                2.4300234941880266e-05
            ],
            [
                1.2751907329024393e-07,
                NaN,
                7.73442776303243e-08,
                2.3823690999323465e-07,
                6.475946438055299e-07,
                2.2603237589938405e-06,
                1.637377448057981e-07,
                7.338212429582604e-07,
                3.059022998581767e-07,
                8.764254764780641e-08
            ],
            [
                4.450851049959619e-07,
                4.785093924362895e-06,
                5.043472278280699e-07,
                3.466327037539638e-07,
                1.5534983101602148e-06,
                6.475948754012522e-07,
                4.450849988811838e-07,
                3.05902226923399e-07,
                1.3709575337078829e-06,
                3.927862002641863e-07
            ],
            [
                9.422448185435711e-07,
                5.71500719531729e-07,
                7.338208055680009e-07,
                9.422442569315887e-07,
                5.043474683204221e-07,
                5.043474683204221e-07,
                1.067703251864202e-06,
                1.7603436330091044e-06,
                3.466327037548308e-07,
                5.04347528440776e-07
            ],
            [
                1.0677032518785256e-06,
                2.260325375634003e-06,
                6.475950297971703e-07,
                3.059021904571643e-07,
                8.315283250371857e-07,
                9.422448185478557e-07,
                5.043474081867732e-07,
                1.2098662604247682e-06,
                1.7603427936263351e-06,
                2.6995774527577444e-07
            ],
            [
                3.0590226338671677e-07,
                2.1024344128660572e-07,
                6.475946437996402e-07,
                8.315277302857965e-07,
                4.450852111148132e-07,
                7.338212429537553e-07,
                8.315278294072958e-07,
                4.4508510499849186e-07,
                1.8553903548231313e-07,
                4.450848927658745e-07
            ],
            [
                NaN,
                1.2098659719757836e-06,
                NaN,
                1.7603438428800754e-06,
                2.561282516066741e-06,
                1.209866260432471e-06,
                NaN,
                8.315277302841894e-07,
                2.5612834320470717e-06,
                NaN
            ],
            [
                3.7266410611296085e-06,
                6.144176799334096e-06,
                1.5534973842076057e-06,
                8.939695238634211e-06,
                5.422218969858371e-06,
                2.902312677150514e-06,
                NaN,
                1.0677029973192638e-06,
                1.5534981249697903e-06,
                4.2228334445658276e-06
            ],
            [
                1.8553910183607374e-07,
                1.1253518888531272e-07,
                1.1253518888531272e-07,
                2.1024341622368903e-07,
                1.6373766672973748e-07,
                1.8553919030858602e-07,
                6.475947981904966e-07,
                2.102434412875379e-07,
                1.2751907329024393e-07,
                1.2751907329024393e-07
            ],
            [
                8.939698435560267e-06,
                4.222834451292594e-06,
                4.785092783371756e-06,
                3.726639728348526e-06,
                1.444980209564556e-07,
                1.2098662604126641e-06,
                4.785096206047877e-06,
                2.5612831266946347e-06,
                4.450851049941403e-07,
                4.785094494672519e-06
            ],
            [
                3.059022269250683e-07,
                5.715003107715166e-07,
                2.2603240284371276e-06,
                1.5534984953453635e-06,
                8.315278294072958e-07,
                1.012999098021058e-05,
                2.5612812947380135e-06,
                1.7603434231777837e-06,
                6.1441767993788005e-06,
                5.715007195431641e-07
            ],
            [
                0.9999995262094986,
                0.9999997897567342,
                0.9999995818811275,
                0.9999992661791951,
                0.999999694097664,
                4.785096206013061e-06,
                0.9999998461826405,
                0.9999997126314468,
                0.9999996743688588,
                0.9999974387171818
            ],
            [
                9.422447062240614e-07,
                9.422448185478557e-07,
                1.7603434231777837e-06,
                2.902312677084523e-06,
                0.9999646437369493,
                2.561283432035425e-06,
                9.422448185478557e-07,
                1.7603427936263351e-06,
                5.715002426439334e-07,
                2.2603242978665707e-06
            ],
            [
                5.043474683204221e-07,
                1.2098659719757836e-06,
                1.9947292459347367e-06,
                4.450851580555361e-07,
                5.715003107738556e-07,
                1.7603440527286572e-06,
                8.315283250371857e-07,
                6.475949526020042e-07,
                8.315278294072958e-07,
                6.475947982002148e-07
            ],
            [
                5.3157900413760374e-08,
                1.6373776432509826e-07,
                1.27519088491875e-07,
                8.7642558095602e-08,
                1.27519088491875e-07,
                7.734423152941018e-08,
                1.8553916819032217e-07,
                1.1253526937697666e-07,
                9.931186222523604e-08,
                1.275190428875671e-07
            ],
            [
                7.889265407255982e-06,
                2.10243290909724e-07,
                3.927860597935108e-07,
                5.043472879525233e-07,
                8.315281267861397e-07,
                7.338210680021253e-07,
                3.927862002641863e-07,
                6.475949525981759e-07,
                1.7603440527046419e-06,
                7.338209805200689e-07
            ],
            [
                0.9999997617630617,
                0.9999992188516696,
                0.9999998555019275,
                0.9999986290429578,
                0.9999995818813767,
                0.9999983463106124,
                0.9999960330145621,
                0.9999985406236059,
                8.939699501416646e-06,
                3.288749457469787e-06
            ],
            [
                5.422220909009474e-06,
                1.0129995810343862e-05,
                6.144176066901277e-06,
                7.338211554783522e-07,
                1.2098653950656417e-06,
                1.0129989772532511e-05,
                2.1444940745839484e-05,
                1.994730434879465e-06,
                1.760344052714248e-06,
                7.889265407255982e-06
            ],
            [
                1.994729008105057e-06,
                2.2603234895289998e-06,
                2.260324297853209e-06,
                1.7603438428740716e-06,
                1.7603434231777837e-06,
                2.260325106237323e-06,
                1.2098662604126641e-06,
                1.994730672668496e-06,
                1.3709567165386693e-06,
                1.5534979397740895e-06
            ],
            [
                1.1253518888531272e-07,
                2.260323758987159e-06,
                6.475945666051092e-07,
                1.7603438428848787e-06,
                5.715006514176113e-07,
                1.4449805540700758e-07,
                5.715002426486762e-07,
                7.734414854792722e-08,
                1.6373774480605869e-07,
                3.466327450765785e-07
            ],
            [
                1.1253508156317518e-07,
                6.825608606148807e-08,
                8.764240137829087e-08,
                1.2751899728311609e-07,
                1.6373764721072816e-07,
                1.1253525596134564e-07,
                9.931198061405701e-08,
                2.382368531929327e-07,
                3.9278610661902853e-07,
                1.4449798650569826e-07
            ],
            [
                1.6373762769138607e-07,
                3.927862470899887e-07,
                3.4663249714612693e-07,
                9.931187406410953e-08,
                6.825608606148807e-08,
                1.6373770576776313e-07,
                4.691164920214251e-08,
                1.4449805540740185e-07,
                1.8553916819032217e-07,
                1.1253521571574156e-07
            ],
            [
                6.475949525981759e-07,
                3.059023727894942e-07,
                2.6995771309523475e-07,
                1.8553914607043678e-07,
                7.338208930391909e-07,
                3.927862002625787e-07,
                2.102434162220159e-07,
                1.6373764720923895e-07,
                5.715007195447234e-07,
                2.382368815916736e-07
            ],
            [
                1.1478769494542698e-05,
                8.93969843573914e-06,
                6.962253760024999e-06,
                1.5534975693979422e-06,
                1.1478764021029928e-05,
                4.450852641737424e-07,
                3.9278610661902853e-07,
                8.315280276626197e-07,
                4.0063696969564425e-05,
                3.7266401726359486e-06
            ],
            [
                3.059021175261338e-07,
                1.8553907971855875e-07,
                3.466326624336003e-07,
                1.6373770576776313e-07,
                2.1024331597262577e-07,
                2.144495608424996e-05,
                2.260325106237323e-06,
                1.637376862489725e-07,
                1.855391239544352e-07,
                3.05902190458764e-07
            ],
            [
                4.4508521110762794e-07,
                6.475947210012481e-07,
                7.338207180761315e-07,
                2.699578740011634e-07,
                2.699577452746696e-07,
                2.3823688159069855e-07,
                7.338208930391909e-07,
                3.927863875584984e-07,
                8.315283250394546e-07,
                5.04347468318358e-07
            ],
            [
                9.422442569315887e-07,
                1.3709568799919866e-06,
                7.889262585886274e-06,
                1.8553919030858602e-07,
                9.422448185534261e-07,
                NaN,
                3.288750241561788e-06,
                9.422445939032799e-07,
                5.043472879540142e-07,
                NaN
            ],
            [
                1.2098659719757836e-06,
                3.4663249714612693e-07,
                2.260324567227179e-06,
                1.2098658277082653e-06,
                3.9278615344178325e-07,
                3.288749457469787e-06,
                3.726638395611981e-06,
                NaN,
                0.9999785550439931,
                1.2098655392871682e-06
            ],
            [
                4.450848927658745e-07,
                5.715006514151423e-07,
                9.422448185510695e-07,
                3.9278615344178325e-07,
                5.043476486915964e-07,
                5.04347528446051e-07,
                1.209866260432471e-06,
                3.927862939126708e-07,
                1.5534971990169383e-06,
                5.043474081993875e-07
            ],
            [
                1.8553916819032217e-07,
                1.209865539295696e-06,
                1.1253521571574156e-07,
                2.102434162245973e-07,
                1.275190732904469e-07,
                2.1024334103505245e-07,
                1.6373766672973748e-07,
                1.275190732904469e-07,
                2.3823690999236795e-07,
                7.73442776300517e-08
            ],
            [
                4.222833444590791e-06,
                2.561282516042282e-06,
                2.5612831267202583e-06,
                2.2603242978871282e-06,
                4.222832941193893e-06,
                6.475947210031623e-07,
                3.2887494574518405e-06,
                1.3007123813193233e-05,
                9.422443692527585e-07,
                4.450848927650143e-07
            ],
            [
                3.4663257978780455e-07,
                7.338209805200689e-07,
                2.6995790618350237e-07,
                3.927862470899887e-07,
                3.059021904559123e-07,
                4.4508494582405734e-07,
                3.059023727894942e-07,
                3.0590226339061185e-07,
                5.043472879525233e-07,
                4.450848927650143e-07
            ],
            [
                1.6373774480605869e-07,
                1.275190580890061e-07,
                4.450852641737424e-07,
                1.6373764721091427e-07,
                1.4449805540740185e-07,
                1.275190884913241e-07,
                8.7642516304188e-08,
                7.73442776300517e-08,
                3.9278605979534166e-07,
                4.450848927658745e-07
            ],
            [
                1.2098658277451275e-06,
                5.043475885674441e-07,
                3.466327863983311e-07,
                3.4663253846718004e-07,
                5.715003789033962e-07,
                1.6373764720923895e-07,
                1.855391681898159e-07,
                1.0677028700363782e-06,
                2.6995771309523475e-07,
                5.715007195353674e-07
            ],
            [
                4.450851049959619e-07,
                7.338208930355202e-07,
                3.927862002625787e-07,
                1.2098655392871682e-06,
                9.422448185478557e-07,
                2.3823690999236795e-07,
                5.043474081993875e-07,
                1.8553916819032217e-07,
                3.4663253846718004e-07,
                NaN
            ],
            [
                4.450848927650143e-07,
                5.043474683204221e-07,
                6.475948754012522e-07,
                3.059023727894942e-07,
                2.10243290909724e-07,
                1.5534981249697903e-06,
                5.715005151606823e-07,
                3.927860597945825e-07,
                2.6995774527577444e-07,
                4.450849988798682e-07
            ],
            [
                1.0129987357287368e-05,
                1.8553905759969634e-07,
                1.6373764720923895e-07,
                7.338211554783522e-07,
                1.1478768126057254e-05,
                5.715002426475718e-07,
                1.7603438428740716e-06,
                3.9278634073098236e-07,
                6.475949526020042e-07,
                5.715007195384861e-07
            ],
            [
                3.9278610661902853e-07,
                4.450849988811838e-07,
                5.715005151606823e-07,
                4.4508494582405734e-07,
                2.6995771309523475e-07,
                8.315277302841894e-07,
                3.9278634073732336e-07,
                2.69957906184239e-07,
                2.382370235933104e-07,
                6.475950298011458e-07
            ],
            [
                5.144221366885164e-05,
                2.3823702359290413e-07,
                1.27519088491875e-07,
                2.902312677150514e-06,
                1.6373774480605869e-07,
                7.338209805240734e-07,
                2.6995774527718623e-07,
                6.475947982037486e-07,
                1.8553905760062447e-07,
                9.422449308748773e-07
            ],
            [
                1.8553916819032217e-07,
                1.4449803818215767e-07,
                2.3823693839290317e-07,
                1.8553910183674878e-07,
                1.444979692800516e-07,
                6.825608606172863e-08,
                NaN,
                8.7642558095602e-08,
                1.2751907329024393e-07,
                3.927863875584984e-07
            ],
            [
                3.927862939126708e-07,
                2.2603242978778778e-06,
                8.315278294072958e-07,
                9.422448185510695e-07,
                1.0677027427600627e-06,
                5.04347468318358e-07,
                2.9023119851781017e-06,
                2.902313369111213e-06,
                2.902312677137316e-06,
                1.2098662604247682e-06
            ],
            [
                2.382369951932796e-07,
                3.4663262111182307e-07,
                1.855391239544352e-07,
                1.125352291309328e-07,
                2.1024331597288867e-07,
                1.2751904288710323e-07,
                2.382370235933104e-07,
                2.3823696679327928e-07,
                5.04347287955046e-07,
                2.3823682479292225e-07
            ],
            [
                2.699578739999358e-07,
                6.475949525919915e-07,
                3.927862002625787e-07,
                5.715003107738556e-07,
                3.927862002625787e-07,
                2.1024334103247107e-07,
                2.3823693838927385e-07,
                7.338207180864763e-07,
                3.4663270374947136e-07,
                3.059021904559123e-07
            ],
            [
                1.444980209564556e-07,
                1.1253513522447425e-07,
                2.1024336609724313e-07,
                1.8553916819032217e-07,
                1.2751899728286965e-07,
                9.931198061405701e-08,
                1.2751910369310194e-07,
                1.855391460719133e-07,
                3.466327037548308e-07,
                3.0590226339061185e-07
            ],
            [
                NaN,
                3.288747889284851e-06,
                7.338212429537553e-07,
                1.9947292459347367e-06,
                3.05902336324494e-07,
                4.450851580555361e-07,
                9.422448185478557e-07,
                3.288749457469787e-06,
                5.422217030747413e-06,
                5.043473480777865e-07
            ],
            [
                5.422221555340727e-06,
                3.288747889229516e-06,
                8.939696304213768e-06,
                1.3709578605617394e-06,
                8.939694172867777e-06,
                2.902311639126627e-06,
                1.1478772230929451e-05,
                2.2603242978665707e-06,
                1.0129989772412744e-05,
                1.6701425826525565e-05
            ],
            [
                1.2751902768568054e-07,
                2.6995774527577444e-07,
                2.699577774589574e-07,
                5.422220909009474e-06,
                4.450851580555361e-07,
                2.6995790618350237e-07,
                1.855391239544352e-07,
                2.3823688159291947e-07,
                1.8553905760062447e-07,
                3.927862002663297e-07
            ]
        ]
    },
    {
        "q_id": "10335_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999996940978462,
                0.9999997897567092,
                0.9999999226557224,
                0.9999987121043241,
                0.9999997761971583,
                0.9999998642566543,
                3.4663266242969896e-07,
                0.9999998642567028,
                0.9999998642566866,
                0.9999995262094423
            ],
            [
                0.999999872480942,
                1.0,
                0.9999998802068873,
                0.99999995860059,
                0.9999999273418616,
                0.9999999317439221,
                0.9999999358794479,
                0.9999999006880195,
                1.0,
                0.9999999273418788
            ],
            [
                0.9999985406243016,
                0.9999992661790198,
                4.450852111100568e-07,
                1.7603425837702984e-06,
                0.9999984465022462,
                0.9999998461826038,
                8.939699501229642e-06,
                0.9999990577554064,
                8.939697369785323e-06,
                0.9999984465022459
            ],
            [
                0.9999999611088904,
                0.9999996072136593,
                0.9999998724809267,
                0.9999999611088487,
                0.9999999656786956,
                0.9999999468421503,
                0.9999994631247403,
                0.9999998802069587,
                0.9999999317439546,
                0.9999999397642151
            ],
            [
                5.715006514105942e-07,
                1.2098655392921197e-06,
                0.9999998642566381,
                0.9999998461827322,
                0.9999999559306259,
                0.9999998724809115,
                0.9999985406237794,
                0.9999999611088858,
                0.9999997300420939,
                0.9999999500628214
            ],
            [
                0.9999998362623529,
                0.9999995549149482,
                0.9999996940976272,
                0.9999998802069159,
                0.9999999611088627,
                0.9999995262094422,
                0.9999952149060809,
                0.9999999006881142,
                1.2098659719716573e-06,
                5.715002426460124e-07
            ],
            [
                0.9999998942830863,
                0.9999934595596608,
                0.9999998874647843,
                0.9999998942829098,
                0.9999995549147359,
                0.9999999317439221,
                0.9999997300422226,
                0.9999999226557409,
                0.9999998724808964,
                0.9999998257021213
            ],
            [
                0.9999999226557316,
                0.9999999530883508,
                0.9999999434137097,
                0.9999996743687034,
                0.9999999273417662,
                0.9999999067050831,
                1.0,
                0.9999999732705507,
                0.999999927341801,
                0.9999995818811275
            ],
            [
                0.9999999273418442,
                1.0,
                0.9999996310114159,
                0.9999997617631469,
                0.9999998024946801,
                0.9999997761971315,
                0.9999997463981334,
                0.9999999611088812,
                0.9999994284995531,
                0.9999997463981334
            ],
            [
                1.76034300345598e-06,
                0.9999987121052455,
                2.6995784182073116e-07,
                0.999999712631481,
                0.9999996940978095,
                0.9999994956525919,
                0.999999872480942,
                0.9999996310115479,
                0.9999999611088858,
                0.999998712104785
            ],
            [
                0.9999999559306312,
                0.9999992661788448,
                0.9999999067051054,
                0.9999998144608981,
                0.999999917667573,
                0.9999998362623334,
                0.9999998724809419,
                0.9999998642566219,
                0.9999998362622357,
                0.9999998724809419
            ],
            [
                2.2603237589542675e-06,
                0.9999987121043241,
                9.422443692555439e-07,
                4.539786322873672e-05,
                0.9999999397642724,
                5.422220262555012e-06,
                0.9999999358794097,
                0.9999991684722699,
                0.999999653367503,
                0.9999938558224728
            ],
            [
                0.9999998724810027,
                0.9999997463980124,
                0.9999998724809571,
                1.300712536350655e-05,
                0.9999999434137434,
                0.9999998802069587,
                0.9999999006879721,
                0.999999712631344,
                1.0,
                0.9999999397642365
            ],
            [
                0.999999814460876,
                4.785096776468749e-06,
                0.9999995262094987,
                0.9999995549151074,
                0.9999998024946801,
                0.9999998555020481,
                0.9999993524053563,
                9.422448185510695e-07,
                0.9999988634365607,
                0.9999996533672136
            ],
            [
                0.999999946842125,
                0.9999999732705538,
                0.9999999123575151,
                0.9999999611088487,
                1.0,
                0.9999999634651705,
                1.0,
                0.9999999358794479,
                0.9999999500627976,
                0.9999999586006245
            ],
            [
                0.9999999434137434,
                0.9999999273417662,
                0.9999999123574419,
                0.9999975938970879,
                0.9999999226557224,
                0.9999999176675731,
                0.9999980052705173,
                0.9999996940976273,
                0.9999995549149482,
                0.9999999123574524
            ],
            [
                0.999999802494633,
                0.9999999067051054,
                1.0,
                0.9999998461826222,
                0.9999997617630333,
                0.9999999067050609,
                0.9999998802069874,
                0.9999998942830485,
                0.999999814460854,
                0.9999999656786793
            ],
            [
                3.726638395611981e-06,
                0.9999991148428591,
                1.1478766757404937e-05,
                0.7057850278370112,
                4.785095065171522e-06,
                1.14787708624228e-05,
                0.9999993524048932,
                0.9999998802069302,
                4.539785782175987e-05,
                0.9999997463981938
            ],
            [
                1.0,
                0.9999997897565588,
                0.9999999123574733,
                0.9999998555020135,
                0.9999999358793944,
                0.9999998362622747,
                0.9999996743687034,
                0.9999998642567028,
                0.9999998555019618,
                0.9999999067050832
            ],
            [
                0.9999985406234314,
                0.9999990577556311,
                0.9999967112493676,
                1.4449807263312446e-07,
                3.466326211105621e-07,
                0.9999938558276001,
                0.9999984465018755,
                1.6373770576776313e-07,
                0.9999993524053563,
                0.9999997761971849
            ],
            [
                0.9999995262093293,
                0.9999997300421904,
                0.9999999317439058,
                0.9999996533673378,
                0.9999998724810027,
                0.9999996940978461,
                0.9999997761971317,
                0.9999994956523516,
                0.9999997463981938,
                0.9999999358793638
            ],
            [
                0.9999999067050276,
                0.9999999468421947,
                0.999999958600659,
                0.9999999273418356,
                0.9999998024946095,
                0.9999999586006295,
                0.9999975938965144,
                0.9999998555019446,
                0.9999999273417837,
                0.999999391641181
            ],
            [
                0.9999995549148951,
                6.144176799227922e-06,
                6.14417533430649e-06,
                0.9999798543116915,
                1.3007133116353526e-05,
                8.481108180210549e-05,
                1.892515049702235e-05,
                0.9999997300422869,
                1.6701419853852583e-05,
                0.9999999067050832
            ],
            [
                7.338210679979539e-07,
                5.715003788993679e-07,
                2.699578418185828e-07,
                1.55349775456958e-06,
                1.994729245917502e-06,
                1.7603436330091044e-06,
                6.475947981975644e-07,
                2.699578096393206e-07,
                4.450852111100568e-07,
                3.4663253846473677e-07
            ],
            [
                0.9999998802068873,
                0.9999999176675239,
                0.9999999317439383,
                0.9999998144608098,
                0.9999978766207791,
                0.9999994284994169,
                0.9999999530883843,
                0.9999969105059222,
                0.9999996533673378,
                0.999999958600595
            ],
            [
                1.6373766672973748e-07,
                1.6373766672888118e-07,
                3.9278615343901467e-07,
                1.1253510839355284e-07,
                5.043474081957179e-07,
                1.9947297215125433e-06,
                3.9278624708775595e-07,
                5.715003107755449e-07,
                6.475950297971703e-07,
                2.3823702359138736e-07
            ],
            [
                1.9947292459265734e-06,
                5.04347528446051e-07,
                2.902312677104321e-06,
                9.422443692489024e-07,
                1.760344052714248e-06,
                2.2603242978665707e-06,
                6.962255419279419e-06,
                2.5612834320214477e-06,
                1.5534973842030142e-06,
                8.315279285351409e-07
            ],
            [
                0.9999996743687422,
                0.9999999123574524,
                0.9999998802069587,
                0.9999997761970247,
                0.9999998257020799,
                0.9999999176675436,
                0.9999989322967486,
                0.9999996743687033,
                0.9999995549150011,
                0.9999998461827139
            ],
            [
                0.9999996743686645,
                1.7603430034743913e-06,
                0.3486451285660856,
                0.00013982212418799027,
                2.561282516042282e-06,
                0.9999999697115912,
                0.9999994956527122,
                5.422218969895357e-06,
                1.7603425837855082e-06,
                0.999999581881277
            ],
            [
                0.9999998362622358,
                0.9999997897566589,
                0.9999997300423191,
                0.9999993106390369,
                6.475951069961737e-07,
                0.9999995549148951,
                0.9999992188518558,
                0.9999938558224701,
                0.9999993106388725,
                0.9999994956523514
            ],
            [
                0.9999996533674204,
                0.9999997463980125,
                0.9999957771645445,
                0.9999994956525318,
                1.0,
                0.9999967112497602,
                0.999999855502048,
                0.9999998362623334,
                0.9999997761971849,
                0.9999997617631753
            ],
            [
                0.9999998724809723,
                0.999999953088334,
                0.9999998802069731,
                0.9999998024946801,
                0.9999999656786793,
                0.9999995549149482,
                0.9999998144608098,
                0.9999995262094422,
                0.9999996072139403,
                0.9999996533672549
            ],
            [
                0.9999998642567351,
                0.9999999586006443,
                0.9999999611088487,
                0.9999999358793562,
                0.9999998724809115,
                0.9999999677581375,
                0.9999999226558515,
                0.999999917667475,
                0.9999999273418615,
                0.9999999748900031
            ],
            [
                3.927861066170637e-07,
                3.059021175247079e-07,
                1.2098652508391807e-06,
                1.637377057673536e-07,
                2.3823685319244518e-07,
                1.637377643243723e-07,
                1.6373764721039308e-07,
                8.31528424162821e-07,
                3.05902263389638e-07,
                3.466325384661554e-07
            ],
            [
                0.9999998555019963,
                0.999999789756659,
                0.9999996072136126,
                0.9999980052709926,
                0.9999996743686645,
                0.9999999273418789,
                0.9999997300422548,
                0.9999998257021214,
                0.9999998461826588,
                0.9999999434137434
            ],
            [
                1.6701429808298613e-05,
                2.9023133690637e-06,
                1.6701429807964442e-05,
                2.3823688159237777e-07,
                4.222832941111319e-06,
                6.475947981975644e-07,
                3.288750241500471e-06,
                6.475948754012522e-07,
                9.422445939032799e-07,
                2.6995784182073116e-07
            ],
            [
                0.9999998362622357,
                0.9999999634652009,
                0.9999999397643083,
                0.9999998461826406,
                1.0,
                1.0,
                0.9999999559305629,
                0.9999999677581028,
                1.0,
                0.9999999656786915
            ],
            [
                1.0,
                0.9999999559306206,
                0.9999999559305996,
                0.9999992188515766,
                0.9999998942829981,
                0.9999999656786915,
                0.9999999397642221,
                0.9999998874649185,
                0.9999999273418616,
                0.9999999397642796
            ],
            [
                0.9999994284993488,
                0.9999991684721709,
                0.9999985406234319,
                0.9999997897566089,
                0.9999991684716752,
                0.9999998257021006,
                0.9999998024945624,
                0.9999999778404922,
                0.9999993524052019,
                0.9999999468421756
            ],
            [
                1.0,
                0.9999999176675829,
                0.9999999611089182,
                1.0,
                1.0,
                0.9999999273418702,
                0.9999999697115949,
                0.9999997617629764,
                0.9999999006881259,
                0.9999999468421756
            ],
            [
                0.9999996743687034,
                0.9999999317439628,
                0.9999996072138466,
                0.9999998555020307,
                0.9999998024946095,
                0.9999980052702789,
                0.9999991148427532,
                0.9999999006881377,
                0.9999999226558054,
                0.9999999358793791
            ],
            [
                0.9999998724809116,
                1.0,
                1.0,
                0.9999999397643011,
                0.9999999634651618,
                0.9999999358794327,
                0.9999990577551818,
                0.9999998257021006,
                0.999999802494586,
                0.9999999317439546
            ],
            [
                0.9999999273417837,
                0.9999990577555189,
                0.999999931743914,
                0.9999998802069302,
                0.9999998024946566,
                0.9999999006880668,
                0.9999999468421249,
                0.9999999634652097,
                0.9999997617630333,
                0.9999997897565588
            ],
            [
                0.9999999586006245,
                0.9999975938965152,
                1.0,
                0.999999114843281,
                0.9999999358793332,
                0.9999999176674848,
                0.9999998642566219,
                0.9999999067050276,
                0.999999900688055,
                0.9999998362622943
            ],
            [
                2.260325375664839e-06,
                1.2751901248454963e-07,
                0.9999993106390368,
                2.9023116391675407e-06,
                3.2887506335906595e-06,
                2.1024326584639497e-07,
                0.9999994956523515,
                6.144177531381426e-06,
                2.2603251062270446e-06,
                2.144494841326852e-05
            ],
            [
                0.9999999468421124,
                0.9999997761971583,
                0.9999999468421124,
                0.9999999434137165,
                0.9999998724809116,
                0.9999999634651574,
                0.9999997617630333,
                0.9999999586006096,
                0.9999998257021421,
                0.9999999559306102
            ],
            [
                0.9999996533672136,
                0.9999998257020798,
                0.9999989969856731,
                0.9999982396565776,
                2.382369667929001e-07,
                2.3823699519290042e-07,
                0.999999855502048,
                0.9999993524054336,
                0.9999989969854337,
                1.370957860567974e-06
            ],
            [
                0.9999999468421693,
                0.9999999358794097,
                0.9999999006881023,
                0.9999995818814266,
                0.9999997126313098,
                0.9999999358794021,
                0.9999998802069302,
                0.9999999468421883,
                0.9999999067050164,
                0.9999999006880904
            ],
            [
                0.9999964991464225,
                0.9999934595604419,
                1.6701423835320418e-05,
                1.5534983101602148e-06,
                2.260325375677174e-06,
                2.260324028427877e-06,
                0.9999997126313098,
                0.999981074856309,
                0.9999952149032271,
                1.9947297215125433e-06
            ],
            [
                0.9999994631249322,
                0.9999988634364251,
                0.9999995262094987,
                0.9999987901337398,
                0.999999057754957,
                0.9999993524051247,
                0.9999997300420939,
                0.9999988634358833,
                0.9999983463106118,
                0.9999989969857924
            ],
            [
                0.9999999434137098,
                0.9999999176674651,
                0.9999994631247402,
                0.9999998362622943,
                0.9999999677581222,
                0.9999999226557131,
                0.9999998555019963,
                0.999999887464771,
                0.9999999500628274,
                0.999999855502048
            ],
            [
                0.999999814460854,
                0.9999999226558423,
                0.9999998144608541,
                0.9999994956524115,
                0.9999982396567872,
                0.9999999697115406,
                0.9999999586006098,
                0.9999999226558515,
                0.9999997761972116,
                0.9999992661792821
            ],
            [
                0.9999998144609205,
                1.0,
                0.9999999067050387,
                0.9999999468421946,
                1.0,
                0.999999900688055,
                1.0,
                0.9999999397642437,
                0.9999999530883563,
                0.9999999006880312
            ],
            [
                5.715005832872586e-07,
                0.9999992661787573,
                0.9999999358793333,
                1.0677026154806063e-06,
                1.0,
                7.3382080556433e-07,
                3.466327450756327e-07,
                1.553497199007048e-06,
                0.999999554914842,
                0.9999999530883341
            ],
            [
                0.9999998362622943,
                0.999999855502048,
                0.9999993106389548,
                0.9999986290424667,
                0.9999998461826771,
                0.9999999006880905,
                1.0,
                0.9999998461827138,
                0.9999975938976619,
                0.9999998024946095
            ],
            [
                0.9999992661786699,
                0.9999987901344614,
                0.999998446502061,
                0.9999996743688586,
                0.9999996310113279,
                0.9999997761970782,
                0.9999998802069445,
                6.962259569484628e-06,
                0.9999995549149482,
                0.9999997761972116
            ],
            [
                3.059021904580685e-07,
                3.726639284103523e-06,
                1.0677029973158649e-06,
                1.0677026154774503e-06,
                0.9999885212346201,
                2.4300246526646385e-05,
                1.994730197090463e-06,
                1.2098655392921197e-06,
                0.9999930377454138,
                3.1201907654207106e-05
            ],
            [
                0.9999999397642365,
                0.9999998144608541,
                0.9999998555019446,
                0.9999998362622943,
                0.9999986290424668,
                1.0,
                0.9999999634651879,
                0.9999998874648782,
                0.999999825702163,
                0.9999999123574732
            ],
            [
                3.2887506335906595e-06,
                0.9999785550413858,
                0.9999977396765116,
                0.0001795279663064015,
                2.902312677084523e-06,
                0.9999910603037067,
                6.962259569630266e-06,
                0.9999989969857925,
                4.785092783454444e-06,
                3.1201922533564516e-05
            ],
            [
                0.9999999611088951,
                0.9999999067050609,
                0.9999999634651748,
                0.9999992188512973,
                0.9999998257021837,
                0.9999993524052021,
                0.9999999559305732,
                0.99999995308839,
                0.9999999226558238,
                0.9999999611088534
            ],
            [
                5.71500651413193e-07,
                0.9999999067049942,
                0.9999999067051388,
                0.9999999273418096,
                0.9999994956525319,
                0.9999999067051499,
                0.9999999358794021,
                0.9999996310116359,
                1.0,
                0.9999999634651531
            ],
            [
                0.9999985406236057,
                0.9999999123574523,
                0.9999997617629764,
                0.9999987901346056,
                0.9999999634651966,
                0.9999993106387903,
                0.9999972735290813,
                2.5612816000646084e-06,
                2.2603242978778778e-06,
                2.902311985146426e-06
            ],
            [
                3.059021175247079e-07,
                2.1024326584582131e-07,
                6.475947981975644e-07,
                1.9947304348595095e-06,
                4.450852641717689e-07,
                3.466325384661554e-07,
                2.6995768091310296e-07,
                3.4663266242969896e-07,
                3.0590215399183813e-07,
                3.927861066170637e-07
            ],
            [
                1.0,
                0.9999998802069017,
                0.9999999067050164,
                0.9999986290431208,
                0.999999887464811,
                0.9999997761972116,
                0.9999996072138467,
                0.9999987901347497,
                0.9999988634357478,
                0.9999999358794327
            ],
            [
                0.9999999176674651,
                1.0,
                1.0,
                0.9999985406237797,
                0.9999997897567342,
                1.0,
                0.9999999530883564,
                0.9999999732705283,
                0.9999999123574419,
                0.99999992265575
            ],
            [
                0.9999921107355415,
                0.9999996533673376,
                0.9999994631250603,
                0.9999988634361543,
                9.931195693628605e-08,
                1.637377448057981e-07,
                5.043476486902204e-07,
                0.9999993524054336,
                1.444979692797559e-07,
                2.1024341622426268e-07
            ],
            [
                6.144174601879434e-06,
                1.855391239539711e-07,
                4.450852641717689e-07,
                2.6995784182073116e-07,
                5.043474683220276e-07,
                3.059021904580685e-07,
                2.5612816000331606e-06,
                1.553497199007048e-06,
                3.059023363231725e-07,
                2.6995771309523475e-07
            ],
            [
                0.9999999434137368,
                0.9999997617630049,
                0.9999996072138935,
                0.9999999468421376,
                0.9999996310114599,
                0.9999998257022045,
                0.9999994956525919,
                0.9999995549148951,
                0.9999996743688586,
                0.999999789756634
            ],
            [
                0.9999998144608098,
                0.9999999468421821,
                0.999999900688055,
                0.9999999273418355,
                0.9999998362622553,
                0.9999994631251883,
                0.9999998874649318,
                0.9999997300421904,
                0.9999997300421583,
                0.9999998362622943
            ],
            [
                1.3709570434122812e-06,
                0.9999997463981031,
                1.2098655392871682e-06,
                4.450849988780466e-07,
                3.4663253846316044e-07,
                5.043473480730849e-07,
                3.927862470861484e-07,
                0.9999993106391191,
                5.043476486902204e-07,
                0.9999991684718735
            ],
            [
                0.9999999273418182,
                0.9999998024947272,
                0.9999998555019274,
                0.9999997897566589,
                0.9999999273418095,
                0.9999999176675829,
                0.9999996310115918,
                0.9999998802069302,
                0.9999989322973849,
                0.9999999067049943
            ],
            [
                0.9999999634651574,
                0.9999999397642939,
                0.9999997463980125,
                0.9999999067050165,
                0.9999997761970782,
                0.9999998802069444,
                0.9999999656786915,
                0.9999995549150014,
                0.999999976411324,
                0.9999997761970515
            ],
            [
                4.785096206013061e-06,
                0.9999999748899912,
                0.9999999358794249,
                0.9999995549147359,
                0.9999997897567092,
                0.9999999611088719,
                1.0,
                0.9999998461826589,
                0.9999998362623137,
                0.9999999468421186
            ],
            [
                1.3007131565140219e-05,
                7.889260704732132e-06,
                2.6995777745711594e-07,
                1.3007134666431358e-05,
                3.059021904580685e-07,
                4.785092783371756e-06,
                1.760344052693435e-06,
                1.4738981971813965e-05,
                7.88926352599354e-06,
                5.715004470295662e-07
            ],
            [
                0.9999988634357477,
                0.9999998461826038,
                0.9999997617630901,
                0.9999995262095552,
                0.9999994631249963,
                0.9999992661788449,
                0.9999996743688975,
                0.999999554914736,
                0.9999994956523516,
                0.9999993916411087
            ],
            [
                0.9999993106386261,
                0.9999997300421904,
                0.9999999273417837,
                0.9999998642566381,
                0.9999997761970515,
                0.99999992265575,
                0.999999653367503,
                0.9999997617630333,
                0.9999994631250602,
                0.9999995549148952
            ],
            [
                0.999999855502048,
                0.9999999317439465,
                0.999999961108909,
                0.999999958600585,
                0.9999998461826588,
                0.9999998024946801,
                0.9999999397642868,
                0.9999999123575151,
                0.9999999559306312,
                1.0
            ],
            [
                0.9999998461826405,
                0.9999998144608983,
                1.3709578605729614e-06,
                0.9999994284994169,
                0.9999970976869786,
                0.9999960330155068,
                0.9999995262093857,
                3.726639728348526e-06,
                1.6373766672973748e-07,
                0.9999981261237236
            ],
            [
                0.9999996072138935,
                0.9999994284996213,
                0.9999989969862708,
                0.9999983463100202,
                0.9999974387187058,
                0.9999977396757032,
                0.9999977396759724,
                0.9999999434137907,
                5.043474683220276e-07,
                0.9999995818810776
            ],
            [
                6.475946438022905e-07,
                0.999999730042287,
                1.444980726324838e-07,
                0.9999994631251242,
                2.6995768091310296e-07,
                0.9999999715466561,
                0.9999996310115039,
                0.9999991684717743,
                2.1024329090929374e-07,
                3.466327863983311e-07
            ],
            [
                0.9999997300423192,
                0.9999998144608319,
                0.9999996310116359,
                0.9999998724809115,
                0.9999994956524718,
                0.9999999226557316,
                0.999999554914736,
                0.9999997126313441,
                0.9999993916406735,
                0.9999987121041708
            ],
            [
                0.9999983463100208,
                0.999999900687984,
                1.444979692800516e-07,
                0.9999998942829477,
                0.9999972735300556,
                0.9999999123575255,
                0.9999997617630901,
                0.999999581881277,
                0.9999998802069873,
                0.9999998362622358
            ],
            [
                0.9999999468421439,
                0.9999999226557962,
                0.9999998461827322,
                0.9999999226557685,
                0.9999983463098232,
                0.9999990577551818,
                0.9999999434137232,
                0.9999992188519492,
                0.9999999317439384,
                0.9999999434137841
            ],
            [
                1.1253521571574156e-07,
                1.994729721518893e-06,
                6.825602910433871e-08,
                1.1253521571574156e-07,
                9.931192141964017e-08,
                4.139938534423022e-08,
                1.1253517547010071e-07,
                6.825600469412533e-08,
                8.764247451307293e-08,
                6.023573475041126e-08
            ],
            [
                0.9999988634357478,
                6.144176799283803e-06,
                0.9999991148426478,
                0.9999982396567874,
                0.9999991684717744,
                0.9999997617630332,
                0.9999921107355383,
                0.9999982396574166,
                0.9999999611088858,
                0.9999938558246696
            ],
            [
                9.422442569315887e-07,
                0.9999998555019618,
                7.338210680021253e-07,
                0.9999998942830358,
                0.9999998724810027,
                4.785095635592258e-06,
                8.315284241650899e-07,
                0.9999998555019963,
                0.9999994284995531,
                3.9278634073732336e-07
            ],
            [
                0.9999999067050609,
                0.9999998874649185,
                0.9999998555020481,
                0.9999993524052794,
                3.9278634073625165e-07,
                3.927861066170637e-07,
                1.5534981249397663e-06,
                0.9999989322966213,
                0.9999995818814266,
                0.9999998024946095
            ],
            [
                3.7266397282926013e-06,
                0.9999993106392013,
                0.999999310638626,
                0.9999999176674848,
                0.9999994284995531,
                0.9999997300420939,
                0.9999999006880786,
                0.9999985406243013,
                0.9999996072136126,
                6.14417753171671e-06
            ],
            [
                0.9999997897565838,
                0.9999999434137502,
                0.9999998724809116,
                0.9999998257021214,
                0.9999997761970248,
                0.9999998874649051,
                0.9999998257021213,
                0.9999996940977731,
                0.9999998642566219,
                0.9999996743688975
            ],
            [
                0.9999998555019619,
                0.9999998362622747,
                0.999999825702059,
                0.9999999611089044,
                0.9999994284993488,
                0.9999998257021213,
                0.9999998942830485,
                0.9999999559306205,
                0.9999925887192523,
                0.9999996533672963
            ],
            [
                0.999999955930589,
                0.9999999791830863,
                1.0,
                0.9999998144609645,
                0.9999999397643011,
                0.9999998024947037,
                0.9999999434137907,
                0.9999993106387081,
                0.9999998257021422,
                0.9999996940977002
            ],
            [
                0.9999988634364254,
                0.9999999530883396,
                0.9999999530883731,
                0.9999994631247403,
                0.9999995818814266,
                0.9999990577551818,
                0.9999999273417922,
                9.931190958076104e-08,
                0.9999998144608097,
                0.9999977396746255
            ],
            [
                0.9999997761971049,
                3.120190021339598e-05,
                3.927862002606139e-07,
                5.715003788993679e-07,
                0.9999998461826038,
                8.315279285251204e-07,
                1.0677024881941248e-06,
                8.939698435454571e-06,
                0.9999995262095551,
                6.475945666009864e-07
            ],
            [
                0.9999999123574419,
                0.9999993916406734,
                0.9999999358793714,
                0.9999999006880549,
                0.9999998802069159,
                0.9999999006881378,
                0.9999997897566089,
                0.9999998144608541,
                0.9999999006881378,
                0.9999993524052793
            ],
            [
                0.9999998144608762,
                0.9999997617631186,
                0.9999998024945624,
                0.9999998942828973,
                0.999999825702059,
                0.9999998874647441,
                0.9999993916407459,
                0.9999998874647575,
                0.9999997617631184,
                0.9999998724809571
            ],
            [
                0.9999987901341727,
                0.9999998874648112,
                0.9999998642567351,
                0.9999999176675142,
                0.999999922655833,
                6.475946438022905e-07,
                0.9999999123575255,
                0.9999999176675731,
                0.9999999006880431,
                0.9999988634365611
            ],
            [
                0.9999997126315496,
                0.9999992661792823,
                4.450852111148132e-07,
                0.9999994631247403,
                0.9999996743688974,
                0.9999998024947037,
                0.9999987121052456,
                0.9999998362622552,
                0.999998005269328,
                0.9999999176674946
            ],
            [
                0.999999855502048,
                0.9999997126315153,
                0.9999997897566089,
                0.9999998942830737,
                0.9999998461826038,
                0.9999998724809115,
                1.0,
                0.9999999226558423,
                0.999999789756659,
                0.9999997300421903
            ],
            [
                0.9999991148427533,
                0.9999999397643011,
                0.9999999226558054,
                4.4508494582405734e-07,
                0.9999980052707549,
                0.9999974387168744,
                5.04347528446051e-07,
                1.9947301970813926e-06,
                0.9999993916411085,
                2.2603251062270446e-06
            ],
            [
                9.422443692489024e-07,
                1.7603436330259153e-06,
                3.4663266243111764e-07,
                3.9278624708775595e-07,
                5.144220139179215e-05,
                2.102433159721477e-07,
                2.5612831266608576e-06,
                1.3007123812980299e-05,
                8.939699501132077e-06,
                7.889266347636241e-06
            ],
            [
                0.9999994631250603,
                0.9999997300422226,
                0.9999996743688975,
                0.9999998362622552,
                0.9999999226558515,
                0.9999996940978462,
                0.9999991148433864,
                0.9999998555019791,
                4.2228334445370225e-06,
                0.9999996072137062
            ],
            [
                2.6995774527657245e-07,
                5.043473480678099e-07,
                1.3709568799823232e-06,
                0.9999998942829476,
                0.999999712631481,
                0.999999607213753,
                8.315281267706361e-07,
                0.9999999611088951,
                1.444979692800516e-07,
                6.475951069932288e-07
            ],
            [
                0.9999998555019447,
                1.0,
                0.9999999317439384,
                0.9999999434138109,
                0.999999789756634,
                0.9999998362622943,
                0.9999997617629766,
                0.9999999123575151,
                0.9999996533672136,
                0.9999998257021422
            ],
            [
                0.9999969105062904,
                0.9999990577555189,
                0.9999986290427939,
                0.9999991684719726,
                0.9999987901337402,
                0.9999989322966213,
                0.9999983463108093,
                0.9999995818813767,
                0.9999993916406734,
                0.9999994284996213
            ],
            [
                0.9999997761972116,
                0.9999987121052454,
                0.9999999697115696,
                2.144495352642369e-05,
                0.9999987901344612,
                8.93970056668775e-06,
                0.9999999611088672,
                0.9999990577549571,
                0.9999988634362897,
                0.9999962733602747
            ],
            [
                0.9999998724809723,
                0.9999998024947273,
                0.9999998642566543,
                0.9999995549148951,
                0.9999998802069873,
                0.9999999358793791,
                0.999999814460854,
                0.9999996940977003,
                0.9999974387180961,
                1.0
            ],
            [
                0.9999999434137097,
                0.9999995549151074,
                0.9999998555019275,
                0.9999999317439302,
                0.9999991148428589,
                0.9999998642566542,
                0.9999999586006493,
                0.9999999273418442,
                0.9999999715466358,
                0.999998239657417
            ],
            [
                1.0,
                0.9999998024946566,
                0.9999999226558423,
                0.9999998802069873,
                0.9999998024946566,
                0.9999999500628453,
                0.9999998642566866,
                0.9999999530884011,
                0.9999998362622552,
                0.9999999434137772
            ],
            [
                0.9999999067051388,
                0.9999999397642294,
                0.9999998874648112,
                0.9999998942829225,
                0.9999999226557131,
                0.999999631011328,
                0.9999999273418182,
                0.9999997463982241,
                0.9999995818810776,
                0.9999998024947038
            ],
            [
                0.9999994631251242,
                0.999999887464838,
                0.999999789756659,
                0.9999997897566841,
                0.9999999434137165,
                0.9999997761971582,
                0.9999997617631469,
                0.9999997897567342,
                0.9999999611088858,
                0.9999999697115587
            ],
            [
                0.9999998024946095,
                0.9999978766222982,
                0.999999653367255,
                0.9999999123575359,
                0.9999993916407459,
                0.999999953088334,
                0.9999998874649318,
                0.9999997126315154,
                0.9999997300422547,
                0.9999972735300563
            ],
            [
                0.9999997617630049,
                0.9999997761972116,
                0.9999998642567028,
                0.9999999317440278,
                0.9999995818811275,
                0.9999997463981334,
                0.9999983463098234,
                0.9999992661792821,
                0.9999993106391192,
                0.99999926617867
            ],
            [
                0.9999998362623332,
                0.9999998362623138,
                0.9999995549149484,
                0.9999996310116359,
                0.9999998642566704,
                0.99999976176309,
                0.9999996072139404,
                0.9999999317439221,
                0.9999998555019447,
                0.9999997300421904
            ],
            [
                0.9999998362622358,
                0.9999999397643011,
                0.999999943413811,
                1.0,
                1.0,
                1.0,
                0.999999900688055,
                1.0,
                0.9999999006881378,
                0.999999917667524
            ],
            [
                0.9999998724809572,
                0.9999997300420939,
                0.9999998461826406,
                0.999999894283061,
                0.9999999176674553,
                0.9999997617631184,
                0.9999997126315154,
                0.9999998555019791,
                0.999999825702059,
                0.9999997761972116
            ],
            [
                0.9999996310115918,
                0.9999992188515766,
                0.9999999656787325,
                0.9999998942829602,
                0.9999999226557776,
                0.9999999358794479,
                0.9999999176675044,
                0.999999946842125,
                0.9999999434138042,
                0.9999999317439383
            ],
            [
                0.9999997897566841,
                0.9999991684718735,
                0.9999999123575882,
                0.9999989322971303,
                0.9999999226558053,
                2.9023133690821773e-06,
                0.9999996743688975,
                0.9999997300421261,
                0.9999996310113279,
                0.9999997126314468
            ],
            [
                0.9999962733598291,
                0.9999993106390369,
                0.9999995262093857,
                0.999999631011416,
                1.4449807263312446e-07,
                9.4224425692559e-07,
                0.9999994631248682,
                6.825606165129312e-08,
                0.9999986290427937,
                0.9999993916407459
            ],
            [
                9.422445939002803e-07,
                1.5534975693869924e-06,
                2.6995777745711594e-07,
                0.9999978766222978,
                2.69957906184239e-07,
                2.561281600076256e-06,
                0.9999977396746252,
                4.450849458200093e-07,
                8.315281267861397e-07,
                1.2751908849088918e-07
            ],
            [
                0.9999999123574419,
                0.9999985406232575,
                5.043474683220276e-07,
                3.059022269250683e-07,
                NaN,
                3.9278615344178325e-07,
                0.9999997463981938,
                0.9999995262092729,
                0.9999989322975122,
                0.9999995818812771
            ],
            [
                0.9999991684721709,
                0.9999998144608098,
                0.9999984465018756,
                0.9999998461826222,
                0.9999994631249962,
                0.9999997463981334,
                0.9999993106389546,
                0.9999982396563679,
                0.9999982396574169,
                0.9999996743686645
            ],
            [
                0.999999802494586,
                0.999999730042287,
                0.9999990577555189,
                0.999999887464932,
                0.9999999123574629,
                0.9999998802069731,
                0.9999998642566381,
                0.9999996743688586,
                0.9999998874647977,
                0.9999998362622553
            ],
            [
                0.9999992661786697,
                0.9999996533673376,
                0.999999352405202,
                0.9999998144609645,
                0.9999999397642867,
                0.9999996533672136,
                0.9999999397643083,
                0.9999998461826222,
                0.999999310638626,
                2.5612834320214477e-06
            ],
            [
                8.939698435454571e-06,
                0.999999927341801,
                0.9999992661788447,
                1.8925150496161756e-05,
                1.9947306726594253e-06,
                5.144219525429276e-05,
                0.9999999176674552,
                5.422221555296344e-06,
                2.561282210701601e-06,
                0.9999999067051388
            ],
            [
                0.999999802494586,
                0.9999998461826037,
                0.9999998362623334,
                0.999999946842144,
                0.9999999006880431,
                0.9999997617631753,
                0.9999998642566866,
                3.466327450756327e-07,
                0.9999984465016908,
                9.422448185435711e-07
            ],
            [
                0.9999998642567351,
                0.9999996310115479,
                0.9999999067050388,
                0.9999998144609645,
                0.9999999317439464,
                0.9999986290429571,
                0.9999998802069017,
                0.9999998362623723,
                0.9999999123575568,
                0.9999998942830233
            ],
            [
                0.9999998724809875,
                0.9999998942830485,
                0.9999998874647709,
                0.9999998257021213,
                0.9999993106387082,
                0.9999992188516695,
                0.9999957771675673,
                0.9999997463980125,
                0.9999985406239538,
                0.9999996743686645
            ],
            [
                1.5534975693933505e-06,
                0.9999999634651661,
                0.9999999530884011,
                0.9999999317439628,
                0.9999998642567189,
                0.9999999358793562,
                0.9999999176674553,
                0.9999999123574732,
                0.9999999123575359,
                0.9999999358793867
            ]
        ]
    },
    {
        "q_id": "10206_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999999611088766,
                0.9999999656786998,
                0.9999999530883509,
                0.9999997126315153,
                0.9999998144608097,
                0.9999998362622358,
                0.9999997617629766,
                0.9999999317439384,
                0.9999998724809875,
                0.999999894283061
            ],
            [
                0.9999998555019791,
                0.9999997300421261,
                0.9999998362623528,
                0.9999998144608762,
                0.999999946842163,
                0.9999999468421124,
                0.9999998942830737,
                0.9999997126314811,
                0.9999989969860318,
                0.9999997897567342
            ],
            [
                1.760343633031919e-06,
                3.7266388398585725e-06,
                1.994729008145876e-06,
                1.553497754583709e-06,
                2.4300232042706045e-05,
                3.726639728348526e-06,
                4.222835458175145e-06,
                0.9999980052695654,
                1.994730672675753e-06,
                1.0129992187658463e-05
            ],
            [
                1.5534981249697903e-06,
                3.7266401726173067e-06,
                1.2098659719757836e-06,
                2.1024344128660572e-07,
                1.7603440527222532e-06,
                2.260325375664839e-06,
                2.2603242978778778e-06,
                1.9947304348595095e-06,
                1.6701417862648148e-05,
                1.5534975693869924e-06
            ],
            [
                0.9999989969855533,
                1.9947297215125433e-06,
                0.999983298574187,
                6.9622579095833456e-06,
                3.059022998569248e-07,
                0.9999975938985219,
                0.9999996533674615,
                0.9999930377429234,
                2.430025232128576e-05,
                4.785095635624897e-06
            ],
            [
                0.9999599362935339,
                0.9999962733589397,
                0.9999962733611608,
                2.260324567302214e-06,
                0.9999785550592668,
                0.999991060301567,
                4.222834451327159e-06,
                8.939696304116203e-06,
                0.9999921107345968,
                0.9999921107402387
            ],
            [
                0.9999998362623723,
                0.9999984465022471,
                0.9999998642566704,
                0.9999997463982241,
                0.9999999226558237,
                0.9999998362623529,
                0.9999998642566381,
                0.9999993524051247,
                0.9999998724810027,
                0.999999900687984
            ],
            [
                0.9999998461826037,
                0.9999998461826771,
                1.6701429808632785e-05,
                0.9999998555019274,
                6.144172404693786e-06,
                7.889262585814522e-06,
                0.9999992661790197,
                0.9999910603058351,
                0.9999998874648917,
                1.7603427936335396e-06
            ],
            [
                1.3007130015677909e-05,
                1.1478766757404937e-05,
                0.9999910603068949,
                1.8553907971855875e-07,
                0.9999982396569971,
                6.47595107001401e-07,
                0.9999687980812294,
                5.715003789033962e-07,
                0.9999995262096116,
                9.422449308716635e-07
            ],
            [
                0.9999997300422547,
                0.9999998942829225,
                0.9999975938985227,
                1.3709576971242028e-06,
                2.2603234895053587e-06,
                0.999999802494633,
                0.9999998144608098,
                0.9999998362622357,
                0.9999994284992806,
                2.6995790618252024e-07
            ],
            [
                1.209865539274514e-06,
                0.9999992661791071,
                3.288749457469787e-06,
                1.0677026154806063e-06,
                0.9999997897565588,
                4.785096776499213e-06,
                0.9999852610215562,
                0.9999982396561573,
                0.9999982396572067,
                2.260324836787226e-06
            ],
            [
                0.9999999559305995,
                0.9999996072137999,
                0.9999998874648915,
                0.9999997463980729,
                0.9999997463980427,
                0.999999887464905,
                0.9999998642567189,
                0.9999997300422869,
                0.9999998461826405,
                0.9999999006880785
            ],
            [
                1.7603430034743913e-06,
                0.9999930377445823,
                1.300713001508642e-05,
                4.785094494783494e-06,
                1.0677032518700286e-06,
                0.999993855825401,
                8.31527928532683e-07,
                0.20181322466072713,
                5.422218969858371e-06,
                0.9999980052695654
            ],
            [
                0.9999998024947037,
                0.9999997761971314,
                0.9999996533673376,
                0.9999998642566381,
                0.9999989322967487,
                0.9999995818812769,
                0.9999996310116359,
                0.9999997126313783,
                0.999997876622045,
                0.9999998555019963
            ],
            [
                0.9999998802069444,
                0.9999998257021007,
                0.9999999067050498,
                0.9999999732705442,
                0.9999999123575881,
                0.9999998942830485,
                0.9999998257021006,
                0.9999998024945624,
                0.9999998802069731,
                0.9999998874648915
            ],
            [
                0.9999998461826589,
                0.9999967112517194,
                0.9999991148432809,
                0.9999999176675828,
                0.9999997897567091,
                0.9999998362622747,
                0.9999996940978096,
                0.9999998024946095,
                0.9999998024946801,
                0.9999998362623723
            ],
            [
                0.9999999273417837,
                0.9999999500628513,
                0.999999927341801,
                0.9999998642566866,
                0.9999999176674945,
                0.9999994284994168,
                0.9999999226557592,
                0.999999900687972,
                0.9999998642566381,
                0.9999999273418616
            ],
            [
                0.9999995818812271,
                1.0677032518785256e-06,
                0.9999995262093292,
                0.9999975938985223,
                0.9999993524054335,
                0.9999999358794402,
                0.9999998257021837,
                0.9999995818812769,
                0.9999977396751643,
                0.9999997617630049
            ],
            [
                0.9999996940977731,
                0.9999998461826037,
                0.9999999715466392,
                0.9999996743688974,
                0.9999998461826589,
                0.9999997300421261,
                1.994730434816876e-06,
                0.9999999067049831,
                0.9999998802069444,
                0.9999998555019275
            ],
            [
                0.9999998642567028,
                0.9999999123575151,
                0.9999998144609645,
                0.9999998362623334,
                0.9999995818812271,
                0.9999996940977732,
                0.9999998874648112,
                0.9999993916408186,
                0.9999999397642653,
                0.9999999397642293
            ],
            [
                0.9999810748562891,
                1.1253524254615121e-07,
                4.785096776499213e-06,
                7.889262585814522e-06,
                6.9622587397397306e-06,
                4.450852641717689e-07,
                5.144221366361183e-05,
                7.338209805170655e-07,
                0.9996200154262819,
                3.466325384661554e-07
            ],
            [
                4.222833444590791e-06,
                7.889262585886274e-06,
                1.1478770862882149e-05,
                3.2887478892683997e-06,
                6.144173869502757e-06,
                2.2603234895372223e-06,
                9.422448185534261e-07,
                7.889262585886274e-06,
                2.2603234895372223e-06,
                1.553497754583709e-06
            ],
            [
                2.260324567337161e-06,
                1.3007128464346676e-05,
                0.9999997761971848,
                0.9999646437535605,
                1.5534973842076057e-06,
                6.1441724046434924e-06,
                0.9999998642566219,
                4.785095635624897e-06,
                2.9023112932177327e-06,
                2.260325106237323e-06
            ],
            [
                0.9999955048168166,
                0.9999991148433868,
                0.9999993524049704,
                0.9999977396765115,
                0.9999998144608319,
                0.9999994284992807,
                0.9999998874649318,
                0.9999998257021837,
                0.9999997463980729,
                2.6995784182073116e-07
            ],
            [
                0.99999911484307,
                0.9999998362623334,
                0.9999995262094988,
                0.9999997617631184,
                0.9999999006880785,
                0.9999974387187082,
                0.9999997897565588,
                0.9999987121052455,
                0.999999953088362,
                0.9999998144608983
            ],
            [
                0.9999962733616052,
                0.9999921107383561,
                0.999994577780386,
                0.9999945777816779,
                0.9999417087345488,
                0.999988521227776,
                0.9999885212277755,
                0.9999910603047645,
                0.9999999500627798,
                0.999972464318766
            ],
            [
                0.9999998802069731,
                0.9999999226558515,
                0.9999999273418616,
                0.9999996310115918,
                0.9999998724809115,
                0.9999999468421756,
                0.9999997463981334,
                0.9999989322973858,
                0.9999998642567189,
                0.9999989969856731
            ],
            [
                7.889266347715168e-06,
                0.9999957771675637,
                8.939693107190907e-06,
                2.5612812947508257e-06,
                8.939700567004841e-06,
                4.222833444590791e-06,
                2.5612828213934817e-06,
                3.726639728348526e-06,
                0.9999982396569969,
                3.726638839878908e-06
            ],
            [
                0.9999997897565587,
                0.9999997126313097,
                0.9999962733598288,
                0.999999391641036,
                0.9999992661788447,
                0.9999996940976272,
                0.9999996072137998,
                0.9999997761970782,
                0.9999993524052793,
                0.9999996072138466
            ],
            [
                0.9999998257021214,
                0.9999999176675239,
                0.9999999468421376,
                0.9999996533672136,
                0.9999996940977732,
                0.9999999176675044,
                0.9999998362623723,
                0.9999998461826772,
                0.999997876620526,
                0.9999998642567189
            ],
            [
                0.9999339478711452,
                0.9940889310124146,
                1.8925155009354808e-05,
                2.260325106237323e-06,
                1.370957860576702e-06,
                0.9859363733054209,
                6.962257909785973e-06,
                0.6224593312018546,
                0.9947798755348471,
                0.999796573075402
            ],
            [
                0.9999993916407459,
                0.9999982396572071,
                0.9999998642566381,
                0.9999995262092163,
                0.9999986290423034,
                0.9999991148432807,
                0.999999814460854,
                0.9999985406239534,
                3.726638395634011e-06,
                0.9999998642567189
            ],
            [
                0.9999998874648112,
                0.9999996310114159,
                0.9999997300422226,
                0.9999995818813269,
                0.9999993106391191,
                0.9999998555020307,
                0.999999855501979,
                0.9999996743688199,
                0.999999653367503,
                0.9999998642566866
            ],
            [
                0.9999969105048168,
                0.999999814460854,
                0.9999997761971583,
                0.999999887464811,
                0.9999996940978096,
                0.9999997300423191,
                0.9999998362622358,
                0.999995214904937,
                0.9999997300422869,
                0.9999998724809723
            ],
            [
                0.9999999067051499,
                0.9999998024946095,
                0.9999993916409636,
                0.9999994631250604,
                0.9999996072137062,
                0.9999998642566219,
                0.9999997463982241,
                0.9999999226557224,
                0.9999997126313098,
                0.9999999006881023
            ],
            [
                0.9999998874647709,
                0.9999999397642293,
                0.999999825702163,
                0.9999997897566089,
                0.9999998362622747,
                0.9999997126314811,
                0.9999995818811275,
                0.9999999123574838,
                0.9999999123575672,
                0.999998863436696
            ],
            [
                0.999999887464744,
                0.9999999317439302,
                0.9999999006880312,
                0.999999855502048,
                0.9999999500628571,
                0.9999997126314811,
                0.999999653367379,
                0.9999999468421503,
                0.9999997126314468,
                0.9999998144609424
            ],
            [
                1.4738983728490028e-05,
                1.3709570434122812e-06,
                2.2603234895289998e-06,
                1.0677026154806063e-06,
                0.9999997126315153,
                0.9999998144609202,
                0.9999998802069444,
                0.9999998257021628,
                3.466327037548308e-07,
                3.466325384661554e-07
            ],
            [
                0.9999756997477396,
                0.9999996743687034,
                0.9999995818813268,
                0.9999999559305995,
                0.9999998802068873,
                0.9999991684716751,
                0.9999999697115479,
                0.9999997300421583,
                0.9999999434137232,
                0.9999997463981939
            ],
            [
                0.9999996310115918,
                0.9999997126314468,
                0.999999789756659,
                0.999999855502048,
                0.9999999586005998,
                0.9999998024946095,
                0.9999996310113719,
                0.999999391641181,
                0.9999997463981636,
                0.9999989969855536
            ],
            [
                3.059022269250683e-07,
                1.2098658277489788e-06,
                2.90231233114251e-06,
                1.7603425837855082e-06,
                1.7603436330179102e-06,
                4.2228324377740105e-06,
                1.7603434231777837e-06,
                7.338212429562581e-07,
                2.9023112932177327e-06,
                3.2887482813149375e-06
            ],
            [
                2.9023119851899796e-06,
                4.785096206076165e-06,
                8.939693107288474e-06,
                1.2098652508347793e-06,
                1.5534971990169383e-06,
                1.5534983101602148e-06,
                0.9999898700066122,
                0.0005527786175322262,
                1.3709568799823232e-06,
                1.8925145985895816e-05
            ],
            [
                3.72664061681327e-06,
                5.422217677028889e-06,
                5.422218969769604e-06,
                1.3007123813382511e-05,
                1.5534975693792215e-06,
                7.889261645269683e-06,
                1.9947297215125433e-06,
                1.3709570434122812e-06,
                1.3709567165530083e-06,
                6.962258739796719e-06
            ],
            [
                4.2228319344021954e-06,
                8.481101107142626e-05,
                2.9023112932177327e-06,
                1.0129987357517693e-05,
                1.4738978458623327e-05,
                1.0677027427471959e-06,
                2.9023119851899796e-06,
                2.561282210740037e-06,
                1.1478764021029928e-05,
                3.535625914621054e-05
            ],
            [
                0.9999998942829602,
                0.9999997300422548,
                0.9999998461826405,
                0.9999997897565838,
                0.9999999397642078,
                0.9999992661788448,
                0.9999996743688975,
                0.9999980052702796,
                0.9999996310115039,
                0.9999998461827321
            ],
            [
                0.9999999358794479,
                0.9999997300422226,
                0.9999999500628334,
                0.9999999715466358,
                0.9999999677581105,
                0.9999998724809571,
                0.9999998724809267,
                5.043476486902204e-07,
                0.9999997617631469,
                0.9999999656786915
            ],
            [
                0.999999814460854,
                0.9999997761970781,
                0.9999997761970248,
                0.9999997126313441,
                0.9999997300422547,
                0.999999802494633,
                0.9999987121043242,
                0.9999997126313098,
                0.9999997463982241,
                0.9999999123574523
            ],
            [
                0.9999998144608762,
                0.9999992661792823,
                0.9999999226557408,
                0.9999997761972116,
                0.9999999358794021,
                0.9999994284995531,
                0.9999970976890542,
                0.9999998942830233,
                1.3709576971316842e-06,
                0.9999999634651444
            ],
            [
                0.9999998024947273,
                0.9999986290421399,
                0.9999985406241276,
                0.9999996743687809,
                0.9999996072137062,
                0.9999995818811772,
                0.9999995549148951,
                0.9999995549150011,
                0.9999985406234314,
                0.9999982396572067
            ],
            [
                0.9999992188514832,
                0.9999945777803863,
                0.9999998024947037,
                0.999989870010232,
                0.9999996940976638,
                0.9999996310115039,
                0.9999997126315154,
                0.9999969105048166,
                0.9999995262094422,
                0.999998126125064
            ],
            [
                0.999999581881277,
                0.9999998461827322,
                0.9999996743688586,
                0.9999989969861511,
                0.9999997761972116,
                0.99999976176309,
                0.9999997761971849,
                0.9999997463981636,
                0.9999983463098234,
                0.9999997897565838
            ],
            [
                0.9999962733602735,
                0.9999999006880194,
                0.9999945777823259,
                0.9999967112505436,
                0.9999999434137232,
                0.9999987121044778,
                0.9999998362623528,
                0.9999997300423191,
                0.9999938558239362,
                0.9999997126314811
            ],
            [
                0.9999885212277771,
                0.999999057755631,
                0.9999852610215582,
                2.260325375677174e-06,
                3.7266401726173067e-06,
                0.9999957771665561,
                2.9023119851781017e-06,
                8.315277302788957e-07,
                7.88926070489716e-06,
                0.9999997761970248
            ],
            [
                0.9999993916408184,
                2.5612831267202583e-06,
                2.561281905376098e-06,
                4.785095635624897e-06,
                6.14417753171671e-06,
                4.222831934379152e-06,
                1.1478765388898939e-05,
                0.9999982396572068,
                5.422217030707961e-06,
                2.9023119851781017e-06
            ],
            [
                1.1478769493916314e-05,
                0.9999996940976636,
                2.260323758987159e-06,
                2.9023123311583482e-06,
                2.902313023130843e-06,
                4.222834451355964e-06,
                1.1478764015361142e-05,
                1.5534975693979422e-06,
                0.999978555046496,
                2.902312677150514e-06
            ],
            [
                0.9999998874647977,
                0.9999998724809723,
                0.9999998802069587,
                0.9999998257022045,
                0.9999999715466323,
                0.9999998642567028,
                0.9999997761970248,
                0.9999998874647977,
                0.9999998555020307,
                0.9999999067050943
            ],
            [
                0.9999986290423032,
                0.9999997761971315,
                0.9999998642566542,
                0.9999974387177899,
                0.999997438717485,
                0.9999997463981636,
                0.9999952149066472,
                0.999999057754957,
                0.9999980052698035,
                4.006371129776199e-05
            ],
            [
                0.9999998024947272,
                0.9999998555019963,
                0.9999998802069159,
                0.9999998257021006,
                0.9999999586006442,
                0.9999997761970515,
                0.999999789756634,
                0.9999998724810027,
                0.999999900688043,
                0.9999998802069444
            ],
            [
                0.9999993524053564,
                0.9999999468421312,
                0.9999999123575987,
                0.9999999732705698,
                0.9999993106387082,
                0.999999887464811,
                0.9999998942830107,
                0.999999789756634,
                0.9999998642567189,
                0.9999998724809116
            ],
            [
                0.9999997761972116,
                0.9999998555019619,
                0.9999998461826588,
                0.9999998461827138,
                0.9999999397642437,
                0.9999998024946095,
                0.9999997897566089,
                0.9999998461826038,
                0.9999998724809571,
                0.999999887464932
            ],
            [
                0.9999999067051054,
                0.9999999358794326,
                0.9999999586005949,
                0.999999887464838,
                0.9999999176675437,
                0.9999997761970781,
                0.99999992265575,
                0.9999998802069302,
                0.999999961108895,
                0.99999992265575
            ],
            [
                0.9999999226557131,
                0.9999999500627857,
                0.9999997300421262,
                0.9999999226557869,
                0.9999999656786915,
                0.9999999067050165,
                0.9999993916411087,
                0.9999999067049831,
                0.9999995818812272,
                0.9999998724808964
            ],
            [
                0.9999997897566841,
                0.9999995818811772,
                0.9999998802069873,
                0.9999998024946566,
                0.9999998642566704,
                0.9999998024945624,
                0.9999998362623138,
                0.9999997897567091,
                0.9999997300420939,
                0.9999996940976273
            ],
            [
                0.9999998555020135,
                0.9999997617631186,
                0.9999998724810027,
                0.9999998024946566,
                0.9999998874648782,
                0.999999894282998,
                0.9999999358794479,
                0.9999998802069302,
                0.9999987121047846,
                0.9999999530883397
            ],
            [
                0.9999998362622358,
                0.9999999634651879,
                0.9999996533675028,
                0.9999987121044791,
                0.9999999500628571,
                0.9999999067050498,
                0.9999997897565838,
                0.9999997463982241,
                0.9999994956527724,
                0.9999999067050943
            ],
            [
                0.9999999273418183,
                0.9999998555019619,
                0.9999999273417836,
                0.9999998874649318,
                0.9999997126313441,
                0.9999999123575255,
                0.99999992265575,
                0.9999999226558423,
                0.9999998024946801,
                0.9999997761970248
            ],
            [
                1.7603425837791042e-06,
                0.9999997897565838,
                0.999999674368781,
                0.9999992188512972,
                0.9999998144608319,
                1.5534983101602148e-06,
                2.5612828213934817e-06,
                0.9999990577549569,
                6.144176066850984e-06,
                0.9999996940978095
            ],
            [
                1.067703124601679e-06,
                1.2098652508424818e-06,
                1.5534973842076057e-06,
                1.760343633031919e-06,
                4.785093353940187e-06,
                2.5612834320563895e-06,
                2.902312331170226e-06,
                8.939698435657833e-06,
                3.2887494574518405e-06,
                1.3709576971463352e-06
            ],
            [
                0.9999986290427932,
                0.9999986290432837,
                0.9999964991447523,
                0.9999987901343167,
                0.9999997463981636,
                0.9999997300422226,
                0.9999998942830359,
                0.9999756997592979,
                0.9999999677581375,
                0.9999998942829351
            ],
            [
                0.9999998724810027,
                0.9999995549150543,
                0.9999994631247403,
                0.9999997126315495,
                0.9999996533672137,
                0.9999996310115479,
                0.9999998257021422,
                0.9999998461827138,
                0.9999998024947273,
                0.9999998257021422
            ],
            [
                3.726638395634011e-06,
                2.260324836787226e-06,
                1.994729008145876e-06,
                3.2887506336086064e-06,
                2.5612834320470717e-06,
                7.889266347715168e-06,
                0.9999998257021421,
                0.999954602147785,
                0.9999996940976272,
                6.962255419868303e-06
            ],
            [
                7.338210679949506e-07,
                7.889263526409699e-06,
                2.3823685319244518e-07,
                4.450849988798682e-07,
                1.4449807263287805e-07,
                7.3382080556433e-07,
                4.222834954801051e-06,
                3.726637951387472e-06,
                1.7603440527222532e-06,
                5.043472879504592e-07
            ],
            [
                0.9999999358793639,
                0.9999999006879838,
                0.9999999123575359,
                0.9999999358793867,
                0.9999999656786793,
                0.9999998642566704,
                0.9999997463982241,
                0.999999900688055,
                0.9999999530883172,
                0.9999999611088487
            ],
            [
                0.9999998642566542,
                9.422450431954847e-07,
                5.043473480777865e-07,
                2.699576809143613e-07,
                3.2887478892504536e-06,
                1.9947304348703948e-06,
                3.05902190458764e-07,
                1.0677029973158649e-06,
                1.0677031245990084e-06,
                7.338212429562581e-07
            ],
            [
                1.0129988564716393e-05,
                3.535626335262457e-05,
                5.8291251642512995e-05,
                4.785095065045315e-06,
                2.4300243627117176e-05,
                7.889261645090304e-06,
                0.0001233945748066501,
                4.222832941111319e-06,
                3.72664061681327e-06,
                4.5397852399094525e-05
            ],
            [
                0.9999998642567189,
                0.9999999123574628,
                0.9999999500628393,
                0.9999998362623528,
                0.9999999634651574,
                0.9999998362622553,
                0.9999999434137165,
                0.9999996940978095,
                0.9999999434137368,
                0.9999999317440197
            ],
            [
                0.9999991148432809,
                4.222834954753043e-06,
                2.2603242978778778e-06,
                3.726639728370556e-06,
                0.9999998144609203,
                0.999999802494633,
                0.320821300824607,
                0.9999997761971583,
                0.9999998642566704,
                1.3709572068522336e-06
            ],
            [
                0.9999996072138466,
                2.90231094723893e-06,
                0.9999998555019963,
                0.9999982396567871,
                0.9999999273418876,
                3.726638395634011e-06,
                3.726639728370556e-06,
                2.9023112932177327e-06,
                9.422449308774482e-07,
                0.9999785550490545
            ],
            [
                0.9999999067049831,
                0.9999996072139403,
                0.9999998024946566,
                0.9999998461826038,
                0.9999998642566704,
                0.999999887464811,
                0.9999998555019275,
                0.9999998461826954,
                0.9999999123574419,
                0.9999999176675829
            ],
            [
                0.999999607213753,
                0.9999994956527724,
                0.9999996072136126,
                0.99999916847227,
                0.9999996940978098,
                0.9999999611088534,
                0.9999996310115038,
                0.9999999397643156,
                0.9999999434137636,
                0.9999999559306154
            ],
            [
                0.999999894283061,
                0.9999999500627738,
                0.9999998555019791,
                0.9999998362622747,
                0.9999998942829981,
                0.9999997463981032,
                0.9999982396569976,
                0.9999998874648782,
                0.9999997761970781,
                0.9999998257020798
            ],
            [
                0.9999997300420939,
                0.9999999715466764,
                0.9999998724808964,
                0.9999999006881496,
                0.9999998461826405,
                0.9999996310115479,
                0.9999997463982241,
                0.9999997300421583,
                0.9999998024946095,
                0.9999996072137998
            ],
            [
                0.9999998144608098,
                0.9999998555019446,
                0.999999855502048,
                0.9999998461826588,
                0.9999999123575151,
                0.9999998874648514,
                0.9999998942830358,
                0.9999999067051388,
                0.9999999226558237,
                0.9999998642567028
            ],
            [
                0.9999995262093292,
                0.9999996533672137,
                0.9999985406234314,
                0.9999998257021006,
                0.9999998555019619,
                0.9999983463098231,
                0.9999997761971583,
                0.999999802494586,
                0.9999998802069302,
                0.999999730042126
            ],
            [
                0.9999151889789512,
                8.315277302841894e-07,
                1.4449795205429202e-07,
                0.9999810748562783,
                0.9999038976080912,
                1.3709575336947905e-06,
                8.315281267861397e-07,
                0.9999885212332473,
                0.9982992772822018,
                8.31528424162821e-07
            ],
            [
                2.382368531929327e-07,
                5.043474683220276e-07,
                5.422220909009474e-06,
                7.338208055664991e-07,
                8.315283250371857e-07,
                5.043474081993875e-07,
                3.927860597945825e-07,
                2.699577774585891e-07,
                1.0677026154774503e-06,
                9.422449308716635e-07
            ],
            [
                0.9999995549147891,
                0.9999998724809875,
                0.9999999634651531,
                0.9999998802069302,
                0.9999999358793715,
                0.9999997761971848,
                0.9999994631251242,
                0.9999997463980427,
                0.9999993524048933,
                0.9999999500628155
            ],
            [
                1.7603438428800754e-06,
                6.144174601991196e-06,
                3.726638395634011e-06,
                0.9999832985762298,
                7.889260704968913e-06,
                7.889266347715168e-06,
                4.785092783519724e-06,
                1.760343633031919e-06,
                2.5612819054133693e-06,
                1.3007125363908762e-05
            ],
            [
                0.9999996743687422,
                0.999999428499485,
                0.9999997617630049,
                0.9999998461826956,
                0.9999999656786915,
                0.9999998024945624,
                0.9999996533672963,
                0.9999996743686645,
                0.999999946842163,
                0.9999999317439628
            ],
            [
                0.9999998724809268,
                0.9999998144608319,
                0.9999993106387903,
                0.9999997617631184,
                0.9999999067050498,
                0.9999997617629764,
                0.9999998362623529,
                0.9999998461826771,
                0.9999998461827138,
                0.9999998555019446
            ],
            [
                9.422448185510695e-07,
                9.422450432014836e-07,
                6.9622587397397306e-06,
                1.1478770862735993e-05,
                2.902312677137316e-06,
                7.889264466725156e-06,
                0.999968798084945,
                0.9999869928730883,
                2.3823688159237777e-07,
                2.260323758987159e-06
            ],
            [
                1.147877359926923e-05,
                7.88926070489716e-06,
                3.288749065406658e-06,
                2.4300232043987867e-05,
                8.315280276607289e-07,
                0.999841563764616,
                6.144173137126169e-06,
                0.9999251537550157,
                1.7603438428800754e-06,
                4.785096206047877e-06
            ],
            [
                0.9999885212291435,
                7.889266347636241e-06,
                0.9999967112513275,
                0.9999993916408908,
                2.902312677137316e-06,
                0.9999999358793409,
                1.994730672668496e-06,
                1.7603425837855082e-06,
                3.726639284125553e-06,
                4.785093353940187e-06
            ],
            [
                0.9999997897567091,
                0.9999997463980427,
                0.9999996072139403,
                0.9999996743686644,
                0.9999998555019446,
                0.9999995818813268,
                0.9999996743687033,
                0.9999998802069731,
                0.9999993524053563,
                0.999999814460876
            ],
            [
                0.9999993524048931,
                2.1444958639072976e-05,
                7.338213304316717e-07,
                2.430024362932722e-05,
                1.0129994602656007e-05,
                4.222834451169694e-06,
                1.3709573702722555e-06,
                1.7603434231705793e-06,
                1.3709576971379186e-06,
                2.9023130230846496e-06
            ],
            [
                0.9999982396567872,
                0.9999988634361543,
                0.9999999067051055,
                0.9999996940977002,
                0.99999886343629,
                0.9999997300421261,
                0.9999999176674651,
                0.9999945777823259,
                0.9999999500627976,
                0.9999999176675632
            ],
            [
                0.9999989322967483,
                6.96225873967641e-06,
                4.539789029616496e-05,
                0.9999998144608317,
                6.962259569560613e-06,
                0.9999785550465105,
                2.9023112932177327e-06,
                0.9999998642567028,
                0.9999724643187565,
                0.9999996072139403
            ],
            [
                8.939695238634211e-06,
                2.9023112932177327e-06,
                8.764245361708445e-08,
                1.3709570434054234e-06,
                5.043473480730849e-07,
                1.5534971990126997e-06,
                1.2751910369275402e-07,
                7.338208055579897e-07,
                9.422450431912e-07,
                2.382369667929001e-07
            ],
            [
                0.999999855501979,
                0.9999998555019274,
                0.9999991684718734,
                0.9999997617630332,
                0.999999789756634,
                0.9999997617631184,
                0.9999998257022045,
                0.999999674368781,
                0.9999997617630332,
                0.9999998642567351
            ],
            [
                5.8291244705086375e-05,
                2.5612825160562587e-06,
                5.4222183235249605e-06,
                1.067703379154416e-06,
                0.9999251537728232,
                1.6701415872659116e-05,
                0.9999991684717743,
                2.3823685319244518e-07,
                9.422449308716635e-07,
                0.9999987901344609
            ],
            [
                0.9999995262094987,
                0.9999987901340283,
                5.829127944863308e-05,
                1.9947299592933255e-06,
                0.9999991684720716,
                0.9999997463980124,
                0.9999993524051247,
                4.222835458148261e-06,
                0.9999983463108085,
                0.9999997761970781
            ],
            [
                0.9999999468421376,
                0.9999989969855536,
                0.9999997897565587,
                0.9999998942829854,
                1.0677026154774503e-06,
                5.8291293348093234e-05,
                0.9999999176675239,
                0.9999990577556308,
                0.9999999226557316,
                5.715002426460124e-07
            ],
            [
                6.144176066943187e-06,
                0.9998766053812974,
                2.2603242978871282e-06,
                1.760343633031919e-06,
                3.726639728370556e-06,
                6.1441731370702875e-06,
                0.999998996985912,
                0.9999977396765107,
                0.9999994956525918,
                6.144175334418252e-06
            ],
            [
                0.9999885212346187,
                0.9999989969861511,
                0.9999995818811772,
                0.9999970976876695,
                0.9999986290427934,
                0.9999998555019446,
                0.9999984465028013,
                0.9999982396559475,
                0.9999998024946095,
                0.999996711250935
            ],
            [
                0.9999993106389549,
                0.9999999006880075,
                0.9999999006880312,
                0.999999917667475,
                0.999999922655833,
                0.999999653367255,
                0.9999997300421583,
                0.9999998874647307,
                0.9999994956527722,
                0.9999977396762435
            ],
            [
                4.222833444590791e-06,
                0.999999218851949,
                0.9999999358793484,
                0.999998005270517,
                3.7266410611296085e-06,
                4.785093353940187e-06,
                1.3709568799919866e-06,
                0.9999996310115038,
                1.7603438428800754e-06,
                9.422448185534261e-07
            ],
            [
                0.9999962733616057,
                1.4738988999940381e-05,
                4.222834451355964e-06,
                2.260324836787226e-06,
                1.209866260432471e-06,
                0.9999993106390368,
                1.0129988564845378e-05,
                2.260325106237323e-06,
                8.939695238536645e-06,
                6.144175334418252e-06
            ],
            [
                0.9999998642566866,
                0.9999999006880668,
                0.9999998942829729,
                0.9999999273418528,
                0.9999999226558054,
                0.9999994956523515,
                0.9999998802069444,
                0.9999998362623334,
                0.9999999358793332,
                0.9999998257021837
            ],
            [
                1.5534971990126997e-06,
                2.260325106237323e-06,
                0.9999998642567189,
                0.9999999434137975,
                1.3709572068478697e-06,
                3.7266410611296085e-06,
                8.939694172867777e-06,
                2.5612828213934817e-06,
                0.9999997126314468,
                2.561281905390075e-06
            ],
            [
                0.9999998642567189,
                0.9999999273418355,
                0.9999999067051054,
                0.999999864256719,
                0.9999999067051165,
                0.9999998802069302,
                0.9999999067050276,
                0.9999998461826405,
                0.9999998942829981,
                0.999999495652532
            ],
            [
                2.2603242978778778e-06,
                1.3709567165617364e-06,
                2.2603242978871282e-06,
                1.209865539295696e-06,
                5.422217677078203e-06,
                2.260325106237323e-06,
                1.0129989772274546e-05,
                1.5534979397790343e-06,
                0.9999921107383596,
                6.144176799283803e-06
            ],
            [
                0.9999998942830737,
                0.9999994284996894,
                0.999999814460876,
                0.9999997897566338,
                0.9999993524053563,
                0.9999996533673376,
                0.9999996310115478,
                0.999999712631481,
                0.9999996940978096,
                0.9999999530883843
            ],
            [
                0.9999999559305576,
                0.9999992188512971,
                0.9999999067050053,
                0.9999998642566866,
                0.9999998802069444,
                0.9999995818812769,
                0.9999997897566089,
                0.9999998942830106,
                0.9999999273418788,
                0.9999998942828973
            ],
            [
                0.9999997761971849,
                0.9999993916411085,
                0.9999997126313098,
                0.9999998942830358,
                0.9999995262094987,
                0.9999992188515766,
                0.9999983463100203,
                0.9999997897565838,
                0.9999996310114159,
                0.9999995262095551
            ],
            [
                0.9999997761970515,
                0.9999998642566381,
                0.9999999006881142,
                0.9999998642566704,
                0.9999998144609424,
                0.9999996940978096,
                0.9999997126313098,
                0.9999999006880668,
                0.9999998642567189,
                0.9999998024945624
            ],
            [
                0.9999999273418009,
                0.9999999067050943,
                0.9999999067050053,
                0.9999987121052458,
                0.9999999176674553,
                0.9999999500628631,
                0.9999999530883285,
                0.9999999226557317,
                0.9999998362622943,
                0.9999999358793715
            ],
            [
                0.9999999358793944,
                0.9999998362622357,
                0.9999999468421947,
                0.9999998942830233,
                0.9999999468420996,
                0.9999999397642797,
                0.9999998555019619,
                0.9999999176674848,
                0.9999998942829602,
                0.9999998874647977
            ],
            [
                0.9999999226558054,
                0.9999993916406734,
                0.9999996940978096,
                0.9999999434137165,
                0.9999999358793943,
                0.9999999317439139,
                0.9999999273418615,
                0.9999994631248043,
                0.9999999317439383,
                0.9999999067051499
            ],
            [
                0.9999997463980729,
                0.99999862904263,
                5.715004470313855e-07,
                0.999999855501979,
                0.9999997617630049,
                0.9999998642566542,
                0.9999997617630332,
                0.999999872480942,
                1.553497754577351e-06,
                0.9999998555019791
            ],
            [
                0.9999990577555187,
                0.9999993916408909,
                2.9023133690821773e-06,
                0.9999997617631753,
                0.999995504820033,
                0.9999997463981938,
                0.999999802494633,
                0.9999996310114599,
                0.9999987901347493,
                0.9999996743686644
            ],
            [
                0.9999997761971582,
                0.9999992661788447,
                0.9999998642566381,
                0.9999999123575569,
                0.9999998555020135,
                0.9999998724809571,
                0.9999998724809724,
                0.9999999006880076,
                0.9999997761970515,
                0.9999998874647709
            ],
            [
                0.9999898700114384,
                0.9999921107374169,
                0.999998446501505,
                1.0129987357517693e-05,
                0.999985261023307,
                1.2098661162056318e-06,
                0.9999251537461387,
                0.9999810748585329,
                0.9999997300421904,
                0.9999997617631469
            ],
            [
                0.9999998257021422,
                0.9999997761972116,
                0.9999998724808964,
                0.9999999067049943,
                0.9999998144609645,
                0.9999997463981636,
                0.9999995818813766,
                0.9999997761972116,
                0.999999607213753,
                0.9999998555019274
            ],
            [
                0.9999980052698034,
                0.9999995818811274,
                0.9999997897566589,
                0.999999814460854,
                0.9999977396751646,
                0.9999977396762415,
                0.9999998642566704,
                0.9999987901337397,
                0.9999997126314811,
                0.9999938558275974
            ],
            [
                6.475949526003845e-07,
                5.715002426460124e-07,
                5.715004470295662e-07,
                5.715004470313855e-07,
                5.043475284430694e-07,
                2.5612812947240366e-06,
                1.370957860567974e-06,
                0.9999997463980427,
                7.3382080556433e-07,
                4.450849988798682e-07
            ],
            [
                0.9999999358793409,
                0.9999999067050276,
                0.9999993106389549,
                0.9999998461826772,
                0.9999998144608319,
                0.9999998362623529,
                0.9999999226558053,
                0.9999995818813268,
                0.9999999273418442,
                0.9999999123575568
            ],
            [
                4.222833444590791e-06,
                1.9947299593014888e-06,
                0.9999998724810026,
                0.999983298578182,
                3.726641061109272e-06,
                1.994730672675753e-06,
                0.9999996743687809,
                0.9999999176675535,
                0.9999999067050609,
                2.90231094723893e-06
            ],
            [
                0.9999997300421261,
                0.9999957771650468,
                0.9999972735303806,
                0.9999996310113279,
                0.9999997463980426,
                0.9999995262092727,
                0.9999972735290805,
                0.999999653367503,
                0.9999546021098021,
                0.9999982396561579
            ]
        ]
    },
    {
        "q_id": "9201_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.7603425837903113e-06,
                1.0677026154827912e-06,
                6.1441767993788005e-06,
                1.7603425837903113e-06,
                3.7266383956509585e-06,
                1.3709575337159875e-06,
                6.144175334510455e-06,
                2.561283126728994e-06,
                4.222834954801051e-06,
                4.222833948008874e-06
            ],
            [
                2.102434162245973e-07,
                9.931195693628605e-08,
                3.4663274507713016e-07,
                2.382370235933104e-07,
                2.2603240284371276e-06,
                0.9999983463096261,
                3.466326211113502e-07,
                3.466326211113502e-07,
                6.475946438055299e-07,
                1.6373764721072816e-07
            ],
            [
                9.422450432030903e-07,
                3.288748281329893e-06,
                0.9999990577549573,
                7.338208055680009e-07,
                2.561281294760143e-06,
                2.6995790618469934e-07,
                4.2228319344021954e-06,
                1.0677027427624903e-06,
                1.9947299593078385e-06,
                1.1478766757853845e-05
            ],
            [
                0.9999996940976273,
                9.93120161310289e-08,
                0.9999992188513903,
                8.764244316973974e-08,
                6.825608606172863e-08,
                0.9999997617630049,
                1.8553910183674878e-07,
                2.102434162245973e-07,
                1.8553910183674878e-07,
                2.10243290909963e-07
            ],
            [
                2.1024329090929374e-07,
                9.931189774187203e-08,
                2.1024341622426268e-07,
                1.855391681898159e-07,
                9.931189774187203e-08,
                1.6373772528677946e-07,
                1.209865827740176e-06,
                1.855391681906175e-07,
                1.6373766672888118e-07,
                1.1253517547010071e-07
            ],
            [
                2.9023133690980155e-06,
                1.8553916819032217e-07,
                3.0590215399183813e-07,
                5.715003107738556e-07,
                1.4449796927932878e-07,
                4.450851580555361e-07,
                3.0590237279032884e-07,
                4.450849988811838e-07,
                2.69957906184239e-07,
                3.9278615344178325e-07
            ],
            [
                3.927862470905692e-07,
                0.999999631011592,
                6.825598028392069e-08,
                1.637377057680051e-07,
                3.224188555067886e-08,
                5.043475885696228e-07,
                3.6534838223576766e-08,
                4.139940508508409e-08,
                2.215950777364157e-08,
                3.2241839428313264e-08
            ],
            [
                1.5534973842076057e-06,
                9.422442569334097e-07,
                5.043475885696228e-07,
                4.785095065232451e-06,
                5.715006514176113e-07,
                6.475947982037486e-07,
                4.785092783519724e-06,
                3.05902263391829e-07,
                9.422443692574719e-07,
                1.3709567165617364e-06
            ],
            [
                1.6373774480605869e-07,
                0.9999974387187064,
                0.9999960330131427,
                1.0677028700422047e-06,
                1.5534971990169383e-06,
                6.1441767993788005e-06,
                0.9999974387165691,
                8.939696304311336e-06,
                0.9999964991451697,
                0.999998629043284
            ],
            [
                5.715006514176113e-07,
                2.2603242978871282e-06,
                7.338213304363436e-07,
                5.715002426475718e-07,
                6.475947982037486e-07,
                1.2098662604247682e-06,
                1.2098656835224664e-06,
                2.260324028427877e-06,
                8.315279285370317e-07,
                1.3007123813559956e-05
            ],
            [
                3.9278634073732336e-07,
                0.9999667858131626,
                1.444980726324838e-07,
                3.7266406168827523e-06,
                5.315788140303327e-08,
                0.9999925887183689,
                0.9999892166916552,
                5.829125165990109e-05,
                8.764254764749753e-08,
                0.9999885212305241
            ],
            [
                5.715005151574337e-07,
                3.059022269250683e-07,
                4.222831934379152e-06,
                1.8553919030826963e-07,
                2.6995768091310296e-07,
                1.275190276853036e-07,
                2.1024329090929374e-07,
                5.043472879540142e-07,
                3.927861534406222e-07,
                3.059023727894942e-07
            ],
            [
                0.9999997300421583,
                0.9999997300421906,
                0.9999996533672965,
                0.9999984465024316,
                3.05902263391829e-07,
                0.9999995549149483,
                2.902310947208574e-06,
                2.699578096403948e-07,
                0.9999996533672137,
                0.9999994631247404
            ],
            [
                8.315279285370317e-07,
                7.889264466868659e-06,
                1.7603438428848787e-06,
                2.561282821402217e-06,
                6.475945666063607e-07,
                5.043473480777865e-07,
                1.3709567165617364e-06,
                9.422442569334097e-07,
                6.475949526020042e-07,
                5.715005832895975e-07
            ],
            [
                1.5534979397790343e-06,
                0.9999998555020136,
                0.999999789756684,
                0.9999997126313783,
                3.466326624336003e-07,
                0.9999998461827139,
                0.999998712104632,
                0.9999995549147359,
                0.9999999006880076,
                0.9999987901341729
            ],
            [
                0.9999985406243017,
                3.9278605979534166e-07,
                0.9999997126314468,
                4.1399365603508136e-08,
                0.9999998362622357,
                0.999998126124394,
                0.9999998362622358,
                0.9999916019249692,
                0.9999982396565775,
                0.9999756997650883
            ],
            [
                1.3709576971463352e-06,
                0.9999974387180978,
                5.043472879540142e-07,
                0.9999756997680005,
                0.9999960330136193,
                0.9999974387184026,
                0.9999599362984408,
                0.9999910602994424,
                1.3709575337159875e-06,
                0.9999985406243017
            ],
            [
                0.9999898700054205,
                0.9999977396757033,
                0.9999938558276054,
                0.9999967112505471,
                0.999994577780386,
                0.9999930377404371,
                0.999997273528432,
                0.9999980052698045,
                0.9999978766207804,
                0.9999885212291522
            ],
            [
                3.466325384661554e-07,
                1.2098659719757836e-06,
                4.450852111148132e-07,
                2.699577774585891e-07,
                7.338213304283347e-07,
                1.209865539274514e-06,
                2.6995771309523475e-07,
                3.927860597945825e-07,
                8.315278294072958e-07,
                3.466327450756327e-07
            ],
            [
                1.2098656835224664e-06,
                0.9999687980998587,
                0.9999960330122032,
                6.605212894856585e-05,
                0.999977172008396,
                0.9998415637666284,
                0.999990483744924,
                0.9999877809225595,
                9.422442569315887e-07,
                0.9999910602994488
            ],
            [
                9.422445939054222e-07,
                8.315279285370317e-07,
                7.338207180898968e-07,
                2.699576809143613e-07,
                5.043472278322555e-07,
                5.71500515161527e-07,
                3.927863875616689e-07,
                2.1444956084718052e-05,
                4.450852641737424e-07,
                1.760342793638743e-06
            ],
            [
                8.764241182641775e-08,
                1.1253526937697666e-07,
                1.1253513522447425e-07,
                2.6995784182183607e-07,
                2.699578096403948e-07,
                1.6373764721072816e-07,
                1.6373772528704005e-07,
                1.4449805540763184e-07,
                1.855391681906175e-07,
                2.102434162245973e-07
            ],
            [
                0.9999991148427534,
                0.9999997617631753,
                0.9999861539888556,
                1.2751899728311609e-07,
                1.1861131322303044e-08,
                0.9999991684718736,
                0.9999997300421262,
                0.9999998942830106,
                8.939694172656384e-06,
                0.9999998642566866
            ],
            [
                0.9999969105048166,
                0.9999996310116358,
                3.927863407379485e-07,
                0.9999998144609424,
                8.315278294114555e-07,
                0.9999994631247402,
                8.315284241650899e-07,
                5.715002426486762e-07,
                3.466325797900508e-07,
                0.9999990577551817
            ],
            [
                1.7603425837903113e-06,
                6.475950298021765e-07,
                7.338207180898968e-07,
                4.22283545819819e-06,
                0.9999930377437526,
                4.7850933539684755e-06,
                4.222834451403972e-06,
                1.6373776432509826e-07,
                1.9947292459406333e-06,
                1.6373772528704005e-07
            ],
            [
                0.9999930377404408,
                2.1024334103581732e-07,
                0.9999978766207793,
                0.999995777166558,
                1.0677027427624903e-06,
                3.466326624336003e-07,
                0.9999992661791076,
                0.9999960330126715,
                6.47595107001401e-07,
                5.043472278322555e-07
            ],
            [
                0.9999989322975121,
                8.31527928532683e-07,
                0.9999975938970879,
                0.999997273529082,
                2.382369951932796e-07,
                9.422444815814404e-07,
                1.4449800373118268e-07,
                0.9999987901341731,
                6.47595107001401e-07,
                0.9999949062925773
            ],
            [
                2.6995784182183607e-07,
                6.475945666063607e-07,
                2.3823693839325527e-07,
                2.5612819054133693e-06,
                7.338207180898968e-07,
                1.3709575337159875e-06,
                1.994729483729522e-06,
                1.0677027427624903e-06,
                9.422442569334097e-07,
                1.0677027427624903e-06
            ],
            [
                2.699577774585891e-07,
                0.9999978766210337,
                0.9999991148429649,
                0.9999990577554068,
                2.3823696679327928e-07,
                1.6373766672973748e-07,
                0.9999997897567091,
                0.9999987901340294,
                0.9999986290431216,
                0.9999516743680607
            ],
            [
                0.9997388097542561,
                4.222834451403972e-06,
                0.9999687980849329,
                4.222832437798974e-06,
                0.999994228081351,
                0.9992903296315696,
                2.382369667929001e-07,
                2.2603248367949354e-06,
                0.9999485578048909,
                7.889265407327733e-06
            ],
            [
                0.9999985406234329,
                6.475947210046347e-07,
                0.9999982396565789,
                3.466325384661554e-07,
                0.9999985406230846,
                0.9999987121050936,
                3.059022269250683e-07,
                1.760343213335281e-06,
                0.9999988634365614,
                1.3709578605729614e-06
            ],
            [
                7.338210680021253e-07,
                1.2098659719757836e-06,
                0.9999945777784507,
                0.9999977396748959,
                0.999998790134173,
                0.999995504818426,
                9.422444815792981e-07,
                0.9999989969854342,
                6.475950298011458e-07,
                0.9999967112493676
            ],
            [
                3.05902263391829e-07,
                9.422449308774482e-07,
                0.9999982396563687,
                0.9999984465028022,
                8.315277302857965e-07,
                8.315284241665078e-07,
                0.9999987901346061,
                0.9999999067050609,
                0.9999992188514839,
                8.764251630441717e-08
            ],
            [
                9.422449308774482e-07,
                3.2887506336235617e-06,
                2.561281294760143e-06,
                5.715003789046955e-07,
                4.450852111135988e-07,
                2.902313369111213e-06,
                1.0677032518814388e-06,
                2.2603251062450327e-06,
                7.338208930443633e-07,
                1.4449800373118268e-07
            ],
            [
                0.9999955048194974,
                4.450852111155216e-07,
                2.699578740011634e-07,
                1.7603438428800754e-06,
                4.539786324145319e-05,
                1.760343213335281e-06,
                1.994729008151319e-06,
                8.315278294114555e-07,
                9.422443692574719e-07,
                3.72663883989755e-06
            ],
            [
                0.999999789756659,
                5.715006514176113e-07,
                1.2098656835252174e-06,
                1.6373774480605869e-07,
                6.47595107001401e-07,
                3.466326624336003e-07,
                3.05902263391829e-07,
                3.4663278639892215e-07,
                0.9999970976876732,
                0.9999952149043679
            ],
            [
                2.699577774589574e-07,
                0.9999970976890563,
                0.9999983463096274,
                5.043476486915964e-07,
                2.699578096403948e-07,
                0.9999988634364257,
                0.9999992661787577,
                0.9999983463096269,
                0.9999964991460079,
                0.9999983463100208
            ],
            [
                0.9999982396561579,
                9.931186222523604e-08,
                0.9999969105048179,
                0.9999949062925721,
                0.9999910602994392,
                1.4449802095666915e-07,
                1.8553910183674878e-07,
                0.9999992661788448,
                0.9999986290432842,
                0.9999991148433864
            ],
            [
                3.288748281329893e-06,
                2.2603251062450327e-06,
                5.715003107767143e-07,
                1.2098661162056318e-06,
                9.422445939054222e-07,
                8.315280276626197e-07,
                2.1024331597262577e-07,
                1.5534973842076057e-06,
                6.475947210046347e-07,
                3.466326211113502e-07
            ],
            [
                1.1253524254650944e-07,
                0.9999960330140898,
                0.9999877809254633,
                3.9278605979534166e-07,
                9.422442569334097e-07,
                1.994729483723626e-06,
                4.4508510499849186e-07,
                0.99998329858216,
                0.999978555054253,
                9.422442569334097e-07
            ],
            [
                0.9999945777829732,
                0.999996910505922,
                1.067703124601679e-06,
                0.9999967112509364,
                0.9999969105055541,
                3.9278629391427843e-07,
                0.9999985406230835,
                0.9999969105062905,
                0.9999978766222984,
                0.9999942280799761
            ],
            [
                1.1253506814842375e-07,
                1.8553910183674878e-07,
                1.1253525596174225e-07,
                1.637376862489725e-07,
                1.4449800373118268e-07,
                1.1253509497883659e-07,
                1.1253516205489029e-07,
                1.6373766672973748e-07,
                2.382368815932174e-07,
                1.855390576008354e-07
            ],
            [
                3.466327037548308e-07,
                9.422448185435711e-07,
                5.715006514176113e-07,
                3.059021175261338e-07,
                3.466327863983311e-07,
                6.475948754012522e-07,
                1.0677028700363782e-06,
                3.466327037548308e-07,
                8.315284241650899e-07,
                5.04347287955046e-07
            ],
            [
                0.9999892166878009,
                0.9999904837460583,
                3.7266388398585725e-06,
                0.9999988634362899,
                3.466327037553825e-07,
                0.9999904837471798,
                0.9999981261248414,
                0.9999967112501534,
                0.9999972735300577,
                0.9999975938970889
            ],
            [
                1.6373764721091427e-07,
                0.9999989969855536,
                1.275189972832538e-07,
                1.6373764721091427e-07,
                0.9999972735300587,
                0.9999599362985427,
                1.855390576008354e-07,
                2.699577452775239e-07,
                0.9999987121044782,
                1.275190124846946e-07
            ],
            [
                0.9999985406243014,
                9.931186222523604e-08,
                7.734425919002834e-08,
                1.4449800373118268e-07,
                0.9999998362623723,
                9.931185038635267e-08,
                7.73442776303243e-08,
                5.315789407685159e-08,
                0.9999996533672136,
                9.931200429212718e-08
            ],
            [
                1.7603425837903113e-06,
                2.699578096393206e-07,
                0.9999885212359889,
                0.9999832985821608,
                2.69957906184239e-07,
                0.9999832985722178,
                1.1253518888531272e-07,
                0.9999984465018762,
                1.6373764721072816e-07,
                5.043472278322555e-07
            ],
            [
                1.4738980215352592e-05,
                9.422443692555439e-07,
                2.2603240284371276e-06,
                5.422221555414699e-06,
                3.927862470899887e-07,
                6.47595107001401e-07,
                6.962258739796719e-06,
                4.785093353940187e-06,
                7.338212429582604e-07,
                5.04347528446051e-07
            ],
            [
                3.927861534431675e-07,
                8.939693107288474e-06,
                1.994729721518893e-06,
                1.637377057680051e-07,
                7.889264466868659e-06,
                7.33821330437595e-07,
                1.4738976701652988e-05,
                1.3709575337159875e-06,
                7.338208055680009e-07,
                0.9999599363032282
            ],
            [
                4.4508515805735777e-07,
                0.999999653367338,
                7.338208930460318e-07,
                0.999999310638791,
                2.699578096403948e-07,
                0.9999998257021837,
                3.466325384682834e-07,
                7.33821330437595e-07,
                5.043475885696228e-07,
                6.475950298021765e-07
            ],
            [
                4.450852111155216e-07,
                1.209865539298447e-06,
                3.9278629391427843e-07,
                5.043476486924565e-07,
                6.144176066901277e-06,
                0.9999885212346237,
                3.7266379514061143e-06,
                1.0677026154806063e-06,
                1.994729008151319e-06,
                2.902312331170226e-06
            ],
            [
                1.7603430034867993e-06,
                0.9999952149049399,
                0.9999960330150346,
                0.9999974387187074,
                1.147876812620341e-05,
                1.5534973842076057e-06,
                3.7266379514061143e-06,
                7.734416698849138e-08,
                1.760342793638743e-06,
                1.3007125363908762e-05
            ],
            [
                0.9999980052707549,
                0.9999989969860319,
                0.9999998874647709,
                0.9999996743686645,
                5.3157837044597743e-08,
                6.475946438055299e-07,
                0.9999998724810027,
                0.9999977396759732,
                0.9999994956526521,
                0.9999991148433864
            ],
            [
                2.3823690999323465e-07,
                1.2751902768612997e-07,
                1.8553910183674878e-07,
                0.9999985406230842,
                0.9999967112521143,
                0.9999978766207801,
                5.043472879540142e-07,
                5.043475885696228e-07,
                0.9999982396567889,
                0.9999957771660564
            ],
            [
                0.999998446502246,
                0.9999997300422548,
                0.9999994284995534,
                0.9999984465018763,
                2.561282210740037e-06,
                0.9999949062931822,
                0.9999975938982364,
                0.9999991148428591,
                3.9278634073732336e-07,
                0.9999989322975125
            ],
            [
                5.4222183235249605e-06,
                3.726639284144195e-06,
                2.902312331170226e-06,
                5.715007195447234e-07,
                1.4449798650551755e-07,
                2.90231094723893e-06,
                2.3823685319244518e-07,
                4.006370652067535e-05,
                3.927862002663297e-07,
                1.4449795205429202e-07
            ],
            [
                8.7642558095602e-08,
                0.9999990577554065,
                1.2751901248454963e-07,
                0.9999998257022045,
                1.1253525596174225e-07,
                0.9999998802069159,
                1.8553907971879076e-07,
                1.4449807263312446e-07,
                0.9999977396751647,
                0.9999991684719728
            ],
            [
                4.450851049991497e-07,
                3.4663262111182307e-07,
                7.338208055680009e-07,
                5.043474683240344e-07,
                2.6995784182183607e-07,
                5.715006514176113e-07,
                0.9999997300422871,
                1.6373766672994222e-07,
                0.9999981261237249,
                0.9999974387165727
            ],
            [
                0.9999987901347502,
                0.9999993106390371,
                1.4449798650569826e-07,
                0.999999168471973,
                3.4663249714612693e-07,
                1.4449800373118268e-07,
                7.338208930460318e-07,
                1.855391239547094e-07,
                0.9999980052700425,
                0.9999997300422228
            ],
            [
                0.9999994284995533,
                0.9999977396765116,
                0.9999999067050831,
                0.9999998144609645,
                0.9999998024947038,
                2.3823685319320354e-07,
                0.9999996533672963,
                1.6701423835320418e-05,
                0.9999994956526521,
                0.999998629042794
            ],
            [
                0.9999957771650495,
                1.7603427936263351e-06,
                0.9999984465022477,
                1.4449803818215767e-07,
                0.9999990577557438,
                0.9999985406239543,
                0.9999960330150344,
                0.9999969105048219,
                0.9999969105059275,
                3.288748281329893e-06
            ],
            [
                0.9999756997477344,
                0.9999898700102401,
                1.2751905808881762e-07,
                6.023568448589658e-08,
                8.764247451307293e-08,
                5.715005151606823e-07,
                1.275190276859705e-07,
                2.6995784182140636e-07,
                9.931187406410953e-08,
                0.9999981261237244
            ],
            [
                3.1201922535494165e-05,
                1.9947290081177566e-06,
                7.338208930460318e-07,
                2.9023112932177327e-06,
                0.9999957771650483,
                0.9999957771675699,
                0.9999885212319171,
                0.9999991148427537,
                1.2098659719757836e-06,
                0.9999687980775371
            ],
            [
                0.9999999559305628,
                1.994729483729522e-06,
                0.9999994631248683,
                0.9999992188519491,
                1.0,
                6.144176066901277e-06,
                0.9999992661790198,
                2.561282516066741e-06,
                7.338207180898968e-07,
                4.222834451403972e-06
            ],
            [
                1.2098652508391807e-06,
                1.0677026154774503e-06,
                2.102434162245973e-07,
                1.760344052714248e-06,
                3.466325797888292e-07,
                1.7603425837791042e-06,
                7.734415776836702e-08,
                0.9999982396563679,
                2.6995784182183607e-07,
                1.6373770576776313e-07
            ],
            [
                6.9622595696935874e-06,
                3.059023727894942e-07,
                3.0590215399183813e-07,
                1.2098662604291696e-06,
                1.9947299593014888e-06,
                9.4224425692559e-07,
                4.2228339479858295e-06,
                6.9622595696935874e-06,
                4.222834954778007e-06,
                1.0129987357407137e-05
            ],
            [
                1.8553919030858602e-07,
                2.699578096393206e-07,
                8.764247451307293e-08,
                1.8553907971855875e-07,
                2.902312677137316e-06,
                1.8553910183674878e-07,
                2.382369667929001e-07,
                6.475947982037486e-07,
                2.9023119851899796e-06,
                1.637377057673536e-07
            ],
            [
                3.059022998581767e-07,
                1.0677027427600627e-06,
                8.764253720001207e-08,
                3.0590237279085045e-07,
                1.6701429807964442e-05,
                3.9278629391427843e-07,
                4.4508515805735777e-07,
                8.764254764780641e-08,
                2.3823690999323465e-07,
                1.637376862489725e-07
            ],
            [
                2.10243290909724e-07,
                1.6373766672973748e-07,
                1.855391239547094e-07,
                1.8553907971855875e-07,
                4.450848927658745e-07,
                1.8553919030858602e-07,
                1.637377057680051e-07,
                8.764242227418718e-08,
                2.699577774585891e-07,
                9.931186222523604e-08
            ],
            [
                2.561282515988704e-06,
                2.1024329090929374e-07,
                1.8553910183607374e-07,
                1.6373764721039308e-07,
                4.450850519403407e-07,
                1.6373768624837685e-07,
                2.3823685318968256e-07,
                1.2098652508347793e-06,
                1.8553919030708836e-07,
                1.6373764721072816e-07
            ],
            [
                0.9999980052707566,
                0.9999995262093294,
                0.9999982396561581,
                0.9999985406230841,
                5.715002426486762e-07,
                5.043476486924565e-07,
                0.9999985406239548,
                0.999994577781039,
                0.9999756997680418,
                0.9999978766222992
            ],
            [
                0.9999798543092,
                1.3709573702822306e-06,
                0.9999646437368102,
                1.0677026154730804e-06,
                3.4663249714451116e-07,
                7.338209805200689e-07,
                1.300712846477255e-05,
                7.338211554783522e-07,
                8.315277302841894e-07,
                0.9997694933166732
            ],
            [
                2.9023119851899796e-06,
                2.561281294760143e-06,
                6.475950298021765e-07,
                6.1441767993788005e-06,
                3.726637951387472e-06,
                4.7850933539684755e-06,
                1.7603425837903113e-06,
                2.2603248367949354e-06,
                4.450850519409479e-07,
                3.7266379514061143e-06
            ],
            [
                0.9999921107402433,
                3.927862002663297e-07,
                3.927862002663297e-07,
                1.855391239544352e-07,
                3.9278610661902853e-07,
                0.9999877809283692,
                0.9999934595627845,
                0.9999970976876702,
                8.764244316973974e-08,
                0.9999970976883635
            ],
            [
                3.7266410611296085e-06,
                0.9999942280806718,
                0.9999957771660576,
                5.715003789046955e-07,
                3.288749065423109e-06,
                0.9999930377446044,
                1.2098652508424818e-06,
                2.5612819054133693e-06,
                7.338208055680009e-07,
                1.9947299593078385e-06
            ],
            [
                0.9999997617631184,
                0.9999986290424668,
                0.9999997463980124,
                6.023572038912295e-08,
                4.6911677163762064e-08,
                0.9999991684720716,
                0.9999957771650478,
                0.9999997463980427,
                0.9999952149032261,
                0.9999996310115918
            ],
            [
                0.9999962733611641,
                0.9999991148432811,
                0.9999999006881497,
                0.9999998461826405,
                0.999998996985673,
                3.2241889394209404e-08,
                0.9999969105062908,
                0.9999999434137704,
                0.9999998802068873,
                0.9999998874647843
            ],
            [
                0.9999987121049387,
                0.9999942280799778,
                0.9999978766210331,
                0.9999974387171818,
                0.9999986290432847,
                0.9999852610162889,
                0.9999785550490706,
                0.9999972735300565,
                0.9999982396567887,
                0.9999967112497621
            ],
            [
                0.999998932297258,
                0.9999982396563684,
                0.9999983463102176,
                0.9999998144608097,
                2.6995790618469934e-07,
                1.1253508156363576e-07,
                0.9999993916411086,
                8.7642558095602e-08,
                0.9999970976890568,
                0.9999991148427534
            ],
            [
                1.6373776432509826e-07,
                9.931186222523604e-08,
                1.0677029973219343e-06,
                1.637377057680051e-07,
                1.6373774480479287e-07,
                1.1253514863909295e-07,
                1.4449798650551755e-07,
                8.764244316973974e-08,
                2.382368531929327e-07,
                2.6995771309523475e-07
            ],
            [
                1.444979692797559e-07,
                4.22283545808297e-06,
                1.2751905808881762e-07,
                4.785095065171522e-06,
                2.3823690999160957e-07,
                3.9278634073625165e-07,
                8.31527928532683e-07,
                3.466326211105621e-07,
                5.715002426475718e-07,
                2.1024344128584085e-07
            ],
            [
                3.4663262111182307e-07,
                3.466326624336003e-07,
                1.3709575337159875e-06,
                9.422443692574719e-07,
                1.067703124601679e-06,
                5.715003107767143e-07,
                3.9278629391427843e-07,
                1.5534971990169383e-06,
                2.2603251062450327e-06,
                3.05902336324494e-07
            ],
            [
                4.785095635655362e-06,
                2.561281294760143e-06,
                5.3157830707696514e-08,
                3.9278634073625165e-07,
                4.785094494811783e-06,
                1.6373762769138607e-07,
                1.6373772528704005e-07,
                4.222832437798974e-06,
                1.5534979397677313e-06,
                1.855391460719133e-07
            ],
            [
                0.9999938558268809,
                0.9999964991447565,
                0.9999957771670641,
                0.9999898700078299,
                0.9999885212360063,
                4.4508515805735777e-07,
                4.785096776499213e-06,
                0.999997593898236,
                6.475949526020042e-07,
                0.9999945777790995
            ],
            [
                7.338210680021253e-07,
                1.3709570434178922e-06,
                7.33821330437595e-07,
                2.6995774527718623e-07,
                3.9278629391427843e-07,
                5.715003107767143e-07,
                3.288749457469787e-06,
                3.059021904580685e-07,
                1.855391681906175e-07,
                2.2603240284371276e-06
            ],
            [
                2.102433660979124e-07,
                1.6373770576776313e-07,
                3.288749457469787e-06,
                5.715006514176113e-07,
                8.764242227418718e-08,
                3.059021175261338e-07,
                1.4449807263312446e-07,
                2.699578096393206e-07,
                1.1253522913127183e-07,
                1.1253513522447425e-07
            ],
            [
                0.999998712104939,
                0.9999982396563697,
                0.9999964991443392,
                4.4508515805735777e-07,
                0.9999962733620541,
                3.72663883989755e-06,
                0.9999980052702802,
                0.9999987121050922,
                0.9999977396754353,
                0.9999983463108092
            ],
            [
                4.450852111155216e-07,
                1.6373764721072816e-07,
                5.043474683204221e-07,
                1.6373772528704005e-07,
                1.1253506814842375e-07,
                2.382370235922541e-07,
                6.475947210046347e-07,
                6.475945666063607e-07,
                3.466325384661554e-07,
                9.931186222523604e-08
            ],
            [
                5.715005832853093e-07,
                5.715005151606823e-07,
                5.04347468323289e-07,
                4.450850519403407e-07,
                1.0677026154806063e-06,
                4.450848927650143e-07,
                3.4663262110945863e-07,
                2.902312677150514e-06,
                4.450851049959619e-07,
                1.370957860576702e-06
            ],
            [
                3.726639284125553e-06,
                0.9999989322966213,
                0.9999972735303807,
                0.9999996743688975,
                0.9999930377445828,
                3.466326211113502e-07,
                8.315278294072958e-07,
                0.9999974387187064,
                0.9999930377404336,
                0.9999945777823253
            ],
            [
                2.102433660979124e-07,
                1.209865539295696e-06,
                1.2098655392921197e-06,
                7.338212429562581e-07,
                1.9947304348703948e-06,
                6.144177531811707e-06,
                2.699576809143613e-07,
                3.4663249714451116e-07,
                1.444980209564556e-07,
                2.902312677137316e-06
            ],
            [
                5.422218969895357e-06,
                1.3007130015677909e-05,
                0.9999949062968216,
                1.2098652508424818e-06,
                1.0677024882029858e-06,
                4.222831934352267e-06,
                0.9990889487893869,
                0.9999546021152963,
                0.9999724642958252,
                0.9999910603047694
            ],
            [
                0.9999949062931887,
                3.7266397283908927e-06,
                0.9999977396762444,
                0.9999967112513314,
                0.999998005269567,
                0.9999977396759739,
                2.699578096403948e-07,
                0.9999957771645499,
                5.043476486924565e-07,
                5.715002426486762e-07
            ],
            [
                4.4508515805735777e-07,
                0.9999991684717745,
                0.9999974387168775,
                0.9999984465016913,
                0.999999057755744,
                1.209865827752005e-06,
                0.999999168472072,
                3.4663262111182307e-07,
                0.9999980052705191,
                3.05902263391829e-07
            ],
            [
                0.9999991148433867,
                0.9999993916407461,
                0.9999996940977732,
                0.9999986290426311,
                1.0677026154827912e-06,
                9.422450432014836e-07,
                0.9999984465028023,
                0.9999993916409636,
                3.4663278639892215e-07,
                4.450850519409479e-07
            ],
            [
                1.6373772528704005e-07,
                7.73441946488886e-08,
                1.444979692800516e-07,
                0.9999969105051879,
                9.931189774187203e-08,
                0.9999974387174874,
                0.9999980052709943,
                4.450848927658745e-07,
                1.1253506814842375e-07,
                8.315278294114555e-07
            ],
            [
                2.3823682479292225e-07,
                5.71500719545698e-07,
                0.9999546021206861,
                0.9999898700078241,
                3.726639284144195e-06,
                4.222834451403972e-06,
                2.1024339116168358e-07,
                1.275190124846946e-07,
                5.043476486924565e-07,
                3.466326624336003e-07
            ],
            [
                5.3157837044597743e-08,
                6.023578501491997e-08,
                1.6373774480605869e-07,
                7.734423152941018e-08,
                7.734423152941018e-08,
                6.825602910433871e-08,
                1.855391239547094e-07,
                7.734424996967756e-08,
                6.023572038912295e-08,
                1.6373772528704005e-07
            ],
            [
                0.99999709768871,
                0.9999970976869806,
                0.9999962733620511,
                0.9999962733598314,
                1.5534971990169383e-06,
                0.9999969105059249,
                0.9999984465022461,
                0.9999996533675031,
                0.9999952149049418,
                0.9999957771675664
            ],
            [
                1.0677029973219343e-06,
                5.043475885696228e-07,
                8.315283250394546e-07,
                1.5534981249697903e-06,
                0.9999994284996894,
                0.9999989322971305,
                0.9999988634362899,
                3.927862470905692e-07,
                1.855391681906175e-07,
                3.059021175261338e-07
            ],
            [
                1.855391239544352e-07,
                2.102434412875379e-07,
                1.4449795205457127e-07,
                1.8553907971855875e-07,
                7.734421308914719e-08,
                3.059022998581767e-07,
                2.1024336609843824e-07,
                2.102433660979124e-07,
                9.931195693628605e-08,
                9.931195693628605e-08
            ],
            [
                1.209865827752005e-06,
                1.760343633031919e-06,
                1.5534971990169383e-06,
                6.962256249935742e-06,
                1.3007130015677909e-05,
                3.120192625482384e-05,
                3.535626336072768e-05,
                3.535624650150453e-05,
                8.939700567094277e-06,
                2.9023116392097746e-06
            ],
            [
                5.043473480777865e-07,
                1.3709572068553509e-06,
                5.715004470326849e-07,
                1.1253506814842375e-07,
                0.9999974387187065,
                9.610239210944684e-05,
                5.715003107767143e-07,
                1.444979692800516e-07,
                6.962254589914941e-06,
                3.466325797896173e-07
            ],
            [
                7.338209805200689e-07,
                1.0677024881980089e-06,
                6.475947210012481e-07,
                1.3709576971425944e-06,
                6.144173137126169e-06,
                6.475945666051092e-07,
                6.475948754012522e-07,
                5.043475885674441e-07,
                6.962255419931625e-06,
                7.338209805170655e-07
            ],
            [
                7.338207180898968e-07,
                3.9278605979534166e-07,
                1.3709575337159875e-06,
                6.475950298021765e-07,
                5.043475284468537e-07,
                1.7603425837903113e-06,
                3.4663278639892215e-07,
                3.9278620026686556e-07,
                7.73442776303243e-08,
                1.6373774480605869e-07
            ],
            [
                0.9999646437324821,
                0.9999898700114501,
                0.9999485577803418,
                8.764244316973974e-08,
                1.855391681906175e-07,
                7.338207180898968e-07,
                0.009708475908421799,
                0.9999967112505467,
                0.9999977396765141,
                2.1024334103581732e-07
            ],
            [
                2.10243290909724e-07,
                3.0590219045914655e-07,
                1.4449800373118268e-07,
                4.450850519409479e-07,
                5.043475885696228e-07,
                5.715005832895975e-07,
                1.209865827752005e-06,
                5.71500719545698e-07,
                3.4663266243308805e-07,
                4.450852641737424e-07
            ],
            [
                0.9999990577552946,
                0.9999975938976634,
                0.9999969105062921,
                0.9999994284992807,
                0.9999983463102183,
                0.9999993106392014,
                0.9999994956527124,
                0.9999980052707562,
                0.9999987901338847,
                0.9999987121052463
            ],
            [
                3.0590237279085045e-07,
                0.9999997126313784,
                0.9999993524052021,
                9.422443692574719e-07,
                0.9999996072138467,
                0.999999887464838,
                0.9999989969861516,
                0.9999995549150014,
                0.9999985406243019,
                0.9999994284996896
            ],
            [
                0.9999977396759743,
                0.9999980052705176,
                0.999998005270995,
                0.9999994631251884,
                0.9999972735284329,
                6.825608606172863e-08,
                0.9999970976866367,
                2.6995790618469934e-07,
                0.9999991148428593,
                0.9999977396751658
            ],
            [
                1.2098652508347793e-06,
                6.47594952595231e-07,
                9.422448185435711e-07,
                3.9278615344178325e-07,
                1.0677032518748838e-06,
                7.889266347636241e-06,
                8.315281267834927e-07,
                1.8925150497435443e-05,
                1.147877359957198e-05,
                3.288749849498565e-06
            ],
            [
                9.931196877517082e-08,
                3.224187786361915e-08,
                0.9999998024947272,
                0.9999970976880185,
                3.653479467066246e-08,
                0.9999910603015827,
                1.9555697023957287e-08,
                3.224189323773857e-08,
                2.3823690999323465e-07,
                3.65348425788669e-08
            ],
            [
                1.1253522913127183e-07,
                0.9999984465024312,
                0.9999998942829098,
                0.9999987901344611,
                0.999996711250936,
                6.825609419848033e-08,
                0.9999985406241276,
                0.9999962733602741,
                6.82560616514716e-08,
                0.9999981261237242
            ],
            [
                7.734416698849138e-08,
                1.2751905808881762e-07,
                1.6373766672973748e-07,
                1.275190884913241e-07,
                1.4449795205429202e-07,
                1.855391239544352e-07,
                1.855391239547094e-07,
                1.4449798650551755e-07,
                3.927862002654366e-07,
                7.338208055664991e-07
            ],
            [
                0.9999934595596657,
                0.9999989322971308,
                0.9999852610233412,
                0.9999934595596646,
                0.9999975938982361,
                1.2751905808881762e-07,
                0.9999982396567874,
                0.9999724643057092,
                8.939699501416646e-06,
                0.9999960330145613
            ],
            [
                0.9999942280779116,
                4.785095635655362e-06,
                0.9999995549151074,
                0.9999993916406735,
                0.9999978766210325,
                0.9999955048173546,
                0.9999969105051876,
                0.9999810748450142,
                5.043475885696228e-07,
                0.999995214904369
            ],
            [
                1.2098656835252174e-06,
                0.9999977396746257,
                0.9999962733602771,
                0.9999983463100206,
                2.382369951932796e-07,
                0.9999972735294086,
                0.9999977396751655,
                2.3823696679327928e-07,
                7.734416698849138e-08,
                0.9999969105055558
            ],
            [
                0.9999810748472743,
                0.999997097689054,
                0.9999945777790955,
                3.927863875616689e-07,
                3.653483822348123e-08,
                1.1253509497883659e-07,
                1.275190276859705e-07,
                0.9999975938979478,
                1.6373762769138607e-07,
                1.2751904288710323e-07
            ],
            [
                1.4449800373118268e-07,
                0.9999996940978825,
                1.1861124252524762e-08,
                6.825608606172863e-08,
                0.9999949062937865,
                5.3157811697009444e-08,
                0.9999984465020606,
                0.9999998724809419,
                1.5229984959425487e-08,
                0.9999972735287558
            ],
            [
                1.5534979397790343e-06,
                3.7266410611296085e-06,
                7.889266347786918e-06,
                1.9947301970972664e-06,
                0.9999975938985224,
                2.9023119851899796e-06,
                7.889265407327733e-06,
                4.785093924389007e-06,
                3.72663883989755e-06,
                1.5534971990169383e-06
            ],
            [
                9.422448185534261e-07,
                1.5534977545886537e-06,
                9.422443692574719e-07,
                1.8553919030858602e-07,
                1.3709570434219446e-06,
                5.71500719545698e-07,
                1.8553919030858602e-07,
                5.4222183235249605e-06,
                1.1253516205489029e-07,
                5.422218969895357e-06
            ],
            [
                5.043472879525233e-07,
                7.338208055664991e-07,
                3.535626757524533e-05,
                2.5612825160562587e-06,
                1.6373774480535133e-07,
                5.715003789017068e-07,
                1.8553907971855875e-07,
                5.043474081993875e-07,
                6.475951069985296e-07,
                4.450852111148132e-07
            ],
            [
                2.699576809143613e-07,
                0.9999921107355495,
                4.785094494811783e-06,
                1.5534971990169383e-06,
                0.9999942280806642,
                2.699578096403948e-07,
                2.2603242978871282e-06,
                5.422221555414699e-06,
                5.715003789046955e-07,
                4.785095065232451e-06
            ],
            [
                3.0590237279032884e-07,
                1.0677028700422047e-06,
                3.9278629391427843e-07,
                5.715003107767143e-07,
                5.04347528446051e-07,
                1.8553916819032217e-07,
                1.444979692800516e-07,
                3.059021175247079e-07,
                3.4663249714612693e-07,
                3.0590237279032884e-07
            ],
            [
                0.9999994631250602,
                0.9999998461826956,
                1.27519088491875e-07,
                6.1441767993788005e-06,
                0.9999995818811774,
                1.209866260432471e-06,
                0.9999990577555189,
                1.6373774480605869e-07,
                1.2751899728311609e-07,
                4.450852641737424e-07
            ]
        ]
    },
    {
        "q_id": "9939_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            64,
            105,
            118
        ],
        "rewards": [
            [
                1.0,
                2.3823696679327928e-07,
                4.0063692188981614e-05,
                2.2159499848790667e-08,
                0.9999999468421756,
                0.9999997463980125,
                8.764245361752286e-08,
                2.8453323536912213e-08,
                4.691162124067829e-08,
                0.9999997617630049
            ],
            [
                1.275190732904469e-07,
                2.1024331597288867e-07,
                3.0590237279085045e-07,
                2.1024336609874897e-07,
                2.699578096403948e-07,
                1.8553914607267268e-07,
                2.1024326584639497e-07,
                1.2098661162056318e-06,
                1.855391239547094e-07,
                2.382369951932796e-07
            ],
            [
                0.9999990577555187,
                2.5110002900238917e-08,
                1.1253513522447425e-07,
                0.9999960330126695,
                0.9999974387171797,
                0.9995121429721594,
                0.9999997463980427,
                1.1253508156363576e-07,
                0.999995777165554,
                0.9999485578050175
            ],
            [
                0.9999998724810027,
                0.9999955048195005,
                0.9999999226557962,
                0.9999972735300581,
                6.825609419848033e-08,
                0.9999997300421906,
                0.9999998144609203,
                0.9999996533673378,
                0.9999996940977368,
                0.9999991148429648
            ],
            [
                0.999999900688055,
                0.9999999434137368,
                0.9999992188518559,
                0.9999981261246177,
                0.9999998642567189,
                0.999999825702163,
                0.9999998802069017,
                0.9999999067050054,
                0.9999987901341729,
                0.9999975938968017
            ],
            [
                2.2603240283888175e-06,
                1.2098653950480359e-06,
                3.7266406168827523e-06,
                1.760343423160973e-06,
                8.315277302747361e-07,
                9.422443692527585e-07,
                1.3709568799760888e-06,
                1.5534973841895917e-06,
                9.422445938557184e-07,
                9.422450431989127e-07
            ],
            [
                0.9999999317439546,
                0.9999999123575255,
                0.9999999006880786,
                0.9999999226557962,
                0.9999996072137531,
                0.9999999176675436,
                0.9999999358794249,
                0.9999986290423043,
                0.9999999123575882,
                0.999999631011548
            ],
            [
                0.9999998642566866,
                4.450851580555361e-07,
                3.0590237279032884e-07,
                2.6995784182140636e-07,
                0.9999999067049832,
                0.9999999176675437,
                0.9999999123575987,
                2.1024334103505245e-07,
                2.1024339116082313e-07,
                5.043476486915964e-07
            ],
            [
                9.931185038635267e-08,
                5.04347528446051e-07,
                1.27519088491875e-07,
                1.9947299593078385e-06,
                1.0677029973192638e-06,
                6.825601283086733e-08,
                5.3157830707696514e-08,
                2.5109996913559987e-08,
                3.059022269250683e-07,
                3.059021175261338e-07
            ],
            [
                0.99999926617902,
                0.9999994631247403,
                0.9999992188512973,
                0.9999993916411812,
                0.9999997897566592,
                0.9999998942830233,
                0.999999864256719,
                0.9999998555019619,
                0.9999996743687422,
                1.8553907971855875e-07
            ],
            [
                9.931186222523604e-08,
                4.1399365603508136e-08,
                1.444980209564556e-07,
                5.3157830707696514e-08,
                7.734423152941018e-08,
                9.931194509740267e-08,
                0.9999993524049704,
                4.139935079796334e-08,
                1.8553919030858602e-07,
                1.1253512180925583e-07
            ],
            [
                0.9999982396567886,
                0.9999998942829098,
                0.9999998802069302,
                2.6995774527718623e-07,
                1.4449805540740185e-07,
                1.2751904288710323e-07,
                8.7642516304188e-08,
                0.9999997617630617,
                0.9999998024947273,
                0.9999969105059239
            ],
            [
                0.9999998642567351,
                0.9999992661790197,
                0.9999997300423192,
                8.764244316973974e-08,
                0.9999996310114599,
                0.9999997761971048,
                1.994729008151319e-06,
                7.73442776303243e-08,
                0.9999998461826772,
                0.9999997617630333
            ],
            [
                0.9999997761971317,
                0.999999872480942,
                0.9999998362622553,
                0.9999998724810027,
                0.9999990577551824,
                0.9999998461826406,
                0.9999990577552945,
                0.9999996533673793,
                0.9999996072138937,
                0.9999998144609645
            ],
            [
                5.04347468323289e-07,
                3.05902263391829e-07,
                8.76424013786396e-08,
                3.224185864592658e-08,
                9.931193325852072e-08,
                5.3157837044597743e-08,
                1.1253526937656726e-07,
                1.6373770576776313e-07,
                4.139941002027314e-08,
                1.637377448057981e-07
            ],
            [
                3.927862939126708e-07,
                1.994730197071414e-06,
                5.715003107715166e-07,
                1.760343213322473e-06,
                1.2098655392871682e-06,
                1.2098659719757836e-06,
                5.715005832853093e-07,
                1.3709567165579959e-06,
                1.670141587208191e-05,
                1.7603427936263351e-06
            ],
            [
                3.05902263391829e-07,
                2.1024341622426268e-07,
                6.023569884718319e-08,
                9.931202796993203e-08,
                1.8553919030858602e-07,
                2.382369667929001e-07,
                5.715002426486762e-07,
                2.1024339116168358e-07,
                2.8453323536912213e-08,
                7.734415776836702e-08
            ],
            [
                1.637377448057981e-07,
                3.05902336324494e-07,
                2.10243290909724e-07,
                3.466327037548308e-07,
                7.338212429582604e-07,
                8.764242227418718e-08,
                2.69957906184239e-07,
                6.825600469412533e-08,
                3.927860597945825e-07,
                4.6911638017556955e-08
            ],
            [
                1.8925152754169532e-05,
                2.561281294760143e-06,
                0.9999994284992808,
                2.1444948415296896e-05,
                1.6701415872659116e-05,
                2.2603245673443566e-06,
                1.0677028700422047e-06,
                0.9999991148427536,
                2.9023119851899796e-06,
                1.067703124601679e-06
            ],
            [
                0.999998712105092,
                1.4449802095609418e-07,
                0.9999955048173534,
                0.9999984465026165,
                8.764241182641775e-08,
                0.9999945777823296,
                0.999998346310415,
                0.9999974387180961,
                6.475947982037486e-07,
                0.9999974387171799
            ],
            [
                0.9999996743688586,
                0.999999057755519,
                0.9999969105044496,
                0.999998540623954,
                0.9999970976866358,
                0.9999988634360194,
                0.9999981261252876,
                5.043476486915964e-07,
                1.5534975693933505e-06,
                0.9999992188517628
            ],
            [
                0.999999310639037,
                0.999999814460854,
                0.9999998874647441,
                0.9999998257021215,
                0.9999999273418615,
                0.9999987901346055,
                0.9999996743687811,
                0.9999988634358837,
                0.9999999317440116,
                9.931193325852072e-08
            ],
            [
                0.9999992188512972,
                0.9999997761971315,
                0.9999999226557685,
                1.0,
                0.9999999273418788,
                0.9999999123575151,
                0.9999999434138043,
                0.999999846182604,
                0.9999999317439953,
                6.023573475041126e-08
            ],
            [
                1.275191036933194e-07,
                0.999999872480942,
                0.9999996940977733,
                0.9999998144608984,
                0.9999986290421408,
                2.753568453792444e-05,
                0.9999982396559498,
                8.315278294072958e-07,
                0.9999993916408186,
                0.9999989969859128
            ],
            [
                0.9999999067051166,
                0.9999996072136595,
                0.9999942280813566,
                6.023569884718319e-08,
                0.9999998461827323,
                0.9999993524048935,
                0.9999970976869823,
                0.9999989322970039,
                0.9999998144608098,
                0.9999999067050387
            ],
            [
                1.0677027427569065e-06,
                8.7642516304188e-08,
                6.475949526020042e-07,
                9.237445171872554e-09,
                4.691161005609407e-08,
                0.9999925887201364,
                6.475945666063607e-07,
                2.10243290909724e-07,
                0.9999998642567028,
                4.139939521459479e-08
            ],
            [
                6.825598842065202e-08,
                0.9999991684718736,
                0.9999994631251884,
                0.999996273358942,
                0.9999989322970034,
                0.9999981261237236,
                0.999997438718708,
                0.9999987901340288,
                0.9999986290432848,
                0.9999993524049705
            ],
            [
                4.4508526417298334e-07,
                2.1024326584639497e-07,
                1.2751907329024393e-07,
                4.450848927621807e-07,
                1.9947304348862686e-06,
                3.2887498495150166e-06,
                1.2751907329024393e-07,
                2.2603240284371276e-06,
                1.760343633031919e-06,
                3.927860597935108e-07
            ],
            [
                0.9999999434137434,
                0.9999999358793485,
                0.9999999176675239,
                0.9999999226557592,
                0.9999999434137636,
                0.9999999123574419,
                0.9999998802069302,
                0.9999999006880785,
                0.9999999123575569,
                0.9999999358794097
            ],
            [
                0.9999996940977002,
                0.9999997463981637,
                0.9999997300422548,
                0.9999977396759729,
                0.9999997761970515,
                0.9999996940977732,
                0.9999989969861515,
                0.99999862904214,
                0.9999989969855535,
                0.9999993916408185
            ],
            [
                0.9999998555019446,
                0.9999997761971049,
                0.9999993524051248,
                0.9999998642566866,
                0.9999997463981939,
                0.9999995549148422,
                4.450852111148132e-07,
                0.9999994631248683,
                0.9999993916410361,
                0.9999998024947038
            ],
            [
                3.288748281329893e-06,
                2.902312677150514e-06,
                9.422448185510695e-07,
                1.6701421845361053e-05,
                1.7603438428800754e-06,
                1.994729483729522e-06,
                2.9023109472494878e-06,
                0.997527376933527,
                NaN,
                8.939696304311336e-06
            ],
            [
                0.9999996940978826,
                0.9999999176675731,
                0.9999998874648112,
                0.9999980052695663,
                0.9999999176675338,
                0.9999999123575359,
                0.999999958600659,
                0.9999999067050276,
                0.9999998362623723,
                0.9999999226557685
            ],
            [
                1.1253506814797596e-07,
                4.139938534423022e-08,
                2.3823690999323465e-07,
                1.6373774480605869e-07,
                4.691164920214251e-08,
                1.2751904288710323e-07,
                1.1253518888531272e-07,
                9.931186222523604e-08,
                1.275190276859705e-07,
                1.1253508156317518e-07
            ],
            [
                1.0,
                0.9999962733598329,
                0.9999998642567028,
                0.9999997761971315,
                0.999999894283061,
                1.0,
                0.9999985406234321,
                0.9999998802069159,
                0.9999995262096119,
                0.9999998802069444
            ],
            [
                0.9999599363175109,
                0.9999964991460054,
                0.9999990577552942,
                0.9999981261250643,
                0.9999985406243015,
                6.825606165129312e-08,
                0.999996711251721,
                0.9999993916409636,
                0.999999931743979,
                0.9999998024947037
            ],
            [
                0.9999974387180973,
                0.99999976176309,
                0.999999495652532,
                0.9999998144609202,
                0.9999990577557435,
                0.9999997897567092,
                0.9999999123575882,
                0.9999999006880312,
                2.699578740011634e-07,
                3.0590215399183813e-07
            ],
            [
                0.9999995549150544,
                0.9999998724808964,
                0.9999998461826588,
                0.9999995549147891,
                8.764254764749753e-08,
                0.9999994284993489,
                0.9999998642566542,
                0.9999995549147361,
                6.825598842065202e-08,
                0.9999998642566543
            ],
            [
                0.9999998874648917,
                0.9999993916409637,
                2.382368247924618e-07,
                0.9999998642566543,
                0.9999998362622943,
                0.999999802494633,
                0.9999945777791021,
                0.9999999273418009,
                0.999999864256622,
                0.999999864256719
            ],
            [
                0.9999998874647307,
                2.10243290909724e-07,
                0.999998126125064,
                0.9999990577556311,
                4.139938534423022e-08,
                0.9999981261252872,
                3.466327037548308e-07,
                1.2751908849167202e-07,
                0.9999997463980125,
                9.93120161306789e-08
            ],
            [
                1.4449800373065699e-07,
                3.927863875616689e-07,
                1.6373770576776313e-07,
                1.855391681898159e-07,
                1.6373762769138607e-07,
                1.8553910183674878e-07,
                5.315780536011123e-08,
                7.889261645427538e-06,
                3.0590215398968196e-07,
                3.4663274507713016e-07
            ],
            [
                0.999999428499349,
                0.9999991684722703,
                0.9999984465024316,
                1.444980209564556e-07,
                0.9999977396746262,
                0.9999969105055566,
                0.9999993524052793,
                1.8553919030708836e-07,
                0.9999978766212863,
                0.9999970976876722
            ],
            [
                1.8553910183607374e-07,
                9.931193325852072e-08,
                9.422448185534261e-07,
                3.059022269250683e-07,
                9.931195693628605e-08,
                3.4663249714612693e-07,
                2.3823699519143784e-07,
                2.6995784182140636e-07,
                7.338207180898968e-07,
                6.475947982037486e-07
            ],
            [
                1.4449807263325588e-07,
                5.315784971839039e-08,
                3.4663274507713016e-07,
                4.691164920214251e-08,
                0.9999982396569972,
                3.2241839428313264e-08,
                7.734421308914719e-08,
                5.422221555380179e-06,
                1.275189972832538e-07,
                2.260324836776948e-06
            ],
            [
                4.139935079796334e-08,
                1.9555664386890228e-08,
                5.04347528446051e-07,
                0.999999855502048,
                4.6911638017556955e-08,
                8.764247451307293e-08,
                4.139938534423022e-08,
                3.2241839428313264e-08,
                9.931187406368048e-08,
                5.315780536011123e-08
            ],
            [
                1.2751904288739315e-07,
                9.931193325852072e-08,
                8.764242227418718e-08,
                1.1253518888531272e-07,
                8.764249540862797e-08,
                1.1253518888531272e-07,
                5.3157837044597743e-08,
                6.023576347299818e-08,
                1.6373776432509826e-07,
                1.6373774480605869e-07
            ],
            [
                0.9999998257022045,
                0.9999999500628274,
                0.9999986290426305,
                0.9999981261252874,
                1.4449807263312446e-07,
                0.9999998461827139,
                0.9999998942829854,
                0.9999999317440117,
                0.999999855502048,
                0.9999998257020799
            ],
            [
                1.0677028700422047e-06,
                0.9999977396754341,
                1.0677024882009222e-06,
                2.5612831267202583e-06,
                0.9999987121046322,
                1.7603427936335396e-06,
                0.9999986290426309,
                4.222835458175145e-06,
                6.47595107001401e-07,
                1.5534975693979422e-06
            ],
            [
                1.275190732904469e-07,
                2.69957906184239e-07,
                2.1024336609843824e-07,
                1.2751908849167202e-07,
                1.8553907971855875e-07,
                1.855391681906175e-07,
                2.1024331597262577e-07,
                1.6373770576776313e-07,
                7.338208930460318e-07,
                1.2751908849167202e-07
            ],
            [
                7.734415776836702e-08,
                0.9999998555020135,
                0.9999998362622944,
                0.9999998942829225,
                0.9999999006879957,
                0.9999997463981032,
                0.9999997300422548,
                0.9999998144609424,
                0.9999997617631753,
                0.9999993916409634
            ],
            [
                0.9999992188515768,
                1.3709576971463352e-06,
                6.825602910433871e-08,
                6.023571320847322e-08,
                6.825598842065202e-08,
                1.0677029973219343e-06,
                6.825598028392069e-08,
                1.637377057680051e-07,
                1.4449802095666915e-07,
                9.422447062294175e-07
            ],
            [
                9.93120161310289e-08,
                1.4449807263312446e-07,
                5.3157900413760374e-08,
                1.4449802095666915e-07,
                1.2751902768612997e-07,
                0.9999996743686645,
                0.9999981261243946,
                0.9999999317440116,
                0.9999996940976638,
                0.9999988634358836
            ],
            [
                5.04347468323289e-07,
                1.5534971990126997e-06,
                0.9999987121041712,
                4.785094494783494e-06,
                3.059022269250683e-07,
                0.9999994631250604,
                2.3823696679327928e-07,
                1.6373766672973748e-07,
                1.1253516205489029e-07,
                1.1253517547010071e-07
            ],
            [
                0.999999802494633,
                0.9999993524051249,
                2.511001487368099e-08,
                1.4449807263312446e-07,
                0.9999983463106122,
                7.734415776836702e-08,
                0.9999998942828973,
                0.9999998024946566,
                0.9999987901343169,
                2.8453367631661124e-08
            ],
            [
                0.9999998802069302,
                0.9999998802069731,
                0.9999998802069445,
                0.999999880206916,
                0.9999991148432811,
                0.9999998642566866,
                0.9999997300423192,
                0.999999789756634,
                0.9999995549149483,
                0.9999998461826223
            ],
            [
                0.9999988634366963,
                2.69957906184239e-07,
                0.9999996072138,
                0.9999989969860321,
                0.9999974387177908,
                0.9999998144609424,
                0.9999995549150013,
                0.9999975938965167,
                0.9999984465018763,
                0.9999967112509374
            ],
            [
                0.9999999176675731,
                7.734421308914719e-08,
                6.825602910433871e-08,
                0.9999998461826771,
                1.4449798650551755e-07,
                6.825606165129312e-08,
                8.764242227418718e-08,
                0.9999997463980427,
                9.931190958076104e-08,
                1.6373774480605869e-07
            ],
            [
                0.9999996072138,
                0.9999997761970782,
                0.9999962733593883,
                0.999999761763147,
                0.9999997463981637,
                0.9999996533674204,
                0.9999995818810776,
                0.999999864256719,
                9.931189774187203e-08,
                0.999999761763005
            ],
            [
                0.9999998802069587,
                0.9999996743687812,
                0.9999998724809724,
                0.9999994284997581,
                0.9999998724809268,
                0.9999998802069731,
                0.9999995549148954,
                0.9999997463981637,
                0.999999631011328,
                1.444980209564556e-07
            ],
            [
                0.9999999530883787,
                1.0,
                0.9999998642567351,
                1.0,
                0.999999927341801,
                1.0,
                0.9999999176674945,
                0.9999998724810027,
                0.9999998874647977,
                0.9999998642566381
            ],
            [
                1.147876812538911e-05,
                1.3709567165617364e-06,
                4.785095635655362e-06,
                1.9947301970972664e-06,
                5.715005151606823e-07,
                5.829127939137956e-05,
                8.315284241650899e-07,
                4.785096776499213e-06,
                3.927862002663297e-07,
                1.7603427936079236e-06
            ],
            [
                6.023579219579052e-08,
                3.466326624336003e-07,
                1.2098652508391807e-06,
                6.82560779249779e-08,
                5.3157887739943563e-08,
                4.1399400149893274e-08,
                1.1253524254650944e-07,
                5.315788140303327e-08,
                3.65348425788669e-08,
                3.466326624336003e-07
            ],
            [
                6.825597214718257e-08,
                5.043475885696228e-07,
                1.1253513522447425e-07,
                8.764245361752286e-08,
                9.931202796993203e-08,
                1.1478770862735993e-05,
                3.9278634073732336e-07,
                1.8553907971855875e-07,
                7.734424996967756e-08,
                6.825600469412533e-08
            ],
            [
                1.6373768624837685e-07,
                6.144173869558639e-06,
                1.8553916819032217e-07,
                6.825604537781398e-08,
                1.0129990979842057e-05,
                6.144174601879434e-06,
                9.931185038635267e-08,
                8.764244316973974e-08,
                0.9999994631247403,
                7.734423152941018e-08
            ],
            [
                0.9999998024946567,
                0.9999999006880431,
                0.9999997300421261,
                0.9999998257021006,
                0.9999996743687422,
                0.9999999530883396,
                0.9999997761971582,
                0.9999998555020481,
                0.999999653367255,
                0.9999999006880904
            ],
            [
                0.9999998802069444,
                0.9999999123574524,
                0.9999996940978096,
                0.9999991684717745,
                0.9999997761971049,
                0.9999996072138936,
                0.999999814460854,
                0.9999991148426481,
                0.9999997617631753,
                0.9999989969860317
            ],
            [
                0.9999999226557409,
                0.9999991148428591,
                0.9999998802069302,
                0.9999999397642078,
                0.9999998874648246,
                0.9999985406243019,
                0.9999996072138467,
                0.9999998942829981,
                0.9999998874647441,
                0.9999989322971305
            ],
            [
                4.139941002027314e-08,
                9.931199245292204e-08,
                5.315780536011123e-08,
                3.4663249714612693e-07,
                9.931193325852072e-08,
                0.9999996743688975,
                0.9999998461827322,
                3.2241847115356483e-08,
                0.9999996940978098,
                3.653484693415755e-08
            ],
            [
                0.9999983463100209,
                0.9999991148427538,
                0.9999999123574942,
                0.9999999273418269,
                0.9999999006881259,
                0.9999997126314468,
                0.9999999226557962,
                0.9999998555019619,
                0.9999998461826038,
                0.9999998802069445
            ],
            [
                1.5534975693979422e-06,
                2.260324028404236e-06,
                2.2603248367656408e-06,
                1.3709578605729614e-06,
                2.5612812947077304e-06,
                1.5534983101478522e-06,
                5.715004470326849e-07,
                1.3709567165530083e-06,
                5.715003107767143e-07,
                4.785092783415276e-06
            ],
            [
                0.9999998942829098,
                0.9999997463980426,
                0.9999990577550696,
                0.999999943413784,
                0.9999980052705173,
                1.0,
                0.9999998461826405,
                4.139938534423022e-08,
                0.9999992188519491,
                0.9999999226558053
            ],
            [
                0.9999996533674204,
                0.9999998024947038,
                0.9999998642566866,
                0.9999996940977733,
                0.9999995818811278,
                0.9999994631251884,
                0.9999994956525322,
                0.9999998461826038,
                0.9999994631251246,
                0.9999998362623529
            ],
            [
                6.825598028392069e-08,
                0.9999967112493694,
                1.2751910369275402e-07,
                0.9999982396567874,
                0.9999990577557434,
                0.9999998257021006,
                0.9999998362623138,
                0.9999990577556311,
                0.9999975938968008,
                0.9999942280813587
            ],
            [
                1.8553905760024476e-07,
                0.9999998461826038,
                0.9999996940977002,
                0.9999980052705176,
                0.999999581881277,
                0.999998712104478,
                1.2098661161982042e-06,
                0.9999995549147891,
                1.2751899728286965e-07,
                0.9999981261239475
            ],
            [
                1.2098653950656417e-06,
                1.5534983101478522e-06,
                6.475948754012522e-07,
                1.8925141473978602e-05,
                5.043475885674441e-07,
                1.3709575337078829e-06,
                8.315281267861397e-07,
                7.889262585814522e-06,
                1.5534975693792215e-06,
                1.0677027427525368e-06
            ],
            [
                3.059023363221292e-07,
                1.5534983101602148e-06,
                6.82560128305259e-08,
                9.931202796957073e-08,
                0.9999996743686257,
                0.9999987901340287,
                0.9999975938985223,
                0.9999996940978098,
                0.9999999317439546,
                1.5534979397740895e-06
            ],
            [
                0.9999989969857935,
                0.9999969105062909,
                0.9999998555019791,
                9.931193325852072e-08,
                4.691162683297406e-08,
                0.9999984465015066,
                0.9999986290424672,
                0.9999980052705187,
                2.1024331597152624e-07,
                0.9999994956524719
            ],
            [
                6.023579219579052e-08,
                2.3823702359290413e-07,
                6.825601283086733e-08,
                2.1024336609874897e-07,
                1.1253525596174225e-07,
                6.825597214718257e-08,
                3.059021175261338e-07,
                9.931195693628605e-08,
                3.0590215398968196e-07,
                1.3709575337159875e-06
            ],
            [
                0.9999991684717743,
                0.9999999273418269,
                0.9999999317439465,
                1.0,
                0.9999980052709935,
                0.9999992661792823,
                0.9999999226557776,
                0.999999900688055,
                0.9999994284992807,
                4.139935079796334e-08
            ],
            [
                0.9999994284997576,
                0.9999978766220472,
                0.9999981261241714,
                0.9999992661792826,
                8.764245361708445e-08,
                0.9999983463110066,
                0.9999997463981939,
                0.9999998144608541,
                0.9999981261246179,
                0.9999991684719727
            ],
            [
                0.9999998144608983,
                0.9999998461826772,
                0.9999984465016909,
                0.999999814460876,
                0.9999995262095551,
                0.9999993106390369,
                0.9999997300423192,
                0.999999057755631,
                0.999997739675165,
                0.9999994956527725
            ],
            [
                0.9999998802069731,
                0.9999999317439384,
                1.855391681906175e-07,
                0.9999977396757035,
                0.9999998362623724,
                6.825604537781398e-08,
                0.9999998555019963,
                0.9999999176675338,
                3.2241847115356483e-08,
                1.27519088491875e-07
            ],
            [
                0.9999999067050387,
                0.999999943413757,
                0.9999999273418616,
                6.825597214718257e-08,
                0.9999999317439627,
                0.9999999358793714,
                0.9999999226558238,
                0.9999999500627798,
                0.9999999358793409,
                0.9999999317439627
            ],
            [
                0.9999996072136593,
                0.999999917667524,
                0.9999998642566543,
                0.9999999226558423,
                0.99999743871718,
                0.9999987901346056,
                0.9999995818812771,
                0.9999996072138466,
                0.999999922655833,
                0.9999991148433864
            ],
            [
                0.9999991148426481,
                6.475949526020042e-07,
                2.1024339116168358e-07,
                6.023574911170301e-08,
                1.1253526937697666e-07,
                7.734426841017797e-08,
                2.382370235933104e-07,
                7.734426841017797e-08,
                1.1253516205489029e-07,
                8.764254764780641e-08
            ],
            [
                0.9999999123574523,
                0.9999996940978096,
                0.9999999006881142,
                0.9999981261241708,
                0.9999999226558423,
                0.9999984465015052,
                0.9999997897565588,
                1.0,
                0.9999999006880668,
                0.9999986290431209
            ],
            [
                1.0,
                0.9999995262094987,
                0.9999962733602743,
                0.9999998802068873,
                1.0,
                0.9999975938976615,
                0.9999985406241281,
                0.9999998555020307,
                0.9999999273418703,
                0.9999999176675534
            ],
            [
                3.059022269254856e-07,
                9.931189774187203e-08,
                1.6373764721072816e-07,
                2.902312677150514e-06,
                0.9999990577554068,
                1.8553914607267268e-07,
                1.4449800373118268e-07,
                6.475950298021765e-07,
                5.315786239218605e-08,
                8.764249540862797e-08
            ],
            [
                0.9999980052707568,
                0.999999730042287,
                2.3823696679327928e-07,
                7.734428685047173e-08,
                0.9999987901340289,
                2.260325106237323e-06,
                0.999997876622298,
                0.9999949062968241,
                1.1253509497883659e-07,
                8.315279285351409e-07
            ],
            [
                0.9999942280806642,
                0.9999952149066509,
                9.422447062240614e-07,
                0.999999931743979,
                0.9999997617631184,
                0.9999999317439302,
                0.9999999358794479,
                0.999999917667475,
                5.043472278299047e-07,
                0.9999999226558423
            ],
            [
                1.553497384196656e-06,
                0.9999978766207802,
                0.9999974387184051,
                0.999988521231923,
                0.9999996533672966,
                1.2098653950656417e-06,
                1.99472924590571e-06,
                6.475950297993789e-07,
                1.0677026154774503e-06,
                1.7603425837791042e-06
            ],
            [
                0.999999653367255,
                3.0590229985449037e-07,
                1.6373774480535133e-07,
                0.9999993524053566,
                0.9999992661786697,
                1.1253509497835043e-07,
                2.38237023590304e-07,
                0.9999978766217917,
                0.9999996940978826,
                0.9999997761971849
            ],
            [
                2.1024336609874897e-07,
                6.825604537781398e-08,
                3.466326624336003e-07,
                1.2751907329024393e-07,
                6.825598028392069e-08,
                9.931185038635267e-08,
                1.637376862489725e-07,
                1.855391681906175e-07,
                1.6373774480605869e-07,
                1.4449807263287805e-07
            ],
            [
                0.9999998257021006,
                0.9999999530883843,
                0.9999998724809267,
                0.9999998144608981,
                0.9999998024946801,
                6.475948753991907e-07,
                0.9999998802069159,
                0.9999999176674357,
                3.9278605979534166e-07,
                0.9999996743687034
            ],
            [
                0.9999999226558515,
                0.9999999176675731,
                0.9999997897566841,
                0.9999995262092729,
                0.9999980052700421,
                1.0,
                9.931198061405701e-08,
                0.9999993106392013,
                0.9999999176675338,
                0.9999997463981636
            ],
            [
                0.9999998257021214,
                0.9999999123575881,
                0.9999994956523515,
                0.9999995549149482,
                0.9999999226558054,
                0.9999994631249324,
                0.9999996743686257,
                3.466327450765785e-07,
                0.9999995262095553,
                0.9999999123575359
            ],
            [
                6.023578501513224e-08,
                7.734421308914719e-08,
                1.8553914607267268e-07,
                7.734428685047173e-08,
                7.734416698849138e-08,
                2.102434412875379e-07,
                6.023569884718319e-08,
                7.734418542875216e-08,
                2.1024334103581732e-07,
                4.691159887151251e-08
            ],
            [
                7.734415776836702e-08,
                4.691168275606451e-08,
                8.76424013786396e-08,
                2.3823696679327928e-07,
                1.27519088491875e-07,
                6.825604537781398e-08,
                5.3157830707696514e-08,
                1.0,
                4.691162124067829e-08,
                6.023572038912295e-08
            ],
            [
                0.9999998724808964,
                0.9999998802069302,
                0.9999999067049943,
                0.999999931743979,
                0.9999998942829854,
                0.9999942280792884,
                0.9999993524054337,
                0.9999999123575046,
                0.9999987121043243,
                0.9999999559305891
            ],
            [
                1.8553919030776337e-07,
                1.8553914607267268e-07,
                9.931202796957073e-08,
                1.8553916819032217e-07,
                1.6373772528704005e-07,
                1.5534975693979422e-06,
                3.466327037548308e-07,
                3.466327450756327e-07,
                9.931195693628605e-08,
                3.0590237279085045e-07
            ],
            [
                3.0590226339061185e-07,
                2.6995790618469934e-07,
                0.9999997761970782,
                0.9999993106389549,
                0.999998790134173,
                0.9999992188513904,
                0.9999999500627798,
                9.931198061405701e-08,
                0.9999988634362902,
                3.927863875616689e-07
            ],
            [
                7.734423152941018e-08,
                0.9999997897567092,
                7.73442776303243e-08,
                8.764253720001207e-08,
                0.999999846182604,
                0.9999989322970035,
                0.9999998144608541,
                0.9999998257022046,
                0.9999996940977367,
                0.9999999067049831
            ],
            [
                1.275190276859705e-07,
                0.999999746398194,
                0.9999983463102176,
                1.275190884913241e-07,
                0.9999985406241276,
                1.275190884913241e-07,
                0.99999963101146,
                0.999995777165553,
                0.9999985406230842,
                0.9999997897566341
            ],
            [
                0.9999997897566841,
                1.0,
                1.0,
                0.9999998802068873,
                1.0,
                0.9999999634652097,
                1.0,
                0.9999995549148953,
                0.9999998802068873,
                0.9999999358794479
            ],
            [
                0.9999995549151075,
                0.9999999434137301,
                0.9999994956526521,
                0.9999999468421249,
                0.9999999397642508,
                0.9999988634362899,
                0.9999993524050476,
                0.9999985406237802,
                0.9999998461826405,
                0.999999814460854
            ],
            [
                1.275190428875671e-07,
                5.3157887739943563e-08,
                8.315277302857965e-07,
                8.7642526752214e-08,
                7.734425919002834e-08,
                3.653484693415755e-08,
                1.275190580890061e-07,
                5.043474683240344e-07,
                4.6911677163762064e-08,
                2.510997296685283e-08
            ],
            [
                4.785092783519724e-06,
                5.043476486924565e-07,
                2.1444945858953813e-05,
                1.1478772231232203e-05,
                1.7603430034867993e-06,
                1.2098659719788098e-06,
                8.939694172957213e-06,
                5.715005832886879e-07,
                1.1478770862882149e-05,
                6.475950298011458e-07
            ],
            [
                0.9999997463981939,
                0.999998932296622,
                0.9999998144608983,
                0.9999994956527122,
                0.9999996533672963,
                0.9999993106386261,
                0.9999957771680725,
                0.9999998144608098,
                0.9999996743687034,
                0.9999997126313784
            ],
            [
                0.9999998802069444,
                0.9999998362622358,
                0.9999997617630333,
                0.9999960330145603,
                0.9999998724809723,
                0.999999887464771,
                0.9999999067051499,
                0.9999998144609424,
                0.9999994956525319,
                0.9999999358794479
            ],
            [
                0.9999998257021837,
                0.9999998461827139,
                0.9999998555019274,
                0.9999996743686645,
                0.9999997617630901,
                0.9999997897565839,
                0.999999931743914,
                0.9999998362623138,
                0.9999992661786702,
                0.9999998724809875
            ],
            [
                0.9999998461826772,
                0.9999999006880312,
                0.9999999067050832,
                0.9999999123574733,
                0.9999998874648246,
                0.9999904837505857,
                0.9999999468421756,
                0.9999990577551818,
                0.9999999397642652,
                0.9999993106386259
            ],
            [
                6.023572038912295e-08,
                2.3823696679327928e-07,
                3.9278605979534166e-07,
                4.450851049991497e-07,
                1.1253525596174225e-07,
                4.691164920214251e-08,
                5.71500719545698e-07,
                1.275190580890061e-07,
                2.3823696679327928e-07,
                2.1024331597288867e-07
            ],
            [
                0.9999997761970515,
                0.9999999317439546,
                6.023577783447482e-08,
                0.9999999123574732,
                0.9999999226557225,
                0.9999999273418442,
                0.9999999176675044,
                0.999999927341801,
                0.9999999067050943,
                0.9999999226558054
            ],
            [
                6.825606165129312e-08,
                0.9999994631248683,
                6.023569884718319e-08,
                6.825600469412533e-08,
                3.2241847115356483e-08,
                8.764249540862797e-08,
                5.315786239218605e-08,
                1.6373762769138607e-07,
                5.3157830707696514e-08,
                8.764243272157922e-08
            ],
            [
                0.9999999530883675,
                9.931193325852072e-08,
                2.845333032070409e-08,
                1.2751899728286965e-07,
                2.6995784182140636e-07,
                9.931193325852072e-08,
                1.2751908849167202e-07,
                6.825602910433871e-08,
                1.2751901248454963e-07,
                1.1861129908347455e-08
            ],
            [
                0.9999962733607168,
                0.9999967112509373,
                5.3157811697009444e-08,
                0.999999864256719,
                0.9999999434137571,
                0.9999998144608983,
                0.9999993106391195,
                0.9999998555019963,
                8.764251630441717e-08,
                0.9999997126314126
            ],
            [
                0.999999352405048,
                0.9999993106386266,
                0.9999969105055555,
                7.338208055664991e-07,
                0.999998446501506,
                0.9999994631247405,
                0.9999995262092165,
                0.9999987121047859,
                4.53978902983119e-05,
                0.999998346310613
            ],
            [
                0.9999997126315155,
                0.9999999468421946,
                0.9999996072136127,
                0.9999999067050387,
                0.9999991148427536,
                0.9999997897567091,
                0.9999999226557224,
                0.9999998874648648,
                0.9999993524051248,
                0.9999992188518563
            ],
            [
                1.0,
                0.9999999123575882,
                0.9999997897566089,
                1.0,
                0.9999999559305524,
                0.9999998802069587,
                0.9999999358793562,
                0.9999999468421312,
                0.9999999530883732,
                0.9999999067051388
            ],
            [
                0.9999975938968022,
                0.9999977396765128,
                0.9999982396559498,
                0.9999957771645462,
                0.9999978766205271,
                0.9999989969856734,
                0.999997876620526,
                0.999999428499349,
                5.715003789033962e-07,
                0.999998126125065
            ],
            [
                1.1253508156363576e-07,
                2.6995771309523475e-07,
                1.6373776432509826e-07,
                1.6373772528704005e-07,
                3.653484693415755e-08,
                2.1024329090929374e-07,
                1.5534984953552536e-06,
                1.370957860576702e-06,
                1.0677029973219343e-06,
                4.4508515805735777e-07
            ],
            [
                7.73441946488886e-08,
                0.9999997300422225,
                0.9999997463981938,
                4.450852641737424e-07,
                4.691161005609407e-08,
                1.8553916819032217e-07,
                0.9999996743687034,
                4.691168275606451e-08,
                1.8553910183674878e-07,
                0.9999998144609424
            ],
            [
                0.9999999176674357,
                0.9999998144608098,
                0.9999997761971049,
                1.1253520230052635e-07,
                0.9999999434137098,
                0.9999999468421377,
                0.9999999397642222,
                0.9999998642567351,
                0.9999998555019619,
                0.9999999273418703
            ],
            [
                0.9999997617631184,
                0.9999999067050943,
                0.9999999559306312,
                0.9999997761970248,
                0.9999985406237797,
                0.999999887464744,
                0.9999997126315496,
                0.9999997617631753,
                8.764243272157922e-08,
                0.9999999397642078
            ],
            [
                0.9999998942830863,
                0.9999989322972584,
                0.9999974387168757,
                0.999999526209386,
                0.9999997897567092,
                0.9999982396565786,
                0.9999998874648649,
                0.9999998144609205,
                1.8553916819032217e-07,
                0.9999974387174868
            ],
            [
                2.6995768091310296e-07,
                4.139941495546278e-08,
                1.6373772528704005e-07,
                7.734417620828269e-08,
                1.2751908849088918e-07,
                2.382370235933104e-07,
                1.2751905808881762e-07,
                3.2241881707064475e-08,
                1.1253518888531272e-07,
                8.764242227418718e-08
            ],
            [
                0.9999995549148952,
                0.9999995818811773,
                0.9999997126313784,
                0.9999996533673791,
                0.9999999006881142,
                0.9999999067050721,
                0.9999998024945624,
                0.9999998144608099,
                0.9999998144609203,
                0.9999993106386261
            ],
            [
                4.139939521459479e-08,
                2.1024336609874897e-07,
                1.6373774480605869e-07,
                5.315786239218605e-08,
                1.4449802095666915e-07,
                6.825600469412533e-08,
                6.825602910433871e-08,
                5.315784971839039e-08,
                3.05902190458764e-07,
                6.023572038912295e-08
            ]
        ]
    },
    {
        "q_id": "9508_mmlu_physics",
        "cot_ids": [
            3,
            7,
            8,
            11,
            14,
            17,
            18,
            19,
            20,
            29,
            31,
            33,
            34,
            35,
            36,
            41,
            43,
            44,
            45,
            46,
            47,
            48,
            59,
            60,
            61,
            67,
            69,
            71,
            77,
            78,
            79,
            81,
            82,
            84,
            86,
            87,
            91,
            92,
            93,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            110,
            112,
            113,
            115,
            117,
            119,
            122,
            123,
            124,
            125
        ],
        "rewards": [
            [
                3.288747889178668e-06,
                1.5534973842030142e-06,
                8.315283250371857e-07,
                8.315284241597959e-07,
                1.8925145985104064e-05,
                1.2098662604192665e-06,
                3.72664061681327e-06,
                1.2098659719757836e-06,
                3.1201911375578156e-05,
                5.71500651413193e-07
            ],
            [
                5.04347468323289e-07,
                6.962256249885085e-06,
                8.481107172292919e-05,
                5.422220262636381e-06,
                7.338208930460318e-07,
                7.484624512911504e-05,
                5.4222176771176554e-06,
                6.475947209953583e-07,
                8.939700566907275e-06,
                1.2098652508424818e-06
            ],
            [
                1.5534981249574276e-06,
                1.7603434231705793e-06,
                1.553498124964492e-06,
                1.5534977545603963e-06,
                1.0677024881980089e-06,
                9.422448185388577e-07,
                NaN,
                1.5534983101393749e-06,
                9.422447062202052e-07,
                3.7266406168403854e-06
            ],
            [
                3.7266379514061143e-06,
                2.6995784182073116e-07,
                3.466326211113502e-07,
                3.05902263389638e-07,
                9.931198061405701e-08,
                3.059022998576899e-07,
                4.450850519403407e-07,
                2.699578096403948e-07,
                5.04347468323289e-07,
                4.4508494582405734e-07
            ],
            [
                9.422450431989127e-07,
                1.0677033791583005e-06,
                6.475947982002148e-07,
                3.288749457469787e-06,
                3.4663249714451116e-07,
                3.927862939126708e-07,
                6.475950297971703e-07,
                9.422442569315887e-07,
                3.0590237279032884e-07,
                3.466327037548308e-07
            ],
            [
                1.4738987243236881e-05,
                NaN,
                4.0063677865600476e-05,
                3.2887502415438413e-06,
                1.670141786325573e-05,
                4.78509392429544e-06,
                3.7266388397721442e-06,
                1.4738989000181669e-05,
                6.1441731370702875e-06,
                1.7603427935342762e-06
            ],
            [
                1.0677028700363782e-06,
                1.3709578605617394e-06,
                6.475951069985296e-07,
                5.715005151574337e-07,
                2.902311639183378e-06,
                2.260324028427877e-06,
                1.9947304348595095e-06,
                3.726638395634011e-06,
                9.422449308774482e-07,
                1.3709570434178922e-06
            ],
            [
                7.734428685047173e-08,
                1.6373774480535133e-07,
                8.764249540862797e-08,
                0.9999898700066286,
                1.4449795205429202e-07,
                3.0590226338838606e-07,
                1.275190732904469e-07,
                2.6995771309523475e-07,
                0.9999810748585739,
                5.715005832886879e-07
            ],
            [
                6.475949526020042e-07,
                1.0677032518785256e-06,
                3.9278634073625165e-07,
                5.71500515159253e-07,
                3.0590215399246414e-07,
                1.0677026154806063e-06,
                3.0590215399183813e-07,
                9.422448185510695e-07,
                2.1024341622426268e-07,
                1.7603438428800754e-06
            ],
            [
                4.006369219233375e-05,
                3.535624649751729e-05,
                1.4738987242432592e-05,
                4.222835458044565e-06,
                6.962258739530771e-06,
                1.4738985485461206e-05,
                8.939693106873817e-06,
                NaN,
                6.144172404587612e-06,
                2.144495608222158e-05
            ],
            [
                1.7603438428740716e-06,
                4.4508494582405734e-07,
                5.422220262636381e-06,
                1.0677033791612137e-06,
                5.043472879540142e-07,
                2.260325106237323e-06,
                1.6701425827133152e-05,
                1.7603440527286572e-06,
                8.315283250371857e-07,
                3.288747889284851e-06
            ],
            [
                1.7603427936335396e-06,
                2.260324028427877e-06,
                9.422448185510695e-07,
                2.9023130231176453e-06,
                6.475946438042047e-07,
                1.553498124964492e-06,
                2.260324836776948e-06,
                3.726639284125553e-06,
                1.0677027427569065e-06,
                8.31527928532683e-07
            ],
            [
                7.338208055664991e-07,
                1.0677032518785256e-06,
                9.422442569315887e-07,
                1.7603440527046419e-06,
                2.2603248367656408e-06,
                4.450851049959619e-07,
                3.927862939113312e-07,
                3.9278615344178325e-07,
                4.4508505193932864e-07,
                1.760344052714248e-06
            ],
            [
                5.715007195447234e-07,
                1.3007134667259441e-05,
                7.889265407090955e-06,
                1.6701423835624208e-05,
                5.04347287955046e-07,
                2.9023112931873767e-06,
                1.994729008145876e-06,
                4.222831934352267e-06,
                2.5612822107167428e-06,
                7.338211554758494e-07
            ],
            [
                1.7603436330179102e-06,
                1.3709576971425944e-06,
                5.715005832827105e-07,
                1.4738985485997396e-05,
                NaN,
                2.260325106237323e-06,
                5.422217030663578e-06,
                1.370957860567974e-06,
                7.338209805224048e-07,
                5.422219616228845e-06
            ],
            [
                3.4663249714451116e-07,
                3.46632497145457e-07,
                2.3823690999236795e-07,
                2.382368815916736e-07,
                3.46632497145457e-07,
                3.927862002641863e-07,
                5.043476486915964e-07,
                8.315284241650899e-07,
                3.466325797888292e-07,
                5.715007195447234e-07
            ],
            [
                1.855391239544352e-07,
                4.450852111155216e-07,
                2.6995784182140636e-07,
                2.1024336609843824e-07,
                3.059022998576899e-07,
                2.1024331597262577e-07,
                2.1024331597262577e-07,
                8.315284241597959e-07,
                1.1253518888531272e-07,
                3.05902263389638e-07
            ],
            [
                2.902312677137316e-06,
                1.994729245917502e-06,
                2.561283432035425e-06,
                3.726641061058432e-06,
                8.315283250305684e-07,
                3.288748673360027e-06,
                4.785096776468749e-06,
                1.2098661161927025e-06,
                8.315280276546789e-07,
                6.144177531660828e-06
            ],
            [
                2.2603253756956754e-06,
                2.2603245673155757e-06,
                4.785095065204162e-06,
                2.5612819053399912e-06,
                3.927863407379485e-07,
                9.422443692574719e-07,
                NaN,
                5.71500719545698e-07,
                1.444979692800516e-07,
                1.3709576971463352e-06
            ],
            [
                2.6995790618469934e-07,
                5.043475885674441e-07,
                3.059022998576899e-07,
                4.450852111148132e-07,
                3.927862939126708e-07,
                1.6373762769138607e-07,
                2.10243290909724e-07,
                6.475947981975644e-07,
                5.715005832886879e-07,
                7.338211554783522e-07
            ],
            [
                4.222833947932061e-06,
                2.2603253756874524e-06,
                4.785093353909723e-06,
                1.2098658277451275e-06,
                1.0677028700130727e-06,
                4.539785782605375e-05,
                3.726641061109272e-06,
                2.1444943302181958e-05,
                3.2887494574518405e-06,
                1.9947304348703948e-06
            ],
            [
                1.370957860576702e-06,
                1.8553910183607374e-07,
                3.05902190458764e-07,
                1.2098662604291696e-06,
                6.144172404738491e-06,
                4.4508494582405734e-07,
                5.043472879540142e-07,
                3.927862470899887e-07,
                8.315282259138311e-07,
                3.72663883989755e-06
            ],
            [
                5.144222592963322e-05,
                3.12019225345861e-05,
                6.144177531381426e-06,
                7.889265407090955e-06,
                1.7603434231777837e-06,
                2.144494330116777e-05,
                5.715005832886879e-07,
                2.7535697664698622e-05,
                6.475950297942253e-07,
                1.0677029973192638e-06
            ],
            [
                7.889265407004852e-06,
                1.9947301970972664e-06,
                1.670142382493073e-05,
                5.715007195447234e-07,
                9.422442569315887e-07,
                7.338211554801876e-07,
                4.2228319341064674e-06,
                1.3007128461507534e-05,
                7.889261645427538e-06,
                1.7603438428800754e-06
            ],
            [
                1.855391681906175e-07,
                5.043475885696228e-07,
                3.9278634073732336e-07,
                3.0590226339061185e-07,
                5.04347468323289e-07,
                2.3823688159291947e-07,
                5.715003107755449e-07,
                1.855391239544352e-07,
                8.315279285351409e-07,
                1.6373764721072816e-07
            ],
            [
                1.9947297215043796e-06,
                1.0677032518748838e-06,
                1.2098662604247682e-06,
                3.927862002663297e-07,
                9.422445939032799e-07,
                3.059023363221292e-07,
                1.2098653950656417e-06,
                3.46632497145457e-07,
                3.288747889284851e-06,
                5.71500515159253e-07
            ],
            [
                2.699578096393206e-07,
                2.6995768091383957e-07,
                4.4508526417298334e-07,
                2.699576809143613e-07,
                2.3823682479292225e-07,
                5.715004470326849e-07,
                2.699576809143613e-07,
                7.338211554801876e-07,
                1.1478765389368729e-05,
                2.102433660979124e-07
            ],
            [
                1.0677028700363782e-06,
                1.0677028700363782e-06,
                8.315281267861397e-07,
                5.715005832886879e-07,
                8.31528424162821e-07,
                7.338208055664991e-07,
                5.715003789033962e-07,
                3.9278615344178325e-07,
                1.7603440527222532e-06,
                7.338207180864763e-07
            ],
            [
                6.475948754012522e-07,
                3.288747889229516e-06,
                8.315281267834927e-07,
                6.144173137126169e-06,
                7.889259764445822e-06,
                1.3709567165530083e-06,
                4.450850519403407e-07,
                1.0677028700363782e-06,
                2.561282210729555e-06,
                2.5612812947508257e-06
            ],
            [
                5.71500651413193e-07,
                8.315281267882195e-07,
                9.422444815792981e-07,
                6.475945666051092e-07,
                2.6995790618350237e-07,
                2.6995790618350237e-07,
                6.475947210012481e-07,
                5.71500515159253e-07,
                3.927862470861484e-07,
                3.9278610661822475e-07
            ],
            [
                1.7603434231833873e-06,
                8.315280276546789e-07,
                9.422448185435711e-07,
                1.5534971990126997e-06,
                3.927862002606139e-07,
                6.475951069985296e-07,
                5.043474683204221e-07,
                2.2603234895289998e-06,
                5.043472879481655e-07,
                5.04347468318358e-07
            ],
            [
                6.475945666051092e-07,
                8.7642516304188e-08,
                1.0677029973219343e-06,
                2.382369667929001e-07,
                6.475951069985296e-07,
                3.927860597945825e-07,
                3.05902190458764e-07,
                3.46632497145457e-07,
                4.4508510499849186e-07,
                1.9947301970972664e-06
            ],
            [
                2.902310947208574e-06,
                4.785095635624897e-06,
                7.338213304196583e-07,
                6.1441731370702875e-06,
                7.889266347715168e-06,
                3.12019150949065e-05,
                1.1478768126057254e-05,
                3.120190765625026e-05,
                6.962256249821764e-06,
                3.120191137126484e-05
            ],
            [
                6.962254589978262e-06,
                8.93970056668775e-06,
                4.450848927658745e-07,
                9.422447062294175e-07,
                4.222832437747125e-06,
                1.3709567165530083e-06,
                NaN,
                3.7266410611296085e-06,
                5.71500515151976e-07,
                1.5534971990126997e-06
            ],
            [
                5.043473480777865e-07,
                1.4449807263312446e-07,
                1.0677029973192638e-06,
                2.69957906184239e-07,
                8.31528424162821e-07,
                1.1253512180925583e-07,
                5.715005151606823e-07,
                8.315284241597959e-07,
                6.475951070002966e-07,
                2.6995774527718623e-07
            ],
            [
                6.475949525981759e-07,
                1.3709570434178922e-06,
                4.222834954778007e-06,
                3.288748281329893e-06,
                5.043473480766399e-07,
                1.6373768624837685e-07,
                5.715003789046955e-07,
                6.475951070002966e-07,
                9.422443692446175e-07,
                1.5534984953510149e-06
            ],
            [
                NaN,
                1.2098659719757836e-06,
                1.4738976701170414e-05,
                1.2098656835224664e-06,
                0.9999706884519323,
                1.8925155009767892e-05,
                1.8925150497848527e-05,
                1.0677029973192638e-06,
                0.9999977396757079,
                0.9999925887228126
            ],
            [
                5.715007195410849e-07,
                1.9947292459265734e-06,
                5.043475885674441e-07,
                2.2603237589542675e-06,
                3.2887478892683997e-06,
                8.315278294038928e-07,
                2.902310947208574e-06,
                1.0677032518785256e-06,
                5.043474683204221e-07,
                1.0677029973158649e-06
            ],
            [
                NaN,
                1.5534984953453635e-06,
                8.315283250371857e-07,
                2.9023119851781017e-06,
                3.059022998576899e-07,
                1.0129992187658463e-05,
                1.7603436330259153e-06,
                4.2228319344021954e-06,
                5.715003107755449e-07,
                7.338209805224048e-07
            ],
            [
                1.0677032518748838e-06,
                1.0677027427600627e-06,
                1.5534971990126997e-06,
                9.422442569315887e-07,
                5.04347468318358e-07,
                1.6373774480535133e-07,
                NaN,
                1.9947301970972664e-06,
                3.059021904559123e-07,
                6.475947981975644e-07
            ],
            [
                8.939695238333382e-06,
                1.6701425826191394e-05,
                5.043475885674441e-07,
                NaN,
                5.4222183235249605e-06,
                8.939695238333382e-06,
                4.785093924362895e-06,
                NaN,
                4.785095065204162e-06,
                7.889261645355786e-06
            ],
            [
                3.288749849477628e-06,
                2.5612816000646084e-06,
                3.2887498495150166e-06,
                1.7603432133296774e-06,
                1.2098656835076114e-06,
                6.9622587396067566e-06,
                2.260325375664839e-06,
                4.785095065132354e-06,
                2.9023109472244114e-06,
                2.9023130231176453e-06
            ],
            [
                7.338211554783522e-07,
                3.0590226339061185e-07,
                3.059023727894942e-07,
                7.338209805224048e-07,
                8.315279285351409e-07,
                2.260324567337161e-06,
                1.855391681898159e-07,
                5.422220262636381e-06,
                6.475945666051092e-07,
                5.715003789046955e-07
            ],
            [
                NaN,
                7.889266347636241e-06,
                1.0677029972993568e-06,
                3.120191137659974e-05,
                7.484623620850474e-05,
                3.726641061085547e-06,
                6.9622587397397306e-06,
                4.222834954778007e-06,
                1.6701419854156377e-05,
                2.2603245673155757e-06
            ],
            [
                5.4222209089700225e-06,
                1.9947292459347367e-06,
                1.0677024881980089e-06,
                7.338212429537553e-07,
                8.315281267800897e-07,
                7.338213304283347e-07,
                2.5612831267202583e-06,
                4.222834954778007e-06,
                NaN,
                1.7603430034743913e-06
            ],
            [
                1.553497754577351e-06,
                3.288749065423109e-06,
                2.2603242978871282e-06,
                3.2887478892504536e-06,
                1.994729245917502e-06,
                2.260325375664839e-06,
                2.5612831266946347e-06,
                1.5534973841895917e-06,
                3.2887482812745586e-06,
                1.0677028700363782e-06
            ],
            [
                5.043476486915964e-07,
                1.5534971990126997e-06,
                1.8553919030858602e-07,
                8.315283250371857e-07,
                1.209865539295696e-06,
                3.288749849477628e-06,
                4.222832941142044e-06,
                1.7603438428460541e-06,
                1.0677027427600627e-06,
                2.5612825160096693e-06
            ],
            [
                5.715003789046955e-07,
                1.0677028700422047e-06,
                1.9947299593014888e-06,
                NaN,
                7.338208930460318e-07,
                1.9947299593078385e-06,
                1.3709576971425944e-06,
                1.3709568799919866e-06,
                2.2603251062450327e-06,
                9.422445939054222e-07
            ],
            [
                3.927862470899887e-07,
                2.260323758987159e-06,
                9.422448185534261e-07,
                3.0590226339061185e-07,
                7.338209805224048e-07,
                8.315278294097538e-07,
                4.4508510499849186e-07,
                1.0677032518814388e-06,
                3.0590226339061185e-07,
                7.338209805224048e-07
            ],
            [
                4.2228339479858295e-06,
                3.4663249714451116e-07,
                1.3709573702778664e-06,
                3.288749457469787e-06,
                4.4508505193932864e-07,
                1.3709567165617364e-06,
                4.450850519403407e-07,
                2.260325106237323e-06,
                2.561282516042282e-06,
                1.2098661162023305e-06
            ],
            [
                9.422448185534261e-07,
                8.315281267882195e-07,
                4.450852111148132e-07,
                5.043473480777865e-07,
                1.0677033791612137e-06,
                2.5612812947508257e-06,
                1.5534977545886537e-06,
                2.3823690999236795e-07,
                8.939694172957213e-06,
                1.3709572068522336e-06
            ],
            [
                2.5612812947077304e-06,
                1.3709576971061233e-06,
                1.0677029972993568e-06,
                5.422217030614265e-06,
                6.144173869312763e-06,
                3.288749457432399e-06,
                1.7603436329978976e-06,
                9.422447062094932e-07,
                1.760344052632596e-06,
                4.785096205882502e-06
            ],
            [
                8.315281267834927e-07,
                3.7266401726359486e-06,
                3.288747889178668e-06,
                2.5612819054028872e-06,
                1.3709568799760888e-06,
                1.6701421845057263e-05,
                1.0677024881980089e-06,
                1.5534981249697903e-06,
                6.144173136952939e-06,
                1.3709573702822306e-06
            ],
            [
                5.422219616184461e-06,
                4.2228324377164004e-06,
                8.939694172770212e-06,
                7.338208055664991e-07,
                5.043475885606781e-07,
                1.5534981249574276e-06,
                1.5534973841895917e-06,
                1.1478766757561534e-05,
                5.422217030747413e-06,
                6.475948754012522e-07
            ],
            [
                3.466327037539638e-07,
                1.4449798650551755e-07,
                3.927862939126708e-07,
                1.994729721482609e-06,
                4.450852111148132e-07,
                2.382368815916736e-07,
                5.715005832853093e-07,
                3.7266410611296085e-06,
                2.699578740011634e-07,
                9.422445939054222e-07
            ],
            [
                4.450850519403407e-07,
                1.760343003481596e-06,
                1.3709572068522336e-06,
                6.475947210031623e-07,
                1.3709576971425944e-06,
                2.3823696679230424e-07,
                8.315284241650899e-07,
                1.760343003481596e-06,
                5.71500515159253e-07,
                1.5534971990126997e-06
            ]
        ]
    },
    {
        "q_id": "9404_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999994284993488,
                0.9999998362622552,
                1.0,
                0.9999646437619967,
                0.9999996533674617,
                0.9999996072136594,
                0.9999998461826405,
                0.9999997617631184,
                0.9999997761970515,
                0.9999990577552943
            ],
            [
                2.1024341622086862e-07,
                7.734425918979532e-08,
                3.05902226923399e-07,
                1.275190580884987e-07,
                1.1253508156363576e-07,
                4.450849988798682e-07,
                3.9278624708775595e-07,
                3.4663262110630603e-07,
                1.4449805540763184e-07,
                1.6373764721091427e-07
            ],
            [
                1.0677032518700286e-06,
                3.466327863983311e-07,
                6.144176799334096e-06,
                1.0677027427525368e-06,
                4.2228349547223175e-06,
                2.561282210740037e-06,
                3.726637951367137e-06,
                1.7603438428800754e-06,
                1.9947304348595095e-06,
                9.422450432014836e-07
            ],
            [
                0.9999975938979503,
                0.9999991148431756,
                0.9999997761970516,
                0.9999970976866326,
                7.338209805240734e-07,
                0.9999997463982241,
                0.9999983463096269,
                0.9999998024946095,
                0.999999789756609,
                0.9999998724809875
            ],
            [
                0.9999998555019446,
                1.0,
                0.9999999397642293,
                0.9999992188518563,
                0.9999999067051055,
                0.9999999634651617,
                0.9999999530883564,
                0.999999946842163,
                1.0,
                0.9999999226557592
            ],
            [
                0.9999998144609424,
                0.9999999468421059,
                0.9999999176674651,
                0.9999994631251883,
                1.0,
                1.0,
                1.0,
                0.9999999006880786,
                0.9999999500628453,
                0.999999631011416
            ],
            [
                0.999999953088362,
                0.9999998555019275,
                0.9999970976880189,
                0.9999999397642867,
                1.0,
                0.9999998144609203,
                0.9999997126313441,
                0.9999995262092164,
                0.9999999067050943,
                0.9999998802069873
            ],
            [
                0.9999945777784526,
                0.999997097689055,
                0.9999988634357482,
                0.9999916019309839,
                0.999999746398194,
                0.9999969105048191,
                0.9999991148431756,
                0.999998346310415,
                0.9999987901340288,
                0.9999993524054338
            ],
            [
                0.9999998362623334,
                1.4449795205429202e-07,
                0.9999997126315496,
                0.9999998144608762,
                0.9999998024946802,
                0.9999997300422548,
                0.9999986290432847,
                0.9999998642566705,
                0.9999998362622358,
                0.9999993524048932
            ],
            [
                0.9999998802069302,
                0.999999969711584,
                0.999999653367255,
                0.9999998555019275,
                0.9999999226557685,
                0.9999997617631469,
                0.9999998461827322,
                0.999999631011416,
                1.0,
                0.9999810748517892
            ],
            [
                1.0,
                0.9999999273418095,
                0.9999999677581336,
                0.9999999586006245,
                0.9999999397642868,
                0.9999999397643012,
                0.9999999559306154,
                1.0,
                0.9999999559306312,
                0.9999999468421503
            ],
            [
                0.999999965678708,
                0.9999998642566543,
                0.9999832985741949,
                0.9999989322968759,
                0.9999999434137434,
                0.9999992661792825,
                1.0,
                0.9999999559305576,
                0.9999999611088951,
                0.9999997463981636
            ],
            [
                0.9999982396561586,
                0.9999989322970038,
                0.9999904837471915,
                3.535625914363812e-05,
                0.9999992661789326,
                0.9999964991468419,
                0.999999352405048,
                0.9999987901340291,
                0.9999995262094988,
                0.9999960330126756
            ],
            [
                6.475950298021765e-07,
                3.5356267573959116e-05,
                1.6373764721039308e-07,
                3.9278634073732336e-07,
                3.05902190458764e-07,
                1.8553905760024476e-07,
                2.6995768091383957e-07,
                1.6373768624837685e-07,
                1.1253506814797596e-07,
                1.994730197090463e-06
            ],
            [
                0.9999992661786704,
                0.9999980052693299,
                1.6373766672973748e-07,
                0.9999993106390372,
                0.9999978766205287,
                0.9999975938979508,
                1.4449805540740185e-07,
                0.9999930377412893,
                0.9999970976883669,
                0.999997876620783
            ],
            [
                0.9999999778405028,
                0.9999991684720718,
                0.9999998942829477,
                0.9999998642566219,
                0.999999953088362,
                1.0,
                0.9999990577556311,
                0.999999939764215,
                0.9999999358794173,
                1.0
            ],
            [
                0.9999998362623723,
                0.9999996743687034,
                0.9999998257021214,
                0.9999999067051054,
                0.9999999176674651,
                0.9999999123575151,
                0.9999999176674454,
                0.9999999123574838,
                0.999999900688055,
                0.9999997617630617
            ],
            [
                0.9999998724809572,
                0.9999998642567351,
                0.9999995549150543,
                0.9999997761971583,
                0.9999999468421249,
                0.9999998555019619,
                0.9999999500628631,
                0.999999922655833,
                1.0,
                0.9999997617630334
            ],
            [
                0.9999997897565588,
                3.466327450765785e-07,
                0.9999999226557684,
                0.9999996072137999,
                0.9999999067051054,
                0.9999910603058358,
                0.999999674368781,
                0.9999995262092163,
                0.9999994284997575,
                0.9999996310114159
            ],
            [
                0.9999998802069587,
                0.9999998874648782,
                0.9999990577552943,
                0.9999998942830611,
                0.9999999634651748,
                0.9999980052709927,
                0.9999998144609424,
                0.9999992661791947,
                0.9999999067049831,
                0.9999998461826772
            ],
            [
                0.9999972735303917,
                0.9999993524052799,
                0.9999942280772346,
                0.9999974387174951,
                0.9999980052698058,
                0.9999949062968477,
                1.2098652508391807e-06,
                0.9999969105044536,
                0.9999967112517266,
                0.9999934595651323
            ],
            [
                7.338210680021253e-07,
                6.475950298011458e-07,
                0.9999999176674651,
                0.9999991684716751,
                1.3709576971425944e-06,
                1.9947304348862686e-06,
                0.999999802494633,
                6.1441746020359e-06,
                2.9023112932177327e-06,
                6.475945666051092e-07
            ],
            [
                7.338210680021253e-07,
                1.9947299592933255e-06,
                1.8925145985895816e-05,
                1.5534971990126997e-06,
                1.300712536408621e-05,
                6.475947210046347e-07,
                6.9622587397397306e-06,
                9.422443692555439e-07,
                7.338211554783522e-07,
                4.53978632394714e-05
            ],
            [
                0.9999995818813767,
                0.9999995262094987,
                0.9999986290431205,
                0.999999922655833,
                0.9999999176675535,
                0.99999976176309,
                0.9999998802069445,
                0.9999998724808964,
                0.9999995262092163,
                0.9999997300421583
            ],
            [
                0.9999999273418355,
                0.9999997897565839,
                0.9999993524051249,
                0.9999999226558515,
                0.9999998461826405,
                0.9999999006880904,
                0.9999998024947037,
                0.9999998257021422,
                0.9999987901341731,
                0.999999946842144
            ],
            [
                0.9999997761970248,
                1.0,
                0.9999995262093292,
                0.9999999530883675,
                1.0,
                0.9999999697115912,
                0.9999999123575046,
                0.9999996072137999,
                0.9999999434137772,
                1.0
            ],
            [
                1.8553919030858602e-07,
                1.1253526937697666e-07,
                7.338209805240734e-07,
                1.6373774480605869e-07,
                2.1024339116168358e-07,
                3.05902263391829e-07,
                2.1024334103581732e-07,
                1.8553914607267268e-07,
                2.6995790618469934e-07,
                1.125351083940518e-07
            ],
            [
                0.9999998257021631,
                0.9999996533674617,
                0.9999997617631469,
                0.9999998024945624,
                0.9999998362623334,
                0.9999996533675032,
                0.9999998802069587,
                0.9999999317440198,
                0.9999999397642653,
                0.9999980052705181
            ],
            [
                2.6995790618469934e-07,
                3.0590237279085045e-07,
                1.855391681898159e-07,
                8.7642558095602e-08,
                3.059022998581767e-07,
                2.102434162245973e-07,
                2.102434412875379e-07,
                2.1024336609874897e-07,
                3.0590215399183813e-07,
                3.4663278639892215e-07
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999530883732,
                0.9999999468421059,
                0.9999999273418183,
                0.9999999586006492,
                1.0,
                0.9999999748900001,
                1.0
            ],
            [
                0.9999993524050478,
                0.9999994284995533,
                0.9999997617630901,
                0.9999972735290811,
                0.9999998024946567,
                0.9999995818812273,
                0.999999939764258,
                0.9999997617630618,
                0.9999993106390371,
                0.9999996310115481
            ],
            [
                0.9999999067051499,
                0.999999922655833,
                0.9999999067051276,
                0.999999581881277,
                0.9999997126315153,
                0.9999998555019619,
                0.9999999123574836,
                0.9999999273418788,
                0.9999999317440035,
                0.9999997761971582
            ],
            [
                0.9999999176674651,
                0.9999998024946801,
                0.9999999317439546,
                0.999999825702059,
                0.9999998724809116,
                0.9999998724808964,
                0.9999998362623138,
                0.9999999559305839,
                0.999999894282935,
                0.9999998802069017
            ],
            [
                0.9999996072137062,
                0.9999996310115039,
                0.9999989969856731,
                9.422444815792981e-07,
                0.9999995262092164,
                1.5534984953510149e-06,
                0.9999960330131419,
                1.209866260432471e-06,
                0.9999995262093858,
                0.9999898700126502
            ],
            [
                0.9999999006880194,
                0.9999998802069302,
                0.99999992265575,
                0.9999999434137233,
                0.9999998724809268,
                0.9999999656787284,
                0.9999998642566543,
                0.9999999226557778,
                0.9999999067050609,
                0.9999998802069159
            ],
            [
                0.9999999006880431,
                0.9999999123574942,
                1.4449802095666915e-07,
                0.9999998802069587,
                2.6995771309523475e-07,
                3.059021904580685e-07,
                0.9999997126313783,
                0.9999998874648917,
                0.9999986290421402,
                0.9999998642567028
            ],
            [
                1.0,
                1.0,
                0.9999998874647709,
                0.9999998555019963,
                0.999999887464744,
                0.9999996533674204,
                0.9999999530883174,
                0.9999999468421059,
                0.9999999123575674,
                0.9999987121043244
            ],
            [
                0.9999998362623528,
                0.9999998874647575,
                0.9999995818810776,
                0.9999998461827139,
                0.9999999358794402,
                0.9999999559305787,
                0.999997097688016,
                0.9999999067050721,
                0.9999999176675535,
                0.9999999530883731
            ],
            [
                0.9999998942829981,
                0.9999997761970781,
                0.999999825702059,
                0.9999998024947037,
                0.9999997300422548,
                0.9999995818812771,
                0.9999998461827322,
                0.9999998642567028,
                0.9999998362622748,
                0.9999997300422548
            ],
            [
                1.209866260432471e-06,
                1.5534981249697903e-06,
                3.927862002663297e-07,
                2.561282516066741e-06,
                1.2098656835224664e-06,
                5.715004470313855e-07,
                1.3709567165579959e-06,
                2.2603245673279107e-06,
                2.9023119851899796e-06,
                6.475951069985296e-07
            ],
            [
                5.715005832886879e-07,
                4.450852111135988e-07,
                3.288749457469787e-06,
                6.475950298011458e-07,
                2.5612819054028872e-06,
                1.3709572068422585e-06,
                1.553497199007048e-06,
                8.315283250371857e-07,
                0.9999975938970888,
                1.553497199007048e-06
            ],
            [
                0.9999998724808964,
                0.9999999530883731,
                0.9999998362623334,
                0.9999996072137999,
                0.9999998144609425,
                1.0,
                0.9999999468421187,
                0.9999998555019275,
                0.9999997761971317,
                0.9999998461826772
            ],
            [
                0.9999992661787575,
                0.9999992661791073,
                0.9999998942830485,
                0.999999887464744,
                0.9999998802069159,
                0.9999999226558332,
                0.9999999634651792,
                0.9999983463096261,
                0.9999996310114159,
                0.9999999358793944
            ],
            [
                1.6373766672888118e-07,
                1.209865827752005e-06,
                2.3823690999290963e-07,
                1.444980209556342e-07,
                4.450849988798682e-07,
                3.059021175247079e-07,
                2.3823682479181176e-07,
                2.69957906184239e-07,
                2.5612819054028872e-06,
                3.059022998569248e-07
            ],
            [
                0.9999998802069445,
                0.9999999397642796,
                0.999999917667524,
                0.9999998461826589,
                0.9999997761971049,
                0.9999998724809875,
                0.9999999123575882,
                0.9999999317439873,
                0.9999999317439302,
                0.9999998724809116
            ],
            [
                3.466325797896173e-07,
                0.9999999358793791,
                0.999999802494586,
                8.939695238634211e-06,
                1.8553914607267268e-07,
                0.9999989969860319,
                3.059022269250683e-07,
                2.6995790618469934e-07,
                0.9999987121046314,
                0.9999998802069302
            ],
            [
                0.9999981261252883,
                0.9999996072137063,
                0.9999993524052794,
                0.9999996743688586,
                0.9999999067050831,
                0.9999993106387903,
                0.999999581881327,
                0.9999998642567351,
                0.9999998257021214,
                0.9999998362623724
            ],
            [
                2.430024073523505e-05,
                8.481108183851022e-05,
                8.939700567004841e-06,
                8.939699501229642e-06,
                1.0677027427600627e-06,
                4.222834954778007e-06,
                6.605216832236121e-05,
                0.999999310639119,
                0.9999997300421583,
                6.475945666033422e-07
            ],
            [
                0.9999997617629766,
                0.9999995549148951,
                0.9999996310113279,
                0.9999998555019618,
                0.9999997617631469,
                0.9999995262094988,
                2.260325375677174e-06,
                0.9999993916411811,
                0.99999976176309,
                0.9999992188519491
            ],
            [
                0.9999997761971317,
                0.9999999397642653,
                2.699576809143613e-07,
                0.999998629042141,
                0.999999789756659,
                2.3823693839325527e-07,
                2.3823682479292225e-07,
                0.9999988634358834,
                0.9999984465018757,
                0.9999998024946095
            ],
            [
                9.931195693628605e-08,
                0.9999999006880785,
                0.9999999226557593,
                0.9999999067051277,
                4.4508505193386385e-07,
                0.9999996533672965,
                6.475948753965404e-07,
                0.999999825702059,
                0.9999997126314126,
                0.9999990577549575
            ],
            [
                0.9999998724809724,
                1.0,
                0.9999997463981032,
                0.9999999559306312,
                0.9999999559305576,
                0.9999999176675632,
                0.9999996743687034,
                0.9999998362623334,
                0.9999999677581414,
                1.0
            ],
            [
                0.9999999317439953,
                0.9999996940976638,
                1.0,
                0.9999997463981031,
                0.9999999123575046,
                1.0,
                0.9999998555020135,
                0.999999917667524,
                0.999999922655833,
                0.9999998802068873
            ],
            [
                1.6373770576776313e-07,
                6.144175334468545e-06,
                5.144219527356777e-05,
                1.012998977264307e-05,
                0.9999975938968017,
                0.9999952149066524,
                0.9999986290426308,
                1.2098652508391807e-06,
                0.9999989322966217,
                0.999998540624302
            ],
            [
                4.0063706519072155e-05,
                3.0590237279085045e-07,
                1.4738983729535602e-05,
                1.2098653950656417e-06,
                5.144219527094787e-05,
                3.0590237279085045e-07,
                1.3709576971379186e-06,
                1.3709572068478697e-06,
                8.315281267861397e-07,
                3.120191137659974e-05
            ],
            [
                0.9999998942829224,
                0.9999999317439383,
                0.9999999273418269,
                0.9999982396565777,
                0.9999999559305786,
                0.9999999123575778,
                0.9999997897565839,
                0.9999999530883228,
                0.9999998874647574,
                0.9999998144608098
            ],
            [
                1.0,
                0.9999999397642436,
                0.9999999358793867,
                0.999999965678712,
                0.9999998555019791,
                0.9999999176674946,
                1.0,
                0.9999999656787161,
                0.9999999067049831,
                0.9999999586006394
            ],
            [
                0.9999991684720717,
                0.9999998024947272,
                0.9999997761972116,
                0.9999997897567342,
                0.9999996533675031,
                0.9999997897567342,
                0.9999998362623723,
                0.9999996533672965,
                0.9999996743686644,
                0.9999998024947273
            ],
            [
                0.9999993106388727,
                0.9999999006881497,
                0.9999996072139403,
                0.9999997126313441,
                0.9999999067051166,
                0.9999995549150014,
                0.9999988634364259,
                0.9999997126314126,
                0.9999997761970248,
                0.999999802494586
            ],
            [
                0.9999998724810027,
                0.9999997300420939,
                0.9999998144608098,
                0.9999996940977733,
                0.999999855502048,
                0.9999999317439058,
                0.9999998144608097,
                0.999999814460854,
                0.9999999500628036,
                0.9999997897565839
            ],
            [
                4.450852111135988e-07,
                3.9278615344178325e-07,
                6.475946438042047e-07,
                2.1024339116082313e-07,
                3.0590237279032884e-07,
                2.1024326584582131e-07,
                4.4508510499849186e-07,
                2.6995784182140636e-07,
                1.2751910369275402e-07,
                3.4663253846718004e-07
            ],
            [
                0.9999999530883285,
                0.9999998874647574,
                0.9999998257020799,
                0.9999999611088487,
                0.9999998362623528,
                0.9999999067051055,
                0.9999999586005999,
                0.9999993916407459,
                0.9999999500628215,
                0.9999997300422548
            ],
            [
                1.3709570434219446e-06,
                1.5534975693933505e-06,
                3.2887506336086064e-06,
                4.7850967763512445e-06,
                1.3709575337078829e-06,
                1.9947292459347367e-06,
                7.338208930391909e-07,
                1.670142383595838e-05,
                2.2603242978871282e-06,
                1.9947292459347367e-06
            ],
            [
                1.8553919030708836e-07,
                0.9999999006880076,
                0.9999998642567351,
                0.999999746398073,
                1.0,
                1.0,
                0.9999998942830358,
                0.9999999176675436,
                0.9999993524052793,
                0.9999999067051166
            ],
            [
                0.9999964991439187,
                0.9999999317439954,
                0.9999998874648782,
                0.9999999123574628,
                0.9999999358793792,
                0.9999949062937868,
                0.9999999559306312,
                0.9999996743688199,
                0.9999999176674945,
                0.9999999176675535
            ],
            [
                3.466326624336003e-07,
                3.927862470905692e-07,
                4.4508510499737865e-07,
                1.3709576971463352e-06,
                2.3823690999290963e-07,
                3.4663249714612693e-07,
                2.561281294760143e-06,
                2.6995790618469934e-07,
                2.699578740032504e-07,
                5.71500515159253e-07
            ],
            [
                0.999999977840516,
                0.9999998461827322,
                1.0,
                0.9999999697115588,
                0.999999953088334,
                0.999999391640746,
                1.0,
                0.9999997761970248,
                0.9999999434137974,
                0.9999999500628274
            ],
            [
                0.9999999226557685,
                0.9999999273417836,
                0.9999998642566381,
                0.9999998461826956,
                0.9999999358794327,
                0.9999999677581567,
                0.9999999634651748,
                0.9999999358793714,
                1.0,
                0.9999999530883675
            ],
            [
                0.9999996310115918,
                0.9999993916408184,
                0.9999998257020798,
                0.9999998874648246,
                0.9999999468421756,
                0.9999995818811276,
                0.9999999123574732,
                0.9999999530883898,
                1.0,
                0.9999998555019619
            ],
            [
                0.9999997617630333,
                0.9999998942829476,
                0.9999996940978826,
                0.9999998144609203,
                0.9999989969862709,
                0.9999995549150543,
                0.9999996533673376,
                0.9999957771665583,
                0.9999985406243015,
                0.9999991684716752
            ],
            [
                1.7603425837855082e-06,
                1.012999098021058e-05,
                2.430024073461624e-05,
                8.315279285351409e-07,
                2.260324567337161e-06,
                0.9999986290432842,
                0.999999114842648,
                1.994730672675753e-06,
                0.9999986290431205,
                1.2098652508424818e-06
            ],
            [
                0.9999999530883843,
                1.0,
                0.9999999500628036,
                0.9999999397642724,
                0.9999998874647843,
                0.9999999434137637,
                0.9999999656786793,
                1.0,
                0.999999969711584,
                0.9999999434137098
            ],
            [
                0.9999998257021213,
                0.9999998874647575,
                0.9999998802069017,
                0.9999992661790199,
                0.9999998461827139,
                0.9999993916411087,
                0.9999997617630901,
                0.9999998144609425,
                0.9999998874648112,
                0.9999989322972578
            ],
            [
                0.9999999123575151,
                0.9999998642566704,
                0.9999997126315153,
                0.9999999067050054,
                0.9999992661792823,
                0.9999998874649318,
                0.9999999397643083,
                0.9999999006879721,
                0.999999872480942,
                0.9999999006881497
            ],
            [
                0.9999998144608097,
                0.999999900688043,
                0.9999999468421756,
                0.9999998874648648,
                1.0,
                0.9999998555019791,
                6.144176066901277e-06,
                0.9999964991443363,
                0.9999998362623138,
                0.9999996310113279
            ],
            [
                0.9999999434137704,
                0.9999998724809267,
                0.9999999397642725,
                1.0,
                0.9999998257021422,
                0.9999999317439059,
                0.9999999273417663,
                1.0,
                0.9999998461827322,
                0.9999997463981939
            ],
            [
                0.9999997617630049,
                0.9999993916409636,
                0.9999997897567092,
                0.9999998642566704,
                0.9999998724809723,
                0.9999996072136126,
                0.9999996743688586,
                0.9999997300422869,
                0.9999999656786833,
                0.9999998724809875
            ],
            [
                0.999999428499417,
                0.9999996072139404,
                0.9999999226557962,
                0.999999946842125,
                0.9999998942829729,
                0.9999999006880195,
                0.999999939764215,
                0.9999998942829854,
                0.9999999397642508,
                1.0
            ],
            [
                0.9999996072137062,
                0.9999999611089182,
                0.9999999358793791,
                0.9999999176674454,
                0.9999999226558423,
                0.999999789756659,
                1.0,
                0.9999998024946095,
                0.9999998144609203,
                0.9999999434137705
            ],
            [
                0.9999999611089043,
                0.9999999559306049,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999273418703,
                0.9999996310116358,
                0.999999961108909,
                1.0
            ],
            [
                0.9999999559305733,
                0.999999943413784,
                0.9999999397642725,
                0.9999998802069587,
                0.9999998362622553,
                0.9999999358794249,
                1.0,
                1.0,
                0.9999997617629766,
                0.9999999468421503
            ],
            [
                2.2603248367512505e-06,
                1.7603427936335396e-06,
                6.475947982037486e-07,
                9.422450431989127e-07,
                8.315283250371857e-07,
                6.9622537599680095e-06,
                2.7535694384081332e-05,
                1.8925143728749452e-05,
                3.288748673360027e-06,
                3.2887498495150166e-06
            ],
            [
                0.9999996310113719,
                0.999999653367503,
                0.9999999358793562,
                0.999999802494633,
                0.999999864256719,
                0.9999994284995531,
                0.9999998257021007,
                0.9999995818810777,
                0.9999998362622943,
                0.9999996310113719
            ],
            [
                0.9999989969860318,
                6.475948754028718e-07,
                1.0677032518814388e-06,
                1.0,
                0.9999980052702797,
                1.0677029973219343e-06,
                0.9999999358793867,
                0.999998629043284,
                0.9999994631248043,
                3.05902263391829e-07
            ],
            [
                0.9999998024946567,
                0.9999999358793485,
                0.9999999317439708,
                0.9999980052702799,
                0.9999994631251243,
                1.0,
                7.734414854823498e-08,
                0.9999998461827138,
                0.9999995549147891,
                0.999999927341801
            ],
            [
                8.315282259138311e-07,
                2.69957906184239e-07,
                1.275190276853036e-07,
                6.47595107001401e-07,
                1.855391239544352e-07,
                1.0677028700422047e-06,
                3.466326211105621e-07,
                2.102433660979124e-07,
                2.699577774585891e-07,
                6.82560779249779e-08
            ],
            [
                1.8553905759969634e-07,
                1.1253506814797596e-07,
                3.4663253846473677e-07,
                0.9999978766220453,
                1.8553907971758842e-07,
                0.9999993524052795,
                0.9999916019299858,
                0.9999987901346061,
                1.4449805540651476e-07,
                0.9999991684720723
            ],
            [
                0.9999999176675632,
                0.9999999006880786,
                0.999999958600659,
                0.9999988634358833,
                0.9999999317439873,
                1.0,
                0.9999996072136593,
                0.999999825702059,
                0.9999997617629766,
                0.9999998942829476
            ],
            [
                0.9999998942829729,
                0.9999999397642078,
                0.9999997300422548,
                0.999999825702163,
                0.9999997463981939,
                0.9999997463980428,
                0.9999998024947037,
                0.999999825702163,
                0.9999997897565838,
                0.9999999397642868
            ],
            [
                0.9999998362622747,
                1.0,
                1.0,
                0.9999998724809268,
                1.0,
                0.9999999397642293,
                0.9999998802069445,
                0.9999997897567342,
                0.9999995549147891,
                0.9999999634652009
            ],
            [
                0.9999999226557409,
                1.0,
                0.999999653367379,
                0.9999999067050499,
                0.9999999273418355,
                0.9999994956523515,
                0.9999999468421567,
                0.9999999634651574,
                1.0,
                0.9999999397643011
            ],
            [
                0.9999992661791073,
                0.9999999434137907,
                0.9999999611088487,
                0.9999998461826771,
                0.9999999226558146,
                0.9999999123575359,
                1.0,
                1.0,
                0.9999999358794249,
                0.9999997761970247
            ],
            [
                3.4663266242969896e-07,
                1.6373764721072816e-07,
                8.764244316973974e-08,
                7.338207180884785e-07,
                3.059022998558814e-07,
                1.855390354818069e-07,
                0.9999989969861514,
                4.450849988780466e-07,
                2.1024329090867228e-07,
                3.0590237279032884e-07
            ],
            [
                1.6373764721039308e-07,
                0.9999996743688199,
                0.9999994956526521,
                6.412056740249439e-08,
                1.6701417862648148e-05,
                0.9999785550439844,
                3.4663253846718004e-07,
                0.9999990577551818,
                9.931202796993203e-08,
                0.999999218851856
            ],
            [
                1.0,
                0.9999998642566381,
                0.9999998144609203,
                0.9999995262094987,
                0.9999996072138001,
                0.9999992661791948,
                0.9999994956527123,
                0.9999993916410361,
                0.9999992188514836,
                0.9999997300420939
            ],
            [
                0.9999999500628036,
                0.9999998362623138,
                0.9999998942830358,
                0.9999998461827322,
                0.9999998724809571,
                0.999999900687984,
                0.9999999468421439,
                0.9999998024946095,
                0.9999997463981334,
                0.9999998257022045
            ],
            [
                0.9999998802068873,
                0.9999998642566866,
                0.9999996533674617,
                0.9999996310114159,
                0.9999999500628394,
                0.9999999067050832,
                0.9999999530883508,
                0.9999996533672963,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999993916408909,
                0.9999998642567028,
                1.0,
                0.9999999468421693,
                0.9999999397642294,
                1.0,
                0.9999997126315153,
                1.0
            ],
            [
                0.9999999434137097,
                0.9999997300421261,
                0.9999998942829602,
                0.9999999559306049,
                0.9999999500627917,
                0.9999999358793409,
                0.9999998724809875,
                0.9999999123575151,
                0.9999999586006542,
                0.999999969711584
            ],
            [
                0.999999802494586,
                0.9999994956527724,
                0.9999993106389548,
                1.0677029973192638e-06,
                0.9999996743688199,
                0.9999997761971583,
                0.9999992188517629,
                0.9999995549150014,
                0.999998790134173,
                0.9999988634366963
            ],
            [
                0.999999631011636,
                0.9999997761970516,
                0.9999998461826956,
                0.999999789756659,
                0.9999994284996895,
                0.9999998874648917,
                0.9999997463981334,
                0.9999998461827323,
                0.9999996940976639,
                1.0
            ],
            [
                0.9999999530883563,
                0.999999927341827,
                0.9999996310115479,
                0.9999999176674357,
                0.999999958600659,
                0.999999931743971,
                0.999999912357442,
                0.9999999226558238,
                3.46632497145457e-07,
                0.9999999226557962
            ],
            [
                0.999999746398073,
                0.9999997300422548,
                0.9999999067050832,
                0.9999998942829855,
                0.9999997300421583,
                0.9999996310114159,
                0.9999992188514838,
                0.9999996940977367,
                0.999999846182714,
                0.9999998362623332
            ],
            [
                0.999999855502048,
                0.9999998724809723,
                0.999996711250937,
                0.9999998555019619,
                0.9999997463982242,
                0.9999997300422226,
                0.999999746398073,
                0.9999998257020798,
                0.9999998461826038,
                0.9999997897566841
            ],
            [
                0.9999999530883172,
                0.9999997300421261,
                0.9999998874647306,
                0.9999967112501545,
                0.9999999656787407,
                0.9999995549151074,
                0.9999993106386259,
                0.9999989969854339,
                0.9999999006881378,
                0.9999996310115039
            ],
            [
                0.9999998024946095,
                0.999999825702059,
                0.9999999358793562,
                9.931190958076104e-08,
                0.9999999468421884,
                0.9999998802069873,
                0.9999998802069445,
                0.9999997761970515,
                0.9999999358794479,
                0.9999999559305996
            ],
            [
                9.422447062294175e-07,
                2.2603242978778778e-06,
                8.315280276580819e-07,
                1.637376862489725e-07,
                1.3709570434219446e-06,
                7.338209805240734e-07,
                1.3709572068522336e-06,
                0.9999998024946566,
                8.315284241650899e-07,
                9.422448185534261e-07
            ],
            [
                2.102434162245973e-07,
                2.6995784182183607e-07,
                3.466325797896173e-07,
                1.2098653950656417e-06,
                2.1024334103581732e-07,
                1.8553910183674878e-07,
                6.825597214718257e-08,
                2.1024336609874897e-07,
                2.1024336609874897e-07,
                1.855391681906175e-07
            ],
            [
                0.9999999317439872,
                0.9999999123575046,
                0.9999999358793792,
                0.9999997761971049,
                0.9999999586006394,
                0.9999999468420996,
                0.9999983463098238,
                0.9999999715466731,
                0.9999999273418789,
                0.9999999176675142
            ],
            [
                0.9999991684717744,
                0.9999998874647575,
                0.9999998555019274,
                0.999999168472171,
                0.9999998555019446,
                0.9999991684719729,
                0.9999998874649051,
                0.9999994284993489,
                0.99999967436882,
                0.9999998555019275
            ],
            [
                0.9999990577550695,
                0.9999992188516696,
                3.059021539909339e-07,
                3.9278634073732336e-07,
                0.9999832985722032,
                2.3823702359290413e-07,
                0.9999987901347497,
                0.9999999226557131,
                1.6373762769138607e-07,
                3.927862470899887e-07
            ],
            [
                0.9999999611088766,
                0.999999814460854,
                1.0,
                0.9999999006880312,
                1.0,
                0.9999999067051499,
                1.0,
                0.999999746398073,
                0.9999998724809724,
                0.9999998257021214
            ],
            [
                0.999999946842163,
                0.9999999500627976,
                0.9999999611088672,
                0.9999999530883228,
                0.9999999468421883,
                0.999999946842144,
                0.9999999530883172,
                0.9999995549149482,
                0.9999999123575464,
                0.9999999397642868
            ],
            [
                0.9999996743688976,
                0.9999997126313098,
                0.9999983463110063,
                0.9999996533674617,
                0.9999998874648246,
                0.9999999358794173,
                0.9999996940978462,
                0.9999998144608983,
                0.9999998642566866,
                0.999999864256719
            ],
            [
                0.9999998724809116,
                0.9999999273418962,
                0.9999997300423193,
                0.9999998362622943,
                0.9999998024946801,
                0.9999999273418183,
                0.9999999358793332,
                0.9999998942830485,
                0.999999887464838,
                0.9999995818812273
            ],
            [
                0.9999998642567351,
                0.9999998257021007,
                0.999999943413784,
                0.9999989969857926,
                0.9999999468421565,
                0.999999943413811,
                0.9999999656787325,
                0.9999996072139403,
                1.0,
                0.9999998724809267
            ],
            [
                0.9999996940977367,
                0.9999997617630901,
                0.9999998802069017,
                0.9999993106390369,
                0.9999997897566841,
                0.9999998874648515,
                0.9999995818810776,
                0.9999998461826956,
                0.999999653367379,
                0.9999998362623334
            ],
            [
                6.47594952603035e-07,
                2.75356812556058e-05,
                3.927860597935108e-07,
                2.1024331597152624e-07,
                2.2603253756956754e-06,
                1.4449800373065699e-07,
                1.5534973842076057e-06,
                1.5534973842076057e-06,
                5.715006514167015e-07,
                9.422444815792981e-07
            ],
            [
                0.9999999358794174,
                0.999999789756609,
                0.9999991684720723,
                2.6995780963846126e-07,
                0.9999999500628095,
                0.9999998257020799,
                0.9999999123574629,
                0.9999998802069445,
                0.9999999123575255,
                0.9999999611088858
            ],
            [
                4.785093353940187e-06,
                1.3709568799919866e-06,
                0.9999916019259725,
                0.9999942280806647,
                3.927863407379485e-07,
                9.422448185534261e-07,
                0.9999990577554065,
                3.7266401726359486e-06,
                0.9999991684719726,
                0.9999993916411085
            ],
            [
                0.9999998874648246,
                0.9999999226558237,
                0.9999999500628334,
                0.9999996533673376,
                0.9999999006880431,
                0.9999998024946096,
                0.9999999317439384,
                0.9999994284997576,
                0.9999997761971849,
                0.9999998144608984
            ],
            [
                0.999999789756634,
                0.999999814460854,
                0.9999996072139403,
                0.9999998802069017,
                0.9999998942829602,
                0.9999997617630901,
                0.9999998724810027,
                0.9999999006881023,
                0.9999998144609205,
                0.9999995262096117
            ],
            [
                0.9999998362622943,
                0.9999990577552945,
                0.9999998144609645,
                0.9999997126313099,
                0.9999991148427539,
                9.422444815765128e-07,
                0.9999997617631754,
                0.9999991148431767,
                0.9999991684721712,
                0.9999987121049401
            ],
            [
                4.4508489275752546e-07,
                3.2887478892683997e-06,
                1.2098661162023305e-06,
                3.2887478892683997e-06,
                1.760343423160973e-06,
                1.0677033791612137e-06,
                2.902311985146426e-06,
                3.726639728348526e-06,
                5.04347348075149e-07,
                4.450852111100568e-07
            ],
            [
                1.855391239544352e-07,
                4.450848927658745e-07,
                7.734423152941018e-08,
                3.927863875616689e-07,
                2.10243290909724e-07,
                5.715005832886879e-07,
                2.6995784182140636e-07,
                2.382368531929327e-07,
                7.338212429582604e-07,
                3.05902190458764e-07
            ]
        ]
    },
    {
        "q_id": "10299_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.999998005269804,
                0.9999999006881497,
                0.9999990577551817,
                0.9999998144608098,
                0.999999855501979,
                0.9999983463100207,
                0.9999995549148951,
                0.9999998362623723,
                0.9999996072137999,
                0.999998126125064
            ],
            [
                0.9999992661788447,
                0.9999992188516699,
                0.999999554914842,
                0.9999996940978827,
                0.9999998642567028,
                0.9999998555019446,
                1.7603425837702984e-06,
                0.9999994956526521,
                0.9999994956527725,
                0.9999996940976273
            ],
            [
                0.9999999067049831,
                0.9999999006880786,
                1.3709570433885908e-06,
                0.9999998555019618,
                0.9999998144609203,
                0.999999631011416,
                0.9999996940978461,
                0.999999653367379,
                0.9999982396574171,
                0.9999992661790197
            ],
            [
                0.9999999226557131,
                0.9999998024947273,
                0.9999997617629764,
                0.999999581881327,
                0.9999998642567028,
                0.9999975938970888,
                0.9999999006880668,
                0.9999995262093857,
                0.999999802494633,
                0.9999997761971849
            ],
            [
                0.999999894282935,
                0.9999998257021006,
                0.9999998724809419,
                0.9999995262092164,
                0.9999993916407459,
                0.9999997126314811,
                0.9999996940977367,
                0.9999995818810776,
                0.9999998642566866,
                0.999999631011328
            ],
            [
                0.999999825702059,
                0.9999997761971315,
                0.9999994956525919,
                0.9999960330155082,
                0.9999989322967487,
                0.9999985406243017,
                0.999999310638626,
                0.9999997897566341,
                0.999998346310218,
                0.9999996072136594
            ],
            [
                0.9999997897565839,
                0.9999998257020798,
                0.999999814460854,
                0.9999997300422226,
                0.9999998724809875,
                0.9999998024947272,
                0.9999998642566704,
                0.9999997617630333,
                0.9999999006879958,
                0.999999631011636
            ],
            [
                0.9999991684717744,
                0.9999999006880195,
                0.9999978766205265,
                0.9999996072138935,
                0.9999999176675534,
                0.999999631011416,
                0.9999995818814266,
                0.9999942280813501,
                0.9999999006880668,
                0.9999998942829729
            ],
            [
                0.9999997617631753,
                0.9999995549148422,
                0.9999991684715762,
                0.9999991148426481,
                0.9999999317440035,
                0.999998996985434,
                0.9999997897566089,
                0.9999998461826222,
                0.9999986290429576,
                0.9999989969859123
            ],
            [
                1.4738980215352592e-05,
                1.5534983101602148e-06,
                2.5612828213934817e-06,
                0.9999972735294057,
                8.315281267882195e-07,
                1.370957860576702e-06,
                2.902312331170226e-06,
                1.3709567165617364e-06,
                4.450850519403407e-07,
                4.450848927658745e-07
            ],
            [
                0.9999998144609424,
                0.9999997897565588,
                0.9999997463981334,
                0.999999935879402,
                0.9999997761971849,
                0.9999996310113279,
                0.9999996743687034,
                0.9999997300421904,
                0.999999653367255,
                0.9999998642566704
            ],
            [
                0.9999989969860335,
                0.9999993524051252,
                0.9999970976880188,
                0.9999983463100235,
                0.9999987121043267,
                0.9999251537649857,
                0.9999987901343186,
                0.9999877809240255,
                0.9999910603037199,
                0.9999980052693305
            ],
            [
                0.9999985406234317,
                0.9999972735297307,
                0.9999987901341727,
                0.9999982396565782,
                0.9999999273417837,
                0.9999995818814266,
                0.9999998461826772,
                0.9999981261237242,
                1.3709576971425944e-06,
                0.9999994956525319
            ],
            [
                0.9999998802068873,
                0.9999998802069444,
                0.9999994631248044,
                0.9999997617631753,
                0.9999997897565839,
                0.9999998362622943,
                0.999999855501979,
                0.9999997617630617,
                0.9999982396574179,
                0.9999997761970782
            ],
            [
                0.9999997126313098,
                0.9999998461827139,
                0.9999996310116359,
                0.9999996310114598,
                0.9999997761970515,
                0.9999990577557435,
                0.9999996072137062,
                0.9999997761971049,
                0.999999761763005,
                0.9999998144609424
            ],
            [
                0.9999998642566381,
                0.9999997897565588,
                0.9999998362623724,
                0.9999997761970781,
                0.9999996940978098,
                0.9999998257021838,
                0.9999998144608762,
                0.9999998024946332,
                0.999999761763147,
                0.9999997300421906
            ],
            [
                0.9999998942829854,
                0.9999996743686257,
                0.9999990577555189,
                0.9999992188515767,
                0.9999998555019619,
                0.9999996310114599,
                0.9999998024947273,
                0.999999631011328,
                0.9999998024947273,
                0.9999995818812272
            ],
            [
                0.9999998642566866,
                0.9999997897567343,
                0.9999998642566219,
                0.9999983463096269,
                0.9999994956526521,
                0.9999995262093858,
                0.9999997463980427,
                0.9999996533672137,
                0.9999989969861516,
                0.9999999273418616
            ],
            [
                0.9999999434137772,
                0.9999998942830737,
                0.999999939764251,
                0.9999997897567342,
                0.999999971546629,
                0.9999996533674617,
                0.9999998642567351,
                0.9999998724808963,
                0.9999999434137773,
                0.9999999273418356
            ],
            [
                0.9999999500628036,
                0.9999989969856734,
                0.99999995860059,
                0.9999997761970515,
                0.9999998724809267,
                0.999999961108909,
                0.9999997463980428,
                0.9999997300421906,
                0.9999999273418355,
                0.9999957771655518
            ],
            [
                0.9999975938982357,
                0.9999983463110065,
                0.9999992188512972,
                0.9999998724810027,
                0.9999952149032266,
                0.9999996072136594,
                0.9999996743687034,
                0.9999996072137063,
                0.999998790134173,
                0.9999981261250643
            ],
            [
                0.9999995818812272,
                0.9999999273417662,
                0.9999998802068873,
                0.9999998642567351,
                0.9999999273418182,
                0.9999996940976638,
                0.9999997617629764,
                0.9999997300421262,
                0.9999997617630049,
                0.999999935879425
            ],
            [
                0.9999996533673376,
                0.9999997126313783,
                0.9999997617630049,
                0.9999995818812272,
                0.9999998461826405,
                0.9999996533673791,
                0.9999998024946095,
                0.9999997300422225,
                0.9999999226557778,
                0.999998712105092
            ],
            [
                0.9999998555019275,
                0.9999998802069874,
                0.9999995818813269,
                0.9999998144608983,
                0.9999996072137063,
                1.0,
                1.0,
                0.9999997300422226,
                0.9999997761972116,
                0.9999996743687034
            ],
            [
                0.9999985406236058,
                0.9999997761970247,
                0.9999993916408185,
                0.9999993106389546,
                6.475947209985977e-07,
                0.999998996986271,
                0.9999942280806637,
                0.9999983463098232,
                0.9999994956524718,
                0.9999997761972116
            ],
            [
                0.9999998724809875,
                0.9999885212277833,
                3.7266379513162962e-06,
                7.338209805090567e-07,
                5.043475885688201e-07,
                7.338209805240734e-07,
                0.999999554914789,
                2.2603253756956754e-06,
                0.9999998802069587,
                0.999999352405202
            ],
            [
                0.9999996940976273,
                0.9999997300421583,
                0.9999996533673791,
                0.9999997126314126,
                0.9999993524054336,
                0.9999990577556311,
                0.999999607213753,
                0.9999993106387906,
                0.9999997463982241,
                0.9999988634360193
            ],
            [
                5.715004470243685e-07,
                0.999999825702163,
                0.9999984465015062,
                0.9999993106386261,
                0.9999993524048932,
                0.9999998024947272,
                0.9999997617630049,
                0.9999987901341729,
                0.9999993524049705,
                0.9999996533675032
            ],
            [
                0.9999997617630333,
                0.9999996743687422,
                0.9999996072137062,
                0.999999730042287,
                0.9999998461826405,
                0.9999994284996895,
                0.9999994956525319,
                0.9999998724809571,
                0.9999997617630049,
                0.9999998555019963
            ],
            [
                0.9999995818812769,
                0.999999802494586,
                5.422217030707961e-06,
                0.9999996072137999,
                9.422449308673789e-07,
                0.9999985406239533,
                0.9999998874648246,
                1.209865683500459e-06,
                0.9999885212291474,
                1.067703379154416e-06
            ],
            [
                0.9999998144609646,
                0.9999930377404432,
                0.999999825702163,
                3.927863875616689e-07,
                4.450852641717689e-07,
                0.9999997300422226,
                0.9999988634362903,
                0.9999955048184275,
                0.9999990577557436,
                0.9999983463104152
            ],
            [
                0.9999998555020481,
                0.9999993916411812,
                0.9999998642566381,
                0.999999802494586,
                0.9999999176674945,
                0.9999998362623137,
                0.9999993106388727,
                5.715007195410849e-07,
                0.9999991684716757,
                0.999999730042287
            ],
            [
                0.9999995549151074,
                3.466325384661554e-07,
                0.9999990577557433,
                1.1478770862067849e-05,
                0.9999942280799775,
                0.9999998802069302,
                0.999999712631344,
                0.9999997897566589,
                0.9999996743686257,
                0.9999998555020307
            ],
            [
                3.4663249714325014e-07,
                0.9999994284996895,
                1.5534979397592542e-06,
                0.9999992188512972,
                0.9999998144609645,
                2.5612819053586272e-06,
                0.9999989322975124,
                0.9999999358793867,
                0.9999997897567091,
                0.9999997463981032
            ],
            [
                0.9999998257021214,
                0.9999998874648112,
                0.999999730042287,
                0.9999999006880668,
                1.0,
                0.9999998024947272,
                0.9999999006880076,
                1.0,
                0.9999998144608983,
                0.9999996743687035
            ],
            [
                0.9999994284995533,
                0.9999998461826589,
                0.9999997126313784,
                0.999998446502061,
                0.9999998024946801,
                0.9999977396751653,
                0.9999987121050922,
                0.9999998942829224,
                0.9999999317439628,
                0.999999554914842
            ],
            [
                0.999999554914842,
                0.9999988634357481,
                0.9999999397642582,
                0.9999997617631184,
                0.9999997761971317,
                0.9999994631248682,
                0.9999998724809116,
                0.9999998257021422,
                0.9999998802069873,
                0.9999997897567342
            ],
            [
                5.715005832872586e-07,
                4.222833444467892e-06,
                4.00636826326273e-05,
                1.7603438428660665e-06,
                0.9999910603058354,
                7.338213304316717e-07,
                9.422444815679433e-07,
                9.422444815679433e-07,
                1.7603436330179102e-06,
                2.260323758923431e-06
            ],
            [
                0.999998005269804,
                6.962255419868303e-06,
                0.9999832985761824,
                2.902313023130843e-06,
                0.999997097686978,
                0.9999251537996863,
                0.9999987901341727,
                0.9999998555019275,
                9.422442569315887e-07,
                0.9999995818811275
            ],
            [
                0.9999998461826222,
                0.9999997463981032,
                1.0,
                0.999999973270557,
                0.9999998362623334,
                0.9999999500628036,
                0.9999999176675338,
                0.9999998724809723,
                0.9999997463981938,
                0.9999998555019791
            ],
            [
                0.9999999176675043,
                0.9999999006880668,
                0.9999999273417663,
                0.9999998144608762,
                0.9999998724809724,
                0.9999998942830233,
                0.9999998144609645,
                0.9999998724809723,
                0.9999999468421883,
                0.9999998802069588
            ],
            [
                0.9999969105051869,
                0.9999980052709933,
                0.9999982396572078,
                0.9999955048162812,
                0.9999975938985232,
                0.9999938558246688,
                1.6373772528677946e-07,
                0.9999989322973851,
                0.9999974387174857,
                8.315277302841894e-07
            ],
            [
                0.999999825702163,
                0.9999984465020607,
                0.9999998461826222,
                0.999999554914789,
                0.9999997897565838,
                0.9999999500627857,
                0.9999993524048931,
                0.9999998461826222,
                0.9999996533672136,
                0.9999989969855536
            ],
            [
                1.209865539295696e-06,
                7.338210680021253e-07,
                2.260325106237323e-06,
                0.9999151889494048,
                0.9999949062950038,
                0.9999949062962249,
                1.2098656835224664e-06,
                0.9999724643122646,
                0.9999756997564291,
                0.9999771719920312
            ],
            [
                4.222833444467892e-06,
                0.9999993106390369,
                0.9999987121050922,
                0.9999995549150544,
                0.9999960330126691,
                0.9999997126313441,
                0.9999970976880166,
                0.999999114843281,
                0.9999978766210323,
                0.9999995262096116
            ],
            [
                0.9999997300421583,
                3.059023363172604e-07,
                0.9999997897566841,
                0.9999997761971317,
                0.9999999123575569,
                0.9999997761971582,
                0.9999998362622553,
                0.9999998874648649,
                0.9999996533672137,
                0.9999996940977732
            ],
            [
                0.9999991684715763,
                0.9999999500628036,
                0.9999996310115479,
                1.0,
                0.9999998257020591,
                0.9999998874649185,
                0.9999995818814266,
                0.9999998257021422,
                0.9999998257021837,
                0.9999997617631469
            ],
            [
                7.338207180801359e-07,
                3.927862470861484e-07,
                6.144177531599359e-06,
                3.927862470861484e-07,
                8.315282259089153e-07,
                7.338211554688417e-07,
                3.05902117523595e-07,
                1.0677029973056687e-06,
                2.3823682479181176e-07,
                6.475947209918244e-07
            ],
            [
                0.9999998874647574,
                0.9999977396762431,
                0.9999991684715762,
                0.999999825702163,
                0.9999997617630334,
                0.9999998942829099,
                0.999999746398073,
                0.9999995262094424,
                0.9999997617630333,
                0.9999997617630617
            ],
            [
                0.9999997126315496,
                0.9999997897565839,
                0.9999998461826222,
                0.999999922655787,
                0.9999996533674617,
                0.9999998942830485,
                0.9999999317440279,
                0.9999999067051387,
                0.9999998724809571,
                0.9999998024946801
            ],
            [
                2.260324836787226e-06,
                0.9999996940978462,
                0.9999892166826493,
                0.9999999067051165,
                0.9999997300421904,
                0.9999995818813766,
                0.9999996743688975,
                0.9999996310114159,
                0.9999994956524717,
                0.9999998555019274
            ],
            [
                0.999981074851795,
                6.144173137170873e-06,
                0.9999955048168166,
                3.726638395634011e-06,
                8.939699501416646e-06,
                0.9999938558268658,
                5.04347528446051e-07,
                0.9999869928746493,
                0.999964643732473,
                1.0
            ],
            [
                1.892514147143123e-05,
                0.999998863435748,
                1.76034300345598e-06,
                0.9999987121041709,
                0.9999998874648648,
                0.9999995818811773,
                0.9999991684715762,
                0.00020342702210072178,
                8.315277302701984e-07,
                5.422217676979575e-06
            ],
            [
                0.9999996940977002,
                0.9999998144608981,
                0.999999631011328,
                0.999999746398073,
                0.9999999468421693,
                0.999999887464838,
                0.9999998144609203,
                0.9999997617629764,
                0.9999998802069302,
                0.9999992188517628
            ],
            [
                0.9999999468421503,
                0.9999999123575987,
                0.9999988634365607,
                0.999999730042126,
                0.9999998942830106,
                0.999999894283061,
                0.9999997617630333,
                0.9999999067050721,
                1.0,
                0.9999999559306101
            ],
            [
                0.999999894282935,
                0.9999997617629764,
                0.9999998362622943,
                0.9999998802068873,
                0.9999999586006542,
                0.9999998144609203,
                0.9999998461826405,
                0.9999999123575046,
                0.9999998461826038,
                0.999999789756634
            ],
            [
                0.9999998942829981,
                0.9999999611089043,
                0.9999999358793639,
                0.9999998874647709,
                0.9999999176675829,
                0.9999999176675338,
                0.9999994631247405,
                0.9999996533673376,
                0.9999996743688976,
                0.9999999434137368
            ],
            [
                0.9999993916408186,
                0.9999997126313098,
                0.999999631011636,
                0.9999998144609425,
                0.9999997617630617,
                0.999999900687984,
                0.9999995549148422,
                0.9999998257020798,
                0.9999995262092729,
                0.9999998555019791
            ],
            [
                0.9999995818813767,
                0.9999997761971582,
                0.9999998362622357,
                3.4663266242575825e-07,
                0.999999653367255,
                0.9999993916411085,
                0.999993037746246,
                0.9999999176674651,
                0.9999982396569975,
                0.9999998024946566
            ],
            [
                0.9999996072136594,
                0.9999986290426308,
                0.9999996533673378,
                0.9999992661790198,
                0.9999997617630617,
                0.9999998874649185,
                0.9999998144609645,
                0.9999991684719727,
                0.9999991684719728,
                0.9999997617629766
            ],
            [
                0.9999999434137435,
                0.9999998461826405,
                0.9999996743686257,
                0.999999581881277,
                2.1024326584582131e-07,
                0.9999997617630617,
                0.9999995262096117,
                0.9999998362622748,
                0.999999789756634,
                0.9999998802069159
            ],
            [
                0.9999646437325226,
                0.999998932297385,
                0.9999832985702084,
                0.999998712104785,
                3.466325384661554e-07,
                0.9999942280799741,
                0.9999987901344614,
                0.9999999559305576,
                0.999992110736491,
                0.9999970976883631
            ],
            [
                0.9999992188512972,
                0.999999943413811,
                0.9999993524052793,
                0.9999999067051388,
                0.999999939764215,
                0.9999989969859123,
                0.9999998802069587,
                0.9999999358794249,
                0.9999996940978826,
                0.9999998144608983
            ],
            [
                0.9999998362622747,
                0.9999998257021007,
                1.0,
                0.9999997761970248,
                0.9999999434137097,
                0.9999999123575672,
                0.9999999067051054,
                0.9999999273417923,
                0.9999997300423191,
                0.9999999434137974
            ],
            [
                0.9999994631249323,
                0.9999999067049831,
                0.9999997126314126,
                0.999998346310415,
                0.9999993106392013,
                0.9999996310116359,
                1.2098659719716573e-06,
                0.999999057754957,
                0.9999999273418615,
                0.9999993524054337
            ],
            [
                1.3709573702722555e-06,
                0.9999988634358836,
                5.04347348075149e-07,
                0.9999955048178923,
                0.9999994284997575,
                0.9999992188516698,
                2.382369667929001e-07,
                0.9999986290421402,
                0.9999964991460057,
                1.8553905760024476e-07
            ],
            [
                0.9999972735297309,
                3.4663266243308805e-07,
                1.9947292459265734e-06,
                3.466326211105621e-07,
                3.9278624708775595e-07,
                0.9999995262094422,
                0.9999989969859124,
                5.715002426475718e-07,
                0.9999997761972116,
                0.9999994631248682
            ],
            [
                1.5534971989992774e-06,
                0.9999997897565588,
                0.9999999317439465,
                2.5612812947240366e-06,
                0.9999994284992809,
                0.9999998461826772,
                2.5612816000646084e-06,
                1.553497199007048e-06,
                0.9999997463980729,
                0.999999730042287
            ],
            [
                0.9999996940977368,
                0.9999949062925729,
                0.9999991148432809,
                0.9999986290426305,
                0.9999996940978096,
                0.9999998362623529,
                0.9999998362623334,
                0.9999999067050387,
                0.9999994956523515,
                0.9999996743686645
            ],
            [
                0.9999998942829224,
                0.9999996533673376,
                0.9999998555019274,
                0.9999998461826588,
                0.9999997761970248,
                0.9999992188519491,
                0.9999989322968759,
                0.9999997126314811,
                0.999999927341827,
                0.9999998724809267
            ],
            [
                0.9999981261248403,
                1.7603440527286572e-06,
                0.9999967112521121,
                0.9999957771675642,
                0.9999989322973848,
                0.9999724642958291,
                0.9999756997679932,
                1.9947299593014888e-06,
                0.9999998461827138,
                1.855391239539711e-07
            ],
            [
                0.9999997463981334,
                0.9999996533672137,
                0.9999989322973849,
                2.902312331170226e-06,
                9.422450431912e-07,
                0.9999964991468399,
                1.9947301970972664e-06,
                0.9999869928668946,
                0.9999999123575359,
                6.9622579095833456e-06
            ],
            [
                9.422443692555439e-07,
                0.9999962733593861,
                3.2887498493983645e-06,
                1.994730672675753e-06,
                0.9999999397642437,
                0.9999998874648245,
                0.9999998555019446,
                0.9999998257021213,
                2.9023119851781017e-06,
                0.9999945777823274
            ],
            [
                0.9999998362623723,
                0.9999997761971048,
                0.9999998555020307,
                0.9999998802069587,
                0.9999998942829224,
                0.9999998144608983,
                0.9999999176675535,
                0.9999993524048931,
                0.9999995262093293,
                0.9999998362623723
            ],
            [
                0.9999999677581028,
                0.9999998461826589,
                0.9999998555019447,
                0.9999999656787243,
                0.9999998144608098,
                0.9999997897566592,
                1.0,
                0.9999997897566841,
                0.9999999500627739,
                0.999999922655833
            ],
            [
                0.9999991684722703,
                0.9999996533675031,
                0.9999997463981637,
                0.999999653367503,
                0.9999989969854342,
                0.9999999006880194,
                8.315281267800897e-07,
                3.0590226338282174e-07,
                8.31528424151477e-07,
                1.209865539274514e-06
            ],
            [
                1.3709576971316842e-06,
                0.99999800527028,
                0.9999993916406734,
                2.9023116391675407e-06,
                0.9999993106387082,
                7.338208055579897e-07,
                0.9999999123575046,
                1.7603430034743913e-06,
                2.2603245673155757e-06,
                0.999999917667524
            ],
            [
                0.9999996310114159,
                0.999999674368781,
                0.9999999226557501,
                0.9999999067050831,
                0.9999996940976272,
                0.9999997897566341,
                0.9999999006880786,
                0.9999996072137531,
                0.9999999358794021,
                0.9999999176675437
            ],
            [
                0.9999998555019619,
                0.9999997761970782,
                0.9999998144608098,
                0.9999986290421407,
                0.9999995549149483,
                0.9999996072137063,
                0.9999999468421249,
                1.0,
                0.9999998144609646,
                0.9999998874649318
            ],
            [
                0.9999996072136126,
                0.9999992188512972,
                0.9999996310114599,
                0.999999391640891,
                0.9999990577549573,
                0.9999992188516695,
                0.9999998642567028,
                0.9999995262094422,
                3.9278634073625165e-07,
                0.9999985406239534
            ],
            [
                0.9999999317440197,
                0.9999997761971317,
                0.9999998362622553,
                0.9999997617630334,
                0.9999998461826038,
                0.9999998555019618,
                0.9999998024947273,
                0.9999998724809267,
                0.9999997761970248,
                0.9999997300421904
            ],
            [
                0.9999986290423041,
                0.9999978766212865,
                0.9999984465024319,
                0.9999942280786046,
                0.9999955048189665,
                0.9999945777829797,
                0.9999991684722705,
                0.9999982396567882,
                0.9999962733607204,
                0.9999974387177927
            ],
            [
                0.9999998642566219,
                0.9999994631251883,
                0.9999998802069302,
                0.9999999006881497,
                0.9999996940977002,
                0.9999998144608319,
                0.999999218851949,
                2.6995784182073116e-07,
                2.2603242978665707e-06,
                0.9999964991460065
            ],
            [
                0.9999999273417837,
                0.9999998724808964,
                0.9999999273418442,
                0.9999998461826405,
                0.9999998362622552,
                0.9999998144609424,
                0.9999998874647843,
                0.9999977396759732,
                0.9999998024946566,
                0.9999999468421883
            ],
            [
                0.9999997300420939,
                9.422445938917108e-07,
                0.9999998642566381,
                0.9999998642567028,
                0.9999997126315153,
                2.3823702359138736e-07,
                0.9999998024947038,
                0.9999999226558515,
                1.2098653950551882e-06,
                0.9999997126314811
            ],
            [
                2.3823690999160957e-07,
                0.9999955048189624,
                0.9999990577549576,
                0.999999789756659,
                0.9999998257020799,
                0.9999993916411813,
                0.9999990577551817,
                0.9999995549151075,
                3.9278605979208185e-07,
                0.9999967112521144
            ],
            [
                0.9999996940977003,
                0.9999983463110065,
                0.9999996940976638,
                0.9999997300422226,
                0.9999991684721711,
                0.999999554914789,
                0.9999994956526522,
                0.9999962733616078,
                0.9999992661791073,
                0.9999994284994852
            ],
            [
                0.9999998461826406,
                0.9999994631247403,
                2.4300252311252174e-05,
                0.9999999067050276,
                0.9999997300421584,
                0.9999998555019791,
                0.9999988634366971,
                0.999999653367503,
                0.9999999006881023,
                0.9999997761970515
            ],
            [
                0.999999495652532,
                0.9999993106391193,
                0.9999984465024313,
                0.9999993524048935,
                0.9999988634361544,
                2.1024341622426268e-07,
                0.99999911484307,
                0.9999996743687422,
                8.315277302788957e-07,
                0.9999960330121986
            ],
            [
                0.9999997897565839,
                0.9999998642567189,
                0.9999998144608319,
                0.9999998942829981,
                0.9999999226557131,
                0.9999998802069731,
                0.9999997761970782,
                0.9999904837494585,
                0.9999988634364256,
                0.999999653367255
            ],
            [
                0.00012339460439135077,
                2.561281600086738e-06,
                3.72663883989755e-06,
                2.90231094723893e-06,
                3.288747889284851e-06,
                1.2098659719661556e-06,
                1.1478764021029928e-05,
                8.315279285251204e-07,
                5.043472278312808e-07,
                1.0677029973219343e-06
            ],
            [
                0.9999999358793867,
                0.9999998257021837,
                0.9999999611089043,
                1.0,
                0.9999999468421756,
                0.9999998642567353,
                0.9999997463981032,
                0.9999998802069445,
                0.9999991148433869,
                0.9999997761970782
            ],
            [
                0.9999998555019274,
                0.9999996743687034,
                0.9999997897565839,
                0.9999998724809724,
                0.9999974387187067,
                0.9999998257021006,
                2.7535704231043113e-05,
                0.999999927341853,
                0.999999894282935,
                0.9999996072136594
            ],
            [
                3.1201911375578156e-05,
                0.9999995262093858,
                0.9999991148430701,
                0.9999967112521135,
                1.4449798650476187e-07,
                0.9999960330136141,
                0.999998126123947,
                0.9999996940977732,
                0.9999998642567028,
                0.9999995262092727
            ],
            [
                0.9999925887219062,
                0.9999991684715762,
                0.9999990577552942,
                0.9999993524049705,
                0.9999991148432811,
                0.9999994631248043,
                0.9999921107346067,
                0.9999994631247404,
                0.9999996940977732,
                0.9999955048162826
            ],
            [
                0.9999998144608983,
                0.9999997463980427,
                0.9999997300422226,
                0.9999998555020309,
                0.9999996072137062,
                0.9999996072138936,
                0.9999997463981334,
                0.9999997300421584,
                0.9999997761971849,
                0.999999789756609
            ],
            [
                1.067703379136937e-06,
                7.338213304316717e-07,
                5.715007195384861e-07,
                1.6701421844085127e-05,
                3.9278615343901467e-07,
                8.315279285251204e-07,
                1.5534975693601474e-06,
                7.338211554725124e-07,
                6.475947981904966e-07,
                5.043474683156057e-07
            ],
            [
                0.9999998555019274,
                0.9999991684719726,
                0.9999982396563682,
                0.9999998144608762,
                0.9999998144608762,
                0.9999998642566219,
                0.9999998802069445,
                0.9999995262092163,
                0.9999995549150013,
                0.9999996072136594
            ],
            [
                8.315281267706361e-07,
                2.3823696679230424e-07,
                8.939696304213768e-06,
                1.6701423835624208e-05,
                6.962254589978262e-06,
                4.450849988798682e-07,
                2.1444950971601277e-05,
                1.3007133116732079e-05,
                2.3823696679230424e-07,
                1.4738978458623327e-05
            ],
            [
                0.9999998642566381,
                0.9999998362622358,
                0.9999991684721711,
                0.9999989322967487,
                0.9999985406230842,
                0.9999992188514838,
                0.9999991684715764,
                0.9999995818814266,
                0.9999982396574175,
                0.9999987901347501
            ],
            [
                5.043474683220276e-07,
                2.699578418198104e-07,
                6.475951069961737e-07,
                4.4508510499737865e-07,
                1.4738978458382043e-05,
                4.22283545819819e-06,
                1.9947297215043796e-06,
                5.715002426460124e-07,
                5.043476486883855e-07,
                1.0677029973158649e-06
            ],
            [
                0.9999969105044487,
                0.9999949062931808,
                0.9999978766220446,
                0.9999975938968013,
                0.9999852610180522,
                0.9999921107393013,
                0.9999992661791074,
                0.9999993524052793,
                0.9999967112521128,
                0.999986992874644
            ],
            [
                1.6373774480605869e-07,
                0.9999970976887088,
                1.760342793583908e-06,
                1.209866260432471e-06,
                1.147877359926923e-05,
                0.999994577782327,
                0.999997097688017,
                0.9999949062962166,
                7.338208055664991e-07,
                0.9999485577927039
            ],
            [
                0.9999997126313784,
                0.9999996072136594,
                0.9999998942829981,
                0.99999916847227,
                0.9999999226557962,
                0.9999993524052021,
                0.9999998724808964,
                0.999999789756634,
                0.9999997761970248,
                0.9999998144609645
            ],
            [
                0.9999999468421122,
                0.9999998461826772,
                0.999999887464838,
                0.9999997897565839,
                0.9999998144608319,
                0.9999999006881023,
                0.9999998942830358,
                0.9999998555019963,
                0.9999998362623723,
                1.0
            ],
            [
                0.9999981261239488,
                0.999998126125065,
                0.9999990577552944,
                0.9999986290429576,
                0.9999993106391196,
                0.9999957771670631,
                0.9999960330121979,
                0.9999994284993491,
                0.9999969105044507,
                0.9999978766212868
            ],
            [
                0.9999999317439059,
                0.9999998024947272,
                0.9999999176674552,
                0.9999998642566866,
                0.9999999006880195,
                0.9999998257022045,
                0.9999997463981636,
                0.9999998461826405,
                0.9999998144608319,
                0.9999999123575359
            ],
            [
                0.9999997463982241,
                0.9999997617630617,
                0.999999894283061,
                0.9999998024945624,
                0.9999997617630049,
                0.9999998802068873,
                0.9999998461826956,
                0.9999997761970248,
                0.9999996940977367,
                0.999999631011416
            ],
            [
                0.9999998555019963,
                0.999999887464932,
                0.9999998144609424,
                0.9999998942830233,
                0.9999993916406734,
                0.9999999176675436,
                0.9999996940977002,
                0.9999994284997575,
                0.9999998642566866,
                0.9999993916411085
            ],
            [
                0.999999872480942,
                0.9999996940978826,
                0.9999995549150014,
                0.9999994956527124,
                0.9999994284997575,
                0.9999998144609203,
                0.9999993916409636,
                0.9999982396565775,
                3.927861534370498e-07,
                0.9999994631249324
            ],
            [
                0.9999996940978462,
                0.9999998024945624,
                1.0,
                0.9999992188513904,
                0.9999996072137999,
                0.9999999530883898,
                0.9999993106390368,
                0.9999998461827322,
                0.9999994284996213,
                0.9999998257021214
            ],
            [
                0.999999674368781,
                0.9999997897567343,
                0.9999998257020591,
                0.9999997126314126,
                0.9999996072136126,
                0.9999997300422228,
                0.9999996940978461,
                0.9999996940978096,
                0.9999998942829225,
                0.9999997126313098
            ],
            [
                5.715002426410745e-07,
                7.338207180801359e-07,
                3.05902226923399e-07,
                1.5534971989992774e-06,
                1.2098662604192665e-06,
                1.7603427936183298e-06,
                6.475949525919915e-07,
                1.0677032518700286e-06,
                5.422218969720291e-06,
                3.7266410609940346e-06
            ],
            [
                1.0,
                0.999999887464838,
                0.9999999397643156,
                0.9999999317439628,
                0.9999998362623528,
                0.9999996940978462,
                0.9999996743686645,
                0.9999998024946095,
                0.9999998362623332,
                0.9999999123575568
            ],
            [
                0.9999998362623529,
                0.999998996985434,
                0.9999998642566219,
                0.9999998642566704,
                0.9999998461826405,
                0.9999998802069445,
                0.9999997761971583,
                0.9999999123575778,
                0.9999999434137773,
                0.9999997300422226
            ],
            [
                0.9999998874647441,
                0.9999999176674651,
                0.9999998724809571,
                0.9999998024945624,
                0.9999942280786026,
                0.9999999067050165,
                0.9999995549148422,
                0.9999998555019791,
                0.9999999468421313,
                0.9999996743686257
            ],
            [
                0.9999998874648112,
                0.9999989969856731,
                0.999999789756634,
                0.9999998724809572,
                0.9999995262093293,
                0.9999998024947272,
                0.9999998874648782,
                0.999999391641036,
                0.9999995818814266,
                0.9999992661792821
            ],
            [
                0.9999993916410361,
                0.9999994956527725,
                0.9999996743686257,
                0.9999999176675437,
                0.9999999123575987,
                0.9999998802069731,
                0.9999998257021837,
                0.9999998362623334,
                0.9999998257022045,
                0.9999998024946566
            ],
            [
                0.9999999273417837,
                0.9999984465018757,
                0.999999495652592,
                0.999999391640891,
                0.9999998642567351,
                0.9999996743686257,
                0.9999994284997575,
                0.9999998362622747,
                0.9999994631247403,
                0.999999631011372
            ],
            [
                0.9999997617630049,
                0.999999961108909,
                1.0,
                0.9999992661792821,
                0.9999993524052792,
                0.9999998257022045,
                0.9999996940978826,
                0.9999999273418182,
                0.9999998362622943,
                0.9999998144609205
            ],
            [
                0.9999997617629766,
                0.999999974890024,
                0.9999998024946566,
                0.9999996940978826,
                0.9999996533674204,
                0.9999998024946567,
                0.9999999176675239,
                0.9999999317439303,
                0.9999997897565588,
                0.9999997897567092
            ],
            [
                0.9999999317440198,
                0.9999997300421584,
                0.999999789756659,
                0.9999998555020309,
                0.9999997617630617,
                0.9999997761971315,
                0.9999996940978826,
                0.9999995262092728,
                0.9999996533672965,
                0.999999653367503
            ],
            [
                0.9999998802068873,
                0.9999998461826956,
                0.9999998257020798,
                0.9999998942830862,
                0.9999998642566866,
                0.9999989969862708,
                0.9999999500628513,
                1.0,
                0.9999999273418355,
                0.9999995262096116
            ],
            [
                0.9999997126314811,
                0.9999977396759733,
                0.9999992188514836,
                0.9999993106392017,
                0.9999994631248683,
                0.9999996533673378,
                0.9999982396567879,
                0.9999991684719727,
                0.999999653367503,
                0.9999994956523516
            ],
            [
                0.9999997463981939,
                0.9999996072138935,
                0.9999998144609424,
                0.9999998555019618,
                0.9999996743687422,
                0.999999917667573,
                0.9999998461826038,
                0.9999997761971049,
                0.9999998362622358,
                0.9999997126315153
            ],
            [
                0.9999998642566381,
                0.9999997897565588,
                0.9999994284994169,
                0.9999999067050388,
                0.9999994631251882,
                0.9999996310115039,
                0.9999998555020307,
                0.9999998362623137,
                0.9999997126313098,
                0.9999998144608098
            ],
            [
                0.9999998642567028,
                0.999999789756659,
                0.9999999123575882,
                0.999999931743914,
                0.9999997126314127,
                0.9999996940976273,
                0.9999998257022046,
                0.9999998024946802,
                0.9999998802069445,
                0.9999998724808964
            ],
            [
                0.9999998802069302,
                0.9999942280806637,
                0.9999999611088487,
                0.9999998024947038,
                0.9999999067050944,
                0.9999998802069587,
                0.9999998802069587,
                0.9999999468421946,
                0.9999957771675667,
                0.9999999317439465
            ]
        ]
    },
    {
        "q_id": "9179_mmlu_physics",
        "cot_ids": [
            1,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            86,
            87,
            88,
            89,
            92,
            93,
            94,
            95,
            96,
            97,
            99,
            100,
            101,
            103,
            104,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            124,
            126
        ],
        "rewards": [
            [
                5.422219616265831e-06,
                8.764245361752286e-08,
                1.8553910183548312e-07,
                1.2751907329024393e-07,
                4.691168275606451e-08,
                1.1253518888531272e-07,
                6.825608606172863e-08,
                2.3823693839290317e-07,
                9.931190958076104e-08,
                1.1253506814842375e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                5.4222183235249605e-06,
                NaN,
                8.939697369980456e-06,
                2.5612819054133693e-06,
                1.994729483729522e-06,
                3.4663249714612693e-07,
                5.043472278312808e-07
            ],
            [
                1.5534979397500702e-06,
                1.7603425837855082e-06,
                1.2098661161982042e-06,
                9.422442569208767e-07,
                7.88926070489716e-06,
                1.5534973841895917e-06,
                1.5534983101549167e-06,
                2.9023119851781017e-06,
                6.475946438055299e-07,
                7.338212429537553e-07
            ],
            [
                8.764249540862797e-08,
                9.931187406410953e-08,
                6.825601283086733e-08,
                2.382370235933104e-07,
                7.338208055680009e-07,
                3.2887506336235617e-06,
                1.0677032518814388e-06,
                8.764241182641775e-08,
                9.931186222523604e-08,
                7.889261645427538e-06
            ],
            [
                0.9998204719707913,
                4.450852111155216e-07,
                1.0677027427624903e-06,
                3.927862002641863e-07,
                NaN,
                1.8553914607267268e-07,
                3.9278629391427843e-07,
                0.9980732651477269,
                2.5612819054133693e-06,
                1.3709575337159875e-06
            ],
            [
                5.04347287955046e-07,
                1.444980209564556e-07,
                1.8553910183674878e-07,
                2.3823682479292225e-07,
                1.2751902768612997e-07,
                2.6995784182140636e-07,
                2.102434162245973e-07,
                3.927863875616689e-07,
                1.1253526937656726e-07,
                1.6373764721072816e-07
            ],
            [
                4.006371129776199e-05,
                NaN,
                3.72663883989755e-06,
                NaN,
                NaN,
                NaN,
                8.939697369980456e-06,
                NaN,
                NaN,
                3.120190021759579e-05
            ],
            [
                6.475950298011458e-07,
                5.715004470313855e-07,
                8.315279285370317e-07,
                1.855391239544352e-07,
                3.9278634073625165e-07,
                2.6995784182140636e-07,
                3.059021175261338e-07,
                2.382368531929327e-07,
                5.71500719545698e-07,
                1.8553919030776337e-07
            ],
            [
                2.382368531929327e-07,
                2.3823688159291947e-07,
                1.8553905760062447e-07,
                1.4449795205429202e-07,
                1.8553916819032217e-07,
                3.059022269250683e-07,
                3.0590237279085045e-07,
                4.4508510499849186e-07,
                3.466325797888292e-07,
                6.475947982037486e-07
            ],
            [
                1.7603430034743913e-06,
                3.7266388398585725e-06,
                2.260325106237323e-06,
                1.670141985446017e-05,
                6.962258739796719e-06,
                8.939698435657833e-06,
                2.5612831267202583e-06,
                1.760343003481596e-06,
                1.5534971990126997e-06,
                7.338208055664991e-07
            ],
            [
                3.9278605979534166e-07,
                3.05902190458764e-07,
                8.315281267882195e-07,
                1.0677029973158649e-06,
                1.067702870039777e-06,
                2.1024336609843824e-07,
                2.382369951932796e-07,
                1.9947292459347367e-06,
                1.760342793638743e-06,
                3.466325384678894e-07
            ],
            [
                2.1024339116168358e-07,
                3.0590237279085045e-07,
                1.7603425837903113e-06,
                0.0021827164128911643,
                4.450852641737424e-07,
                2.699577774585891e-07,
                5.043472278322555e-07,
                6.47595107001401e-07,
                3.288749849529972e-06,
                5.04347468323289e-07
            ],
            [
                8.93969950101825e-06,
                3.288750633545794e-06,
                8.315282259151545e-07,
                6.475950298021765e-07,
                4.222832437798974e-06,
                2.9023116392097746e-06,
                2.3823685319320354e-07,
                4.222833947960866e-06,
                3.288748281329893e-06,
                5.715006514176113e-07
            ],
            [
                3.927862002663297e-07,
                2.1024336609843824e-07,
                2.382369951932796e-07,
                3.05902336324494e-07,
                3.927862002663297e-07,
                1.2098661162056318e-06,
                4.450852111155216e-07,
                4.4508515805735777e-07,
                3.9278615344178325e-07,
                1.7603430034867993e-06
            ],
            [
                NaN,
                1.994730672675753e-06,
                5.715003107767143e-07,
                NaN,
                2.1024339116168358e-07,
                NaN,
                3.4663249714612693e-07,
                NaN,
                4.222831934379152e-06,
                NaN
            ],
            [
                1.8553903548287212e-07,
                5.043474082012222e-07,
                1.275190580890061e-07,
                1.637376862489725e-07,
                8.315277302857965e-07,
                2.10243290909963e-07,
                1.1253526937697666e-07,
                9.422450432030903e-07,
                1.0677027427624903e-06,
                2.699577130960941e-07
            ],
            [
                2.9023112931873767e-06,
                6.144176799283803e-06,
                1.5534975693979422e-06,
                3.7266392839425286e-06,
                2.7535704232595768e-05,
                1.209866260432471e-06,
                2.902312677150514e-06,
                1.4738983729535602e-05,
                2.7535704232595768e-05,
                NaN
            ],
            [
                6.475945666051092e-07,
                6.475947210012481e-07,
                3.059022269250683e-07,
                2.9023119851899796e-06,
                8.315279285351409e-07,
                2.2603251062450327e-06,
                1.5534971990126997e-06,
                1.5534983101602148e-06,
                1.3709570434178922e-06,
                1.9947297215125433e-06
            ],
            [
                NaN,
                NaN,
                5.715003789046955e-07,
                3.0590219045914655e-07,
                2.3823696679327928e-07,
                1.8553914607267268e-07,
                2.699576809143613e-07,
                3.0590237279085045e-07,
                3.466327450765785e-07,
                1.275190580890061e-07
            ],
            [
                3.120191137762131e-05,
                4.691162124067829e-08,
                6.023569166654288e-08,
                1.6373764721072816e-07,
                1.2751901248454963e-07,
                7.734414854823498e-08,
                4.139934586278605e-08,
                2.3823690999323465e-07,
                2.6995790618469934e-07,
                8.7642516304188e-08
            ],
            [
                8.315278294072958e-07,
                1.7603438428800754e-06,
                2.902312677137316e-06,
                1.994729245917502e-06,
                5.422217677028889e-06,
                5.043475885674441e-07,
                2.2603245673155757e-06,
                2.260323758987159e-06,
                5.715006514167015e-07,
                1.3709578605455302e-06
            ],
            [
                NaN,
                8.315284241665078e-07,
                3.4663274507713016e-07,
                3.05902336324494e-07,
                2.3823693839325527e-07,
                NaN,
                5.043475885696228e-07,
                7.338207180898968e-07,
                2.561283126728994e-06,
                1.760342793638743e-06
            ],
            [
                9.422442569315887e-07,
                6.475949526020042e-07,
                6.475947210046347e-07,
                1.0129989772532511e-05,
                6.475949526020042e-07,
                1.760343003481596e-06,
                4.450848927658745e-07,
                3.927862002663297e-07,
                3.466326211113502e-07,
                1.2098656835224664e-06
            ],
            [
                1.2751910369343538e-07,
                0.9999985406232584,
                1.2098659719788098e-06,
                1.0677024882029858e-06,
                NaN,
                NaN,
                7.33821330437595e-07,
                1.7603425837903113e-06,
                5.043474683240344e-07,
                NaN
            ],
            [
                8.315279285370317e-07,
                7.734418542875216e-08,
                7.338207180898968e-07,
                3.927863407379485e-07,
                9.422442569315887e-07,
                NaN,
                6.47595107001401e-07,
                7.338211554813555e-07,
                9.422450432030903e-07,
                5.71500719545698e-07
            ],
            [
                1.2751899728286965e-07,
                9.422448185510695e-07,
                2.1024339116168358e-07,
                7.734414854823498e-08,
                6.023577783447482e-08,
                1.637376862489725e-07,
                1.670141587208191e-05,
                1.637377057680051e-07,
                4.6911677163762064e-08,
                3.726638395634011e-06
            ],
            [
                NaN,
                5.043475885696228e-07,
                5.715006514176113e-07,
                8.315284241650899e-07,
                2.2603240284371276e-06,
                NaN,
                NaN,
                7.338209805090567e-07,
                NaN,
                7.338208930460318e-07
            ],
            [
                NaN,
                NaN,
                1.855391239547094e-07,
                6.47594875403829e-07,
                4.4508499888275247e-07,
                NaN,
                5.043475284468537e-07,
                7.338211554813555e-07,
                3.9278629391427843e-07,
                8.315279285370317e-07
            ],
            [
                2.3823685319244518e-07,
                1.994729483729522e-06,
                NaN,
                4.450851049991497e-07,
                2.1024336609874897e-07,
                3.05902336324494e-07,
                1.2098652508424818e-06,
                2.699576809143613e-07,
                6.475947210031623e-07,
                1.0677024882029858e-06
            ],
            [
                7.338210679979539e-07,
                2.561282516066741e-06,
                2.5612831267202583e-06,
                NaN,
                1.4449798650551755e-07,
                5.043473480777865e-07,
                1.370957860576702e-06,
                2.3823702359290413e-07,
                1.3709567165617364e-06,
                NaN
            ],
            [
                6.825601283086733e-08,
                1.4449805540763184e-07,
                1.8553903548231313e-07,
                7.734415776836702e-08,
                1.8553905760024476e-07,
                1.1253513522447425e-07,
                2.1024331597262577e-07,
                1.8553914607267268e-07,
                1.275191036933194e-07,
                1.6373764721072816e-07
            ],
            [
                4.450850519403407e-07,
                3.726639284144195e-06,
                5.422220262636381e-06,
                1.209865539298447e-06,
                1.0677024882009222e-06,
                2.260325106237323e-06,
                1.7603430034867993e-06,
                1.994729721518893e-06,
                1.9947304348862686e-06,
                1.3709568799919866e-06
            ],
            [
                5.043474082005342e-07,
                1.8553907971855875e-07,
                1.4449807263287805e-07,
                6.023578501513224e-08,
                3.4663249714612693e-07,
                4.691161005609407e-08,
                4.2228339479858295e-06,
                3.0590219045914655e-07,
                1.4449805540763184e-07,
                6.962258739796719e-06
            ],
            [
                1.994729483729522e-06,
                3.288749849529972e-06,
                2.6995774527718623e-07,
                3.2887494574832472e-06,
                3.9278605979534166e-07,
                4.4508515805735777e-07,
                3.927863407379485e-07,
                2.902312677150514e-06,
                1.3709567165617364e-06,
                1.855390354818069e-07
            ],
            [
                1.855391239539711e-07,
                8.315280276505193e-07,
                8.315278294072958e-07,
                5.715004470243685e-07,
                6.475947209918244e-07,
                7.338212429582604e-07,
                7.338213304283347e-07,
                5.043474683204221e-07,
                9.422443692446175e-07,
                6.144173136019732e-06
            ],
            [
                4.4508510499849186e-07,
                1.855391681906175e-07,
                7.338207180898968e-07,
                5.043474082012222e-07,
                5.422221555414699e-06,
                1.994729483729522e-06,
                5.422221555414699e-06,
                1.012998977264307e-05,
                2.382370235933104e-07,
                2.5612834320563895e-06
            ],
            [
                9.931202796993203e-08,
                1.855391681898159e-07,
                3.927862470899887e-07,
                1.125352291309328e-07,
                2.1024331597262577e-07,
                8.764244316973974e-08,
                1.4449795205429202e-07,
                9.931193325852072e-08,
                7.734414854823498e-08,
                5.04347528446051e-07
            ],
            [
                2.260324028443809e-06,
                2.2603248367949354e-06,
                4.450848927637999e-07,
                8.764244316973974e-08,
                NaN,
                1.473898900066424e-05,
                6.962256249935742e-06,
                9.422449308789479e-07,
                7.338208930460318e-07,
                4.785093924389007e-06
            ],
            [
                3.927863875616689e-07,
                2.1024341622426268e-07,
                NaN,
                2.699577774589574e-07,
                5.715005832895975e-07,
                NaN,
                6.47594952603035e-07,
                3.9278620026686556e-07,
                NaN,
                NaN
            ],
            [
                1.8553914607267268e-07,
                8.764254764749753e-08,
                2.1024341622368903e-07,
                1.8553910183674878e-07,
                3.4663249714451116e-07,
                1.444980209564556e-07,
                1.6373770576776313e-07,
                2.5612812947077304e-06,
                3.05902190458764e-07,
                5.043472879540142e-07
            ],
            [
                NaN,
                NaN,
                5.043473480777865e-07,
                1.6373762769138607e-07,
                0.9998766054259762,
                6.962257079889302e-06,
                1.209866260432471e-06,
                5.043476486924565e-07,
                NaN,
                8.31528325040778e-07
            ],
            [
                3.9278610661822475e-07,
                3.0590237279032884e-07,
                2.1024326584639497e-07,
                3.059022269250683e-07,
                9.422442569315887e-07,
                3.927862470899887e-07,
                1.5534981249697903e-06,
                6.475947982037486e-07,
                3.059022998576899e-07,
                5.04347287955046e-07
            ],
            [
                3.0590226338838606e-07,
                NaN,
                7.338212429504183e-07,
                4.785092783519724e-06,
                8.315281267800897e-07,
                3.927862470899887e-07,
                1.3709570434122812e-06,
                9.422449308774482e-07,
                5.04347528440776e-07,
                5.043475885674441e-07
            ],
            [
                2.6995784182140636e-07,
                8.315278294114555e-07,
                2.3823702359290413e-07,
                NaN,
                8.315277302857965e-07,
                1.6373766672994222e-07,
                2.699578740032504e-07,
                1.6373764721072816e-07,
                3.0590237279032884e-07,
                NaN
            ],
            [
                2.561283126728994e-06,
                1.3709572068522336e-06,
                1.7603430034867993e-06,
                1.553497754592186e-06,
                5.043475885696228e-07,
                NaN,
                3.927862470899887e-07,
                4.4508515805735777e-07,
                1.9947292459406333e-06,
                1.2098656835252174e-06
            ],
            [
                1.9947297215125433e-06,
                5.715005151606823e-07,
                5.715002426475718e-07,
                1.5534977545886537e-06,
                2.9023123311583482e-06,
                1.2098659719757836e-06,
                2.3823685319244518e-07,
                9.931195693628605e-08,
                1.067703124601679e-06,
                3.059022998576899e-07
            ],
            [
                7.338212429582604e-07,
                5.043476486924565e-07,
                3.0590237279085045e-07,
                3.9278615344178325e-07,
                3.0590237279032884e-07,
                5.043475885696228e-07,
                1.6373766672973748e-07,
                3.466325797888292e-07,
                2.382370235933104e-07,
                1.4449805540763184e-07
            ],
            [
                5.043475284468537e-07,
                NaN,
                2.1024336609874897e-07,
                3.4663262111182307e-07,
                1.2098661162023305e-06,
                NaN,
                1.855391681906175e-07,
                5.422217677152175e-06,
                3.4663262111182307e-07,
                1.637376862489725e-07
            ],
            [
                6.47594952603035e-07,
                7.33821330437595e-07,
                8.315277302857965e-07,
                1.9947297215125433e-06,
                1.5534977545886537e-06,
                8.315279285370317e-07,
                3.059022998581767e-07,
                1.994729008145876e-06,
                7.338208055680009e-07,
                3.927862470899887e-07
            ],
            [
                1.0677026154806063e-06,
                1.2098659719788098e-06,
                5.043475284468537e-07,
                4.4508505193932864e-07,
                1.2098652508424818e-06,
                1.5534973842076057e-06,
                1.5534975693979422e-06,
                5.715002426475718e-07,
                9.422448185534261e-07,
                4.2228319344021954e-06
            ],
            [
                5.043472278322555e-07,
                8.315278294114555e-07,
                2.260324567337161e-06,
                2.5612825160562587e-06,
                NaN,
                4.4508510499737865e-07,
                8.315281267834927e-07,
                8.315283250394546e-07,
                3.466326211113502e-07,
                7.338213304316717e-07
            ],
            [
                8.315277302857965e-07,
                NaN,
                7.338211554813555e-07,
                NaN,
                NaN,
                1.9947292459406333e-06,
                1.7603425837903113e-06,
                1.7603430034867993e-06,
                NaN,
                NaN
            ],
            [
                7.338208930460318e-07,
                1.5534975693869924e-06,
                NaN,
                0.9999785550439896,
                5.715006514176113e-07,
                5.715004470334646e-07,
                1.3709575337159875e-06,
                1.5534984953552536e-06,
                3.4663274507713016e-07,
                1.3709568799823232e-06
            ],
            [
                2.1024336609874897e-07,
                7.338208055680009e-07,
                1.3709575337159875e-06,
                1.4449800373118268e-07,
                2.699576809143613e-07,
                1.6373766672973748e-07,
                7.338207180898968e-07,
                5.715003107767143e-07,
                9.931188590299572e-08,
                1.6373776432509826e-07
            ],
            [
                0.9999756997651024,
                5.715006514176113e-07,
                3.466326624336003e-07,
                3.726639284144195e-06,
                1.5534973842076057e-06,
                7.338207180898968e-07,
                2.1024331597288867e-07,
                5.043473480784173e-07,
                8.315282259138311e-07,
                4.4508515805735777e-07
            ],
            [
                9.422450431860582e-07,
                1.3709576971379186e-06,
                1.7603434231385591e-06,
                5.04347348075149e-07,
                8.315278294001114e-07,
                1.3709568799823232e-06,
                1.0677024881829577e-06,
                1.7603436330091044e-06,
                1.5534983101478522e-06,
                1.3709573702722555e-06
            ],
            [
                1.3709570434219446e-06,
                1.2098655392921197e-06,
                1.5534979397790343e-06,
                1.2098659719788098e-06,
                2.2603240284371276e-06,
                1.7603438428800754e-06,
                1.3709576971463352e-06,
                1.2098652508424818e-06,
                1.9947301970972664e-06,
                NaN
            ],
            [
                2.2603242978778778e-06,
                5.4222176771176554e-06,
                1.9947297215125433e-06,
                2.2603234895289998e-06,
                1.553498124964492e-06,
                NaN,
                3.2887506336086064e-06,
                5.422220909009474e-06,
                2.561281600076256e-06,
                1.9947299592933255e-06
            ],
            [
                3.288749849529972e-06,
                1.0677027427624903e-06,
                1.760342793638743e-06,
                1.0129988565084915e-05,
                3.466326624336003e-07,
                1.209865827752005e-06,
                2.2603248367949354e-06,
                1.0677032518814388e-06,
                1.7603440527334603e-06,
                8.315278294114555e-07
            ],
            [
                5.715005832886879e-07,
                1.670141786295194e-05,
                1.994729483723626e-06,
                6.962259569750576e-06,
                8.315283250394546e-07,
                2.5612812947508257e-06,
                1.994730672668496e-06,
                3.726637951387472e-06,
                7.889259764517575e-06,
                7.889266347636241e-06
            ],
            [
                1.5534973841705173e-06,
                6.144174601935314e-06,
                3.726638839806038e-06,
                1.4738976701170414e-05,
                8.315278294072958e-07,
                1.4738976700929127e-05,
                2.902312677137316e-06,
                4.785094494716039e-06,
                7.889260704818233e-06,
                2.1444958637356654e-05
            ],
            [
                2.3823690999160957e-07,
                0.005220125495272452,
                1.0129988565084915e-05,
                2.1024339116134898e-07,
                3.9278629391427843e-07,
                3.0590226339061185e-07,
                2.382370235933104e-07,
                4.450850519409479e-07,
                1.1253509497883659e-07,
                1.8553910183674878e-07
            ],
            [
                2.102434412875379e-07,
                6.475947982022763e-07,
                1.3709568799919866e-06,
                2.2603248367949354e-06,
                1.0677024882009222e-06,
                8.315282259138311e-07,
                3.9278605979534166e-07,
                4.785094494811783e-06,
                3.466327450765785e-07,
                1.994729721518893e-06
            ],
            [
                8.315277302857965e-07,
                1.5534981249697903e-06,
                8.315278294114555e-07,
                1.0677033791612137e-06,
                0.9999546021152791,
                9.422449308774482e-07,
                2.5612825160562587e-06,
                1.209865827752005e-06,
                1.6373764721072816e-07,
                1.2098659719788098e-06
            ],
            [
                3.059022998576899e-07,
                3.059022998576899e-07,
                3.9278615344178325e-07,
                5.043474081993875e-07,
                2.3823702359290413e-07,
                6.475950298011458e-07,
                1.3709575337159875e-06,
                2.69957906184239e-07,
                1.2751904288739315e-07,
                2.902311639073834e-06
            ],
            [
                4.450852641737424e-07,
                3.466327037548308e-07,
                2.10243290909724e-07,
                NaN,
                2.9023116392097746e-06,
                8.315279285370317e-07,
                1.2098652508391807e-06,
                3.927862470899887e-07,
                7.338209805240734e-07,
                5.715006514176113e-07
            ],
            [
                7.338207180898968e-07,
                NaN,
                NaN,
                5.422220909041528e-06,
                9.422443692574719e-07,
                NaN,
                5.043474683240344e-07,
                8.31528325040778e-07,
                2.2603248367949354e-06,
                6.47594952603035e-07
            ],
            [
                2.561281600086738e-06,
                4.222833947932061e-06,
                1.6701421845361053e-05,
                1.3709567165530083e-06,
                6.144176066521288e-06,
                1.0677033791612137e-06,
                6.144172404738491e-06,
                4.0063706519072155e-05,
                NaN,
                1.0129993395336818e-05
            ],
            [
                6.47594952603035e-07,
                1.0677029973219343e-06,
                3.9278629391427843e-07,
                5.043472278322555e-07,
                4.450848927658745e-07,
                5.043476486924565e-07,
                8.315277302857965e-07,
                3.288749849529972e-06,
                5.04347287955046e-07,
                7.338207180898968e-07
            ],
            [
                8.315277302857965e-07,
                4.450852641737424e-07,
                4.450852111148132e-07,
                5.04347468323289e-07,
                NaN,
                NaN,
                1.0677027427624903e-06,
                NaN,
                3.9278605979534166e-07,
                3.466326624336003e-07
            ],
            [
                0.00012339460443623593,
                0.9998766053960557,
                1.1253513522447425e-07,
                4.450848927658745e-07,
                5.1442207537151994e-05,
                3.927863875616689e-07,
                NaN,
                5.144221366885164e-05,
                0.9998766054694448,
                1.275191036933194e-07
            ],
            [
                9.422443692555439e-07,
                2.2603242978871282e-06,
                3.288750241561788e-06,
                1.5534983101602148e-06,
                NaN,
                NaN,
                7.338211554801876e-07,
                NaN,
                5.04347468323289e-07,
                1.0677024882009222e-06
            ],
            [
                2.9023119851899796e-06,
                6.475949526003845e-07,
                1.3709575337159875e-06,
                2.902312331170226e-06,
                6.144172404738491e-06,
                8.315278294114555e-07,
                1.2098656835224664e-06,
                1.209865539295696e-06,
                3.72663883989755e-06,
                2.9023119851899796e-06
            ],
            [
                1.6373772528677946e-07,
                3.927862470899887e-07,
                3.05902336324494e-07,
                6.962257909785973e-06,
                1.7603430034743913e-06,
                4.222833444590791e-06,
                3.466325797896173e-07,
                1.6373772528704005e-07,
                2.6995784182183607e-07,
                2.102434162245973e-07
            ],
            [
                7.889263526345123e-06,
                2.5612825160562587e-06,
                4.785093924362895e-06,
                1.4738983729535602e-05,
                1.7603438428800754e-06,
                4.222832437798974e-06,
                2.9023123311583482e-06,
                5.422220909009474e-06,
                1.5534973842030142e-06,
                3.726638839878908e-06
            ],
            [
                2.1024331597262577e-07,
                3.927862002663297e-07,
                3.9278615344178325e-07,
                3.466327037553825e-07,
                1.4449800373065699e-07,
                3.4663274507713016e-07,
                1.8553907971855875e-07,
                8.315277302841894e-07,
                4.450852111135988e-07,
                3.9278629391427843e-07
            ],
            [
                5.043475885696228e-07,
                2.382369951932796e-07,
                2.6995784182183607e-07,
                1.6373772528704005e-07,
                2.3823696679327928e-07,
                4.4508515805735777e-07,
                NaN,
                6.023577783447482e-08,
                3.4663249714612693e-07,
                5.715006514176113e-07
            ],
            [
                2.2603240284371276e-06,
                9.422445939054222e-07,
                1.6373770576776313e-07,
                1.5534971990126997e-06,
                1.4449798650551755e-07,
                7.338208055680009e-07,
                7.338212429582604e-07,
                5.043473480777865e-07,
                1.8553905760062447e-07,
                2.6995784182183607e-07
            ],
            [
                8.315283250394546e-07,
                1.3709575337016483e-06,
                4.785092783519724e-06,
                1.3007126914435202e-05,
                6.9622587397397306e-06,
                1.209865539295696e-06,
                1.7603430034867993e-06,
                2.2603253756874524e-06,
                1.2098652508391807e-06,
                1.8553905760062447e-07
            ],
            [
                6.475951069985296e-07,
                1.7603440527334603e-06,
                NaN,
                1.994729483729522e-06,
                3.288747889284851e-06,
                6.475950298021765e-07,
                NaN,
                2.3823693839290317e-07,
                6.144175334468545e-06,
                8.315279285370317e-07
            ],
            [
                NaN,
                3.9278620026686556e-07,
                3.535625493182252e-05,
                1.8553910183674878e-07,
                NaN,
                5.71500515161527e-07,
                NaN,
                1.3709570434122812e-06,
                9.422450432030903e-07,
                1.4449800373118268e-07
            ],
            [
                2.1024339116168358e-07,
                1.8553905760062447e-07,
                3.9278610661902853e-07,
                1.855391239544352e-07,
                4.450852111155216e-07,
                3.466325797888292e-07,
                1.4449798650551755e-07,
                2.382370235933104e-07,
                2.6995784182140636e-07,
                3.4663278639892215e-07
            ],
            [
                5.715005832895975e-07,
                3.4663266243308805e-07,
                NaN,
                1.3709567165617364e-06,
                2.6995774527577444e-07,
                2.260325106237323e-06,
                1.4449795205472734e-07,
                3.466325797888292e-07,
                7.338210680021253e-07,
                NaN
            ],
            [
                3.46632497145457e-07,
                3.059022269250683e-07,
                3.059022269250683e-07,
                1.2751901248454963e-07,
                2.1024336609843824e-07,
                2.6995771309523475e-07,
                2.1024331597262577e-07,
                1.855391681906175e-07,
                3.46632497145457e-07,
                1.2751902768612997e-07
            ],
            [
                NaN,
                3.927863407379485e-07,
                2.902312677150514e-06,
                5.71500719545698e-07,
                8.315277302841894e-07,
                2.3823688159291947e-07,
                2.260324567337161e-06,
                9.422448185534261e-07,
                5.715004470326849e-07,
                6.60521761905875e-05
            ],
            [
                1.7603438428740716e-06,
                6.475947210012481e-07,
                6.475947210012481e-07,
                7.338208055489796e-07,
                5.715003789017068e-07,
                3.9278638755456876e-07,
                5.043472879525233e-07,
                9.4224425692559e-07,
                6.475951069985296e-07,
                5.043475885634304e-07
            ],
            [
                0.015906389729159955,
                9.422450432014836e-07,
                0.00023050679810176722,
                7.338208055680009e-07,
                NaN,
                5.715006514167015e-07,
                NaN,
                NaN,
                5.04347468323289e-07,
                NaN
            ],
            [
                1.9947304348862686e-06,
                NaN,
                0.00010889696127518294,
                3.726639728370556e-06,
                9.422444815814404e-07,
                2.902312677150514e-06,
                3.7266410611296085e-06,
                2.260323758939877e-06,
                2.5612831267202583e-06,
                3.466325384678894e-07
            ],
            [
                2.6995790618469934e-07,
                3.9278629391427843e-07,
                NaN,
                2.3823688159237777e-07,
                9.422442569315887e-07,
                3.288749065423109e-06,
                5.043475885674441e-07,
                1.3709568799919866e-06,
                3.0590237279032884e-07,
                8.315281267861397e-07
            ],
            [
                5.043476486915964e-07,
                9.422442569315887e-07,
                1.2098653950480359e-06,
                3.2887482812745586e-06,
                1.0677029973192638e-06,
                2.260325106237323e-06,
                3.288748673360027e-06,
                1.8553910183674878e-07,
                1.0129989772274546e-05,
                1.0677032518785256e-06
            ],
            [
                4.4508510499737865e-07,
                2.69957906184239e-07,
                2.6995784182073116e-07,
                8.315282259138311e-07,
                2.382369951932796e-07,
                3.9278634073732336e-07,
                1.4449798650551755e-07,
                1.4449795205429202e-07,
                1.27519088491875e-07,
                1.855391239544352e-07
            ],
            [
                3.4663262111182307e-07,
                3.466325797888292e-07,
                NaN,
                4.450852111155216e-07,
                8.315278294114555e-07,
                7.33821330437595e-07,
                5.71500515161527e-07,
                8.315277302857965e-07,
                8.315279285370317e-07,
                1.7603425837903113e-06
            ],
            [
                1.1253506814797596e-07,
                1.5534977545886537e-06,
                NaN,
                5.715002426475718e-07,
                1.8553907971855875e-07,
                9.422449308774482e-07,
                2.3823682479181176e-07,
                7.338212429582604e-07,
                1.855391681906175e-07,
                1.8553905760024476e-07
            ],
            [
                9.422445939032799e-07,
                7.338211554783522e-07,
                3.059022998576899e-07,
                4.450852111135988e-07,
                5.043472879540142e-07,
                3.46632497145457e-07,
                2.3823702359290413e-07,
                1.2098662604291696e-06,
                2.699577774585891e-07,
                1.6373776432509826e-07
            ],
            [
                5.043474683240344e-07,
                5.043475885696228e-07,
                NaN,
                1.5534984953552536e-06,
                9.422447062294175e-07,
                3.466325797900508e-07,
                3.466326624336003e-07,
                1.855390576008354e-07,
                8.31528325040778e-07,
                NaN
            ],
            [
                6.475948754028718e-07,
                5.043473480777865e-07,
                6.962254589978262e-06,
                4.4508510499849186e-07,
                1.5534975693869924e-06,
                1.067703124601679e-06,
                5.422219616228845e-06,
                1.3709573702856596e-06,
                4.4508510499849186e-07,
                1.3709570434219446e-06
            ],
            [
                3.0590215399183813e-07,
                3.4663278639892215e-07,
                1.2098653950606901e-06,
                3.927862939113312e-07,
                1.0677024881980089e-06,
                6.475951069961737e-07,
                2.382369667929001e-07,
                5.715007195431641e-07,
                3.9278615344178325e-07,
                6.475951069961737e-07
            ],
            [
                2.3823702359290413e-07,
                2.6995784182140636e-07,
                3.059023727894942e-07,
                4.450850519403407e-07,
                1.8553916819032217e-07,
                3.466327037512053e-07,
                1.209865827752005e-06,
                1.3709575337159875e-06,
                2.3823690999063455e-07,
                1.855391681891831e-07
            ],
            [
                4.2228334445658276e-06,
                1.0677029973158649e-06,
                6.962255419728997e-06,
                1.5534979397740895e-06,
                1.3709570434178922e-06,
                1.1478764021029928e-05,
                2.2603234895053587e-06,
                1.5534984953199313e-06,
                1.2098661161927025e-06,
                3.2887486733420804e-06
            ],
            [
                1.6373768624837685e-07,
                7.33821330437595e-07,
                2.90231094723893e-06,
                5.71500515161527e-07,
                2.6995790618469934e-07,
                3.9278629391427843e-07,
                1.0677024882029858e-06,
                1.8553919030858602e-07,
                1.067703124601679e-06,
                5.043475885696228e-07
            ],
            [
                8.315281267861397e-07,
                7.338212429582604e-07,
                4.450848927658745e-07,
                NaN,
                8.315281267861397e-07,
                1.0677033791612137e-06,
                5.043476486915964e-07,
                8.315284241650899e-07,
                2.2603234895372223e-06,
                7.338210680021253e-07
            ],
            [
                4.22283545819819e-06,
                7.33821330437595e-07,
                5.715004470334646e-07,
                7.338207180898968e-07,
                6.475945666063607e-07,
                NaN,
                3.726639284144195e-06,
                1.994729721518893e-06,
                NaN,
                NaN
            ],
            [
                8.939697368842181e-06,
                1.2098661161927025e-06,
                2.5612816000646084e-06,
                3.2887502409830123e-06,
                2.2603248367512505e-06,
                3.288749849209925e-06,
                9.422448185510695e-07,
                3.7266401726359486e-06,
                2.902313369111213e-06,
                1.0677027427600627e-06
            ],
            [
                4.450852111155216e-07,
                1.3709576971425944e-06,
                2.1024334103581732e-07,
                1.3709576971463352e-06,
                5.715002426460124e-07,
                8.939700567004841e-06,
                5.715006514167015e-07,
                2.561281600086738e-06,
                1.7603425837903113e-06,
                3.466326624336003e-07
            ],
            [
                5.715006514176113e-07,
                1.7603440527286572e-06,
                2.260324836787226e-06,
                1.5534971990169383e-06,
                3.4663274507713016e-07,
                NaN,
                7.338208930460318e-07,
                4.4508494582405734e-07,
                1.0677027427624903e-06,
                4.4508515805735777e-07
            ],
            [
                7.338208055680009e-07,
                2.2603248367949354e-06,
                3.9278605979534166e-07,
                3.059022998576899e-07,
                NaN,
                4.4508494582405734e-07,
                3.05902336324494e-07,
                7.338208930460318e-07,
                3.927862470899887e-07,
                NaN
            ],
            [
                3.53562549305363e-05,
                3.466327863983311e-07,
                0.9999151889385698,
                9.931196877517082e-08,
                1.1253524254615121e-07,
                3.4663262111182307e-07,
                1.855390576008354e-07,
                3.65348425788669e-08,
                7.734421308914719e-08,
                1.4449807263287805e-07
            ],
            [
                1.5534975693933505e-06,
                3.726638395634011e-06,
                2.2603251062147097e-06,
                2.561282210740037e-06,
                1.760343003481596e-06,
                1.9947299593014888e-06,
                NaN,
                9.422445939032799e-07,
                1.370957860567974e-06,
                8.939695238536645e-06
            ],
            [
                5.715005151606823e-07,
                6.475950298021765e-07,
                3.9278629391427843e-07,
                3.059022998581767e-07,
                9.422443692574719e-07,
                7.338209805240734e-07,
                1.637377448057981e-07,
                7.88926446679691e-06,
                1.3709572068522336e-06,
                6.475945666063607e-07
            ]
        ]
    },
    {
        "q_id": "9331_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999984465015057,
                0.9999981261243949,
                1.2098659719788098e-06,
                0.9999991148429647,
                0.9999980052700425,
                0.9999982396561581,
                0.9999985406230846,
                1.8553919030858602e-07,
                0.9999990577554068,
                0.9999985406243023
            ],
            [
                5.144219527356777e-05,
                7.338208930460318e-07,
                2.5612819054133693e-06,
                3.059022998581767e-07,
                2.9023112932296107e-06,
                1.3007126914612648e-05,
                8.315282259138311e-07,
                3.05902263391829e-07,
                7.33821330437595e-07,
                1.6373776432509826e-07
            ],
            [
                4.4508526417298334e-07,
                4.4508494582314646e-07,
                1.209865539295696e-06,
                2.3823696679230424e-07,
                9.422444815814404e-07,
                1.994729008145876e-06,
                5.04347287955046e-07,
                5.043473480766399e-07,
                1.275190580884987e-07,
                1.1253517547010071e-07
            ],
            [
                9.422450431954847e-07,
                9.422442569315887e-07,
                7.338209805170655e-07,
                8.315282259089153e-07,
                1.0677027427525368e-06,
                6.475951069985296e-07,
                7.338209805200689e-07,
                1.7603427936263351e-06,
                5.715003788993679e-07,
                9.4224425692559e-07
            ],
            [
                8.315277302841894e-07,
                2.6995774527718623e-07,
                7.338209805224048e-07,
                6.475951069985296e-07,
                5.04347528446051e-07,
                NaN,
                5.043472879525233e-07,
                3.927862002663297e-07,
                5.715002426475718e-07,
                1.0677024881980089e-06
            ],
            [
                5.043476486915964e-07,
                1.2098661162056318e-06,
                2.699578096393206e-07,
                4.785095065232451e-06,
                3.4663249714650126e-07,
                3.05902263391829e-07,
                1.2751902768612997e-07,
                3.927860597945825e-07,
                3.927863407379485e-07,
                7.338207180864763e-07
            ],
            [
                1.5534975693979422e-06,
                1.4449802095666915e-07,
                NaN,
                5.043475284468537e-07,
                3.7266383956509585e-06,
                2.699578096403948e-07,
                1.0677026154827912e-06,
                2.3823693839325527e-07,
                6.962258739796719e-06,
                1.3709575337159875e-06
            ],
            [
                1.3709567165617364e-06,
                4.222832941193893e-06,
                8.315282259138311e-07,
                1.760342793638743e-06,
                1.5534971990169383e-06,
                1.370957860576702e-06,
                1.0677028700422047e-06,
                2.5612819054133693e-06,
                1.7603425837855082e-06,
                NaN
            ],
            [
                1.855391239544352e-07,
                NaN,
                1.275190276859705e-07,
                8.315284241665078e-07,
                6.475950298011458e-07,
                2.1024341622426268e-07,
                1.2751905808881762e-07,
                2.3823702359290413e-07,
                1.1253513522447425e-07,
                0.9999785550466243
            ],
            [
                NaN,
                1.209866260432471e-06,
                1.760342793638743e-06,
                3.05902263391829e-07,
                1.7603438428800754e-06,
                4.4508515805735777e-07,
                1.7603430034867993e-06,
                3.2887506336086064e-06,
                4.450852641737424e-07,
                1.7603425837903113e-06
            ],
            [
                2.260324836787226e-06,
                0.9999934595596728,
                NaN,
                0.9999990577551828,
                0.9999452402244314,
                0.9999991148428592,
                0.9999974387165722,
                0.9999987121047869,
                NaN,
                NaN
            ],
            [
                6.47595107001401e-07,
                1.4449796928021588e-07,
                NaN,
                0.0005527787493163986,
                1.2098659719788098e-06,
                6.47595107001401e-07,
                1.0677028700422047e-06,
                4.450850519409479e-07,
                3.05902263391829e-07,
                7.338211554813555e-07
            ],
            [
                3.288749065423109e-06,
                3.9278629391427843e-07,
                3.535623807260338e-05,
                5.715003107755449e-07,
                3.288748281329893e-06,
                2.2603253756956754e-06,
                6.144175334468545e-06,
                1.3007123813193233e-05,
                2.2603234895372223e-06,
                1.9947292459406333e-06
            ],
            [
                1.2751907329024393e-07,
                2.6995771309523475e-07,
                1.8553903548231313e-07,
                1.275190276853036e-07,
                8.315280276456036e-07,
                7.734421308914719e-08,
                8.315282259051341e-07,
                1.637377448057981e-07,
                2.382369383923073e-07,
                1.8553905759969634e-07
            ],
            [
                1.370957860576702e-06,
                1.760343213335281e-06,
                0.9999904837438824,
                1.3007133116732079e-05,
                7.889261645427538e-06,
                0.9999843104560537,
                NaN,
                NaN,
                5.04347287955046e-07,
                9.422450432014836e-07
            ],
            [
                NaN,
                NaN,
                9.422443692574719e-07,
                NaN,
                8.315284241650899e-07,
                NaN,
                NaN,
                NaN,
                2.9023109472494878e-06,
                3.0590219045914655e-07
            ],
            [
                2.260324567337161e-06,
                1.9947299593014888e-06,
                4.450848927650143e-07,
                3.53562422882756e-05,
                1.2098662604291696e-06,
                0.9998204719510341,
                1.760343633031919e-06,
                2.902312677150514e-06,
                1.7603430034867993e-06,
                2.2603237589542675e-06
            ],
            [
                8.939694172957213e-06,
                NaN,
                8.939697369980456e-06,
                2.260324836787226e-06,
                2.4300249425247723e-05,
                4.450850519403407e-07,
                7.889266347786918e-06,
                3.7266410611296085e-06,
                0.9999756997628324,
                5.422217030747413e-06
            ],
            [
                8.764248496084983e-08,
                4.450852641737424e-07,
                2.1024339116168358e-07,
                1.637376862489725e-07,
                1.275190732904469e-07,
                2.6995784182183607e-07,
                5.715006514176113e-07,
                3.059022998581767e-07,
                2.10243290909963e-07,
                3.927863875616689e-07
            ],
            [
                1.8553916819032217e-07,
                1.1253526937656726e-07,
                4.4508510499849186e-07,
                1.4449798650551755e-07,
                5.043476486915964e-07,
                2.1024326584639497e-07,
                1.444979692800516e-07,
                4.4508515805735777e-07,
                3.0590226339061185e-07,
                1.4449805540740185e-07
            ],
            [
                6.962257079889302e-06,
                3.466326624336003e-07,
                9.422447062294175e-07,
                1.0677024882029858e-06,
                4.222833948008874e-06,
                7.338207180898968e-07,
                NaN,
                4.222834954801051e-06,
                1.2098659719788098e-06,
                6.475945666063607e-07
            ],
            [
                NaN,
                0.9999921107383795,
                2.5612819054133693e-06,
                1.2098659719788098e-06,
                1.7603425837903113e-06,
                9.422444815814404e-07,
                1.3709568799919866e-06,
                1.067703124601679e-06,
                1.2098662604291696e-06,
                2.90231094723893e-06
            ],
            [
                2.144495864059426e-05,
                1.0677027427624903e-06,
                5.715006514176113e-07,
                NaN,
                1.4738981972564636e-05,
                NaN,
                1.209865827752005e-06,
                8.315278294114555e-07,
                3.927862470905692e-07,
                NaN
            ],
            [
                NaN,
                0.9999945777829773,
                5.715005832872586e-07,
                3.2887506336235617e-06,
                2.1024334103581732e-07,
                4.450850519409479e-07,
                1.8925141473978602e-05,
                5.4222183235249605e-06,
                1.3709576971463352e-06,
                1.994729008151319e-06
            ],
            [
                1.2098652508424818e-06,
                5.043475885696228e-07,
                NaN,
                3.927862002663297e-07,
                4.450852111148132e-07,
                9.422450432014836e-07,
                3.726639284144195e-06,
                2.561282210740037e-06,
                3.05902263391829e-07,
                4.450852641737424e-07
            ],
            [
                9.422445939054222e-07,
                0.9999885212360102,
                4.006368264282944e-05,
                7.889262585886274e-06,
                5.715003789046955e-07,
                5.04347468323289e-07,
                7.484621836619826e-05,
                6.962257079889302e-06,
                1.2098661162056318e-06,
                1.7603438428800754e-06
            ],
            [
                1.7603425837855082e-06,
                5.04347468323289e-07,
                1.209866260432471e-06,
                1.3709572068522336e-06,
                1.5534975693979422e-06,
                1.209866260432471e-06,
                3.726637951387472e-06,
                5.715006514167015e-07,
                3.726639284144195e-06,
                2.902312677150514e-06
            ],
            [
                1.7603440527286572e-06,
                1.9947294837154625e-06,
                2.102434162245973e-07,
                1.0677029973192638e-06,
                1.4738981971813965e-05,
                1.067702870039777e-06,
                6.475949526003845e-07,
                2.5612825160562587e-06,
                4.222833947960866e-06,
                6.14417753171671e-06
            ],
            [
                8.315278294072958e-07,
                5.043475885674441e-07,
                6.475951069985296e-07,
                4.450849458218309e-07,
                5.715005832853093e-07,
                4.4508494582314646e-07,
                7.338207180864763e-07,
                1.0677024881980089e-06,
                7.338211554783522e-07,
                5.715007195431641e-07
            ],
            [
                3.7266383956509585e-06,
                0.9999869928669735,
                0.999964643737402,
                NaN,
                2.3823690999290963e-07,
                0.9999945777829922,
                0.9999985406241294,
                1.0677029973219343e-06,
                3.05902263391829e-07,
                5.043472278322555e-07
            ],
            [
                3.0590237279032884e-07,
                NaN,
                NaN,
                1.9947304348862686e-06,
                NaN,
                5.04347468323289e-07,
                NaN,
                2.382370235922541e-07,
                5.715003789046955e-07,
                2.3823696679230424e-07
            ],
            [
                0.9999996072138934,
                1.3709576971463352e-06,
                1.3709572068522336e-06,
                0.9999993524048932,
                0.9999982396574177,
                0.9999952149072351,
                1.1478770862882149e-05,
                0.9999962733602753,
                2.1444940746307572e-05,
                0.9999980052693301
            ],
            [
                1.2751905808881762e-07,
                1.8553907971855875e-07,
                1.4449805540740185e-07,
                7.734421308914719e-08,
                2.1024326584639497e-07,
                1.2751904288710323e-07,
                1.6373770576776313e-07,
                3.927860597945825e-07,
                3.059022269250683e-07,
                4.4508510499849186e-07
            ],
            [
                8.315279285351409e-07,
                5.715005151606823e-07,
                7.338208930460318e-07,
                1.0677024882009222e-06,
                3.7266401726359486e-06,
                4.450850519403407e-07,
                7.338207180864763e-07,
                8.315284241650899e-07,
                8.315281267861397e-07,
                8.315284241650899e-07
            ],
            [
                1.6701423836262173e-05,
                NaN,
                NaN,
                2.5612831267202583e-06,
                0.9999969105055578,
                3.466327037553825e-07,
                1.209865539295696e-06,
                4.222832437798974e-06,
                9.422442569315887e-07,
                2.260324567337161e-06
            ],
            [
                6.825600469412533e-08,
                1.27519088491875e-07,
                5.315781803390236e-08,
                4.6911638017556955e-08,
                NaN,
                4.6911677163762064e-08,
                6.023569884718319e-08,
                1.1253509497883659e-07,
                1.8553914607267268e-07,
                8.76424013786396e-08
            ],
            [
                6.962257909842961e-06,
                0.9999989322968765,
                5.829125165990109e-05,
                1.5534984953552536e-06,
                0.999999581881327,
                3.120190765829341e-05,
                7.889264466868659e-06,
                0.9999892166839464,
                1.209865539298447e-06,
                0.9999990577551819
            ],
            [
                NaN,
                2.1444950971601277e-05,
                NaN,
                1.0677028700422047e-06,
                3.059022998581767e-07,
                3.05902263391829e-07,
                5.043475885696228e-07,
                1.8925157265710765e-05,
                4.450850519409479e-07,
                3.288749849529972e-06
            ],
            [
                2.3823702359290413e-07,
                3.9278605979534166e-07,
                1.8553910183607374e-07,
                5.043473480777865e-07,
                1.6373766672973748e-07,
                7.338208930460318e-07,
                2.6995774527718623e-07,
                2.6995771309523475e-07,
                3.0590237279032884e-07,
                2.6995784182140636e-07
            ],
            [
                3.4663274507713016e-07,
                1.209866260432471e-06,
                2.2603234895372223e-06,
                4.785094494811783e-06,
                NaN,
                1.0677026154827912e-06,
                0.0001795279449767558,
                2.9023119851899796e-06,
                1.0677032518814388e-06,
                9.422443692574719e-07
            ],
            [
                8.315281267882195e-07,
                3.2887502415767434e-06,
                1.760342793638743e-06,
                5.715006514176113e-07,
                1.7603425837903113e-06,
                4.785094494811783e-06,
                5.715002426486762e-07,
                1.0677028700422047e-06,
                2.9023109472494878e-06,
                1.2751901248454963e-07
            ],
            [
                1.994729483729522e-06,
                6.47595107001401e-07,
                7.338207180898968e-07,
                NaN,
                5.043475284468537e-07,
                NaN,
                NaN,
                7.338208930460318e-07,
                3.466326624336003e-07,
                1.0677028700422047e-06
            ],
            [
                1.4449803818215767e-07,
                1.1253513522447425e-07,
                1.1253506814842375e-07,
                2.102434412875379e-07,
                2.3823685319320354e-07,
                1.275190276859705e-07,
                9.931193325852072e-08,
                2.102434162245973e-07,
                6.47595107001401e-07,
                6.023568448589658e-08
            ],
            [
                9.422450432030903e-07,
                NaN,
                2.699577130960941e-07,
                9.931198061405701e-08,
                2.5612834320563895e-06,
                NaN,
                1.0677028700422047e-06,
                9.422448185534261e-07,
                1.275190732904469e-07,
                4.450851049991497e-07
            ],
            [
                0.9999852610128437,
                NaN,
                7.338209805240734e-07,
                5.04347287955046e-07,
                3.927862002663297e-07,
                0.9999955048184407,
                4.785095065232451e-06,
                3.120190765625026e-05,
                NaN,
                0.9999970976869831
            ],
            [
                2.561281600086738e-06,
                4.785095065232451e-06,
                1.2098661162056318e-06,
                2.902312331170226e-06,
                2.260323758987159e-06,
                1.209865827752005e-06,
                0.9999949062950045,
                3.05902226923399e-07,
                3.9278615344178325e-07,
                0.9999987901340288
            ],
            [
                2.561282210729555e-06,
                1.0677029973192638e-06,
                1.147877359957198e-05,
                6.144175334418252e-06,
                6.144173137126169e-06,
                9.422442569315887e-07,
                2.561281294760143e-06,
                1.9947304348703948e-06,
                5.422220262636381e-06,
                1.370957860576702e-06
            ],
            [
                1.275190276859705e-07,
                NaN,
                1.27519088491875e-07,
                1.6373774480605869e-07,
                4.691162124067829e-08,
                3.466326624336003e-07,
                4.450851049991497e-07,
                9.931185038635267e-08,
                1.275190428875671e-07,
                2.699578740032504e-07
            ],
            [
                3.05902263391829e-07,
                0.9999988634364259,
                0.999999218851763,
                NaN,
                0.9999983463102192,
                0.9999986290429582,
                0.9999992188514838,
                1.2098653950656417e-06,
                5.043475885696228e-07,
                0.9999986290432856
            ],
            [
                1.5534973842076057e-06,
                1.8553910183674878e-07,
                6.47595107001401e-07,
                4.4508510499849186e-07,
                1.637376862489725e-07,
                4.450848927658745e-07,
                5.04347287955046e-07,
                4.450851049991497e-07,
                1.067703124601679e-06,
                1.3709573702778664e-06
            ],
            [
                2.382369667929001e-07,
                3.0590215399281185e-07,
                2.2603245673443566e-06,
                1.637377448057981e-07,
                4.450852111148132e-07,
                2.382369667929001e-07,
                2.902313023130843e-06,
                2.1024331597262577e-07,
                1.0677029973219343e-06,
                2.3823693839290317e-07
            ],
            [
                5.715006514176113e-07,
                1.0129987357517693e-05,
                5.043475885696228e-07,
                1.300712536408621e-05,
                1.0677029973219343e-06,
                4.450850519409479e-07,
                1.8553907971855875e-07,
                6.605213683024311e-05,
                8.939700567094277e-06,
                1.2098661162056318e-06
            ],
            [
                3.466327037539638e-07,
                9.422442569290178e-07,
                4.4508494582314646e-07,
                5.71500515159253e-07,
                4.222834451382849e-06,
                1.2098662604291696e-06,
                1.760342793638743e-06,
                7.338207180898968e-07,
                5.422220262636381e-06,
                2.3823685319244518e-07
            ],
            [
                3.9278605979534166e-07,
                1.760343633031919e-06,
                1.209865539295696e-06,
                1.1253518888531272e-07,
                NaN,
                2.561282516066741e-06,
                7.338208055680009e-07,
                1.2751901248454963e-07,
                3.72663883989755e-06,
                1.0677024881980089e-06
            ],
            [
                2.561282516066741e-06,
                9.422449308748773e-07,
                3.726638395634011e-06,
                7.889260704818233e-06,
                2.9023123311583482e-06,
                3.288749065423109e-06,
                1.3709576971379186e-06,
                1.994730434879465e-06,
                2.9023130231176453e-06,
                7.338212429582604e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                0.9999885212292247,
                1.147876812620341e-05,
                1.5534981249697903e-06,
                NaN,
                5.422218969895357e-06,
                0.9999989969862724,
                1.0677026154806063e-06
            ],
            [
                1.637376862489725e-07,
                7.889259764517575e-06,
                1.2751902768612997e-07,
                3.466325797900508e-07,
                3.466326624336003e-07,
                2.1024331597288867e-07,
                2.382368815932174e-07,
                4.4508515805735777e-07,
                1.5534971990169383e-06,
                9.931186222523604e-08
            ],
            [
                5.715006514176113e-07,
                0.00043055704090494114,
                0.9999986290432847,
                6.962258739796719e-06,
                0.9999822214481885,
                1.0129989772532511e-05,
                1.7603430034867993e-06,
                3.059022269254856e-07,
                3.927863875616689e-07,
                1.0677029973219343e-06
            ],
            [
                8.315281267882195e-07,
                3.9278610661366994e-07,
                1.2098662604291696e-06,
                1.3709575337078829e-06,
                5.715005151606823e-07,
                4.4508515805199415e-07,
                8.315281267800897e-07,
                1.2098659719757836e-06,
                1.855391681898159e-07,
                1.2098659719757836e-06
            ],
            [
                1.1253516205489029e-07,
                7.734421308914719e-08,
                9.931187406410953e-08,
                9.931193325852072e-08,
                1.2751908849167202e-07,
                2.1024336609843824e-07,
                1.1253525596134564e-07,
                4.1399365603508136e-08,
                1.1253509497883659e-07,
                8.764244316973974e-08
            ],
            [
                1.994730672668496e-06,
                5.422217030707961e-06,
                3.2887506336235617e-06,
                1.553497199007048e-06,
                2.90231094702116e-06,
                2.5612816000331606e-06,
                1.2098652508287273e-06,
                4.0063682641226247e-05,
                8.939699501132077e-06,
                3.726639728370556e-06
            ],
            [
                0.9999925887219067,
                0.9999945777810404,
                9.931193325852072e-08,
                0.9999980052700426,
                9.422448185534261e-07,
                5.04347287955046e-07,
                0.9999980052700427,
                2.561281600086738e-06,
                0.9999970976869796,
                8.939696304311336e-06
            ],
            [
                6.023576347299818e-08,
                7.338209805224048e-07,
                5.715003107755449e-07,
                4.4508510499849186e-07,
                4.4508510499849186e-07,
                2.1024326584639497e-07,
                1.9947301970972664e-06,
                6.475945666063607e-07,
                1.0677032518785256e-06,
                2.6995784182140636e-07
            ],
            [
                2.902312331170226e-06,
                1.370957860576702e-06,
                5.715002426486762e-07,
                8.315279285370317e-07,
                4.785096206076165e-06,
                NaN,
                1.760342793638743e-06,
                5.043476486924565e-07,
                6.144172404738491e-06,
                8.315277302857965e-07
            ],
            [
                9.422443692574719e-07,
                NaN,
                2.260324028443809e-06,
                9.422443692574719e-07,
                3.7266383956509585e-06,
                2.2603251062450327e-06,
                0.9999885212305261,
                0.9999986290423037,
                0.99999976176309,
                1.5534973842076057e-06
            ],
            [
                8.315278294114555e-07,
                0.9999964991468433,
                7.338207180898968e-07,
                9.931185038635267e-08,
                3.466327037553825e-07,
                1.4738978458623327e-05,
                2.902312331170226e-06,
                4.785095065232451e-06,
                1.209865827752005e-06,
                5.715006514176113e-07
            ],
            [
                1.5534975693979422e-06,
                3.927862002663297e-07,
                2.561282210740037e-06,
                2.902312677137316e-06,
                8.315283250394546e-07,
                0.9999955048184427,
                8.315280276626197e-07,
                6.962254589978262e-06,
                1.0677027427600627e-06,
                0.9999810748474042
            ],
            [
                1.0677027427624903e-06,
                1.1478769494542698e-05,
                3.7266383956509585e-06,
                1.0129994603006104e-05,
                1.7603438428848787e-06,
                7.484620052444058e-05,
                8.315284241665078e-07,
                6.475949526020042e-07,
                5.422221555414699e-06,
                1.7603425837903113e-06
            ],
            [
                0.9999771720112064,
                NaN,
                2.2603242978871282e-06,
                1.553497199007048e-06,
                1.3007123813382511e-05,
                0.00017952796636908967,
                1.5534975693933505e-06,
                0.999996499144344,
                0.999998629043121,
                NaN
            ],
            [
                3.9278629391427843e-07,
                2.5612819054133693e-06,
                4.4508494582405734e-07,
                2.5612828213934817e-06,
                7.338212429582604e-07,
                2.5612819054133693e-06,
                1.3709575337159875e-06,
                6.475946438055299e-07,
                1.0677027427624903e-06,
                9.422442569315887e-07
            ],
            [
                4.785093924389007e-06,
                4.4508515805735777e-07,
                8.939696304311336e-06,
                2.699578096403948e-07,
                9.422443692574719e-07,
                3.9278620026686556e-07,
                3.4663262111182307e-07,
                6.47595107001401e-07,
                5.1442225934873024e-05,
                1.209865827752005e-06
            ],
            [
                1.8553919030776337e-07,
                3.0590215399183813e-07,
                3.0590233632400716e-07,
                3.466327450765785e-07,
                2.699577774585891e-07,
                9.422448185534261e-07,
                4.450852641717689e-07,
                3.927862002663297e-07,
                2.102434412871794e-07,
                2.6995771309523475e-07
            ],
            [
                3.288748281329893e-06,
                1.1253526937656726e-07,
                2.3823690999323465e-07,
                2.102434162245973e-07,
                0.9999987901337404,
                9.931200429212718e-08,
                6.825608606148807e-08,
                NaN,
                3.4663274507713016e-07,
                1.1253510839355284e-07
            ],
            [
                3.466327037548308e-07,
                NaN,
                3.726639284144195e-06,
                5.043476486915964e-07,
                1.0677027427624903e-06,
                2.9023112932296107e-06,
                5.04347287955046e-07,
                6.475947982037486e-07,
                NaN,
                6.475949526020042e-07
            ],
            [
                4.450852641737424e-07,
                3.059022998581767e-07,
                6.475947982037486e-07,
                1.5534977545886537e-06,
                2.1444950971601277e-05,
                8.764249540862797e-08,
                1.5534971990169383e-06,
                2.902312331170226e-06,
                5.422219616265831e-06,
                0.9999986290424681
            ],
            [
                8.315277302857965e-07,
                2.699577130960941e-07,
                1.0677033791630344e-06,
                3.9278620026686556e-07,
                NaN,
                6.475950298021765e-07,
                3.466326624336003e-07,
                NaN,
                5.71500515161527e-07,
                NaN
            ],
            [
                0.9999995262093294,
                0.999997876621539,
                5.422217030781934e-06,
                0.999999428499417,
                0.9999982396574192,
                0.9999964991455916,
                0.9999996533674205,
                1.2098656835252174e-06,
                0.9999992661788452,
                0.9999987901340289
            ],
            [
                2.6995784182183607e-07,
                2.382369951932796e-07,
                1.9947301970972664e-06,
                3.288749849529972e-06,
                5.715002426486762e-07,
                3.4663274507713016e-07,
                8.315282259138311e-07,
                3.4663274507713016e-07,
                1.5534971990126997e-06,
                1.6373774480605869e-07
            ],
            [
                4.785095635655362e-06,
                NaN,
                5.422220262636381e-06,
                0.9999623635440937,
                0.9999974387187105,
                0.0001795280091877212,
                5.14422075345321e-05,
                1.9947301970972664e-06,
                4.222833444590791e-06,
                0.9999885212360257
            ],
            [
                2.9023119851899796e-06,
                6.475947982037486e-07,
                8.939695238634211e-06,
                0.9999989322972577,
                5.715006514176113e-07,
                0.9999990577550697,
                0.9999992661791075,
                3.927862470905692e-07,
                0.9999993524048935,
                2.9023116392097746e-06
            ],
            [
                NaN,
                0.9999938558261353,
                0.9999983463110071,
                0.999978555043981,
                0.9999982396561589,
                8.939699501416646e-06,
                5.04347287955046e-07,
                NaN,
                0.9999980052705177,
                0.999998932296749
            ],
            [
                3.466327037553825e-07,
                4.4508515805735777e-07,
                NaN,
                9.422444815814404e-07,
                2.10243290909963e-07,
                7.338207180898968e-07,
                1.209865827752005e-06,
                2.2603234895372223e-06,
                1.2098659719788098e-06,
                9.422444815814404e-07
            ],
            [
                5.715003107767143e-07,
                2.699578096403948e-07,
                1.6373764721072816e-07,
                1.4449800373118268e-07,
                1.8553914607267268e-07,
                7.889265407255982e-06,
                2.1024339116082313e-07,
                2.1024326584639497e-07,
                3.927863407379485e-07,
                3.059022269250683e-07
            ],
            [
                6.144176799334096e-06,
                1.8553910183607374e-07,
                5.715006514176113e-07,
                2.1024336609874897e-07,
                2.3823696679327928e-07,
                0.9999945777791024,
                6.475945666063607e-07,
                NaN,
                8.315278294114555e-07,
                0.9999938558239456
            ],
            [
                1.012999218776902e-05,
                1.1478770862882149e-05,
                NaN,
                8.48110110788306e-05,
                3.4663253846718004e-07,
                2.90231094723893e-06,
                4.222834954801051e-06,
                0.9999952149066627,
                NaN,
                1.994729483723626e-06
            ],
            [
                2.3823690999323465e-07,
                1.637376862489725e-07,
                1.5534971990169383e-06,
                7.33821330437595e-07,
                5.043475885696228e-07,
                1.370957860576702e-06,
                2.699577774589574e-07,
                4.4508515805735777e-07,
                3.9278615343901467e-07,
                1.067703124601679e-06
            ],
            [
                0.9999949062968294,
                8.315277302857965e-07,
                3.466326624336003e-07,
                6.962253760024999e-06,
                5.71500719545698e-07,
                1.0129994603006104e-05,
                2.9023119851899796e-06,
                3.0590215399281185e-07,
                9.422442569334097e-07,
                1.5534984953552536e-06
            ],
            [
                1.444979692800516e-07,
                1.855391239544352e-07,
                2.699576809143613e-07,
                4.450850519403407e-07,
                1.6373776432509826e-07,
                1.8553905760062447e-07,
                1.8553907971855875e-07,
                1.2751908849167202e-07,
                2.10243290909724e-07,
                2.382370235933104e-07
            ],
            [
                7.338209805240734e-07,
                5.71500719545698e-07,
                1.2098659719788098e-06,
                9.422443692574719e-07,
                2.902312331170226e-06,
                2.6995774527718623e-07,
                2.3823702359290413e-07,
                4.222833444590791e-06,
                9.422448185534261e-07,
                2.4300249425247723e-05
            ],
            [
                3.4663249714612693e-07,
                1.8553916819032217e-07,
                2.3823702359290413e-07,
                1.8553916819032217e-07,
                2.382369667929001e-07,
                3.927860597935108e-07,
                5.043474081993875e-07,
                4.450849988811838e-07,
                3.4663266243308805e-07,
                6.475949526003845e-07
            ],
            [
                1.209865539295696e-06,
                1.2098656835224664e-06,
                1.0677026154806063e-06,
                1.0677027427600627e-06,
                8.315282259138311e-07,
                3.466327037548308e-07,
                7.338209805224048e-07,
                3.4663266243308805e-07,
                5.043473480777865e-07,
                1.209866260432471e-06
            ],
            [
                1.3007130015677909e-05,
                0.9999990577557443,
                3.7266383956509585e-06,
                0.9999991148426483,
                0.9999989969860321,
                0.9999938558224941,
                0.9999996743686647,
                1.7603438428848787e-06,
                0.9999987121047856,
                2.3823690999323465e-07
            ],
            [
                5.71500515161527e-07,
                2.9023119851899796e-06,
                6.47594952603035e-07,
                3.05902263391829e-07,
                3.9278620026686556e-07,
                3.466325797900508e-07,
                3.466325797900508e-07,
                6.1441767993788005e-06,
                1.5534984953552536e-06,
                9.422444815814404e-07
            ],
            [
                NaN,
                2.2603245673443566e-06,
                2.5612828213934817e-06,
                8.315277302857965e-07,
                0.9999972735300573,
                7.338207180898968e-07,
                1.7603425837903113e-06,
                2.2603240284371276e-06,
                1.7603425837903113e-06,
                0.999998446502247
            ],
            [
                NaN,
                NaN,
                1.1478765389514884e-05,
                3.466327450765785e-07,
                8.315279285370317e-07,
                1.2098652508391807e-06,
                2.4300237838535383e-05,
                5.043475284468537e-07,
                1.0677032518814388e-06,
                6.962254589978262e-06
            ],
            [
                3.466327037553825e-07,
                1.0677028700320085e-06,
                2.699578096403948e-07,
                7.338207180864763e-07,
                1.0677032518748838e-06,
                5.043475284468537e-07,
                7.338211554783522e-07,
                5.043475284430694e-07,
                3.4663274507713016e-07,
                4.222834954801051e-06
            ],
            [
                4.2228339479858295e-06,
                5.043476486915964e-07,
                4.222834451382849e-06,
                1.444980209564556e-07,
                2.3823696679327928e-07,
                2.260324028427877e-06,
                7.338209805224048e-07,
                NaN,
                2.902313023130843e-06,
                2.902311639183378e-06
            ],
            [
                4.785094494811783e-06,
                3.0590219045914655e-07,
                2.5612831267202583e-06,
                2.2603253756956754e-06,
                2.902312331170226e-06,
                2.1444945858953813e-05,
                7.484626297687326e-05,
                3.9278629391427843e-07,
                5.043473480777865e-07,
                3.466326624336003e-07
            ],
            [
                3.4663278639892215e-07,
                3.9278629391427843e-07,
                3.4663274507713016e-07,
                9.931193325852072e-08,
                1.27519088491875e-07,
                3.4663249714612693e-07,
                3.05902336324494e-07,
                1.4449795205429202e-07,
                8.764249540862797e-08,
                7.734421308914719e-08
            ],
            [
                0.9999977396746266,
                0.99999649914559,
                0.9999984465024325,
                0.9999984465018769,
                0.9999972735307076,
                0.9999989322967494,
                0.999998790134606,
                0.9999960330131458,
                0.9999974387174861,
                0.9999989969859123
            ],
            [
                0.9999969105062917,
                0.9999980052700419,
                4.785095065232451e-06,
                1.3709575337159875e-06,
                8.315279285370317e-07,
                0.9999997126314811,
                0.9999985406243022,
                0.9999975938965157,
                0.9999910603005258,
                0.9999974387180968
            ],
            [
                7.734424996967756e-08,
                1.2751910369343538e-07,
                8.764242227418718e-08,
                8.764254764780641e-08,
                2.102433660979124e-07,
                2.1024341622426268e-07,
                3.927862470905692e-07,
                6.475947210046347e-07,
                9.931202796993203e-08,
                1.4449803818215767e-07
            ],
            [
                2.260323758987159e-06,
                3.466326624322211e-07,
                1.5534977545886537e-06,
                3.466326211105621e-07,
                2.699578740032504e-07,
                9.422448185534261e-07,
                3.466325797888292e-07,
                5.04347287955046e-07,
                1.760342793638743e-06,
                3.059023363231725e-07
            ],
            [
                2.1024326584639497e-07,
                1.5534981249697903e-06,
                3.927860597935108e-07,
                5.715007195431641e-07,
                4.450850519403407e-07,
                3.4663266243111764e-07,
                4.4508515805199415e-07,
                6.475950298011458e-07,
                8.315283250394546e-07,
                3.927860597935108e-07
            ],
            [
                4.2228339479858295e-06,
                6.475947210046347e-07,
                1.4738983729535602e-05,
                1.209865827752005e-06,
                1.2098661162056318e-06,
                NaN,
                NaN,
                2.5612831267202583e-06,
                1.4738983729535602e-05,
                1.5534977545886537e-06
            ],
            [
                3.7266410611296085e-06,
                6.962257079832313e-06,
                0.9999852610113383,
                0.9999969105066636,
                0.0002034269737015615,
                1.5534979397790343e-06,
                1.1478773599425825e-05,
                0.9999969105048225,
                NaN,
                NaN
            ],
            [
                3.466326211113502e-07,
                1.0677029973219343e-06,
                6.475949526020042e-07,
                1.5534983101602148e-06,
                5.04347468323289e-07,
                1.370957533676711e-06,
                0.9999952149066671,
                NaN,
                8.315279285351409e-07,
                1.5534983101602148e-06
            ],
            [
                1.3709570434178922e-06,
                1.2098662604247682e-06,
                1.0677026154730804e-06,
                NaN,
                7.889260704631679e-06,
                1.0677029973219343e-06,
                8.315283250371857e-07,
                1.2098658277451275e-06,
                4.450851580555361e-07,
                9.4224425692559e-07
            ],
            [
                5.043476486924565e-07,
                1.30071315662049e-05,
                8.315282259151545e-07,
                6.475945666063607e-07,
                5.71500515161527e-07,
                0.9999974387174869,
                1.7603440527334603e-06,
                1.3709573702856596e-06,
                0.9999995262096119,
                2.10243290909724e-07
            ],
            [
                3.05902263391829e-07,
                9.422443692574719e-07,
                2.6995771309523475e-07,
                5.043475284468537e-07,
                1.4449798650569826e-07,
                6.475945666063607e-07,
                5.043476486924565e-07,
                1.4449803818215767e-07,
                2.6995784182140636e-07,
                7.338207180898968e-07
            ],
            [
                1.4449805540740185e-07,
                1.1253509497883659e-07,
                3.4663274507713016e-07,
                1.2751901248454963e-07,
                2.382370235933104e-07,
                NaN,
                1.855391239547094e-07,
                2.6995784182183607e-07,
                3.4663278639892215e-07,
                9.422444815814404e-07
            ],
            [
                1.7603438428800754e-06,
                2.260324567337161e-06,
                2.2603234895372223e-06,
                1.0677032518785256e-06,
                1.2098653950656417e-06,
                1.994729721518893e-06,
                1.5534977545886537e-06,
                8.315282259138311e-07,
                7.338208055579897e-07,
                1.209866260432471e-06
            ],
            [
                6.475947982037486e-07,
                3.0590219045914655e-07,
                1.209866260432471e-06,
                3.9278605979534166e-07,
                0.00043055709228439695,
                8.764241182641775e-08,
                3.9278610661902853e-07,
                5.043475885696228e-07,
                7.338209805240734e-07,
                7.338208930460318e-07
            ],
            [
                1.7603430034867993e-06,
                3.927861534431675e-07,
                4.4508515805735777e-07,
                1.3709575337159875e-06,
                1.855391239547094e-07,
                8.315284241665078e-07,
                6.475950298021765e-07,
                4.450851049991497e-07,
                0.9999921107346156,
                4.4508515805735777e-07
            ],
            [
                0.00023050674322105578,
                5.043475885696228e-07,
                4.4508515805735777e-07,
                NaN,
                1.2098659719788098e-06,
                3.4663262111182307e-07,
                2.2603251062450327e-06,
                6.47595107001401e-07,
                2.260324567337161e-06,
                5.422220909041528e-06
            ],
            [
                6.825598028392069e-08,
                5.043475885696228e-07,
                2.3823696679327928e-07,
                9.422447062294175e-07,
                6.962257909842961e-06,
                7.33821330437595e-07,
                2.1024339116168358e-07,
                2.1024331597288867e-07,
                NaN,
                4.450851049991497e-07
            ],
            [
                2.699577774589574e-07,
                1.1253521571603583e-07,
                1.2751910369343538e-07,
                1.275189972832538e-07,
                2.3823685319320354e-07,
                3.288749849529972e-06,
                NaN,
                6.023577065381482e-08,
                1.275190580890061e-07,
                2.699577130960941e-07
            ],
            [
                3.9278620026686556e-07,
                0.9999516743450014,
                2.699577774585891e-07,
                2.699577774589574e-07,
                1.0129987357517693e-05,
                8.315277302857965e-07,
                1.3007134667436886e-05,
                1.3709573702856596e-06,
                2.3823693839325527e-07,
                5.043472879525233e-07
            ],
            [
                NaN,
                2.2603242978871282e-06,
                NaN,
                NaN,
                NaN,
                1.760342793638743e-06,
                1.2098661162056318e-06,
                2.2603248367949354e-06,
                9.422443692555439e-07,
                3.72663883989755e-06
            ],
            [
                1.2751901248391176e-07,
                6.023574911170301e-08,
                0.9999985406232597,
                0.9999822214524511,
                1.3709572068522336e-06,
                2.1024341622426268e-07,
                2.6995784182140636e-07,
                1.637377643243723e-07,
                1.8553910183674878e-07,
                3.9278605979534166e-07
            ],
            [
                0.9999964991455914,
                0.9999904837449334,
                0.9999898700066846,
                0.999998005269331,
                1.3709567165617364e-06,
                NaN,
                6.962259569750576e-06,
                NaN,
                1.5534973842076057e-06,
                1.760343213335281e-06
            ],
            [
                1.6373766672994222e-07,
                1.1253509497883659e-07,
                5.144220140264605e-05,
                6.9622537599680095e-06,
                1.8553903548287212e-07,
                5.043475284468537e-07,
                4.450852111155216e-07,
                4.4508494582405734e-07,
                2.6995790618350237e-07,
                7.338213304363436e-07
            ]
        ]
    },
    {
        "q_id": "9898_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            24,
            25,
            27,
            28,
            29,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            88,
            89,
            90,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999985406236054,
                0.9999990577551818,
                0.9999962733620503,
                0.9999972735287553,
                0.9999972735290805,
                0.9999962733589407,
                0.9999989322972576,
                0.9999994956525919,
                5.715002426475718e-07,
                NaN
            ],
            [
                0.9998415638219873,
                0.9999989322970031,
                1.6373772528704005e-07,
                2.699577774589574e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                3.4663278639892215e-07,
                NaN
            ],
            [
                1.2098652508391807e-06,
                2.260324028427877e-06,
                6.475950298011458e-07,
                1.0677032518814388e-06,
                1.0677024881980089e-06,
                3.288749849529972e-06,
                4.222832941193893e-06,
                9.422443692555439e-07,
                1.3709573702778664e-06,
                1.2098662604247682e-06
            ],
            [
                7.338207180898968e-07,
                6.475947210031623e-07,
                6.475950298011458e-07,
                1.067703379154416e-06,
                2.2603237589779086e-06,
                1.5534984953552536e-06,
                8.315282259089153e-07,
                5.715003107767143e-07,
                9.4224425692559e-07,
                7.338211554783522e-07
            ],
            [
                3.059022269250683e-07,
                0.9999934595643424,
                6.475947210031623e-07,
                3.927862470899887e-07,
                4.4508510499849186e-07,
                5.71500719545698e-07,
                5.715003789046955e-07,
                6.475946438055299e-07,
                NaN,
                1.0677029973219343e-06
            ],
            [
                1.370957370247318e-06,
                3.927863875616689e-07,
                1.9947294837154625e-06,
                4.450851580566494e-07,
                3.2887486732358968e-06,
                1.3709570434178922e-06,
                5.715005832886879e-07,
                1.0677029973114952e-06,
                1.0677033791612137e-06,
                5.043472278322555e-07
            ],
            [
                3.726641061085547e-06,
                9.422449308774482e-07,
                1.2098652508391807e-06,
                3.726641061027928e-06,
                1.9947299592933255e-06,
                1.209866260432471e-06,
                7.338213304363436e-07,
                2.2603234895176927e-06,
                6.475947982037486e-07,
                1.3709568799760888e-06
            ],
            [
                1.5534983101602148e-06,
                6.475945666033422e-07,
                8.315281267834927e-07,
                1.5534973842076057e-06,
                7.338208930460318e-07,
                0.9999885212291666,
                0.9999898700054115,
                1.8925148242250705e-05,
                8.315281267834927e-07,
                7.338210679909462e-07
            ],
            [
                0.9999930377429272,
                2.5612819054133693e-06,
                9.422450432030903e-07,
                2.902312677150514e-06,
                9.422443692574719e-07,
                4.22283545819819e-06,
                2.753569766795419e-05,
                4.450851049991497e-07,
                3.927863875616689e-07,
                4.006370652067535e-05
            ],
            [
                1.8553910183674878e-07,
                3.4663262111182307e-07,
                2.699577452775239e-07,
                5.715005832895975e-07,
                NaN,
                2.699577452775239e-07,
                NaN,
                7.338207180898968e-07,
                8.31528325040778e-07,
                NaN
            ],
            [
                4.450848927658745e-07,
                3.466326624336003e-07,
                NaN,
                8.315278294114555e-07,
                2.5612819054133693e-06,
                1.147877359957198e-05,
                3.466326624336003e-07,
                3.466327037553825e-07,
                1.1478768126057254e-05,
                1.4449807263312446e-07
            ],
            [
                NaN,
                9.422449308789479e-07,
                1.994729008151319e-06,
                1.4449807263325588e-07,
                2.699577774589574e-07,
                4.450850519409479e-07,
                3.466326624336003e-07,
                5.043472278322555e-07,
                3.466327037553825e-07,
                1.6373764721072816e-07
            ],
            [
                0.9999962733589421,
                0.9999996743688975,
                0.9999964991443355,
                0.9999985406237794,
                0.9999898700054058,
                0.9999974387174857,
                0.9999996072136126,
                0.9999938558261336,
                0.9999978766215389,
                0.9999972735300555
            ],
            [
                1.760342793638743e-06,
                0.9999985406243014,
                1.2751902768612997e-07,
                1.6373766672994222e-07,
                4.450850519403407e-07,
                1.8553910183674878e-07,
                0.999088948853177,
                1.5534971990169383e-06,
                2.102434162245973e-07,
                NaN
            ],
            [
                2.699577774589574e-07,
                1.27519088491875e-07,
                3.9278620026686556e-07,
                NaN,
                1.637376862489725e-07,
                2.6995784182183607e-07,
                2.102434162245973e-07,
                5.71500719545698e-07,
                NaN,
                2.1024334103581732e-07
            ],
            [
                8.315281267834927e-07,
                1.3709576971061233e-06,
                1.553498495308628e-06,
                1.0677031245783732e-06,
                1.3007126914245925e-05,
                1.3709567165461505e-06,
                1.4738988999940381e-05,
                3.535626335944147e-05,
                1.2098661161927025e-06,
                4.222834954607099e-06
            ],
            [
                0.9999687980849847,
                0.999988521229157,
                0.9999877809210906,
                1.2098659719757836e-06,
                1.0677026154774503e-06,
                4.5397884884891014e-05,
                2.902312331170226e-06,
                0.9999843104446947,
                1.0677033791612137e-06,
                5.144219527356777e-05
            ],
            [
                1.7603438428800754e-06,
                1.5534973841895917e-06,
                1.2098653950656417e-06,
                7.338210680021253e-07,
                8.315281267800897e-07,
                7.338209805170655e-07,
                6.475950297942253e-07,
                1.0677029973192638e-06,
                1.3709570433979422e-06,
                5.422218323093458e-06
            ],
            [
                4.222834451254188e-06,
                4.222832941034507e-06,
                2.9023116391675407e-06,
                1.760344052714248e-06,
                6.1441746016670885e-06,
                2.5612825160096693e-06,
                1.9947301970451086e-06,
                1.1478766755734576e-05,
                3.726638839806038e-06,
                1.3709576971160984e-06
            ],
            [
                1.5534973842030142e-06,
                2.9023112932177327e-06,
                2.260324836787226e-06,
                2.902313369111213e-06,
                6.144175334468545e-06,
                1.994729721518893e-06,
                1.3709568799879344e-06,
                NaN,
                1.9947304348862686e-06,
                1.7603427936183298e-06
            ],
            [
                7.338208055579897e-07,
                2.102434412871794e-07,
                2.10243290909724e-07,
                1.370957860576702e-06,
                3.4663249714612693e-07,
                3.9278610661902853e-07,
                7.338210680021253e-07,
                2.102434412875379e-07,
                2.6995768091383957e-07,
                5.043472879540142e-07
            ],
            [
                1.0677026154730804e-06,
                9.422450431912e-07,
                7.338211554783522e-07,
                1.5534971989907999e-06,
                4.785093353940187e-06,
                1.2098661161982042e-06,
                9.422443692489024e-07,
                3.9278605978797364e-07,
                1.0677032518700286e-06,
                9.422443692489024e-07
            ],
            [
                1.3709567165617364e-06,
                1.5534984953453635e-06,
                5.715004470313855e-07,
                6.475950298011458e-07,
                6.475950298011458e-07,
                3.4663249714451116e-07,
                3.9278634073625165e-07,
                5.04347468323289e-07,
                3.7266401726173067e-06,
                3.46632497145457e-07
            ],
            [
                6.475947982046322e-07,
                4.4508499888275247e-07,
                1.3709570434250617e-06,
                7.338207180898968e-07,
                NaN,
                NaN,
                NaN,
                7.338212429594283e-07,
                3.466326624336003e-07,
                5.715005832895975e-07
            ],
            [
                6.475949526020042e-07,
                5.715004470326849e-07,
                1.1253517547010071e-07,
                2.10243290909963e-07,
                2.1024336609874897e-07,
                2.69957906184239e-07,
                3.05902263391829e-07,
                1.444979692800516e-07,
                6.825602910433871e-08,
                3.927863407379485e-07
            ],
            [
                8.315281267861397e-07,
                4.450852111135988e-07,
                7.338209805200689e-07,
                3.46632497145457e-07,
                5.715003789033962e-07,
                2.382370235922541e-07,
                3.4663249714325014e-07,
                3.466327450765785e-07,
                7.338213304316717e-07,
                4.450851580555361e-07
            ],
            [
                3.927861066170637e-07,
                0.999995777167567,
                NaN,
                8.764251630441717e-08,
                2.3823682479292225e-07,
                0.9999992188514835,
                1.4449800373118268e-07,
                7.734424996967756e-08,
                0.9999962733602741,
                5.043474683240344e-07
            ],
            [
                2.6995784182183607e-07,
                NaN,
                0.9999952149066488,
                5.715006514176113e-07,
                6.475950298021765e-07,
                6.47595107001401e-07,
                2.1024334103581732e-07,
                NaN,
                5.71500719545698e-07,
                2.10243290909963e-07
            ],
            [
                2.9023116391477434e-06,
                4.222834451355964e-06,
                1.2098661161789477e-06,
                6.962254589781966e-06,
                5.043472879525233e-07,
                1.5534973841705173e-06,
                2.4300249425247723e-05,
                NaN,
                1.3709567165530083e-06,
                1.0677027427471959e-06
            ],
            [
                0.9999810748517849,
                0.9999798543140377,
                0.9996646499374011,
                0.9999832985702228,
                0.9999785550439555,
                0.00013982207421714976,
                0.9999599362936861,
                0.9999706884476387,
                3.726637951367137e-06,
                0.9999861539888738
            ],
            [
                1.9947299593078385e-06,
                1.3709567165617364e-06,
                6.475947982037486e-07,
                1.0677026154806063e-06,
                NaN,
                5.043476486915964e-07,
                5.043475284430694e-07,
                NaN,
                4.222834451355964e-06,
                9.422445939054222e-07
            ],
            [
                5.715002426486762e-07,
                1.1253510839355284e-07,
                3.4663266243308805e-07,
                7.338210680021253e-07,
                6.475945666063607e-07,
                2.3823688159237777e-07,
                NaN,
                5.71500719545698e-07,
                2.382368247924618e-07,
                3.927862470899887e-07
            ],
            [
                3.466327037553825e-07,
                7.338208055680009e-07,
                7.338208930460318e-07,
                6.475946438055299e-07,
                2.5612834320563895e-06,
                6.1441746020359e-06,
                1.0677028700422047e-06,
                1.760343633031919e-06,
                7.338207180898968e-07,
                2.9023116392097746e-06
            ],
            [
                1.0677033791612137e-06,
                2.260324028427877e-06,
                1.760343213335281e-06,
                1.3709573702856596e-06,
                2.2603234895289998e-06,
                1.209865539295696e-06,
                1.0677026154806063e-06,
                1.5534971990126997e-06,
                3.7266406168827523e-06,
                2.902313369111213e-06
            ],
            [
                1.4449807263312446e-07,
                1.7603438428848787e-06,
                1.3709567165617364e-06,
                7.338209805240734e-07,
                2.561282210701601e-06,
                1.7603440527286572e-06,
                2.9023119851899796e-06,
                1.5534971990169383e-06,
                1.760342793638743e-06,
                3.4663249714612693e-07
            ],
            [
                3.46632497145457e-07,
                3.7266406168827523e-06,
                2.10243290909724e-07,
                2.753568453792444e-05,
                1.2098662604291696e-06,
                2.561283432035425e-06,
                9.422445939002803e-07,
                5.715007195447234e-07,
                3.535625071730638e-05,
                NaN
            ],
            [
                1.9947297215043796e-06,
                2.9023126771227976e-06,
                3.726638395611981e-06,
                6.962257079832313e-06,
                1.0129989772274546e-05,
                8.939696304116203e-06,
                3.726638395611981e-06,
                1.0677032518748838e-06,
                2.5612828213934817e-06,
                5.715004470313855e-07
            ],
            [
                2.260325375677174e-06,
                5.422220909009474e-06,
                1.760343213335281e-06,
                1.3709567165530083e-06,
                3.726638839878908e-06,
                1.2098653950656417e-06,
                9.422449308774482e-07,
                1.7603434231833873e-06,
                8.939697369882888e-06,
                1.2098658277451275e-06
            ],
            [
                6.475947982002148e-07,
                3.288747889284851e-06,
                4.2228349546493465e-06,
                5.043474683204221e-07,
                3.9278615344178325e-07,
                8.31527928532683e-07,
                9.422449308716635e-07,
                9.422445939002803e-07,
                1.994729483723626e-06,
                4.450848927650143e-07
            ],
            [
                2.561282210701601e-06,
                1.7603432132464244e-06,
                1.7603430034655858e-06,
                6.144173869502757e-06,
                2.2603251062013478e-06,
                3.288750241473551e-06,
                2.9023126770343703e-06,
                2.9023123310290063e-06,
                2.2603251060142746e-06,
                7.889266347248781e-06
            ],
            [
                2.5612819054133693e-06,
                1.2098658277451275e-06,
                2.902312677150514e-06,
                1.7603440527286572e-06,
                1.2098659719788098e-06,
                1.067702870039777e-06,
                1.2098661162056318e-06,
                1.2098658277489788e-06,
                2.5612825160562587e-06,
                4.785095635624897e-06
            ],
            [
                7.338212429582604e-07,
                1.994729483729522e-06,
                3.2887502415767434e-06,
                2.260324567337161e-06,
                2.561282821402217e-06,
                1.6701429808632785e-05,
                3.466326624336003e-07,
                4.222832941193893e-06,
                3.466326211113502e-07,
                4.450848927658745e-07
            ],
            [
                4.22283545819819e-06,
                7.889266347786918e-06,
                1.5534971990169383e-06,
                1.760342793638743e-06,
                5.043473480777865e-07,
                4.222833444590791e-06,
                1.6701415872659116e-05,
                0.9999910603005098,
                1.3709573702856596e-06,
                0.9999964991468413
            ],
            [
                5.422219616140078e-06,
                2.5612812947380135e-06,
                6.144175334468545e-06,
                1.0677032518748838e-06,
                4.222834451327159e-06,
                2.7535697666401535e-05,
                1.9947306726594253e-06,
                2.5612812947508257e-06,
                8.939699501229642e-06,
                8.93969310675186e-06
            ],
            [
                1.209865683518615e-06,
                7.338209805224048e-07,
                1.0677029973192638e-06,
                2.2603242978665707e-06,
                7.889266347636241e-06,
                8.939700567094277e-06,
                1.2098655392811161e-06,
                1.2098659719716573e-06,
                1.994730434879465e-06,
                8.315284241597959e-07
            ],
            [
                0.9999949062943974,
                1.9947297214944016e-06,
                0.9999810748518383,
                7.338207180898968e-07,
                0.9999955048184275,
                0.9999993524053564,
                4.222833947820683e-06,
                0.999997876621287,
                0.9999970976876716,
                0.9999982396567882
            ],
            [
                2.260323758987159e-06,
                2.6995777745711594e-07,
                1.0677024882009222e-06,
                2.561283126728994e-06,
                3.05902190458764e-07,
                1.4449805540700758e-07,
                5.043476486915964e-07,
                3.288748281329893e-06,
                3.9278610661366994e-07,
                2.6995784182073116e-07
            ],
            [
                1.0677032518814388e-06,
                3.927862002663297e-07,
                7.338212429582604e-07,
                1.2098653950692178e-06,
                2.9023116391978967e-06,
                3.2887502415767434e-06,
                1.6701421845361053e-05,
                3.927860597945825e-07,
                2.3823682479292225e-07,
                3.466327863983311e-07
            ],
            [
                6.475950298011458e-07,
                2.9023116392097746e-06,
                3.7266406168827523e-06,
                3.927862470899887e-07,
                7.338213304363436e-07,
                1.9947292459347367e-06,
                5.715005832886879e-07,
                4.450850519403407e-07,
                3.9278610661902853e-07,
                2.382369667929001e-07
            ],
            [
                2.1024336609874897e-07,
                4.450848927658745e-07,
                7.338209805224048e-07,
                NaN,
                9.422445939054222e-07,
                3.4663249714612693e-07,
                NaN,
                3.0590237279085045e-07,
                3.0590237279085045e-07,
                NaN
            ],
            [
                1.760343213335281e-06,
                1.5534983101602148e-06,
                9.422449308774482e-07,
                2.9023116392097746e-06,
                8.315282259138311e-07,
                5.04347528446051e-07,
                6.475950298011458e-07,
                1.0677024881980089e-06,
                6.144172404738491e-06,
                2.5612819054133693e-06
            ],
            [
                1.7603434231705793e-06,
                0.9999916019249699,
                0.9999949062956073,
                0.9999687980998413,
                0.9999942280806612,
                0.9999910603037034,
                4.7850933538313875e-06,
                7.338210679979539e-07,
                9.422449308673789e-07,
                6.475947981975644e-07
            ],
            [
                1.99473067264854e-06,
                1.3709572068522336e-06,
                8.315278294072958e-07,
                1.994730197071414e-06,
                2.9023112931688987e-06,
                8.315278294072958e-07,
                2.2603234895176927e-06,
                6.962256249682458e-06,
                8.315282259089153e-07,
                2.561283432035425e-06
            ],
            [
                3.46632497145457e-07,
                2.3823688159291947e-07,
                3.466325384678894e-07,
                3.059021539909339e-07,
                1.0677029973192638e-06,
                1.067703124601679e-06,
                6.475946438022905e-07,
                6.475949526003845e-07,
                5.043476486915964e-07,
                5.043474683156057e-07
            ],
            [
                0.9999970976876722,
                0.9999910603026442,
                0.9999964991443371,
                0.9999952149032325,
                1.0129988564974359e-05,
                0.9999925887201382,
                2.2603242978871282e-06,
                8.315282259009745e-07,
                3.927863875616689e-07,
                0.9999985406230844
            ],
            [
                8.315284241665078e-07,
                4.450851049991497e-07,
                1.8553914607267268e-07,
                3.9278605979534166e-07,
                6.475945666063607e-07,
                1.3709573702856596e-06,
                NaN,
                2.699576809143613e-07,
                NaN,
                NaN
            ],
            [
                0.9999706884615873,
                0.9999869928653495,
                6.475949526020042e-07,
                0.9999898700054137,
                0.9999978766210336,
                6.475947210046347e-07,
                0.999989870011456,
                2.1444948415296896e-05,
                2.260323758987159e-06,
                1.9947301970972664e-06
            ],
            [
                1.3709568799919866e-06,
                4.450850519403407e-07,
                8.315282259089153e-07,
                0.9999945777823274,
                4.450849988798682e-07,
                1.7603440527222532e-06,
                5.715002426460124e-07,
                3.466327450756327e-07,
                NaN,
                1.7603436330259153e-06
            ],
            [
                NaN,
                8.76424013786396e-08,
                5.043472278322555e-07,
                3.9278629391427843e-07,
                9.422443692574719e-07,
                1.147876812620341e-05,
                NaN,
                1.760343633031919e-06,
                NaN,
                NaN
            ],
            [
                4.450852111155216e-07,
                5.715005832895975e-07,
                4.450850519409479e-07,
                1.0677029973219343e-06,
                1.8553910183674878e-07,
                3.9278629391427843e-07,
                3.466326624336003e-07,
                2.6995790618469934e-07,
                5.043475885696228e-07,
                7.338208055680009e-07
            ],
            [
                NaN,
                0.9999925887174891,
                1.9947301970972664e-06,
                0.9999962733598313,
                0.9999921107336718,
                0.9999930377437655,
                0.9999930377462529,
                0.9999960330136166,
                0.9999970976887095,
                6.144177531660828e-06
            ],
            [
                7.338212429582604e-07,
                NaN,
                1.2098661162056318e-06,
                1.3709568799919866e-06,
                9.422450431989127e-07,
                NaN,
                1.0677032518814388e-06,
                2.9023116392097746e-06,
                2.902312677150514e-06,
                2.561281600076256e-06
            ],
            [
                3.2887502415767434e-06,
                6.47595107001401e-07,
                NaN,
                4.4508515805735777e-07,
                1.0677029973219343e-06,
                9.422443692574719e-07,
                6.962259569750576e-06,
                NaN,
                5.715002426486762e-07,
                1.209865539298447e-06
            ],
            [
                1.5534979397740895e-06,
                3.9278624708775595e-07,
                2.9023116392097746e-06,
                1.3709573702722555e-06,
                2.902312677137316e-06,
                6.962253759904688e-06,
                1.9947292459265734e-06,
                6.47594952595231e-07,
                6.475950298011458e-07,
                1.994730197090463e-06
            ],
            [
                NaN,
                1.7603438428800754e-06,
                3.288749065423109e-06,
                4.222832941193893e-06,
                8.939694172957213e-06,
                3.7266401726359486e-06,
                3.726639728370556e-06,
                3.7266401726173067e-06,
                1.0677029973192638e-06,
                1.0677032518814388e-06
            ],
            [
                3.466326211113502e-07,
                1.4449798650551755e-07,
                3.466327450756327e-07,
                1.4449803818215767e-07,
                3.059023727894942e-07,
                2.1024336609724313e-07,
                3.9278615344178325e-07,
                7.338210680002898e-07,
                1.8553919030858602e-07,
                3.9278638755992735e-07
            ],
            [
                1.0677026154827912e-06,
                NaN,
                NaN,
                2.2603242978943238e-06,
                1.0677027427624903e-06,
                3.466325797900508e-07,
                5.422220909041528e-06,
                1.7603438428848787e-06,
                1.209865827752005e-06,
                NaN
            ],
            [
                NaN,
                1.553498124964492e-06,
                2.561282516066741e-06,
                9.422443692489024e-07,
                1.5534971990126997e-06,
                2.9023116391978967e-06,
                6.962254589978262e-06,
                9.422448185435711e-07,
                1.209866260432471e-06,
                2.902313023130843e-06
            ],
            [
                NaN,
                7.889264466725156e-06,
                6.962253759904688e-06,
                1.7603427936335396e-06,
                1.4738985485997396e-05,
                8.315281267882195e-07,
                1.0677029973158649e-06,
                1.3007125363719486e-05,
                4.222834451292594e-06,
                1.9947301970972664e-06
            ],
            [
                4.450849458218309e-07,
                8.315283250305684e-07,
                2.9023133690980155e-06,
                0.9975273771787441,
                2.260325106237323e-06,
                6.475948753965404e-07,
                1.5534983101478522e-06,
                3.059022269250683e-07,
                1.0677024881887838e-06,
                1.994729483705484e-06
            ],
            [
                0.9999988634366963,
                0.9999985406237799,
                0.9999964991443372,
                0.9999990577556311,
                0.9999952149037985,
                0.9999996940977003,
                0.9999974387168753,
                0.9999967112501551,
                0.9999988634366962,
                0.999996273358941
            ],
            [
                3.05902190458764e-07,
                1.5534983101602148e-06,
                1.9947299593078385e-06,
                3.7266410611465547e-06,
                3.288747889284851e-06,
                2.902311639183378e-06,
                6.1441760667392215e-06,
                9.422443692574719e-07,
                3.7266406165827946e-06,
                1.209866260432471e-06
            ],
            [
                5.043475284468537e-07,
                3.9278605979534166e-07,
                NaN,
                NaN,
                3.288749849529972e-06,
                2.2603248367949354e-06,
                7.338212429594283e-07,
                NaN,
                1.3709575337159875e-06,
                6.475946438055299e-07
            ],
            [
                2.10243290909963e-07,
                NaN,
                6.82560779249779e-08,
                NaN,
                NaN,
                5.3157887739943563e-08,
                0.9999706884616136,
                6.825597214718257e-08,
                3.059022269254856e-07,
                NaN
            ],
            [
                8.315282259138311e-07,
                1.3007133116542802e-05,
                5.043472879540142e-07,
                3.9278610661902853e-07,
                7.3382080556433e-07,
                1.9947299593078385e-06,
                1.0677024881980089e-06,
                4.4508526417298334e-07,
                1.760343213335281e-06,
                3.927860597945825e-07
            ],
            [
                5.715003789033962e-07,
                7.338213304316717e-07,
                1.3709568799760888e-06,
                1.2098659719441482e-06,
                7.338212429582604e-07,
                7.338209805170655e-07,
                6.144177531767002e-06,
                7.338207180864763e-07,
                NaN,
                7.338207180884785e-07
            ],
            [
                6.475945666063607e-07,
                1.067703124601679e-06,
                8.315277302841894e-07,
                NaN,
                1.994729008151319e-06,
                3.9278610661902853e-07,
                1.760343213335281e-06,
                1.3709575337159875e-06,
                NaN,
                3.9278629391427843e-07
            ],
            [
                0.9999980052700428,
                0.9999990577549577,
                0.9999949062950054,
                2.260323758987159e-06,
                0.9999949062968232,
                0.9999991148429646,
                1.9947299593078385e-06,
                0.9999921107355532,
                0.9999980052702804,
                0.9999960330155074
            ],
            [
                1.7603427936079236e-06,
                8.315281267834927e-07,
                9.422450431954847e-07,
                1.7603425837606927e-06,
                1.553497199007048e-06,
                NaN,
                1.2098662604291696e-06,
                NaN,
                1.9947304348862686e-06,
                6.962253760024999e-06
            ],
            [
                1.5534983101602148e-06,
                2.561283432035425e-06,
                1.2098653950551882e-06,
                3.726637951079042e-06,
                1.0677032518700286e-06,
                1.3709570434054234e-06,
                1.7603427936263351e-06,
                1.0677032518578904e-06,
                1.9947290081286418e-06,
                1.9947292458930106e-06
            ],
            [
                1.0677032518785256e-06,
                5.043474081993875e-07,
                2.90231094723893e-06,
                1.7603430034867993e-06,
                1.0677029973219343e-06,
                1.0677026154827912e-06,
                1.7603440527334603e-06,
                1.2098656835224664e-06,
                4.450849988811838e-07,
                NaN
            ],
            [
                5.043474683240344e-07,
                4.450852641737424e-07,
                2.2603242978871282e-06,
                1.5534971990169383e-06,
                7.338208055680009e-07,
                6.475947209985977e-07,
                1.1478765388105516e-05,
                8.939697369882888e-06,
                1.2098661162056318e-06,
                0.9999942280779124
            ],
            [
                NaN,
                3.059023727894942e-07,
                5.043472278312808e-07,
                1.7603432133296774e-06,
                5.715003107755449e-07,
                1.9947299592933255e-06,
                2.6995774527718623e-07,
                8.31528424162821e-07,
                9.422449308716635e-07,
                5.715003107738556e-07
            ],
            [
                2.102433159721477e-07,
                3.059021175255426e-07,
                0.8354835371034368,
                4.4508515805735777e-07,
                3.927862470861484e-07,
                3.059023727894942e-07,
                5.043474081993875e-07,
                4.4508505193932864e-07,
                8.315284241560147e-07,
                8.315279285370317e-07
            ],
            [
                4.450848927650143e-07,
                7.338209805170655e-07,
                1.0677032518700286e-06,
                1.5534983101602148e-06,
                4.450851580540182e-07,
                1.0677024882009222e-06,
                7.338210680021253e-07,
                3.059022998576899e-07,
                8.315279285351409e-07,
                6.962258739796719e-06
            ],
            [
                0.9999785550541752,
                9.422447062294175e-07,
                0.9999986290432842,
                NaN,
                0.999997273528431,
                0.9997694933744279,
                0.9999980052700425,
                0.9999980052709931,
                0.999994577779099,
                0.9999975938985225
            ],
            [
                2.260325106237323e-06,
                1.3709572068422585e-06,
                2.260324836787226e-06,
                4.2228319344021954e-06,
                5.71500651413193e-07,
                1.2098653950656417e-06,
                2.561282210740037e-06,
                1.5534971990126997e-06,
                3.2887478892683997e-06,
                2.902313023130843e-06
            ],
            [
                1.3709567165617364e-06,
                0.9999960330136181,
                3.726639728370556e-06,
                0.9999898700126635,
                1.6701423836262173e-05,
                6.144176799334096e-06,
                0.9999925887192563,
                1.4738987243478167e-05,
                1.3007130015677909e-05,
                1.3709573702822306e-06
            ],
            [
                1.2098658277451275e-06,
                1.2098652508287273e-06,
                8.315281267861397e-07,
                1.7603436330091044e-06,
                8.315284241560147e-07,
                7.338209805200689e-07,
                5.043475284430694e-07,
                2.2603251061664e-06,
                2.902311639073834e-06,
                7.338210680021253e-07
            ],
            [
                5.04347287955046e-07,
                7.338207180898968e-07,
                7.338211554783522e-07,
                1.0677029973219343e-06,
                4.450848927650143e-07,
                9.42244256915735e-07,
                8.315279285370317e-07,
                5.715003789046955e-07,
                2.5612834320563895e-06,
                3.466327450765785e-07
            ],
            [
                6.144175334468545e-06,
                4.785092783519724e-06,
                6.475947210012481e-07,
                1.8925157265332104e-05,
                NaN,
                7.889260704968913e-06,
                3.2887482812745586e-06,
                6.144176066795103e-06,
                2.9023133690980155e-06,
                1.3709573702822306e-06
            ],
            [
                3.288749457469787e-06,
                6.475948754028718e-07,
                9.422447062294175e-07,
                4.4508526417298334e-07,
                NaN,
                5.043474683220276e-07,
                4.450849988798682e-07,
                1.370957860576702e-06,
                3.2887506336235617e-06,
                1.0677032518814388e-06
            ],
            [
                6.144177530425867e-06,
                2.5612825160271407e-06,
                1.9947294835630703e-06,
                5.422218323019487e-06,
                1.4738988990959142e-05,
                8.93969630388855e-06,
                1.2098652508347793e-06,
                2.9023133690980155e-06,
                6.962257079775324e-06,
                6.962255419728997e-06
            ],
            [
                1.2098661162056318e-06,
                1.7603434231833873e-06,
                3.466326624336003e-07,
                2.9023112932177327e-06,
                1.994729483723626e-06,
                2.260324567337161e-06,
                2.9023119851899796e-06,
                2.902312331170226e-06,
                1.760343213335281e-06,
                1.9947297215125433e-06
            ],
            [
                2.902312677150514e-06,
                4.222831934248571e-06,
                9.4224425692559e-07,
                6.962259569750576e-06,
                4.785095635655362e-06,
                1.0677024881980089e-06,
                1.2098658277451275e-06,
                3.288747889284851e-06,
                8.315281267834927e-07,
                1.5534981249496567e-06
            ],
            [
                1.8553916819032217e-07,
                3.05902263391829e-07,
                0.9999843104540457,
                NaN,
                6.475949526003845e-07,
                8.315283250371857e-07,
                6.475950298011458e-07,
                3.927862939126708e-07,
                NaN,
                8.315280276626197e-07
            ],
            [
                0.9999832985801788,
                0.9999898700114467,
                0.999968798096133,
                0.9999974387168742,
                0.99999211073366,
                0.9999832985722024,
                1.2098659719788098e-06,
                3.466326211113502e-07,
                0.9998911030665246,
                0.9999885212359899
            ],
            [
                NaN,
                1.3709573702856596e-06,
                0.999997876621793,
                5.71500719545698e-07,
                4.4508494582314646e-07,
                0.9999930377462486,
                0.9999964991468427,
                0.9999916019239741,
                7.338212429582604e-07,
                5.043475885696228e-07
            ],
            [
                1.994729721518893e-06,
                9.422443692555439e-07,
                1.3709568799919866e-06,
                8.315281267882195e-07,
                2.3823690999323465e-07,
                1.2751910369310194e-07,
                9.422442569315887e-07,
                2.102434412875379e-07,
                1.5534981249697903e-06,
                1.6701423836262173e-05
            ],
            [
                5.715005832895975e-07,
                8.939693106873817e-06,
                NaN,
                9.422449308716635e-07,
                2.6995784182073116e-07,
                6.47595107001401e-07,
                5.043475284430694e-07,
                8.315277302841894e-07,
                1.0677032518748838e-06,
                5.715005832853093e-07
            ],
            [
                3.927860597945825e-07,
                2.382368815932174e-07,
                2.3823682479181176e-07,
                2.90231233114251e-06,
                8.93969950101825e-06,
                5.715004470326849e-07,
                1.5534979397677313e-06,
                2.5612812946890944e-06,
                3.0590237279085045e-07,
                2.3823693839325527e-07
            ],
            [
                1.760344052714248e-06,
                3.2887494574518405e-06,
                1.3709570434178922e-06,
                2.902312677150514e-06,
                1.9947297215043796e-06,
                4.2228339479858295e-06,
                1.2098655392871682e-06,
                1.7603440527286572e-06,
                2.90231094723893e-06,
                3.53562549305363e-05
            ],
            [
                9.422449308774482e-07,
                5.422217677152175e-06,
                1.2098656835224664e-06,
                3.9278610661902853e-07,
                6.962253760024999e-06,
                6.475950298011458e-07,
                1.0677024881980089e-06,
                2.2603245673443566e-06,
                2.902312331170226e-06,
                1.9947299593078385e-06
            ],
            [
                1.553497199007048e-06,
                1.6701421844419295e-05,
                3.7266397283908927e-06,
                2.902313022984344e-06,
                2.9023133690188264e-06,
                4.785093353909723e-06,
                0.9999724643158637,
                1.9947301970287804e-06,
                1.994730434879465e-06,
                7.88926070489716e-06
            ],
            [
                5.4222183235249605e-06,
                1.3709575337078829e-06,
                6.475945666033422e-07,
                1.2098662604247682e-06,
                1.2098659719788098e-06,
                4.785095635655362e-06,
                5.422220262636381e-06,
                1.994730672668496e-06,
                6.475950298021765e-07,
                1.5534971990126997e-06
            ],
            [
                3.927860597945825e-07,
                1.5534971990126997e-06,
                8.315281267861397e-07,
                1.5534975693933505e-06,
                2.382369383923073e-07,
                1.7603432133296774e-06,
                1.2098659719524008e-06,
                8.315277302841894e-07,
                8.315277302788957e-07,
                2.6995790618350237e-07
            ],
            [
                NaN,
                1.0677029973192638e-06,
                4.539788488687281e-05,
                NaN,
                1.3709575337159875e-06,
                6.475947982037486e-07,
                6.475945666063607e-07,
                0.9999756997651154,
                9.422442569097361e-07,
                2.3823688159291947e-07
            ],
            [
                3.927862470905692e-07,
                1.2098661162056318e-06,
                9.422443692574719e-07,
                3.288749065436569e-06,
                7.338207180898968e-07,
                3.2887506336235617e-06,
                1.9947301970972664e-06,
                1.5534984953552536e-06,
                1.0677029973192638e-06,
                1.5534975693979422e-06
            ],
            [
                1.1253525596174225e-07,
                1.4449796928021588e-07,
                3.0590219045914655e-07,
                2.3823682479181176e-07,
                2.699577774589574e-07,
                9.931200429212718e-08,
                5.043475885696228e-07,
                2.382368815932174e-07,
                3.05902263391829e-07,
                3.059022269254856e-07
            ],
            [
                1.7603430034867993e-06,
                5.043475885696228e-07,
                2.3823693839325527e-07,
                3.4663262111182307e-07,
                3.927862002663297e-07,
                NaN,
                3.927863407379485e-07,
                6.962258739796719e-06,
                NaN,
                1.3709575337159875e-06
            ],
            [
                3.726638839806038e-06,
                1.4738985484227961e-05,
                1.7603438428660665e-06,
                5.422221555380179e-06,
                3.7266392839832006e-06,
                5.829128635171172e-05,
                1.2098653950656417e-06,
                8.939693106329072e-06,
                2.1444950965282096e-05,
                3.535626756251187e-05
            ],
            [
                5.422219616140078e-06,
                3.726639728262097e-06,
                1.3007126914435202e-05,
                3.7266379513434106e-06,
                0.0003353500294748882,
                NaN,
                1.5534983101478522e-06,
                4.22283545808297e-06,
                NaN,
                3.726641061109272e-06
            ],
            [
                8.315281267861397e-07,
                1.9947304348862686e-06,
                NaN,
                1.0677032518814388e-06,
                5.422217677152175e-06,
                0.9998415637277744,
                4.222832941193893e-06,
                9.422450431989127e-07,
                6.475947982037486e-07,
                3.059022998581767e-07
            ],
            [
                5.715004470326849e-07,
                NaN,
                7.338211554783522e-07,
                9.422447062294175e-07,
                9.422447062270609e-07,
                1.2098652508424818e-06,
                2.2603242978943238e-06,
                2.260323758987159e-06,
                3.927862939126708e-07,
                8.315281267882195e-07
            ]
        ]
    },
    {
        "q_id": "9580_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            19,
            20,
            22,
            23,
            25,
            26,
            27,
            28,
            29,
            33,
            34,
            35,
            37,
            38,
            40,
            41,
            43,
            45,
            47,
            48,
            50,
            51,
            53,
            54,
            55,
            57,
            58,
            59,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            88,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            104,
            105,
            106,
            107,
            108,
            110,
            111,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124
        ],
        "rewards": [
            [
                1.4738980215352592e-05,
                1.4449798650551755e-07,
                1.6373766672973748e-07,
                7.338208055664991e-07,
                2.3823693839290317e-07,
                3.466325797896173e-07,
                3.927860597945825e-07,
                3.466326211113502e-07,
                2.69957906184239e-07,
                2.3823693839290317e-07
            ],
            [
                1.2751899728311609e-07,
                2.10243290909724e-07,
                9.931193325852072e-08,
                1.637377057680051e-07,
                5.043473480777865e-07,
                2.102434412875379e-07,
                1.8553919030858602e-07,
                6.475945666063607e-07,
                3.05902190458764e-07,
                2.1024331597262577e-07
            ],
            [
                5.715004470334646e-07,
                0.999903897562948,
                3.05902336324494e-07,
                7.338207180898968e-07,
                0.9999996743687424,
                0.9999983463100223,
                1.8553910183674878e-07,
                0.9999997761971317,
                0.9999994284996896,
                0.9999982396574177
            ],
            [
                2.561282210740037e-06,
                2.2603234895289998e-06,
                5.422219616140078e-06,
                3.288749457469787e-06,
                2.902311639183378e-06,
                6.144175334418252e-06,
                7.338208055664991e-07,
                1.0129989772532511e-05,
                2.561281600076256e-06,
                3.7266410611296085e-06
            ],
            [
                6.023568448589658e-08,
                6.023578501513224e-08,
                1.1253524254650944e-07,
                8.31528325040778e-07,
                7.338212429582604e-07,
                2.382368815932174e-07,
                3.05902336324494e-07,
                5.043475885696228e-07,
                7.734414854823498e-08,
                7.734428685047173e-08
            ],
            [
                0.9999975938982386,
                0.9999964991443432,
                0.9999972735303857,
                1.1253526937697666e-07,
                0.9999969105048327,
                NaN,
                0.9999972735290831,
                0.999993459562821,
                0.9999987121043258,
                1.6373774480605869e-07
            ],
            [
                8.939695238536645e-06,
                1.994730434847717e-06,
                1.3007134667070165e-05,
                3.0590226339061185e-07,
                1.3709567165530083e-06,
                4.4508526417298334e-07,
                1.209866260432471e-06,
                1.0677026154806063e-06,
                3.466327863983311e-07,
                2.2603234895289998e-06
            ],
            [
                2.699578740032504e-07,
                6.475947210012481e-07,
                7.338211554783522e-07,
                3.9278634073732336e-07,
                3.05902190458764e-07,
                4.7850933538313875e-06,
                3.927862470899887e-07,
                2.699577774585891e-07,
                4.2228324377740105e-06,
                1.3709570434219446e-06
            ],
            [
                8.939699501132077e-06,
                3.726637951387472e-06,
                8.939698435560267e-06,
                1.5534971990126997e-06,
                5.043473480777865e-07,
                2.7535697667202906e-05,
                3.9278634073732336e-07,
                8.315279285351409e-07,
                2.753568453712307e-05,
                2.260325106237323e-06
            ],
            [
                1.1253509497883659e-07,
                6.475946438055299e-07,
                1.0677027427624903e-06,
                1.2098659719757836e-06,
                9.931187406410953e-08,
                1.637377057680051e-07,
                2.382369951932796e-07,
                6.9622587397397306e-06,
                4.785093924362895e-06,
                1.1253526937697666e-07
            ],
            [
                1.8553919030858602e-07,
                0.9999921107336746,
                0.9999974387187072,
                0.9999986290426325,
                0.9999756997627787,
                1.0677028700422047e-06,
                0.9999934595596705,
                0.9999969105051889,
                0.999998932297258,
                6.023571320847322e-08
            ],
            [
                0.9999516743631313,
                1.275190732904469e-07,
                0.9999952149055187,
                7.338208930460318e-07,
                0.9999955048162893,
                NaN,
                NaN,
                NaN,
                3.4663274507713016e-07,
                0.999996910504085
            ],
            [
                2.102434162245973e-07,
                1.0677027427340866e-06,
                1.2098655392811161e-06,
                5.422220262555012e-06,
                1.9947306726358406e-06,
                7.338208055680009e-07,
                1.994729483694599e-06,
                1.5534975693869924e-06,
                1.760343423160973e-06,
                3.927862002641863e-07
            ],
            [
                1.1253526937697666e-07,
                7.889265407327733e-06,
                3.059022269254856e-07,
                1.1253512180925583e-07,
                6.825608606172863e-08,
                2.382368815932174e-07,
                2.699578096403948e-07,
                8.764254764780641e-08,
                2.3823693839325527e-07,
                8.315281267882195e-07
            ],
            [
                1.27519088491875e-07,
                1.994730672668496e-06,
                NaN,
                3.927862470899887e-07,
                3.288748673360027e-06,
                2.2603253756956754e-06,
                1.6701429808298613e-05,
                3.288750241561788e-06,
                1.1478764021029928e-05,
                1.6373774480605869e-07
            ],
            [
                6.475951069932288e-07,
                1.3709576971463352e-06,
                1.5534973842030142e-06,
                2.2603253756874524e-06,
                2.561283432035425e-06,
                1.209866260432471e-06,
                3.288750241561788e-06,
                1.7603427936335396e-06,
                1.3709570434219446e-06,
                1.760343003481596e-06
            ],
            [
                2.699578740032504e-07,
                1.7603438428800754e-06,
                4.4508494582405734e-07,
                2.3823696679327928e-07,
                5.04347468323289e-07,
                3.4663266243308805e-07,
                9.422443692555439e-07,
                2.382369667929001e-07,
                1.1253513522447425e-07,
                2.3823688159291947e-07
            ],
            [
                9.931200429212718e-08,
                1.1253526937697666e-07,
                1.637377057680051e-07,
                8.76424013786396e-08,
                1.4449795205472734e-07,
                1.4449802095666915e-07,
                8.315283250371857e-07,
                1.4449805540763184e-07,
                1.1253513522447425e-07,
                7.734428685047173e-08
            ],
            [
                3.466326624336003e-07,
                2.102434412875379e-07,
                2.1024334103505245e-07,
                1.8553905760062447e-07,
                5.715006514105942e-07,
                2.382370235933104e-07,
                1.6373776432509826e-07,
                2.3823685319244518e-07,
                1.209866260432471e-06,
                6.47595107001401e-07
            ],
            [
                6.825601283086733e-08,
                5.315780536011123e-08,
                7.734423152941018e-08,
                7.734428685047173e-08,
                8.764247451307293e-08,
                6.144176799334096e-06,
                1.275190580884987e-07,
                8.7642526752214e-08,
                1.2098659719716573e-06,
                5.315786239218605e-08
            ],
            [
                2.382368531929327e-07,
                9.931187406410953e-08,
                3.4663278639892215e-07,
                3.4663262111182307e-07,
                5.715006514176113e-07,
                1.1253506814842375e-07,
                1.4449800373118268e-07,
                1.2751908849167202e-07,
                2.699578740032504e-07,
                1.8553914607267268e-07
            ],
            [
                4.2228339479858295e-06,
                NaN,
                6.144176066850984e-06,
                4.785095635624897e-06,
                1.3709567165617364e-06,
                5.422218969858371e-06,
                1.3007123813193233e-05,
                2.4300252321904572e-05,
                3.2887478892683997e-06,
                1.0677027427600627e-06
            ],
            [
                7.889265407177056e-06,
                5.422217030747413e-06,
                3.0590237279032884e-07,
                6.47595107001401e-07,
                2.6995790618350237e-07,
                2.3823688159291947e-07,
                1.2098661162056318e-06,
                3.53562549305363e-05,
                2.3823693839290317e-07,
                5.715004470313855e-07
            ],
            [
                1.30071315662049e-05,
                7.734416698849138e-08,
                4.222835458148261e-06,
                2.561282821402217e-06,
                5.144221980055201e-05,
                0.9999251538003163,
                1.4738980215593877e-05,
                6.962256249935742e-06,
                2.3823696679327928e-07,
                2.4300249423302888e-05
            ],
            [
                4.450852641717689e-07,
                1.2098652508424818e-06,
                1.4449800373065699e-07,
                1.6373776432509826e-07,
                2.1024334103581732e-07,
                3.05902117523595e-07,
                1.0677029973192638e-06,
                5.043473480777865e-07,
                2.260325375677174e-06,
                1.760343003481596e-06
            ],
            [
                2.5612819054133693e-06,
                1.30071315662049e-05,
                3.7266383954560706e-06,
                1.5534981249697903e-06,
                7.889259764445822e-06,
                NaN,
                1.7603427936263351e-06,
                1.3007126914435202e-05,
                3.927860597945825e-07,
                3.288749065423109e-06
            ],
            [
                1.8553907971855875e-07,
                2.902312677150514e-06,
                5.043475885674441e-07,
                NaN,
                6.475950298011458e-07,
                1.0129988565084915e-05,
                6.962253760024999e-06,
                1.7603438428800754e-06,
                3.726638839833152e-06,
                1.7603440527286572e-06
            ],
            [
                1.637376862489725e-07,
                1.275190428875671e-07,
                4.691160446380562e-08,
                6.825609419848033e-08,
                9.422443692574719e-07,
                1.4449798650569826e-07,
                1.1253525596174225e-07,
                1.1253525596174225e-07,
                1.275190732904469e-07,
                6.023577065381482e-08
            ],
            [
                5.3157837044597743e-08,
                2.699578096403948e-07,
                5.043472278322555e-07,
                3.4663262111182307e-07,
                1.4449800373118268e-07,
                1.1253506814842375e-07,
                9.93120161310289e-08,
                6.825609419848033e-08,
                2.382369951932796e-07,
                1.4449800373118268e-07
            ],
            [
                2.382368815932174e-07,
                3.7266406168827523e-06,
                1.1253508156363576e-07,
                2.6995790618469934e-07,
                0.9999785550517057,
                1.5534984953552536e-06,
                8.315277302857965e-07,
                6.825602910433871e-08,
                8.315280276626197e-07,
                1.0677027427624903e-06
            ],
            [
                5.3157811697009444e-08,
                3.0590237279085045e-07,
                3.9278610661902853e-07,
                8.315281267882195e-07,
                9.422442569315887e-07,
                6.47595107001401e-07,
                4.450852111155216e-07,
                NaN,
                2.699578096403948e-07,
                1.1253516205489029e-07
            ],
            [
                4.450850519409479e-07,
                1.067703124601679e-06,
                1.2098662604291696e-06,
                3.466327037553825e-07,
                5.043473480777865e-07,
                1.637376862489725e-07,
                3.466326211113502e-07,
                1.27519088491875e-07,
                5.715006514176113e-07,
                3.4663249714612693e-07
            ],
            [
                3.05902190458764e-07,
                6.475946438055299e-07,
                8.315277302857965e-07,
                2.6995771309523475e-07,
                1.444979692800516e-07,
                5.043472879525233e-07,
                3.466327863983311e-07,
                3.4663249714612693e-07,
                5.043474081993875e-07,
                2.3823685319244518e-07
            ],
            [
                1.1253525596134564e-07,
                3.46632497145457e-07,
                3.05902263391829e-07,
                1.275190276859705e-07,
                3.0590226339061185e-07,
                4.450852641737424e-07,
                4.450851049959619e-07,
                3.9278615344178325e-07,
                8.315280276626197e-07,
                1.4449798650476187e-07
            ],
            [
                0.9999938558254118,
                5.315789407685159e-08,
                8.7642526752214e-08,
                0.9999967112497666,
                0.9999934595643456,
                0.9999949062937954,
                0.9999921107383807,
                1.4449798650551755e-07,
                2.699576809143613e-07,
                0.9999938558232155
            ],
            [
                4.450848927637999e-07,
                3.05902263391829e-07,
                4.4508494582405734e-07,
                1.0129987357287368e-05,
                5.043476486915964e-07,
                1.994729008145876e-06,
                6.825608606172863e-08,
                3.288747889284851e-06,
                2.699577774585891e-07,
                3.05902190458764e-07
            ],
            [
                1.370957860576702e-06,
                1.6373774480605869e-07,
                2.3823690999323465e-07,
                3.4663274507713016e-07,
                1.7603434231833873e-06,
                2.144495864059426e-05,
                3.535624650279074e-05,
                4.2228319344021954e-06,
                3.059022269254856e-07,
                1.8553910183674878e-07
            ],
            [
                9.422445939032799e-07,
                8.315277302841894e-07,
                2.144495097113319e-05,
                1.4449807263312446e-07,
                5.715004470295662e-07,
                6.605212107986466e-05,
                1.1478770862882149e-05,
                2.1024326584639497e-07,
                2.3823702359290413e-07,
                2.699578740032504e-07
            ],
            [
                2.3823682479292225e-07,
                1.8553919030858602e-07,
                6.825602910433871e-08,
                1.8553905760062447e-07,
                5.315789407685159e-08,
                1.4449796928021588e-07,
                8.315278294097538e-07,
                0.004609571371737637,
                2.6995774527718623e-07,
                1.6373776432509826e-07
            ],
            [
                0.9999955048184321,
                0.9999898700066315,
                0.00026119034036714984,
                7.734416698849138e-08,
                0.9999996743687812,
                2.102434162245973e-07,
                1.637376862489725e-07,
                0.9999972735297334,
                0.9999992661792827,
                2.699577130960941e-07
            ],
            [
                2.902313023130843e-06,
                8.315280276626197e-07,
                3.059022998576899e-07,
                6.475949526020042e-07,
                1.4738978458623327e-05,
                5.715005832886879e-07,
                5.715005832895975e-07,
                1.5534981249697903e-06,
                3.466325797896173e-07,
                1.4449800373065699e-07
            ],
            [
                2.4300252321904572e-05,
                5.043473480777865e-07,
                NaN,
                4.4508494582405734e-07,
                1.7603425837903113e-06,
                2.9023119851899796e-06,
                3.059022269250683e-07,
                4.785096776499213e-06,
                2.69957906184239e-07,
                1.5534984953510149e-06
            ],
            [
                5.715005832895975e-07,
                2.6995784182183607e-07,
                2.430025232247918e-05,
                2.2603251062450327e-06,
                1.5534984953552536e-06,
                1.3007134667436886e-05,
                2.5612834320563895e-06,
                1.7603440527334603e-06,
                3.7266379514061143e-06,
                5.715005832886879e-07
            ],
            [
                2.102434162245973e-07,
                8.315281267861397e-07,
                1.4449796928021588e-07,
                3.059023727894942e-07,
                3.466327037539638e-07,
                1.5534979397829198e-06,
                3.05902117523595e-07,
                7.338208055680009e-07,
                1.4449798650551755e-07,
                7.338209805240734e-07
            ],
            [
                9.422445939002803e-07,
                3.726639728370556e-06,
                3.2887482813149375e-06,
                8.939697369980456e-06,
                8.939698435560267e-06,
                1.8553907971855875e-07,
                1.2098662604291696e-06,
                8.31528424162821e-07,
                3.466326624336003e-07,
                6.144175334468545e-06
            ],
            [
                3.9278629391427843e-07,
                1.2751901248454963e-07,
                9.931198061405701e-08,
                3.9278629391427843e-07,
                1.8553916819032217e-07,
                2.699577774589574e-07,
                1.1253524254650944e-07,
                4.4508515805735777e-07,
                2.1024331597288867e-07,
                1.2751902768612997e-07
            ],
            [
                3.0590226339061185e-07,
                5.04347287955046e-07,
                1.5534984953552536e-06,
                8.31528325040778e-07,
                3.05902190458764e-07,
                8.315281267882195e-07,
                1.3709570434219446e-06,
                5.043476486924565e-07,
                NaN,
                8.315283250394546e-07
            ],
            [
                0.999997438718709,
                3.4663266243308805e-07,
                3.9278610661902853e-07,
                0.9999952149072199,
                1.4449798650569826e-07,
                0.9999964991439193,
                1.2751901248454963e-07,
                2.6995790618469934e-07,
                0.9999942280779165,
                9.931185038635267e-08
            ],
            [
                2.2603240284371276e-06,
                5.043473480777865e-07,
                1.8553919030858602e-07,
                6.475947210046347e-07,
                3.0590237279032884e-07,
                1.855391239547094e-07,
                NaN,
                1.0677029973219343e-06,
                1.27519088491875e-07,
                3.288748673376478e-06
            ],
            [
                5.715005151606823e-07,
                7.338212429582604e-07,
                1.2098659719757836e-06,
                9.422443692555439e-07,
                6.475947210012481e-07,
                5.04347468323289e-07,
                2.5612828213818346e-06,
                5.043474081993875e-07,
                1.3709575337125585e-06,
                8.315281267861397e-07
            ],
            [
                1.6373766672994222e-07,
                7.889266347786918e-06,
                NaN,
                1.7603430034867993e-06,
                4.4508515805735777e-07,
                5.043475885696228e-07,
                7.338207180898968e-07,
                7.338210680021253e-07,
                1.8553910183674878e-07,
                6.475949526020042e-07
            ],
            [
                4.6911677163762064e-08,
                3.059021175261338e-07,
                6.023568448589658e-08,
                5.043475885696228e-07,
                1.7603438428800754e-06,
                3.0590219045914655e-07,
                6.47595107001401e-07,
                1.275190580890061e-07,
                0.9999984465026165,
                4.4508515805735777e-07
            ],
            [
                1.4449798650551755e-07,
                1.275190580890061e-07,
                1.8553914607267268e-07,
                1.9947299593078385e-06,
                1.994729483729522e-06,
                2.6995774527718623e-07,
                5.422220262636381e-06,
                1.8553910183674878e-07,
                2.3823696679327928e-07,
                1.0129988565084915e-05
            ],
            [
                8.481108183851022e-05,
                3.0590237279032884e-07,
                0.0004878572385288399,
                6.605214470327124e-05,
                3.0590237279085045e-07,
                2.3823682479317953e-07,
                1.1253522913127183e-07,
                3.059022269250683e-07,
                1.553497754583709e-06,
                3.059021175261338e-07
            ],
            [
                NaN,
                6.47595107001401e-07,
                6.962258739796719e-06,
                1.8553919030858602e-07,
                NaN,
                1.6373772528704005e-07,
                5.715003107755449e-07,
                9.422442569315887e-07,
                2.382370235922541e-07,
                3.927863407379485e-07
            ],
            [
                5.043473480777865e-07,
                3.927862002663297e-07,
                1.5534983101602148e-06,
                1.3709575337159875e-06,
                1.9947304348862686e-06,
                5.715005832886879e-07,
                1.5534983101602148e-06,
                5.04347468323289e-07,
                1.3709568799919866e-06,
                8.315281267882195e-07
            ],
            [
                3.927863875616689e-07,
                1.637377057680051e-07,
                2.699578740032504e-07,
                7.73442776303243e-08,
                8.315279285370317e-07,
                2.10243290909724e-07,
                4.450852641737424e-07,
                6.962253760024999e-06,
                2.2603234895372223e-06,
                2.1024331597262577e-07
            ],
            [
                6.825606978822427e-08,
                9.93119806143167e-08,
                1.3440417781598893e-08,
                0.9998911030807137,
                1.2751905808881762e-07,
                3.46632497145457e-07,
                8.7642558095602e-08,
                1.6701423836262173e-05,
                0.999954602142463,
                0.9999251537920666
            ],
            [
                2.699576809143613e-07,
                1.2751899728311609e-07,
                2.382368815932174e-07,
                9.931190958076104e-08,
                3.05902190458764e-07,
                5.043476486924565e-07,
                3.927862939126708e-07,
                3.466326624336003e-07,
                2.3823690999323465e-07,
                8.7642558095602e-08
            ],
            [
                5.04347287955046e-07,
                2.699578096403948e-07,
                2.382368247924618e-07,
                3.0590215399183813e-07,
                9.422449308774482e-07,
                1.855391239544352e-07,
                5.715006514176113e-07,
                4.450848927658745e-07,
                4.785095635655362e-06,
                8.76424013786396e-08
            ],
            [
                1.637377057680051e-07,
                1.275190732904469e-07,
                1.6373774480605869e-07,
                6.825597214718257e-08,
                8.764254764780641e-08,
                1.2098653950716937e-06,
                9.931186222523604e-08,
                4.4508515805735777e-07,
                3.059022998581767e-07,
                3.05902190458764e-07
            ],
            [
                1.2098662604291696e-06,
                3.726638839878908e-06,
                3.7266401726173067e-06,
                1.012999098021058e-05,
                8.93969950132721e-06,
                7.338211554783522e-07,
                1.012999098021058e-05,
                7.338213304363436e-07,
                1.553497199007048e-06,
                3.726638839878908e-06
            ],
            [
                3.288748673360027e-06,
                2.561281600086738e-06,
                6.144177531767002e-06,
                1.3007133116542802e-05,
                3.059022998558814e-07,
                3.535625493182252e-05,
                1.2098656835224664e-06,
                6.962255419931625e-06,
                6.825606165129312e-08,
                5.715005832895975e-07
            ],
            [
                1.0677032518814388e-06,
                1.8553907971855875e-07,
                9.931200429212718e-08,
                0.9999997897567092,
                9.931189774187203e-08,
                0.9999997897566592,
                0.9999995262094424,
                0.9999988634362902,
                0.999996273359833,
                0.9999988634357481
            ],
            [
                3.059022998576899e-07,
                2.6995784182183607e-07,
                1.370957860576702e-06,
                1.6373774480605869e-07,
                5.715003789046955e-07,
                NaN,
                1.4449807263312446e-07,
                5.715006514176113e-07,
                3.059022998576899e-07,
                2.2603248367949354e-06
            ],
            [
                6.475949526020042e-07,
                1.3007128464346676e-05,
                4.222834954778007e-06,
                3.726638395611981e-06,
                8.315279285351409e-07,
                5.043473480777865e-07,
                1.9947299593014888e-06,
                1.9947297215043796e-06,
                6.605217618626244e-05,
                5.4222183235249605e-06
            ],
            [
                4.450850519403407e-07,
                4.4508510499849186e-07,
                2.102434162245973e-07,
                1.4449805540763184e-07,
                1.27519088491875e-07,
                2.5612819054133693e-06,
                9.422450432014836e-07,
                5.71500719545698e-07,
                1.0677032518814388e-06,
                8.764242227418718e-08
            ],
            [
                1.209866260432471e-06,
                3.9278615344178325e-07,
                2.430024073523505e-05,
                5.043473480777865e-07,
                7.338207180898968e-07,
                9.422444815765128e-07,
                1.760343213335281e-06,
                4.22283545819819e-06,
                2.9023119851781017e-06,
                9.422442569315887e-07
            ],
            [
                2.9023116392097746e-06,
                4.785092783371756e-06,
                3.9278629391427843e-07,
                9.422443692555439e-07,
                5.71500719545698e-07,
                1.553497754577351e-06,
                1.0677026154827912e-06,
                1.3709575337159875e-06,
                1.0677027427600627e-06,
                1.0677033791612137e-06
            ],
            [
                3.9278610661902853e-07,
                5.4222183235249605e-06,
                2.3823685319174098e-07,
                1.1253514863968147e-07,
                3.2887506336235617e-06,
                3.927863407379485e-07,
                8.315282259138311e-07,
                8.31527928532683e-07,
                2.4300243631890864e-05,
                3.120190393487965e-05
            ],
            [
                5.422219616265831e-06,
                2.5612834320563895e-06,
                3.05902336324494e-07,
                1.3709575337159875e-06,
                1.067703124601679e-06,
                1.0677033791612137e-06,
                3.288749849529972e-06,
                2.2603251062450327e-06,
                6.475947982037486e-07,
                4.785093353940187e-06
            ],
            [
                7.338211554783522e-07,
                5.715005832886879e-07,
                2.9023126771227976e-06,
                5.422217030707961e-06,
                5.043474081993875e-07,
                3.1201900218617364e-05,
                3.288748281329893e-06,
                2.9023133690980155e-06,
                5.715003789033962e-07,
                8.939695238634211e-06
            ],
            [
                3.9278610661902853e-07,
                1.2098653950656417e-06,
                8.315283250371857e-07,
                3.059022269250683e-07,
                1.5534984953510149e-06,
                5.715003789046955e-07,
                3.927862002663297e-07,
                5.043472879540142e-07,
                1.3709568799879344e-06,
                4.785096776499213e-06
            ],
            [
                9.422443692574719e-07,
                1.1253512180925583e-07,
                1.6373764721091427e-07,
                2.699577774589574e-07,
                6.825601283086733e-08,
                9.931187406410953e-08,
                8.315277302857965e-07,
                2.10243290909963e-07,
                2.1024336609874897e-07,
                1.1253526937697666e-07
            ],
            [
                1.8553907971855875e-07,
                3.2887502415767434e-06,
                2.3823693839325527e-07,
                9.931195693628605e-08,
                3.2887494574832472e-06,
                3.1201915096836145e-05,
                2.902312677150514e-06,
                8.315277302857965e-07,
                1.4449800373118268e-07,
                1.5534977545886537e-06
            ],
            [
                3.059021175261338e-07,
                2.6995768091310296e-07,
                2.1024334103581732e-07,
                8.315280276626197e-07,
                3.05902263389638e-07,
                5.715003107767143e-07,
                1.855390354818069e-07,
                3.059021539909339e-07,
                2.699578740032504e-07,
                3.927862939126708e-07
            ],
            [
                6.144172404738491e-06,
                2.6995784182183607e-07,
                3.1201907657271834e-05,
                1.8553919030858602e-07,
                3.2887502415243994e-06,
                7.338210680021253e-07,
                3.7266379514061143e-06,
                3.9278605979534166e-07,
                1.8553905760062447e-07,
                1.444979692800516e-07
            ],
            [
                9.93119806143167e-08,
                2.699577452775239e-07,
                1.6373766672994222e-07,
                2.1024326584702836e-07,
                1.2098659719788098e-06,
                3.0590215399281185e-07,
                NaN,
                3.059022269254856e-07,
                3.05902263391829e-07,
                8.764251630441717e-08
            ],
            [
                0.9999997761970248,
                4.450850519403407e-07,
                0.9999996310113282,
                4.785095065171522e-06,
                2.10243290909724e-07,
                1.6373766672973748e-07,
                0.9999997761970515,
                0.9999997617630901,
                1.275190428875671e-07,
                1.5534971990126997e-06
            ],
            [
                5.043474683204221e-07,
                8.315278294072958e-07,
                1.7603438428740716e-06,
                1.3709567165530083e-06,
                1.0677032518748838e-06,
                3.059023727894942e-07,
                8.315281267834927e-07,
                8.315280276546789e-07,
                3.466325797896173e-07,
                1.760344052714248e-06
            ],
            [
                7.889263526180094e-06,
                4.785093353940187e-06,
                3.288748673376478e-06,
                2.90231094723893e-06,
                1.3709575337125585e-06,
                4.785096776499213e-06,
                1.670142582682936e-05,
                4.785093353940187e-06,
                4.222832437798974e-06,
                6.475951069985296e-07
            ],
            [
                1.3709570434178922e-06,
                2.1444945858485726e-05,
                2.5612828213352452e-06,
                5.422217677152175e-06,
                8.939693107190907e-06,
                8.315284241560147e-07,
                1.994729008145876e-06,
                1.6701427818034747e-05,
                4.222834451382849e-06,
                3.2887478892504536e-06
            ],
            [
                1.8925157265710765e-05,
                2.2603251062450327e-06,
                1.7603430034867993e-06,
                4.785096205973894e-06,
                3.927863407379485e-07,
                1.7603438428848787e-06,
                1.6373762769187936e-07,
                3.927863407379485e-07,
                8.764244316973974e-08,
                6.962257079832313e-06
            ],
            [
                3.059022998576899e-07,
                2.1024336609874897e-07,
                6.475947210046347e-07,
                2.699578096403948e-07,
                8.764249540862797e-08,
                1.8553910183607374e-07,
                1.855391681906175e-07,
                6.023569884718319e-08,
                2.699576809143613e-07,
                5.043476486924565e-07
            ],
            [
                1.2098659719788098e-06,
                3.2887502415767434e-06,
                1.012999098021058e-05,
                1.0677028700422047e-06,
                1.994729483729522e-06,
                1.3007131566370516e-05,
                3.7266397283908927e-06,
                1.892515049819277e-05,
                5.422218969895357e-06,
                1.2098656835224664e-06
            ],
            [
                1.855391239544352e-07,
                1.8553914607267268e-07,
                5.715002426486762e-07,
                2.699577774585891e-07,
                3.059022998576899e-07,
                1.8553916819032217e-07,
                2.3823702359290413e-07,
                5.043476486915964e-07,
                2.699578740032504e-07,
                1.6373772528704005e-07
            ],
            [
                3.05902226923399e-07,
                1.3709567165579959e-06,
                9.422442569315887e-07,
                2.2603240284371276e-06,
                3.466326624336003e-07,
                2.699578096393206e-07,
                1.5534981249697903e-06,
                2.260325106237323e-06,
                1.5534975693979422e-06,
                7.338208055664991e-07
            ],
            [
                7.338209805240734e-07,
                3.927862470899887e-07,
                2.6995790618469934e-07,
                3.9278610661902853e-07,
                6.475947982037486e-07,
                4.4508494582405734e-07,
                9.931187406410953e-08,
                4.450852111155216e-07,
                3.05902190458764e-07,
                8.315281267882195e-07
            ],
            [
                0.9999986290432843,
                2.382369383923073e-07,
                0.9999952149043724,
                6.825597214718257e-08,
                7.734424996987981e-08,
                0.9999977396754348,
                0.9999970976883642,
                1.275189972832538e-07,
                1.637377057680051e-07,
                0.9999990577557437
            ],
            [
                2.102434412875379e-07,
                1.5534981249736758e-06,
                1.3709576971463352e-06,
                0.9999904837460831,
                NaN,
                0.9999989969855535,
                4.450848927658745e-07,
                4.450852111135988e-07,
                0.9999987121049385,
                0.9999955048173601
            ],
            [
                2.4300243631272052e-05,
                1.8925148241080285e-05,
                4.0063677865600476e-05,
                2.5612828213818346e-06,
                3.1201922533564516e-05,
                1.760343213322473e-06,
                1.5534971990126997e-06,
                NaN,
                4.222834451355964e-06,
                NaN
            ],
            [
                0.9999964991443424,
                0.9999921107355614,
                3.0590226339061185e-07,
                0.9999962733598359,
                8.315279285370317e-07,
                0.9999967112505489,
                2.3823690999323465e-07,
                0.9999972735284338,
                0.9999957771681041,
                0.9999977396759757
            ],
            [
                3.05902336324494e-07,
                2.3823690999290963e-07,
                3.0590237279032884e-07,
                2.5612828213934817e-06,
                3.9278610661902853e-07,
                1.8553907971855875e-07,
                2.561281600086738e-06,
                1.8553905759969634e-07,
                1.8553907971855875e-07,
                3.466325797896173e-07
            ],
            [
                2.10243290909963e-07,
                6.825609419848033e-08,
                5.715005832895975e-07,
                2.382368815932174e-07,
                9.93120161310289e-08,
                5.715002426486762e-07,
                1.855391239547094e-07,
                2.6995784182183607e-07,
                1.637376862489725e-07,
                7.734415776836702e-08
            ],
            [
                5.04347468323289e-07,
                2.561282516066741e-06,
                2.102434412875379e-07,
                0.9999599363158032,
                2.1024334103581732e-07,
                1.1253506814842375e-07,
                2.699576809143613e-07,
                2.102434412875379e-07,
                3.059022269254856e-07,
                2.3823688159291947e-07
            ],
            [
                5.043476486915964e-07,
                9.422449308774482e-07,
                4.450852111148132e-07,
                6.475945666051092e-07,
                1.9947304348862686e-06,
                2.3823690999236795e-07,
                9.422444815765128e-07,
                2.9023119851899796e-06,
                4.450848927650143e-07,
                5.71500719545698e-07
            ],
            [
                1.7603440527046419e-06,
                1.994729483723626e-06,
                9.422444815765128e-07,
                7.338212429537553e-07,
                3.4663253846718004e-07,
                7.338209805224048e-07,
                2.6995771309523475e-07,
                4.450852111148132e-07,
                1.5534981249574276e-06,
                1.0677026154730804e-06
            ],
            [
                6.023576347315567e-08,
                0.999997593896802,
                0.9999972735287564,
                3.65348425788669e-08,
                0.9999991148430705,
                0.9999877809181955,
                0.9999987121049385,
                0.9999987121050926,
                0.9999987121044777,
                0.9999996072138936
            ],
            [
                2.699577774589574e-07,
                1.8553919030858602e-07,
                2.699577774589574e-07,
                1.4449798650569826e-07,
                6.023578501513224e-08,
                1.4449795205472734e-07,
                1.6373762769138607e-07,
                1.4449800373065699e-07,
                1.1253522913127183e-07,
                1.2751901248454963e-07
            ]
        ]
    },
    {
        "q_id": "10355_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            9,
            10,
            11,
            12,
            14,
            17,
            18,
            20,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            29,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            42,
            44,
            45,
            46,
            48,
            49,
            50,
            52,
            53,
            56,
            58,
            59,
            60,
            62,
            64,
            65,
            69,
            70,
            73,
            74,
            75,
            76,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            87,
            89,
            92,
            95,
            96,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            119,
            121,
            122,
            123,
            126,
            127
        ],
        "rewards": [
            [
                7.338211554783522e-07,
                1.2098656835224664e-06,
                1.3709570434178922e-06,
                3.288748673376478e-06,
                NaN,
                4.4508510499849186e-07,
                3.4663278639892215e-07,
                1.1478765389222573e-05,
                NaN,
                NaN
            ],
            [
                8.939693107093343e-06,
                9.422445938861406e-07,
                2.2603245673155757e-06,
                4.222834954753043e-06,
                1.7603438428660665e-06,
                1.3709575337078829e-06,
                1.3709572068354007e-06,
                1.7603440526662173e-06,
                1.994729483705484e-06,
                3.288750241500471e-06
            ],
            [
                1.0677024881980089e-06,
                3.2887506335906595e-06,
                1.994730434879465e-06,
                1.5534981249574276e-06,
                3.288748673360027e-06,
                NaN,
                1.99472924590571e-06,
                2.902312677137316e-06,
                NaN,
                1.5534971990126997e-06
            ],
            [
                2.5612834320214477e-06,
                1.2098655392871682e-06,
                3.05902117523595e-07,
                3.288749457469787e-06,
                5.715003788993679e-07,
                9.422450431989127e-07,
                4.4508515805199415e-07,
                2.6995790618252024e-07,
                1.99472900813862e-06,
                4.450849458218309e-07
            ],
            [
                9.422443692555439e-07,
                1.7603434231833873e-06,
                2.2603242978871282e-06,
                6.475947210031623e-07,
                1.3709567165617364e-06,
                2.5612831267202583e-06,
                1.0677026154806063e-06,
                1.5534971990126997e-06,
                2.5612812947508257e-06,
                2.5612828213934817e-06
            ],
            [
                4.222834451382849e-06,
                6.962254589851619e-06,
                7.88926446679691e-06,
                6.144173869558639e-06,
                3.726639284144195e-06,
                2.561281600076256e-06,
                4.785096206047877e-06,
                1.760343003481596e-06,
                7.889261645355786e-06,
                NaN
            ],
            [
                3.466326211105621e-07,
                1.0677027427471959e-06,
                1.0677032518814388e-06,
                5.715003107755449e-07,
                1.0677028700422047e-06,
                NaN,
                1.7603434231833873e-06,
                4.222834954778007e-06,
                1.994730197090463e-06,
                8.315281267861397e-07
            ],
            [
                7.338212429582604e-07,
                1.3709567165617364e-06,
                2.3823685319244518e-07,
                5.71500719545698e-07,
                1.3709567165617364e-06,
                1.5534979397790343e-06,
                4.222832941193893e-06,
                2.6995771309523475e-07,
                3.4663249714451116e-07,
                6.962257079832313e-06
            ],
            [
                2.2603251062270446e-06,
                1.3709576971242028e-06,
                6.475947209918244e-07,
                6.144172404587612e-06,
                1.5534977545603963e-06,
                2.5612831267202583e-06,
                3.9278634073098236e-07,
                6.144176066850984e-06,
                2.2603237589779086e-06,
                1.3709575336947905e-06
            ],
            [
                8.939695238634211e-06,
                1.0129993394959082e-05,
                5.422220909009474e-06,
                2.9023133690980155e-06,
                6.144176799283803e-06,
                1.0129995810343862e-05,
                1.4738978458140753e-05,
                6.144172404587612e-06,
                3.7266388398585725e-06,
                3.2887506336086064e-06
            ],
            [
                1.8925150497848527e-05,
                3.726638839878908e-06,
                1.3709572068478697e-06,
                3.466327037548308e-07,
                6.144175334468545e-06,
                3.2887494574518405e-06,
                9.422443692555439e-07,
                1.760343003481596e-06,
                1.5534975693933505e-06,
                1.0677024881980089e-06
            ],
            [
                1.012999460278499e-05,
                1.3007125363057018e-05,
                5.422220908876325e-06,
                2.902312331125353e-06,
                3.7266401725935817e-06,
                1.0129987357287368e-05,
                1.3007125363719486e-05,
                1.3709568799760888e-06,
                2.902312331125353e-06,
                4.785095065132354e-06
            ],
            [
                6.475950298011458e-07,
                5.715007195431641e-07,
                2.5612831266946347e-06,
                4.785096776499213e-06,
                5.71500515159253e-07,
                1.3709578605729614e-06,
                8.315281267861397e-07,
                1.0677026154774503e-06,
                NaN,
                2.5612819054028872e-06
            ],
            [
                2.2603234895372223e-06,
                5.4222183235249605e-06,
                2.260323758987159e-06,
                3.7266410611296085e-06,
                7.889259764517575e-06,
                1.7603438428800754e-06,
                3.9278634073732336e-07,
                NaN,
                3.2887506336235617e-06,
                1.7603427936335396e-06
            ],
            [
                2.5612819054028872e-06,
                4.222834954778007e-06,
                2.260324567337161e-06,
                1.3709573702822306e-06,
                4.2228329411708495e-06,
                6.144173869603344e-06,
                1.6701429808632785e-05,
                1.7603440527286572e-06,
                4.450848927637999e-07,
                1.6701421845057263e-05
            ],
            [
                1.3709575337078829e-06,
                1.7603434231777837e-06,
                1.0677024881980089e-06,
                2.1444958640087166e-05,
                2.2603242978778778e-06,
                3.726638395634011e-06,
                6.1441746018123775e-06,
                7.889260704818233e-06,
                2.561282516042282e-06,
                1.4738983728784933e-05
            ],
            [
                NaN,
                6.962258739796719e-06,
                3.9278610661902853e-07,
                1.3709576971425944e-06,
                1.7603436330259153e-06,
                8.315284241650899e-07,
                4.450848927650143e-07,
                1.2098652508424818e-06,
                NaN,
                8.315278294114555e-07
            ],
            [
                1.3709567165579959e-06,
                1.994729959270648e-06,
                1.3709568799760888e-06,
                9.422443692446175e-07,
                5.422218969818919e-06,
                8.315281267834927e-07,
                3.288747889229516e-06,
                7.338212429420757e-07,
                2.2603234895053587e-06,
                3.288748673319648e-06
            ],
            [
                NaN,
                2.260324028427877e-06,
                1.1478769494083349e-05,
                5.422217030747413e-06,
                4.785095635624897e-06,
                4.222834954778007e-06,
                1.99472900813862e-06,
                6.962256249885085e-06,
                4.222834451382849e-06,
                1.3709572068522336e-06
            ],
            [
                1.0129988564974359e-05,
                6.962257909785973e-06,
                1.0129987357287368e-05,
                1.9947299593014888e-06,
                3.2887478892683997e-06,
                3.7266401726359486e-06,
                1.7603434231777837e-06,
                4.222835458117536e-06,
                NaN,
                1.7603440527286572e-06
            ],
            [
                1.994729008145876e-06,
                NaN,
                9.422447062294175e-07,
                2.1444948415296896e-05,
                1.3007130015488633e-05,
                1.7603440527222532e-06,
                1.30071315662049e-05,
                1.300712536350655e-05,
                1.8925150497435443e-05,
                9.422449308748773e-07
            ],
            [
                1.9947299593014888e-06,
                1.300712846477255e-05,
                9.422448185478557e-07,
                1.670141587208191e-05,
                1.4738981971813965e-05,
                6.144176066795103e-06,
                2.902312677137316e-06,
                3.288748673360027e-06,
                1.2098652508391807e-06,
                1.0677029973192638e-06
            ],
            [
                1.0677032518748838e-06,
                2.2603234895289998e-06,
                1.7603440527286572e-06,
                1.2098659719757836e-06,
                2.9023116391675407e-06,
                2.9023112931873767e-06,
                8.315277302819205e-07,
                1.1478769494396542e-05,
                2.561283432035425e-06,
                4.222833444590791e-06
            ],
            [
                4.222831934379152e-06,
                1.5534971990126997e-06,
                9.422448185478557e-07,
                3.288748673360027e-06,
                8.315284241650899e-07,
                1.012999218776902e-05,
                6.144177531767002e-06,
                1.1478766757561534e-05,
                4.222833444590791e-06,
                1.2098662604291696e-06
            ],
            [
                2.1024331597262577e-07,
                4.450848927650143e-07,
                3.4663253846718004e-07,
                2.3823699519290042e-07,
                1.3709572068522336e-06,
                4.450848927650143e-07,
                2.102434412875379e-07,
                NaN,
                3.927862002663297e-07,
                2.3823688159291947e-07
            ],
            [
                7.338208055680009e-07,
                3.0590237279032884e-07,
                4.450851049991497e-07,
                5.043476486915964e-07,
                2.9023109472494878e-06,
                1.8553914607267268e-07,
                2.1024336609843824e-07,
                6.475946438055299e-07,
                6.475949526020042e-07,
                1.209865827752005e-06
            ],
            [
                1.2098656835224664e-06,
                4.539789029616496e-05,
                2.90231094723893e-06,
                4.450850519403407e-07,
                1.0129989772532511e-05,
                7.338208055664991e-07,
                5.715005151606823e-07,
                7.88926446679691e-06,
                6.475947982037486e-07,
                NaN
            ],
            [
                4.222834954753043e-06,
                1.553497384196656e-06,
                7.338209805224048e-07,
                3.726637951367137e-06,
                4.222834954753043e-06,
                1.0677032518814388e-06,
                6.475947210031623e-07,
                2.9023112932045342e-06,
                2.2603251062270446e-06,
                1.3709567165579959e-06
            ],
            [
                3.059021175261338e-07,
                1.0677029973158649e-06,
                NaN,
                2.9023119851781017e-06,
                1.0677032518814388e-06,
                6.475949526020042e-07,
                3.927862002663297e-07,
                1.3709572068522336e-06,
                4.450850519403407e-07,
                7.338212429582604e-07
            ],
            [
                NaN,
                9.422442569290178e-07,
                2.9023133690821773e-06,
                3.05902263389638e-07,
                7.338213304316717e-07,
                9.422445939032799e-07,
                5.043474081957179e-07,
                2.2603242978778778e-06,
                6.475945666051092e-07,
                1.7603436330259153e-06
            ],
            [
                1.0129990980100021e-05,
                2.9023112932045342e-06,
                2.561282210729555e-06,
                2.9023112932045342e-06,
                1.8925155009354808e-05,
                6.144176799283803e-06,
                1.5534973841705173e-06,
                3.288748673319648e-06,
                5.422217677028889e-06,
                1.760344052714248e-06
            ],
            [
                1.3007123812980299e-05,
                1.1478765388711023e-05,
                3.535625914363812e-05,
                8.939693107093343e-06,
                1.0129995810463632e-05,
                4.222832437747125e-06,
                1.6701415872385704e-05,
                3.2887478892504536e-06,
                2.753569438157704e-05,
                1.670142980726572e-05
            ],
            [
                1.2098655392871682e-06,
                1.9947292459347367e-06,
                2.3823685319174098e-07,
                5.043474081993875e-07,
                4.222835458148261e-06,
                7.338212429537553e-07,
                1.7603430034743913e-06,
                1.855391239544352e-07,
                5.043472879525233e-07,
                NaN
            ],
            [
                5.422217030747413e-06,
                2.9023123311583482e-06,
                4.2228319344021954e-06,
                2.5612825160562587e-06,
                5.422217677078203e-06,
                4.78509278348926e-06,
                2.260324836776948e-06,
                1.0129995810463632e-05,
                1.3709576971425944e-06,
                5.422217030747413e-06
            ],
            [
                7.889265407004852e-06,
                3.7266406168624155e-06,
                1.5534981249496567e-06,
                1.147876949310201e-05,
                7.889259764273619e-06,
                1.0677024881829577e-06,
                9.422447062240614e-07,
                3.726641061109272e-06,
                2.902312677060767e-06,
                1.994729245878497e-06
            ],
            [
                1.0129995810343862e-05,
                6.962257079775324e-06,
                NaN,
                NaN,
                1.2098653950656417e-06,
                1.2098656835224664e-06,
                1.6701419854156377e-05,
                2.260325375664839e-06,
                3.7266397282926013e-06,
                NaN
            ],
            [
                1.994730434879465e-06,
                2.9023116391675407e-06,
                5.715003788993679e-07,
                7.338207180864763e-07,
                8.939695238439078e-06,
                8.315280276546789e-07,
                1.2098662604291696e-06,
                1.9947299593014888e-06,
                6.475948754012522e-07,
                1.5534984953298217e-06
            ],
            [
                2.699576809143613e-07,
                3.9278610661902853e-07,
                3.4663249714451116e-07,
                3.4663266243308805e-07,
                3.05902190458764e-07,
                2.699576809143613e-07,
                3.927860597945825e-07,
                3.927860597945825e-07,
                1.0129993395217047e-05,
                3.927860597945825e-07
            ],
            [
                3.05902263391829e-07,
                1.855391239544352e-07,
                3.466325797888292e-07,
                6.475947210046347e-07,
                2.382369383923073e-07,
                3.466327037548308e-07,
                NaN,
                1.6373768624837685e-07,
                2.699577774585891e-07,
                3.9278634073732336e-07
            ],
            [
                1.6701421845057263e-05,
                3.9278634073732336e-07,
                8.939696304311336e-06,
                1.994730672675753e-06,
                6.962259569630266e-06,
                3.927860597945825e-07,
                2.260325106237323e-06,
                1.9947297215043796e-06,
                2.699578096393206e-07,
                1.209865539295696e-06
            ],
            [
                8.315277302841894e-07,
                2.5612834320470717e-06,
                NaN,
                2.7535697667202906e-05,
                1.760343213335281e-06,
                NaN,
                1.2098659719757836e-06,
                2.260324567337161e-06,
                1.994729008145876e-06,
                1.4738985485997396e-05
            ],
            [
                6.144175334468545e-06,
                7.338208930443633e-07,
                7.338208930443633e-07,
                9.422445939054222e-07,
                5.04347468323289e-07,
                6.962254589914941e-06,
                8.315284241650899e-07,
                1.0677033791583005e-06,
                7.338213304343413e-07,
                1.9947299593014888e-06
            ],
            [
                NaN,
                5.829126554578343e-05,
                0.0005527786162137415,
                6.9622587396067566e-06,
                2.260324297853209e-06,
                0.00013982212420629982,
                4.0063696966212295e-05,
                8.93969736942758e-06,
                1.1478770862735993e-05,
                2.2603234895176927e-06
            ],
            [
                1.209866260432471e-06,
                1.7603438428800754e-06,
                1.994729008145876e-06,
                1.5534971990169383e-06,
                1.9947301970972664e-06,
                9.422448185534261e-07,
                1.7603440527286572e-06,
                1.1478766757718129e-05,
                2.260324567337161e-06,
                9.422450432014836e-07
            ],
            [
                3.9278610661902853e-07,
                7.338210680021253e-07,
                8.315283250394546e-07,
                6.475948754012522e-07,
                1.5534981249697903e-06,
                3.9278634073732336e-07,
                1.2098659719757836e-06,
                8.315284241650899e-07,
                2.3823690999290963e-07,
                5.715005832886879e-07
            ],
            [
                2.561283432035425e-06,
                3.2887478892683997e-06,
                1.5534971990169383e-06,
                2.5612828213352452e-06,
                3.7266401726359486e-06,
                4.7850967763512445e-06,
                1.370957860567974e-06,
                1.2098655392871682e-06,
                2.2603242978665707e-06,
                3.535624650021832e-05
            ],
            [
                1.209866260432471e-06,
                5.715002426486762e-07,
                7.338210680021253e-07,
                6.475950298011458e-07,
                3.9278610661902853e-07,
                1.0677033791612137e-06,
                6.144172404738491e-06,
                8.315284241650899e-07,
                9.422442569315887e-07,
                6.475950298011458e-07
            ],
            [
                5.4222209089700225e-06,
                9.422445939032799e-07,
                0.9999978766212859,
                1.7603440527222532e-06,
                4.785094494783494e-06,
                4.2228334445658276e-06,
                8.315284241597959e-07,
                1.5534975693933505e-06,
                1.9947299592933255e-06,
                3.288749457469787e-06
            ],
            [
                NaN,
                1.0677024881887838e-06,
                8.939698435560267e-06,
                1.7603432133136672e-06,
                NaN,
                4.785096206013061e-06,
                5.715003107755449e-07,
                NaN,
                NaN,
                8.481106160734935e-05
            ],
            [
                3.927860597945825e-07,
                3.466325384661554e-07,
                2.3823690999063455e-07,
                2.699577774585891e-07,
                2.6995771309523475e-07,
                2.260324028427877e-06,
                9.422444815765128e-07,
                8.315279285351409e-07,
                1.209866260432471e-06,
                8.315279285351409e-07
            ],
            [
                4.450852111148132e-07,
                1.209866260432471e-06,
                6.144172404693786e-06,
                2.6995774527718623e-07,
                NaN,
                6.475950298011458e-07,
                5.715003107767143e-07,
                1.994730672675753e-06,
                8.315277302841894e-07,
                1.0677024882009222e-06
            ],
            [
                1.3709570434178922e-06,
                1.0677028700363782e-06,
                1.3007134667070165e-05,
                1.2098662604247682e-06,
                1.3709572068422585e-06,
                1.994730197071414e-06,
                1.0677032518748838e-06,
                9.422444815765128e-07,
                6.144176066901277e-06,
                3.288748281295496e-06
            ],
            [
                8.315283250371857e-07,
                1.3709567165579959e-06,
                1.994730197090463e-06,
                8.315281267861397e-07,
                1.3709570434178922e-06,
                9.422448185510695e-07,
                7.338207180864763e-07,
                6.475947210012481e-07,
                3.927862939126708e-07,
                5.04347468323289e-07
            ],
            [
                1.0677032518748838e-06,
                9.422442569097361e-07,
                3.927862470861484e-07,
                5.715003107738556e-07,
                9.422442569208767e-07,
                5.043472879525233e-07,
                7.338212429537553e-07,
                1.3709570434178922e-06,
                1.0677026154730804e-06,
                1.9947306726594253e-06
            ],
            [
                3.535625914363812e-05,
                1.4738980215352592e-05,
                3.535625071473396e-05,
                2.9023133690637e-06,
                3.1201911375578156e-05,
                1.300713311614059e-05,
                3.1201907657271834e-05,
                2.4300234941261454e-05,
                1.473898197154587e-05,
                4.785096205930373e-06
            ],
            [
                1.3709570434178922e-06,
                4.785096206047877e-06,
                1.9947297215125433e-06,
                2.561283432005142e-06,
                1.3709567165579959e-06,
                1.9947297215125433e-06,
                3.288748673376478e-06,
                1.209865539295696e-06,
                4.2228339479858295e-06,
                1.5534983101602148e-06
            ],
            [
                1.012999460278499e-05,
                1.7603440527286572e-06,
                1.5534977545886537e-06,
                8.315280276546789e-07,
                8.315280276626197e-07,
                1.3709567165617364e-06,
                6.962256249821764e-06,
                3.2887502415767434e-06,
                NaN,
                4.785096776499213e-06
            ],
            [
                1.9947306726594253e-06,
                1.760344052714248e-06,
                3.288749457409966e-06,
                4.785095635624897e-06,
                1.5534973841895917e-06,
                3.12019150949065e-05,
                1.0129988564716393e-05,
                2.2603245673155757e-06,
                1.3709575337078829e-06,
                9.422443692446175e-07
            ],
            [
                0.00012339460442007728,
                9.422445939002803e-07,
                6.962259569630266e-06,
                7.338208055664991e-07,
                4.222834451382849e-06,
                2.2603234895289998e-06,
                4.2228339479858295e-06,
                4.222832941142044e-06,
                5.422219616184461e-06,
                1.2098655392871682e-06
            ],
            [
                4.4508515805735777e-07,
                7.88926446679691e-06,
                1.637376862489725e-07,
                4.4508494582405734e-07,
                5.043474081993875e-07,
                3.7266410611296085e-06,
                1.9947299593078385e-06,
                2.9023116392097746e-06,
                5.715006514176113e-07,
                1.0677028700422047e-06
            ],
            [
                5.422218323487975e-06,
                NaN,
                1.5534971990126997e-06,
                1.0129989772274546e-05,
                3.2887502415243994e-06,
                1.4738988999940381e-05,
                1.1478766757561534e-05,
                3.2887502415438413e-06,
                7.338209805224048e-07,
                4.222833947897496e-06
            ],
            [
                3.7266410611296085e-06,
                1.0677026154806063e-06,
                4.222832941193893e-06,
                2.5612828213934817e-06,
                1.7603434231833873e-06,
                0.9996646499094872,
                5.422219616265831e-06,
                1.3709573702822306e-06,
                3.466326211113502e-07,
                2.5612831267202583e-06
            ],
            [
                2.260325106237323e-06,
                2.2603242978871282e-06,
                4.2228339479858295e-06,
                3.05902190458764e-07,
                1.5534983101602148e-06,
                4.450850519403407e-07,
                1.5534971990126997e-06,
                1.3709575337125585e-06,
                1.2098658277451275e-06,
                1.209865539295696e-06
            ],
            [
                8.315282259138311e-07,
                9.422448185510695e-07,
                1.7603438428800754e-06,
                1.5534973842076057e-06,
                1.6701415872659116e-05,
                1.9947297215125433e-06,
                7.889265407327733e-06,
                1.3007128465151102e-05,
                7.338212429537553e-07,
                6.475947210046347e-07
            ],
            [
                3.9278634073732336e-07,
                9.422447062294175e-07,
                NaN,
                5.715003789046955e-07,
                5.043474683204221e-07,
                6.475948754012522e-07,
                5.04347468323289e-07,
                8.315281267882195e-07,
                1.1478772231086046e-05,
                4.222832437639588e-06
            ],
            [
                2.6995771309523475e-07,
                3.059022269250683e-07,
                1.2098659719788098e-06,
                2.699578096393206e-07,
                2.699576809143613e-07,
                7.338208055680009e-07,
                3.05902336324494e-07,
                6.475950298011458e-07,
                2.2603234895372223e-06,
                2.1024344128584085e-07
            ],
            [
                7.88926446679691e-06,
                1.3709575337078829e-06,
                4.785094494783494e-06,
                1.3709570434178922e-06,
                NaN,
                8.315277302841894e-07,
                7.889259764517575e-06,
                NaN,
                4.785094494783494e-06,
                2.561281600076256e-06
            ],
            [
                8.315277302841894e-07,
                1.7603438428740716e-06,
                9.422445939032799e-07,
                3.288750241500471e-06,
                3.288749457469787e-06,
                2.260325106237323e-06,
                2.561282516066741e-06,
                8.315279285351409e-07,
                2.260325106237323e-06,
                3.7266410611296085e-06
            ],
            [
                3.0590237278838124e-07,
                5.715003789017068e-07,
                NaN,
                3.0590215399183813e-07,
                3.059021904559123e-07,
                4.450848927637999e-07,
                5.04347348075149e-07,
                2.382369667929001e-07,
                7.338209805200689e-07,
                NaN
            ],
            [
                1.209866260432471e-06,
                5.043475885696228e-07,
                7.338208055680009e-07,
                4.450852641737424e-07,
                8.315280276626197e-07,
                5.043476486924565e-07,
                5.715003107767143e-07,
                3.466327037553825e-07,
                3.927863875616689e-07,
                2.1024334103581732e-07
            ],
            [
                7.889262585886274e-06,
                1.5534971990126997e-06,
                2.4300234941261454e-05,
                1.1478773599425825e-05,
                4.2228324377740105e-06,
                7.889266347715168e-06,
                1.9947304348862686e-06,
                6.9622537599680095e-06,
                1.3709575337078829e-06,
                2.90231233114251e-06
            ],
            [
                2.2603234895372223e-06,
                5.422221555380179e-06,
                3.7266410611296085e-06,
                1.3709570434178922e-06,
                2.260325106237323e-06,
                6.962255419931625e-06,
                0.9999945777803935,
                2.902312677137316e-06,
                1.2098659719757836e-06,
                1.3709576971425944e-06
            ],
            [
                8.939697369882888e-06,
                6.475948754012522e-07,
                9.422450431989127e-07,
                2.5612825160562587e-06,
                7.338208055664991e-07,
                9.422448185388577e-07,
                8.315283250371857e-07,
                9.422442569290178e-07,
                1.0677032518785256e-06,
                1.7603438428740716e-06
            ],
            [
                2.56128159999123e-06,
                5.715003107715166e-07,
                1.147877359872636e-05,
                4.222832941072913e-06,
                2.5612812946890944e-06,
                7.889263526266196e-06,
                1.473898197154587e-05,
                7.88926164518358e-06,
                2.260325375664839e-06,
                3.726641061085547e-06
            ],
            [
                4.785094494750855e-06,
                5.422221555414699e-06,
                1.5534977545886537e-06,
                2.2603242978871282e-06,
                NaN,
                8.315283250371857e-07,
                1.7603440527286572e-06,
                2.5612828213818346e-06,
                9.422443692555439e-07,
                1.7603425837855082e-06
            ],
            [
                7.338211554783522e-07,
                8.315283250371857e-07,
                7.338209805200689e-07,
                3.726638839878908e-06,
                5.422218969769604e-06,
                5.715005832886879e-07,
                1.0677027427471959e-06,
                8.315279285351409e-07,
                2.902311639183378e-06,
                2.260324836776948e-06
            ],
            [
                8.315281267861397e-07,
                1.2098659719757836e-06,
                2.5612819054028872e-06,
                1.5534971990126997e-06,
                3.2887482813149375e-06,
                6.144176066901277e-06,
                3.2887482813149375e-06,
                1.0677026154806063e-06,
                9.422450431989127e-07,
                1.3709572068522336e-06
            ],
            [
                6.9622579095833456e-06,
                1.0129989772412744e-05,
                1.9947304348703948e-06,
                6.1441731370702875e-06,
                6.144174601935314e-06,
                4.785096776394765e-06,
                3.2887482812506295e-06,
                1.1478772230929451e-05,
                2.902311985146426e-06,
                1.994729245917502e-06
            ],
            [
                0.9999810748517938,
                4.450849988811838e-07,
                3.4663266243308805e-07,
                0.9999877809211145,
                1.0677027427600627e-06,
                6.475948754012522e-07,
                4.450851580566494e-07,
                0.9999756997477903,
                4.2228319344021954e-06,
                1.209865539295696e-06
            ],
            [
                6.962255419931625e-06,
                3.288748673376478e-06,
                NaN,
                2.561281294760143e-06,
                NaN,
                8.939694172957213e-06,
                2.561282516066741e-06,
                1.067703124601679e-06,
                1.0677033791612137e-06,
                6.144177531811707e-06
            ],
            [
                2.2603234895289998e-06,
                2.4300232043987867e-05,
                4.785096776468749e-06,
                1.9947294837154625e-06,
                7.88926446679691e-06,
                9.422444815792981e-07,
                8.315279285351409e-07,
                8.315279285351409e-07,
                3.2887506336086064e-06,
                4.785092783519724e-06
            ],
            [
                2.10243290909724e-07,
                1.275190428875671e-07,
                8.764242227418718e-08,
                1.275190428875671e-07,
                6.023568448589658e-08,
                4.450851580555361e-07,
                2.3823693839325527e-07,
                1.1253509497883659e-07,
                8.315278294114555e-07,
                3.059021175261338e-07
            ],
            [
                4.5397884884891014e-05,
                3.288750241561788e-06,
                8.939694172867777e-06,
                4.785095635624897e-06,
                1.3709567165530083e-06,
                8.315281267861397e-07,
                NaN,
                7.889263526345123e-06,
                7.889262585814522e-06,
                5.715003107755449e-07
            ],
            [
                3.120191881207863e-05,
                1.2098662604247682e-06,
                2.9023119851635836e-06,
                1.553497384196656e-06,
                1.4738988999940381e-05,
                3.726639728348526e-06,
                1.1478768125911099e-05,
                3.288749849498565e-06,
                1.6701423835320418e-05,
                1.5534981249574276e-06
            ],
            [
                4.222834451327159e-06,
                1.0677028700320085e-06,
                2.2603234895053587e-06,
                3.7266406168403854e-06,
                1.7603436330179102e-06,
                2.2603234895053587e-06,
                2.902311639183378e-06,
                9.422448185435711e-07,
                2.902311639183378e-06,
                4.22283545808297e-06
            ],
            [
                3.059022998576899e-07,
                5.043476486902204e-07,
                2.2603242978871282e-06,
                3.927860597945825e-07,
                1.5534975693979422e-06,
                3.466326211113502e-07,
                3.059022998576899e-07,
                1.7603425837855082e-06,
                1.2098662604291696e-06,
                7.338209805224048e-07
            ],
            [
                5.715003788993679e-07,
                4.450850519403407e-07,
                2.2603242978665707e-06,
                2.2603242978778778e-06,
                1.553497754577351e-06,
                4.222831934352267e-06,
                1.9947299592933255e-06,
                5.715003107655392e-07,
                8.939696304116203e-06,
                4.222835458148261e-06
            ],
            [
                3.7266406168827523e-06,
                6.144176799283803e-06,
                3.7266406168827523e-06,
                3.7266410611296085e-06,
                1.1478772231086046e-05,
                6.605212894856585e-05,
                2.902313369111213e-06,
                1.4738976701411704e-05,
                5.829127250060064e-05,
                2.902310947208574e-06
            ],
            [
                1.3007134667070165e-05,
                NaN,
                3.535624650150453e-05,
                1.5534983101393749e-06,
                2.2603242978665707e-06,
                NaN,
                1.3709567165579959e-06,
                1.3709567165530083e-06,
                1.0677026154730804e-06,
                1.9947301970813926e-06
            ],
            [
                1.1478766757718129e-05,
                6.475945666051092e-07,
                2.1444943302181958e-05,
                2.1444948415296896e-05,
                1.0677032518814388e-06,
                2.2603248367949354e-06,
                0.9999952149060783,
                4.785093353940187e-06,
                1.9947304348862686e-06,
                8.939698435657833e-06
            ]
        ]
    },
    {
        "q_id": "10090_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            69,
            70,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            82,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            95,
            96,
            97,
            98,
            101,
            102,
            103,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                8.315284241665078e-07,
                8.315281267882195e-07,
                2.102434162245973e-07,
                3.9278610661902853e-07,
                2.1024339116168358e-07,
                1.0677029973219343e-06,
                1.6373766672994222e-07,
                2.6995790618469934e-07,
                2.1024339116168358e-07,
                1.4449798650551755e-07
            ],
            [
                3.9278615344178325e-07,
                6.475948754012522e-07,
                1.067702870039777e-06,
                5.715003107755449e-07,
                1.5534984953453635e-06,
                9.422447062270609e-07,
                7.338209805224048e-07,
                2.260324028427877e-06,
                1.3709567165579959e-06,
                1.067702870039777e-06
            ],
            [
                5.715005151606823e-07,
                9.422443692574719e-07,
                2.10243290909724e-07,
                1.3709575337159875e-06,
                3.9278629391427843e-07,
                3.927863875616689e-07,
                1.0677029973219343e-06,
                4.450851049991497e-07,
                3.927863407379485e-07,
                1.27519088491875e-07
            ],
            [
                8.764253720001207e-08,
                8.764244316973974e-08,
                1.4449800373118268e-07,
                7.338212429594283e-07,
                3.9278629391427843e-07,
                4.4508515805735777e-07,
                1.275190276859705e-07,
                2.699578740032504e-07,
                1.6373772528704005e-07,
                1.275190580890061e-07
            ],
            [
                9.931190958076104e-08,
                6.47595107001401e-07,
                5.043472278322555e-07,
                1.0677032518814388e-06,
                3.9278610661902853e-07,
                1.5534971990169383e-06,
                1.0677028700422047e-06,
                1.7603425837903113e-06,
                3.9278605979534166e-07,
                3.927862002663297e-07
            ],
            [
                NaN,
                5.71500719545698e-07,
                1.7603425837903113e-06,
                5.04347287955046e-07,
                6.962259569750576e-06,
                2.2603245673443566e-06,
                5.422221555414699e-06,
                5.71500719545698e-07,
                8.315277302857965e-07,
                8.939697370069891e-06
            ],
            [
                1.4449807263312446e-07,
                5.043476486924565e-07,
                2.1024336609874897e-07,
                5.715006514176113e-07,
                9.422444815814404e-07,
                1.760342793638743e-06,
                2.3823688159237777e-07,
                1.0677028700422047e-06,
                5.043472278322555e-07,
                NaN
            ],
            [
                2.3823690999063455e-07,
                6.1441767993788005e-06,
                5.422217030781934e-06,
                5.04347528446051e-07,
                5.04347348075149e-07,
                1.670142980893658e-05,
                6.475950298011458e-07,
                2.699577774560111e-07,
                3.466327450765785e-07,
                1.3007123813382511e-05
            ],
            [
                1.5534977545886537e-06,
                NaN,
                2.2603245673443566e-06,
                2.5612834320563895e-06,
                9.422445939054222e-07,
                NaN,
                3.2887494574832472e-06,
                1.5534977545886537e-06,
                5.715005832853093e-07,
                3.288749457469787e-06
            ],
            [
                5.043476486924565e-07,
                6.47595107001401e-07,
                1.3709575337159875e-06,
                1.637376862489725e-07,
                5.043475284468537e-07,
                1.6373774480605869e-07,
                2.1024334103581732e-07,
                3.05902336324494e-07,
                1.8553914607267268e-07,
                3.059022998581767e-07
            ],
            [
                2.1024341622368903e-07,
                2.1024331597152624e-07,
                3.9278634073732336e-07,
                3.4663249714325014e-07,
                2.102433911580983e-07,
                3.927861066170637e-07,
                3.05902226922147e-07,
                3.05902190458764e-07,
                3.927862470899887e-07,
                8.764254764749753e-08
            ],
            [
                3.288747889284851e-06,
                1.5534975693869924e-06,
                1.994730197090463e-06,
                1.0129988564974359e-05,
                2.902312677137316e-06,
                5.715002426475718e-07,
                2.90231094723893e-06,
                3.927860597945825e-07,
                3.2887498495150166e-06,
                1.0677027427600627e-06
            ],
            [
                1.1253518888531272e-07,
                1.0677029973219343e-06,
                5.043475885696228e-07,
                2.699577774589574e-07,
                3.466327450765785e-07,
                1.8553919030776337e-07,
                3.466325384678894e-07,
                1.4449796927932878e-07,
                2.3823685319244518e-07,
                3.0590237279085045e-07
            ],
            [
                9.422449308716635e-07,
                2.3823702359290413e-07,
                5.715003789046955e-07,
                7.338207180864763e-07,
                2.699577774585891e-07,
                3.0590237279085045e-07,
                3.9278634073732336e-07,
                5.043472879504592e-07,
                9.422447062270609e-07,
                1.209865827752005e-06
            ],
            [
                9.931200429212718e-08,
                1.275190124846946e-07,
                5.315786239218605e-08,
                1.4449795205472734e-07,
                0.9999885212318835,
                2.699577130960941e-07,
                8.7642558095602e-08,
                1.4449800373118268e-07,
                1.6373764721072816e-07,
                0.9999785550464982
            ],
            [
                3.059023727894942e-07,
                2.699577774560111e-07,
                2.699578740011634e-07,
                4.450849988758202e-07,
                7.338208055536515e-07,
                2.1024334103505245e-07,
                1.8553905759969634e-07,
                5.043474683204221e-07,
                3.466327037548308e-07,
                3.4663249714451116e-07
            ],
            [
                3.4663266242969896e-07,
                2.699579061798195e-07,
                3.059023727869902e-07,
                2.382369667892166e-07,
                2.6995774527577444e-07,
                5.043475885674441e-07,
                2.699577774560111e-07,
                3.927862002641863e-07,
                5.715005151574337e-07,
                1.6373766672888118e-07
            ],
            [
                5.715003107755449e-07,
                5.422221555380179e-06,
                1.760343633031919e-06,
                1.1478766757718129e-05,
                6.144172404693786e-06,
                2.5612812947508257e-06,
                4.785093924362895e-06,
                2.561282210740037e-06,
                9.422443692555439e-07,
                4.4508494582405734e-07
            ],
            [
                NaN,
                4.4508515805735777e-07,
                1.3709576971463352e-06,
                5.71500719545698e-07,
                6.962257079832313e-06,
                6.47595107001401e-07,
                7.338207180898968e-07,
                NaN,
                NaN,
                5.715005832895975e-07
            ],
            [
                4.450851049991497e-07,
                3.288749065423109e-06,
                9.422445939032799e-07,
                NaN,
                2.260323758987159e-06,
                3.927862470905692e-07,
                6.475950298021765e-07,
                1.2098653950716937e-06,
                NaN,
                1.5534971990126997e-06
            ],
            [
                1.9947304348862686e-06,
                3.2887506336086064e-06,
                2.902312677150514e-06,
                8.315280276580819e-07,
                2.902312677104321e-06,
                3.7266406168827523e-06,
                2.699577452746696e-07,
                5.422218323487975e-06,
                1.5534981249574276e-06,
                1.5534975693869924e-06
            ],
            [
                NaN,
                6.144176066943187e-06,
                3.927862470899887e-07,
                5.715003789046955e-07,
                6.475947982037486e-07,
                9.422448185534261e-07,
                1.3709573702822306e-06,
                1.147877359957198e-05,
                1.209865539295696e-06,
                1.0677027427600627e-06
            ],
            [
                3.4663249714612693e-07,
                1.0677032518748838e-06,
                5.715005832886879e-07,
                5.715003107767143e-07,
                1.5534973842076057e-06,
                3.288749849529972e-06,
                1.0677033791612137e-06,
                1.9947304348862686e-06,
                8.315279285351409e-07,
                7.338212429582604e-07
            ],
            [
                1.0677029973219343e-06,
                1.855391239547094e-07,
                1.444980209564556e-07,
                NaN,
                3.466326624336003e-07,
                3.4663274507713016e-07,
                6.475946438055299e-07,
                5.04347287955046e-07,
                1.4449803818215767e-07,
                6.475945666063607e-07
            ],
            [
                0.9999916019279765,
                0.9999982396559484,
                0.9999989969856733,
                3.288749457469787e-06,
                0.9999994631249962,
                0.9999869928669071,
                0.9999980052693281,
                0.9999952149072199,
                0.9999997300421903,
                0.9999955048189606
            ],
            [
                2.1444950971601277e-05,
                3.927863875616689e-07,
                5.043474683240344e-07,
                9.422448185534261e-07,
                3.466327037553825e-07,
                1.994729483729522e-06,
                1.3709575337159875e-06,
                2.2603234895372223e-06,
                8.315277302857965e-07,
                4.22283545819819e-06
            ],
            [
                1.8553919030858602e-07,
                5.043475885696228e-07,
                1.0677029973219343e-06,
                5.043472278322555e-07,
                5.043472278322555e-07,
                0.9999934595620003,
                0.9999957771665592,
                2.102434412875379e-07,
                6.475948754028718e-07,
                1.0677027427624903e-06
            ],
            [
                1.6373776432509826e-07,
                NaN,
                3.9278629391427843e-07,
                2.3823693839325527e-07,
                2.1024334103581732e-07,
                3.466326624336003e-07,
                4.450850519409479e-07,
                9.93120161310289e-08,
                NaN,
                7.338207180898968e-07
            ],
            [
                0.9999810748519224,
                0.9999957771645519,
                0.9998601779296259,
                0.9999930377446096,
                0.999959936322726,
                0.9999687980887872,
                0.9999892166839661,
                0.9999910603048007,
                0.9999852610216075,
                0.9998601779617774
            ],
            [
                2.5612819054133693e-06,
                5.043473480777865e-07,
                5.043475885696228e-07,
                1.9947301970972664e-06,
                2.699578740032504e-07,
                1.0677024882029858e-06,
                6.47595107001401e-07,
                6.1441767993788005e-06,
                1.5534975693979422e-06,
                2.382370235933104e-07
            ],
            [
                2.10243290909724e-07,
                5.715003789046955e-07,
                1.5534973842076057e-06,
                3.466327037539638e-07,
                5.715006514167015e-07,
                3.466327037548308e-07,
                1.2098653950692178e-06,
                3.0590226339061185e-07,
                3.466327450765785e-07,
                1.0677032518814388e-06
            ],
            [
                2.3823693839290317e-07,
                0.9999942280813648,
                0.9999993524052793,
                0.9999989322975122,
                0.9999993106388724,
                0.9999991684718734,
                1.5534983101644536e-06,
                5.043475885696228e-07,
                8.315284241650899e-07,
                4.450852641737424e-07
            ],
            [
                2.382368815932174e-07,
                NaN,
                3.9278629391427843e-07,
                7.338212429594283e-07,
                4.4508515805735777e-07,
                3.05902263391829e-07,
                3.466326624336003e-07,
                8.315277302857965e-07,
                NaN,
                5.715006514176113e-07
            ],
            [
                1.2751904288710323e-07,
                3.4663249714451116e-07,
                1.4449805540585765e-07,
                1.855391239544352e-07,
                1.760342793638743e-06,
                1.6373774480535133e-07,
                2.1024341622297196e-07,
                1.2751901248391176e-07,
                1.209866260432471e-06,
                5.315789407666425e-08
            ],
            [
                1.1253512180925583e-07,
                1.27519073289925e-07,
                2.102434412875379e-07,
                6.475947982037486e-07,
                6.475947210046347e-07,
                1.6373764721072816e-07,
                6.475949526020042e-07,
                8.315282259138311e-07,
                2.2603234895372223e-06,
                1.8553910183607374e-07
            ],
            [
                2.1024326584639497e-07,
                6.475945666063607e-07,
                2.3823690999290963e-07,
                3.927863875616689e-07,
                2.6995784182183607e-07,
                1.2098659719788098e-06,
                8.315279285370317e-07,
                9.422449308774482e-07,
                5.043473480777865e-07,
                1.855391239544352e-07
            ],
            [
                0.00010889693531733128,
                0.9999599363174791,
                2.1444953527944967e-05,
                0.9999964991460073,
                0.9999339478715132,
                3.4663249714451116e-07,
                0.9999756997680187,
                0.9998601779438178,
                5.829127945202588e-05,
                0.9999942280799784
            ],
            [
                7.484626290009348e-05,
                7.889262585441413e-06,
                4.785094494402695e-06,
                7.889260703906985e-06,
                3.535625913952226e-05,
                1.3007128463873485e-05,
                2.7535684529910724e-05,
                1.4738983727256784e-05,
                4.785093924103951e-06,
                1.6701417862648148e-05
            ],
            [
                8.7642558095602e-08,
                1.2751905808881762e-07,
                1.5534975693979422e-06,
                2.3823690999063455e-07,
                8.764247451307293e-08,
                9.422443692574719e-07,
                6.023568448589658e-08,
                3.05902263391829e-07,
                1.27519088491875e-07,
                1.8553916819032217e-07
            ],
            [
                9.422444815814404e-07,
                2.382368815932174e-07,
                1.855390576008354e-07,
                1.6373770576776313e-07,
                1.6373772528704005e-07,
                3.7266383956509585e-06,
                1.8553910183674878e-07,
                2.699577130960941e-07,
                8.764244316973974e-08,
                1.994729483729522e-06
            ],
            [
                0.9999822214524933,
                0.9999869928746676,
                0.9999898700102583,
                0.9999991684720718,
                0.9999599363127282,
                0.9999861539938203,
                0.9999955048168209,
                0.9999822214524642,
                2.561281600086738e-06,
                4.539785241676547e-05
            ],
            [
                1.9947304348862686e-06,
                6.475949526020042e-07,
                5.043473480777865e-07,
                2.382368531929327e-07,
                8.315283250371857e-07,
                NaN,
                1.2098661162056318e-06,
                1.3709573702822306e-06,
                6.475948753930064e-07,
                6.475951069961737e-07
            ],
            [
                4.450850519403407e-07,
                6.962256249885085e-06,
                1.5534983101644536e-06,
                1.7603430034867993e-06,
                8.315278294114555e-07,
                1.0129993395336818e-05,
                1.4738987243478167e-05,
                5.715007195447234e-07,
                2.102434412875379e-07,
                5.043473480777865e-07
            ],
            [
                1.9947299593078385e-06,
                9.422445939032799e-07,
                1.4738989000422955e-05,
                9.422448185478557e-07,
                NaN,
                5.715003789017068e-07,
                1.3709573702822306e-06,
                3.726638839878908e-06,
                8.939698435657833e-06,
                1.670141985446017e-05
            ],
            [
                8.315278294114555e-07,
                2.3823693839325527e-07,
                1.2098656835224664e-06,
                5.715005832886879e-07,
                2.5612825160271407e-06,
                2.6995790618252024e-07,
                8.315278293838516e-07,
                9.4224425692559e-07,
                2.2603234895053587e-06,
                1.553497384180408e-06
            ],
            [
                3.0590237279032884e-07,
                0.9999972735300571,
                0.01590638961253321,
                1.9947301970972664e-06,
                NaN,
                NaN,
                0.9999934595627853,
                3.4663278639892215e-07,
                0.9999885212291557,
                NaN
            ],
            [
                3.535625914093709e-05,
                1.0677024881980089e-06,
                4.006371128945452e-05,
                3.2887490653872164e-06,
                5.715004470313855e-07,
                5.715003788993679e-07,
                1.6701427817427163e-05,
                2.5612819054028872e-06,
                8.315283250371857e-07,
                1.012998977213635e-05
            ],
            [
                3.0590226339061185e-07,
                5.04347348070562e-07,
                3.466327037539638e-07,
                1.5534977545886537e-06,
                1.0677024882009222e-06,
                1.3709573702822306e-06,
                8.315278294072958e-07,
                5.04347528446051e-07,
                1.5534973842076057e-06,
                7.338210680021253e-07
            ],
            [
                1.7603427936335396e-06,
                4.785092783454444e-06,
                5.043476486915964e-07,
                1.5534981249697903e-06,
                1.0677029973192638e-06,
                8.315281267861397e-07,
                8.315283250371857e-07,
                3.05902226922147e-07,
                5.715003107755449e-07,
                1.3709575337078829e-06
            ],
            [
                2.10243290909724e-07,
                1.2098662604247682e-06,
                1.0677026154730804e-06,
                6.475949526020042e-07,
                8.315281267861397e-07,
                1.994730434879465e-06,
                4.785094494783494e-06,
                2.2603234895289998e-06,
                1.209865539295696e-06,
                3.288748281295496e-06
            ],
            [
                6.475948754012522e-07,
                1.209865539295696e-06,
                1.8553903548231313e-07,
                2.6995774527718623e-07,
                2.699576809143613e-07,
                1.5534975693869924e-06,
                4.2228319344021954e-06,
                3.2887498495150166e-06,
                2.6995790618350237e-07,
                8.939695238333382e-06
            ],
            [
                0.99999550481896,
                0.9999967112501527,
                0.9999983463102174,
                0.9999972735300566,
                0.9999945777823257,
                0.9999910603069053,
                NaN,
                0.9999724642958349,
                0.9999982396561579,
                0.999995504817356
            ],
            [
                0.9999952149043666,
                1.275189972832538e-07,
                3.059021175261338e-07,
                1.8553910183674878e-07,
                6.023577065381482e-08,
                9.931190958076104e-08,
                3.4663266243308805e-07,
                4.450848927658745e-07,
                1.2098653950692178e-06,
                4.4508510499849186e-07
            ],
            [
                7.338212429582604e-07,
                5.715003789046955e-07,
                3.927860597945825e-07,
                1.9947301970972664e-06,
                7.338211554783522e-07,
                2.69957906184239e-07,
                7.338209805224048e-07,
                3.927862470899887e-07,
                5.04347528446051e-07,
                8.315281267882195e-07
            ],
            [
                1.1478770862735993e-05,
                8.315278294072958e-07,
                0.9999984465016909,
                0.9999952149066528,
                7.338207180801359e-07,
                0.9998415637463127,
                0.9999646437367209,
                0.9997965730533289,
                0.9998204719495896,
                NaN
            ],
            [
                9.931189774187203e-08,
                3.466326624336003e-07,
                7.338208930460318e-07,
                2.1024336609874897e-07,
                5.043476486924565e-07,
                2.382369951932796e-07,
                1.4449802095666915e-07,
                1.4449800373118268e-07,
                3.059021175261338e-07,
                5.043475885696228e-07
            ],
            [
                2.5612819054133693e-06,
                4.450848927650143e-07,
                3.927862002663297e-07,
                2.10243290909724e-07,
                9.422444815814404e-07,
                5.715005151606823e-07,
                2.6995784182140636e-07,
                4.450850519403407e-07,
                2.3823690999290963e-07,
                3.9278610661902853e-07
            ],
            [
                3.466327863983311e-07,
                5.715004470313855e-07,
                1.0677032518785256e-06,
                3.059021175261338e-07,
                5.715004470313855e-07,
                1.3709567165530083e-06,
                2.699578096393206e-07,
                1.637377448057981e-07,
                4.4508494582405734e-07,
                6.475947982037486e-07
            ],
            [
                6.47595107001401e-07,
                1.1253520229983549e-07,
                NaN,
                NaN,
                5.043472278322555e-07,
                8.315282259089153e-07,
                2.1024326584505647e-07,
                1.209865827752005e-06,
                3.466327863961242e-07,
                1.209866260432471e-06
            ],
            [
                4.450850519403407e-07,
                6.144173137170873e-06,
                1.994729721518893e-06,
                1.8553903548231313e-07,
                7.338212429582604e-07,
                1.6373772528704005e-07,
                5.4222209089700225e-06,
                1.2751899728311609e-07,
                1.0677029973219343e-06,
                3.05902190458764e-07
            ],
            [
                3.927862002663297e-07,
                2.382369951932796e-07,
                5.715007195447234e-07,
                1.7603425837903113e-06,
                3.288747889284851e-06,
                6.962259569750576e-06,
                1.3709567165617364e-06,
                4.2228319344021954e-06,
                8.315283250371857e-07,
                8.315284241650899e-07
            ],
            [
                0.9999952149072218,
                0.9999945777790962,
                0.9999785550413904,
                3.059021175261338e-07,
                0.999968798088666,
                0.9999952149043676,
                NaN,
                0.9999982396574173,
                0.9999945777810352,
                0.9999877809196267
            ],
            [
                0.9999785550414021,
                0.0140636272111219,
                8.315283250394546e-07,
                3.059023727894942e-07,
                6.023568448565689e-08,
                0.9999687980775283,
                2.1024341622426268e-07,
                0.9999852610162897,
                1.8553919030776337e-07,
                0.9999994956525318
            ],
            [
                1.209865827752005e-06,
                1.4449796927932878e-07,
                2.699576809143613e-07,
                2.1024336609843824e-07,
                2.3823693839290317e-07,
                2.1024331597288867e-07,
                0.9999993916408183,
                3.466326211113502e-07,
                1.8553916819032217e-07,
                2.699578740032504e-07
            ],
            [
                1.0677029973219343e-06,
                6.475945666051092e-07,
                1.994729483705484e-06,
                1.5534971990169383e-06,
                5.422219616265831e-06,
                1.067703124601679e-06,
                3.059022998569248e-07,
                5.043474081993875e-07,
                1.0129994603006104e-05,
                2.902312331170226e-06
            ],
            [
                2.69957906184239e-07,
                8.315282259138311e-07,
                3.2887498495150166e-06,
                3.059021175261338e-07,
                8.315279285370317e-07,
                2.102434412875379e-07,
                5.043475885696228e-07,
                1.2098656835224664e-06,
                4.4508515805735777e-07,
                5.715002426486762e-07
            ],
            [
                8.939693107093343e-06,
                5.715003107715166e-07,
                7.338212429562581e-07,
                1.209865539295696e-06,
                8.315284241597959e-07,
                1.0677033791583005e-06,
                3.726641061058432e-06,
                4.222834954778007e-06,
                2.260324836787226e-06,
                1.3709572068522336e-06
            ],
            [
                2.1024336609843824e-07,
                3.4663278639892215e-07,
                3.927863875616689e-07,
                1.6373772528704005e-07,
                1.0677029973219343e-06,
                6.475951070002966e-07,
                6.475947982037486e-07,
                6.47595107001401e-07,
                8.315283250394546e-07,
                3.2887506336235617e-06
            ],
            [
                0.9999991148429643,
                0.9999987121050918,
                0.9999983463110059,
                0.9999984465016906,
                0.9999972735284307,
                NaN,
                0.9999930377454158,
                0.9999983463106117,
                0.9999978766220449,
                0.9999984465015053
            ],
            [
                1.370957860576702e-06,
                3.059021175261338e-07,
                7.338207180898968e-07,
                2.9023116392097746e-06,
                3.726639284144195e-06,
                NaN,
                1.5534983101644536e-06,
                1.892515501014656e-05,
                2.5612819054133693e-06,
                8.315277302857965e-07
            ],
            [
                1.0677029973158649e-06,
                9.422447062294175e-07,
                2.102433410343832e-07,
                3.466325797896173e-07,
                2.5612825160562587e-06,
                2.6995784182140636e-07,
                1.209866260432471e-06,
                1.4738980215352592e-05,
                9.422448185510695e-07,
                1.0129995810463632e-05
            ],
            [
                0.9999964991439194,
                1.067703124601679e-06,
                1.4738978458382043e-05,
                0.9999988634366973,
                0.9999623635621966,
                0.9999957771670707,
                0.9999251537644848,
                0.9999975938965162,
                0.9999934595604456,
                2.3823690999236795e-07
            ],
            [
                7.33821330437595e-07,
                7.889263526409699e-06,
                7.33821330437595e-07,
                6.144177531811707e-06,
                3.2887494574832472e-06,
                2.699578096403948e-07,
                NaN,
                NaN,
                5.715006514176113e-07,
                NaN
            ],
            [
                1.2098653950656417e-06,
                1.892515049819277e-05,
                5.715003789017068e-07,
                0.9998766054557134,
                1.0677033791612137e-06,
                3.466327037548308e-07,
                1.3007130015677909e-05,
                1.0677026154806063e-06,
                7.88926446679691e-06,
                0.9991959141697353
            ],
            [
                0.9999990577550697,
                0.9999957771660574,
                0.9999949062950025,
                0.9999987121050923,
                0.9999930377445897,
                0.9999832985742607,
                0.9999995262093858,
                0.9999983463106125,
                0.9999969105051867,
                3.927862002663297e-07
            ],
            [
                3.9278624708775595e-07,
                5.715003789033962e-07,
                3.466325797896173e-07,
                8.315278294072958e-07,
                7.338213304363436e-07,
                3.466325797888292e-07,
                4.450848927650143e-07,
                3.0590226339061185e-07,
                3.927862939126708e-07,
                3.927860597935108e-07
            ],
            [
                8.315281267834927e-07,
                0.9999955048162846,
                0.999569442968865,
                0.9999832985761962,
                0.9998415637657939,
                0.9999687980961138,
                0.9997388097247923,
                0.9999910603047703,
                0.9991959141658069,
                0.9994472212646724
            ],
            [
                5.043472879540142e-07,
                5.043475885696228e-07,
                1.5534973842076057e-06,
                3.9278629391427843e-07,
                5.715006514176113e-07,
                9.422448185435711e-07,
                8.315284241665078e-07,
                2.2603253756956754e-06,
                8.315277302857965e-07,
                1.0677032518785256e-06
            ],
            [
                1.275190732904469e-07,
                2.90231094723893e-06,
                5.043472879540142e-07,
                1.0677024882029858e-06,
                1.5534975693979422e-06,
                5.4222183235249605e-06,
                5.04347528446051e-07,
                8.315277302857965e-07,
                1.637376862489725e-07,
                NaN
            ],
            [
                NaN,
                5.71500719545698e-07,
                7.734424996987981e-08,
                8.315279285370317e-07,
                1.275190124846946e-07,
                2.3823699519290042e-07,
                1.8553919030858602e-07,
                3.466326624336003e-07,
                9.931185038635267e-08,
                2.382370235933104e-07
            ],
            [
                0.9999985406241281,
                5.043474683204221e-07,
                5.422221555414699e-06,
                4.7850933539684755e-06,
                0.9999972735303813,
                3.059022998581767e-07,
                0.9999989322973851,
                2.10243290909724e-07,
                3.4663278639892215e-07,
                3.927862002663297e-07
            ],
            [
                3.466326624336003e-07,
                6.475950298021765e-07,
                NaN,
                5.043474683240344e-07,
                7.338211554813555e-07,
                5.715004470334646e-07,
                5.715004470334646e-07,
                2.3823690999323465e-07,
                1.0129988565084915e-05,
                2.3823693839325527e-07
            ],
            [
                3.927863407379485e-07,
                7.338212429594283e-07,
                3.05902263391829e-07,
                1.5534984953552536e-06,
                5.715003107767143e-07,
                4.222832437798974e-06,
                1.6373764721072816e-07,
                7.338207180898968e-07,
                6.475950298011458e-07,
                3.2887502415767434e-06
            ],
            [
                1.0,
                1.2098656835252174e-06,
                4.450851049991497e-07,
                5.715005832895975e-07,
                7.33821330437595e-07,
                5.043476486924565e-07,
                1.209865827752005e-06,
                3.466326624336003e-07,
                NaN,
                5.715006514176113e-07
            ],
            [
                6.475946438055299e-07,
                3.466327037553825e-07,
                2.260323758987159e-06,
                NaN,
                1.0677033791612137e-06,
                4.450848927658745e-07,
                3.927863875616689e-07,
                1.5534975693979422e-06,
                1.067703124601679e-06,
                3.927863875616689e-07
            ],
            [
                1.2751901248454963e-07,
                3.4663278639892215e-07,
                3.72663883989755e-06,
                6.962257909842961e-06,
                6.475945666063607e-07,
                7.338207180898968e-07,
                4.4508494582405734e-07,
                2.9023109472494878e-06,
                5.043476486924565e-07,
                5.043476486915964e-07
            ],
            [
                4.450852111155216e-07,
                1.3709575337159875e-06,
                1.855391681906175e-07,
                5.715003107738556e-07,
                7.338212429594283e-07,
                2.699578740032504e-07,
                1.9947299593078385e-06,
                2.260324028443809e-06,
                1.5534975693979422e-06,
                1.9947299593078385e-06
            ],
            [
                1.275190276859705e-07,
                1.8553914607267268e-07,
                3.4663278639892215e-07,
                3.05902190458764e-07,
                1.8553905760062447e-07,
                1.1253518888531272e-07,
                1.2098659719788098e-06,
                2.699577774585891e-07,
                1.8553905760024476e-07,
                2.3823696679327928e-07
            ],
            [
                1.4449807263312446e-07,
                1.6373774480605869e-07,
                9.931193325797878e-08,
                1.0677028700422047e-06,
                2.699576809143613e-07,
                3.05902190458764e-07,
                2.102434412875379e-07,
                3.059022998581767e-07,
                1.3709568799919866e-06,
                1.637376862489725e-07
            ],
            [
                2.1024326584639497e-07,
                7.338207180864763e-07,
                7.338213304363436e-07,
                1.2098662604291696e-06,
                1.7603434231833873e-06,
                7.338208055664991e-07,
                5.043475885674441e-07,
                2.1024326584639497e-07,
                1.0677032518814388e-06,
                1.2098661162056318e-06
            ],
            [
                NaN,
                0.9999339478246086,
                0.9999892166826745,
                0.9999417087138649,
                3.0590237279032884e-07,
                3.535625914492432e-05,
                2.3823693839290317e-07,
                0.9998601779272639,
                0.9980732650496721,
                0.9999599363175459
            ],
            [
                2.9023123311583482e-06,
                8.315279285351409e-07,
                3.466326211113502e-07,
                5.043476486915964e-07,
                6.475949526020042e-07,
                2.6995784182140636e-07,
                2.699577774585891e-07,
                9.422443692555439e-07,
                6.475945666063607e-07,
                3.927862470899887e-07
            ],
            [
                3.05902263391829e-07,
                1.2098659719788098e-06,
                2.2603253756956754e-06,
                1.5534975693979422e-06,
                2.561281294760143e-06,
                3.059022998581767e-07,
                NaN,
                6.962253760024999e-06,
                1.1253509497883659e-07,
                2.1024334103581732e-07
            ],
            [
                8.939699501416646e-06,
                0.9999151889799723,
                3.726639284144195e-06,
                1.5534981249697903e-06,
                1.7603440527286572e-06,
                0.9999964991439205,
                1.3007133116732079e-05,
                0.9999955048195005,
                0.9999964991439205,
                7.88926446679691e-06
            ],
            [
                1.3709573702856596e-06,
                3.9278610661902853e-07,
                3.288749849529972e-06,
                3.059021175261338e-07,
                1.760342793638743e-06,
                1.5534973842076057e-06,
                2.1024339116168358e-07,
                8.315279285370317e-07,
                1.8553914607267268e-07,
                2.3823690999290963e-07
            ],
            [
                0.999989870011456,
                0.9999955048200341,
                5.422218323487975e-06,
                4.539787947147079e-05,
                0.9995694428211521,
                6.144172404693786e-06,
                3.4663274507713016e-07,
                6.144172404693786e-06,
                3.1201907657271834e-05,
                1.3007126914435202e-05
            ],
            [
                0.9999599362936495,
                1.3709576971463352e-06,
                2.260323758987159e-06,
                0.999979854309256,
                0.9999706884510978,
                0.9997694932892076,
                1.0677029973219343e-06,
                1.8925157265710765e-05,
                0.9999877809240091,
                0.9999724642960395
            ],
            [
                1.0677028700422047e-06,
                2.699576809143613e-07,
                NaN,
                7.338209805240734e-07,
                NaN,
                3.9278620026686556e-07,
                5.715003107767143e-07,
                4.785096206076165e-06,
                1.994729721518893e-06,
                1.994729483729522e-06
            ],
            [
                9.422447062294175e-07,
                1.99472900813862e-06,
                3.9278615344178325e-07,
                4.450848927650143e-07,
                7.338207180898968e-07,
                3.9278605979534166e-07,
                2.1024341622426268e-07,
                2.2603242978871282e-06,
                8.315279285370317e-07,
                1.370957860576702e-06
            ],
            [
                0.9999974387168765,
                6.962257079889302e-06,
                2.4300232045225487e-05,
                0.9999981261241716,
                5.422219616265831e-06,
                2.2603245673443566e-06,
                6.475949526003845e-07,
                0.9999985406234319,
                1.5534977545886537e-06,
                2.902312677150514e-06
            ],
            [
                4.222831934352267e-06,
                9.422450432014836e-07,
                3.288748673360027e-06,
                7.338209805224048e-07,
                9.422448185478557e-07,
                1.7603434231777837e-06,
                2.260324028427877e-06,
                9.422443692555439e-07,
                3.288749457469787e-06,
                8.315280276580819e-07
            ],
            [
                2.382368531929327e-07,
                1.8553914607267268e-07,
                3.059022269250683e-07,
                5.04347287955046e-07,
                3.927863875616689e-07,
                4.450849988811838e-07,
                3.9278610661902853e-07,
                2.3823688159291947e-07,
                3.0590237279032884e-07,
                1.6373764721072816e-07
            ],
            [
                7.338213304363436e-07,
                2.561283126728994e-06,
                3.726639284125553e-06,
                9.422447062294175e-07,
                1.0677032518785256e-06,
                NaN,
                5.043472879540142e-07,
                NaN,
                9.422445939032799e-07,
                2.260324836776948e-06
            ],
            [
                5.715005832886879e-07,
                3.0590226339061185e-07,
                2.6995784182140636e-07,
                3.927862002663297e-07,
                5.043473480777865e-07,
                3.466326211113502e-07,
                5.043472278322555e-07,
                1.2098656835224664e-06,
                3.05902190458764e-07,
                1.5534975693979422e-06
            ],
            [
                5.715002426486762e-07,
                1.760342793638743e-06,
                8.315281267861397e-07,
                0.9999974387174855,
                2.6995790618469934e-07,
                2.4300243631890864e-05,
                1.0677032518814388e-06,
                0.99999879013374,
                0.9999151889289281,
                3.059022998576899e-07
            ],
            [
                5.715006514176113e-07,
                0.9999955048173548,
                0.999997097688709,
                0.9999987901346054,
                0.9999975938976615,
                0.9999980052702797,
                0.999996273360718,
                0.9999988634358834,
                1.4738981972564636e-05,
                0.9999991684717744
            ],
            [
                3.0590237279085045e-07,
                NaN,
                3.05902263391829e-07,
                5.715006514176113e-07,
                3.4663274507713016e-07,
                3.927863407379485e-07,
                8.315281267834927e-07,
                1.4449798650569826e-07,
                2.3823690999323465e-07,
                3.466327037553825e-07
            ],
            [
                5.04347468323289e-07,
                2.561281294760143e-06,
                1.9947292459406333e-06,
                7.338211554813555e-07,
                1.9947292459347367e-06,
                9.931200429212718e-08,
                3.726639284144195e-06,
                1.4449802095666915e-07,
                1.8553910183674878e-07,
                1.8553910183674878e-07
            ],
            [
                5.043476486924565e-07,
                3.4663262111182307e-07,
                7.338213304363436e-07,
                3.466325797888292e-07,
                1.637376862489725e-07,
                8.31528325040778e-07,
                7.338207180898968e-07,
                1.7603430034867993e-06,
                2.1024339116168358e-07,
                2.3823690999323465e-07
            ],
            [
                5.4222183235249605e-06,
                8.939695238634211e-06,
                1.3007130015677909e-05,
                4.785096206076165e-06,
                NaN,
                2.561281905390075e-06,
                1.5534983101602148e-06,
                6.144177531811707e-06,
                6.962259569750576e-06,
                7.338211554783522e-07
            ],
            [
                1.5534983101602148e-06,
                1.1478764020883773e-05,
                1.2098662604247682e-06,
                2.144495608378187e-05,
                8.939698435560267e-06,
                1.1478772231086046e-05,
                1.6701421845361053e-05,
                1.760343213322473e-06,
                3.466327863983311e-07,
                4.0063677865600476e-05
            ]
        ]
    },
    {
        "q_id": "9422_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            15,
            26,
            89,
            92,
            108
        ],
        "rewards": [
            [
                0.9999988634358832,
                0.9999981261246169,
                0.9999989969854339,
                1.3709575337125585e-06,
                0.9999995818811275,
                0.9999988634364252,
                2.3823688159291947e-07,
                4.2228319344021954e-06,
                2.3823690999290963e-07,
                0.9999916019309786
            ],
            [
                6.023576347299818e-08,
                6.023573475041126e-08,
                9.931189774187203e-08,
                1.444980726324838e-07,
                2.3823690999290963e-07,
                9.422443692489024e-07,
                2.6995771309523475e-07,
                1.2751910369275402e-07,
                5.829127250399344e-05,
                1.1253526937656726e-07
            ],
            [
                3.059022269250683e-07,
                2.1024341622426268e-07,
                1.2751907329024393e-07,
                2.1024341622426268e-07,
                1.1253517547010071e-07,
                3.466327037553825e-07,
                9.931189774187203e-08,
                6.023571320847322e-08,
                1.1253509497883659e-07,
                5.3157830707696514e-08
            ],
            [
                6.825604537781398e-08,
                0.9999869928653483,
                9.931187406368048e-08,
                1.6373766672888118e-07,
                1.2751905808881762e-07,
                1.1253525596055243e-07,
                1.2751904288710323e-07,
                6.825608606100697e-08,
                9.931195693628605e-08,
                9.931188590255539e-08
            ],
            [
                4.6911638017556955e-08,
                0.9999910603026371,
                0.9999957771670611,
                1.3709575337159875e-06,
                8.764252675194995e-08,
                8.315278294114555e-07,
                8.764253719973308e-08,
                0.9999974387168751,
                0.9999977396754338,
                1.8553914607267268e-07
            ],
            [
                1.3709570434054234e-06,
                5.715006513952608e-07,
                3.0590215399183813e-07,
                1.7603427935678977e-06,
                5.715005151606823e-07,
                5.04347287945184e-07,
                8.315278294001114e-07,
                1.855391239544352e-07,
                8.315279285370317e-07,
                1.9947306726594253e-06
            ],
            [
                0.9999988634361542,
                0.9999977396757024,
                0.9999962733598294,
                0.9999995262094421,
                0.9999988634364252,
                2.9023123311055552e-06,
                0.9999962733616065,
                0.9999987901343169,
                0.9999977396748946,
                0.999998346309626
            ],
            [
                4.222834451382849e-06,
                1.1253506814842375e-07,
                2.102433410343832e-07,
                1.6701421845361053e-05,
                1.275190276859705e-07,
                0.9999985406239534,
                1.4449803818215767e-07,
                1.1253512180925583e-07,
                0.9999957771675645,
                1.855391681906175e-07
            ],
            [
                0.9995121427709511,
                0.999998346310612,
                0.9999981261246175,
                0.9999983463110064,
                NaN,
                0.9999832985702084,
                0.9999925887219007,
                5.043476486902204e-07,
                0.9999852610162969,
                0.9999892166865054
            ],
            [
                2.102433159721477e-07,
                4.691164920214251e-08,
                0.9999910603058315,
                9.931195693628605e-08,
                1.4449802095609418e-07,
                0.9999930377429269,
                4.6911638017556955e-08,
                1.275190580884987e-07,
                1.855391239539711e-07,
                0.9999972735290809
            ],
            [
                7.734421308914719e-08,
                4.450852111135988e-07,
                1.275190276859705e-07,
                1.067702870039777e-06,
                2.1024341622426268e-07,
                5.3157830707696514e-08,
                0.9999832985821582,
                3.927863875616689e-07,
                2.6995774527657245e-07,
                9.931198061405701e-08
            ],
            [
                1.6373776432509826e-07,
                0.9999910603015729,
                1.27519088491875e-07,
                1.1253513522447425e-07,
                2.1024339116168358e-07,
                8.315281267882195e-07,
                1.1253506814842375e-07,
                1.444980209564556e-07,
                2.382368247924618e-07,
                1.1253520230052635e-07
            ],
            [
                8.764244316973974e-08,
                2.3823685319244518e-07,
                0.9999998461826405,
                0.9999997761971315,
                9.931196877517082e-08,
                0.9999969105044494,
                0.9999251537907063,
                0.9999938558261341,
                0.999998932297003,
                6.825600469412533e-08
            ],
            [
                6.825597214718257e-08,
                4.139939521459479e-08,
                9.931190958076104e-08,
                9.931198061405701e-08,
                1.6373764721072816e-07,
                8.764247451307293e-08,
                9.93120161310289e-08,
                7.734414854823498e-08,
                1.855391460719133e-07,
                9.93118503859575e-08
            ],
            [
                0.9999925887201329,
                0.9999970976866321,
                0.9999987121041705,
                0.9999957771675642,
                0.9999982396561578,
                9.422447062240614e-07,
                5.043475284447896e-07,
                0.99999834631002,
                0.9999938558261331,
                0.9999930377429253
            ],
            [
                0.9999910603047665,
                0.999997438717179,
                6.825600469412533e-08,
                7.734421308914719e-08,
                2.845333032070409e-08,
                1.2751905808881762e-07,
                0.9999997617631184,
                1.1253513522447425e-07,
                0.9999724643089218,
                1.6373768624874915e-07
            ],
            [
                7.889259764445822e-06,
                6.825598842065202e-08,
                7.734423152941018e-08,
                1.2751899728286965e-07,
                1.855391239544352e-07,
                0.9999810748540244,
                1.2751905808881762e-07,
                9.931200429181105e-08,
                4.139934092760465e-08,
                7.734422230927814e-08
            ],
            [
                3.9278638756099906e-07,
                5.3157837044597743e-08,
                1.3709576971242028e-06,
                1.0677032518578904e-06,
                8.764241182641775e-08,
                1.5534973841309562e-06,
                7.734416698815724e-08,
                5.715002426343175e-07,
                0.999996033012669,
                8.764240137829087e-08
            ],
            [
                0.9999964991451695,
                1.8553905759969634e-07,
                0.9999910602994387,
                6.825602910433871e-08,
                1.4449798650551755e-07,
                5.04347468323289e-07,
                6.825606165129312e-08,
                0.9999967112497598,
                4.1399375473868e-08,
                2.5109981946866052e-08
            ],
            [
                2.1024331597262577e-07,
                6.825602910433871e-08,
                1.444980726324838e-07,
                2.5110005893648856e-08,
                8.764249540862797e-08,
                5.315787506598473e-08,
                2.5110008886993497e-08,
                5.315784971839039e-08,
                1.3709568799919866e-06,
                5.043475885657239e-07
            ],
            [
                0.9999910603015725,
                0.9999991684719725,
                0.9999991684718734,
                0.9999983463106116,
                0.9999785550567114,
                0.9999982396563677,
                0.9999987121044777,
                0.9999975938979481,
                0.9999945777823263,
                0.9999987121050917
            ],
            [
                0.9999978766212856,
                0.9999972735297313,
                0.9999996072136126,
                0.9999984465028016,
                0.9999869928761992,
                0.9999992188519489,
                1.7603438428848787e-06,
                0.9999934595651171,
                0.9999955048168168,
                3.9278605979534166e-07
            ],
            [
                0.9999938558224701,
                0.9999996940977731,
                1.6373764721072816e-07,
                1.8553919030776337e-07,
                0.9999995262093292,
                3.0590215399183813e-07,
                9.931187406410953e-08,
                2.6995774527718623e-07,
                0.9999989322971302,
                0.9999998461826956
            ],
            [
                2.1024326584639497e-07,
                1.6701415872385704e-05,
                9.931193325852072e-08,
                1.4449798650417048e-07,
                7.734421308914719e-08,
                9.931187406410953e-08,
                1.8553905760062447e-07,
                1.27519088491875e-07,
                3.05902263389638e-07,
                2.382369951932796e-07
            ],
            [
                0.9999962733589413,
                0.9999997126314125,
                1.2098659719757836e-06,
                0.9999991148430699,
                1.4449800373118268e-07,
                0.9999999317439384,
                1.9947292459347367e-06,
                1.8553919030858602e-07,
                0.9999832985741958,
                0.999985261012769
            ],
            [
                0.9999969105044487,
                6.144176066943187e-06,
                0.9999981261237243,
                0.9999877809239939,
                3.9278624708775595e-07,
                1.4449805540740185e-07,
                2.1024341622426268e-07,
                0.9999984465026164,
                0.999997593898522,
                1.8553905760062447e-07
            ],
            [
                1.4449805540763184e-07,
                2.102434162245973e-07,
                0.9999646437535755,
                0.9999978766210325,
                1.1253513522447425e-07,
                2.1024334103581732e-07,
                2.699576809143613e-07,
                2.1024336609843824e-07,
                7.73441946488886e-08,
                0.9999998144608319
            ],
            [
                0.9999930377412624,
                0.9999991148433864,
                0.9999969105062911,
                0.9999967112493687,
                0.9999997463981938,
                0.9999998362623332,
                0.9999898700054055,
                0.9999994631249323,
                0.9999978766212854,
                0.9999992661786699
            ],
            [
                9.931195693628605e-08,
                2.382368247924618e-07,
                3.927861534406222e-07,
                3.466326211105621e-07,
                3.0590222692437275e-07,
                1.6373772528677946e-07,
                1.994730672668496e-06,
                8.315282259089153e-07,
                3.466327863983311e-07,
                2.3823688159237777e-07
            ],
            [
                6.475947981975644e-07,
                1.0677032518501217e-06,
                1.1478765389368729e-05,
                2.1024334103581732e-07,
                1.1253520229983549e-07,
                5.043474081957179e-07,
                0.999992588719252,
                3.9278610661902853e-07,
                8.764242227418718e-08,
                2.6995784182073116e-07
            ],
            [
                0.9999982396559486,
                0.9999892166916606,
                0.9999724643024226,
                0.9999985406239539,
                0.9999991684715762,
                0.9999822214502979,
                0.999999391641036,
                0.9999925887174858,
                0.9999977396748954,
                0.9999646437409779
            ],
            [
                5.315789407666425e-08,
                2.1024336609638268e-07,
                5.043475284430694e-07,
                1.8553919030708836e-07,
                2.1024339116082313e-07,
                0.999999428499485,
                0.9999970976887087,
                1.8553910183548312e-07,
                8.764243272157922e-08,
                7.73442776300517e-08
            ],
            [
                4.691168275606451e-08,
                0.9999995818812769,
                NaN,
                0.9999970976890543,
                3.059021175255426e-07,
                1.855391239544352e-07,
                4.1399375473868e-08,
                2.75356812556058e-05,
                4.450852111155216e-07,
                1.855391681906175e-07
            ],
            [
                0.9999970976873246,
                2.3823682479181176e-07,
                2.6995771309523475e-07,
                5.715006514167015e-07,
                6.825608606148807e-08,
                1.1253508156363576e-07,
                1.1253506814797596e-07,
                0.9999996072136594,
                1.637377448057981e-07,
                2.1024334103352274e-07
            ],
            [
                0.9999938558232094,
                0.9999986290429574,
                0.9999967112513288,
                0.999997097689055,
                0.9999986290429578,
                0.9999980052705174,
                0.99999879013374,
                0.9999997300422869,
                0.9999957771650486,
                0.9999991148432813
            ],
            [
                0.9999970976883623,
                0.9999978766207798,
                0.9999978766207801,
                1.6373770576776313e-07,
                2.699576809143613e-07,
                NaN,
                1.4449803818215767e-07,
                0.9999984465020613,
                1.5534981249397663e-06,
                0.9999832985801769
            ],
            [
                0.999999495652532,
                0.9999974387165697,
                0.9999992661791949,
                0.9999986290426305,
                0.99999886343629,
                0.9999957771655512,
                0.9999994284996214,
                0.9999970976887085,
                0.9999978766212856,
                0.999998126124841
            ],
            [
                0.9999984465015049,
                0.999997593897662,
                0.9999991684720716,
                0.999998932297003,
                1.1253510839355284e-07,
                0.9999993916411085,
                0.9999987121044777,
                1.275190428875671e-07,
                0.9999967112513277,
                0.9999999317440279
            ],
            [
                0.9999921107392997,
                8.764254764749753e-08,
                1.1253506814842375e-07,
                0.999981074858559,
                0.9999339478793599,
                0.999989870010236,
                1.3709576971463352e-06,
                2.3823682478975334e-07,
                9.931192141912081e-08,
                1.1478773599425825e-05
            ],
            [
                2.3823688159291947e-07,
                0.9999974387187067,
                8.764247451307293e-08,
                8.764247451307293e-08,
                1.6373766672973748e-07,
                1.6373766672973748e-07,
                3.288747889284851e-06,
                1.8553910183607374e-07,
                7.73441946488886e-08,
                9.931189774187203e-08
            ],
            [
                2.5612831265630198e-06,
                0.9999988634358831,
                6.825605351413404e-08,
                1.9947290081177566e-06,
                3.653482080235082e-08,
                1.7603427935967163e-06,
                0.9999997897567091,
                0.9999998024945624,
                0.9999995818810776,
                1.8553905760024476e-07
            ],
            [
                0.9999756997621798,
                0.9999982396565775,
                6.825606978801862e-08,
                1.3709570434122812e-06,
                1.855391681906175e-07,
                1.6373776432481905e-07,
                9.931193325852072e-08,
                1.1253508156363576e-07,
                1.855391239544352e-07,
                0.9999994284993488
            ],
            [
                0.9999992661792823,
                0.9999938558275993,
                0.9999955048189598,
                0.9999978766220446,
                3.2887494574832472e-06,
                0.9999810748450022,
                0.9999978766205259,
                1.6373766672973748e-07,
                0.9999930377462447,
                0.9999987121049384
            ],
            [
                2.1024341622426268e-07,
                0.9999993106387082,
                2.102433159721477e-07,
                0.9999969105055543,
                8.315280276607289e-07,
                3.059021539909339e-07,
                0.9999724643023616,
                3.927862470899887e-07,
                0.9998766054693945,
                0.999999391641036
            ],
            [
                8.764254764780641e-08,
                3.4663266242969896e-07,
                1.1253508156363576e-07,
                3.4663266242969896e-07,
                1.444980209564556e-07,
                1.8553919030826963e-07,
                4.691160446380562e-08,
                6.825604537781398e-08,
                3.059021175261338e-07,
                1.994729721482609e-06
            ],
            [
                3.059023363231725e-07,
                0.999994906296823,
                2.1024326584639497e-07,
                6.825601283086733e-08,
                1.637377057673536e-07,
                4.1399375473868e-08,
                1.1253506814797596e-07,
                5.043475284468537e-07,
                0.9999989322970031,
                1.2751910369275402e-07
            ],
            [
                0.9999938558224708,
                0.9999993916406733,
                1.9555694692738946e-08,
                1.1253512180925583e-07,
                0.9999991684718733,
                4.139941495546278e-08,
                0.9999852610197986,
                0.9999987901347493,
                5.715007195447234e-07,
                0.9999930377412619
            ],
            [
                0.9999988634366963,
                0.9999987901343169,
                0.9999999358794173,
                0.9999994956523516,
                0.9999994956525919,
                2.561283431942246e-06,
                0.9999998802069159,
                8.315283250371857e-07,
                0.9999997463980125,
                0.9999992188512972
            ],
            [
                8.764252675194995e-08,
                2.6995768091383957e-07,
                0.9999981261250638,
                9.931196877517082e-08,
                9.93118503859575e-08,
                1.1253520229983549e-07,
                4.139939027941221e-08,
                0.9999983463098229,
                0.9999952149055069,
                2.1024326584639497e-07
            ],
            [
                0.9999832985781775,
                0.9999964991455872,
                9.931194509740267e-08,
                0.9999987121050917,
                0.9999942280772215,
                6.962258739796719e-06,
                1.2098653950656417e-06,
                8.764252675194995e-08,
                8.764249540862797e-08,
                2.1444953527476883e-05
            ],
            [
                7.33821330437595e-07,
                1.5534981249736758e-06,
                2.561281600086738e-06,
                1.5534984953552536e-06,
                3.2887502415767434e-06,
                8.939700567094277e-06,
                1.275191036933194e-07,
                9.422442569334097e-07,
                1.9947304348862686e-06,
                8.481101104983024e-05
            ],
            [
                1.7603438428660665e-06,
                5.3157887739943563e-08,
                2.1024339116168358e-07,
                1.6373764721072816e-07,
                5.71500651413193e-07,
                0.9999974387187064,
                9.422445939002803e-07,
                0.9999989322966213,
                2.102434162245973e-07,
                NaN
            ],
            [
                0.9999974387177907,
                0.9999974387177906,
                1.275190732904469e-07,
                1.5534981249697903e-06,
                2.699576809143613e-07,
                0.9999984465015053,
                1.4449805540740185e-07,
                2.102434412875379e-07,
                8.764241182641775e-08,
                3.9278605979534166e-07
            ],
            [
                0.9999991148428587,
                0.9999991684720716,
                0.9999970976880161,
                3.4663253846718004e-07,
                0.9999997126315153,
                6.475947982022763e-07,
                0.9999990577557434,
                0.9999985406241274,
                1.2751901248454963e-07,
                0.9999960330155062
            ],
            [
                0.999996910505922,
                0.9999810748495466,
                0.9999869928746445,
                6.825601283086733e-08,
                4.450852111155216e-07,
                1.3007126914612648e-05,
                4.450852111155216e-07,
                1.0677033791291683e-06,
                0.9999485577620861,
                1.0677031245623505e-06
            ],
            [
                5.315784971839039e-08,
                4.691162124067829e-08,
                0.9999980052705171,
                8.764241182605906e-08,
                0.9999885212332532,
                0.999999953088362,
                0.9999998942829603,
                8.764247451307293e-08,
                0.99999862904263,
                6.023577065363335e-08
            ],
            [
                0.9999038976195779,
                0.9999989969855534,
                6.1441746020359e-06,
                0.9999991684720717,
                0.9999964991443352,
                0.9999852610162767,
                0.9999646437451205,
                0.9999960330155064,
                0.9999938558268658,
                0.9999938558232031
            ],
            [
                9.931189774140912e-08,
                8.764247451307293e-08,
                7.338208055664991e-07,
                9.931188590255539e-08,
                0.9999916019239712,
                9.422443692555439e-07,
                4.450852641717689e-07,
                7.3382080556433e-07,
                4.4508510499849186e-07,
                4.450852641717689e-07
            ],
            [
                0.9999983463108089,
                5.3157837044597743e-08,
                3.535625071344775e-05,
                1.8553914607267268e-07,
                0.9995694430166496,
                0.9999785550541535,
                0.9999885212359824,
                3.120191881525687e-05,
                0.9999832985781617,
                1.2098661161861e-06
            ],
            [
                8.764241182641775e-08,
                1.6373774480605869e-07,
                0.9999962733607176,
                1.637377643243723e-07,
                0.9999952149043669,
                2.1024344128584085e-07,
                4.450851580555361e-07,
                2.1024334103581732e-07,
                1.1253512180925583e-07,
                1.8553919030858602e-07
            ],
            [
                1.4449807263287805e-07,
                0.9999869928746475,
                0.9999995549151074,
                4.691168275606451e-08,
                4.139940508508409e-08,
                7.734421308914719e-08,
                4.691168275606451e-08,
                9.931185038635267e-08,
                1.6373764721072816e-07,
                3.653485564473625e-08
            ],
            [
                3.059021175261338e-07,
                0.9999982396572075,
                0.9999981261237239,
                0.9999952149032277,
                0.9999957771680698,
                0.999979854302014,
                1.2098658277489788e-06,
                0.9999945777823274,
                0.9999962733616082,
                0.9999955048194963
            ],
            [
                1.855390576008354e-07,
                1.2751905808881762e-07,
                1.2751910369310194e-07,
                2.561282516066741e-06,
                0.9999810748563055,
                4.4508515805735777e-07,
                0.999994228081351,
                6.475947981975644e-07,
                7.734425918979532e-08,
                3.0590222692437275e-07
            ],
            [
                1.1478766757718129e-05,
                2.1024341622426268e-07,
                3.4663262110945863e-07,
                1.6373770576776313e-07,
                1.2098661162056318e-06,
                2.699576809143613e-07,
                1.0677032518785256e-06,
                NaN,
                1.1478770862882149e-05,
                6.475947210031623e-07
            ],
            [
                0.999999428499485,
                0.9999785550439309,
                7.889261645427538e-06,
                0.9999980052700417,
                9.931187406368048e-08,
                0.9999987121043241,
                0.99999862904214,
                2.1024331597262577e-07,
                0.9999989322972577,
                0.999998446502246
            ],
            [
                3.653481209178873e-08,
                1.9555664386890228e-08,
                0.9999993106387902,
                2.5109975960189263e-08,
                1.3709575337078829e-06,
                1.760344052693435e-06,
                1.2751908849167202e-07,
                1.4449795205429202e-07,
                0.9999983463100204,
                1.9947290080125335e-06
            ],
            [
                6.825609419823202e-08,
                2.6995768091310296e-07,
                0.999996499144335,
                6.825604537741048e-08,
                5.315787506598473e-08,
                1.2751907329024393e-07,
                8.764243272157922e-08,
                1.275190124842887e-07,
                1.4449802095609418e-07,
                7.734414854792722e-08
            ],
            [
                1.4449807263312446e-07,
                1.5534971990169383e-06,
                3.466325797900508e-07,
                0.9999987121041708,
                2.1024326584639497e-07,
                8.764242227418718e-08,
                9.931186222523604e-08,
                7.338208930460318e-07,
                4.4508494582405734e-07,
                7.73441946488886e-08
            ],
            [
                1.9947292459406333e-06,
                6.825598028364134e-08,
                1.7603438428848787e-06,
                6.47594952603035e-07,
                1.8553914607237736e-07,
                3.9278634073625165e-07,
                1.1253508156363576e-07,
                9.422443692574719e-07,
                5.04347287955046e-07,
                3.9278634073732336e-07
            ],
            [
                0.999999391641181,
                3.0590237279085045e-07,
                5.043474683220276e-07,
                0.9999987901341727,
                1.4449805540740185e-07,
                0.9999990577549572,
                0.9999988634362896,
                0.9999984465022461,
                7.338210680021253e-07,
                0.9999972735307059
            ],
            [
                5.043472879525233e-07,
                1.4449798650476187e-07,
                2.382369383923073e-07,
                1.6373774480479287e-07,
                6.144176066901277e-06,
                2.699578740011634e-07,
                3.466326624336003e-07,
                3.05902226923399e-07,
                9.931196877456114e-08,
                1.8553907971855875e-07
            ],
            [
                2.3823682479181176e-07,
                5.3157811697009444e-08,
                6.475948754012522e-07,
                6.825604537781398e-08,
                3.46632497145457e-07,
                4.785093353626844e-06,
                3.9278605979534166e-07,
                1.1253517547010071e-07,
                6.825606978801862e-08,
                2.10243290909724e-07
            ],
            [
                7.734425918979532e-08,
                2.382370235922541e-07,
                NaN,
                7.338207180898968e-07,
                3.466327450756327e-07,
                2.382369667929001e-07,
                0.9999978766210325,
                1.4449798650476187e-07,
                1.1253520230052635e-07,
                1.6373774480535133e-07
            ],
            [
                3.059022998576899e-07,
                2.3823696679230424e-07,
                6.475949526003845e-07,
                2.3823690999160957e-07,
                0.00010889689638175376,
                3.05902336324494e-07,
                0.9999938558275974,
                1.8553907971758842e-07,
                9.931202796957073e-08,
                4.6911660386730734e-08
            ],
            [
                1.370957370247318e-06,
                0.9999993524052022,
                0.9999991148433864,
                0.9999997126314469,
                8.764252675194995e-08,
                0.9999991148431754,
                0.9999999006880075,
                0.9999989322970033,
                0.999999554914789,
                0.9999970976890556
            ],
            [
                0.9999957771665592,
                0.9999989322975122,
                0.9999994284997575,
                0.9999998942830863,
                0.9999989322971304,
                1.444980209564556e-07,
                0.9999987901347498,
                1.637377057680051e-07,
                0.9999992661791947,
                0.999999057754957
            ],
            [
                0.9999978766212856,
                NaN,
                0.9999977396746259,
                0.999998126123947,
                0.9999994284996894,
                3.224185480240153e-08,
                9.931186222523604e-08,
                1.27519088491875e-07,
                6.023572038912295e-08,
                0.9999994631249961
            ],
            [
                2.699578740032504e-07,
                8.315280276626197e-07,
                1.0677033791612137e-06,
                3.059021175247079e-07,
                1.444980381819277e-07,
                8.764245361752286e-08,
                5.043472278322555e-07,
                2.699578740032504e-07,
                6.023578501513224e-08,
                2.699578740032504e-07
            ],
            [
                0.9999999226557316,
                5.04347287955046e-07,
                5.315781803390236e-08,
                0.9999921107383615,
                0.999993037746246,
                0.9999934595627804,
                0.9999989969854338,
                0.9999998642567351,
                1.275190124842887e-07,
                0.9999993524053563
            ],
            [
                NaN,
                9.931193325852072e-08,
                9.931202796957073e-08,
                0.9999957771670607,
                0.9999810748585536,
                3.4663266243111764e-07,
                9.422450431912e-07,
                0.9999996940978096,
                1.0677028700363782e-06,
                3.46632497145457e-07
            ],
            [
                0.9999987121049384,
                1.0677029973056687e-06,
                0.9999942280820379,
                0.9999962733593852,
                1.2098662603961589e-06,
                0.9999982396574172,
                0.999995214905509,
                0.9999967112493677,
                0.9999994284995531,
                1.553497384180408e-06
            ],
            [
                0.9999942280772224,
                0.9999987901343169,
                0.9999952149060775,
                0.9999957771655527,
                0.9999982396572067,
                0.9999996533673376,
                1.4449807263325588e-07,
                0.9999952149055068,
                0.9999916019279789,
                0.9999974387171799
            ],
            [
                2.561282210740037e-06,
                1.370957860576702e-06,
                1.2098656835252174e-06,
                0.9999952149043657,
                1.3709576971463352e-06,
                1.7603434231833873e-06,
                0.9999756997534945,
                6.475950298021765e-07,
                2.3823696679327928e-07,
                2.3823682479181176e-07
            ],
            [
                4.1399365603508136e-08,
                1.275191036933194e-07,
                0.9999991148432809,
                9.931200429181105e-08,
                0.9999989969862708,
                1.1253520230052635e-07,
                2.1024329090867228e-07,
                0.9999994631248682,
                0.9999989969859121,
                6.962256249885085e-06
            ],
            [
                0.9999975938985225,
                1.8553905760062447e-07,
                0.9999988634361544,
                0.9999964991468413,
                1.8553903548231313e-07,
                0.9999756997506362,
                3.927862470899887e-07,
                0.9999987901347497,
                4.222831934379152e-06,
                1.0677027427624903e-06
            ],
            [
                0.9999990577557435,
                0.9999949062943931,
                0.9999885212318844,
                0.9999987121052453,
                0.9999339478320198,
                0.9999417087554472,
                0.9999970976873247,
                0.9999687980961285,
                0.9999993524051247,
                0.9999930377429272
            ],
            [
                3.05902117523595e-07,
                0.9999960330126695,
                2.6995768091310296e-07,
                3.9278634073625165e-07,
                5.043473480777865e-07,
                2.6995787400208416e-07,
                1.8553919030776337e-07,
                2.6995768091310296e-07,
                2.3823699519290042e-07,
                5.04347408197782e-07
            ],
            [
                1.9947304348862686e-06,
                0.9999989322973847,
                1.6373776432481905e-07,
                1.637376276909393e-07,
                7.73441946488886e-08,
                1.4449798650551755e-07,
                9.93118503859575e-08,
                6.023572038912295e-08,
                6.825606978801862e-08,
                5.3157900413566986e-08
            ],
            [
                1.4449795205429202e-07,
                1.1253513522447425e-07,
                2.3823693839325527e-07,
                0.9999869928761997,
                5.715005151574337e-07,
                5.715005832886879e-07,
                1.6373766672973748e-07,
                2.3823699519290042e-07,
                1.4449795205429202e-07,
                3.9278605979208185e-07
            ],
            [
                0.9999999067050276,
                0.9999981261237239,
                0.9999962733607194,
                0.9999969105066585,
                0.9999998144608319,
                0.999941708755583,
                6.023572038882162e-08,
                0.9999967112493686,
                0.9999964991443355,
                0.9999955048184241
            ],
            [
                1.1253514863909295e-07,
                1.637376862478556e-07,
                5.3157837044597743e-08,
                7.734416698815724e-08,
                2.3823690999160957e-07,
                7.734428685019034e-08,
                1.637376862478556e-07,
                6.825598842035714e-08,
                1.8553910183548312e-07,
                1.4449795205429202e-07
            ],
            [
                0.9999945777823268,
                1.6373770576776313e-07,
                4.691162683297406e-08,
                6.825598028392069e-08,
                6.825600469412533e-08,
                7.73442776303243e-08,
                0.9999975938973746,
                8.764244316973974e-08,
                0.9999982396561575,
                9.931194509740267e-08
            ],
            [
                4.691161005609407e-08,
                NaN,
                1.2751910369310194e-07,
                3.059023363231725e-07,
                5.315789407666425e-08,
                1.3709572068522336e-06,
                1.2751907328949007e-07,
                2.382370235933104e-07,
                2.3823690999323465e-07,
                2.1024334103581732e-07
            ],
            [
                0.9999251537372257,
                5.043473480730849e-07,
                4.785093353874907e-06,
                1.4449795205429202e-07,
                1.637377448057981e-07,
                5.04347348075149e-07,
                2.3823702359290413e-07,
                1.0677026154619133e-06,
                8.481102118700006e-05,
                2.1024336609843824e-07
            ],
            [
                4.785095065093186e-06,
                1.6373766672973748e-07,
                2.2603242978213447e-06,
                2.2603248367358324e-06,
                1.0677028700203557e-06,
                1.0677033791495609e-06,
                1.1253509497883659e-07,
                1.7603425837606927e-06,
                8.315282259117513e-07,
                7.889265406294507e-06
            ],
            [
                2.3823699519143784e-07,
                0.9994472212615209,
                3.9278634073732336e-07,
                8.315282259009745e-07,
                5.715007195447234e-07,
                6.475947210012481e-07,
                1.8553905759969634e-07,
                4.2228319344021954e-06,
                1.637377057680051e-07,
                3.059021904571643e-07
            ],
            [
                2.10243290909724e-07,
                2.6995784182183607e-07,
                2.6995790618469934e-07,
                6.825609419848033e-08,
                2.382369951932796e-07,
                3.653485128944664e-08,
                1.275189972832538e-07,
                0.9999991148428589,
                1.0677033791612137e-06,
                1.9947301970972664e-06
            ],
            [
                0.9999993106392012,
                0.9999997617630333,
                0.9999997617630049,
                0.9999952149037956,
                0.9999980052707553,
                0.9999998724809875,
                0.9999995818811275,
                0.999999825702059,
                0.9999995549151074,
                0.9999998461826956
            ],
            [
                0.9999977396757032,
                0.9999991684719727,
                0.9999998144608319,
                0.9999955048194951,
                0.9999995818813269,
                0.9999996072138936,
                8.315284241597959e-07,
                0.9999984465024313,
                0.9999997761970782,
                0.9999992188517628
            ],
            [
                3.2887498493983645e-06,
                6.023571320847322e-08,
                0.9999985406237797,
                1.2751908849167202e-07,
                0.999996499144753,
                0.9999810748585601,
                4.4508505193932864e-07,
                0.9999987121047849,
                3.726641061058432e-06,
                1.553497384180408e-06
            ],
            [
                1.855391460719133e-07,
                1.4449798650476187e-07,
                5.715003107755449e-07,
                8.764248496084983e-08,
                1.1253506814797596e-07,
                3.0590215399183813e-07,
                6.023577065363335e-08,
                1.6373776432481905e-07,
                3.4663266243111764e-07,
                9.931189774187203e-08
            ],
            [
                3.466326624336003e-07,
                0.9999993916408183,
                6.475950298021765e-07,
                9.422450432030903e-07,
                0.9999987901340283,
                1.855391460719133e-07,
                0.9999151889790118,
                0.9999975938985217,
                4.450850519409479e-07,
                0.9940889320221037
            ],
            [
                1.637377057673536e-07,
                6.023576347299818e-08,
                2.6995774527718623e-07,
                1.1253509497883659e-07,
                8.764253719973308e-08,
                0.9999957771655538,
                2.1024326584639497e-07,
                6.02357921955714e-08,
                1.4449802095609418e-07,
                9.931193325852072e-08
            ],
            [
                1.855391239544352e-07,
                0.9999885212318825,
                2.1024341622368903e-07,
                1.6373770576776313e-07,
                3.2887506336235617e-06,
                1.444979692800516e-07,
                0.9999964991451702,
                0.9999988634360186,
                1.2098661162056318e-06,
                1.994729483729522e-06
            ],
            [
                0.9999999273417837,
                0.9999975938982347,
                0.9999972735284304,
                1.4449807263287805e-07,
                2.3823696679230424e-07,
                4.1399365603508136e-08,
                0.9999756997534958,
                3.927862470899887e-07,
                3.466325384678894e-07,
                0.9999967112521124
            ],
            [
                1.6373774480535133e-07,
                1.2098659719524008e-06,
                1.4449805540651476e-07,
                3.059021904571643e-07,
                1.7603430034439723e-06,
                1.6373764720990908e-07,
                1.6701427815999337e-05,
                2.3823690998803445e-07,
                1.275190276853036e-07,
                3.0590237278838124e-07
            ],
            [
                0.999996711250152,
                1.892515049819277e-05,
                1.6373774480535133e-07,
                8.315281267882195e-07,
                3.059022998569248e-07,
                2.3823685319244518e-07,
                2.9023112932296107e-06,
                1.3709576971463352e-06,
                1.7603436330259153e-06,
                8.315277302857965e-07
            ],
            [
                1.4449802095609418e-07,
                5.315780536011123e-08,
                0.9999756997621798,
                9.931189774187203e-08,
                0.999998996985912,
                1.8925148241872038e-05,
                2.4300243631890864e-05,
                0.9999994284995531,
                0.9999997761970248,
                3.4663266243308805e-07
            ],
            [
                3.0590233632400716e-07,
                6.475945666009864e-07,
                0.999998446502246,
                4.450851049959619e-07,
                1.3709576971425944e-06,
                7.338209805200689e-07,
                9.422450431912e-07,
                2.102433159721477e-07,
                9.931187406410953e-08,
                7.338211554725124e-07
            ],
            [
                1.9947304348862686e-06,
                7.338207180898968e-07,
                1.0677032518814388e-06,
                4.450848927658745e-07,
                4.450852111155216e-07,
                3.927862002663297e-07,
                1.637377448057981e-07,
                1.2751899728311609e-07,
                4.450848927658745e-07,
                4.450850519403407e-07
            ],
            [
                0.9999969105048172,
                4.6911677163762064e-08,
                7.73442776303243e-08,
                0.9999987901344612,
                5.715005832895975e-07,
                0.9999949062962162,
                0.9999925887183725,
                2.3823699519290042e-07,
                3.653479902594117e-08,
                2.382368247924618e-07
            ],
            [
                2.1024336609843824e-07,
                1.855391239547094e-07,
                3.059022998569248e-07,
                2.1024344128660572e-07,
                1.275190124842887e-07,
                3.466326211105621e-07,
                1.4449807263312446e-07,
                1.2751908849167202e-07,
                1.2751904288739315e-07,
                1.4449805540763184e-07
            ],
            [
                1.2098652508056196e-06,
                1.4449802095609418e-07,
                2.1024331597262577e-07,
                1.4449807263287805e-07,
                3.9278610661822475e-07,
                1.855391681906175e-07,
                7.734423152941018e-08,
                7.73442776300517e-08,
                1.0677026154551157e-06,
                8.76424013786396e-08
            ],
            [
                0.999796573027139,
                2.6995774527657245e-07,
                1.9947301969217434e-06,
                9.422443692390473e-07,
                3.059022998576899e-07,
                1.8553916819032217e-07,
                2.5612831267202583e-06,
                7.338210679755959e-07,
                1.2098655392811161e-06,
                1.6701421845057263e-05
            ],
            [
                6.825601283086733e-08,
                2.260323758882316e-06,
                6.47594566597747e-07,
                9.931185038635267e-08,
                1.4449800373098553e-07,
                7.73441946488886e-08,
                1.2751904288739315e-07,
                4.691165479443628e-08,
                1.1253517547010071e-07,
                3.466327037548308e-07
            ],
            [
                5.043473480777865e-07,
                0.9999991148433864,
                1.6373766672973748e-07,
                4.450849988811838e-07,
                2.102433410343832e-07,
                1.8553916819032217e-07,
                0.9999942280799751,
                2.1024341622426268e-07,
                0.999999218851949,
                3.059022269250683e-07
            ],
            [
                1.1253521571574156e-07,
                9.422447061953531e-07,
                6.825602910433871e-08,
                1.9947294835866542e-06,
                6.475948753991907e-07,
                3.653479902594117e-08,
                8.764245361752286e-08,
                9.931186222523604e-08,
                7.73442776303243e-08,
                8.764247451307293e-08
            ],
            [
                9.931189774187203e-08,
                6.023573475041126e-08,
                7.73441946488886e-08,
                8.764254764780641e-08,
                2.699577774585891e-07,
                1.2751901248454963e-07,
                6.825598842065202e-08,
                7.734415776836702e-08,
                2.382368247924618e-07,
                5.3157843381493685e-08
            ],
            [
                6.023573475041126e-08,
                1.4449805540740185e-07,
                9.931193325852072e-08,
                1.8553905760024476e-07,
                2.1024339116082313e-07,
                2.382369667929001e-07,
                1.8553907971813685e-07,
                3.0590222692437275e-07,
                4.6911660386730734e-08,
                9.931192141964017e-08
            ],
            [
                1.3709573702722555e-06,
                0.9999986290427936,
                0.9999938558232049,
                0.9999945777816815,
                1.3709575337016483e-06,
                0.9999977396765113,
                0.9999975938965147,
                1.7603440526806268e-06,
                0.9999988634357478,
                1.553498495338299e-06
            ],
            [
                0.9999991684721707,
                0.9999785550464871,
                0.9999998024945624,
                0.9999970976866321,
                0.9999930377445846,
                0.99999976176309,
                0.9999988634365607,
                9.931190958076104e-08,
                3.466326211105621e-07,
                0.9999995549150543
            ],
            [
                0.9999832985742033,
                0.9999949062949997,
                0.9999994631249323,
                3.726638395611981e-06,
                0.9999994956523515,
                0.9999991684716752,
                0.9999985406230836,
                0.9999992188514834,
                0.999998346310612,
                3.288750241561788e-06
            ],
            [
                9.931195693628605e-08,
                3.4663274507713016e-07,
                0.9999974387174858,
                1.637377643243723e-07,
                8.764247451307293e-08,
                1.7603430034867993e-06,
                9.422448185510695e-07,
                5.043476486924565e-07,
                1.4449805540740185e-07,
                3.927860597945825e-07
            ],
            [
                6.82560779249779e-08,
                1.8553907971879076e-07,
                0.999995504820031,
                0.9999251537642548,
                1.7603440527334603e-06,
                0.9999962733620515,
                0.9999985406241276,
                1.8553905760062447e-07,
                0.9999980052700417,
                0.9999989969861512
            ],
            [
                7.734419464850171e-08,
                0.9999974387174853,
                3.059021175247079e-07,
                0.9999967112505436,
                5.04347348075149e-07,
                7.338207180884785e-07,
                0.9999910603058351,
                6.144172404693786e-06,
                0.9999992661789322,
                1.8553907971682908e-07
            ],
            [
                0.9999983463104147,
                0.9999756997621958,
                4.785093924389007e-06,
                3.059021175261338e-07,
                0.9999988634365606,
                0.9999938558254025,
                0.999981074849529,
                0.9999967112497606,
                0.9999955048200319,
                0.9999960330121953
            ],
            [
                0.9999151889185471,
                0.9999997761971315,
                0.9999996533673376,
                0.9999999176675632,
                0.9999996310115039,
                0.9999417087347529,
                0.9999998642566866,
                0.9999998144609645,
                0.9999996533672136,
                0.9999998362622553
            ],
            [
                1.8553910183548312e-07,
                1.9947306726358406e-06,
                1.3709572068422585e-06,
                8.3152792852928e-07,
                8.764242227418718e-08,
                4.4508515805735777e-07,
                7.734414854823498e-08,
                9.422442569334097e-07,
                1.2751905808881762e-07,
                5.04347468323289e-07
            ]
        ]
    },
    {
        "q_id": "9746_mmlu_physics",
        "cot_ids": [
            4,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            19,
            22,
            24,
            27,
            32,
            36,
            37,
            40,
            42,
            43,
            47,
            53,
            54,
            57,
            58,
            59,
            61,
            62,
            63,
            65,
            68,
            69,
            72,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            85,
            86,
            88,
            90,
            92,
            93,
            97,
            101,
            102,
            104,
            106,
            111,
            112,
            116,
            119,
            120,
            121,
            122,
            123,
            127
        ],
        "rewards": [
            [
                6.96225873967641e-06,
                4.222833444590791e-06,
                1.8925141473599938e-05,
                1.553497754583709e-06,
                5.422221555380179e-06,
                6.144177531767002e-06,
                2.2603237589779086e-06,
                1.9947299593014888e-06,
                1.1478766757718129e-05,
                4.222833444590791e-06
            ],
            [
                1.760343213322473e-06,
                7.338207180864763e-07,
                5.043473480777865e-07,
                3.9278615344178325e-07,
                3.4663249714612693e-07,
                6.475949525981759e-07,
                3.9278615344178325e-07,
                2.561281600086738e-06,
                1.0677032518748838e-06,
                5.04347468323289e-07
            ],
            [
                1.8553905760062447e-07,
                9.422449308774482e-07,
                5.715006514176113e-07,
                0.9999756997651104,
                8.315282259138311e-07,
                1.209866260432471e-06,
                5.315787506598473e-08,
                3.4663278639892215e-07,
                0.9999646437409598,
                0.9999038975739655
            ],
            [
                0.9999952149049377,
                0.9999921107374183,
                0.9999599363222348,
                0.999995777166055,
                0.9999785550567378,
                0.9999991148429646,
                0.9999967112517204,
                3.4663249714612693e-07,
                0.9999869928653509,
                1.067703124601679e-06
            ],
            [
                2.1024339116168358e-07,
                3.0590219045914655e-07,
                2.3823690999323465e-07,
                3.0590215399281185e-07,
                3.9278610661902853e-07,
                3.4663274507713016e-07,
                2.382369951932796e-07,
                2.6995790618469934e-07,
                2.1024339116134898e-07,
                2.3823690999323465e-07
            ],
            [
                1.8553905760062447e-07,
                1.6373764721072816e-07,
                2.6995790618469934e-07,
                1.8553910183674878e-07,
                3.05902336324494e-07,
                NaN,
                NaN,
                5.043474683240344e-07,
                6.475945666063607e-07,
                1.7603425837903113e-06
            ],
            [
                5.04347528446051e-07,
                1.6373766672973748e-07,
                5.04347528446051e-07,
                2.699576809143613e-07,
                4.4508515805735777e-07,
                3.466327037548308e-07,
                1.1253526937697666e-07,
                1.3709572068553509e-06,
                5.04347287955046e-07,
                8.315283250394546e-07
            ],
            [
                1.7603425837702984e-06,
                1.0677027427600627e-06,
                2.902311639183378e-06,
                1.994730672668496e-06,
                6.144176066901277e-06,
                9.422449308774482e-07,
                1.994729008145876e-06,
                1.760343003481596e-06,
                1.5534971990126997e-06,
                4.539787406217992e-05
            ],
            [
                7.33821330437595e-07,
                NaN,
                6.962258739796719e-06,
                3.535625071602016e-05,
                3.7266383956509585e-06,
                2.9023119851899796e-06,
                1.1478764021029928e-05,
                8.315279285370317e-07,
                NaN,
                2.2603240284371276e-06
            ],
            [
                2.2603251062450327e-06,
                2.5612828213818346e-06,
                1.3007130015677909e-05,
                9.422447062294175e-07,
                5.043476486924565e-07,
                5.715003789046955e-07,
                2.699578096403948e-07,
                2.382369951932796e-07,
                3.288748673376478e-06,
                1.0677024882009222e-06
            ],
            [
                0.9999980052705173,
                0.001501182319381871,
                0.9999904837505862,
                0.9999960330140879,
                0.9999910603058331,
                1.2098661162056318e-06,
                0.9999925887219018,
                0.010986943106231547,
                0.9999916019259717,
                8.315279285370317e-07
            ],
            [
                0.9999885212291469,
                3.059022998581767e-07,
                1.7603438428800754e-06,
                0.9999957771655504,
                0.9999957771665574,
                1.4449795205472734e-07,
                0.9999996743686257,
                0.9999967112505435,
                2.2603251062450327e-06,
                0.9999960330150327
            ],
            [
                1.6373774480535133e-07,
                1.5534981249697903e-06,
                1.8553907971879076e-07,
                1.4449798650569826e-07,
                1.855391239547094e-07,
                1.4449807263312446e-07,
                3.927862470899887e-07,
                7.734416698849138e-08,
                1.1253508156363576e-07,
                2.699577774589574e-07
            ],
            [
                6.475950298011458e-07,
                7.338208930460318e-07,
                8.315278294072958e-07,
                1.5534971990126997e-06,
                4.785092783519724e-06,
                1.0677029973192638e-06,
                2.561282516066741e-06,
                6.475946437966953e-07,
                2.260324028427877e-06,
                3.4663253846718004e-07
            ],
            [
                6.1441746020359e-06,
                1.2098661162023305e-06,
                1.994729483694599e-06,
                6.475947982002148e-07,
                1.209865539295696e-06,
                1.5534983101602148e-06,
                2.5612816000331606e-06,
                8.315278294097538e-07,
                1.7603434231777837e-06,
                9.422448185510695e-07
            ],
            [
                1.6373768624837685e-07,
                9.931187406410953e-08,
                1.8553907971855875e-07,
                8.764244316973974e-08,
                1.2751908849167202e-07,
                1.4449795205429202e-07,
                1.2751899728311609e-07,
                1.3709567165579959e-06,
                0.9999869928715471,
                6.475949526020042e-07
            ],
            [
                1.0129988565084915e-05,
                7.338207180898968e-07,
                1.3007126914612648e-05,
                2.1024339116168358e-07,
                8.939695238536645e-06,
                NaN,
                1.2098662604247682e-06,
                1.012999098021058e-05,
                6.475946438055299e-07,
                1.0677032518814388e-06
            ],
            [
                3.927863875616689e-07,
                1.3709568799760888e-06,
                9.42244930862237e-07,
                1.0677026154806063e-06,
                4.450852111155216e-07,
                5.715006514040971e-07,
                3.927862470899887e-07,
                6.475945666063607e-07,
                1.209865539298447e-06,
                1.2098662604291696e-06
            ],
            [
                6.475947982037486e-07,
                5.043475885674441e-07,
                9.422444815792981e-07,
                2.382369951932796e-07,
                4.4508515805735777e-07,
                5.715005832886879e-07,
                6.475950298011458e-07,
                5.715005151606823e-07,
                1.209865827752005e-06,
                1.3709575337078829e-06
            ],
            [
                2.699576809143613e-07,
                1.209865539298447e-06,
                4.450849988811838e-07,
                2.2603248367949354e-06,
                2.2603248367949354e-06,
                1.1253526937697666e-07,
                4.450850519409479e-07,
                NaN,
                1.9947301970972664e-06,
                8.764251630441717e-08
            ],
            [
                2.902312677150514e-06,
                1.1253508156363576e-07,
                8.315283250371857e-07,
                6.47595107001401e-07,
                2.1024326584702836e-07,
                NaN,
                3.9278615344178325e-07,
                NaN,
                5.043474683240344e-07,
                3.466325797900508e-07
            ],
            [
                3.4663274507713016e-07,
                3.466327863983311e-07,
                0.999996273362051,
                5.04347287955046e-07,
                0.9999942280779116,
                2.10243290909724e-07,
                0.9999869928684467,
                7.88926446679691e-06,
                2.2603234895372223e-06,
                9.931185038635267e-08
            ],
            [
                8.764254764780641e-08,
                3.726638395634011e-06,
                1.4449803818215767e-07,
                5.3157811697009444e-08,
                1.1478769494083349e-05,
                3.059022269250683e-07,
                0.9999339478318334,
                4.4508515805735777e-07,
                5.715007195447234e-07,
                0.999959936303112
            ],
            [
                7.338209805224048e-07,
                1.4449802095666915e-07,
                3.9278605979534166e-07,
                5.04347468323289e-07,
                5.715005832886879e-07,
                1.637377057680051e-07,
                1.6373766672994222e-07,
                1.1253525596174225e-07,
                3.05902263391829e-07,
                4.450852641737424e-07
            ],
            [
                6.825609419848033e-08,
                0.9999942280799738,
                1.1253508156363576e-07,
                0.999981074856302,
                0.9999898700078197,
                4.4508515805735777e-07,
                0.9999910603037002,
                0.9999852610162928,
                1.1253512180925583e-07,
                1.1253524254615121e-07
            ],
            [
                0.00037998457645977785,
                2.561282210740037e-06,
                NaN,
                1.2098662604291696e-06,
                1.209865539295696e-06,
                3.927862470899887e-07,
                3.726641061085547e-06,
                1.7603434231833873e-06,
                8.315278294072958e-07,
                2.260324567337161e-06
            ],
            [
                7.338212429582604e-07,
                3.927863875616689e-07,
                4.450850519403407e-07,
                9.422444815792981e-07,
                NaN,
                5.043472879540142e-07,
                3.927863407379485e-07,
                5.043472278322555e-07,
                2.699577774585891e-07,
                2.9023116392097746e-06
            ],
            [
                3.7266397283908927e-06,
                1.9947299593078385e-06,
                2.902312331170226e-06,
                1.3709573702822306e-06,
                2.2603253756956754e-06,
                NaN,
                NaN,
                1.5534979397740895e-06,
                3.927862470899887e-07,
                1.0677029973219343e-06
            ],
            [
                6.962253760024999e-06,
                1.0677029973192638e-06,
                2.5612812947508257e-06,
                1.30071315662049e-05,
                3.288749457469787e-06,
                1.760343003481596e-06,
                1.4738985486506781e-05,
                9.422445939032799e-07,
                1.3007126914435202e-05,
                1.7603440527286572e-06
            ],
            [
                NaN,
                1.0677032518814388e-06,
                2.6995790618469934e-07,
                1.855391681906175e-07,
                4.450851580555361e-07,
                6.144173137126169e-06,
                8.315283250371857e-07,
                4.4508494582405734e-07,
                7.734428685047173e-08,
                8.76424013786396e-08
            ],
            [
                NaN,
                1.2751905808881762e-07,
                1.370957860576702e-06,
                1.855391681906175e-07,
                4.450852641737424e-07,
                1.370957860576702e-06,
                4.450849988811838e-07,
                NaN,
                1.7603440527046419e-06,
                1.6373766672973748e-07
            ],
            [
                1.3709567165617364e-06,
                2.90231094723893e-06,
                3.2887498494551953e-06,
                1.1253524254650944e-07,
                2.382369951932796e-07,
                5.043472278322555e-07,
                6.962259569750576e-06,
                1.0677026154806063e-06,
                2.382369667929001e-07,
                2.2603234895372223e-06
            ],
            [
                5.043472278322555e-07,
                2.102434162245973e-07,
                2.6995790618469934e-07,
                6.475946438055299e-07,
                3.4663249714612693e-07,
                4.450852641737424e-07,
                1.6373764721072816e-07,
                3.059022998581767e-07,
                1.444980209564556e-07,
                2.3823688159291947e-07
            ],
            [
                2.382369667914917e-07,
                1.8553914607267268e-07,
                1.6373774480605869e-07,
                2.1024341622426268e-07,
                4.450852641737424e-07,
                1.8553914607267268e-07,
                3.059022998576899e-07,
                1.4449798650551755e-07,
                1.4449807263312446e-07,
                2.1024334103581732e-07
            ],
            [
                5.71500719545698e-07,
                5.043472879525233e-07,
                3.466326624336003e-07,
                0.9999952149055071,
                0.9999810748585568,
                0.9999869928730926,
                0.9999785550516107,
                NaN,
                0.999993855823936,
                1.0677032518814388e-06
            ],
            [
                7.338210680021253e-07,
                NaN,
                NaN,
                4.4508515805735777e-07,
                1.209866260432471e-06,
                8.315279285370317e-07,
                3.726637951367137e-06,
                1.5534971990169383e-06,
                1.9947301970972664e-06,
                1.0677031245990084e-06
            ],
            [
                4.2228334445370225e-06,
                2.260324836787226e-06,
                2.5612831267202583e-06,
                4.222834451355964e-06,
                1.3709567165386693e-06,
                2.7535694385633984e-05,
                3.7266410611296085e-06,
                NaN,
                4.0063711294555596e-05,
                3.120191509592808e-05
            ],
            [
                2.561281905390075e-06,
                2.260324297853209e-06,
                1.5534975693869924e-06,
                5.715007195447234e-07,
                8.315281267834927e-07,
                4.222832941111319e-06,
                1.7603436330259153e-06,
                2.561283432035425e-06,
                7.338208055680009e-07,
                2.260324836776948e-06
            ],
            [
                2.5612825160562587e-06,
                5.043474081993875e-07,
                3.2887478892683997e-06,
                1.3709567165617364e-06,
                6.144176799334096e-06,
                1.7603438428740716e-06,
                1.4738989000422955e-05,
                1.2098656835252174e-06,
                1.3709576971425944e-06,
                1.3709570434219446e-06
            ],
            [
                1.7603440527286572e-06,
                1.7603434231777837e-06,
                5.422221555340727e-06,
                5.422220909009474e-06,
                1.9947297215043796e-06,
                2.260325106237323e-06,
                4.006368264282944e-05,
                5.715005832886879e-07,
                1.3709575337078829e-06,
                3.7266406168624155e-06
            ],
            [
                NaN,
                6.144175334468545e-06,
                NaN,
                1.5534981249697903e-06,
                1.209866260432471e-06,
                1.2098653950656417e-06,
                3.927862002641863e-07,
                1.6701421845057263e-05,
                NaN,
                5.715005832886879e-07
            ],
            [
                9.422444815792981e-07,
                3.288750241561788e-06,
                2.5612834320470717e-06,
                1.760343213335281e-06,
                9.422442569208767e-07,
                4.450850519403407e-07,
                2.90231094723893e-06,
                7.338208055664991e-07,
                1.3709570434178922e-06,
                4.222832437798974e-06
            ],
            [
                6.144172404693786e-06,
                2.260323758923431e-06,
                1.5534981249397663e-06,
                1.0677029972745947e-06,
                1.994730434879465e-06,
                1.994729008145876e-06,
                1.9947290081286418e-06,
                5.4222202621161125e-06,
                1.994729245878497e-06,
                2.9023126770343703e-06
            ],
            [
                7.734416698849138e-08,
                2.1024334103581732e-07,
                9.422444815814404e-07,
                8.315279285370317e-07,
                1.1253508156363576e-07,
                2.3823696679327928e-07,
                0.9999646437493799,
                1.637376862489725e-07,
                2.699578740032504e-07,
                2.1024339116168358e-07
            ],
            [
                1.209865539295696e-06,
                9.422444815765128e-07,
                NaN,
                8.315283250371857e-07,
                1.2098652508424818e-06,
                1.5534975693933505e-06,
                9.422443692574719e-07,
                1.2098659719757836e-06,
                1.9947292459265734e-06,
                1.3709573702822306e-06
            ],
            [
                3.4663278639892215e-07,
                2.6995784182140636e-07,
                2.382369951932796e-07,
                7.73442776303243e-08,
                3.059022998576899e-07,
                1.1253516205489029e-07,
                2.382368247924618e-07,
                8.764249540862797e-08,
                2.3823699519290042e-07,
                1.275190732904469e-07
            ],
            [
                7.734414854823498e-08,
                1.1253516205489029e-07,
                2.382368247924618e-07,
                NaN,
                6.825598028392069e-08,
                1.4449802095666915e-07,
                7.73441946488886e-08,
                7.73442776303243e-08,
                1.6373772528704005e-07,
                3.4663274507713016e-07
            ],
            [
                2.382370235933104e-07,
                1.3709573702778664e-06,
                1.6373768624837685e-07,
                8.315281267882195e-07,
                1.2098661162056318e-06,
                9.422444815792981e-07,
                4.450848927650143e-07,
                3.466326211113502e-07,
                3.059022269250683e-07,
                1.4738976701411704e-05
            ],
            [
                NaN,
                0.9999957771655517,
                0.9999038975624249,
                7.484625405027093e-05,
                0.999999495652592,
                0.9999957771665575,
                1.7603425837606927e-06,
                0.9999962733602735,
                1.3709570434219446e-06,
                0.9999978766215382
            ],
            [
                3.288748673360027e-06,
                4.4508510499849186e-07,
                1.994729008145876e-06,
                2.69957906184239e-07,
                NaN,
                1.3709576971463352e-06,
                2.2603234895176927e-06,
                1.994729245917502e-06,
                2.5612831267202583e-06,
                1.5534973842030142e-06
            ],
            [
                1.9947301970972664e-06,
                NaN,
                6.475947210031623e-07,
                7.338207180864763e-07,
                2.5612828213934817e-06,
                2.382369383923073e-07,
                8.315281267882195e-07,
                3.288749065423109e-06,
                3.92786340734912e-07,
                9.42244930862237e-07
            ],
            [
                1.5534983101602148e-06,
                NaN,
                4.785093353940187e-06,
                7.889266347786918e-06,
                6.144176799334096e-06,
                5.04347468323289e-07,
                3.4663274507713016e-07,
                6.144173137170873e-06,
                2.2603242978871282e-06,
                1.994730197071414e-06
            ],
            [
                0.9999994956525919,
                4.450852111155216e-07,
                3.726639284144195e-06,
                0.9999989322972576,
                0.9999885212305142,
                0.9999960330126687,
                0.9999910603005051,
                0.999998629042957,
                0.9999921107374218,
                0.9999990577555186
            ],
            [
                6.475946438042047e-07,
                6.825609419848033e-08,
                8.76424013786396e-08,
                1.8553919030858602e-07,
                1.275190124846946e-07,
                3.4663274507713016e-07,
                1.4449798650551755e-07,
                6.475949525981759e-07,
                1.275190124846946e-07,
                1.637377057680051e-07
            ],
            [
                3.7266406168624155e-06,
                2.902312331081799e-06,
                8.315281267834927e-07,
                1.5534971990126997e-06,
                1.760343003481596e-06,
                2.260325375634003e-06,
                1.2098662604192665e-06,
                8.315279285351409e-07,
                6.475947982002148e-07,
                5.043475885696228e-07
            ],
            [
                1.6373766672994222e-07,
                3.7266406168403854e-06,
                1.9947306726358406e-06,
                7.338208930460318e-07,
                1.2098661162056318e-06,
                2.2603248367949354e-06,
                2.699577452775239e-07,
                3.4663262111182307e-07,
                2.260323489435463e-06,
                7.338207180898968e-07
            ],
            [
                3.927863875616689e-07,
                5.315786239218605e-08,
                9.422447062294175e-07,
                8.315281267882195e-07,
                7.73442776303243e-08,
                4.006370652067535e-05,
                3.7266406168827523e-06,
                1.9947299593014888e-06,
                3.0590237279085045e-07,
                1.5534983101602148e-06
            ],
            [
                1.370957860576702e-06,
                7.338210680021253e-07,
                1.1478772231086046e-05,
                1.5534984953552536e-06,
                1.0677032518814388e-06,
                1.370957860576702e-06,
                1.3709576971379186e-06,
                7.338207180864763e-07,
                4.785095065232451e-06,
                2.902313369111213e-06
            ],
            [
                2.144495608424996e-05,
                4.785095065171522e-06,
                2.561282516066741e-06,
                1.2098652508424818e-06,
                4.785096206013061e-06,
                1.5534975693869924e-06,
                2.260324567337161e-06,
                2.561283432035425e-06,
                4.222834451292594e-06,
                3.288748673295719e-06
            ],
            [
                3.466327037553825e-07,
                7.734421308914719e-08,
                5.043472278322555e-07,
                1.8553919030826963e-07,
                1.994729483729522e-06,
                2.382368531929327e-07,
                0.9999687980812701,
                3.653479031538012e-08,
                5.3157811697009444e-08,
                3.9278629391427843e-07
            ],
            [
                6.144175334418252e-06,
                2.260324836776948e-06,
                1.1478768126057254e-05,
                6.475951069985296e-07,
                4.785093924362895e-06,
                8.315282259117513e-07,
                2.902310947190096e-06,
                1.553497384180408e-06,
                7.889263526345123e-06,
                2.9023112931688987e-06
            ],
            [
                5.043475284468537e-07,
                0.9999930377445863,
                1.8553905760062447e-07,
                0.9999843104521764,
                1.1253525596174225e-07,
                0.9999832985781749,
                0.9999869928684678,
                4.785096206076165e-06,
                1.5534977545886537e-06,
                2.102434162245973e-07
            ],
            [
                0.9997694933424888,
                6.825600469412533e-08,
                4.1399390279513406e-08,
                7.734428685047173e-08,
                9.931185038635267e-08,
                8.764244316973974e-08,
                6.825601283086733e-08,
                1.1253506814842375e-07,
                5.315787506612373e-08,
                9.931185038635267e-08
            ],
            [
                1.444979692797559e-07,
                0.9999646437325821,
                0.9999952149049391,
                0.9999898700078194,
                0.9999785550439478,
                0.9999990577549575,
                1.855391681906175e-07,
                0.9999945777803898,
                0.9999916019239732,
                0.9999955048173546
            ],
            [
                7.33821330437595e-07,
                1.9947292459347367e-06,
                1.0677029973219343e-06,
                3.2887498495150166e-06,
                8.315281267861397e-07,
                1.275190580890061e-07,
                8.315279285370317e-07,
                6.475948754012522e-07,
                3.059023727894942e-07,
                9.422444815792981e-07
            ]
        ]
    },
    {
        "q_id": "9272_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            33,
            34,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            69,
            71,
            72,
            73,
            74,
            75,
            77,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            90,
            92,
            93,
            94,
            95,
            96,
            97,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                NaN,
                1.7603425837903113e-06,
                0.9995694428482823,
                2.2603251062450327e-06,
                1.1478769494542698e-05,
                0.9999925887166204,
                6.475950298021765e-07,
                2.9023116392097746e-06,
                2.902312331170226e-06,
                0.9999974387171836
            ],
            [
                6.144176799334096e-06,
                NaN,
                4.222834451382849e-06,
                1.9947297214944016e-06,
                5.422219616265831e-06,
                3.72663883989755e-06,
                6.144176799283803e-06,
                1.300713466685723e-05,
                2.9023119851781017e-06,
                7.88926446679691e-06
            ],
            [
                5.715006514176113e-07,
                1.209866260432471e-06,
                1.0677027427624903e-06,
                1.3709570434178922e-06,
                4.450849988811838e-07,
                1.9947304348862686e-06,
                1.5534977545886537e-06,
                1.209865539295696e-06,
                3.9278615344178325e-07,
                9.422445939054222e-07
            ],
            [
                5.04347287955046e-07,
                4.4508515805735777e-07,
                3.4663249714612693e-07,
                1.275190124846946e-07,
                2.699577774585891e-07,
                5.422219616265831e-06,
                3.927863875616689e-07,
                3.466326624336003e-07,
                NaN,
                5.715003789017068e-07
            ],
            [
                1.2098656835224664e-06,
                4.4508494582314646e-07,
                1.0677032518785256e-06,
                NaN,
                8.315278294114555e-07,
                1.0677027427600627e-06,
                7.338209805224048e-07,
                9.422444815814404e-07,
                9.422450431989127e-07,
                8.315279285370317e-07
            ],
            [
                0.9999993524049704,
                0.9999992661791947,
                0.999999391640891,
                0.9999987121043244,
                0.999999218851949,
                7.889263526409699e-06,
                0.9999988634358833,
                0.9999993916410361,
                0.9999952149066503,
                0.9999974387177902
            ],
            [
                6.475945666051092e-07,
                2.3823685319244518e-07,
                9.422448185534261e-07,
                3.9278629391427843e-07,
                2.1024341622368903e-07,
                6.475949526020042e-07,
                1.3709576971463352e-06,
                5.043472879540142e-07,
                3.927863407379485e-07,
                3.05902190458764e-07
            ],
            [
                1.6373772528704005e-07,
                9.422444815814404e-07,
                2.3823702359290413e-07,
                NaN,
                3.927862470905692e-07,
                1.4449807263312446e-07,
                1.6373774480605869e-07,
                6.475949526020042e-07,
                2.6995790618469934e-07,
                5.715006514176113e-07
            ],
            [
                1.760343213335281e-06,
                NaN,
                8.315279285351409e-07,
                1.0677024881980089e-06,
                1.5534975693979422e-06,
                3.9278629391427843e-07,
                8.939697369882888e-06,
                4.450848927658745e-07,
                1.3709575337159875e-06,
                3.2887502415767434e-06
            ],
            [
                9.422444815814404e-07,
                1.6701415872659116e-05,
                NaN,
                3.466325797896173e-07,
                0.9999985406237809,
                0.9999983463104151,
                1.3709567165617364e-06,
                3.72663883989755e-06,
                0.9999993916407461,
                7.338208055680009e-07
            ],
            [
                5.715005832895975e-07,
                3.05902263391829e-07,
                7.338208930460318e-07,
                3.288748673376478e-06,
                1.3709576971463352e-06,
                1.0677026154806063e-06,
                5.71500719545698e-07,
                1.637376862489725e-07,
                NaN,
                NaN
            ],
            [
                5.715003789046955e-07,
                8.315277302857965e-07,
                9.422448185534261e-07,
                1.855391681906175e-07,
                1.4449798650551755e-07,
                3.4663249714451116e-07,
                1.275190276859705e-07,
                1.4449800373065699e-07,
                1.275190732904469e-07,
                1.4449807263312446e-07
            ],
            [
                6.475949526020042e-07,
                NaN,
                NaN,
                2.1024339116168358e-07,
                7.338208930460318e-07,
                NaN,
                7.338211554783522e-07,
                1.994729721518893e-06,
                0.03308598089141841,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.7535700948722127e-05,
                5.715006514176113e-07,
                NaN,
                0.9999785550465982,
                2.9023116392097746e-06
            ],
            [
                2.1024331597288867e-07,
                4.4508515805735777e-07,
                0.9999970976869818,
                1.1253506814842375e-07,
                1.275190428875671e-07,
                3.4663278639892215e-07,
                2.1024339116168358e-07,
                1.6373764721072816e-07,
                2.699578740032504e-07,
                6.475947982037486e-07
            ],
            [
                0.9999975938970902,
                0.9999990577551824,
                0.9999970976873302,
                2.5612831267202583e-06,
                0.9999904837494753,
                1.2098658277489788e-06,
                3.2887506335906595e-06,
                6.475946438055299e-07,
                4.222832941193893e-06,
                0.9999957771675728
            ],
            [
                1.2098661162056318e-06,
                7.889260704968913e-06,
                1.2098662604291696e-06,
                5.422221555380179e-06,
                4.785096206076165e-06,
                9.422443692555439e-07,
                6.962254589978262e-06,
                9.422444815814404e-07,
                1.5534971990169383e-06,
                5.422217677152175e-06
            ],
            [
                1.147877359957198e-05,
                4.222834451382849e-06,
                NaN,
                6.962258739796719e-06,
                8.939695238634211e-06,
                0.00010889696127518294,
                1.6701421845361053e-05,
                1.5534973842076057e-06,
                4.539787947559951e-05,
                6.962255419931625e-06
            ],
            [
                NaN,
                1.994729483723626e-06,
                5.829125860453825e-05,
                NaN,
                0.9999771720084085,
                NaN,
                6.144176066901277e-06,
                0.9999822214545938,
                0.9999741325630135,
                5.8291265555961825e-05
            ],
            [
                3.288748673376478e-06,
                2.2603240284371276e-06,
                5.422217677152175e-06,
                3.7266383956509585e-06,
                4.22283545819819e-06,
                NaN,
                1.7603430034867993e-06,
                0.9999646437326103,
                1.5534971990126997e-06,
                2.902312677150514e-06
            ],
            [
                0.9669140226838876,
                1.5534983101644536e-06,
                4.785094494811783e-06,
                0.9991959140500603,
                1.0129988565084915e-05,
                1.6701417863559525e-05,
                1.0129994602895546e-05,
                2.699578740032504e-07,
                8.939693107288474e-06,
                NaN
            ],
            [
                5.4222176771176554e-06,
                1.4738980215352592e-05,
                4.222833947960866e-06,
                1.5534979397740895e-06,
                2.7535691101761522e-05,
                3.726639728370556e-06,
                2.7535697667202906e-05,
                1.5534975693933505e-06,
                1.8925145985895816e-05,
                1.4738980215352592e-05
            ],
            [
                9.422448185534261e-07,
                0.9999995262093293,
                1.5534975693979422e-06,
                0.9999978766215398,
                5.04347528446051e-07,
                0.9999983463104156,
                1.8925148241872038e-05,
                1.994729483723626e-06,
                1.7603440527286572e-06,
                1.5534977545886537e-06
            ],
            [
                1.8925148242250705e-05,
                1.0677032518814388e-06,
                1.3709576971425944e-06,
                1.553497384196656e-06,
                1.5534981249697903e-06,
                1.0677032518785256e-06,
                1.5534973841895917e-06,
                9.422445939032799e-07,
                2.5612828213934817e-06,
                1.8925141473978602e-05
            ],
            [
                4.785092783519724e-06,
                1.8925157266089433e-05,
                8.315283250371857e-07,
                NaN,
                4.4508510499849186e-07,
                2.7535694384882703e-05,
                5.422220909009474e-06,
                0.0001398221242266438,
                5.715005151606823e-07,
                4.785093924362895e-06
            ],
            [
                6.475950298021765e-07,
                1.7603438428800754e-06,
                3.4663266243308805e-07,
                1.3007133116732079e-05,
                1.0677032518814388e-06,
                1.7603425837903113e-06,
                1.0677026154806063e-06,
                7.338208055680009e-07,
                1.2098656835224664e-06,
                5.715003107767143e-07
            ],
            [
                7.338211554783522e-07,
                1.2098661161927025e-06,
                2.2603251062270446e-06,
                1.9947294837154625e-06,
                3.2887506336235617e-06,
                9.422448185478557e-07,
                3.726639728262097e-06,
                1.3709573702722555e-06,
                3.726638839806038e-06,
                1.3709573702822306e-06
            ],
            [
                3.0590219045914655e-07,
                1.4449795205472734e-07,
                5.315784971839039e-08,
                1.1253506814842375e-07,
                1.8553919030858602e-07,
                2.1024334103581732e-07,
                1.4449807263325588e-07,
                1.1253525596174225e-07,
                2.3823690999323465e-07,
                8.764254764780641e-08
            ],
            [
                NaN,
                5.422220909009474e-06,
                7.338208930460318e-07,
                7.889266347786918e-06,
                NaN,
                3.7266406168827523e-06,
                6.962258739796719e-06,
                NaN,
                8.939700567094277e-06,
                1.994729483729522e-06
            ],
            [
                1.994729483729522e-06,
                5.422221555414699e-06,
                NaN,
                1.892514598627448e-05,
                NaN,
                NaN,
                NaN,
                NaN,
                7.33821330437595e-07,
                NaN
            ],
            [
                1.6701427818034747e-05,
                NaN,
                8.315281267882195e-07,
                6.144175334468545e-06,
                2.260324836776948e-06,
                5.422220909009474e-06,
                5.422219616140078e-06,
                7.889262585814522e-06,
                1.8925150497848527e-05,
                5.422217030747413e-06
            ],
            [
                2.2603253756956754e-06,
                1.3709573702856596e-06,
                1.5534971990169383e-06,
                5.715006514176113e-07,
                2.1444943302650045e-05,
                6.475947210046347e-07,
                2.561281294760143e-06,
                5.04347287955046e-07,
                1.0677024882009222e-06,
                9.422448185510695e-07
            ],
            [
                7.338208930460318e-07,
                3.0590237279032884e-07,
                NaN,
                5.04347287955046e-07,
                8.315279285370317e-07,
                3.059021175261338e-07,
                3.927863875616689e-07,
                3.927862939126708e-07,
                3.9278615344178325e-07,
                5.715002426486762e-07
            ],
            [
                NaN,
                8.315284241650899e-07,
                1.0677026154806063e-06,
                3.059022998576899e-07,
                1.5534983101644536e-06,
                NaN,
                8.939700567004841e-06,
                6.475947210046347e-07,
                NaN,
                9.422448185534261e-07
            ],
            [
                1.5534973842076057e-06,
                8.315278294114555e-07,
                2.6995784182183607e-07,
                3.059021175261338e-07,
                5.715003789033962e-07,
                NaN,
                1.5534971990169383e-06,
                3.2887502415767434e-06,
                NaN,
                1.7603425837903113e-06
            ],
            [
                9.422444815814404e-07,
                3.9278605979534166e-07,
                2.102434162245973e-07,
                4.4508494582405734e-07,
                6.47595107001401e-07,
                NaN,
                2.102434162245973e-07,
                3.288749849529972e-06,
                5.04347528446051e-07,
                4.222834451403972e-06
            ],
            [
                4.785094494811783e-06,
                6.962258739796719e-06,
                1.5534984953552536e-06,
                1.7603425837903113e-06,
                8.939697370069891e-06,
                3.466326211113502e-07,
                2.5612834320563895e-06,
                4.785096206076165e-06,
                9.422442569315887e-07,
                1.9947299593078385e-06
            ],
            [
                1.4738985486506781e-05,
                6.962257079832313e-06,
                NaN,
                0.001325022125291243,
                4.222834954778007e-06,
                NaN,
                7.338209805133949e-07,
                3.288748281329893e-06,
                2.561283432035425e-06,
                3.288749457469787e-06
            ],
            [
                1.8553903548287212e-07,
                6.825598842065202e-08,
                6.023571320847322e-08,
                9.93120161310289e-08,
                1.4449805540763184e-07,
                1.1253508156363576e-07,
                1.6373766672994222e-07,
                6.825609419848033e-08,
                2.10243290909963e-07,
                1.1253508156363576e-07
            ],
            [
                2.1024341622426268e-07,
                3.927863407379485e-07,
                2.3823690999323465e-07,
                2.6995774527718623e-07,
                2.3823688159291947e-07,
                1.637377448057981e-07,
                1.4449805540740185e-07,
                4.4508515805735777e-07,
                2.6995784182140636e-07,
                1.6373776432509826e-07
            ],
            [
                3.5356238073889594e-05,
                1.1478769494542698e-05,
                4.785093924389007e-06,
                6.475947982037486e-07,
                9.422443692574719e-07,
                2.699578096403948e-07,
                1.2098652508424818e-06,
                3.9278629391427843e-07,
                1.6373762769138607e-07,
                1.855391681906175e-07
            ],
            [
                5.422219616265831e-06,
                8.315278294072958e-07,
                2.2603237589779086e-06,
                2.2603248367949354e-06,
                6.144176799283803e-06,
                1.5534983101478522e-06,
                1.5534981249574276e-06,
                4.785092783519724e-06,
                2.5612825160562587e-06,
                1.9947299593014888e-06
            ],
            [
                NaN,
                5.043473480777865e-07,
                0.9999998257020799,
                3.466327037548308e-07,
                2.2603248367949354e-06,
                4.53978902983119e-05,
                1.5534984953552536e-06,
                3.927862470899887e-07,
                1.067703124601679e-06,
                NaN
            ],
            [
                1.067703124601679e-06,
                NaN,
                4.4508494582405734e-07,
                3.466325797888292e-07,
                5.715003789046955e-07,
                3.288748673376478e-06,
                1.0129987357407137e-05,
                6.475949526020042e-07,
                3.7266397283908927e-06,
                5.043476486915964e-07
            ],
            [
                2.2603234895289998e-06,
                5.422220262636381e-06,
                1.7603427936263351e-06,
                5.422220262636381e-06,
                3.7266406168827523e-06,
                1.2098662604291696e-06,
                6.962253760024999e-06,
                8.315279285370317e-07,
                6.144173869603344e-06,
                7.338213304363436e-07
            ],
            [
                3.7266410611465547e-06,
                6.144176066943187e-06,
                4.450852641737424e-07,
                NaN,
                NaN,
                7.338212429594283e-07,
                NaN,
                1.3709576971463352e-06,
                9.422443692574719e-07,
                9.422448185534261e-07
            ],
            [
                1.7603438428800754e-06,
                8.315279285370317e-07,
                8.315277302841894e-07,
                3.4663278639892215e-07,
                1.7603425837903113e-06,
                1.8553907971855875e-07,
                3.059022269250683e-07,
                4.4508515805735777e-07,
                6.475947982037486e-07,
                3.466325797896173e-07
            ],
            [
                8.939696304311336e-06,
                2.5612828213934817e-06,
                4.222834954778007e-06,
                1.0677027427600627e-06,
                1.0129993395336818e-05,
                2.2603245673443566e-06,
                7.88926446679691e-06,
                3.288749065406658e-06,
                1.5534984953298217e-06,
                3.2887494574518405e-06
            ],
            [
                8.315277302857965e-07,
                1.0677029973219343e-06,
                1.0677032518814388e-06,
                4.785093924389007e-06,
                1.2098656835252174e-06,
                5.043476486924565e-07,
                4.450851049991497e-07,
                9.422450432014836e-07,
                5.043474082005342e-07,
                3.466326624336003e-07
            ],
            [
                4.222834954753043e-06,
                0.999995504817361,
                0.9999877809255228,
                2.1444943301674863e-05,
                4.2228339479858295e-06,
                0.9999983463104166,
                0.9997388097593934,
                0.9999485577992689,
                0.9999957771650548,
                0.9999970976880176
            ],
            [
                1.994730434847717e-06,
                1.6701419854156377e-05,
                4.785094494716039e-06,
                3.288750241500471e-06,
                2.9023109471689794e-06,
                5.422219616140078e-06,
                1.3709568799760888e-06,
                1.994729008105057e-06,
                1.3709567165579959e-06,
                2.2603240284371276e-06
            ],
            [
                1.067703124601679e-06,
                1.209866260432471e-06,
                5.71500719545698e-07,
                5.043476486915964e-07,
                1.5534984953552536e-06,
                2.1024331597262577e-07,
                1.5534971990169383e-06,
                NaN,
                2.1024334103581732e-07,
                5.043472278322555e-07
            ],
            [
                1.760343003481596e-06,
                5.043476486924565e-07,
                2.9023116391978967e-06,
                1.3709576971425944e-06,
                2.2603242978943238e-06,
                3.288750241561788e-06,
                9.422443692574719e-07,
                1.5534971990126997e-06,
                NaN,
                1.7603430034867993e-06
            ],
            [
                0.9999967112513322,
                NaN,
                4.222834451382849e-06,
                2.4300243631890864e-05,
                7.889261645427538e-06,
                3.288748673376478e-06,
                9.422444815814404e-07,
                6.475947210046347e-07,
                2.2603234895372223e-06,
                1.8925155009767892e-05
            ],
            [
                0.9999989322971305,
                0.999997876622298,
                0.9999975938965147,
                0.9999991684718736,
                0.9999977396762425,
                0.9999898700054247,
                0.9999983463102184,
                0.9999960330121983,
                0.9999986290426307,
                0.9999960330145609
            ],
            [
                5.715005832886879e-07,
                8.315278294072958e-07,
                2.561281600086738e-06,
                8.315284241650899e-07,
                1.9947292459347367e-06,
                1.7603430034867993e-06,
                9.422448185510695e-07,
                3.288749849529972e-06,
                1.760343003481596e-06,
                1.0677029973192638e-06
            ],
            [
                0.999997097689058,
                2.144495864059426e-05,
                2.699578096403948e-07,
                NaN,
                1.892515049819277e-05,
                3.9278629391427843e-07,
                0.9999991684720722,
                0.9999991148427542,
                4.2228339479858295e-06,
                0.99987660545634
            ],
            [
                1.4449798650551755e-07,
                0.9999988634360195,
                2.10243290909724e-07,
                3.05902336324494e-07,
                3.0590237279085045e-07,
                2.6995774527718623e-07,
                2.699576809143613e-07,
                2.10243290909724e-07,
                5.043473480777865e-07,
                2.1024326584582131e-07
            ],
            [
                6.475950298011458e-07,
                8.315279285351409e-07,
                2.5612828213934817e-06,
                1.7603434231777837e-06,
                4.785093353940187e-06,
                2.90231094723893e-06,
                5.043475284447896e-07,
                3.288748281329893e-06,
                1.5534975693933505e-06,
                7.338213304343413e-07
            ],
            [
                3.7266401726359486e-06,
                1.0129993395336818e-05,
                NaN,
                NaN,
                5.422218969895357e-06,
                2.260325106237323e-06,
                2.9023112932296107e-06,
                4.22283545819819e-06,
                NaN,
                1.7603440527334603e-06
            ],
            [
                8.315279285351409e-07,
                1.3709570434178922e-06,
                4.4508494582314646e-07,
                3.0590237279085045e-07,
                6.475945666063607e-07,
                4.450852111155216e-07,
                1.2098661162056318e-06,
                3.466325797896173e-07,
                7.338208930460318e-07,
                3.4663274507713016e-07
            ],
            [
                2.902313023130843e-06,
                7.338208930460318e-07,
                2.902313369111213e-06,
                5.715003107767143e-07,
                9.422443692555439e-07,
                5.043473480777865e-07,
                1.370957860576702e-06,
                1.3709576971463352e-06,
                1.3709572068522336e-06,
                1.4738981972564636e-05
            ],
            [
                3.9278629391427843e-07,
                1.0677026154774503e-06,
                9.422447062294175e-07,
                6.9622595696935874e-06,
                1.370957860576702e-06,
                2.902311984915459e-06,
                2.753568453712307e-05,
                1.553497754577351e-06,
                1.9947301970106386e-06,
                1.5534979397740895e-06
            ],
            [
                9.422443692574719e-07,
                0.9999810748541399,
                1.7603425837903113e-06,
                1.0677027427624903e-06,
                8.31528325040778e-07,
                NaN,
                NaN,
                3.927863875616689e-07,
                3.059022998581767e-07,
                0.999991060300512
            ],
            [
                NaN,
                2.9023112932296107e-06,
                6.475950298011458e-07,
                4.22283545819819e-06,
                3.927863407379485e-07,
                1.3709573702856596e-06,
                1.2098656835252174e-06,
                8.939697370069891e-06,
                9.422444815814404e-07,
                6.144172404738491e-06
            ],
            [
                7.338209805240734e-07,
                1.5534979397790343e-06,
                3.0590237279032884e-07,
                4.450848927658745e-07,
                1.4449803818215767e-07,
                1.0677027427624903e-06,
                1.9947299593078385e-06,
                1.6373776432509826e-07,
                3.2887482813149375e-06,
                5.715004470326849e-07
            ],
            [
                NaN,
                4.4508494582405734e-07,
                5.715005832853093e-07,
                6.475947210012481e-07,
                1.0677027427624903e-06,
                3.0590215399183813e-07,
                6.144177531811707e-06,
                5.715002426475718e-07,
                2.9023112932296107e-06,
                1.3709576971463352e-06
            ],
            [
                7.338212429537553e-07,
                1.5534977545886537e-06,
                8.315281267861397e-07,
                3.46632497145457e-07,
                1.8553905760062447e-07,
                8.315277302841894e-07,
                5.715004470313855e-07,
                9.422443692555439e-07,
                1.3709567165617364e-06,
                2.2603248367949354e-06
            ],
            [
                0.9999986290426317,
                0.9999987121052478,
                0.9999982396563734,
                0.9999992188512976,
                0.999998996985793,
                1.4738981972564636e-05,
                1.892515501014656e-05,
                0.9999990577549578,
                0.9999962733602774,
                0.9999980052705186
            ],
            [
                1.0677026154827912e-06,
                NaN,
                1.3709567165617364e-06,
                NaN,
                1.30071315662049e-05,
                1.4738981972323349e-05,
                2.260323758987159e-06,
                2.7535694384882703e-05,
                NaN,
                1.0129992187658463e-05
            ],
            [
                2.5612828213690224e-06,
                1.3709572068522336e-06,
                8.315282259089153e-07,
                4.785093353909723e-06,
                1.1478764020883773e-05,
                1.2098659719757836e-06,
                2.90231094723893e-06,
                2.9023109471689794e-06,
                3.726641061085547e-06,
                1.3007125363908762e-05
            ],
            [
                3.059022269250683e-07,
                3.05902336324494e-07,
                1.0677028700422047e-06,
                NaN,
                NaN,
                6.475950298011458e-07,
                9.422448185534261e-07,
                3.927862470899887e-07,
                2.90231094723893e-06,
                1.9947299593078385e-06
            ],
            [
                3.288747889284851e-06,
                8.315279285351409e-07,
                1.3709576971425944e-06,
                1.6701423836262173e-05,
                6.475950298011458e-07,
                9.422448185510695e-07,
                4.222834954778007e-06,
                6.475947210012481e-07,
                7.889261645427538e-06,
                1.5534977545886537e-06
            ],
            [
                4.785093924389007e-06,
                1.5534983101644536e-06,
                7.338208930460318e-07,
                3.0590226339061185e-07,
                5.043475885696228e-07,
                3.466326211113502e-07,
                2.382369667929001e-07,
                2.1024326584639497e-07,
                2.3823690999290963e-07,
                1.067703124601679e-06
            ],
            [
                1.994729721518893e-06,
                2.561282210740037e-06,
                2.382370235922541e-07,
                2.5612828213934817e-06,
                9.422445939054222e-07,
                1.3709576971425944e-06,
                2.2603242978778778e-06,
                1.3709573702822306e-06,
                2.2603242978871282e-06,
                1.0677033791612137e-06
            ],
            [
                3.7266406168827523e-06,
                5.422219616228845e-06,
                1.2098653950692178e-06,
                3.288748673376478e-06,
                5.04347287955046e-07,
                1.012999218776902e-05,
                6.475950298011458e-07,
                5.715003789033962e-07,
                1.3007125363908762e-05,
                1.5534979397740895e-06
            ],
            [
                1.2098653950692178e-06,
                1.2098662604247682e-06,
                5.715003107738556e-07,
                2.382370235933104e-07,
                8.315277302841894e-07,
                1.2098652508424818e-06,
                1.3709572068478697e-06,
                2.260324836776948e-06,
                1.5534979397592542e-06,
                2.4300252321904572e-05
            ],
            [
                0.999982221439741,
                1.209865539298447e-06,
                0.9999869928731278,
                2.1024339116168358e-07,
                0.9999975938965167,
                5.043475284468537e-07,
                0.9999810748587905,
                NaN,
                0.9999861539938427,
                NaN
            ],
            [
                2.3823682479292225e-07,
                7.338208055680009e-07,
                5.043476486924565e-07,
                3.466327037553825e-07,
                1.3709576971463352e-06,
                1.8553907971855875e-07,
                3.059022998569248e-07,
                1.855391239547094e-07,
                1.27519088491875e-07,
                6.475945666063607e-07
            ],
            [
                1.5534975693979422e-06,
                1.9947301970972664e-06,
                6.1441767993788005e-06,
                8.315277302841894e-07,
                2.902312677150514e-06,
                7.889266347786918e-06,
                1.9947301970972664e-06,
                1.6701417863559525e-05,
                1.7603438428800754e-06,
                9.422443692574719e-07
            ],
            [
                6.475947210046347e-07,
                1.5534981249697903e-06,
                3.927862470899887e-07,
                3.0590237279032884e-07,
                3.0590226339061185e-07,
                8.315279285370317e-07,
                3.4663249714612693e-07,
                3.0590237279085045e-07,
                1.275190580890061e-07,
                1.760343003481596e-06
            ],
            [
                6.475949526020042e-07,
                2.10243290909724e-07,
                2.699578740032504e-07,
                2.6995774527718623e-07,
                2.1024331597262577e-07,
                3.4663262111182307e-07,
                2.3823702359290413e-07,
                3.059022998581767e-07,
                2.699578740032504e-07,
                6.475947210046347e-07
            ],
            [
                3.4663278639892215e-07,
                1.0677028700422047e-06,
                1.0677028700422047e-06,
                1.209866260432471e-06,
                5.715003789046955e-07,
                3.0590237279032884e-07,
                7.338208055680009e-07,
                8.939693107288474e-06,
                2.90231094723893e-06,
                5.04347528446051e-07
            ],
            [
                NaN,
                1.0677031245905116e-06,
                4.222835458148261e-06,
                1.2098655392871682e-06,
                1.7603430034743913e-06,
                0.9999974387171812,
                NaN,
                0.9999955048173635,
                1.9947304348703948e-06,
                3.288748281329893e-06
            ],
            [
                6.47595107001401e-07,
                2.561281600086738e-06,
                3.9278605979534166e-07,
                5.422220262636381e-06,
                NaN,
                6.475947982037486e-07,
                4.2228319344021954e-06,
                NaN,
                2.902313023130843e-06,
                4.222834954801051e-06
            ],
            [
                2.699578096403948e-07,
                3.4663278639892215e-07,
                3.4663262111182307e-07,
                2.6995774527718623e-07,
                3.927863407379485e-07,
                3.05902336324494e-07,
                9.931199245322124e-08,
                3.059022998581767e-07,
                6.47595107001401e-07,
                5.043476486924565e-07
            ],
            [
                NaN,
                6.9622587397397306e-06,
                1.0677026154619133e-06,
                2.5612816000646084e-06,
                NaN,
                3.726639728224814e-06,
                4.785096776394765e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                1.7603427936335396e-06,
                4.222833444590791e-06,
                8.315277302857965e-07,
                1.012998977264307e-05,
                2.9023119851899796e-06,
                1.209865827752005e-06,
                6.1441767993788005e-06,
                4.785096206076165e-06,
                1.4449803818215767e-07,
                5.715003107767143e-07
            ],
            [
                NaN,
                6.962257909842961e-06,
                1.300712536408621e-05,
                2.2603251062450327e-06,
                NaN,
                2.9023116392097746e-06,
                NaN,
                2.902312331170226e-06,
                3.059022269250683e-07,
                8.939699501416646e-06
            ],
            [
                NaN,
                1.994729008145876e-06,
                5.715006514176113e-07,
                1.209866260432471e-06,
                1.0677033791612137e-06,
                4.222834954801051e-06,
                6.962258739796719e-06,
                9.422445939032799e-07,
                5.715005832886879e-07,
                NaN
            ],
            [
                6.825608606172863e-08,
                5.315788140303327e-08,
                1.637376862489725e-07,
                NaN,
                1.5534981249736758e-06,
                1.6373764721091427e-07,
                6.023576347299818e-08,
                1.275190580890061e-07,
                2.1024334103581732e-07,
                1.0677029973219343e-06
            ],
            [
                0.9999964991455909,
                0.9999921107383908,
                0.9999925887183855,
                0.9999982396567896,
                0.9999980052702806,
                0.99999457778234,
                7.338208055664991e-07,
                0.9999986290424687,
                0.9999810748518253,
                0.99999823965721
            ],
            [
                5.043472879540142e-07,
                0.999995504820042,
                0.9999771719925945,
                3.288748673360027e-06,
                1.9947292459347367e-06,
                4.785093353940187e-06,
                0.9999892166916841,
                1.300712536408621e-05,
                0.999986153992416,
                0.9999724643156983
            ],
            [
                4.4508515805735777e-07,
                6.475945666063607e-07,
                2.3823696679327928e-07,
                2.3823690999323465e-07,
                9.422444815765128e-07,
                3.4663274507713016e-07,
                3.4663274507713016e-07,
                8.31527928532683e-07,
                6.475950298021765e-07,
                2.260324836776948e-06
            ],
            [
                3.288749457469787e-06,
                6.962254589978262e-06,
                2.4300232043987867e-05,
                9.422447062294175e-07,
                1.9947301970972664e-06,
                1.6701415872385704e-05,
                1.2098661162056318e-06,
                2.260324567337161e-06,
                5.422220262636381e-06,
                4.222835458175145e-06
            ],
            [
                1.3709576971425944e-06,
                4.785093924362895e-06,
                2.2603251062270446e-06,
                6.9622595696935874e-06,
                1.4738981972323349e-05,
                1.7603436330179102e-06,
                6.475945666051092e-07,
                2.3823690999323465e-07,
                1.0677033791612137e-06,
                2.6995790618469934e-07
            ],
            [
                7.338209805224048e-07,
                3.059022269250683e-07,
                2.6995771309523475e-07,
                6.144175334468545e-06,
                1.760343213335281e-06,
                2.561282821402217e-06,
                2.561281294760143e-06,
                4.4508510499849186e-07,
                NaN,
                4.4508494582405734e-07
            ],
            [
                7.338211554783522e-07,
                1.0677026154806063e-06,
                1.209865539295696e-06,
                3.466325797896173e-07,
                1.7603430034867993e-06,
                1.0677026154827912e-06,
                4.222833444590791e-06,
                7.338207180898968e-07,
                9.422450432014836e-07,
                3.288747889284851e-06
            ],
            [
                5.422217030781934e-06,
                6.605212895721594e-05,
                NaN,
                3.7266401726359486e-06,
                6.475946438055299e-07,
                9.422444815814404e-07,
                3.288747889284851e-06,
                0.9999978766223007,
                0.9999877809283901,
                0.9999987121043257
            ],
            [
                NaN,
                2.9023112932177327e-06,
                8.315279285370317e-07,
                7.338211554801876e-07,
                3.7266406168827523e-06,
                1.2098661162056318e-06,
                1.0677032518814388e-06,
                9.422444815814404e-07,
                1.209865539295696e-06,
                5.715005832886879e-07
            ],
            [
                6.47594952603035e-07,
                3.7266406168827523e-06,
                5.715005151606823e-07,
                3.059021175261338e-07,
                3.0590237279032884e-07,
                1.0677026154806063e-06,
                3.466327037548308e-07,
                1.2098661162056318e-06,
                4.450848927650143e-07,
                1.0677032518814388e-06
            ],
            [
                NaN,
                1.8553907971879076e-07,
                2.3823690999323465e-07,
                3.4663262111182307e-07,
                2.6995774527718623e-07,
                NaN,
                2.699576809143613e-07,
                3.927862002663297e-07,
                3.927863407379485e-07,
                3.9278605979534166e-07
            ],
            [
                7.338209805240734e-07,
                6.144172404738491e-06,
                9.422448185534261e-07,
                1.5534971990169383e-06,
                3.466326624336003e-07,
                3.927863875616689e-07,
                2.9023116392097746e-06,
                1.0677032518814388e-06,
                3.9278629391427843e-07,
                3.2887506336235617e-06
            ],
            [
                1.3709568799823232e-06,
                5.04347528446051e-07,
                2.5612834320563895e-06,
                7.338208930460318e-07,
                1.0677032518814388e-06,
                9.422443692574719e-07,
                4.450851049991497e-07,
                1.760342793638743e-06,
                2.260323758987159e-06,
                1.994729008151319e-06
            ],
            [
                3.7266401726173067e-06,
                2.561282516042282e-06,
                5.422220262636381e-06,
                2.561281600076256e-06,
                1.0677027427525368e-06,
                5.8291258607931044e-05,
                8.939698435657833e-06,
                5.8291251656508296e-05,
                2.260324836787226e-06,
                6.60521761905875e-05
            ],
            [
                2.561281294760143e-06,
                NaN,
                1.209866260432471e-06,
                4.785093924389007e-06,
                7.338211554813555e-07,
                9.422442569334097e-07,
                5.043473480777865e-07,
                1.3709575337159875e-06,
                4.222834954801051e-06,
                2.260324028443809e-06
            ],
            [
                2.1024336609843824e-07,
                1.3007134667259441e-05,
                6.962258739796719e-06,
                7.338213304363436e-07,
                6.475945666051092e-07,
                4.222834954801051e-06,
                1.0677032518785256e-06,
                7.338209805224048e-07,
                1.3709572068522336e-06,
                NaN
            ],
            [
                8.315279285351409e-07,
                4.450852111135988e-07,
                9.422448185510695e-07,
                6.475950297993789e-07,
                1.0677029973192638e-06,
                2.6995784182140636e-07,
                1.2098653950692178e-06,
                1.5534971990126997e-06,
                6.475950298011458e-07,
                8.315283250371857e-07
            ],
            [
                1.5534979397740895e-06,
                8.315279285351409e-07,
                4.222833444590791e-06,
                1.2098659719788098e-06,
                NaN,
                1.7603427936335396e-06,
                7.338213304363436e-07,
                3.288749849498565e-06,
                1.9947292459265734e-06,
                6.1441746020359e-06
            ],
            [
                0.9999989969857939,
                0.9999967112493735,
                0.9999938558246819,
                1.0677026154806063e-06,
                0.9999952149032336,
                0.9999975938970903,
                0.9999960330141066,
                0.9999910603069249,
                0.9999962733593929,
                0.9999987901341741
            ],
            [
                NaN,
                5.715005832895975e-07,
                NaN,
                1.5534973842076057e-06,
                7.338207180898968e-07,
                NaN,
                5.04347468323289e-07,
                NaN,
                NaN,
                5.422217677152175e-06
            ]
        ]
    },
    {
        "q_id": "9878_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998724809116,
                0.9999999006880668,
                0.9999999468421883,
                1.0,
                0.9999985406241282,
                0.9999999530883452,
                0.9999999006881497,
                0.9999998802069587,
                0.999999802494586,
                0.999999802494633
            ],
            [
                0.9999998724810027,
                0.999999391641036,
                0.9999984465015062,
                0.9999999176674357,
                0.9999997300422548,
                0.9999991684718738,
                0.9999994631249323,
                0.9999967112513319,
                0.9999999273418615,
                0.9999988634357483
            ],
            [
                0.9999998461826038,
                0.9999999434137907,
                0.9999995549151076,
                0.9999998724809116,
                0.9999990577556312,
                0.9999998362623138,
                0.9999969105040849,
                0.999997273528758,
                0.9999999317439139,
                0.9999995262094987
            ],
            [
                0.9999999226557317,
                0.9999998257022045,
                0.9999998461826222,
                0.999999802494586,
                0.9999997897567091,
                0.9999994284994169,
                0.9999995549150013,
                0.9999996533674617,
                0.9999999176675338,
                0.9999992661792826
            ],
            [
                0.9999988634361549,
                0.9999992188514837,
                0.9999982396574175,
                0.9999981261241713,
                0.9999993916408911,
                0.9999997761971583,
                0.9999998461826956,
                0.9999998024946567,
                0.9999993524052794,
                0.9999999123574419
            ],
            [
                0.9999998724810027,
                0.9999983463104157,
                0.9999999226557224,
                0.9999998802068873,
                0.9999981261243948,
                0.99999976176309,
                0.9999998642566866,
                0.999999352405125,
                0.9999998461826956,
                0.9999998144609203
            ],
            [
                0.9999964991460073,
                0.9999998257020798,
                0.9999994631251884,
                0.9999998257022046,
                0.9999995818811275,
                0.9999997761970248,
                0.9999997761971049,
                0.9999998555020136,
                0.9999996940977003,
                0.9999977396757044
            ],
            [
                0.9999992188515767,
                0.999999581881277,
                0.9999997617631469,
                0.9999991684718739,
                0.9999998942829854,
                0.9999994956527725,
                0.9999980052709941,
                0.9999990577551824,
                0.9999999226557593,
                0.9999992188515767
            ],
            [
                0.9999997617631186,
                0.9999999176675338,
                0.9999998555020307,
                0.9999998362623528,
                0.9999988634357481,
                0.9999996940976273,
                0.9999998461826956,
                0.999999712631481,
                0.9999991148433867,
                0.9999998724808964
            ],
            [
                0.9999977396748962,
                0.9999998461826589,
                0.9999991684719727,
                0.9999993106388727,
                0.9999993106391191,
                0.9999990577556314,
                0.9999942280792881,
                0.9999994956527726,
                0.9999993524048932,
                0.9999995262092163
            ],
            [
                0.9999984465018761,
                0.9999999500628513,
                0.9999952149066539,
                0.999998239656998,
                0.999999631011416,
                0.999999922655833,
                0.9999994956527725,
                0.9999999067051165,
                0.9999998555019963,
                0.9999996940977367
            ],
            [
                0.999999746398073,
                0.9999998642566704,
                0.9999996940978826,
                0.9999999006880431,
                0.999999939764251,
                0.9999998362622747,
                0.9999997126315153,
                0.9999999434137434,
                0.999999057755519,
                0.9999999176674454
            ],
            [
                0.9999998257021214,
                0.999999922655833,
                0.9999995818811774,
                0.9999999226557316,
                1.0,
                0.999999825702059,
                0.9999995262093858,
                0.9999999273418355,
                0.9999997761971315,
                0.9999994284992808
            ],
            [
                0.9999996533674617,
                0.9999994631249963,
                0.9999994284996213,
                0.9999991684715762,
                0.9999995262092165,
                0.99999916847227,
                0.9999994631249962,
                0.9999990577557435,
                0.9999987901337407,
                0.9999992188515767
            ],
            [
                0.999999266179195,
                0.9999987121044782,
                0.9999993524052794,
                0.9999996072136594,
                0.9999999067049831,
                0.9999993106387906,
                0.999999746398073,
                0.999999218851577,
                0.9999967112513304,
                0.9999997761970247
            ],
            [
                0.9999995818811773,
                0.9999996743686645,
                0.9999998257021006,
                0.999999825702163,
                0.9999999176675535,
                0.9999998802069159,
                0.9999995818813269,
                0.9999995818810776,
                0.9999994284995534,
                0.9999996533674617
            ],
            [
                2.9023109472244114e-06,
                6.475947982037486e-07,
                6.475949526003845e-07,
                7.338209805224048e-07,
                6.9622595696935874e-06,
                2.260324567337161e-06,
                1.0677027427525368e-06,
                1.7603430034743913e-06,
                1.5534971990169383e-06,
                1.3709568799879344e-06
            ],
            [
                0.9999996072137062,
                0.9999991148431755,
                0.9999998874647709,
                0.9999952149060809,
                0.9999996072138467,
                0.9999998257020799,
                0.9999998802069874,
                0.9999994284996896,
                0.9999986290426307,
                0.9999996940978462
            ],
            [
                0.9999996310113279,
                0.99999992265575,
                0.9999997463980125,
                0.999999802494586,
                0.9999998144608319,
                0.9999999006881142,
                0.9999996940978461,
                0.999999917667475,
                0.9999998642566219,
                0.9999996940978096
            ],
            [
                0.9999996310113719,
                0.9999994631251884,
                0.9999989322975122,
                0.9999998874648246,
                0.9999999006879957,
                0.9999999176675436,
                0.9999998144609203,
                0.9999999358793715,
                0.9999988634360187,
                0.9999999500627739
            ],
            [
                0.9999998024947038,
                0.999999789756659,
                0.9999983463108093,
                0.9999993106388726,
                0.999999218851856,
                0.9999978766220452,
                0.9999987121041711,
                0.9999989969855538,
                0.9999987901346057,
                0.9999998555020136
            ],
            [
                0.9999997897566592,
                0.9999997897565588,
                0.9999996940978826,
                0.9999994956524718,
                0.9999996743687035,
                0.9999994631251883,
                0.9999999123575987,
                0.9999998144608983,
                0.999999887464932,
                0.9999998024946566
            ],
            [
                0.9999984465024315,
                0.9999996533674202,
                0.9999999176675142,
                0.9999998024947038,
                0.9999998942829225,
                0.999999352405125,
                0.9999998724809723,
                0.9999999358793715,
                0.9999998257021837,
                0.9999998555019274
            ],
            [
                0.9999998461826588,
                0.9999998461827322,
                0.9999980052693301,
                0.9999997300422548,
                0.9999996072137999,
                0.999999631011372,
                0.9999995818813767,
                0.9999987121047854,
                0.9999991148430705,
                0.9999997761971315
            ],
            [
                0.9999993916406735,
                0.9999978766212867,
                0.9999997463980125,
                0.9999970976869812,
                1.0,
                0.9999977396748959,
                0.9999998802069731,
                0.9999993524054339,
                0.9999998555020481,
                0.9999997126315496
            ],
            [
                0.9999997300423192,
                0.999999581881277,
                0.999999168472171,
                0.9999996940977731,
                0.9999998461826222,
                0.9999998144608319,
                0.9999994631249322,
                0.9999998642567028,
                0.999999114842648,
                0.9999995262094423
            ],
            [
                0.9999995262093292,
                0.999997097688017,
                0.999999631011548,
                0.999998629042631,
                0.9999993916408186,
                0.9999995262093857,
                0.9999997617630617,
                0.9999985406243019,
                9.422444815679433e-07,
                0.9999998724808963
            ],
            [
                0.9999994631250604,
                0.9999994631250604,
                0.9999994631250605,
                0.9999996743687422,
                0.9999998555020307,
                0.9999997897565839,
                0.9999998144609646,
                0.9999999273417922,
                0.9999997897567343,
                0.999999789756634
            ],
            [
                0.9999998144608098,
                0.9999999397643011,
                0.9999995549148422,
                0.9999999176675731,
                0.9999999317439302,
                0.9999997617630901,
                0.9999997761971849,
                0.9999989969854342,
                0.9999974387168761,
                0.9999962733611647
            ],
            [
                0.9999999530883563,
                0.9999997761970248,
                0.9999999468421567,
                0.9999996743687422,
                0.9999998257020591,
                0.9999999067051054,
                0.9999998555019618,
                0.9999999226557131,
                0.9999996743688199,
                0.9999999226557592
            ],
            [
                0.9999999226557409,
                0.9999998724809723,
                0.9999997463980427,
                0.9999997126313784,
                0.9999999176674454,
                0.9999999067051165,
                0.9999987121050926,
                0.9999993524049707,
                0.9999978766222991,
                0.9999994284995533
            ],
            [
                0.999999814460876,
                0.9999997300422869,
                0.9999996072139404,
                0.9999994284995533,
                0.9999997617630049,
                0.9999994284997576,
                0.9999998555020481,
                0.9999999067050832,
                0.9999998362622358,
                0.9999999006881378
            ],
            [
                0.9999993106387904,
                0.9999995818810777,
                0.9999998461826771,
                0.9999994631250605,
                0.9999985406237795,
                0.9999994631251242,
                0.9999993916406735,
                0.9999985406234319,
                0.9999997897567343,
                0.9999997617630049
            ],
            [
                0.9999999226557961,
                0.9999998024947273,
                0.9999993106392013,
                0.999999746398073,
                0.9999981261237247,
                0.9999994956526523,
                0.9999994284992809,
                0.999998346310415,
                0.999999730042255,
                0.999999746398073
            ],
            [
                0.9999999226557685,
                0.9999999123574733,
                0.9999992188513903,
                0.9999999530883283,
                0.9999999634651443,
                0.9999994956526521,
                0.9999999006880904,
                0.9999999586006098,
                0.9999999634652009,
                1.0
            ],
            [
                0.9999998874647307,
                0.9999994956527123,
                0.9999995818811773,
                0.9999998724809875,
                0.9999992661787576,
                0.999999825702163,
                0.9999995549150544,
                0.9999997463982241,
                0.9999996072138,
                0.999999631011416
            ],
            [
                1.0,
                0.999999900687984,
                0.9999997126315496,
                0.9999998802069731,
                1.0,
                1.0,
                0.9999998461826956,
                0.9999998257021214,
                0.9999999273417663,
                1.0
            ],
            [
                0.999999631011548,
                0.9999996533672137,
                0.9999998555019447,
                0.9999995549149482,
                0.9999997761971317,
                0.9999996533672963,
                0.9999999176674456,
                0.9999998024946095,
                0.9999998802068873,
                0.9999996743688975
            ],
            [
                0.9999998461826589,
                0.9999996940978096,
                0.9999997617630333,
                0.9999997897567091,
                0.9999995818810777,
                0.9999998362622358,
                0.999999887464838,
                0.9999998874647306,
                0.9999983463096269,
                0.9999998874647843
            ],
            [
                0.9999997126313441,
                0.99999926617867,
                0.9999996310114599,
                0.999999887464838,
                0.9999995262092728,
                0.9999998461826771,
                0.9999998144608541,
                0.9999997897567343,
                0.9999998024947038,
                0.9999988634360194
            ],
            [
                0.9999993524052795,
                0.9999993106386262,
                0.9999999226557593,
                0.9999996072139403,
                0.9999996072136126,
                0.9999996743688975,
                0.9999993106387085,
                0.9999998024947037,
                0.9999992661788449,
                0.9999997300421904
            ],
            [
                0.9999998942829476,
                0.9999988634357484,
                0.9999992661791075,
                0.9999993916410361,
                0.9999994284996214,
                0.9999999067051055,
                1.0,
                0.9999998802069302,
                0.9999998802069017,
                0.9999985406237801
            ],
            [
                0.9999994284992814,
                0.9999997897566089,
                0.9999998362623332,
                0.9999998942829477,
                0.9999999358793944,
                0.9999999317439384,
                0.9999990577549577,
                0.9999998642567028,
                0.9999997463981031,
                0.9999987121046321
            ],
            [
                0.9999997126314125,
                0.9999997126315154,
                0.9999996940978826,
                0.9999997617629766,
                0.9999999067051499,
                0.9999994956527124,
                0.9999997300421262,
                0.9999989969857932,
                0.9999998362622943,
                0.9999997126314126
            ],
            [
                0.9999996072136594,
                0.9999997300423191,
                0.9999996533674617,
                0.9999996310114159,
                0.9999998555019275,
                0.9999996940977003,
                0.9999997761971317,
                0.9999994631251884,
                0.9999996310116359,
                0.9999999358794173
            ],
            [
                0.9999999006880195,
                0.999999789756634,
                0.9999996743688586,
                0.9999999358794249,
                0.9999999317440197,
                0.9999997300421904,
                0.999999730042094,
                0.9999999530883452,
                0.999999428499417,
                0.9999998555020481
            ],
            [
                0.9999998642567189,
                0.9999978766215402,
                0.999999653367255,
                0.9999998642566866,
                0.9999992661790197,
                0.9999981261237241,
                0.9999999176675436,
                0.9999997300421584,
                0.9999999123575882,
                0.9999997761972116
            ],
            [
                0.999999631011592,
                0.9999997300422548,
                0.9999997617630049,
                0.9999999123574419,
                0.9999996533673378,
                0.9999998724808964,
                0.9999995549150544,
                0.9999999500627917,
                0.9999991148428591,
                0.9999998461826223
            ],
            [
                0.9999981261237242,
                0.9999999006880786,
                0.9999982396572079,
                0.9999994956524118,
                0.9999996940978096,
                0.9999957771655524,
                0.999999730042287,
                0.9999991684715762,
                0.9999990577554068,
                0.9999997126313783
            ],
            [
                0.9999997617630901,
                0.9999999176675436,
                0.9999995818812273,
                0.9999996940978098,
                0.9999998144608762,
                0.9999996743687034,
                0.9999998642567028,
                0.9999997463980729,
                0.9999997463982242,
                0.9999998724808964
            ],
            [
                0.9999998362623138,
                0.9999998555019963,
                0.999997876621539,
                0.9999995262095551,
                0.9999991148431756,
                0.9999999273418962,
                0.9999994631250604,
                0.9999994631248044,
                0.9999995262094423,
                0.9999995549149482
            ],
            [
                0.9999998144609645,
                0.9999996533672965,
                0.9999998461826222,
                0.9999970976880185,
                0.999999825702163,
                0.9999995262093858,
                0.9999995818813269,
                0.9999987121044782,
                0.9999996533673791,
                0.9999994956524119
            ],
            [
                0.9999999176675535,
                0.9999969105044498,
                0.999998346311006,
                0.9999994956524717,
                0.9999998724809572,
                0.9999997300422548,
                0.9999997617631184,
                0.9999987901343168,
                0.9999997761970248,
                0.9999987901346055
            ],
            [
                0.9999998461826038,
                0.999999581881277,
                0.9999997761971583,
                0.9999998555019618,
                0.9999997300421584,
                0.9999998461827139,
                0.9999998642567351,
                0.9999998024945624,
                0.9999993524048932,
                0.9999998362623138
            ],
            [
                0.9999996533674617,
                0.9999999273418961,
                0.9999974387165709,
                0.9999991684718738,
                0.9999998461826222,
                0.9999994956524718,
                0.9999997617630333,
                0.9999998642566219,
                0.999999894282935,
                0.9999993524053566
            ],
            [
                0.9999998642566219,
                0.9999996072137062,
                0.9999994631249963,
                0.999998540623606,
                0.9999996533673791,
                0.9999998362623138,
                0.9999998642567028,
                0.9999995549147891,
                0.9999997300421583,
                0.9999997897565588
            ],
            [
                0.999999057755182,
                0.999999730042287,
                0.9999997126313441,
                0.9999996743687811,
                0.9999994284995533,
                0.9999996940977002,
                0.9999998362623334,
                0.9999998555019791,
                0.9999997617630617,
                0.9999997617630049
            ],
            [
                0.9999987901338849,
                0.9999998257022045,
                0.9999998144609424,
                0.9999995818812771,
                0.9999998461826222,
                0.999999631011328,
                0.9999999123575046,
                0.9999990577554065,
                0.9999998461827139,
                0.9999998257021838
            ],
            [
                0.9999995818813269,
                0.9999984465020614,
                0.9999985406239552,
                0.9999994631249963,
                0.9999993106388728,
                0.9999983463100217,
                0.9999996940976272,
                0.9999986290426311,
                0.9999970976873263,
                0.9999998024946566
            ],
            [
                1.0,
                0.9999999468421503,
                0.9999998942828973,
                0.9999998942829098,
                0.999999554914736,
                1.0,
                0.9999999176675632,
                0.9999998555019275,
                0.9999998555020135,
                0.9999996743688975
            ],
            [
                0.9999995549148952,
                0.999999554914736,
                0.9999999006879957,
                0.9999987901338852,
                0.9999998874648245,
                0.9999998144608319,
                0.9999987901343171,
                0.999999789756609,
                0.9999994284996213,
                0.9999998024946566
            ],
            [
                0.9999998362622357,
                0.9999997126315496,
                0.9999987121047853,
                0.9999999176675535,
                1.0,
                0.9999997617631184,
                1.0,
                0.9999999273418616,
                0.9999997761972116,
                0.9999999123574838
            ],
            [
                0.9999999226557132,
                0.9999994956527725,
                0.9999996743687422,
                0.9999998461826038,
                0.9999998724809116,
                0.9999997463982242,
                0.9999997300421262,
                0.9999996072139404,
                0.9999998144608541,
                0.9999998024947272
            ],
            [
                0.9999993524052793,
                0.9999978766217922,
                0.9999997761971315,
                0.9999997126313783,
                0.9999994956527724,
                0.9999998642566543,
                0.999999746398073,
                0.9999990577554068,
                0.9999993916409637,
                0.9999998024947037
            ],
            [
                0.9999998642566704,
                0.9999994956525319,
                0.9999997617630617,
                0.9999999226557593,
                0.9999996940976639,
                0.9999994956526522,
                0.999999931743979,
                0.9999998144608098,
                0.9999999358793792,
                0.999999631011592
            ],
            [
                0.9999996533674204,
                0.9999996310113279,
                0.999999581881277,
                0.9999999500627976,
                0.9999993106387084,
                0.9999998942830737,
                0.9999997761970248,
                0.999999674368781,
                0.9999992661789323,
                0.9999997617630617
            ],
            [
                0.9999997126314468,
                0.999999554914736,
                0.9999994956525321,
                0.9999997617631184,
                0.9999983463096269,
                0.9999980052707561,
                0.9999995818812272,
                0.9999997126315154,
                0.9999995549147891,
                0.9999997761970516
            ],
            [
                0.9999998724809268,
                0.9999999176674454,
                0.9999999500628036,
                0.9999999586006146,
                0.9999998802069445,
                0.9999999317440035,
                0.9999995262093294,
                0.9999998724808964,
                0.9999999358793867,
                0.9999999317439546
            ],
            [
                1.0,
                0.9999998555020135,
                0.9999996940978098,
                0.9999999067051388,
                0.9999997617631753,
                0.9999998802069445,
                0.9999991684720719,
                0.9999994631248044,
                0.9999997897566841,
                0.9999987121047852
            ],
            [
                0.9999998724810027,
                0.9999993106387082,
                0.9999996940978826,
                0.9999997617629764,
                0.9999997761972116,
                0.9999997897566089,
                0.9999997126313098,
                0.999999906705061,
                0.9999996940976638,
                0.9999999559305787
            ],
            [
                0.9999998874647575,
                0.9999993106391194,
                0.9999997617630333,
                0.999999391640746,
                0.9999994284997578,
                0.999999495652532,
                0.9999998257020798,
                0.9999997617630901,
                0.9999995262092163,
                0.9999992661791075
            ],
            [
                0.9999997761971582,
                0.9999998555020481,
                0.999997097686635,
                0.9999998942829854,
                0.9999999176674749,
                0.9999998642566704,
                0.9999998461827139,
                1.0,
                0.9999996743688586,
                0.9999984465020614
            ],
            [
                0.9999991684717748,
                0.999999266178845,
                1.0,
                0.9999991684722701,
                0.9999999500628393,
                0.9999989322972578,
                0.999999218851856,
                0.9999999176675632,
                0.9999997761970516,
                0.999999495652592
            ],
            [
                0.9999999176675634,
                1.0,
                0.9999999317439384,
                1.0,
                0.9999999123575255,
                1.0,
                0.9999998461826588,
                0.9999994284994851,
                0.9999996743687422,
                0.999995214905512
            ],
            [
                0.9999998555019275,
                0.9999998024946095,
                0.9999998024946095,
                0.9999996310115039,
                0.9999996743687422,
                0.9999990577552945,
                0.9999993916411811,
                0.9999995262092729,
                0.9999997300423192,
                0.9999995818813767
            ],
            [
                0.999999802494633,
                0.9999996940976273,
                0.9999998555019963,
                0.9999997617630334,
                0.9999998642566219,
                0.9999996743688586,
                0.9999999358793639,
                0.9999998724809875,
                0.9999995262094988,
                0.999999653367503
            ],
            [
                0.9999986290424668,
                0.9999986290429574,
                0.9999999317439464,
                0.9999992661790199,
                0.9999994631251883,
                0.9999998802069587,
                0.9999991684715763,
                0.9999998555019447,
                0.9999998024946566,
                0.9999967112497625
            ],
            [
                0.999999114842648,
                0.9999996310116359,
                0.9999997463980125,
                0.9999999317440034,
                0.9999995818813768,
                0.9999998024945624,
                0.9999985406237802,
                0.9999995818812272,
                0.9999999317440116,
                0.9999998642566704
            ],
            [
                0.9999995262092728,
                0.9999998024945624,
                0.9999990577554067,
                0.9999994956523516,
                0.9999999226557961,
                0.9999999226558054,
                0.9999998724809419,
                0.9999994631247403,
                0.999999653367379,
                0.9999998362623723
            ],
            [
                0.9999998461826222,
                0.9999999123574941,
                0.9999993106391193,
                0.9999997300423192,
                0.9999997761970782,
                0.9999994284996213,
                0.999988521227805,
                0.999999607213753,
                0.9999977396757036,
                0.9999992661791948
            ],
            [
                0.9999992661792824,
                0.9999962733598321,
                0.999995214904946,
                0.9999977396748964,
                0.9999997617631753,
                0.9999998257020799,
                0.9999921107383771,
                0.9999999317440279,
                0.9999989969859128,
                0.9999999006881259
            ],
            [
                0.9999999500627739,
                0.9999989322966217,
                0.999998790134173,
                0.9999998555019447,
                0.9999998642566704,
                0.9999994956526521,
                0.9999983463106125,
                0.9999998724809267,
                0.9999967112505476,
                0.999999789756609
            ],
            [
                0.9999977396762428,
                0.9999993524052021,
                0.9999993524050477,
                0.9999992188516698,
                0.9999992188519492,
                0.99999787662154,
                0.9999996310114599,
                0.9999991684720718,
                0.9999994956523515,
                0.9999994284996895
            ],
            [
                0.9999997126314469,
                0.999999789756659,
                0.999999730042094,
                0.9999997617631753,
                0.999999674368781,
                0.999999789756634,
                0.9999997897565588,
                0.9999996072137999,
                0.9999998724809875,
                0.9999993106392014
            ],
            [
                0.999999802494586,
                0.9999998555019619,
                0.9999998257022045,
                0.9999999530883731,
                0.9999999273418876,
                0.999999631011328,
                0.9999999273418355,
                0.9999999397643083,
                0.999999906705061,
                0.999999927341853
            ],
            [
                0.9999999273418183,
                0.9999996533672963,
                0.9999999434137705,
                0.9999997463981032,
                0.9999999358793409,
                0.999999631011328,
                0.9999998802069017,
                0.9999997126314811,
                0.9999998257021628,
                1.0
            ],
            [
                0.9999994956526522,
                0.9999997126314811,
                0.9999998724809419,
                0.9999998461826954,
                0.9999991148426479,
                0.9999997617631469,
                0.9999999226557131,
                0.9999962733598332,
                0.9999996072137999,
                0.9999988634357481
            ],
            [
                0.9999998642567028,
                0.9999994284996895,
                0.9999993524054337,
                0.9999916019279871,
                0.9999996743687422,
                0.9999999226558146,
                0.9999986290432844,
                0.999998629043121,
                0.999999931743979,
                0.9999993524050478
            ],
            [
                0.9999993106387907,
                0.999997273530059,
                0.9999994284995533,
                0.9999995549147892,
                0.9999994631248044,
                0.9999997463980729,
                0.9999972735307087,
                0.9999998724809267,
                0.9999996072137999,
                0.999998629043285
            ],
            [
                0.9999999176675632,
                0.9999995549149483,
                0.999999922655833,
                0.9999999317439465,
                0.9999999123575778,
                0.9999997126313783,
                0.9999999358793944,
                1.0,
                0.9999998724809267,
                1.0
            ],
            [
                0.9999997617630901,
                0.9999997463980125,
                0.9999999500628155,
                0.9999997300422226,
                0.9999996310115918,
                0.9999999176675338,
                0.9999996940978462,
                0.9999999006881259,
                0.999999802494633,
                0.9999995818812273
            ],
            [
                0.999999218851856,
                0.999999428499417,
                0.9999986290431211,
                0.9999999176675338,
                0.9999977396762432,
                0.999999526209499,
                0.9999998362622358,
                0.9999999273418096,
                1.0,
                0.9999998642567028
            ],
            [
                0.9999991148427535,
                0.9999997617631754,
                0.9999992188516701,
                0.9999997761971317,
                0.9999997300422226,
                0.9999998461826956,
                0.9999996940976638,
                0.9999996533672963,
                0.9999989969859123,
                0.9999995818812273
            ],
            [
                0.9999996940977367,
                0.9999999067049831,
                0.9999983463106122,
                0.9999998642567351,
                0.999999855501979,
                0.999998712104785,
                0.9999997300421261,
                0.999999391641036,
                0.9999998642567351,
                0.9999998461826588
            ],
            [
                0.999997876622299,
                0.9999997300422226,
                0.9999983463106129,
                0.9999998024947037,
                0.9999998144609203,
                0.9999995818812771,
                0.9999997300423192,
                0.9999967112497649,
                0.9999997617630617,
                0.9999997463980427
            ],
            [
                0.9999993106391193,
                0.9999997126314468,
                0.9999995262094987,
                0.9999998362623529,
                0.9999991684716757,
                0.9999993916406735,
                0.9999994631248044,
                0.9999999123575882,
                0.999999495652592,
                0.9999978766215402
            ],
            [
                0.9999998642566704,
                0.9999983463102184,
                0.9999999530883452,
                0.9999997463982241,
                0.9999991148427539,
                0.9999991684716754,
                0.9999998802069159,
                0.9999992188512973,
                0.9999998642567028,
                0.9999998724809724
            ],
            [
                0.9999997126314811,
                0.9999995549150544,
                0.9999995549151075,
                0.9999998257020798,
                0.9999993524052021,
                0.9999994631251882,
                0.999998540623606,
                0.9999990577556312,
                0.9999997617629766,
                0.9999996743688199
            ],
            [
                0.9999998144609645,
                0.9999998724809268,
                0.9999992188518559,
                0.9999997463982241,
                0.9999998942830737,
                0.9999997761970247,
                0.9999996310114599,
                0.9999996940976273,
                0.9999997617631752,
                0.9999997617631469
            ],
            [
                0.9999996940977367,
                0.9999987121050921,
                0.9999978766205274,
                0.9999997300421904,
                0.9999998874647977,
                0.9999980052695662,
                0.9999982396559478,
                0.9999997300422548,
                0.9999994631248043,
                0.9999910603037034
            ],
            [
                0.9999997463981636,
                0.9999996940977368,
                0.9999996533672137,
                0.9999999123575046,
                0.9999994956524116,
                0.9999999176675436,
                0.9999988634361545,
                0.999999802494633,
                0.9999999176674357,
                0.9999984465018767
            ],
            [
                0.9999997617631753,
                0.999999526209386,
                0.999999266178845,
                0.9999994956525922,
                0.9999993916411087,
                0.9999994284995535,
                0.9999991148430701,
                0.9999986290427947,
                0.9999994284994852,
                0.9999989322968766
            ],
            [
                0.9999999123574836,
                0.9999998802069302,
                0.9999999530883508,
                0.9999998642567028,
                0.9999999500628453,
                0.9999999530883787,
                0.999999939764258,
                0.9999998724810027,
                0.9999999006880075,
                0.9999995549150543
            ],
            [
                0.999998540623432,
                0.9999994956527725,
                0.9999997761972116,
                0.9999997617631186,
                0.9999993524052022,
                0.9999998724809875,
                0.9999999006880312,
                0.9999997300422548,
                0.9999999006881378,
                0.9999998724808963
            ],
            [
                0.9999991684719727,
                0.9999999006880076,
                0.9999998024947273,
                0.9999996940976273,
                0.9999999317440035,
                0.9999998555019274,
                0.9999998461826772,
                0.999999495652532,
                0.9999999176675142,
                0.999999581881277
            ],
            [
                0.9999999434137098,
                0.9999999176675142,
                0.9999999273418269,
                0.9999993106388727,
                0.9999999226557593,
                0.9999997300420939,
                0.9999999273418702,
                0.9999998874647307,
                1.0,
                0.999999887464905
            ],
            [
                0.9999996743686257,
                0.9999992661790196,
                0.9999999006881259,
                0.9999996743688586,
                1.0,
                0.9999999006879721,
                0.9999990577555188,
                0.9999984465026165,
                0.9999999226557685,
                0.9999997300423192
            ],
            [
                0.9999995818813768,
                0.9999995262092729,
                0.9999998461826406,
                0.9999985406234319,
                0.9999996310113719,
                0.9999996072138467,
                0.9999996310114159,
                0.9999993524050479,
                0.9999996940976639,
                0.9999998362622552
            ],
            [
                0.9999995549149482,
                0.9999975938976615,
                0.9999998362622747,
                0.9999852610233756,
                0.9999996940978461,
                0.9999990577554069,
                0.9999991148430702,
                0.9999992188514834,
                0.9999988634362902,
                0.9999996310115039
            ],
            [
                0.99999976176309,
                0.9999998555019447,
                0.9999988634361551,
                0.9999980052698048,
                0.9999987121041712,
                0.9999998802069587,
                0.9999991684715763,
                0.999998346310021,
                0.9999962733602755,
                0.9999999273417923
            ],
            [
                0.999999789756659,
                0.9999999317439627,
                0.9999998874648112,
                1.0,
                0.9999999559306101,
                0.9999998942830485,
                0.9999999226557408,
                0.9999998555020309,
                0.9999999123575987,
                0.999999887464905
            ],
            [
                0.9999998642566705,
                0.9999999067050943,
                0.9999989322971308,
                0.9999996533672965,
                0.9999998362623138,
                0.9999999434138043,
                0.9999999273417749,
                0.9999997897567091,
                0.9999996072137063,
                0.9999993106387904
            ],
            [
                0.9999998642566704,
                0.9999999067050053,
                0.9999998024946095,
                0.9999997761971582,
                0.9999998024947038,
                0.999999352404971,
                0.9999998555019618,
                0.9999998024947037,
                0.9999998362622748,
                0.9999998555019446
            ],
            [
                0.9999998144608983,
                0.9999980052707552,
                0.9999994284996895,
                0.9999998802069302,
                0.9999999123574838,
                0.9999967112493708,
                0.9999970976883641,
                0.9999998461826405,
                0.9999998257021837,
                0.9999993524053565
            ],
            [
                0.9999997300423192,
                0.9999996072137999,
                0.9999992661786701,
                0.9999997300421262,
                0.9999996743686645,
                0.9999997761971849,
                0.9999998724809116,
                0.999999674368781,
                0.9999997300422548,
                0.9999992188516696
            ],
            [
                0.9999996310113279,
                0.999999922655787,
                0.9999998724809116,
                0.9999999123575255,
                0.9999998144609645,
                0.9999998461827138,
                0.9999998642566866,
                0.9999998642566866,
                1.0,
                0.9999998642566381
            ],
            [
                0.9999997617629764,
                0.9999999559305733,
                0.9999998642567353,
                0.9999997126313098,
                0.999999855502048,
                0.999999495652592,
                0.9999997300423192,
                0.9999998257021837,
                0.9999999067050276,
                0.9999996743688586
            ],
            [
                0.9999995262094422,
                0.9999999273417662,
                1.0,
                0.9999999273418528,
                0.9999997617629764,
                0.999999939764251,
                0.9999999123575151,
                1.0,
                0.999999554914736,
                0.9999995549147359
            ],
            [
                0.9999998802069587,
                0.9999999176675632,
                0.9999991148428591,
                0.9999999176675239,
                0.9999998942829098,
                0.9999998461826771,
                0.9999997463980729,
                0.9999996072137999,
                0.9999952149038001,
                0.9999999559305681
            ],
            [
                0.9999988634358846,
                0.9999997300421904,
                0.9999997463980427,
                0.9999960330131458,
                0.9999999067051276,
                0.9999987901343178,
                0.999999789756659,
                0.9999991148429647,
                0.9999998555019963,
                0.9999980052709937
            ],
            [
                0.9999995818812273,
                0.9999998724808963,
                0.9999999123575255,
                0.999999887464932,
                0.9999997126314811,
                0.9999999006881259,
                0.9999998802069159,
                0.9999997126314126,
                0.9999995262092163,
                0.9999998642566866
            ],
            [
                0.9999995818814266,
                0.9999997897566841,
                0.9999993524052022,
                0.9999999611088672,
                0.999999789756634,
                0.9999993106390371,
                0.9999999067050054,
                0.9999995549148422,
                0.9999998461827322,
                0.9999993916410362
            ],
            [
                0.9999997617631186,
                0.9999997897567092,
                0.9999997463980729,
                0.9999997761970781,
                0.9999998024946332,
                0.9999998724810027,
                0.9999991684720726,
                0.9999998024947273,
                0.9999996940978098,
                0.999998996985434
            ],
            [
                0.9999993916409636,
                0.9999994956523517,
                0.9999996310116359,
                0.9999989322967491,
                0.9999998642566866,
                0.9999999123575151,
                0.9999994956524118,
                0.9999998144609203,
                0.9999987121041712,
                0.9999998257021421
            ],
            [
                0.9999995262095552,
                0.9999997617630901,
                0.9999995818811276,
                0.9999981261237247,
                0.9999978766217921,
                0.9999993106387083,
                0.9999997897565588,
                0.9999989969859123,
                0.9999998802068873,
                0.999999554914736
            ],
            [
                0.9999998461826956,
                0.9999992188518562,
                0.9999981261239487,
                0.9999997617631469,
                0.9999998802069731,
                0.9999996940976273,
                0.9999988634366966,
                0.9999996533672552,
                0.9999969105040825,
                0.9999999176674357
            ],
            [
                0.9999997126314811,
                0.9999997126315153,
                0.9999997617631754,
                0.9999997463981939,
                0.9999999006880312,
                0.9999998942830233,
                0.9999987121043247,
                0.9999975938970891,
                0.9999995818811773,
                0.9999998024946566
            ],
            [
                0.9999999123574941,
                0.9999995549148951,
                0.9999996310114599,
                0.9999991148432811,
                0.9999998362622943,
                0.9999997463982241,
                0.9999996533674204,
                0.999998005269329,
                0.9999998362622944,
                0.9999987901337404
            ]
        ]
    },
    {
        "q_id": "10293_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                6.82560779249779e-08,
                1.0677028700363782e-06,
                1.2098661161982042e-06,
                1.8553910183674878e-07,
                1.5534981249496567e-06,
                9.422443692527585e-07,
                2.382368815932174e-07,
                1.067703251864202e-06,
                5.715005832886879e-07,
                2.699578740032504e-07
            ],
            [
                3.9278629391427843e-07,
                3.9278629391427843e-07,
                3.9278615344267634e-07,
                6.475949526020042e-07,
                8.76424013786396e-08,
                1.3709575337159875e-06,
                5.04347287955046e-07,
                2.1024336609874897e-07,
                3.4663262111182307e-07,
                4.139940508508409e-08
            ],
            [
                0.9999988634361549,
                0.9999989969857928,
                0.9999996310113719,
                0.9999997761970781,
                0.999998239657207,
                0.9999949062968239,
                0.9999982396567879,
                0.9999996310114598,
                0.9999991684721709,
                0.9999982396563681
            ],
            [
                1.209866260432471e-06,
                8.315279285370317e-07,
                8.315284241650899e-07,
                2.2603240284371276e-06,
                1.0677027427569065e-06,
                5.715006514167015e-07,
                1.760343003481596e-06,
                1.7603425837903113e-06,
                2.561281600076256e-06,
                6.962254589914941e-06
            ],
            [
                0.9999997126314125,
                0.9999998802069302,
                0.9999975938968013,
                0.9999987121046313,
                0.9999957771645439,
                0.9999934595596598,
                8.764247451307293e-08,
                0.9999990577555187,
                0.9999996743686257,
                0.9999996940978825
            ],
            [
                2.699577452775239e-07,
                8.764241182641775e-08,
                2.382370235933104e-07,
                3.466326624336003e-07,
                5.043473480777865e-07,
                1.3709575337016483e-06,
                6.47595107001401e-07,
                8.315277302819205e-07,
                1.3709575337125585e-06,
                1.4449800373118268e-07
            ],
            [
                1.7603430034867993e-06,
                0.000626334257685222,
                7.338207180898968e-07,
                1.0677032518814388e-06,
                6.475949526020042e-07,
                3.05902263391829e-07,
                4.450848927658745e-07,
                2.2603234895372223e-06,
                1.5534983101644536e-06,
                1.0677028700422047e-06
            ],
            [
                0.9999984465024314,
                0.9999996072138935,
                0.999997438717485,
                0.9999996743688199,
                0.9999996072137999,
                0.9999974387168746,
                0.9999977396757037,
                0.9999995262094422,
                0.9999992188517628,
                0.9999974387171799
            ],
            [
                0.9999960330136158,
                0.9999964991447534,
                1.275190428875671e-07,
                5.315789407685159e-08,
                0.9999945777816805,
                0.9999955048200346,
                0.9999969105044489,
                0.9999978766220443,
                1.4449800373118268e-07,
                1.4449805540763184e-07
            ],
            [
                5.715003107767143e-07,
                9.422445939054222e-07,
                3.0590215399183813e-07,
                2.3823685319244518e-07,
                1.3709576971463352e-06,
                1.760343213335281e-06,
                3.4663249714612693e-07,
                3.927863875616689e-07,
                3.9278634073732336e-07,
                6.475946438042047e-07
            ],
            [
                1.209865539298447e-06,
                2.699578096403948e-07,
                1.2098656835252174e-06,
                5.715004470334646e-07,
                7.338209805240734e-07,
                3.05902263391829e-07,
                1.1253525596174225e-07,
                1.2751901248454963e-07,
                1.275190124846946e-07,
                2.699577774589574e-07
            ],
            [
                0.9999999397642293,
                0.9999980052709929,
                0.9999990577554065,
                0.9999992188513902,
                0.999999802494586,
                0.9999989969859122,
                0.9999987901341728,
                0.9999996310114599,
                0.9999998461826405,
                0.9999996072139402
            ],
            [
                7.73442776303243e-08,
                1.275190580890061e-07,
                1.6373774480605869e-07,
                6.825597214718257e-08,
                1.8553910183674878e-07,
                6.023573475041126e-08,
                6.825601283086733e-08,
                1.27519088491875e-07,
                8.7642558095602e-08,
                1.6373772528704005e-07
            ],
            [
                1.8553914607267268e-07,
                9.422445939054222e-07,
                1.444979692800516e-07,
                9.422445939054222e-07,
                4.4508494582405734e-07,
                9.931195693628605e-08,
                2.699578740032504e-07,
                1.2098661162056318e-06,
                1.2751902768612997e-07,
                8.315280276626197e-07
            ],
            [
                0.9999987901344618,
                1.27519088491875e-07,
                0.999998996985434,
                3.927863407379485e-07,
                0.9999964991464236,
                0.9999984465015057,
                0.9999910603069098,
                5.715005832895975e-07,
                0.9999974387184037,
                1.5534984953552536e-06
            ],
            [
                1.0677024881980089e-06,
                2.1444945858953813e-05,
                NaN,
                3.4663249714612693e-07,
                5.1442207537151994e-05,
                2.2603245673443566e-06,
                5.043475885696228e-07,
                1.9947306726811958e-06,
                1.5534971990126997e-06,
                5.043472879540142e-07
            ],
            [
                3.4663274507713016e-07,
                1.2098661162023305e-06,
                8.315277302819205e-07,
                5.043472278322555e-07,
                5.043475885696228e-07,
                3.653484693415755e-08,
                1.4449798650551755e-07,
                9.93120161310289e-08,
                3.9278629391427843e-07,
                3.927863407379485e-07
            ],
            [
                1.2098661162023305e-06,
                1.2751902768612997e-07,
                2.6995774527718623e-07,
                1.0677026154806063e-06,
                8.315278294097538e-07,
                1.994729483723626e-06,
                2.902313369111213e-06,
                8.315277302841894e-07,
                2.90231094723893e-06,
                1.1253526937697666e-07
            ],
            [
                0.9999989969855534,
                1.7603438428800754e-06,
                0.9999969105048185,
                0.9999892166903822,
                1.209865539295696e-06,
                0.999997273528756,
                0.9999994631248041,
                1.1478770862735993e-05,
                0.9999987121046315,
                0.9999945777816811
            ],
            [
                1.1253513522447425e-07,
                1.1253506814842375e-07,
                6.825608606172863e-08,
                7.734416698849138e-08,
                5.715003789046955e-07,
                2.6995790618469934e-07,
                3.120190021759579e-05,
                7.734426841017797e-08,
                1.3709575337159875e-06,
                9.422443692555439e-07
            ],
            [
                1.5534971990126997e-06,
                1.2098659719716573e-06,
                7.338208055680009e-07,
                3.224188555067886e-08,
                7.3382080556433e-07,
                5.043474683204221e-07,
                3.466327450765785e-07,
                9.422445939032799e-07,
                1.0677032518700286e-06,
                2.699577774585891e-07
            ],
            [
                0.9999989969860321,
                0.9999975938973784,
                0.9999974387174875,
                0.99999823965742,
                0.9999967112497655,
                0.9999967112509396,
                0.9999957771670683,
                0.9999952149055163,
                0.9999996310115918,
                0.9999984465022477
            ],
            [
                0.9999991684718739,
                0.9999990577552946,
                0.999998005270281,
                0.9999991148427537,
                0.9999987901338849,
                0.9999949062962167,
                0.9999985406241281,
                0.9999983463104161,
                0.9999975938976627,
                0.9999960330136192
            ],
            [
                1.4449803818215767e-07,
                2.1024336609843824e-07,
                7.73441946488886e-08,
                1.1253518888531272e-07,
                9.931189774187203e-08,
                9.931185038635267e-08,
                2.699577774585891e-07,
                1.27519088491875e-07,
                6.825601283086733e-08,
                1.1253513522447425e-07
            ],
            [
                0.9999957771645486,
                0.9999993916407458,
                0.9999985406236058,
                0.999998863436155,
                0.999998540623432,
                0.9999987901341727,
                0.999998540623258,
                0.9999977396759742,
                0.9999984465016911,
                0.9999996533674202
            ],
            [
                2.3823699519290042e-07,
                3.9278629391427843e-07,
                1.3709567165617364e-06,
                1.6373764721072816e-07,
                1.7603434231833873e-06,
                2.382369667929001e-07,
                1.1253516205489029e-07,
                2.6995784182140636e-07,
                2.69957906184239e-07,
                5.715004470313855e-07
            ],
            [
                8.315281267882195e-07,
                9.422443692574719e-07,
                5.71500719545698e-07,
                1.0677032518814388e-06,
                8.315277302857965e-07,
                1.8553905760062447e-07,
                1.209866260432471e-06,
                1.4449803818215767e-07,
                8.315279285370317e-07,
                1.7603425837903113e-06
            ],
            [
                0.9999810748495322,
                0.9999832985841555,
                0.9999756997679976,
                1.3007131566015624e-05,
                2.260324567337161e-06,
                0.9999832985722086,
                1.2098652508287273e-06,
                2.6995784182183607e-07,
                5.043472278322555e-07,
                6.023579219579052e-08
            ],
            [
                0.9999999273417923,
                0.9999998362622552,
                0.9999998362623332,
                0.9999999006880312,
                0.9999996533674204,
                0.9999991684719727,
                0.9999998942830106,
                0.9999986290429573,
                0.9999997617630617,
                0.9999964991447544
            ],
            [
                6.605212107986466e-05,
                5.043475885688201e-07,
                8.315284241665078e-07,
                2.561283126728994e-06,
                2.561282821402217e-06,
                8.315277302841894e-07,
                8.939694172957213e-06,
                5.043475885696228e-07,
                6.475949526020042e-07,
                3.6534838223576766e-08
            ],
            [
                9.931199245322124e-08,
                8.764244316973974e-08,
                2.5110011880337063e-08,
                6.825597214718257e-08,
                5.3157887739943563e-08,
                8.76424013786396e-08,
                1.9555690030300874e-08,
                6.023578501513224e-08,
                2.8453323536912213e-08,
                1.955569236151977e-08
            ],
            [
                0.999997593897088,
                0.9999974387171806,
                0.9999964991439187,
                0.9999984465028018,
                0.9999984465026164,
                0.9999995262094987,
                0.9999977396746256,
                0.9999985406237797,
                0.9999978766205263,
                0.9999970976873246
            ],
            [
                0.9999997126314126,
                0.999999391641036,
                0.9999997463980125,
                0.9999996743686645,
                0.9999983463100207,
                0.9999989322971307,
                1.2098659719757836e-06,
                0.9999967112493687,
                0.9999981261239476,
                0.9999984465018759
            ],
            [
                1.5534984953510149e-06,
                2.561283432035425e-06,
                2.3823693839325527e-07,
                1.209865827740176e-06,
                1.7603436330179102e-06,
                1.0677032518814388e-06,
                6.825598028392069e-08,
                1.6373762769138607e-07,
                3.2887482813149375e-06,
                4.450851580566494e-07
            ],
            [
                0.9999978766207792,
                0.9999985406236058,
                0.9999986290432843,
                0.9999995549150545,
                0.9999990577554067,
                0.9999995818813269,
                0.9999995262094987,
                0.999997739675973,
                0.9999993524049706,
                0.9999984465028019
            ],
            [
                0.9999869928731,
                7.734418542875216e-08,
                9.931193325852072e-08,
                1.444980209564556e-07,
                1.6373770576776313e-07,
                0.00013982204091004735,
                1.275190276859705e-07,
                1.6373776432509826e-07,
                8.76424013786396e-08,
                9.93118503859575e-08
            ],
            [
                0.9999994631248043,
                0.9999993106388725,
                0.9999992188519492,
                0.9999995818813767,
                0.9999995262092164,
                0.999998712104479,
                0.9999996072138467,
                0.999999168472171,
                0.999999310639037,
                0.9999997463982241
            ],
            [
                0.9999983463102174,
                0.9999988634364255,
                0.9999993106386259,
                0.9999984465022463,
                0.9999997617631753,
                0.9999989322967486,
                0.9999996940976638,
                0.9999988634362902,
                0.9999993524053564,
                0.9999980052705174
            ],
            [
                0.9999974387168746,
                0.9999969105055548,
                0.9999991684722702,
                0.9999975938979486,
                0.9999984465026164,
                0.9999945777816803,
                0.9999983463098234,
                0.9999986290423037,
                0.9999962733607186,
                0.9999984465026166
            ],
            [
                3.05902263391829e-07,
                2.699578740032504e-07,
                1.444979692800516e-07,
                9.931187406410953e-08,
                8.315284241665078e-07,
                8.315278294114555e-07,
                1.1253524254650944e-07,
                2.102434412875379e-07,
                5.715006514176113e-07,
                3.466326624336003e-07
            ],
            [
                2.5612812947508257e-06,
                1.7603432133296774e-06,
                6.144175334367959e-06,
                2.561283432035425e-06,
                1.3709575337016483e-06,
                2.5612831267086116e-06,
                1.2098661161982042e-06,
                2.561282210701601e-06,
                1.5534979397677313e-06,
                3.288749065406658e-06
            ],
            [
                9.931193325852072e-08,
                9.931189774187203e-08,
                1.4449805540740185e-07,
                1.4449796928021588e-07,
                6.82560779249779e-08,
                1.4449807263312446e-07,
                1.4449805540740185e-07,
                1.6373774480605869e-07,
                1.275190580890061e-07,
                1.1253508156363576e-07
            ],
            [
                3.726639284144195e-06,
                5.043475284468537e-07,
                2.2603245673279107e-06,
                7.338209805240734e-07,
                1.209865827752005e-06,
                4.785094494811783e-06,
                4.450848927658745e-07,
                1.5534983101644536e-06,
                1.7603438428740716e-06,
                6.47595107001401e-07
            ],
            [
                0.9999981261243945,
                0.9999994284996213,
                0.9999988634357482,
                0.9999991148432814,
                0.9999996310114161,
                0.999998932297258,
                0.9999980052702812,
                0.999999631011636,
                0.9999993106386261,
                0.9999987121052458
            ],
            [
                0.9999993916411812,
                0.9999996533672139,
                0.9999997126314811,
                0.9999996072137531,
                0.9999995549148952,
                0.9999981261248411,
                0.9999994631247404,
                0.9999987901338846,
                0.999999631011504,
                0.9999992661788449
            ],
            [
                0.999997593897375,
                0.9999970976883622,
                0.9999978766212855,
                0.9999982396561583,
                0.9999977396751646,
                0.9999987901338847,
                0.9999993524048933,
                0.9999977396751646,
                0.9999996533672137,
                0.9999964991455875
            ],
            [
                0.9999990577554065,
                0.9999987121046318,
                0.9999995549149482,
                0.9999996743686257,
                0.9999991684718734,
                0.9999996310115039,
                0.9999987121046315,
                0.9999996940976638,
                0.9999997126315495,
                0.9999997126314811
            ],
            [
                2.9023119851899796e-06,
                9.931202796993203e-08,
                5.715006514167015e-07,
                1.4449796928021588e-07,
                1.7603438428800754e-06,
                1.275190428875671e-07,
                0.9999970976873243,
                4.450851049991497e-07,
                3.2887502415767434e-06,
                1.1253525596174225e-07
            ],
            [
                2.382368531929327e-07,
                5.715006514176113e-07,
                4.450848927658745e-07,
                9.422443692574719e-07,
                3.05902263391829e-07,
                3.9278620026686556e-07,
                1.7603438428848787e-06,
                1.5534983101644536e-06,
                9.422449308774482e-07,
                2.699578096403948e-07
            ],
            [
                0.9999938558239464,
                0.9999980052693296,
                0.9999989969861511,
                0.9999970976869809,
                0.9999984465016915,
                0.9999990577549571,
                0.9999969105062928,
                0.9999969105048183,
                0.9999972735300563,
                0.9999974387177926
            ],
            [
                0.9999988634365607,
                0.9999982396567889,
                0.9999925887166109,
                0.9999984465020612,
                0.9999978766215396,
                0.9999993524052022,
                0.9999993106391192,
                0.9999984465016909,
                0.9999996310113279,
                0.9999992661789324
            ],
            [
                1.1253513522447425e-07,
                3.9278629391427843e-07,
                1.0677028700422047e-06,
                2.3823696679327928e-07,
                1.0677027427624903e-06,
                2.2603253756956754e-06,
                3.466326211113502e-07,
                6.475945666063607e-07,
                5.715007195447234e-07,
                1.855391681906175e-07
            ],
            [
                0.99999743871718,
                0.9999978766212853,
                0.9999987901344618,
                0.999998863436019,
                0.9999984465024315,
                0.999998932297003,
                0.9999995262095552,
                0.9999997617630617,
                0.9999993916407458,
                0.9999982396565781
            ],
            [
                0.9999964991439235,
                0.9999985406232603,
                0.9999989322971313,
                0.9999988634360204,
                0.9999972735284374,
                0.9999986290427959,
                0.999998996985435,
                0.9999991148429649,
                0.9999964991443424,
                0.9999974387168766
            ],
            [
                6.825598028392069e-08,
                1.4449800373118268e-07,
                8.315284241650899e-07,
                3.653482951291499e-08,
                8.764245361752286e-08,
                8.764245361752286e-08,
                6.023572038912295e-08,
                6.825604537781398e-08,
                7.734421308914719e-08,
                6.825598028392069e-08
            ],
            [
                0.9999975938979486,
                6.47595107001401e-07,
                5.04347287955046e-07,
                8.315280276626197e-07,
                8.315282259138311e-07,
                5.043474683240344e-07,
                1.855391239547094e-07,
                1.0677032518814388e-06,
                1.8553905760062447e-07,
                0.9999985406237799
            ],
            [
                0.9999994956526521,
                0.999999218851949,
                0.9999996072138466,
                0.9999996072139403,
                0.9999986290423039,
                0.9999998724809267,
                0.9999989322972578,
                0.9999993524053564,
                0.9999996072139403,
                0.9999989969861515
            ],
            [
                2.699577774585891e-07,
                7.338208930460318e-07,
                3.9278610661902853e-07,
                2.699577774585891e-07,
                3.05902336324494e-07,
                9.422443692574719e-07,
                1.1253509497883659e-07,
                1.8553907971855875e-07,
                6.47595107001401e-07,
                1.8553905760062447e-07
            ],
            [
                0.9999997761971317,
                0.9999994956524717,
                0.9999992188514836,
                0.9999998024947038,
                0.9999997761970781,
                0.9999998724809875,
                0.9999978766217933,
                0.9999998024947273,
                0.9999986290424674,
                0.9999987121044781
            ],
            [
                0.9999996743687034,
                0.9999986290424671,
                0.9999996533674617,
                0.999998996986271,
                0.9999993916411085,
                0.999996499146005,
                0.9999993106386261,
                0.9999981261250641,
                0.9999986290431205,
                0.9999990577551822
            ],
            [
                9.931189774187203e-08,
                6.825604537781398e-08,
                9.931189774187203e-08,
                3.4663274507713016e-07,
                6.023569884718319e-08,
                1.8553914607267268e-07,
                7.734424996967756e-08,
                8.764242227418718e-08,
                7.734421308914719e-08,
                7.734418542875216e-08
            ],
            [
                0.9999983463100208,
                0.9999989969855538,
                0.9999987121044783,
                0.9999995549147891,
                0.9999998724809723,
                0.9999991148430698,
                0.9999998257021837,
                0.9999996743687422,
                0.9999998461826038,
                0.9999980052707562
            ],
            [
                1.6373774480605869e-07,
                2.699578740032504e-07,
                7.338208930460318e-07,
                3.927860597945825e-07,
                9.931202796993203e-08,
                2.1024341622426268e-07,
                1.4449802095666915e-07,
                1.0677028700422047e-06,
                3.9278629391427843e-07,
                7.734418542875216e-08
            ],
            [
                1.0677026154827912e-06,
                1.0677026154806063e-06,
                8.939695238634211e-06,
                1.7603427936335396e-06,
                6.475946438022905e-07,
                1.2098658277489788e-06,
                7.338212429582604e-07,
                3.059022998581767e-07,
                8.315281267882195e-07,
                1.0677027427600627e-06
            ],
            [
                3.059022269250683e-07,
                5.829124471187197e-05,
                4.450850519403407e-07,
                7.338209805224048e-07,
                1.5534979397740895e-06,
                1.3709572068553509e-06,
                3.4663274507713016e-07,
                3.288749849529972e-06,
                5.715006514176113e-07,
                5.043476486915964e-07
            ],
            [
                6.023579219579052e-08,
                7.73441946488886e-08,
                5.315780536011123e-08,
                6.023579219579052e-08,
                1.275190428875671e-07,
                1.6373764721072816e-07,
                2.1024336609843824e-07,
                1.1253517547010071e-07,
                1.4449807263312446e-07,
                1.4449805540651476e-07
            ],
            [
                0.9999964991439183,
                0.9999997761972116,
                0.9999998257020798,
                0.9999993524053563,
                0.9999977396751644,
                0.9999985406230838,
                0.9999997126314811,
                0.9999999273418702,
                0.9999995818811773,
                0.9999989322972576
            ],
            [
                2.6995774527718623e-07,
                2.3823693839325527e-07,
                1.4449803818215767e-07,
                4.139934092760465e-08,
                1.1253514863968147e-07,
                4.691160446380562e-08,
                5.3157887739943563e-08,
                9.931202796993203e-08,
                1.1253512180925583e-07,
                1.444979692800516e-07
            ],
            [
                0.9999969105040808,
                NaN,
                0.9999949062950025,
                0.9999949062931797,
                0.9999977396754353,
                0.9999982396559484,
                0.9999980052695663,
                0.9999967112493685,
                0.9999756997535455,
                0.999975699765101
            ],
            [
                0.999995777165049,
                0.9999981261246177,
                3.927862002663297e-07,
                0.999998446502802,
                0.999998346311006,
                0.9999987901343169,
                0.9999983463102181,
                0.9999991148433868,
                0.9999987121052458,
                0.9999978766210332
            ],
            [
                0.9999989969862709,
                0.9999997761970247,
                0.99999976176309,
                0.9999995818811773,
                0.9999996940977732,
                0.9999994956525919,
                0.9999997463980125,
                0.9999990577557436,
                0.9999998724809419,
                0.99999992265575
            ],
            [
                9.931187406410953e-08,
                3.466326624336003e-07,
                9.931185038635267e-08,
                3.653485128944664e-08,
                6.144173137170873e-06,
                4.69116603868534e-08,
                2.8453360847853877e-08,
                2.5110005893648856e-08,
                1.6373764721091427e-07,
                1.3007134667436886e-05
            ],
            [
                0.9999996310115479,
                0.9999977396754338,
                0.9999969105040818,
                0.9999960330155143,
                0.9999991148429649,
                0.9999974387165704,
                0.9999980052709926,
                0.9999993106390369,
                0.9999991148428589,
                0.9999980052702797
            ],
            [
                0.9999983463096269,
                0.9999997761971315,
                0.9999975938965148,
                0.999999495652532,
                0.9999995549151075,
                0.9999998362622553,
                0.9999997617630334,
                0.9999998144608541,
                0.9999978766207812,
                0.9999991148428592
            ],
            [
                0.9999978766222981,
                0.9999960330121968,
                0.9999985406230838,
                0.999999922655833,
                0.9999999273418528,
                0.9999925887201364,
                0.9999998555020135,
                0.9999977396762422,
                0.9999980052693282,
                0.9999957771655518
            ],
            [
                3.9278629391427843e-07,
                9.422445939054222e-07,
                9.422443692574719e-07,
                0.9999983463100206,
                2.382370235933104e-07,
                5.71500719545698e-07,
                1.1253525596174225e-07,
                7.338209805240734e-07,
                7.33821330437595e-07,
                9.422444815814404e-07
            ],
            [
                2.6995784182140636e-07,
                9.931198061405701e-08,
                2.3823688159291947e-07,
                0.9999998144609646,
                0.999999674368781,
                5.715006514167015e-07,
                1.6373762769138607e-07,
                1.6373766672973748e-07,
                5.715003107755449e-07,
                5.04347528446051e-07
            ],
            [
                3.059022998581767e-07,
                8.939697369980456e-06,
                4.450848927650143e-07,
                3.288748673319648e-06,
                4.450850519403407e-07,
                2.9023133690980155e-06,
                2.10243290909724e-07,
                1.7603436330259153e-06,
                1.8553905760062447e-07,
                3.0590237279085045e-07
            ],
            [
                9.931202796993203e-08,
                2.3823690999323465e-07,
                5.715005151606823e-07,
                5.3157837044597743e-08,
                6.023569884718319e-08,
                8.764254764780641e-08,
                1.8553919030858602e-07,
                1.2751902768612997e-07,
                8.764247451307293e-08,
                6.023579219579052e-08
            ],
            [
                5.715003789046955e-07,
                6.475945666051092e-07,
                7.338209805240734e-07,
                1.2098661162023305e-06,
                6.475949526020042e-07,
                7.338212429537553e-07,
                1.0677027427600627e-06,
                4.450850519403407e-07,
                2.699577774585891e-07,
                6.475948754028718e-07
            ],
            [
                0.9999997463980427,
                0.9999980052693286,
                0.9999964991455907,
                0.9999916019249738,
                0.9999990577552946,
                0.99999800527028,
                0.9999983463110068,
                1.0677029973114952e-06,
                0.9999987901347502,
                0.9999994631248043
            ],
            [
                0.9999949062956099,
                0.9999980052698044,
                0.9999988634366963,
                0.9999972735307067,
                0.9999981261246177,
                0.9999987901344615,
                0.9999984465016909,
                0.999997876622298,
                0.9999986290421403,
                0.9999977396751658
            ],
            [
                0.9999989322966212,
                0.9999994631248683,
                0.9999978766205263,
                0.9999989322971304,
                0.9999984465022461,
                0.9999989969859124,
                0.9999977396754345,
                0.999998932296876,
                0.9999993524051248,
                0.9999982396561579
            ],
            [
                0.9999991148433873,
                0.9999991684718738,
                0.9999706884619578,
                0.9999986290426306,
                2.9023119851899796e-06,
                0.9999949062962212,
                2.102434162245973e-07,
                0.999999391640964,
                3.288747889284851e-06,
                7.338209805224048e-07
            ],
            [
                0.9999974387168752,
                4.222833444590791e-06,
                0.9999972735307063,
                0.9999983463106122,
                7.734414854823498e-08,
                0.9999921107355418,
                0.9999955048200341,
                0.999995504817356,
                0.9999980052705177,
                0.9999980052700427
            ],
            [
                2.10243290909724e-07,
                8.764254764780641e-08,
                9.931202796993203e-08,
                2.3823685319320354e-07,
                2.1024334103581732e-07,
                2.699577774585891e-07,
                3.05902263391829e-07,
                8.764244316973974e-08,
                1.1253508156363576e-07,
                2.3823690999323465e-07
            ],
            [
                0.9999974387184017,
                0.9999991684715762,
                0.9999996940978826,
                0.9999993916408184,
                0.999998346310218,
                0.9999978766220453,
                0.9999987901338844,
                0.9999991684715761,
                0.9999982396572077,
                0.9999993916409635
            ],
            [
                4.139940508508409e-08,
                9.422443692574719e-07,
                0.999991060306912,
                NaN,
                1.0677028700422047e-06,
                1.4449803818215767e-07,
                7.734426841017797e-08,
                0.999989216686507,
                0.9999957771650487,
                0.9999832985702463
            ],
            [
                0.9999994631251883,
                0.9999978766220453,
                0.9999992188514837,
                0.9999987901338847,
                0.9999983463100209,
                0.9999994631251882,
                0.9999967112517214,
                0.9999993106391193,
                0.9999967112497611,
                0.9999994284997575
            ],
            [
                0.9999994956527122,
                0.9999993106388727,
                0.9999992188513903,
                0.9999984465016906,
                0.9999994956527725,
                0.9999993106388726,
                0.999998239657417,
                0.9999995262092164,
                0.999994906293786,
                0.9999992661790198
            ],
            [
                1.067703379154416e-06,
                0.9999921107336583,
                6.475950297993789e-07,
                2.2603234895289998e-06,
                6.023568448589658e-08,
                5.043475885696228e-07,
                1.2098655392921197e-06,
                9.422448185388577e-07,
                3.4663274507713016e-07,
                7.734418542875216e-08
            ],
            [
                0.9999983463098239,
                0.9999993916411811,
                0.9999960330121971,
                0.9999996533672552,
                0.9999972735300561,
                0.9999995262093858,
                0.999998863435884,
                0.9999995549150544,
                0.9999992188515764,
                0.9999964991439199
            ],
            [
                0.9999992188516698,
                0.99999862904214,
                0.9999988634362899,
                0.9999997897566841,
                0.9999998257021006,
                0.99999967436882,
                0.9999982396567876,
                0.9999997300423192,
                0.9999997761971583,
                0.999996273361609
            ],
            [
                1.1253506814842375e-07,
                8.315277302857965e-07,
                1.3709570434122812e-06,
                1.4449805540763184e-07,
                1.637377448057981e-07,
                7.734416698849138e-08,
                5.04347468323289e-07,
                3.4663278639892215e-07,
                7.73441946488886e-08,
                5.043472278322555e-07
            ],
            [
                6.023573475041126e-08,
                1.4449805540740185e-07,
                4.691162124067829e-08,
                7.734421308914719e-08,
                6.825598028364134e-08,
                9.931186222523604e-08,
                9.931186222482958e-08,
                8.764244316973974e-08,
                7.734421308914719e-08,
                6.023576347299818e-08
            ],
            [
                4.4508515805735777e-07,
                1.4449807263312446e-07,
                2.3823690999323465e-07,
                2.5612834320563895e-06,
                5.715005832886879e-07,
                1.2751908849167202e-07,
                2.3823682479292225e-07,
                9.422443692574719e-07,
                3.059022998581767e-07,
                2.102434162245973e-07
            ],
            [
                2.69957906184239e-07,
                1.4449798650569826e-07,
                9.422445939032799e-07,
                2.1024331597262577e-07,
                2.1024334103505245e-07,
                1.8553919030858602e-07,
                8.315281267861397e-07,
                1.6373776432509826e-07,
                4.4508494582405734e-07,
                8.315282259138311e-07
            ],
            [
                5.043475885696228e-07,
                0.9999972735307062,
                7.3382080556433e-07,
                1.2098658277451275e-06,
                1.3709576971379186e-06,
                9.422450432014836e-07,
                6.475945666063607e-07,
                2.6995790618469934e-07,
                3.466326624336003e-07,
                5.715003789046955e-07
            ],
            [
                4.78509278348926e-06,
                3.726641061027928e-06,
                2.9023130230846496e-06,
                1.0677032518748838e-06,
                2.260324028427877e-06,
                9.422450431989127e-07,
                1.5534984953453635e-06,
                2.902312677084523e-06,
                1.5534973841895917e-06,
                4.785093353874907e-06
            ],
            [
                9.931189774187203e-08,
                1.8553914607267268e-07,
                6.825600469412533e-08,
                2.699576809143613e-07,
                8.764241182641775e-08,
                2.260323758987159e-06,
                1.3709567165617364e-06,
                1.1253522913127183e-07,
                7.734416698849138e-08,
                7.338208930460318e-07
            ],
            [
                1.3709573702566696e-06,
                1.5534975693792215e-06,
                1.3709576971425944e-06,
                9.422444815726566e-07,
                1.209865539295696e-06,
                1.0677028700320085e-06,
                7.338213304316717e-07,
                6.475947982037486e-07,
                8.315282259089153e-07,
                5.043473480730849e-07
            ],
            [
                0.9999952149043672,
                1.4449805540763184e-07,
                4.691168275606451e-08,
                0.9999930377462466,
                5.315789407685159e-08,
                4.4508494582314646e-07,
                0.9999934595643382,
                4.1399400149893274e-08,
                1.1253506814842375e-07,
                0.9999910603026364
            ],
            [
                0.9999952149060803,
                0.9999972735297316,
                0.9999990577552943,
                0.9999977396762431,
                0.9999997300421262,
                0.9999980052695663,
                0.9999980052695664,
                0.9999985406239533,
                0.9999964991447542,
                0.9999993524049705
            ],
            [
                1.553498124964492e-06,
                3.2887478892055875e-06,
                1.209866260432471e-06,
                3.288747889284851e-06,
                1.4738978458623327e-05,
                1.9947306726594253e-06,
                4.0063701745046735e-05,
                7.889266347786918e-06,
                1.2098653950551882e-06,
                3.12019225345861e-05
            ],
            [
                1.2751901248454963e-07,
                6.825597214718257e-08,
                1.2751899728311609e-07,
                1.1253506814842375e-07,
                1.1253513522447425e-07,
                1.4449805540763184e-07,
                6.023578501513224e-08,
                1.1253512180925583e-07,
                6.825609419848033e-08,
                0.9999785550490534
            ],
            [
                1.1253512180925583e-07,
                5.3157837044597743e-08,
                1.1253516205489029e-07,
                1.275190276859705e-07,
                1.275190580890061e-07,
                7.73441946488886e-08,
                2.102434412875379e-07,
                7.889264466868659e-06,
                9.931202796993203e-08,
                7.734416698849138e-08
            ],
            [
                0.9999999006879957,
                0.00012339453089103153,
                0.9999997300422869,
                0.9999996310115918,
                0.9999982396574174,
                0.9999998461826405,
                0.9999994631248043,
                0.9999985406234317,
                0.9999999123574836,
                0.9999990577550697
            ],
            [
                8.31528424162821e-07,
                6.475947982037486e-07,
                1.3709570434178922e-06,
                6.475945666063607e-07,
                2.561282210729555e-06,
                2.260323758987159e-06,
                2.3823696679327928e-07,
                3.466326624336003e-07,
                2.699578096403948e-07,
                1.6373770576776313e-07
            ],
            [
                4.222834451327159e-06,
                1.3709573702822306e-06,
                9.931185038635267e-08,
                5.715003107755449e-07,
                2.561281905376098e-06,
                2.6995790618469934e-07,
                1.0677033791583005e-06,
                1.2098653950606901e-06,
                5.715003107767143e-07,
                1.7603425837791042e-06
            ],
            [
                0.9999998144608097,
                0.9999977396759725,
                0.9999995818811275,
                0.9999999067051499,
                0.9999997761971049,
                0.9999998257021213,
                0.9999999273418788,
                0.9999996072138466,
                0.999999789756634,
                0.9999999067050832
            ],
            [
                9.931198061405701e-08,
                3.927862939126708e-07,
                1.2751904288710323e-07,
                9.931193325852072e-08,
                1.6373764721072816e-07,
                9.931193325852072e-08,
                2.382370235922541e-07,
                7.338210680021253e-07,
                4.22283545819819e-06,
                2.3823688159291947e-07
            ],
            [
                3.224186633297071e-08,
                4.139935079796334e-08,
                7.734428685047173e-08,
                7.734428685047173e-08,
                1.0677027427624903e-06,
                1.1253526937656726e-07,
                3.224186633297071e-08,
                7.73441946488886e-08,
                6.825601283086733e-08,
                1.9555664386890228e-08
            ],
            [
                0.999998126124618,
                0.9999987121052459,
                0.9999981261252883,
                0.9999984465024322,
                0.9999974387165713,
                0.9999970976887111,
                0.9999981261248411,
                7.338212429582604e-07,
                0.9999988634366971,
                0.9999970976869793
            ],
            [
                0.99999743871749,
                0.9999970976869837,
                0.9999949062931792,
                0.999998540624129,
                0.9999984465018765,
                0.9999983463104156,
                0.9999989969855546,
                0.9999957771680701,
                0.9999977396762435,
                0.9999934595627961
            ],
            [
                4.4508510499849186e-07,
                2.5109981946866052e-08,
                6.475947210046347e-07,
                1.2098659719788098e-06,
                3.0590226339137693e-07,
                3.466325384678894e-07,
                7.889262585541864e-06,
                3.466326624336003e-07,
                3.466327037553825e-07,
                9.931202796993203e-08
            ],
            [
                1.1253521571574156e-07,
                1.275190428875671e-07,
                9.422449308748773e-07,
                1.2098658277335738e-06,
                6.475951069985296e-07,
                5.043474082005342e-07,
                1.2751901248454963e-07,
                6.475947210046347e-07,
                8.764245361752286e-08,
                2.6995784182140636e-07
            ],
            [
                3.4663278639892215e-07,
                2.69957906184239e-07,
                5.04347468323289e-07,
                7.734421308914719e-08,
                6.825602910433871e-08,
                8.764253720001207e-08,
                5.315784971839039e-08,
                1.6373774480605869e-07,
                2.382370235922541e-07,
                2.699578096393206e-07
            ],
            [
                1.4449805540763184e-07,
                7.734416698849138e-08,
                5.3157837044597743e-08,
                9.931187406410953e-08,
                1.6373764721072816e-07,
                1.1253512180925583e-07,
                3.9278620026686556e-07,
                5.3157830707696514e-08,
                1.6373766672994222e-07,
                1.1253509497883659e-07
            ],
            [
                7.734415776836702e-08,
                3.466326211113502e-07,
                7.734418542875216e-08,
                3.927862470899887e-07,
                3.2241881707148775e-08,
                5.3157887739943563e-08,
                6.023568448589658e-08,
                6.825598028392069e-08,
                5.315780536011123e-08,
                1.4449796928021588e-07
            ],
            [
                1.0677028700422047e-06,
                2.5612834320470717e-06,
                6.475947982037486e-07,
                1.0677033791612137e-06,
                5.715005832895975e-07,
                2.382370235933104e-07,
                1.994729483729522e-06,
                5.043475284468537e-07,
                1.2098661162056318e-06,
                1.3709572068553509e-06
            ],
            [
                0.9999987901340288,
                0.9999987121044781,
                0.9999985406230839,
                0.9999998024946802,
                0.9999995549150545,
                0.9999997126315496,
                0.9999995818811275,
                0.9999994284994852,
                0.9999995549147361,
                0.9999995262092164
            ],
            [
                0.9999970976883626,
                1.209865827752005e-06,
                0.9999960330131418,
                0.9999983463102173,
                0.9999952149072202,
                7.734428685047173e-08,
                2.6995774527718623e-07,
                0.9999852610145304,
                0.9999975938973753,
                0.9999991148426479
            ]
        ]
    },
    {
        "q_id": "9452_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            69,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998874648246,
                0.9999998724809116,
                0.9999999226558146,
                0.9999989969859125,
                0.9999996533675031,
                0.9999997126314126,
                0.9999998362623528,
                0.9999985406241279,
                0.999999495652592,
                0.9999997463981636
            ],
            [
                9.422448185510695e-07,
                0.9999972735300597,
                5.422217677152175e-06,
                1.760344052714248e-06,
                9.422450431989127e-07,
                9.422445939054222e-07,
                1.994729483729522e-06,
                2.699578096393206e-07,
                1.2098652508424818e-06,
                9.422445939054222e-07
            ],
            [
                8.315282259089153e-07,
                1.5534979397790343e-06,
                6.962257079832313e-06,
                7.889266347715168e-06,
                1.8925148241080285e-05,
                1.2098659719716573e-06,
                4.0063701745046735e-05,
                1.2098656835136636e-06,
                1.994730672668496e-06,
                3.2887486733420804e-06
            ],
            [
                0.9999996072138936,
                0.9999998362622552,
                0.9999998802069445,
                0.999999864256719,
                0.9999994284994853,
                0.9999998555019447,
                0.9999998874648515,
                0.9999996940977732,
                0.9999996533672965,
                0.9999997126315153
            ],
            [
                1.7603430034743913e-06,
                6.475951069985296e-07,
                3.2887506336235617e-06,
                6.475947210031623e-07,
                1.3709572068422585e-06,
                1.2098659719757836e-06,
                5.04347468323289e-07,
                1.209866260432471e-06,
                9.422450431989127e-07,
                2.260324028427877e-06
            ],
            [
                0.9999999273418789,
                0.9999998942830106,
                0.9999999176675829,
                0.9999998874648245,
                0.9999995818810776,
                0.9999997300422548,
                0.9999997300423192,
                0.9999999500628453,
                0.999999894283061,
                0.9999999273418962
            ],
            [
                0.9999996940978827,
                0.9999989969854354,
                0.9999996743687812,
                0.9999993916408916,
                0.999999310638791,
                0.9999991148432817,
                0.9999996310114603,
                0.9999993916407466,
                0.9999996743687424,
                0.9999994956523522
            ],
            [
                0.9999999006880904,
                0.9999999123574419,
                0.9999997463980428,
                0.9999999397643011,
                0.9999999358794174,
                0.999999935879425,
                0.9999999358794174,
                1.0,
                0.9999999123574733,
                0.9999999006881142
            ],
            [
                0.9999997300422226,
                0.9999998144608762,
                0.9999990577551832,
                0.9999995818812772,
                0.9999993524048942,
                0.9999996743686647,
                0.9999996310116358,
                0.99999963101146,
                0.9999997300423193,
                0.9999991148429651
            ],
            [
                3.927860597945825e-07,
                0.9999993916411811,
                0.9999771720057034,
                0.9999998724809723,
                0.9999998642566381,
                0.999999894283061,
                0.9999975938970891,
                0.9999994284992807,
                2.699577774585891e-07,
                0.9999993916406735
            ],
            [
                0.9999998942830233,
                0.9999996940977732,
                0.9999998555020481,
                0.9999998362622552,
                0.9999996940978462,
                0.9999994284997575,
                0.9999997761971315,
                0.9999998362623724,
                0.9999997300422548,
                0.999999607213753
            ],
            [
                4.450852111148132e-07,
                3.7266388398585725e-06,
                5.715003107767143e-07,
                1.0129994602895546e-05,
                6.475949525981759e-07,
                3.466325384661554e-07,
                3.059023727894942e-07,
                3.927862939126708e-07,
                1.7603434231833873e-06,
                4.222834954753043e-06
            ],
            [
                0.999999526209386,
                0.9999987901347507,
                0.9999994631251887,
                0.9999994284997582,
                0.9999994956524721,
                0.9999991684715772,
                0.9999996533672552,
                0.9999996533672966,
                0.9999995818810782,
                0.9999991684718744
            ],
            [
                0.9999997761970515,
                0.9999998555020136,
                0.9999998555019791,
                0.999999730042287,
                0.9999997463980126,
                0.9999996940977732,
                0.9999995549150544,
                0.9999998802069302,
                0.9999997617630618,
                0.9999998362623529
            ],
            [
                0.9999992661787577,
                0.999999802494586,
                0.9999991684717751,
                0.999999653367503,
                0.9999997300423191,
                0.9999994631248686,
                0.9999997463980731,
                0.999999825702059,
                0.9999996310115921,
                0.9999998461827322
            ],
            [
                0.9999996310113722,
                0.9999997761971852,
                0.9999997126315155,
                0.999999730042255,
                0.9999993916409646,
                0.9999989322973859,
                0.999999310639202,
                0.9999998942829603,
                0.9999997126313785,
                0.9999995549151078
            ],
            [
                0.9999994284995535,
                0.9999998024947273,
                0.9999994956525922,
                0.9999998024946801,
                0.9999998024946803,
                0.9999997761970782,
                0.9999998362622358,
                0.9999996310114162,
                0.9999994956524719,
                0.9999997126313784
            ],
            [
                0.9999993916409636,
                0.999999526209499,
                0.9999996310113721,
                0.9999998555019791,
                0.9999995549148953,
                0.9999993916410362,
                0.9999998461826405,
                0.9999992188515769,
                0.9999997617631186,
                0.9999994631247405
            ],
            [
                0.9999998461827139,
                1.4738983729535602e-05,
                0.0001088969223388039,
                0.9999997761971315,
                6.475945666063607e-07,
                0.9999997617629766,
                0.9999980052698041,
                0.9999843104544471,
                0.9999972735297316,
                0.001032230972771653
            ],
            [
                0.9999999006880195,
                0.999999730042287,
                0.9999994956524719,
                0.9999996940977003,
                0.9999997761970515,
                0.9999997463981637,
                0.9999998555019619,
                0.9999997126313784,
                0.9999997126313783,
                0.9999988634362907
            ],
            [
                1.209865539295696e-06,
                3.0590237279085045e-07,
                3.72663883989755e-06,
                2.5612819054028872e-06,
                1.6373772528704005e-07,
                2.1444950970626095e-05,
                1.1478764020883773e-05,
                2.5612828213934817e-06,
                7.338208930460318e-07,
                0.00010889694829665246
            ],
            [
                1.5534981249697903e-06,
                9.61024150359243e-05,
                6.475945666051092e-07,
                1.444980381819277e-07,
                0.9999989969857931,
                2.753569766795419e-05,
                2.5612828213934817e-06,
                1.3709567165617364e-06,
                5.043472278322555e-07,
                2.102434162245973e-07
            ],
            [
                0.9999999273418528,
                0.9999998942830485,
                0.999999953088334,
                0.9999998555019619,
                0.9999999530883731,
                0.9999999317439383,
                0.9999999358794096,
                0.9999998724809723,
                0.9999999586005949,
                0.9999999317439139
            ],
            [
                1.7603438428800754e-06,
                1.0677027427600627e-06,
                1.5534979397790343e-06,
                6.475947982037486e-07,
                2.561281905390075e-06,
                6.475947982037486e-07,
                8.315284241650899e-07,
                1.6701425826191394e-05,
                1.7603427936335396e-06,
                5.422220262555012e-06
            ],
            [
                1.012999218776902e-05,
                2.699576809143613e-07,
                1.067703379154416e-06,
                1.3709567165530083e-06,
                1.2098662604291696e-06,
                0.0008040857693749599,
                2.902313023130843e-06,
                5.422217030781934e-06,
                2.561282516066741e-06,
                1.3709576971425944e-06
            ],
            [
                0.9999994284997576,
                0.9999989969859158,
                0.9999992188513912,
                0.9999995262094994,
                0.9999993106389552,
                0.9999995818811283,
                0.9999994956525324,
                0.9999981261243982,
                0.9999992188513913,
                0.9999993106387915
            ],
            [
                9.931185038635267e-08,
                7.338212429594283e-07,
                1.4449802095666915e-07,
                8.7642526752214e-08,
                9.422445939054222e-07,
                2.10243290909963e-07,
                9.931199245322124e-08,
                1.275189972832538e-07,
                2.699577130960941e-07,
                1.6373764721091427e-07
            ],
            [
                4.785095635655362e-06,
                0.9999988634366982,
                1.3709570434178922e-06,
                NaN,
                2.3823688158658173e-07,
                1.5534973842076057e-06,
                2.7535681254804434e-05,
                0.01798621236374456,
                4.222834954778007e-06,
                3.288749849529972e-06
            ],
            [
                1.9947299592933255e-06,
                9.422447062270609e-07,
                5.422218323399208e-06,
                1.3709575337078829e-06,
                1.7603432133296774e-06,
                6.9622595696935874e-06,
                3.2887502415243994e-06,
                2.2603242978778778e-06,
                1.994730434879465e-06,
                3.288749849498565e-06
            ],
            [
                8.481102117280838e-05,
                1.9947297215043796e-06,
                2.1444953527476883e-05,
                5.1442238195844654e-05,
                2.430024073399743e-05,
                6.962255419804982e-06,
                2.7535697667202906e-05,
                4.006368741510365e-05,
                8.93969950132721e-06,
                7.889261645269683e-06
            ],
            [
                0.9999980052693286,
                0.9999997463980126,
                0.9999994631251244,
                0.9999992661789325,
                0.9999997300421263,
                0.9999988634364261,
                0.9999992661788449,
                0.9999997617630333,
                0.9999996743686259,
                3.7266383956509585e-06
            ],
            [
                0.9999999067050498,
                0.9999997897566841,
                0.999999730042094,
                0.9999999317439058,
                0.9999999317440035,
                0.9999999006880431,
                0.9999994284996213,
                0.9999999273418703,
                0.9999998362622552,
                0.9999996940978098
            ],
            [
                0.99999926617867,
                0.999999674368781,
                0.9999998257021423,
                0.9999998724808964,
                0.9999999067051055,
                0.9999999226558515,
                0.9999996072137531,
                0.9999997617631754,
                0.9999998461826038,
                0.9999998642566219
            ],
            [
                1.7603427936183298e-06,
                0.9999996533672553,
                0.9999996310115484,
                1.99472900813862e-06,
                4.785094494750855e-06,
                6.9622595696935874e-06,
                2.2603234895176927e-06,
                0.9999995549148424,
                6.962256249885085e-06,
                4.222835458148261e-06
            ],
            [
                9.610240358212368e-05,
                0.9999972735284332,
                3.726639284144195e-06,
                0.9999970976887108,
                2.1444948415296896e-05,
                0.99999649914476,
                0.0005527785515758354,
                0.9999921107336889,
                0.999996499145189,
                0.999994228079291
            ],
            [
                0.9999998024947037,
                0.9999992661787572,
                0.9999998555020481,
                0.9999998642566704,
                0.9999998874649318,
                0.9999998724810027,
                0.9999999397642293,
                0.999999912357442,
                0.9999999397642437,
                0.999999653367503
            ],
            [
                0.9999998461827323,
                0.9999998362622358,
                0.9999998642566543,
                0.9999998942829098,
                0.9999996940978098,
                0.9999998362622748,
                0.999999631011504,
                0.999999776197185,
                0.9999998724809723,
                0.9999999067050832
            ],
            [
                0.9999998642566866,
                0.9999997761970248,
                0.9999998461826038,
                0.9999997463982241,
                0.9999997617631754,
                0.9999997897566841,
                0.9999995818810776,
                0.9999996310115479,
                0.9999997761971315,
                0.9999996533673791
            ],
            [
                0.9999996940978096,
                0.9999996310115922,
                0.9999996072137063,
                0.9999997126314812,
                0.9999998724809116,
                0.9999998257021838,
                0.9999996940976273,
                0.9999995549148953,
                0.9999996940976638,
                0.9999998555019619
            ],
            [
                8.93969950132721e-06,
                0.00017952792355046838,
                0.9999989322967506,
                3.1201926253802263e-05,
                5.4222183234485234e-06,
                6.605213682591808e-05,
                0.0028009268910341163,
                1.9947297214944016e-06,
                0.00048785706377366264,
                3.2887478892683997e-06
            ],
            [
                4.785096776499213e-06,
                2.2603237589779086e-06,
                9.422444815814404e-07,
                6.144175334468545e-06,
                1.994729008145876e-06,
                1.0677027427600627e-06,
                1.994729008145876e-06,
                5.715007195447234e-07,
                5.043474082005342e-07,
                1.3709576971463352e-06
            ],
            [
                0.9999998555019446,
                0.9999998461826772,
                0.9999997463980427,
                0.9999996940978098,
                0.9999997463981637,
                0.9999996533673378,
                0.9999999006879721,
                0.9999998642566381,
                0.9999998362622357,
                0.9999998144609645
            ],
            [
                0.9999999634651661,
                1.0,
                0.9999999434138043,
                NaN,
                0.999999906705061,
                1.0,
                0.9999999697115803,
                0.9999999317440198,
                0.9999999006880668,
                0.9999999468421883
            ],
            [
                0.9999996533672139,
                0.999999631011328,
                0.9999993106392016,
                0.9999993106387086,
                0.9999996072138938,
                0.9999997463981636,
                0.9999991684716757,
                0.9999997126313785,
                0.9999989322972582,
                0.9999996533673792
            ],
            [
                0.9999993916409646,
                0.9999991684716769,
                0.9999992188516716,
                0.999998126124177,
                0.999999352405435,
                0.9999989969855556,
                0.9999996743688976,
                0.9999982396559495,
                0.9999991684717762,
                0.9999993106391195
            ],
            [
                0.9999995818813769,
                0.9999997617631469,
                0.9999997761970516,
                0.9999997897566592,
                0.9999996533674618,
                0.9999996072136128,
                0.9999997463980732,
                0.9999997300422552,
                0.9999997463980126,
                0.9999996533673376
            ],
            [
                1.0,
                0.9999999226557131,
                0.9999999006880431,
                0.9999999123575777,
                0.999999789756684,
                0.9999998642567028,
                0.9999999067049943,
                0.9999998874648782,
                0.9999999397642725,
                0.9999999176674651
            ],
            [
                7.338207180898968e-07,
                0.999999581881277,
                0.9999998874647574,
                8.315280276607289e-07,
                0.9999998461826405,
                5.043472879540142e-07,
                0.9999996940978096,
                1.0677032518814388e-06,
                0.9999992188513906,
                0.9999991148432816
            ],
            [
                0.999999864256719,
                0.9999996310116359,
                0.9999998144608319,
                0.9999997897566841,
                0.9999998024947037,
                0.999999825702059,
                0.99999967436882,
                0.9999995818811774,
                0.999999631011636,
                0.9999998024946095
            ],
            [
                1.1478764020727177e-05,
                2.1024334103505245e-07,
                5.715003789033962e-07,
                9.422445939032799e-07,
                5.715003789046955e-07,
                1.1478769494396542e-05,
                2.69957906184239e-07,
                4.4508510499849186e-07,
                1.9947299593014888e-06,
                3.2887482813149375e-06
            ],
            [
                0.9999997463981033,
                0.9999998724809875,
                0.9999998642566219,
                0.9999998461826956,
                0.9999998144609203,
                0.9999998555019791,
                0.9999998257021838,
                0.9999996940977733,
                0.999999761763147,
                0.9999997761971049
            ],
            [
                0.9999995818811277,
                1.2098656835224664e-06,
                0.9999996072137063,
                4.450849988798682e-07,
                4.222835458148261e-06,
                0.9999992188517628,
                2.260324567337161e-06,
                0.9999997897566841,
                7.338211554783522e-07,
                9.422448185510695e-07
            ],
            [
                0.9999999123575255,
                0.9999998257020799,
                0.9999999226558237,
                0.9999998874647977,
                0.9999998461827322,
                0.9999998942829477,
                0.9999999176675142,
                0.9999999067050053,
                0.9999995818811275,
                0.9999999434137704
            ],
            [
                0.9999996743687811,
                0.9999997761971315,
                0.9999994631251883,
                0.9999998724809723,
                0.9999997761972116,
                0.9999996743687034,
                0.9999997126313784,
                0.9999997617631753,
                0.9999998024946567,
                0.9999993106386262
            ],
            [
                0.9999999397642724,
                0.9999999586006393,
                0.9999997761971849,
                0.9999999273417749,
                1.760342793638743e-06,
                0.9999998555019963,
                0.999999927341853,
                1.0,
                0.9999999123575255,
                0.9999998874647575
            ],
            [
                0.9999957771665786,
                0.9999989322972586,
                1.2098662604247682e-06,
                0.999988521227886,
                0.0001795279449767558,
                0.9999987121043261,
                0.9999972735303905,
                0.9999994631248049,
                2.2603234895289998e-06,
                0.999999391640674
            ],
            [
                0.9999993916410367,
                0.9999993524048937,
                0.9999992661786704,
                0.9999993106390374,
                0.9999990577551825,
                0.9999990577554078,
                0.9999998874648112,
                0.999998996986152,
                0.9999992188515782,
                0.9999993106392018
            ],
            [
                0.9999989969855557,
                0.9999994284997584,
                0.999999114843177,
                0.9999991148428611,
                0.999999266179021,
                0.9999991684718748,
                0.9999996743686259,
                0.9999990577549592,
                0.9999992661792838,
                5.043476486915964e-07
            ],
            [
                0.9999987121047876,
                0.999998446502804,
                6.1441746020359e-06,
                9.422444815765128e-07,
                0.9999992661791072,
                7.889261645427538e-06,
                0.9999983463106143,
                0.9999995262092731,
                1.1478765389368729e-05,
                8.315277302788957e-07
            ],
            [
                1.147877359957198e-05,
                2.9023133690980155e-06,
                2.9023112932177327e-06,
                1.1478766757718129e-05,
                0.0005527787491877658,
                1.3709576971463352e-06,
                2.5612819054028872e-06,
                9.422449308774482e-07,
                1.760342793638743e-06,
                1.1478765389222573e-05
            ],
            [
                1.0677028700320085e-06,
                3.53562549305363e-05,
                8.939700566801578e-06,
                5.043475885674441e-07,
                5.715003789017068e-07,
                1.9947299593014888e-06,
                1.99472900813862e-06,
                2.260324028427877e-06,
                9.422444815765128e-07,
                2.9023133690980155e-06
            ],
            [
                0.9999998144608098,
                0.9999996072139403,
                0.9999994956525919,
                0.999999939764251,
                0.999998446502617,
                0.999999789756659,
                0.9999998642567353,
                0.9999992188513902,
                0.9999995549148422,
                0.9999997126314812
            ],
            [
                0.9999997300422871,
                0.9999998555020481,
                0.9999997761970781,
                0.9999998024946567,
                0.9999993524050481,
                0.9999997126313784,
                0.9999996072137063,
                0.999999428499349,
                0.9999996533674206,
                0.9999995262093859
            ],
            [
                9.422447062270609e-07,
                7.889259764445822e-06,
                4.4508505193932864e-07,
                3.466325797888292e-07,
                3.927862002654366e-07,
                1.3709572068478697e-06,
                4.450849988811838e-07,
                7.338208055664991e-07,
                3.927862470890063e-07,
                1.5534981249697903e-06
            ],
            [
                0.9999991684721716,
                0.9999996940977004,
                0.9999996533674619,
                0.9999993916406739,
                0.9999998461826405,
                0.9999992661786702,
                0.9999997300422873,
                0.9999997300422228,
                0.9999993106386265,
                0.9999995818814269
            ],
            [
                0.9999997761971583,
                0.999999761763005,
                0.999999653367255,
                0.9999998024946566,
                0.9999997761971049,
                0.9999995262093294,
                0.9999996072137998,
                0.9999997761970515,
                0.9999995818811275,
                0.9999994631249962
            ],
            [
                1.8925150497435443e-05,
                1.0129993394959082e-05,
                5.82912516497227e-05,
                3.535625071473396e-05,
                4.006368741510365e-05,
                0.002472623456408402,
                2.430024652792821e-05,
                1.4738976700929127e-05,
                1.892514598469098e-05,
                2.4300249423965898e-05
            ],
            [
                0.9999991148429646,
                0.9999987121046316,
                0.999999825702059,
                0.9999992661791947,
                0.9999998362622553,
                0.999999352405202,
                0.9999998942830862,
                0.9999994631251883,
                0.9999942280779116,
                8.315282259138311e-07
            ],
            [
                2.102434412875379e-07,
                1.6373764721072816e-07,
                1.8553916819032217e-07,
                1.2098656835224664e-06,
                2.382370235933104e-07,
                2.699577774585891e-07,
                1.444979692800516e-07,
                1.8553907971855875e-07,
                2.699576809143613e-07,
                5.04347287955046e-07
            ],
            [
                4.450852641737424e-07,
                7.338208055664991e-07,
                6.962253760024999e-06,
                1.7603425837855082e-06,
                4.22283545819819e-06,
                1.7603434231833873e-06,
                1.5534975693979422e-06,
                1.209866260432471e-06,
                1.5534979397790343e-06,
                4.450848927650143e-07
            ],
            [
                0.9999987901347502,
                1.012999218752948e-05,
                0.0001398220408897034,
                4.222833444590791e-06,
                0.9999994956526526,
                0.9999994631250607,
                6.9622587397397306e-06,
                1.7603425837791042e-06,
                6.962257909722651e-06,
                0.0011695100157864463
            ],
            [
                3.05902263391829e-07,
                1.1253506814842375e-07,
                7.338212429594283e-07,
                2.6995774527718623e-07,
                8.764242227418718e-08,
                2.1024341622426268e-07,
                4.450852111155216e-07,
                3.466325797896173e-07,
                1.4449796928021588e-07,
                2.6995784182140636e-07
            ],
            [
                0.9999998724809572,
                0.999999958600585,
                0.9999999434137773,
                0.9999999434137636,
                0.9999998802069873,
                0.9999999434137233,
                1.0,
                1.0,
                0.9999999006880905,
                0.999999894282935
            ],
            [
                0.9999998144608983,
                0.9999997463980126,
                0.9999998642567028,
                0.9999996310115041,
                0.9999998642567028,
                0.9999997761970516,
                0.999999694097664,
                0.9999998144608099,
                0.9999996533672967,
                1.0
            ],
            [
                3.120192625482384e-05,
                8.939698435657833e-06,
                1.2098662604192665e-06,
                1.1478764021029928e-05,
                8.939694172867777e-06,
                NaN,
                8.939700567004841e-06,
                1.8925150497848527e-05,
                7.484624512911504e-05,
                2.5612828213690224e-06
            ],
            [
                0.9999993524052792,
                0.9999998724809572,
                0.9999997761970515,
                2.5612819054133693e-06,
                0.9999989969862709,
                0.9999996743687034,
                0.9999996940977367,
                0.9999997761972116,
                0.9999843104540438,
                0.999999939764294
            ],
            [
                1.2098655392921197e-06,
                8.939696304311336e-06,
                1.067703124601679e-06,
                4.222833444590791e-06,
                5.422217030747413e-06,
                4.785093353940187e-06,
                5.422218323487975e-06,
                2.5612828213934817e-06,
                1.5534981249697903e-06,
                3.4663253846718004e-07
            ],
            [
                8.315284241597959e-07,
                6.475945666051092e-07,
                8.315283250371857e-07,
                6.962255419931625e-06,
                7.889259764445822e-06,
                3.4663249714612693e-07,
                8.315281267882195e-07,
                3.726637951387472e-06,
                6.475949526020042e-07,
                1.0677024881980089e-06
            ],
            [
                0.9999998802069159,
                0.9999987901343179,
                0.9999993106389551,
                0.9999994284994171,
                0.9999993106389552,
                0.9999993916411088,
                0.9999991148428594,
                0.9999993916408187,
                0.9999993524048938,
                0.9999970976887097
            ],
            [
                1.553497199007048e-06,
                1.760343423160973e-06,
                1.7603427936335396e-06,
                1.0677027427471959e-06,
                3.535625493182252e-05,
                3.2887506336235617e-06,
                5.422218323487975e-06,
                2.260325106237323e-06,
                3.927863875616689e-07,
                9.422445939032799e-07
            ],
            [
                0.9999994631249324,
                0.9999997126315154,
                0.9999993916411088,
                0.9999988634366972,
                0.9999988634362903,
                0.9999994956527126,
                0.9999984465022467,
                0.9999989969862718,
                0.9999995818810777,
                0.9999995818811277
            ],
            [
                0.9999994284993491,
                0.999999789756659,
                0.9999998461827322,
                0.9999997463981334,
                0.9999995549148951,
                0.9999993916411087,
                0.9999996072137062,
                0.9999992661790201,
                0.999999495652592,
                0.9999996743687422
            ],
            [
                2.3823696679327928e-07,
                9.931187406410953e-08,
                2.1024331597262577e-07,
                1.1253517547010071e-07,
                2.102434412875379e-07,
                2.699578740032504e-07,
                9.931198061405701e-08,
                6.023578501491997e-08,
                1.6373770576776313e-07,
                8.764245361752286e-08
            ],
            [
                8.315281267882195e-07,
                6.475948754012522e-07,
                6.475947210012481e-07,
                4.450849988811838e-07,
                6.962257909722651e-06,
                6.475949526020042e-07,
                1.0677029973192638e-06,
                1.209865539295696e-06,
                1.5534975693979422e-06,
                1.5534977545886537e-06
            ],
            [
                9.422442569315887e-07,
                2.5612831267086116e-06,
                7.338207180864763e-07,
                0.9999988634357491,
                0.9999987121052478,
                2.260325106237323e-06,
                0.9999992661787587,
                0.9999993106386276,
                3.2887498495150166e-06,
                6.962257909785973e-06
            ],
            [
                0.9999997300423192,
                0.9999995262095552,
                0.999999789756609,
                0.9999995549148951,
                0.9999998257021214,
                0.999999802494633,
                0.9999995549149483,
                0.9999996743688975,
                0.9999997897565589,
                0.9999997761971583
            ],
            [
                0.9999999176674945,
                0.999999789756659,
                0.9999999176675142,
                0.9999998874649185,
                0.9999998942830358,
                0.9999999226558054,
                0.9999999273417923,
                0.999999802494586,
                0.9999999067049942,
                0.9999998555019447
            ],
            [
                0.9999995262092166,
                0.9999995549148956,
                0.9999993916406738,
                0.9999996940978463,
                0.999999310639202,
                0.9999997761972117,
                0.9999995549147361,
                0.999999846182714,
                0.9999995818812274,
                0.9999998461826589
            ],
            [
                2.2603251062147097e-06,
                9.422443692489024e-07,
                4.450852641717689e-07,
                3.9278615344178325e-07,
                4.4508510499737865e-07,
                6.475951069985296e-07,
                2.2603245673155757e-06,
                3.9278634073625165e-07,
                0.9999984465016913,
                3.0590211752206485e-07
            ],
            [
                0.9999997897566841,
                0.9999998362623724,
                0.9999990577556322,
                0.9999991684715771,
                0.999999310638956,
                0.9999998724809723,
                0.9999995549150545,
                0.9999996533674205,
                0.9999993106392016,
                0.99999967436882
            ],
            [
                1.5534975693979422e-06,
                3.288749065423109e-06,
                1.7603434231777837e-06,
                1.209865539295696e-06,
                9.422445939032799e-07,
                1.2098656835224664e-06,
                8.315277302841894e-07,
                8.315281267882195e-07,
                1.760343003481596e-06,
                1.7603440527286572e-06
            ],
            [
                0.9999986290424671,
                0.9999990577557435,
                0.9999991684718736,
                0.9999997761970781,
                0.9999992661790198,
                0.9999993524049706,
                0.9999995549148951,
                0.9999997300422547,
                0.9999994631248682,
                0.999998996985434
            ],
            [
                0.9999998362623529,
                0.9999999434137502,
                0.999999846182604,
                0.999999746398073,
                0.9999998874648648,
                0.9999999067051054,
                0.9999998024946096,
                0.9999997761970515,
                0.9999997300423192,
                0.9999997300422548
            ],
            [
                0.9999998874649318,
                0.99999995308839,
                0.9999999697115876,
                0.9999999123575987,
                0.9999998461826222,
                0.9999998642566219,
                0.9999999226557684,
                0.9999996310114599,
                6.962256249885085e-06,
                0.9999999677581414
            ],
            [
                6.9622579096593295e-06,
                0.999999495652412,
                0.9999898700066998,
                2.260325106237323e-06,
                0.9999980052709976,
                9.422448185534261e-07,
                9.422444815814404e-07,
                0.9999934595597106,
                0.999998629042959,
                2.561282210740037e-06
            ],
            [
                0.9999991684717754,
                0.999998540623607,
                0.9999989322972594,
                0.9999993916411092,
                0.9999964991447639,
                0.9999989322973862,
                0.9999994956525325,
                0.999999391640747,
                1.3709572068522336e-06,
                0.9999989322970042
            ],
            [
                0.9999997126315497,
                0.9999997300421584,
                0.9999997126314129,
                0.9999994631248684,
                0.9999997463980125,
                0.9999997617631754,
                0.9999995549148956,
                0.9999997463980732,
                0.9999997761970516,
                0.9999995262094429
            ],
            [
                0.9999992661790198,
                0.9999998024947038,
                0.9999998642566866,
                0.999998346309626,
                0.9999996533674202,
                0.999999802494633,
                0.9999999358794402,
                0.9999998461826222,
                0.999999352405202,
                0.9999999317439873
            ],
            [
                1.473898900066424e-05,
                7.338208055664991e-07,
                1.0677026154730804e-06,
                1.0677024882009222e-06,
                7.3382080556433e-07,
                1.553497754577351e-06,
                9.422443692489024e-07,
                1.2098652508347793e-06,
                9.422448185510695e-07,
                6.475949525981759e-07
            ],
            [
                0.999999218851856,
                0.9999991684722702,
                0.9999997300421261,
                0.9999997126314812,
                0.999999554914736,
                0.9999994284996215,
                0.9999996072138467,
                0.9999993916410361,
                0.9999995549149484,
                0.9999996743687422
            ],
            [
                0.9999997761970247,
                0.9999995818813767,
                0.999999352405202,
                0.9999988634361546,
                0.9999995262094423,
                0.9999996072137063,
                0.9999995262094422,
                0.9999994956525319,
                0.9999999176675142,
                0.9999994631249324
            ],
            [
                0.9999998724809875,
                0.9999964991443349,
                0.9999995549150543,
                0.999999894283061,
                0.999999653367379,
                0.9999999559306102,
                0.9999987901346057,
                0.9999993524050478,
                0.9999997300422548,
                0.9999998461826222
            ],
            [
                0.9999997617630901,
                0.9999997897566089,
                0.9999997126313099,
                0.9999997761971048,
                0.9999995818814267,
                0.9999995262094424,
                NaN,
                0.9999994956524719,
                0.9999995818814267,
                0.9999998555019447
            ],
            [
                0.9999996743686645,
                0.9999998024947273,
                0.9999997126315153,
                0.9999997463981334,
                0.9999998257021837,
                0.9999997126313098,
                0.9999998257022045,
                0.9999998802069874,
                0.9999997126314468,
                0.9999998362623139
            ],
            [
                0.999999814460854,
                0.9999998555020307,
                0.9999998461827139,
                0.9999999559305943,
                0.9999999176675535,
                0.9999999764113662,
                0.9999998802069302,
                0.9999994631249962,
                0.9999996743686259,
                0.9999999611088487
            ],
            [
                2.561282210729555e-06,
                1.760343003481596e-06,
                6.475950298011458e-07,
                1.067703124601679e-06,
                1.0677029973192638e-06,
                1.0677026154806063e-06,
                9.422448185510695e-07,
                3.059022998576899e-07,
                8.315279285370317e-07,
                1.067703124601679e-06
            ],
            [
                1.6701423835624208e-05,
                0.0008040860546027804,
                1.3007126914245925e-05,
                2.4300243630653244e-05,
                4.006368741670684e-05,
                8.939698435454571e-06,
                8.939694172656384e-06,
                1.8925143729162536e-05,
                2.430025232128576e-05,
                2.260324028427877e-06
            ],
            [
                0.9999999468421249,
                0.9999997617631754,
                0.9999999358793867,
                0.9999998461826589,
                0.9999997897567342,
                0.9999999067051499,
                0.9999996533673791,
                1.0,
                0.9999998802069445,
                0.9999998724809723
            ],
            [
                0.9999987121044781,
                0.99999976176309,
                0.9999996533673378,
                0.9999995818812272,
                0.9999921107393479,
                0.9999997617631184,
                0.9999993106389549,
                0.9999996072138468,
                0.9999996940978826,
                0.9999990577551819
            ],
            [
                9.422444815814404e-07,
                1.7603440527286572e-06,
                4.450849988811838e-07,
                1.0677029973219343e-06,
                6.475950298021765e-07,
                1.209865539295696e-06,
                3.9278634073732336e-07,
                7.33821330437595e-07,
                6.475950298021765e-07,
                8.315277302857965e-07
            ],
            [
                0.9999993916409641,
                2.5612819054133693e-06,
                0.9999977396754371,
                1.1478765389368729e-05,
                0.9999987121041714,
                0.9999877809197883,
                4.222832941193893e-06,
                1.7603434231833873e-06,
                7.889266347786918e-06,
                2.1444953527944967e-05
            ],
            [
                0.9999999317440035,
                0.9999999226557408,
                0.9999999067050943,
                0.9999997463980427,
                0.9999998257021007,
                0.9999999500628453,
                0.9999999317440117,
                0.9999994284992806,
                0.999999894282935,
                0.9999999317439954
            ],
            [
                0.9999999006879958,
                0.9999996533673791,
                0.999999746398073,
                0.9999998642566381,
                0.9999999500628631,
                0.9999998724808963,
                0.9999999468421883,
                0.9999998362622552,
                0.9999998362622553,
                0.9999998874649185
            ],
            [
                8.315283250394546e-07,
                1.3709568799919866e-06,
                3.05902336324494e-07,
                2.902312677150514e-06,
                3.726638839878908e-06,
                3.466326211113502e-07,
                1.0677033791612137e-06,
                1.2751908849167202e-07,
                4.785092783519724e-06,
                4.785092783519724e-06
            ],
            [
                0.9999999226557962,
                0.9999998555019274,
                0.9999999176675338,
                0.9999999123575987,
                0.9999998362623723,
                0.9999998257022045,
                0.9999994631249965,
                0.9999996743687035,
                0.9999994284994852,
                0.9999996743687034
            ],
            [
                0.9999999006880668,
                0.9999998257021837,
                0.9999998257021837,
                0.9999998555020307,
                0.9999998555019619,
                0.9999998802068873,
                0.9999998024946801,
                0.9999999176674651,
                0.9999998874647575,
                0.9999999397642294
            ],
            [
                0.0046095722199697015,
                1.3709568799823232e-06,
                2.260323758987159e-06,
                7.889263526266196e-06,
                0.9999904837439014,
                9.422448185510695e-07,
                1.994729483723626e-06,
                1.7603427936335396e-06,
                0.9999985406234373,
                0.9999995818813772
            ],
            [
                0.999999814460876,
                0.9999997126315153,
                0.9999998144608981,
                0.999999900688055,
                0.9999998802069444,
                0.9999998257021007,
                0.9999998024947038,
                0.9999998555019963,
                0.9999998362622943,
                0.9999997617630901
            ],
            [
                1.0,
                6.962257079832313e-06,
                1.0,
                0.9999999176674357,
                2.5612819054133693e-06,
                0.9999999358793332,
                0.9999997300421262,
                0.9999998942829477,
                0.9999998874649051,
                2.5612819054028872e-06
            ],
            [
                6.475947210046347e-07,
                1.0677024882009222e-06,
                3.05902263391829e-07,
                5.715005832895975e-07,
                5.043475885696228e-07,
                2.902312677137316e-06,
                2.699578740032504e-07,
                4.450852111155216e-07,
                4.450852111155216e-07,
                1.9947299593078385e-06
            ],
            [
                6.144176799283803e-06,
                4.785096206047877e-06,
                2.2603240284371276e-06,
                4.785094494783494e-06,
                2.9023112931873767e-06,
                1.7603440527222532e-06,
                3.288749849498565e-06,
                NaN,
                8.939699501229642e-06,
                1.2098659719757836e-06
            ],
            [
                0.9999999067049943,
                0.9999998942829981,
                0.999999943413784,
                0.9999999176674749,
                0.9999999468421946,
                0.9999999176674651,
                0.9999999434137165,
                0.9999999123575255,
                0.9999999006881023,
                0.9999997300422226
            ]
        ]
    },
    {
        "q_id": "10040_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.9947304348862686e-06,
                4.785096206076165e-06,
                3.2887506336235617e-06,
                6.475945666051092e-07,
                1.8553919030858602e-07,
                0.9999861539938648,
                1.2098656835224664e-06,
                3.05902190458764e-07,
                3.2887506336235617e-06,
                2.3823688159291947e-07
            ],
            [
                5.422217030781934e-06,
                5.715004470334646e-07,
                1.8553910183674878e-07,
                3.466327037553825e-07,
                1.0677027427624903e-06,
                1.7603440527334603e-06,
                2.561281294760143e-06,
                1.994729721518893e-06,
                1.275190732904469e-07,
                2.561281294760143e-06
            ],
            [
                2.144494841482881e-05,
                0.999999730042094,
                0.9999993524052021,
                0.9999997300421907,
                0.9999996940977368,
                1.4738980215593877e-05,
                0.9999998555020307,
                0.9999995549151076,
                0.9999997300421584,
                6.144176066943187e-06
            ],
            [
                1.8553919030858602e-07,
                0.9999991148428601,
                4.785095065171522e-06,
                0.9999974387165712,
                8.939696304311336e-06,
                5.829126555256903e-05,
                0.9999984465020644,
                0.9999988634357488,
                6.023573475041126e-08,
                0.9999974387171816
            ],
            [
                0.9999985406243039,
                5.043472278322555e-07,
                0.9999925887183817,
                1.2751908849167202e-07,
                2.2603251062147097e-06,
                1.3709573702856596e-06,
                1.0677029973219343e-06,
                0.999996711251725,
                0.9999975938976626,
                8.315278294114555e-07
            ],
            [
                0.9999998802069731,
                0.9999995818811276,
                5.043473480777865e-07,
                0.9999995549148952,
                0.9999997126314812,
                0.9999990577556312,
                0.9999987121052454,
                0.9999994631249963,
                0.9999994631251243,
                1.0677033791495609e-06
            ],
            [
                0.9999993916407461,
                0.9999994284996897,
                1.1253520230052635e-07,
                0.9999981261250644,
                0.9999983463108096,
                1.670142980920999e-05,
                0.9999994284996216,
                0.9999996940978463,
                0.999999391641109,
                0.9999997300421583
            ],
            [
                2.2603242978778778e-06,
                3.7266397283908927e-06,
                1.7603432133296774e-06,
                5.715003789046955e-07,
                8.939698435560267e-06,
                7.338207180884785e-07,
                1.9947292459347367e-06,
                4.222834451327159e-06,
                5.715002426460124e-07,
                3.4663274507713016e-07
            ],
            [
                1.7603432133136672e-06,
                6.475946437996402e-07,
                9.4224425692559e-07,
                7.338212429537553e-07,
                7.338209805170655e-07,
                1.760344052714248e-06,
                5.04347528440776e-07,
                6.475949525981759e-07,
                7.338212429537553e-07,
                3.0590226339061185e-07
            ],
            [
                0.9999993524048936,
                0.9999994956527127,
                0.9999997617629764,
                5.422217030781934e-06,
                0.9999997126314469,
                0.9999998642566219,
                0.9999998642567028,
                0.9999991148433867,
                0.9999999176675338,
                0.9999999358794327
            ],
            [
                1.275190124846946e-07,
                7.889260704968913e-06,
                5.043475885696228e-07,
                1.275189972832538e-07,
                3.9278629391427843e-07,
                0.9999892166839485,
                0.9999852610145673,
                2.3823690999323465e-07,
                1.0677029973219343e-06,
                0.999966785805288
            ],
            [
                0.9999998362622358,
                0.9999997126313784,
                0.9999996940978462,
                0.9999998144609424,
                1.4738978458623327e-05,
                0.9999998257022046,
                0.9999995818812273,
                0.9999997126315497,
                1.9947304348862686e-06,
                0.9999998257021838
            ],
            [
                0.9999994284996896,
                0.9999994631249965,
                0.9999977396754356,
                0.9999990577555194,
                1.855391239544352e-07,
                0.9999991684722708,
                0.999998996985554,
                0.9999989969862716,
                0.9999989322975132,
                0.9999993916411088
            ],
            [
                2.902313023130843e-06,
                2.2603242978871282e-06,
                1.0677024882029858e-06,
                8.315277302857965e-07,
                2.1024334103581732e-07,
                9.422442569334097e-07,
                1.5534971990169383e-06,
                3.288748281329893e-06,
                3.0590219045914655e-07,
                7.338209805240734e-07
            ],
            [
                0.9999998024947038,
                0.9999996533675031,
                0.9999999006881496,
                0.9999998257020591,
                0.9999998144609646,
                0.9999997617630902,
                0.999999880206916,
                0.9999996310113721,
                0.9999997126315497,
                0.9999997761972117
            ],
            [
                6.962253760024999e-06,
                0.9999992188516699,
                2.6995774527718623e-07,
                1.7603425837791042e-06,
                0.9999989969860325,
                5.715005151606823e-07,
                0.9999993106387084,
                2.7535684538675727e-05,
                1.7603438428800754e-06,
                0.9999989322968765
            ],
            [
                0.999999581881377,
                0.9999991684718745,
                0.9999996940977004,
                2.902313023130843e-06,
                0.9999998362622358,
                0.9999996743687035,
                0.9999987901337419,
                0.9999992661790202,
                0.9999997300422228,
                0.9999995262094991
            ],
            [
                1.4449805540763184e-07,
                0.9999993106387906,
                0.9999996533672965,
                5.422221555380179e-06,
                0.9999991684715762,
                0.9999993524054338,
                0.9999989322972579,
                0.99999967436882,
                0.9999993106386262,
                0.999999352405434
            ],
            [
                0.9999987901338849,
                0.9999980052702797,
                4.2228319344021954e-06,
                0.999996711251329,
                2.4300237838535383e-05,
                0.999999730042255,
                0.9999978766205264,
                0.9999982396572082,
                0.9999988634361556,
                0.9999969105048194
            ],
            [
                6.825609419848033e-08,
                8.764241182641775e-08,
                1.4449798650569826e-07,
                4.691162124067829e-08,
                1.8553907971879076e-07,
                1.4449800373118268e-07,
                7.734415776836702e-08,
                3.4663262111182307e-07,
                9.93120161310289e-08,
                9.931200429212718e-08
            ],
            [
                0.9999993524048935,
                0.9999996310114162,
                0.9999996310115481,
                2.4300232045225487e-05,
                0.9999994284994851,
                0.9999990577555189,
                0.9999996072136595,
                1.0129988565084915e-05,
                0.9999990577552943,
                0.9999974387168757
            ],
            [
                0.9999987901346079,
                0.9999982396572108,
                0.9999992188519493,
                0.9999987121049395,
                0.9999998461826038,
                0.9999997463980428,
                0.999998446501692,
                2.4300252321904572e-05,
                0.9999992661790205,
                0.9999998802068873
            ],
            [
                3.927862470899887e-07,
                2.699578740032504e-07,
                1.0677033791612137e-06,
                1.8553919030858602e-07,
                8.315278294114555e-07,
                1.8553916819032217e-07,
                0.9999904837517326,
                1.5534971990126997e-06,
                3.927862939126708e-07,
                2.699578740032504e-07
            ],
            [
                4.450848927637999e-07,
                6.475945666051092e-07,
                7.338212429537553e-07,
                5.04347528440776e-07,
                1.2098656835136636e-06,
                1.0677024881980089e-06,
                1.2098656835224664e-06,
                4.4508526417014975e-07,
                9.422447062202052e-07,
                8.315283250371857e-07
            ],
            [
                7.338207180864763e-07,
                1.3709570434178922e-06,
                5.043474081993875e-07,
                1.0677027427600627e-06,
                1.2098655392921197e-06,
                3.12019039369228e-05,
                1.9947304348862686e-06,
                8.315279285351409e-07,
                2.2603234894745224e-06,
                1.9947292459347367e-06
            ],
            [
                8.939700567094277e-06,
                7.889262585958025e-06,
                5.422221555414699e-06,
                1.3007131566370516e-05,
                1.7603440527334603e-06,
                1.0677028700422047e-06,
                2.5612834320563895e-06,
                1.1478772231232203e-05,
                1.994729483729522e-06,
                4.22283545819819e-06
            ],
            [
                0.9999999006881142,
                0.999999855501979,
                0.9999998802069444,
                2.2603234895372223e-06,
                0.9999998461826038,
                0.9999993524052022,
                0.9999987901341734,
                7.889265407327733e-06,
                0.9999998555020309,
                0.9999998642566219
            ],
            [
                2.699577774589574e-07,
                1.2098659719788098e-06,
                1.6373762769138607e-07,
                2.260324836787226e-06,
                2.1444953527944967e-05,
                6.475949526020042e-07,
                0.9999984465015069,
                2.260325375664839e-06,
                3.72663883989755e-06,
                9.422448185534261e-07
            ],
            [
                0.9999991684720723,
                0.9999992661787577,
                1.3007126914612648e-05,
                0.00015843617925971086,
                8.93969843573914e-06,
                0.9999942280786012,
                0.9999991148432813,
                0.9999987121052463,
                0.0002611903099837353,
                8.764245361752286e-08
            ],
            [
                3.9278629391427843e-07,
                5.715006514176113e-07,
                1.8553910183674878e-07,
                3.4663262111182307e-07,
                3.466326624336003e-07,
                5.04347287955046e-07,
                8.315279285370317e-07,
                1.637377057680051e-07,
                4.691162683297406e-08,
                4.4508515805735777e-07
            ],
            [
                5.043473480777865e-07,
                9.422448185534261e-07,
                0.9999934595620116,
                1.670141786325573e-05,
                0.9999938558268939,
                7.889260704968913e-06,
                0.9999904837460678,
                6.144176799334096e-06,
                1.209866260432471e-06,
                1.994730672675753e-06
            ],
            [
                6.962257909722651e-06,
                6.475950298011458e-07,
                1.012999218776902e-05,
                1.7603434231705793e-06,
                8.315278294072958e-07,
                1.5534984953199313e-06,
                3.0590237279085045e-07,
                4.450849988811838e-07,
                3.466327037539638e-07,
                3.4663278639738526e-07
            ],
            [
                0.99999967436882,
                0.9999989969856731,
                0.9999994631251884,
                0.9999992661788449,
                0.9999991684722704,
                0.9999994284995533,
                0.9999995262093859,
                0.9999997126315154,
                0.9999995262092728,
                6.605216832236121e-05
            ],
            [
                2.699578096403948e-07,
                0.9999998724809572,
                0.9999980052695667,
                8.315277302819205e-07,
                0.9999989969856731,
                0.9999989322970031,
                3.288748281329893e-06,
                0.9999990577550694,
                0.9999991684720718,
                1.8553910183674878e-07
            ],
            [
                0.999996033012675,
                2.9023130230846496e-06,
                4.222832941193893e-06,
                1.3709568799823232e-06,
                1.3709568799879344e-06,
                3.466325797888292e-07,
                2.561281600086738e-06,
                7.338209805200689e-07,
                1.553498124964492e-06,
                6.475950298011458e-07
            ],
            [
                0.9999991684722704,
                0.9999974387187074,
                0.9999997617631753,
                0.9999994284993488,
                0.9999991684718738,
                0.9999996940976638,
                0.9999998362622944,
                0.9999995549150544,
                0.9999996743686647,
                0.9999993524049705
            ],
            [
                1.0129988564974359e-05,
                0.9999989322971312,
                0.9999994956525924,
                0.9999992188516701,
                0.9999992188519494,
                0.9999994956525924,
                0.9999995262096121,
                0.9999993916411091,
                0.9999984465016926,
                0.9999994284992813
            ],
            [
                3.0590215399183813e-07,
                1.2751902768612997e-07,
                1.8553903548231313e-07,
                9.931189774187203e-08,
                2.5612834320563895e-06,
                1.6373772528704005e-07,
                1.6373774480605869e-07,
                1.2751902768612997e-07,
                1.209865827752005e-06,
                2.1024344128660572e-07
            ],
            [
                8.939700567094277e-06,
                0.9999978766212866,
                0.9999989322971309,
                0.999998932296749,
                3.535624650150453e-05,
                0.9999991148432813,
                0.9999991684722702,
                0.9999993106388736,
                5.422217677078203e-06,
                2.3823702359290413e-07
            ],
            [
                1.0677024881941248e-06,
                1.0677024881887838e-06,
                1.7603432133296774e-06,
                3.927860597945825e-07,
                9.422445939002803e-07,
                2.5612812947240366e-06,
                9.422445939032799e-07,
                7.338212429582604e-07,
                3.927862002663297e-07,
                9.422449308673789e-07
            ],
            [
                1.4449795205429202e-07,
                1.4449798650569826e-07,
                5.3157900413760374e-08,
                1.6373770576776313e-07,
                2.1444953527944967e-05,
                2.3823685319244518e-07,
                7.734423152941018e-08,
                1.2751908849167202e-07,
                9.931187406410953e-08,
                2.102434412875379e-07
            ],
            [
                0.999999746398073,
                2.144495864106235e-05,
                0.9999989969859123,
                0.9999996940976273,
                0.9999994631251243,
                0.9999993524051248,
                0.9999997761971049,
                0.9999997761970248,
                0.999999526209273,
                0.9999998724809115
            ],
            [
                6.144177531767002e-06,
                2.1444940745839484e-05,
                1.9947301970972664e-06,
                9.422445939032799e-07,
                3.9278634073732336e-07,
                8.481102118021275e-05,
                2.2603234895372223e-06,
                1.209866260432471e-06,
                0.002182716149709392,
                2.430024652792821e-05
            ],
            [
                0.9999989969861518,
                0.9999993106387906,
                0.9999995262094424,
                0.9999997126314812,
                0.9999993106388734,
                0.9999996072138002,
                0.9999996940977003,
                0.9999997761971317,
                0.9999988634358838,
                0.9999994284994854
            ],
            [
                0.9999988634361554,
                0.9999982396567886,
                1.2098653950692178e-06,
                1.5534971990126997e-06,
                7.889260704968913e-06,
                0.9999980052698048,
                0.9999986290431212,
                0.9999991684719727,
                2.2603248367949354e-06,
                5.422220262636381e-06
            ],
            [
                1.994729483729522e-06,
                4.4508515805735777e-07,
                2.2603253756956754e-06,
                1.5534971990169383e-06,
                4.22283545819819e-06,
                3.05902263391829e-07,
                3.059022269250683e-07,
                1.3709576971463352e-06,
                8.939693107288474e-06,
                1.7603425837903113e-06
            ],
            [
                5.043473480730849e-07,
                1.2098659719716573e-06,
                1.2098653950551882e-06,
                1.0677029973056687e-06,
                9.422443692489024e-07,
                1.3709567165530083e-06,
                6.475951069961737e-07,
                1.3709575337016483e-06,
                2.699578096403948e-07,
                5.043476486902204e-07
            ],
            [
                1.3709575336947905e-06,
                2.2603248367512505e-06,
                4.222834954280646e-06,
                4.222832437798974e-06,
                9.4224425692559e-07,
                1.1478764021029928e-05,
                1.3709575337125585e-06,
                3.7266401725681614e-06,
                1.9947294837154625e-06,
                1.0677028700363782e-06
            ],
            [
                1.300712536408621e-05,
                5.715005151606823e-07,
                2.3823688159291947e-07,
                0.9999997126314126,
                9.422443692574719e-07,
                2.1024339116168358e-07,
                1.3709575337159875e-06,
                9.42244256915735e-07,
                2.3823682479292225e-07,
                3.53562549329801e-05
            ],
            [
                0.9999998024947038,
                0.99999921885167,
                0.9999994284995534,
                5.422221555414699e-06,
                1.6701427818338537e-05,
                0.9999417087277297,
                0.9999989322975126,
                0.9999822214481721,
                0.9999994284994174,
                8.764249540862797e-08
            ],
            [
                1.6373766672973748e-07,
                8.93969843573914e-06,
                3.927863407379485e-07,
                6.144173869603344e-06,
                0.9999998555019964,
                0.9999987121047857,
                3.535625071602016e-05,
                9.422443692574719e-07,
                0.9999975938982357,
                1.5534984953552536e-06
            ],
            [
                5.043475885696228e-07,
                7.338210680021253e-07,
                3.4663278639892215e-07,
                2.144495608378187e-05,
                4.450850519409479e-07,
                2.102434162245973e-07,
                9.422442569334097e-07,
                7.338208930460318e-07,
                8.31528325040778e-07,
                1.3709567165617364e-06
            ],
            [
                1.994730672668496e-06,
                NaN,
                7.484625405027093e-05,
                5.715003789046955e-07,
                6.144173869603344e-06,
                3.288749457469787e-06,
                1.892515501014656e-05,
                NaN,
                5.422220909009474e-06,
                1.1478770862735993e-05
            ],
            [
                5.04347468323289e-07,
                3.059022998581767e-07,
                2.1024339116168358e-07,
                9.931202796993203e-08,
                7.338207180898968e-07,
                9.422447062294175e-07,
                3.7266383956509585e-06,
                1.5534983101644536e-06,
                8.315283250394546e-07,
                7.338207180898968e-07
            ],
            [
                1.370957860576702e-06,
                3.2887506336235617e-06,
                5.715003789046955e-07,
                1.5534973842076057e-06,
                9.422445939054222e-07,
                1.1478766757718129e-05,
                5.715005832895975e-07,
                3.7266410611296085e-06,
                1.3709572068522336e-06,
                4.4508510499849186e-07
            ],
            [
                2.2603234895372223e-06,
                5.715005151606823e-07,
                1.147877359957198e-05,
                1.3709567165617364e-06,
                4.450849988811838e-07,
                3.7266410611296085e-06,
                1.012998977264307e-05,
                3.466325797896173e-07,
                1.9947304348862686e-06,
                1.4738978458623327e-05
            ],
            [
                2.699576809143613e-07,
                2.260323758987159e-06,
                2.2603248367949354e-06,
                4.4508505193932864e-07,
                1.3709576971425944e-06,
                6.475947982037486e-07,
                1.7603425837903113e-06,
                2.5612819054028872e-06,
                3.059022269254856e-07,
                5.422220262636381e-06
            ],
            [
                0.9999986290426306,
                0.9999996743688976,
                7.734415776836702e-08,
                4.450848927658745e-07,
                9.931189774187203e-08,
                0.9999989322973851,
                0.9999993916409636,
                0.9999998144609646,
                0.9999997126314126,
                2.699577774585891e-07
            ],
            [
                0.9999987901338846,
                4.222832941193893e-06,
                0.9999989322971308,
                2.902312677150514e-06,
                0.9999992661787579,
                0.9999993106392017,
                0.999999653367462,
                1.3007125363908762e-05,
                0.9999996533675032,
                0.9999997463980731
            ],
            [
                4.222833948008874e-06,
                1.9947299593078385e-06,
                0.0006263341658335579,
                1.0677024882029858e-06,
                1.3709576971425944e-06,
                8.315279285370317e-07,
                1.2098659719788098e-06,
                7.33821330437595e-07,
                3.9278610661902853e-07,
                5.715005151606823e-07
            ],
            [
                0.9999972735290847,
                0.999998005269806,
                0.9999967112513323,
                0.9999969105055572,
                0.9999983463106132,
                0.999998932297386,
                0.9999982396574187,
                0.9999977396765141,
                0.00037998448684954363,
                0.9999984465018772
            ],
            [
                6.605217618626244e-05,
                0.9999982396565795,
                0.9999991684716755,
                1.8925155009354808e-05,
                0.9999984465028029,
                5.144223205871514e-05,
                0.9999989322973859,
                0.9999975938973781,
                0.9999986290421407,
                8.481103128159609e-05
            ],
            [
                5.715002426486762e-07,
                1.760343003481596e-06,
                2.9023119851899796e-06,
                2.699578096403948e-07,
                1.209865827752005e-06,
                7.338210680021253e-07,
                3.466326211113502e-07,
                2.69957906184239e-07,
                6.144175334510455e-06,
                3.059021175261338e-07
            ],
            [
                0.9999962733616159,
                0.9999987121047873,
                0.9999984465018779,
                0.9999967112517251,
                1.5534975693979422e-06,
                2.102434162245973e-07,
                0.9999972735290933,
                0.9999974387174918,
                0.9999978766223045,
                0.9999974387165719
            ],
            [
                1.27519088491875e-07,
                8.764244316973974e-08,
                3.466326624336003e-07,
                5.043476486924565e-07,
                2.3823690999323465e-07,
                2.3823693839325527e-07,
                1.0677024882029858e-06,
                6.962257909842961e-06,
                7.338207180898968e-07,
                5.715003789046955e-07
            ],
            [
                5.715003107755449e-07,
                3.466327037539638e-07,
                8.764245361752286e-08,
                1.8553916819032217e-07,
                1.4449802095609418e-07,
                2.3823690999323465e-07,
                5.043472879525233e-07,
                2.6995771309523475e-07,
                3.46632497145457e-07,
                1.4449805540740185e-07
            ],
            [
                0.9999996940977368,
                3.466325797900508e-07,
                0.9999998802069587,
                0.9999997897566341,
                0.9999997463980729,
                1.8553914607267268e-07,
                2.1024334103581732e-07,
                0.9999998362623335,
                8.315277302841894e-07,
                0.9999995549151076
            ],
            [
                0.9999992661792824,
                3.059022269250683e-07,
                5.04347287955046e-07,
                0.999999789756659,
                7.734421308914719e-08,
                0.9999992661791948,
                3.4663278639892215e-07,
                2.6995774527718623e-07,
                0.9999989322971308,
                1.1253520230052635e-07
            ],
            [
                NaN,
                NaN,
                0.9998766054706261,
                NaN,
                1.370957860576702e-06,
                0.00026119027893155484,
                NaN,
                0.9999987121047855,
                5.04347468323289e-07,
                0.9997965729560688
            ],
            [
                0.9999995549149483,
                0.9999995549151075,
                0.9999997617630617,
                3.72663883989755e-06,
                0.9999990577554067,
                3.72663883989755e-06,
                0.9999989969859123,
                3.120190393794438e-05,
                0.9999991684720722,
                0.9999993916407462
            ],
            [
                0.9999930377462608,
                0.9999997463981639,
                0.9999995262092732,
                0.9999997761972118,
                0.9999987901344616,
                0.9999985406230849,
                0.9999994284995535,
                0.9999989969857935,
                0.9999996072137531,
                0.999999266179108
            ],
            [
                0.999999631011416,
                0.999999894282935,
                0.9999994284997575,
                0.9999991148431756,
                0.9999993524052793,
                0.9999995818813269,
                0.9999991684721709,
                0.999994577782974,
                0.9999969105048203,
                0.9999996533674617
            ],
            [
                0.9999989322972579,
                0.9999997126313442,
                4.7850933539684755e-06,
                5.8291272507386246e-05,
                0.9999993106387085,
                0.9999993524049707,
                0.9999996533673378,
                0.9999991148427542,
                0.9999982396567885,
                0.9999990577556314
            ],
            [
                1.0677032518748838e-06,
                5.715004470272272e-07,
                1.3709572068422585e-06,
                1.2098655392871682e-06,
                0.9999916019270014,
                0.9999832985702809,
                1.2098653950606901e-06,
                1.2098658277451275e-06,
                1.2098653950606901e-06,
                5.715007195431641e-07
            ],
            [
                0.9999970976887137,
                0.9999980052709949,
                0.9999977396746337,
                0.9999967112501594,
                0.9999988634362903,
                0.9999969105051967,
                0.9999960330155195,
                0.0011695100176903016,
                0.9999921107364914,
                0.9999975938968054
            ],
            [
                5.71500719545698e-07,
                1.4449798650569826e-07,
                3.059021175261338e-07,
                3.927863407379485e-07,
                1.8553919030858602e-07,
                2.1024336609874897e-07,
                2.3823693839325527e-07,
                1.6373772528704005e-07,
                6.475946438055299e-07,
                5.04347468323289e-07
            ],
            [
                5.8291293348093234e-05,
                0.9999997761972116,
                0.9999994631249326,
                0.9999996533673792,
                0.9999997761970782,
                0.9999997126314812,
                0.9999988634361551,
                1.8925145985895816e-05,
                0.9999998555019619,
                0.9999996533673376
            ],
            [
                0.9999999006880431,
                0.9999994956527126,
                0.999998540623606,
                0.9999998874647441,
                0.999999712631447,
                0.9999999176675143,
                0.9999993106391193,
                0.999999631011504,
                0.999999776197025,
                0.9999998555020135
            ],
            [
                1.0,
                0.9999997761970782,
                6.144173137170873e-06,
                0.9999999176675634,
                0.9999989322970031,
                0.9999999434137435,
                0.9999998942828973,
                0.9999999067050832,
                0.9999999468421946,
                1.1478769494542698e-05
            ],
            [
                3.927860597945825e-07,
                3.927861534406222e-07,
                3.927862939126708e-07,
                3.466327450765785e-07,
                7.338208930391909e-07,
                5.043475885674441e-07,
                4.4508494582314646e-07,
                2.3823688159291947e-07,
                1.0677024881829577e-06,
                3.0590215399183813e-07
            ],
            [
                0.9999981261237263,
                0.9999955048189743,
                0.9999994631251887,
                0.9999975938982372,
                0.99999709768802,
                0.9999994284994854,
                0.9999980052695694,
                0.9999964991443409,
                6.475946438055299e-07,
                0.999995777166058
            ],
            [
                3.288750241561788e-06,
                0.9999993524049708,
                8.939693107288474e-06,
                0.9999993106388738,
                1.012999218776902e-05,
                0.99999671125017,
                0.9999992661792828,
                0.9999994284994861,
                0.9999994956527126,
                0.9999992188518565
            ],
            [
                1.4449805540763184e-07,
                3.4663278639892215e-07,
                0.9999964991455927,
                1.444980209564556e-07,
                8.315283250371857e-07,
                7.889266347786918e-06,
                1.7603438428800754e-06,
                8.315278294114555e-07,
                9.61024035541569e-05,
                6.962257079832313e-06
            ],
            [
                0.9999925887220952,
                5.8291279438030564e-05,
                8.315281267882195e-07,
                8.315281267861397e-07,
                0.9999934595636396,
                0.9999904837520285,
                0.9999892166891815,
                2.26032402841657e-06,
                0.9999930377454708,
                1.994729483705484e-06
            ],
            [
                0.9999969105063081,
                1.1478765389222573e-05,
                0.9999984465016946,
                0.9999991148433875,
                6.962256249935742e-06,
                0.9999981261248446,
                0.9999981261246218,
                1.892514598551715e-05,
                0.9999975938965214,
                0.9999981261250712
            ],
            [
                1.2098662604291696e-06,
                4.785096776499213e-06,
                1.5534981249697903e-06,
                2.2603240284371276e-06,
                5.422221555380179e-06,
                6.144176066901277e-06,
                1.0129993395336818e-05,
                1.7603427936335396e-06,
                8.315284241650899e-07,
                9.422450431989127e-07
            ],
            [
                0.999999114842965,
                0.999998239656999,
                1.5534975693979422e-06,
                0.9999993916407464,
                2.90231233114251e-06,
                2.2603242978871282e-06,
                9.422442569315887e-07,
                8.939697369980456e-06,
                1.1478769494396542e-05,
                1.9947294837154625e-06
            ],
            [
                1.8553919030858602e-07,
                3.9278615344178325e-07,
                1.3709572068522336e-06,
                5.1442238195844654e-05,
                8.939699501229642e-06,
                9.422443692555439e-07,
                6.9622537599680095e-06,
                1.5534981249697903e-06,
                6.475947210031623e-07,
                2.561282516066741e-06
            ],
            [
                0.9999998144608319,
                0.9999992188513904,
                0.9999995818810776,
                0.9999998942830358,
                0.9999999273417663,
                0.9999999397642725,
                1.4449795205429202e-07,
                0.9999998362623138,
                0.9999999176675338,
                0.9999999067050164
            ],
            [
                0.99999967436882,
                0.999998996986152,
                0.9999984465026175,
                0.9999995262093861,
                0.9999992188516701,
                0.9999995262094425,
                0.9999987901337409,
                0.9999996743688977,
                0.9999993916408191,
                0.9999996533672967
            ],
            [
                0.999999631011328,
                0.9999996940978826,
                0.9999998555020307,
                1.6373768624837685e-07,
                5.715003107767143e-07,
                0.9999999317440279,
                0.999999939764215,
                0.9999999226558053,
                0.9999993916411086,
                0.9999999226558423
            ],
            [
                0.9999998257021838,
                0.9999998257022046,
                0.9999993524052023,
                0.9999998874648112,
                0.9999997300422228,
                5.1442207537151994e-05,
                0.9999998802069017,
                0.9999995818811277,
                0.9999998144609205,
                0.9999998144608541
            ],
            [
                1.6373770576776313e-07,
                6.962257079889302e-06,
                0.9999981261243949,
                1.275190124846946e-07,
                0.9999998461826772,
                0.9999996072136595,
                0.9999998942830862,
                4.785094494783494e-06,
                5.715006514176113e-07,
                0.9999993916411088
            ],
            [
                2.9023119851899796e-06,
                4.0063696969564425e-05,
                1.994730197090463e-06,
                5.715006514176113e-07,
                1.5534975693933505e-06,
                3.726638839878908e-06,
                2.5612822107167428e-06,
                8.315278294114555e-07,
                1.7603430034867993e-06,
                8.939700567094277e-06
            ],
            [
                0.9999995262095552,
                0.9999997463980125,
                0.9999996533673791,
                0.9999987121046313,
                0.9999998802069731,
                0.9999998724809419,
                0.9999993524048932,
                0.9999991684721709,
                0.9999999067050164,
                0.9999999006880668
            ],
            [
                2.5612834320563895e-06,
                2.561282821402217e-06,
                1.7603440527334603e-06,
                2.902312331170226e-06,
                1.7603425837855082e-06,
                3.288749849529972e-06,
                7.889265407327733e-06,
                6.962258739796719e-06,
                1.7603425837903113e-06,
                4.222833948008874e-06
            ],
            [
                6.47594952603035e-07,
                8.315278294114555e-07,
                8.315279285370317e-07,
                8.315284241665078e-07,
                1.5534977545886537e-06,
                9.422444815814404e-07,
                1.7603425837903113e-06,
                1.760343213335281e-06,
                5.715006514176113e-07,
                3.9278605979534166e-07
            ],
            [
                0.9999990577554075,
                0.9999994284995538,
                0.9999984465018773,
                0.9999987901347513,
                0.9999989969854344,
                0.9999989322975132,
                0.9999981261243953,
                0.9999996310114163,
                0.9999978766210346,
                0.9999983463096289
            ],
            [
                0.9999998362622553,
                0.999999730042094,
                0.9999999123575046,
                0.9999998024946567,
                0.9999999397643011,
                0.9999997463980428,
                0.9999999273418355,
                0.9999999176674651,
                1.994729008145876e-06,
                0.9999998724809571
            ],
            [
                0.9999998461826038,
                0.9999996743688975,
                0.9999998362622552,
                0.9999989322967487,
                6.144172404738491e-06,
                0.9999992188514837,
                0.9999996940977004,
                0.9999998642566704,
                0.999999653367503,
                0.999999428499281
            ],
            [
                4.785092783149804e-06,
                1.3709570434122812e-06,
                6.962257079465052e-06,
                3.726641061085547e-06,
                1.5534973842030142e-06,
                7.338208930460318e-07,
                2.9023109472244114e-06,
                5.422217030747413e-06,
                1.760343213322473e-06,
                2.902313369111213e-06
            ],
            [
                0.999999526209499,
                0.9999995818811278,
                0.9999989969860321,
                0.999999168471874,
                0.9999991684718743,
                0.9999993524054339,
                0.9999981261243962,
                0.9999994956525923,
                0.999998996986033,
                0.9999989969855535
            ],
            [
                0.9999989969857938,
                0.9999991684720725,
                0.9999987901344618,
                0.9999997463982242,
                0.9999962733607254,
                0.9999934595651339,
                0.9999985406232603,
                0.9999994284995538,
                0.9999996310116361,
                0.9999993916408189
            ],
            [
                0.9999994956524119,
                3.288749065423109e-06,
                1.3007128464961824e-05,
                0.9999993106391193,
                0.9999977396746281,
                0.9999987121043256,
                0.9999996310115482,
                0.9999646437367545,
                0.9999969105059279,
                8.93969950132721e-06
            ],
            [
                0.9999990577549581,
                2.2603245673443566e-06,
                5.043474081993875e-07,
                3.0590219045914655e-07,
                9.422447062294175e-07,
                9.422442569334097e-07,
                1.3709568799919866e-06,
                3.9278605979534166e-07,
                1.3709572068553509e-06,
                0.9999989969861518
            ],
            [
                0.9999998724809116,
                0.9999998257021422,
                0.9999988634358838,
                0.9999998461826954,
                0.9999994631247404,
                0.9999995818812273,
                0.9999995262094988,
                0.999999776197025,
                0.9999997300422548,
                0.9999993916409635
            ],
            [
                8.315278294097538e-07,
                1.0677032518785256e-06,
                1.2098655392871682e-06,
                7.338212429582604e-07,
                3.927862470890063e-07,
                3.2887478892504536e-06,
                5.715003789017068e-07,
                2.902312677137316e-06,
                5.422220262636381e-06,
                5.715003789033962e-07
            ],
            [
                8.315283250260307e-07,
                7.338211554783522e-07,
                4.4508505193791187e-07,
                9.4224425692559e-07,
                1.553498124964492e-06,
                2.382368531929327e-07,
                1.7603432133032607e-06,
                2.6995774527577444e-07,
                9.422450431989127e-07,
                3.4663274507098256e-07
            ],
            [
                2.3823690999323465e-07,
                0.999999218851577,
                1.209866260432471e-06,
                1.209865827752005e-06,
                4.006367786720367e-05,
                0.9999938558246856,
                1.4738983729053029e-05,
                4.785095635655362e-06,
                2.1024334103581732e-07,
                9.93120161310289e-08
            ],
            [
                1.0677032518785256e-06,
                1.8925145985895816e-05,
                4.450848927650143e-07,
                4.222833444590791e-06,
                1.4738981972564636e-05,
                4.222832941193893e-06,
                1.7603427936335396e-06,
                5.71500515159253e-07,
                1.1478769494396542e-05,
                1.3709567165579959e-06
            ],
            [
                1.7603434231833873e-06,
                9.422447062294175e-07,
                1.2098652508424818e-06,
                1.0677032518814388e-06,
                1.2098659719788098e-06,
                5.043472278322555e-07,
                1.6373772528704005e-07,
                1.994729483729522e-06,
                8.764244316973974e-08,
                7.338208930460318e-07
            ],
            [
                3.9278629391427843e-07,
                4.4508515805735777e-07,
                4.222834451403972e-06,
                1.8553903548287212e-07,
                7.73442776303243e-08,
                8.764254764780641e-08,
                5.043475885696228e-07,
                2.699578096393206e-07,
                1.6373774480605869e-07,
                1.4449795205472734e-07
            ],
            [
                0.9999997300421904,
                0.9999993524054339,
                0.999999789756659,
                0.9999994284995535,
                0.9999997761970515,
                0.9999993524050478,
                0.9999997897566592,
                0.99999926617867,
                0.9999995262092729,
                0.9999998461826223
            ],
            [
                3.05902263391829e-07,
                3.4663274507713016e-07,
                8.315277302788957e-07,
                1.1253509497883659e-07,
                3.466325797888292e-07,
                7.338207180898968e-07,
                4.4508510499737865e-07,
                6.144176066943187e-06,
                3.4663278639892215e-07,
                1.8553907971879076e-07
            ],
            [
                3.1201922535494165e-05,
                0.0001398220742354593,
                1.2751901248454963e-07,
                2.699578740032504e-07,
                6.1441746020359e-06,
                2.3823688159291947e-07,
                0.9999994631249322,
                3.9278615344178325e-07,
                3.9278634073732336e-07,
                1.3709572068522336e-06
            ],
            [
                1.3007123813382511e-05,
                7.734416698849138e-08,
                1.0,
                0.00020342697378147203,
                2.10243290909724e-07,
                0.999988521234621,
                2.2603234895372223e-06,
                1.27519088491875e-07,
                3.0590219045914655e-07,
                1.994729008151319e-06
            ],
            [
                3.4663249714451116e-07,
                6.475945666009864e-07,
                3.0590226338838606e-07,
                6.475948754012522e-07,
                5.715005832827105e-07,
                3.059021175247079e-07,
                8.3152792852928e-07,
                5.043474081993875e-07,
                4.4508515805199415e-07,
                6.475951069985296e-07
            ],
            [
                1.0677024881980089e-06,
                2.9023119851781017e-06,
                1.0677026154806063e-06,
                5.715003107755449e-07,
                0.9999986290423049,
                5.043472879540142e-07,
                9.422444815765128e-07,
                9.422448185510695e-07,
                1.5534979397740895e-06,
                5.422217030747413e-06
            ],
            [
                0.9999996743688977,
                7.338213304363436e-07,
                0.9999992188519495,
                1.275191036933194e-07,
                0.9999996072137535,
                2.3823690999323465e-07,
                6.023573475041126e-08,
                3.05902263391829e-07,
                0.9999997126313099,
                0.9999987901347498
            ],
            [
                5.715005832886879e-07,
                8.315279285351409e-07,
                1.7603430034867993e-06,
                3.927862939126708e-07,
                5.043476486915964e-07,
                6.962257079832313e-06,
                1.2098658277489788e-06,
                1.1478770862735993e-05,
                8.315281267861397e-07,
                7.338208055680009e-07
            ],
            [
                0.9999990577550703,
                0.9999997300421907,
                0.9999989969855536,
                0.9999993106387906,
                0.9999991148426485,
                0.9999980052702807,
                0.9999996310116362,
                0.9999995262092165,
                0.9999996072136129,
                0.9999996533675031
            ],
            [
                0.9999989969854345,
                1.0129993395336818e-05,
                0.9999997761972117,
                0.999999761763147,
                7.484626297687326e-05,
                0.9999994956525922,
                0.9999995549147891,
                0.9999994284995533,
                0.9999992661788448,
                0.9999998555020481
            ],
            [
                0.999999114843284,
                0.999999310639202,
                0.99999521490495,
                1.0129992187658463e-05,
                4.222834954753043e-06,
                3.726637951367137e-06,
                0.9999991684717751,
                0.00015843617918594497,
                0.9999989969861526,
                1.8925141473978602e-05
            ],
            [
                0.999998540623954,
                1.067703124601679e-06,
                4.222834954801051e-06,
                0.9999998024946566,
                3.726639284144195e-06,
                0.9999992188514837,
                0.9999983463098242,
                1.8553910183674878e-07,
                0.9999992188519491,
                0.9999995818811774
            ],
            [
                0.9999996072136126,
                0.9999992188512973,
                0.9999997761971583,
                0.999999789756609,
                8.315284241665078e-07,
                0.9999996743688587,
                0.999999789756609,
                0.9999988634361545,
                0.999998932296749,
                0.9999994631251244
            ],
            [
                0.9999962733620712,
                3.059022998576899e-07,
                0.9999967112493722,
                0.9999983463096284,
                0.9999991684715771,
                0.9999984465026182,
                0.9999955048168306,
                0.9999994956527126,
                0.9999960330150409,
                0.9999960330145771
            ],
            [
                1.4449805540700758e-07,
                0.9999998362622553,
                0.9999930377404375,
                1.6373770576776313e-07,
                0.999998996986032,
                0.9999986290426309,
                0.9999980052705183,
                3.653479902594117e-08,
                0.9999978766207804,
                5.3157830707696514e-08
            ],
            [
                0.9999998144608983,
                1.1478770862882149e-05,
                0.9999994631249963,
                7.889260704968913e-06,
                1.8553903548287212e-07,
                0.9999996743687422,
                0.999998712104478,
                0.99999967436882,
                0.9999995262095552,
                4.785094494811783e-06
            ]
        ]
    },
    {
        "q_id": "9796_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            9,
            10,
            14,
            15,
            17,
            19,
            21,
            22,
            26,
            27,
            28,
            31,
            33,
            34,
            35,
            36,
            37,
            40,
            41,
            46,
            47,
            49,
            51,
            52,
            54,
            55,
            56,
            58,
            59,
            61,
            63,
            65,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            74,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            88,
            89,
            90,
            92,
            94,
            95,
            96,
            99,
            100,
            102,
            105,
            107,
            109,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            122,
            123,
            124,
            127
        ],
        "rewards": [
            [
                6.475950298011458e-07,
                5.71500515159253e-07,
                9.422443692574719e-07,
                9.422444815814404e-07,
                1.5534983101644536e-06,
                5.043475885696228e-07,
                1.0677033791612137e-06,
                8.315284241650899e-07,
                5.715003107767143e-07,
                7.33821330437595e-07
            ],
            [
                2.699577774585891e-07,
                6.475949526020042e-07,
                1.9947304348862686e-06,
                5.04347287955046e-07,
                2.699576809143613e-07,
                5.715002426486762e-07,
                2.561281294760143e-06,
                4.4508505193932864e-07,
                4.450850519403407e-07,
                5.04347287955046e-07
            ],
            [
                1.067702870039777e-06,
                NaN,
                8.315280276580819e-07,
                1.5534979397790343e-06,
                1.994730672668496e-06,
                1.994729008145876e-06,
                3.2887478892683997e-06,
                1.7603440527286572e-06,
                9.422443692555439e-07,
                8.315284241650899e-07
            ],
            [
                6.475948754012522e-07,
                2.2603237589779086e-06,
                2.6995774527577444e-07,
                1.2098659719757836e-06,
                6.475950298011458e-07,
                6.475947210031623e-07,
                7.338209805224048e-07,
                6.47594952595231e-07,
                1.994730197090463e-06,
                5.4222183234485234e-06
            ],
            [
                2.6995790618350237e-07,
                4.450852641737424e-07,
                6.475948754012522e-07,
                7.338211554783522e-07,
                9.422444815792981e-07,
                1.2098658277489788e-06,
                2.1024334103352274e-07,
                5.04347528446051e-07,
                NaN,
                NaN
            ],
            [
                5.043475885688201e-07,
                1.5534973842076057e-06,
                3.7266410611296085e-06,
                1.9947301970972664e-06,
                5.422217677152175e-06,
                4.222832437798974e-06,
                1.9947292459347367e-06,
                9.93120161306789e-08,
                2.5612831267202583e-06,
                3.7266397283908927e-06
            ],
            [
                1.0677027427600627e-06,
                5.04347528446051e-07,
                7.338213304363436e-07,
                6.475945666051092e-07,
                1.3709567165617364e-06,
                2.3823688159291947e-07,
                7.338209805240734e-07,
                8.315282259138311e-07,
                8.315279285351409e-07,
                3.059021175261338e-07
            ],
            [
                1.0677028700422047e-06,
                1.5534981249697903e-06,
                1.4449803818215767e-07,
                6.023578501513224e-08,
                8.939694172957213e-06,
                0.0001233946338036995,
                3.2887498495150166e-06,
                4.222833444590791e-06,
                5.422218969895357e-06,
                7.889266347786918e-06
            ],
            [
                NaN,
                NaN,
                2.5612834320563895e-06,
                2.902313023130843e-06,
                NaN,
                1.209866260432471e-06,
                2.90231094723893e-06,
                9.422445939054222e-07,
                1.8553919030858602e-07,
                NaN
            ],
            [
                9.422450431989127e-07,
                3.726637951367137e-06,
                2.2603242978871282e-06,
                3.2887506336235617e-06,
                2.5612819054028872e-06,
                4.785092783519724e-06,
                4.222832941193893e-06,
                4.450852111148132e-07,
                6.1441746020359e-06,
                6.144177531767002e-06
            ],
            [
                3.72663883989755e-06,
                1.7603430034867993e-06,
                5.422221555414699e-06,
                0.9999151889691621,
                5.04347287955046e-07,
                0.9999967112513287,
                5.422218969895357e-06,
                3.288748281329893e-06,
                0.9999949062962203,
                8.315277302841894e-07
            ],
            [
                1.637377643243723e-07,
                1.8553907971855875e-07,
                4.4508505193932864e-07,
                2.1024326584639497e-07,
                5.043475885696228e-07,
                2.6995774527657245e-07,
                1.8553907971855875e-07,
                1.4449798650476187e-07,
                8.315278294097538e-07,
                2.3823702359290413e-07
            ],
            [
                1.5534973842076057e-06,
                7.338211554801876e-07,
                6.475951069985296e-07,
                6.475949526003845e-07,
                1.3709576971379186e-06,
                9.422448185510695e-07,
                1.5534979397740895e-06,
                5.715003789046955e-07,
                7.889261645090304e-06,
                1.0677027427600627e-06
            ],
            [
                3.4663249714612693e-07,
                1.9947304348862686e-06,
                8.315279285370317e-07,
                3.4663249714612693e-07,
                3.9278610661902853e-07,
                5.715002426486762e-07,
                5.043476486924565e-07,
                3.927862002663297e-07,
                NaN,
                3.059022998569248e-07
            ],
            [
                8.939697369980456e-06,
                1.9947304348862686e-06,
                6.47595107001401e-07,
                1.209866260432471e-06,
                9.422447062270609e-07,
                NaN,
                6.962258739796719e-06,
                9.422447062294175e-07,
                1.9947301970972664e-06,
                4.22283545819819e-06
            ],
            [
                4.2228339479858295e-06,
                0.9999988634362901,
                1.012999218776902e-05,
                0.9999982396567882,
                6.144173137170873e-06,
                0.9999970976873275,
                0.9999985406232584,
                0.9999982396561586,
                0.999999391641181,
                0.9999995262094988
            ],
            [
                2.260325106237323e-06,
                9.422450431989127e-07,
                4.4508526417298334e-07,
                5.715003107755449e-07,
                5.04347287955046e-07,
                1.2098653950656417e-06,
                6.475949525981759e-07,
                3.4663253846473677e-07,
                6.475949525981759e-07,
                2.6995790618469934e-07
            ],
            [
                9.422447062294175e-07,
                3.9278634073732336e-07,
                4.785095065204162e-06,
                1.4738980215352592e-05,
                1.6701427818034747e-05,
                1.6701429808298613e-05,
                2.2603253756874524e-06,
                3.288749065423109e-06,
                2.260323758987159e-06,
                3.7266406168827523e-06
            ],
            [
                4.450849988811838e-07,
                2.902310947208574e-06,
                3.927862939126708e-07,
                3.927861534406222e-07,
                9.42244256915735e-07,
                3.9278610661902853e-07,
                4.222834451327159e-06,
                3.927860597935108e-07,
                4.450848927650143e-07,
                3.927862002654366e-07
            ],
            [
                4.4508494582405734e-07,
                0.9999916019309938,
                NaN,
                0.9999962733616097,
                0.999966785789406,
                0.9999910602994504,
                2.75356812556058e-05,
                0.999985261023348,
                0.9999964991447562,
                4.222834954778007e-06
            ],
            [
                3.288749457469787e-06,
                8.315279285351409e-07,
                5.4222183235249605e-06,
                7.889261645427538e-06,
                5.043474081993875e-07,
                1.209865539295696e-06,
                1.0677029973192638e-06,
                3.2887478892683997e-06,
                1.3709568799823232e-06,
                2.3823699519225038e-07
            ],
            [
                4.785096776499213e-06,
                5.422218323487975e-06,
                4.006371129615879e-05,
                2.1444940745839484e-05,
                0.9999970976890554,
                4.785095065232451e-06,
                1.6701419854156377e-05,
                7.889265407327733e-06,
                6.144173137170873e-06,
                0.9999960330136183
            ],
            [
                1.0677033791612137e-06,
                2.5612812947240366e-06,
                7.338207180898968e-07,
                1.209865827752005e-06,
                1.3709576971463352e-06,
                1.2098652508424818e-06,
                8.315277302857965e-07,
                7.338208930460318e-07,
                1.5534971990169383e-06,
                1.2098659719788098e-06
            ],
            [
                5.04347408197782e-07,
                7.338213304363436e-07,
                1.4449805540700758e-07,
                6.475945666033422e-07,
                9.422443692527585e-07,
                3.05902117523595e-07,
                3.059022998569248e-07,
                3.927863875616689e-07,
                1.2098653950656417e-06,
                2.2603242978871282e-06
            ],
            [
                4.78509278348926e-06,
                3.288747889284851e-06,
                2.260325106237323e-06,
                2.561281600076256e-06,
                2.2603237589779086e-06,
                1.3709572068522336e-06,
                6.475947982002148e-07,
                3.726639284125553e-06,
                NaN,
                2.260324567337161e-06
            ],
            [
                4.2228339479858295e-06,
                1.9947301970972664e-06,
                NaN,
                NaN,
                2.902312677150514e-06,
                1.5534981249697903e-06,
                2.902313023130843e-06,
                1.209865539295696e-06,
                1.2098661162023305e-06,
                NaN
            ],
            [
                1.5534984953453635e-06,
                2.902311639183378e-06,
                3.2887478892504536e-06,
                4.450849458179853e-07,
                1.9947304348703948e-06,
                7.338207180864763e-07,
                1.760344052714248e-06,
                5.043472879481655e-07,
                3.288750241561788e-06,
                2.2603234895176927e-06
            ],
            [
                8.315284241650899e-07,
                3.059022269250683e-07,
                2.5612819054133693e-06,
                9.422449308774482e-07,
                2.2603240284371276e-06,
                1.275190124842887e-07,
                NaN,
                2.5612819054028872e-06,
                2.2603253756956754e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                7.338207180898968e-07,
                4.4508499888219586e-07,
                4.450851049991497e-07,
                1.209865539298447e-06,
                6.47595107001401e-07,
                2.2603251062450327e-06,
                NaN,
                1.0677026154827912e-06
            ],
            [
                1.6373776432481905e-07,
                2.902313023130843e-06,
                9.931192141964017e-08,
                2.1024336609874897e-07,
                1.8553907971855875e-07,
                4.785092783519724e-06,
                1.6373764721072816e-07,
                2.9023112932177327e-06,
                9.931193325852072e-08,
                1.5534975693979422e-06
            ],
            [
                1.5534971990169383e-06,
                6.475950298011458e-07,
                3.927862470890063e-07,
                1.994729721518893e-06,
                3.927862470899887e-07,
                1.9947301970972664e-06,
                3.0590237279032884e-07,
                4.450852111148132e-07,
                5.715002426475718e-07,
                1.994729483723626e-06
            ],
            [
                3.1201922535494165e-05,
                NaN,
                3.927863407379485e-07,
                5.043474082012222e-07,
                8.315280276626197e-07,
                1.3709568799919866e-06,
                4.4508515805735777e-07,
                3.9278629391427843e-07,
                9.422445939054222e-07,
                7.889266347786918e-06
            ],
            [
                7.338210680021253e-07,
                1.0677033791612137e-06,
                8.315281267882195e-07,
                3.9278610661902853e-07,
                3.4663266243308805e-07,
                8.315278294114555e-07,
                4.4508515805735777e-07,
                2.5612831267202583e-06,
                2.1024326584582131e-07,
                6.47595107001401e-07
            ],
            [
                2.1024341622426268e-07,
                3.059021175261338e-07,
                5.043474081957179e-07,
                2.6995784182073116e-07,
                3.059022998581767e-07,
                1.6373764721072816e-07,
                3.927862002663297e-07,
                2.6995771309523475e-07,
                NaN,
                9.422445939032799e-07
            ],
            [
                3.059023727894942e-07,
                6.475947210012481e-07,
                4.4508494582314646e-07,
                4.450851580555361e-07,
                6.475947210046347e-07,
                5.715003107738556e-07,
                7.338208930460318e-07,
                5.715006514167015e-07,
                1.7603425837855082e-06,
                5.715006514151423e-07
            ],
            [
                2.5612828213934817e-06,
                5.043473480777865e-07,
                2.561282210740037e-06,
                1.0677028700422047e-06,
                6.475947982037486e-07,
                2.5612819054133693e-06,
                1.3709572068522336e-06,
                1.209866260432471e-06,
                8.939697369980456e-06,
                2.561282210740037e-06
            ],
            [
                2.90231094723893e-06,
                3.726639284125553e-06,
                7.889261645427538e-06,
                5.422220909009474e-06,
                3.2887506336235617e-06,
                9.422444815814404e-07,
                1.209865539295696e-06,
                8.939700567094277e-06,
                5.422217677152175e-06,
                1.0129988565084915e-05
            ],
            [
                1.3709570434054234e-06,
                2.6995784182140636e-07,
                6.475947982002148e-07,
                3.466325797896173e-07,
                5.715007195431641e-07,
                1.3709576971242028e-06,
                1.209865539295696e-06,
                2.902312677137316e-06,
                8.31528424151477e-07,
                9.42244256915735e-07
            ],
            [
                1.994729721518893e-06,
                4.450849988811838e-07,
                5.715005151606823e-07,
                3.059021175261338e-07,
                3.120190021657421e-05,
                3.4663266243308805e-07,
                3.5356267573959116e-05,
                4.4508494582314646e-07,
                1.5534981249697903e-06,
                6.962256249821764e-06
            ],
            [
                6.144174601588856e-06,
                6.144173869312763e-06,
                2.902310947208574e-06,
                2.430025232128576e-05,
                1.3007130014873483e-05,
                8.481103127419174e-05,
                5.4222202624563834e-06,
                2.5612812947077304e-06,
                1.2098659719441482e-06,
                7.484621834931761e-05
            ],
            [
                9.422443692574719e-07,
                2.2603248367949354e-06,
                4.785093924330255e-06,
                1.994729483729522e-06,
                4.785092783454444e-06,
                NaN,
                1.209865827752005e-06,
                8.315284241665078e-07,
                1.5534984953552536e-06,
                2.5612834320563895e-06
            ],
            [
                2.144494841326852e-05,
                3.059022269250683e-07,
                2.260325375650449e-06,
                4.222832941193893e-06,
                8.939700567004841e-06,
                5.422218969858371e-06,
                1.760343003481596e-06,
                3.2887506336235617e-06,
                9.422445939032799e-07,
                3.726639284144195e-06
            ],
            [
                1.209865827752005e-06,
                6.475947210046347e-07,
                4.450852111155216e-07,
                1.4449800373065699e-07,
                5.715006514176113e-07,
                1.7603430034867993e-06,
                3.9278605979534166e-07,
                3.059022269254856e-07,
                6.475946438055299e-07,
                3.059022998569248e-07
            ],
            [
                6.962257909785973e-06,
                6.1441746020359e-06,
                1.209865827740176e-06,
                2.9023119851781017e-06,
                NaN,
                0.9997388097572731,
                3.288750241561788e-06,
                3.726637951387472e-06,
                4.222835458175145e-06,
                1.0677028700363782e-06
            ],
            [
                6.475946438055299e-07,
                8.315278294114555e-07,
                1.3709576971463352e-06,
                4.450852641737424e-07,
                5.715005832886879e-07,
                8.315280276626197e-07,
                5.04347528446051e-07,
                4.450852641737424e-07,
                3.0590237279085045e-07,
                3.9278629391427843e-07
            ],
            [
                5.04347528446051e-07,
                1.7603425837791042e-06,
                1.3709576971242028e-06,
                1.7603432133136672e-06,
                2.902312331125353e-06,
                1.067703379154416e-06,
                5.043476486883855e-07,
                5.715004470313855e-07,
                9.422444815726566e-07,
                7.338208930443633e-07
            ],
            [
                1.5534983101602148e-06,
                8.315280276607289e-07,
                3.927861066170637e-07,
                1.209866260432471e-06,
                1.5534973842030142e-06,
                5.715003107738556e-07,
                8.315277302819205e-07,
                1.067702870039777e-06,
                3.927862939136532e-07,
                5.043476486915964e-07
            ],
            [
                5.043474683204221e-07,
                1.3709576971425944e-06,
                2.9023119851899796e-06,
                3.726638839878908e-06,
                3.72663883989755e-06,
                7.889262585814522e-06,
                1.3709576971425944e-06,
                9.422442569315887e-07,
                9.422448185478557e-07,
                1.760343003481596e-06
            ],
            [
                1.2751908849167202e-07,
                3.466327450756327e-07,
                1.855391239547094e-07,
                2.6995784182140636e-07,
                2.699577774585891e-07,
                2.3823690999160957e-07,
                1.855391681906175e-07,
                2.1024336609724313e-07,
                2.382369667929001e-07,
                9.422449308748773e-07
            ],
            [
                6.475947982022763e-07,
                9.422445939032799e-07,
                5.715007195431641e-07,
                3.9278610661902853e-07,
                5.715007195447234e-07,
                1.209865539295696e-06,
                1.2098661162056318e-06,
                1.7603434231833873e-06,
                NaN,
                2.5612834320470717e-06
            ],
            [
                4.4508494582405734e-07,
                2.3823696679230424e-07,
                1.8553914607237736e-07,
                3.4663249714612693e-07,
                NaN,
                1.2751899728311609e-07,
                1.6373762769138607e-07,
                2.902311639126627e-06,
                2.102433159721477e-07,
                6.475948754012522e-07
            ],
            [
                1.3709567165617364e-06,
                2.5612831267202583e-06,
                3.927862470899887e-07,
                2.561281600076256e-06,
                1.9947304348862686e-06,
                3.288749457469787e-06,
                2.5612828213934817e-06,
                5.71500515159253e-07,
                2.9023112932177327e-06,
                2.9023133690980155e-06
            ],
            [
                3.466327037548308e-07,
                1.6701419853852583e-05,
                8.315281267861397e-07,
                2.2603234895289998e-06,
                1.3709576971316842e-06,
                5.715005832886879e-07,
                3.2887494574518405e-06,
                5.043474683220276e-07,
                6.475947210031623e-07,
                2.260324297853209e-06
            ],
            [
                2.6995784182140636e-07,
                3.288748281329893e-06,
                1.760342793638743e-06,
                1.2098661162056318e-06,
                7.338209805240734e-07,
                3.4663278639892215e-07,
                1.5534977545886537e-06,
                2.5612831267202583e-06,
                1.209865539295696e-06,
                1.5534977545886537e-06
            ],
            [
                4.785093924362895e-06,
                0.9999960330131507,
                3.7266397283908927e-06,
                0.9999967112517242,
                1.209866260432471e-06,
                1.4738981972323349e-05,
                0.9999949062962216,
                1.5534981249697903e-06,
                2.1444945858953813e-05,
                5.422217030781934e-06
            ],
            [
                9.422448185478557e-07,
                4.785095635624897e-06,
                NaN,
                5.715005832886879e-07,
                2.2603240284371276e-06,
                1.994729008145876e-06,
                1.7603427936263351e-06,
                NaN,
                3.2887478892504536e-06,
                5.422217030747413e-06
            ],
            [
                2.9023119851781017e-06,
                5.422217677078203e-06,
                1.0677026154806063e-06,
                8.315282259089153e-07,
                4.785096776499213e-06,
                7.338208930443633e-07,
                1.3007123813382511e-05,
                4.222831934379152e-06,
                1.2098658277451275e-06,
                2.9023112932177327e-06
            ],
            [
                4.785095635624897e-06,
                1.2098658277451275e-06,
                2.260325106237323e-06,
                2.5612828213934817e-06,
                4.5397852414783676e-05,
                1.0677024881980089e-06,
                4.222832437798974e-06,
                4.785092783519724e-06,
                1.0129987357287368e-05,
                0.0010322312168200367
            ],
            [
                3.7266401726359486e-06,
                3.466326211113502e-07,
                2.2603251062147097e-06,
                2.5612831267202583e-06,
                1.0129988564974359e-05,
                6.1441746020359e-06,
                1.2098661161982042e-06,
                3.2887478892683997e-06,
                7.88926070489716e-06,
                2.5612825160562587e-06
            ],
            [
                3.466325384678894e-07,
                1.0129995810463632e-05,
                2.561282821402217e-06,
                1.4738987243478167e-05,
                1.3709576971463352e-06,
                1.3709573702856596e-06,
                5.043473480777865e-07,
                2.2603253756956754e-06,
                1.0677024882029858e-06,
                2.2603251062450327e-06
            ],
            [
                2.902312677150514e-06,
                4.450850519403407e-07,
                5.043475885688201e-07,
                2.6995784182073116e-07,
                1.0677033791612137e-06,
                3.059022998576899e-07,
                5.715003789046955e-07,
                2.9023130231176453e-06,
                8.939699501416646e-06,
                2.1024336609843824e-07
            ],
            [
                7.338213304363436e-07,
                1.0677027427600627e-06,
                0.5312093733737563,
                1.7603425837855082e-06,
                8.315284241597959e-07,
                1.7603427936335396e-06,
                8.315282259138311e-07,
                9.422445939032799e-07,
                9.422450431989127e-07,
                2.2603234895289998e-06
            ],
            [
                0.9999988634360191,
                3.7266397283908927e-06,
                3.1201907657271834e-05,
                0.9999977396765153,
                0.9999981261248421,
                1.9947301970972664e-06,
                6.144173137170873e-06,
                NaN,
                0.9999982396561584,
                3.120192625482384e-05
            ],
            [
                1.2098652508347793e-06,
                NaN,
                1.5534981249697903e-06,
                3.535623807260338e-05,
                4.785096776433933e-06,
                1.7603440527222532e-06,
                9.422445939054222e-07,
                3.4663257978465195e-07,
                4.222835458148261e-06,
                6.144176799334096e-06
            ],
            [
                1.7603440527286572e-06,
                4.222833444590791e-06,
                3.2887506336086064e-06,
                1.0677033791612137e-06,
                2.902313369111213e-06,
                2.902312677150514e-06,
                6.144175334468545e-06,
                6.144176799334096e-06,
                2.2603248367656408e-06,
                1.994729483729522e-06
            ],
            [
                1.9947299592933255e-06,
                1.670141786231398e-05,
                1.3709576971242028e-06,
                4.785094494672519e-06,
                4.222831934248571e-06,
                2.144494330116777e-05,
                2.26032402841657e-06,
                8.93969630388855e-06,
                3.7266388398585725e-06,
                2.7535700947019215e-05
            ],
            [
                2.5612819053586272e-06,
                8.939700566801578e-06,
                2.9023109471188266e-06,
                2.7535697664698622e-05,
                6.962256249758443e-06,
                1.3007133115903994e-05,
                1.2098658277264215e-06,
                1.7603438428564603e-06,
                1.5534975693869924e-06,
                4.222832437639588e-06
            ],
            [
                7.338212429562581e-07,
                5.043472879540142e-07,
                3.927862002606139e-07,
                5.04347348075149e-07,
                3.059021175247079e-07,
                NaN,
                2.6995777745711594e-07,
                5.715003107755449e-07,
                2.699577130944368e-07,
                1.1253520230052635e-07
            ],
            [
                1.1478768125911099e-05,
                7.338212429582604e-07,
                6.475949526020042e-07,
                2.2603248367949354e-06,
                NaN,
                3.288748281329893e-06,
                1.0129994602895546e-05,
                3.2887502415767434e-06,
                8.315280276607289e-07,
                3.059022998576899e-07
            ],
            [
                1.0129988565084915e-05,
                NaN,
                4.450852111148132e-07,
                2.902312677150514e-06,
                2.90231094723893e-06,
                9.422444815814404e-07,
                1.5534981249697903e-06,
                7.338212429582604e-07,
                9.422443692574719e-07,
                1.209866260432471e-06
            ],
            [
                2.1024341622426268e-07,
                5.715005151606823e-07,
                NaN,
                5.715002426475718e-07,
                4.450852111148132e-07,
                5.043472879540142e-07,
                3.927862002663297e-07,
                2.3823699519290042e-07,
                3.466325797888292e-07,
                5.043476486915964e-07
            ],
            [
                1.0677029973219343e-06,
                4.222833444467892e-06,
                2.6995774527718623e-07,
                3.7266406168827523e-06,
                4.222832437798974e-06,
                1.4449805540740185e-07,
                9.422448185534261e-07,
                3.927863875616689e-07,
                4.4508494582405734e-07,
                1.5534971990169383e-06
            ],
            [
                7.338210680021253e-07,
                8.315278294114555e-07,
                3.059022998581767e-07,
                9.422449308774482e-07,
                3.0590237279085045e-07,
                1.7603438428800754e-06,
                1.0677032518785256e-06,
                4.450852111148132e-07,
                1.2098659719757836e-06,
                5.04347287955046e-07
            ],
            [
                9.422448185478557e-07,
                1.5534977545886537e-06,
                1.855391239544352e-07,
                1.3709567165530083e-06,
                3.7266401726359486e-06,
                3.927862002663297e-07,
                3.288749457469787e-06,
                3.7266397283908927e-06,
                3.0590226339061185e-07,
                9.422447062094932e-07
            ],
            [
                4.450848927599543e-07,
                3.288749457469787e-06,
                1.3709567165579959e-06,
                2.9023133690980155e-06,
                2.5612812947380135e-06,
                1.9947304348862686e-06,
                3.288749457469787e-06,
                NaN,
                2.430024652854702e-05,
                1.9947292459347367e-06
            ],
            [
                9.422442569315887e-07,
                7.338207180898968e-07,
                2.10243290909724e-07,
                2.10243290909724e-07,
                2.699577774585891e-07,
                3.4663266242969896e-07,
                1.6373776432509826e-07,
                6.475947982037486e-07,
                1.1253520230052635e-07,
                3.9278634073732336e-07
            ],
            [
                3.7266406168624155e-06,
                2.5612819054028872e-06,
                3.726641061058432e-06,
                1.6701429808632785e-05,
                1.1478772230929451e-05,
                2.144495864059426e-05,
                5.422218323349895e-06,
                1.14787708624228e-05,
                4.785093924330255e-06,
                1.3007131565613412e-05
            ]
        ]
    },
    {
        "q_id": "10152_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999990577557435,
                1.444980209564556e-07,
                3.0590237279085045e-07,
                0.9999998257022045,
                0.9999997463981938,
                3.05902263391829e-07,
                6.475951070002966e-07,
                1.0677027427624903e-06,
                0.999998446501876,
                3.059021175261338e-07
            ],
            [
                0.9999996310116359,
                0.999999495652592,
                NaN,
                0.9999983463100206,
                1.9947301970972664e-06,
                0.9999975938965158,
                0.9999983463098238,
                0.9999485577865307,
                5.043475885696228e-07,
                0.9999957771680709
            ],
            [
                0.9999985406237797,
                1.2098661162056318e-06,
                5.715005832886879e-07,
                1.6373776432509826e-07,
                3.4663249714612693e-07,
                3.466326624336003e-07,
                1.2098661162056318e-06,
                1.7603440527334603e-06,
                5.715006514176113e-07,
                0.9999972735303809
            ],
            [
                1.0677028700422047e-06,
                1.4738978458623327e-05,
                6.475947210046347e-07,
                5.043472879525233e-07,
                1.5534981249574276e-06,
                2.382370235933104e-07,
                7.338207180898968e-07,
                2.1024339116168358e-07,
                1.2098661162056318e-06,
                0.9999975938968018
            ],
            [
                0.9999986290429578,
                4.450848927650143e-07,
                1.2751902768612997e-07,
                0.9999994284995534,
                2.10243290909724e-07,
                3.0590237279085045e-07,
                0.9999962733607226,
                0.9999952149038013,
                2.6995790618469934e-07,
                1.6373774480605869e-07
            ],
            [
                0.999996910505922,
                0.9999998555019446,
                0.9999996072138935,
                0.9999998724809572,
                0.9999988634358833,
                0.9999996533672963,
                0.99999879013374,
                0.9999986290432838,
                0.9999980052707549,
                0.9999991684718735
            ],
            [
                1.3709567165617364e-06,
                0.9998601778601696,
                1.3709576971425944e-06,
                0.9999945777803864,
                1.8925150497848527e-05,
                1.0677029973219343e-06,
                1.994729721518893e-06,
                1.2098659719788098e-06,
                4.4508494582405734e-07,
                0.9999967112501523
            ],
            [
                0.9999999006881022,
                5.715004470313855e-07,
                3.466325797900508e-07,
                0.9999485577864916,
                3.9278610661902853e-07,
                7.338208055664991e-07,
                3.059022269250683e-07,
                0.0005527787488983423,
                1.2098653950656417e-06,
                1.855391681906175e-07
            ],
            [
                6.475946438055299e-07,
                4.4508494582314646e-07,
                8.315277302841894e-07,
                0.9999975938973761,
                1.6373776432509826e-07,
                0.9999978766212865,
                0.9999978766207795,
                2.102433660979124e-07,
                2.6995774527718623e-07,
                0.9999930377445954
            ],
            [
                3.059021904580685e-07,
                2.2603253756956754e-06,
                3.059022998576899e-07,
                4.785092783519724e-06,
                6.475945666051092e-07,
                4.450848927637999e-07,
                7.338208930460318e-07,
                3.466326211113502e-07,
                1.0677031245990084e-06,
                1.0677027427624903e-06
            ],
            [
                9.931202796993203e-08,
                7.338212429582604e-07,
                0.9999998642566866,
                0.9999999273418876,
                0.9999994956526521,
                5.715002426475718e-07,
                0.9999998874647307,
                0.9999995262093857,
                0.9999988634365609,
                0.9999996743688586
            ],
            [
                0.9999978766217914,
                5.04347528446051e-07,
                0.9999981261248405,
                0.9999980052705171,
                4.785095635655362e-06,
                0.9999988634357477,
                7.3382080556433e-07,
                1.0677026154806063e-06,
                0.9999756997650979,
                0.9999898700066139
            ],
            [
                0.9999904837437845,
                2.5612812947240366e-06,
                0.9999832985801692,
                1.6373766672973748e-07,
                0.9999975938979483,
                0.9999955048178881,
                3.05902336324494e-07,
                6.825608606172863e-08,
                2.10243290909724e-07,
                0.99999862904214
            ],
            [
                3.9278605979534166e-07,
                0.9999964991468396,
                9.93120161310289e-08,
                1.444979692797559e-07,
                1.8553916819032217e-07,
                5.043472278322555e-07,
                0.9999988634357481,
                NaN,
                2.382370235933104e-07,
                0.9999038975625242
            ],
            [
                0.9999869928762035,
                1.5534981249291695e-06,
                1.2098653950551882e-06,
                1.275190580884987e-07,
                1.6373770576776313e-07,
                1.637377057680051e-07,
                2.3823685319320354e-07,
                2.699578096403948e-07,
                1.6373764721039308e-07,
                3.9278605979534166e-07
            ],
            [
                2.3823693839325527e-07,
                1.3709576971463352e-06,
                2.699576809146529e-07,
                3.0590215399281185e-07,
                5.043472278322555e-07,
                1.275190732904469e-07,
                5.043475284468537e-07,
                7.734415776836702e-08,
                2.10243290909724e-07,
                9.422442569334097e-07
            ],
            [
                1.1253512180925583e-07,
                0.9999964991464227,
                1.855391239544352e-07,
                0.999998629043284,
                3.0590237279032884e-07,
                2.10243290909724e-07,
                3.4663278639892215e-07,
                3.4663278639892215e-07,
                2.6995784182140636e-07,
                2.6995774527718623e-07
            ],
            [
                2.382370235933104e-07,
                0.9999967112497614,
                0.9999942280806653,
                0.9999982396561581,
                1.1253512180925583e-07,
                3.927862002641863e-07,
                1.6373764721072816e-07,
                2.102433660979124e-07,
                3.466327037548308e-07,
                1.637377057673536e-07
            ],
            [
                0.9999756997622029,
                0.999993855825401,
                3.05902263389638e-07,
                4.450848927658745e-07,
                9.422443692574719e-07,
                1.4449798650551755e-07,
                1.6373774480605869e-07,
                1.8553905760024476e-07,
                0.9999967112493683,
                5.043475885696228e-07
            ],
            [
                7.338212429582604e-07,
                3.466327037553825e-07,
                1.9947299592933255e-06,
                7.484623619706945e-05,
                2.9023119851781017e-06,
                2.3823688159291947e-07,
                1.6373774480605869e-07,
                1.3007130015488633e-05,
                6.475947210046347e-07,
                2.902312677150514e-06
            ],
            [
                6.475949526020042e-07,
                2.6995790618469934e-07,
                5.715003789046955e-07,
                3.4663274507713016e-07,
                8.315278294114555e-07,
                0.9999898700054091,
                4.450851580566494e-07,
                0.9999975938965155,
                3.726637951387472e-06,
                1.994729483723626e-06
            ],
            [
                4.450850519403407e-07,
                0.9999962733598305,
                5.043474683220276e-07,
                1.7603427936335396e-06,
                3.9278624708775595e-07,
                NaN,
                5.715002426475718e-07,
                2.260325375677174e-06,
                2.561283432035425e-06,
                1.760343003481596e-06
            ],
            [
                0.9999485577804977,
                0.9999998144608097,
                1.2098652508391807e-06,
                0.9999977396748948,
                1.0129988564716393e-05,
                0.9999995818810776,
                0.999998790134317,
                0.9999998144608098,
                0.9999993106391191,
                0.9999997617630048
            ],
            [
                0.999998446502246,
                0.9999998555020307,
                0.9998415638034237,
                0.9999998144608098,
                0.9999997617630617,
                0.9999982396561579,
                0.9999984465022459,
                0.9999977396751644,
                0.9999987901346055,
                3.059022269250683e-07
            ],
            [
                0.9999990577554065,
                0.9999898700066098,
                1.3709575337078829e-06,
                4.222831934379152e-06,
                0.9999992661790197,
                0.002472622913714792,
                0.9999992188514835,
                0.999999428499485,
                1.5534983101644536e-06,
                0.9999970976873244
            ],
            [
                0.9999974387165692,
                0.9999986290429577,
                0.9999987901340285,
                0.9999982396574172,
                8.315278294114555e-07,
                0.9999989322975126,
                0.9999980052709935,
                0.9999970976890549,
                2.3823682479292225e-07,
                0.9999989322971305
            ],
            [
                6.023577783447482e-08,
                1.2098652508391807e-06,
                1.1478768126057254e-05,
                0.9999599363222681,
                1.2098661161982042e-06,
                0.9999977396748962,
                1.3007134667070165e-05,
                7.338212429562581e-07,
                0.9999910603058344,
                1.994729245878497e-06
            ],
            [
                3.059022269250683e-07,
                0.9999974387171798,
                3.059022998576899e-07,
                1.067703379154416e-06,
                9.422443692446175e-07,
                1.8553905760062447e-07,
                1.7603430034743913e-06,
                1.4738985486506781e-05,
                1.994729245917502e-06,
                2.1444940745839484e-05
            ],
            [
                1.8925148241872038e-05,
                1.3709572068522336e-06,
                1.3007123813382511e-05,
                2.4300243631272052e-05,
                7.338212429562581e-07,
                1.9947292459347367e-06,
                3.7266401726173067e-06,
                1.760343213335281e-06,
                1.3709568799823232e-06,
                1.4738978458382043e-05
            ],
            [
                3.288748281329893e-06,
                1.8553919030858602e-07,
                1.9947292459347367e-06,
                4.4508515805735777e-07,
                1.0677033791583005e-06,
                4.4508510499849186e-07,
                2.6995790618469934e-07,
                2.3823682479292225e-07,
                1.5534977545886537e-06,
                5.4222183235249605e-06
            ],
            [
                1.855391681906175e-07,
                7.734414854823498e-08,
                0.9999994956527722,
                0.9997965729312374,
                0.9999949062968234,
                1.6373774480605869e-07,
                0.9999898700126507,
                9.931187406410953e-08,
                0.9999975938970876,
                0.9999832985801701
            ],
            [
                5.422220909009474e-06,
                NaN,
                0.00012339457500953096,
                4.785096206076165e-06,
                0.9999991148431754,
                0.9999934595635617,
                0.9999934595627777,
                0.9999983463098234,
                7.338210680002898e-07,
                0.9999960330121961
            ],
            [
                1.5534973841895917e-06,
                2.1024339116168358e-07,
                0.9999892166903565,
                0.9999952149072192,
                0.9999998257021421,
                0.9999990577551818,
                3.4663266243111764e-07,
                0.9999975938973749,
                2.5612812947508257e-06,
                0.999968798073809
            ],
            [
                4.450850519403407e-07,
                0.9999706884651424,
                0.999987780918169,
                0.9999810748517881,
                1.2098652508287273e-06,
                2.9023119851899796e-06,
                2.9023116391978967e-06,
                8.315277302841894e-07,
                0.9999921107346011,
                2.561281905376098e-06
            ],
            [
                0.999998932297003,
                2.102434412875379e-07,
                2.3823690999290963e-07,
                0.9999996940978825,
                0.9999996533672137,
                8.315278294097538e-07,
                1.444980209564556e-07,
                9.931199245322124e-08,
                0.999999746398224,
                0.9999983463106116
            ],
            [
                0.9999998874648112,
                0.9999972735307058,
                0.9999998724810027,
                0.99999886343629,
                0.999998005270517,
                0.9999994631250603,
                0.9999999358793944,
                0.9999993106392012,
                1.0677033791583005e-06,
                0.999992588720134
            ],
            [
                1.637376862489725e-07,
                2.4300234941880266e-05,
                4.450852111155216e-07,
                3.05902263391829e-07,
                1.4449805540763184e-07,
                1.8553914607267268e-07,
                1.2098659719788098e-06,
                1.5534984953552536e-06,
                2.3823690999290963e-07,
                3.0590226339137693e-07
            ],
            [
                6.475950298011458e-07,
                4.785093353940187e-06,
                3.927862939136532e-07,
                0.9999969105040806,
                7.338210679979539e-07,
                0.9999955048184251,
                0.9999785550541931,
                1.5534973842076057e-06,
                1.8553907971855875e-07,
                0.9999964991464236
            ],
            [
                0.999996033015034,
                0.9999962733602746,
                0.9999724643089779,
                0.9999967112521128,
                0.9999485577620203,
                0.9999810748517881,
                0.9999980052709929,
                6.475949526020042e-07,
                0.999992110733659,
                0.9999898700090303
            ],
            [
                2.902311985146426e-06,
                8.315282259051341e-07,
                5.422217677078203e-06,
                2.561283126679493e-06,
                3.7266379513162962e-06,
                4.450851580555361e-07,
                1.994729721482609e-06,
                1.7603430034743913e-06,
                1.5534984953298217e-06,
                9.422447062202052e-07
            ],
            [
                0.9999991148429643,
                1.6373766672973748e-07,
                0.9999975938982351,
                0.9999970976880158,
                0.9999960330145597,
                0.9999991684722699,
                0.9999885212277845,
                0.9999960330150331,
                0.9999869928684445,
                NaN
            ],
            [
                0.9999990577557434,
                0.9999994284994851,
                0.9995121427786431,
                1.8553905760062447e-07,
                0.9999983463102179,
                3.05902263391829e-07,
                0.9999991684721709,
                0.9999998144609424,
                1.4449800373118268e-07,
                9.931190958076104e-08
            ],
            [
                5.04347348075149e-07,
                5.043474081993875e-07,
                1.6701425827133152e-05,
                1.5534971990126997e-06,
                7.338209805224048e-07,
                2.382369383923073e-07,
                3.927862939126708e-07,
                1.3709570434178922e-06,
                6.475947981975644e-07,
                6.475947982002148e-07
            ],
            [
                0.9999975938965147,
                0.9999978766215387,
                0.9999998461827139,
                2.7535681254003062e-05,
                NaN,
                7.338210680021253e-07,
                1.553497754583709e-06,
                0.9999991684722701,
                0.9999997761971048,
                0.9999977396759725
            ],
            [
                0.9999996310116359,
                0.9999998144609646,
                0.9999997300421904,
                0.9999998942829854,
                0.9999949062956093,
                0.9999985406239535,
                0.9999992661792824,
                2.3823696679327928e-07,
                0.9999949062950007,
                0.9999990577557435
            ],
            [
                0.9999993106391191,
                1.553497384196656e-06,
                1.3709570434122812e-06,
                1.5534983101602148e-06,
                1.3709572068522336e-06,
                4.222833947960866e-06,
                2.9023130231176453e-06,
                1.9947299593014888e-06,
                1.5534973842030142e-06,
                1.209866260432471e-06
            ],
            [
                6.023569884718319e-08,
                3.059021539909339e-07,
                0.9999978766207803,
                1.2098659719788098e-06,
                4.4508494582405734e-07,
                7.338210680002898e-07,
                6.47594566597747e-07,
                0.9999904837517338,
                3.9278605979208185e-07,
                6.475945666051092e-07
            ],
            [
                0.9999987121041707,
                2.699578740032504e-07,
                0.9999994956524115,
                0.9999756997593205,
                0.9999960330126704,
                0.9999962733620511,
                0.999997593897375,
                7.734424996987981e-08,
                8.315282259138311e-07,
                7.734428685047173e-08
            ],
            [
                1.8553907971855875e-07,
                4.450851580540182e-07,
                2.3823693839290317e-07,
                1.3709568799919866e-06,
                3.466325797888292e-07,
                9.422448185534261e-07,
                1.3709573702822306e-06,
                3.059021904580685e-07,
                2.10243290909724e-07,
                1.0677032518814388e-06
            ],
            [
                1.275190580890061e-07,
                2.699576809143613e-07,
                1.444979692800516e-07,
                2.382370235933104e-07,
                2.1024331597262577e-07,
                2.6995790618469934e-07,
                1.855391239544352e-07,
                3.927862002663297e-07,
                1.8553905760062447e-07,
                0.9999869928669034
            ],
            [
                1.9947299593078385e-06,
                9.422445939054222e-07,
                7.734425919002834e-08,
                1.1253508156363576e-07,
                1.855391681906175e-07,
                8.315279285370317e-07,
                0.9998766054258307,
                2.5612819054133693e-06,
                0.9999960330140881,
                8.315280276626197e-07
            ],
            [
                1.6373772528704005e-07,
                0.9999038975508887,
                4.139941002027314e-08,
                0.9999251537909144,
                0.999999168471576,
                5.315789407685159e-08,
                0.9999997761971848,
                1.637376862489725e-07,
                0.9999989969857925,
                0.9999972735297306
            ],
            [
                0.9999998461826588,
                0.9999998724810027,
                0.9999997300422869,
                0.9999994284997575,
                0.9999982396559478,
                0.9999997617629766,
                0.999999674368781,
                0.9999988634364252,
                0.9999998724810027,
                0.9999982396574172
            ],
            [
                NaN,
                7.734428685047173e-08,
                9.931189774187203e-08,
                9.931196877517082e-08,
                2.3823688159237777e-07,
                7.734415776836702e-08,
                3.4663266243308805e-07,
                8.764244316973974e-08,
                1.855391239544352e-07,
                3.22418970812682e-08
            ],
            [
                1.637377057680051e-07,
                4.6911665979156514e-08,
                3.4663262111182307e-07,
                1.3709572068522336e-06,
                1.1253506814842375e-07,
                2.1024334103581732e-07,
                1.1253524254650944e-07,
                9.931199245322124e-08,
                1.444979692800516e-07,
                0.9999988634361542
            ],
            [
                5.043474081993875e-07,
                2.90231094723893e-06,
                0.999891103105457,
                1.2098652508424818e-06,
                4.450849458200093e-07,
                8.315279285351409e-07,
                1.0677026154806063e-06,
                1.0677033791612137e-06,
                1.3709573702822306e-06,
                9.422448185510695e-07
            ],
            [
                1.3709567165579959e-06,
                1.370956716529941e-06,
                0.9999955048178889,
                8.315282259009745e-07,
                1.2098655392662613e-06,
                1.5534983101478522e-06,
                0.9999992188515764,
                0.9999989969860316,
                6.475945666051092e-07,
                6.475951069961737e-07
            ],
            [
                2.3823696679230424e-07,
                9.931185038635267e-08,
                0.0001584362925687936,
                1.7603425837702984e-06,
                1.5534971989907999e-06,
                1.0677029972745947e-06,
                1.0677029973192638e-06,
                1.3709568799760888e-06,
                1.0677028700266676e-06,
                1.7603434231241496e-06
            ],
            [
                6.475947982037486e-07,
                0.9999983463110066,
                5.043474081993875e-07,
                9.931190958076104e-08,
                0.9999974387171815,
                0.999994577779096,
                1.1253509497883659e-07,
                3.466325797896173e-07,
                6.475950298011458e-07,
                2.3823688159291947e-07
            ],
            [
                6.475947210031623e-07,
                1.1253512180925583e-07,
                5.715005832895975e-07,
                1.067703124601679e-06,
                7.338209805240734e-07,
                1.2098661162056318e-06,
                1.5534973842076057e-06,
                3.05902263391829e-07,
                2.6995790618469934e-07,
                9.422448185534261e-07
            ],
            [
                3.4663266243111764e-07,
                1.9947292459347367e-06,
                3.7266401726359486e-06,
                6.962257079832313e-06,
                6.962254589978262e-06,
                NaN,
                3.927862470899887e-07,
                5.715005832886879e-07,
                0.999994906295609,
                6.47595107001401e-07
            ],
            [
                0.9999970976876709,
                6.475946438055299e-07,
                3.4663262111182307e-07,
                3.4663274507713016e-07,
                4.2228339479858295e-06,
                2.1024334103581732e-07,
                6.475950298021765e-07,
                0.999996910504082,
                0.9999978766212858,
                0.9999980052700418
            ],
            [
                1.4449802095666915e-07,
                3.466327037553825e-07,
                4.785093924389007e-06,
                2.6995784182140636e-07,
                2.6995790618469934e-07,
                7.338208930460318e-07,
                1.2751905808881762e-07,
                6.475947982037486e-07,
                3.0590237279032884e-07,
                3.466326624336003e-07
            ],
            [
                5.715004470326849e-07,
                7.734418542875216e-08,
                9.422445939054222e-07,
                4.4508494582405734e-07,
                9.422443692574719e-07,
                3.0590237279085045e-07,
                5.715006514176113e-07,
                1.444979692797559e-07,
                5.043475885696228e-07,
                6.475945666063607e-07
            ],
            [
                2.2603251062450327e-06,
                6.47595107001401e-07,
                1.1478769494396542e-05,
                4.450851580566494e-07,
                2.382369951932796e-07,
                0.9999969105066595,
                0.0003353500311432834,
                0.00033535007141893293,
                4.450852641717689e-07,
                0.9999962733589421
            ],
            [
                8.315277302857965e-07,
                1.0677027427624903e-06,
                2.382368247909451e-07,
                4.4508515805735777e-07,
                9.422442569315887e-07,
                1.7603425837903113e-06,
                3.288749849529972e-06,
                1.9947299593014888e-06,
                6.47594952603035e-07,
                9.422443692574719e-07
            ],
            [
                2.6995784182183607e-07,
                2.382369667929001e-07,
                5.043476486915964e-07,
                3.059022998581767e-07,
                1.6373762769138607e-07,
                3.059022998576899e-07,
                1.1253509497883659e-07,
                1.3709567165617364e-06,
                1.1253506814797596e-07,
                1.5534981249697903e-06
            ],
            [
                0.9999955048173516,
                7.33821330437595e-07,
                2.6995768091383957e-07,
                1.637377057673536e-07,
                4.450852111148132e-07,
                3.466326624336003e-07,
                0.9999988634362897,
                2.382370235933104e-07,
                3.05902336324494e-07,
                5.043474683240344e-07
            ],
            [
                0.9999904837494514,
                1.5534975693979422e-06,
                6.144173869558639e-06,
                1.0677027427624903e-06,
                0.9999921107336626,
                0.9999832985762254,
                0.9999687980812584,
                0.00012339456028720406,
                3.9278605979534166e-07,
                0.9999978766220452
            ],
            [
                3.4663249714612693e-07,
                5.715004470326849e-07,
                9.422445939054222e-07,
                2.382369951932796e-07,
                1.2751902768612997e-07,
                0.9999910603068997,
                3.927863407379485e-07,
                1.2098659719788098e-06,
                2.699578096403948e-07,
                3.4663278639892215e-07
            ],
            [
                0.9999952149060815,
                1.209866260432471e-06,
                2.1444940745839484e-05,
                0.9999485578049998,
                1.553497199007048e-06,
                1.0677032518785256e-06,
                4.450852641737424e-07,
                0.9999151889186113,
                2.3823693839290317e-07,
                1.855391239544352e-07
            ],
            [
                1.994729008145876e-06,
                1.3709575337159875e-06,
                1.855391239544352e-07,
                2.5612834320470717e-06,
                4.785096776499213e-06,
                1.4738983729535602e-05,
                1.444980209564556e-07,
                4.450852641737424e-07,
                5.715003789033962e-07,
                7.338213304363436e-07
            ],
            [
                1.7603440527334603e-06,
                2.1024334103581732e-07,
                1.0677027427624903e-06,
                5.043472278322555e-07,
                2.699576809143613e-07,
                3.2887506336235617e-06,
                6.475945666063607e-07,
                1.3709578605542582e-06,
                5.422218969720291e-06,
                1.553497199007048e-06
            ],
            [
                9.422448185534261e-07,
                1.5534975693869924e-06,
                6.475947210031623e-07,
                0.9999995262095551,
                7.338213304363436e-07,
                1.3709576971463352e-06,
                0.9999974387187056,
                7.734414854823498e-08,
                0.9999970976880153,
                1.3709570434178922e-06
            ],
            [
                1.209865683518615e-06,
                8.315283250343497e-07,
                9.422443692574719e-07,
                5.715002426460124e-07,
                7.338209805240734e-07,
                1.760342793638743e-06,
                2.382370235933104e-07,
                1.5534977545384963e-06,
                8.315282259089153e-07,
                9.422447062270609e-07
            ],
            [
                8.315279285351409e-07,
                5.043476486915964e-07,
                2.6995784182140636e-07,
                0.9999980052695665,
                2.5612819054028872e-06,
                5.043472879540142e-07,
                0.9999916019269782,
                0.9999970976866337,
                5.715005151606823e-07,
                7.73442776303243e-08
            ],
            [
                5.315789407685159e-08,
                0.999999428499417,
                7.734426841017797e-08,
                0.999998005269329,
                0.9999995818811773,
                0.9999964991447525,
                0.9999972735307063,
                0.9999987121047854,
                0.9999996072138467,
                0.9999995262094988
            ],
            [
                2.1024344128660572e-07,
                0.9999974387171802,
                3.466326624336003e-07,
                3.0590237279085045e-07,
                1.2098652508424818e-06,
                4.450848927658745e-07,
                0.9999910603069044,
                1.4449805540740185e-07,
                3.927862470899887e-07,
                6.475946438055299e-07
            ],
            [
                9.422445939032799e-07,
                1.5534984953453635e-06,
                2.9023133690980155e-06,
                0.9999945777829726,
                2.5612828213934817e-06,
                1.3709567165579959e-06,
                1.994729483723626e-06,
                1.1253506814842375e-07,
                1.994729245917502e-06,
                1.3709567165579959e-06
            ],
            [
                8.764244316973974e-08,
                0.999997876621539,
                0.999998540623954,
                0.9999987121043242,
                9.931193325852072e-08,
                6.475950298011458e-07,
                0.9999986290421403,
                0.9999997761972115,
                0.999998540623606,
                0.9999969105066592
            ],
            [
                0.9999980052698046,
                0.9999967112509369,
                2.5612819054133693e-06,
                0.9999989969856734,
                0.9999885212318875,
                6.475945666063607e-07,
                0.9999993916408185,
                0.9999984465022461,
                0.9999994631249324,
                0.9999964991451701
            ],
            [
                2.3823690999323465e-07,
                6.47595107001401e-07,
                1.4449800373065699e-07,
                2.699578096403948e-07,
                5.715003107767143e-07,
                3.466327037553825e-07,
                1.8553905760062447e-07,
                1.275190580890061e-07,
                NaN,
                9.93120161310289e-08
            ],
            [
                1.7603434231097403e-06,
                1.2098655392811161e-06,
                8.315277302819205e-07,
                1.3709575336947905e-06,
                1.3709575337016483e-06,
                5.422217030781934e-06,
                1.2098659719716573e-06,
                5.715003107767143e-07,
                1.0677027427569065e-06,
                2.260324297853209e-06
            ],
            [
                0.9999987121041706,
                0.9999988634361543,
                0.9999981261248404,
                1.2751899728311609e-07,
                0.9999989969860317,
                0.9999970976876705,
                0.9999885212264134,
                0.9999978766217917,
                0.9999980052700418,
                0.9999982396559483
            ],
            [
                0.999998005269804,
                0.9999925887166033,
                3.05902336324494e-07,
                0.9999942280779116,
                9.422443692574719e-07,
                0.9999925887165999,
                5.043472879504592e-07,
                7.338208930460318e-07,
                0.9999970976887099,
                0.9998911031306377
            ],
            [
                2.7535681254804434e-05,
                0.9999949062962175,
                0.9999945777816828,
                7.889262585886274e-06,
                5.043474081993875e-07,
                0.9999798543140487,
                1.5534975693869924e-06,
                0.9999516743563799,
                3.7266410611296085e-06,
                0.9999925887183746
            ],
            [
                1.7603430034743913e-06,
                2.1024339116168358e-07,
                0.9999992661786699,
                8.31528424162821e-07,
                1.8553910183674878e-07,
                0.9999983463102181,
                3.059021175261338e-07,
                3.4663274507713016e-07,
                1.6373772528704005e-07,
                1.8553914607267268e-07
            ],
            [
                1.8553919030858602e-07,
                1.4449805540763184e-07,
                7.338210680021253e-07,
                8.764254764780641e-08,
                0.9999993524054336,
                5.715003107767143e-07,
                2.699577452775239e-07,
                2.3823688159291947e-07,
                0.9999996310116359,
                1.1253522913127183e-07
            ],
            [
                3.059022998576899e-07,
                2.6995784182140636e-07,
                2.3823696679327928e-07,
                4.450852641717689e-07,
                9.422449308774482e-07,
                1.8553903548231313e-07,
                1.2751904288739315e-07,
                8.764247451307293e-08,
                1.0677029973219343e-06,
                8.315279285351409e-07
            ],
            [
                0.9999988634360187,
                1.637377057680051e-07,
                0.9999985406243019,
                2.1024336609874897e-07,
                0.999996499145171,
                8.315284241650899e-07,
                0.9999977396746268,
                0.9999960330140875,
                3.466325384678894e-07,
                1.4449800373118268e-07
            ],
            [
                0.9999916019269768,
                3.059021539909339e-07,
                8.764240137829087e-08,
                1.6373776432481905e-07,
                5.715005832872586e-07,
                2.561281600076256e-06,
                2.102433159721477e-07,
                1.444980726324838e-07,
                1.2098658277451275e-06,
                2.3823696679230424e-07
            ],
            [
                1.892515501014656e-05,
                3.927862002663297e-07,
                3.059022998576899e-07,
                4.006367786720367e-05,
                1.275190580890061e-07,
                0.999992588718367,
                1.3709573702822306e-06,
                4.4508510499849186e-07,
                4.785094494783494e-06,
                8.315283250371857e-07
            ],
            [
                1.3007126914435202e-05,
                0.9999985406237801,
                6.144175334468545e-06,
                0.9999975938979486,
                0.00010889688339134737,
                1.012999218776902e-05,
                2.75356812556058e-05,
                3.726638395634011e-06,
                7.889260704968913e-06,
                0.9999843104540428
            ],
            [
                1.2098659719716573e-06,
                5.043476486915964e-07,
                6.475947210031623e-07,
                9.931185038635267e-08,
                5.715007195447234e-07,
                1.275190580890061e-07,
                4.450852641737424e-07,
                1.3709572068522336e-06,
                1.209865539295696e-06,
                1.8553905760062447e-07
            ],
            [
                1.1253524254650944e-07,
                4.2228339479858295e-06,
                1.444979692800516e-07,
                6.825598842065202e-08,
                0.9999985406237794,
                1.8553910183674878e-07,
                0.9999974387165699,
                7.33821330437595e-07,
                9.931186222523604e-08,
                9.931202796993203e-08
            ],
            [
                1.444979692800516e-07,
                7.338212429582604e-07,
                7.338213304363436e-07,
                4.4508505193932864e-07,
                2.699576809121209e-07,
                6.475948753991907e-07,
                2.6995768091383957e-07,
                9.931185038635267e-08,
                7.338208930443633e-07,
                3.059022998581767e-07
            ],
            [
                0.9999949062968251,
                0.999998712104785,
                2.382370235933104e-07,
                1.855391239544352e-07,
                8.764244316973974e-08,
                0.9999955048173532,
                0.9999949062968243,
                1.4449805540763184e-07,
                0.9999985406241275,
                0.999995777166055
            ],
            [
                0.9999978766212866,
                1.5534979397500702e-06,
                0.9999988634357476,
                1.9947297215125433e-06,
                0.9999925887201371,
                0.9999910603047736,
                6.475945666051092e-07,
                1.067702870039777e-06,
                3.927863875616689e-07,
                7.338213304283347e-07
            ],
            [
                2.699577774585891e-07,
                8.315279285351409e-07,
                2.6995790618252024e-07,
                2.6995768091310296e-07,
                2.902313023130843e-06,
                3.466327037548308e-07,
                5.715005832872586e-07,
                1.9947304348862686e-06,
                5.043473480777865e-07,
                4.4508505193932864e-07
            ],
            [
                9.422450432014836e-07,
                9.931189774187203e-08,
                2.9023119851899796e-06,
                1.2751904288739315e-07,
                4.222835458117536e-06,
                3.059021175247079e-07,
                1.8553907971855875e-07,
                4.450848927658745e-07,
                2.699576809143613e-07,
                1.3709576971463352e-06
            ],
            [
                4.222832437798974e-06,
                1.7603427936335396e-06,
                1.5534973842030142e-06,
                5.715003789033962e-07,
                NaN,
                1.1253522913127183e-07,
                1.9947301970972664e-06,
                1.209865539295696e-06,
                3.466327863983311e-07,
                2.260325106237323e-06
            ],
            [
                0.9999977396754338,
                0.9999986290431205,
                0.9999993916411085,
                2.102433159721477e-07,
                0.9999998024946095,
                0.9999997761970248,
                0.9999986290423036,
                0.9999993106389548,
                0.99999886343629,
                0.9999967112513283
            ],
            [
                1.3709576971463352e-06,
                0.9999985406243015,
                0.9999998362623529,
                1.7603434231833873e-06,
                0.9999998642566542,
                1.275190428875671e-07,
                0.9999952149049377,
                0.9999991148429644,
                0.9999964991443355,
                0.9999998461826222
            ],
            [
                0.9999996072137998,
                0.9999999530883228,
                1.5534983101549167e-06,
                0.9999952149060805,
                0.9999998461826588,
                9.422442569315887e-07,
                0.9999974387171798,
                8.315284241597959e-07,
                0.9999991684721707,
                0.9999989969861515
            ],
            [
                0.9999987901338845,
                0.9999984465024315,
                0.9999977396751646,
                0.9999987901341731,
                0.9999945777784502,
                0.9999885212332532,
                9.422443692555439e-07,
                0.9999991684717743,
                0.9999687980961804,
                0.9999992661786699
            ],
            [
                0.9999987121047854,
                0.9999985406230847,
                9.422450431912e-07,
                0.9999977396751658,
                0.9999957771680741,
                0.9999978766215387,
                0.9999995549149483,
                0.9999987121052457,
                0.9999993106386263,
                0.9999984465016912
            ],
            [
                0.9999646437536056,
                0.9999997126313783,
                0.9999810748472906,
                0.9999985406236058,
                0.9999975938979487,
                0.9999985406241276,
                8.315277302841894e-07,
                0.9999952149037987,
                0.9998415637846411,
                2.1024331597288867e-07
            ],
            [
                7.338212429582604e-07,
                8.315280276626197e-07,
                5.715005151606823e-07,
                5.315780536011123e-08,
                2.10243290909963e-07,
                2.260324567337161e-06,
                1.637376862489725e-07,
                5.715002426486762e-07,
                1.30071315662049e-05,
                0.9999977396759733
            ],
            [
                3.927863875616689e-07,
                2.902312677137316e-06,
                1.855391681906175e-07,
                0.9999969105055555,
                0.9999981261243949,
                0.999997739674897,
                3.288750633545794e-06,
                4.450852111148132e-07,
                5.715002426486762e-07,
                1.2098659719716573e-06
            ],
            [
                0.999994577779739,
                0.9999989322973849,
                0.9999992661789323,
                0.9999975938970875,
                0.9999988634361544,
                1.855391681906175e-07,
                0.9999998555019446,
                0.9999999434138109,
                0.9999998642567028,
                4.450851580566494e-07
            ],
            [
                1.3709573702822306e-06,
                6.475947982037486e-07,
                1.3709576971425944e-06,
                0.9999967112493677,
                7.338212429562581e-07,
                0.9999942280813496,
                1.209865539295696e-06,
                2.4300234941261454e-05,
                1.1253508156363576e-07,
                4.222834451355964e-06
            ],
            [
                3.7266410611296085e-06,
                0.9999985406237797,
                1.855391681898159e-07,
                1.6373764720990908e-07,
                0.9999785550439683,
                3.927863875616689e-07,
                0.9999904837460488,
                8.76424013786396e-08,
                6.475947982002148e-07,
                0.9999969105044493
            ],
            [
                0.9999599363174355,
                6.475949526020042e-07,
                0.9999989969856731,
                0.9999995262095551,
                0.9999957771650473,
                0.9999994284997575,
                1.0677024881941248e-06,
                0.9999975938985217,
                0.9999989322970031,
                0.9999993106388725
            ],
            [
                5.04347287955046e-07,
                3.059022998576899e-07,
                2.699578740032504e-07,
                0.9999977396757036,
                0.9999934595627781,
                0.9999989322975125,
                0.9999964991443364,
                1.275190580890061e-07,
                0.9999986290421404,
                0.9999975938976622
            ],
            [
                2.69957906184239e-07,
                3.9278610661822475e-07,
                4.4508494582405734e-07,
                5.715007195447234e-07,
                1.2098653950692178e-06,
                3.2887494574518405e-06,
                5.715003107755449e-07,
                8.315280276626197e-07,
                5.04347287955046e-07,
                4.4508510499849186e-07
            ],
            [
                1.0129987357407137e-05,
                0.9999892166878142,
                0.9999771720029089,
                0.9999892166903822,
                0.9999843104503422,
                0.9999945777823325,
                0.9999955048184346,
                0.9999955048168249,
                0.9999810748563194,
                0.999991601927003
            ],
            [
                3.9278634073732336e-07,
                0.9999930377412711,
                3.4663249714612693e-07,
                8.315279285351409e-07,
                6.475949526020042e-07,
                1.4738976701170414e-05,
                0.9999962733593869,
                5.715002426486762e-07,
                6.475949526020042e-07,
                1.2098653950692178e-06
            ],
            [
                0.9999985406241282,
                0.9999151889692868,
                7.338207180898968e-07,
                3.05902336324494e-07,
                2.382370235933104e-07,
                0.9999910603026397,
                0.9999981261248411,
                0.9999989969861515,
                0.9999983463096265,
                0.9999982396559483
            ],
            [
                2.3823688159291947e-07,
                9.422449308716635e-07,
                3.927860597945825e-07,
                4.450848927650143e-07,
                1.0677026154806063e-06,
                8.315280276626197e-07,
                6.144175334468545e-06,
                1.4449798650551755e-07,
                1.637377057680051e-07,
                1.8553903548231313e-07
            ],
            [
                5.715003789033962e-07,
                1.1253509497883659e-07,
                3.9278610661902853e-07,
                0.9999798543116437,
                0.9999975938973742,
                9.422442569290178e-07,
                3.4663249714612693e-07,
                2.6995790618469934e-07,
                4.450848927658745e-07,
                3.927862002663297e-07
            ],
            [
                9.422447062294175e-07,
                3.466327037548308e-07,
                1.0677032518814388e-06,
                1.067703124601679e-06,
                9.422447062294175e-07,
                3.1201900218617364e-05,
                1.855391460719133e-07,
                0.00010889688339134737,
                4.2228339479858295e-06,
                1.1253510839355284e-07
            ],
            [
                0.9998415638229095,
                0.9999972735284315,
                1.2098653950692178e-06,
                0.9999982396565775,
                0.9999945777784506,
                0.9999962733620507,
                0.9999910603047706,
                0.9999945777829723,
                1.209865827752005e-06,
                0.9999985406241281
            ],
            [
                7.889261645427538e-06,
                6.1441767993788005e-06,
                1.2098659719788098e-06,
                NaN,
                1.0129995810463632e-05,
                1.760343213335281e-06,
                5.043472879540142e-07,
                1.5534977545886537e-06,
                4.785094494811783e-06,
                7.338212429582604e-07
            ],
            [
                2.2603242978871282e-06,
                0.9999981261246174,
                1.760343213335281e-06,
                5.71500719545698e-07,
                0.9999988634365607,
                3.059021175255426e-07,
                1.3709567165617364e-06,
                1.275190428875671e-07,
                3.059022998581767e-07,
                3.927860597945825e-07
            ],
            [
                9.93120161310289e-08,
                0.9999998362623529,
                2.699577452775239e-07,
                1.275190428875671e-07,
                0.999998790134317,
                1.6373776432481905e-07,
                0.9999623635395607,
                0.9999981261248411,
                0.9999869928653495,
                0.9999996940977002
            ],
            [
                1.275190428875671e-07,
                5.715006514167015e-07,
                3.2887506336086064e-06,
                1.1253520230052635e-07,
                1.4738980215352592e-05,
                7.338213304363436e-07,
                2.4300243631272052e-05,
                3.4663249714612693e-07,
                5.715006514167015e-07,
                7.484621835530752e-05
            ],
            [
                2.699578418198104e-07,
                1.760343003481596e-06,
                4.785096206013061e-06,
                4.2228334445658276e-06,
                2.9023112932177327e-06,
                1.209865250822125e-06,
                3.726638395634011e-06,
                8.315284241560147e-07,
                2.2603248367512505e-06,
                2.5612828213934817e-06
            ],
            [
                0.9999997463981334,
                0.9999910603037038,
                0.9999999067050609,
                0.9999938558246705,
                0.9999985406237797,
                0.9999977396746255,
                0.9999892166916508,
                7.734425919002834e-08,
                2.3823693839325527e-07,
                2.3823690999290963e-07
            ]
        ]
    },
    {
        "q_id": "9737_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            66,
            117
        ],
        "rewards": [
            [
                2.1024341622368903e-07,
                1.0677033791612137e-06,
                5.71500651413193e-07,
                0.9999978766215387,
                5.043473480777865e-07,
                7.338209805224048e-07,
                3.059022269250683e-07,
                3.059022269250683e-07,
                0.9999974387165689,
                6.825602910433871e-08
            ],
            [
                0.9999986290423032,
                0.9999998555020307,
                0.9999998257021628,
                0.9999997617631752,
                0.9999999123575674,
                0.9999998024947037,
                0.9999998874648514,
                0.9999998802069587,
                6.825609419848033e-08,
                0.9999998724809115
            ],
            [
                6.825608606148807e-08,
                0.999990483744915,
                0.9999999176675829,
                0.9999999500627916,
                0.9999999358793485,
                6.825600469412533e-08,
                0.9999994631248684,
                4.139934586278605e-08,
                0.9999998024947273,
                2.8453364239757298e-08
            ],
            [
                1.855391239544352e-07,
                0.9999972735307059,
                0.9999916019269782,
                0.999999653367503,
                0.999989216690361,
                0.9999960330150338,
                0.9999991684722701,
                0.9999972735303817,
                0.9999987121050921,
                0.9999987121041708
            ],
            [
                6.475951069961737e-07,
                2.3823688159237777e-07,
                0.9999986290427936,
                3.9278610661822475e-07,
                1.855391681906175e-07,
                0.9999921107383631,
                0.9999985406239534,
                1.9555671380533023e-08,
                1.0677032518700286e-06,
                0.9999978766215387
            ],
            [
                0.9999982396569973,
                0.9999992661791948,
                0.9999999123575046,
                0.9999996310113719,
                6.023578501513224e-08,
                0.999998005270993,
                0.999999554914789,
                0.9999998874648648,
                0.9999984465018757,
                0.9999998362623138
            ],
            [
                1.2751905808881762e-07,
                6.023571320847322e-08,
                1.1253506814842375e-07,
                2.510998494020641e-08,
                5.315784971839039e-08,
                1.1253518888531272e-07,
                9.931190958076104e-08,
                7.734426841017797e-08,
                5.3157811697009444e-08,
                1.1253513522447425e-07
            ],
            [
                0.9999996533673376,
                0.9999998024945624,
                0.9999998144608098,
                0.9999998942830611,
                0.9999994284997575,
                0.999999730042126,
                0.99999976176309,
                0.9999998362623528,
                0.9999990577551817,
                0.9999997897567091
            ],
            [
                0.999999825702163,
                0.9999995262093293,
                5.315780536011123e-08,
                8.7642516304188e-08,
                8.764241182641775e-08,
                9.422450432014836e-07,
                0.9999998942830611,
                6.023572038912295e-08,
                0.9999978766215384,
                4.691159887151251e-08
            ],
            [
                0.9999990577557433,
                0.9999990577555187,
                0.9999993106389546,
                4.691159887151251e-08,
                0.9999984465016902,
                5.043476486924565e-07,
                0.9999999006880312,
                NaN,
                0.9999945777816783,
                0.9999999067051387
            ],
            [
                0.9999869928731012,
                0.9999998257021213,
                0.9999925887192567,
                0.9999997126315495,
                0.9999969105048181,
                0.999999391641036,
                0.9999993524053563,
                0.9999994284994169,
                0.9999988634358834,
                0.9999994284992806
            ],
            [
                6.825598842065202e-08,
                1.1253526937697666e-07,
                1.275191036933194e-07,
                0.9999985406241274,
                3.059021175255426e-07,
                1.6373766672973748e-07,
                7.734421308914719e-08,
                1.1253509497883659e-07,
                9.931189774187203e-08,
                1.2751905808881762e-07
            ],
            [
                1.0677033791583005e-06,
                2.699578096403948e-07,
                9.422442569290178e-07,
                6.475945666063607e-07,
                5.043474683220276e-07,
                1.9947304348862686e-06,
                6.475945666063607e-07,
                3.466325384678894e-07,
                6.475946438022905e-07,
                5.71500719545698e-07
            ],
            [
                1.444980209564556e-07,
                0.9999991684718735,
                0.9999988634366963,
                0.9999997761971315,
                1.6373764721072816e-07,
                3.288749065423109e-06,
                0.9999994956525319,
                2.3823688159291947e-07,
                5.715005151606823e-07,
                0.9999952149037967
            ],
            [
                2.1024334103581732e-07,
                8.764241182641775e-08,
                5.715003107755449e-07,
                0.9999984465018753,
                1.4449798650551755e-07,
                0.9999960330145613,
                2.1024334103581732e-07,
                6.825600469412533e-08,
                0.9999996310113279,
                3.288748673360027e-06
            ],
            [
                0.9999995818811773,
                1.4449800373118268e-07,
                0.9999998942829477,
                0.9999995549150543,
                0.9999998642566704,
                0.9999994284997575,
                0.9999990577556309,
                0.9999997300421904,
                4.450850519403407e-07,
                0.9999994284992806
            ],
            [
                1.2751899728286965e-07,
                8.764246406483893e-08,
                6.825598028392069e-08,
                6.825602910433871e-08,
                8.764242227418718e-08,
                1.4449798650551755e-07,
                1.125352291309328e-07,
                8.764246406483893e-08,
                6.023576347299818e-08,
                2.1024341622426268e-07
            ],
            [
                6.023579219579052e-08,
                5.315781803390236e-08,
                0.9999998724809572,
                NaN,
                0.9999921107392986,
                0.9999996310115918,
                8.7642558095602e-08,
                0.999991060306899,
                0.9999998362623529,
                8.764251630441717e-08
            ],
            [
                8.31527928532683e-07,
                0.9999990577550695,
                3.2887502415767434e-06,
                0.9999978766205259,
                2.102434412875379e-07,
                3.059022998576899e-07,
                0.9999995262093857,
                0.9999987121041709,
                0.9999982396572072,
                0.9999992661788448
            ],
            [
                0.9999987901338843,
                0.9999992188514835,
                2.2603240284371276e-06,
                1.2751904288710323e-07,
                2.9023133690980155e-06,
                1.8553916819032217e-07,
                1.994730672668496e-06,
                0.9999982396561579,
                0.9999980052695663,
                0.9999938558246707
            ],
            [
                0.9999994631251242,
                0.9999998024947272,
                0.9999995818811773,
                0.9999997617630049,
                0.9999998144609203,
                0.9999992188514835,
                0.9999988634357477,
                0.9999724642991037,
                0.9999993524050477,
                0.9999997617630617
            ],
            [
                3.653479902594117e-08,
                2.1024339116168358e-07,
                2.9023116392097746e-06,
                1.6373776432509826e-07,
                1.275190428875671e-07,
                1.0677024882029858e-06,
                3.2241847115356483e-08,
                6.825604537781398e-08,
                1.0677029973158649e-06,
                3.653485564473625e-08
            ],
            [
                2.699577452775239e-07,
                1.9947299592570416e-06,
                1.2098652508287273e-06,
                1.637377448057981e-07,
                4.1399365603508136e-08,
                3.2887482811220126e-06,
                1.6373766672973748e-07,
                8.764244316973974e-08,
                1.5534981249574276e-06,
                9.931189774187203e-08
            ],
            [
                2.699577774585891e-07,
                2.1024336609843824e-07,
                9.931189774187203e-08,
                9.931190958076104e-08,
                9.931193325852072e-08,
                5.315781803390236e-08,
                9.931198061405701e-08,
                8.764241182641775e-08,
                7.734418542875216e-08,
                1.1253509497883659e-07
            ],
            [
                8.764247451307293e-08,
                4.1399365603508136e-08,
                2.3823702359290413e-07,
                0.9999885212291505,
                0.9999996743687422,
                1.1253516205489029e-07,
                1.209865827740176e-06,
                1.2751904288710323e-07,
                2.5109990926882483e-08,
                0.9999978766222981
            ],
            [
                0.9999998362622358,
                0.9999995549151074,
                0.9999998362623138,
                0.9999999358793867,
                0.9999999006880314,
                0.9999999123575151,
                0.999999352405202,
                0.9999994284992806,
                0.9999993106391191,
                0.9999995262095552
            ],
            [
                2.215948399905957e-08,
                0.999997438718706,
                0.9999998461827322,
                5.315784971839039e-08,
                0.9999988634360187,
                1.3709567165530083e-06,
                0.9999997300422225,
                0.9999999006879838,
                4.1399375473868e-08,
                0.9999993524051247
            ],
            [
                0.9999998642566866,
                0.9999998362622552,
                4.450850519403407e-07,
                0.9999998642566381,
                0.999999802494633,
                0.999999789756659,
                0.999996499144335,
                0.9999987901346054,
                0.9999998642566542,
                0.9999989969855535
            ],
            [
                0.9999980052698041,
                0.9999988634362899,
                0.9999998724809419,
                0.9999993916407459,
                0.9999952149072189,
                0.9999999123574523,
                0.9999997617630616,
                0.999999114843281,
                0.9999995549149481,
                0.9999994631250603
            ],
            [
                6.023573475041126e-08,
                9.931202796993203e-08,
                3.9278605979534166e-07,
                1.637377448057981e-07,
                8.764245361752286e-08,
                6.023569166654288e-08,
                7.734424996967756e-08,
                7.734421308914719e-08,
                1.8553910183607374e-07,
                4.4508494582405734e-07
            ],
            [
                5.043474683240344e-07,
                6.47595107001401e-07,
                9.422444815814404e-07,
                2.2603245673443566e-06,
                9.422450432030903e-07,
                1.7603430034867993e-06,
                1.855390576008354e-07,
                7.338207180898968e-07,
                5.043474082012222e-07,
                6.47594875403829e-07
            ],
            [
                9.93120161310289e-08,
                2.6995784182140636e-07,
                7.734414854823498e-08,
                1.8553919030858602e-07,
                1.8553919030858602e-07,
                0.9999987901347496,
                6.023574911170301e-08,
                2.699578740032504e-07,
                3.4663262111182307e-07,
                0.9999969105062907
            ],
            [
                0.9999995262095551,
                0.9999987901347497,
                0.9999997897567342,
                0.9999993524054337,
                0.9999998144609645,
                0.9999970976869796,
                0.9999992661788447,
                0.9999981261243942,
                0.9999994284992807,
                0.999998996986271
            ],
            [
                0.9999970976887085,
                0.999997739676512,
                0.9999885212346167,
                0.9999981261246171,
                0.9999978766222977,
                0.9999986290427937,
                0.9999930377420956,
                0.9999969105051857,
                0.9999992661788447,
                0.9999934595651181
            ],
            [
                6.825600469412533e-08,
                8.764245361752286e-08,
                3.059022998576899e-07,
                3.224185480240153e-08,
                4.450850519403407e-07,
                2.3823699519290042e-07,
                6.825601283086733e-08,
                3.05902190458764e-07,
                9.931187406410953e-08,
                6.475946438055299e-07
            ],
            [
                4.691162683297406e-08,
                1.2751901248454963e-07,
                5.315781803390236e-08,
                1.553498124964492e-06,
                6.023572038912295e-08,
                4.450848927658745e-07,
                1.1253513522447425e-07,
                1.8553910183607374e-07,
                0.9999994631249961,
                3.2241839428313264e-08
            ],
            [
                0.9999999006880549,
                0.9999998642566542,
                0.9999992188513902,
                0.9999999317439954,
                5.715003107767143e-07,
                0.9999999226557869,
                1.275190428875671e-07,
                0.999999674368781,
                0.9999999317439384,
                0.9999984465022459
            ],
            [
                0.9999960330145661,
                2.1024341622426268e-07,
                1.855391239544352e-07,
                2.902312677150514e-06,
                0.9999957771680735,
                3.059021175261338e-07,
                3.9278610661902853e-07,
                6.475947210031623e-07,
                1.8553903548231313e-07,
                0.9999991684722699
            ],
            [
                0.9999981261239471,
                1.6373776432509826e-07,
                3.22418970812682e-08,
                2.511001487368099e-08,
                1.6373770576776313e-07,
                7.734415776836702e-08,
                4.691167716359673e-08,
                5.3157900413760374e-08,
                0.9999984465018756,
                3.927863407379485e-07
            ],
            [
                2.3823693839325527e-07,
                8.31528325040778e-07,
                7.338208930460318e-07,
                1.5534984953552536e-06,
                7.338208930460318e-07,
                1.1478772231232203e-05,
                6.47594952603035e-07,
                4.222834451403972e-06,
                9.422448185510695e-07,
                1.994729008151319e-06
            ],
            [
                1.6373772528704005e-07,
                4.4508510499849186e-07,
                0.9999852610215588,
                1.6373762769138607e-07,
                3.927860597945825e-07,
                1.6373764721072816e-07,
                6.023569166654288e-08,
                1.1253516205489029e-07,
                9.422449308748773e-07,
                8.315281267861397e-07
            ],
            [
                5.043474081993875e-07,
                0.9999810748427634,
                3.726637951387472e-06,
                0.9999998555020306,
                1.3709576971425944e-06,
                0.9999994956526521,
                0.9999980052693278,
                0.9999994631250602,
                5.715003789017068e-07,
                0.9999998724809724
            ],
            [
                9.931193325852072e-08,
                3.53562422882756e-05,
                4.450852111155216e-07,
                9.422442569334097e-07,
                6.962255419982281e-06,
                1.0129987357517693e-05,
                4.785092783545836e-06,
                3.7266383956509585e-06,
                8.315283250371857e-07,
                2.6995790618469934e-07
            ],
            [
                1.3709567165579959e-06,
                0.9999934595627786,
                0.9999986290421402,
                9.931189774187203e-08,
                9.422445939002803e-07,
                4.450852111135988e-07,
                0.9999991148429644,
                0.999999607213753,
                0.9999993106389548,
                0.999997593897661
            ],
            [
                0.9999992188516696,
                0.9999997761971048,
                0.9999990577551819,
                0.9999974387180963,
                0.9999983463102173,
                0.999999266179282,
                3.059022269250683e-07,
                0.9999993106389546,
                0.9999996940976273,
                0.9999991148429646
            ],
            [
                0.999999894282998,
                5.315780536011123e-08,
                0.9999999006881023,
                0.9999992661787573,
                0.9999910603068993,
                3.6534807736504303e-08,
                0.9999998802069302,
                0.9999986290427936,
                0.9999999559306153,
                0.9999977396751644
            ],
            [
                1.5534983101602148e-06,
                3.059022269250683e-07,
                2.6995774527718623e-07,
                6.475949526020042e-07,
                1.892515049819277e-05,
                3.05902190458764e-07,
                4.785093353940187e-06,
                3.466326211105621e-07,
                6.475947210046347e-07,
                2.1024341622426268e-07
            ],
            [
                5.04347468323289e-07,
                0.9999962733593847,
                0.9999998802069873,
                0.9999998257021837,
                0.9999985406239534,
                4.139934092760465e-08,
                0.9999998362622747,
                1.5534971990169383e-06,
                0.9999998461827139,
                0.9999987901341727
            ],
            [
                7.73441946488886e-08,
                4.691160446380562e-08,
                1.637377057680051e-07,
                9.931192141912081e-08,
                4.450852111148132e-07,
                1.4449795205429202e-07,
                7.734428685019034e-08,
                6.023569884692295e-08,
                0.9999990577552942,
                3.6534807736504303e-08
            ],
            [
                1.6373764721072816e-07,
                2.2159470790999714e-08,
                6.825602910433871e-08,
                4.1399365603508136e-08,
                2.2159505132025125e-08,
                6.825598028392069e-08,
                5.04347468323289e-07,
                1.5229966803871924e-08,
                6.023569884718319e-08,
                5.3157830707696514e-08
            ],
            [
                2.3823690999290963e-07,
                1.5534981249736758e-06,
                4.139941495546278e-08,
                0.9999993524048931,
                0.9999999358793561,
                0.9999992661788447,
                0.9999599362935921,
                0.9999810748562856,
                5.315780536011123e-08,
                1.275190124846946e-07
            ],
            [
                0.9999998461826772,
                0.9999999226558146,
                0.9999999273418355,
                0.9999999123575778,
                0.9999999067050832,
                0.9999999123575046,
                0.9999999067049942,
                2.6995774527718623e-07,
                0.9999999006880312,
                0.9999999468421503
            ],
            [
                3.9278605979534166e-07,
                1.4449805540740185e-07,
                2.1024339116168358e-07,
                4.1399365603508136e-08,
                5.043474081993875e-07,
                9.931202796957073e-08,
                1.1253518888531272e-07,
                6.825606165129312e-08,
                6.825602910433871e-08,
                6.023574911170301e-08
            ],
            [
                6.825598028392069e-08,
                2.510998494020641e-08,
                2.382368531929327e-07,
                5.315784971839039e-08,
                4.691159887151251e-08,
                1.3709578605729614e-06,
                2.382369951932796e-07,
                1.4449800373118268e-07,
                4.450849988811838e-07,
                4.450851580566494e-07
            ],
            [
                8.315283250394546e-07,
                2.1024326584639497e-07,
                6.47595107001401e-07,
                1.9947292459347367e-06,
                1.2098658277451275e-06,
                4.222834954801051e-06,
                3.927862470905692e-07,
                1.8553916819032217e-07,
                1.9947299593078385e-06,
                4.450849988811838e-07
            ],
            [
                0.9999885212359875,
                0.9999997300420939,
                0.9999998555019791,
                0.9999999006881141,
                0.9999998724809724,
                0.9999997897565588,
                0.9999998802068873,
                0.9999999397642294,
                2.8453326928809566e-08,
                0.9999999067049942
            ],
            [
                0.9999987901340285,
                1.3440422588263833e-08,
                0.9999998724809419,
                0.9999992188516696,
                0.9999995549151074,
                0.9999986290423033,
                0.9999993106391191,
                0.9999984465024311,
                0.9999987121043241,
                0.9999987121052454
            ],
            [
                4.222832437798974e-06,
                1.6373766672973748e-07,
                5.715006514176113e-07,
                1.5534983101644536e-06,
                1.760343633031919e-06,
                7.338207180898968e-07,
                2.4300243631890864e-05,
                2.9023119851899796e-06,
                6.825608606172863e-08,
                7.338210680021253e-07
            ],
            [
                4.691168275606451e-08,
                5.315789407685159e-08,
                4.691160446380562e-08,
                6.023568448589658e-08,
                7.734415776836702e-08,
                5.3157900413760374e-08,
                8.31528325021115e-07,
                6.475945666051092e-07,
                3.927862939136532e-07,
                1.5534983101301911e-06
            ],
            [
                1.8553916819032217e-07,
                0.9999962733607193,
                3.059022998576899e-07,
                4.6911638017556955e-08,
                7.734418542875216e-08,
                0.9999980052705171,
                1.444979692797559e-07,
                7.734424996967756e-08,
                0.9999981261241705,
                1.209865827752005e-06
            ],
            [
                0.9999996072136125,
                0.9999998362623138,
                0.9999985406236054,
                0.9999983463098232,
                0.999999789756634,
                0.9999997300422547,
                0.9999998874648245,
                0.9999990577557434,
                0.9999993916409634,
                0.9999996743686257
            ],
            [
                1.0129993395336818e-05,
                0.999996910504449,
                0.9999986290431208,
                0.9999970976887079,
                0.9999991148433868,
                0.9999993524050477,
                NaN,
                0.9999892166890761,
                0.9999687980850376,
                7.338209805240734e-07
            ],
            [
                9.931187406410953e-08,
                6.825597214718257e-08,
                3.2241889394209404e-08,
                3.2241847115356483e-08,
                1.8553905760062447e-07,
                1.275190276859705e-07,
                2.6995784182140636e-07,
                4.4508505193932864e-07,
                2.8453323536912213e-08,
                1.8553914607267268e-07
            ],
            [
                2.6995768091383957e-07,
                4.450852641717689e-07,
                5.715005832872586e-07,
                3.9278634073625165e-07,
                1.3709573702778664e-06,
                8.31528424162821e-07,
                8.315282259117513e-07,
                5.715005832872586e-07,
                7.338208930421943e-07,
                1.0677033791583005e-06
            ],
            [
                1.2751910369275402e-07,
                3.9278624708775595e-07,
                2.6995777745711594e-07,
                2.1024331597262577e-07,
                6.825606165129312e-08,
                1.1253526937656726e-07,
                2.102433410343832e-07,
                6.023573475041126e-08,
                0.9999991684717744,
                1.637377448057981e-07
            ],
            [
                9.422442569334097e-07,
                5.71500719545698e-07,
                1.1253525596174225e-07,
                0.999999802494586,
                9.931198061405701e-08,
                3.059021175261338e-07,
                1.275189972832538e-07,
                0.9999998642567189,
                0.9999998555020135,
                0.9999972735307051
            ],
            [
                4.139934586278605e-08,
                0.9999993524050477,
                6.144172404738491e-06,
                0.9999989969862709,
                0.9999994284992806,
                0.9999992661791949,
                0.9999997126315495,
                0.999999581881277,
                0.9999994631251883,
                0.9999992661791947
            ],
            [
                0.9999994631247402,
                0.9999998362622943,
                0.9999996533674204,
                0.9999987121043243,
                0.9999984465022459,
                0.9999993524051247,
                0.9999982396569972,
                0.9999989969862708,
                0.9999967112513278,
                0.9999994631249322
            ],
            [
                3.927862002663297e-07,
                4.4508494582405734e-07,
                2.3823699519290042e-07,
                3.4663262110945863e-07,
                2.382369383923073e-07,
                3.4663249714612693e-07,
                2.382369667929001e-07,
                1.6373776432509826e-07,
                2.102434412875379e-07,
                9.931190958076104e-08
            ],
            [
                0.9999998802069302,
                0.9999995549148952,
                0.9999996533672549,
                0.9999986290423034,
                0.9999993916406734,
                0.9999993106389548,
                0.9999999123574942,
                0.9999994631251882,
                0.999998932297003,
                0.9999997761970248
            ],
            [
                2.1024334103581732e-07,
                0.9999994631251883,
                0.9999989969859121,
                1.2098656835224664e-06,
                0.9999994284996895,
                0.9999978766212853,
                0.9999955048200314,
                0.9999994284992807,
                0.00029595713534180163,
                1.3709576971463352e-06
            ],
            [
                0.9999997126313784,
                0.9999998942829602,
                0.9999988634358833,
                0.9999993106387083,
                0.9999988634358833,
                0.999999922655833,
                0.9999987121052454,
                0.9999995549150543,
                0.9999998942829728,
                0.999999428499485
            ],
            [
                0.9999991684719726,
                0.9999991148433865,
                0.9999977396757035,
                0.9999989322973849,
                0.9999993916407459,
                6.825598028392069e-08,
                0.999997273530381,
                1.1253526937697666e-07,
                1.3709568799823232e-06,
                0.999995214907219
            ],
            [
                1.2751899728286965e-07,
                1.8553903548231313e-07,
                2.1024334103505245e-07,
                3.059022269250683e-07,
                1.4449795205429202e-07,
                1.1253526937656726e-07,
                1.8553903548231313e-07,
                2.561281600086738e-06,
                4.691162124067829e-08,
                1.4449796927932878e-07
            ],
            [
                0.9999995262094422,
                8.764247451307293e-08,
                0.9999996072137999,
                0.9999989969855536,
                0.9999980052698038,
                0.9999995818812272,
                0.9999994284996213,
                0.9999994956527123,
                0.9999994631248682,
                0.999998239656997
            ],
            [
                1.0677032518785256e-06,
                9.931189774187203e-08,
                1.444980209564556e-07,
                0.9999990577550695,
                2.10243290909724e-07,
                2.1024336609874897e-07,
                6.023569166654288e-08,
                0.9999977396757032,
                6.825598028364134e-08,
                1.4449798650551755e-07
            ],
            [
                0.9999991684716754,
                0.9999997897565588,
                0.9999983463100207,
                0.9999991148429644,
                7.338208930443633e-07,
                0.9999987121049384,
                0.9999986290423034,
                1.27519088491875e-07,
                1.0677026154774503e-06,
                0.9999993524053563
            ],
            [
                8.315277302857965e-07,
                0.9999984465026167,
                0.9999930377437581,
                5.315789407685159e-08,
                1.3709575337159875e-06,
                2.2603248367949354e-06,
                0.9999991148431755,
                3.4663262111182307e-07,
                0.9999967112521124,
                1.4449800373118268e-07
            ],
            [
                1.855391239544352e-07,
                1.2751899728286965e-07,
                4.139939521459479e-08,
                1.4449798650551755e-07,
                8.764247451307293e-08,
                1.637377448057981e-07,
                7.734421308914719e-08,
                6.825598028392069e-08,
                0.9999986290424667,
                1.1253516205489029e-07
            ],
            [
                0.999998346310415,
                0.9999938558276004,
                0.9999998144608098,
                0.9999992188516696,
                0.9999998461826771,
                0.9999996940976638,
                0.9999980052705184,
                0.9999980052702793,
                0.999999391640891,
                0.9999996072137999
            ],
            [
                2.3823688159237777e-07,
                8.764244316973974e-08,
                6.825598842065202e-08,
                6.825598842065202e-08,
                0.9999989322966211,
                4.450851049991497e-07,
                3.224184327183648e-08,
                1.4449798650569826e-07,
                4.691162124067829e-08,
                2.8453371023563735e-08
            ],
            [
                1.125352291309328e-07,
                5.315783704433184e-08,
                6.825600469380719e-08,
                1.1253520230052635e-07,
                9.931192141912081e-08,
                1.1253516205489029e-07,
                5.315786239218605e-08,
                2.1024344128584085e-07,
                1.8553910183607374e-07,
                4.450851049959619e-07
            ],
            [
                6.475947210046347e-07,
                1.8553910183674878e-07,
                2.845337441546675e-08,
                4.691162124067829e-08,
                1.0677029973219343e-06,
                3.466325797896173e-07,
                1.2098661162056318e-06,
                9.93120161310289e-08,
                1.637377057680051e-07,
                1.209865539298447e-06
            ],
            [
                0.9999998874647977,
                0.9999994956527722,
                0.999999310638626,
                0.9999998461827139,
                0.9999997300423191,
                0.9999993524054335,
                0.9999998461827139,
                0.9999999226558515,
                0.9999999067051165,
                0.9999998461826589
            ],
            [
                0.9999998144608319,
                0.9999987901340283,
                0.9999994631247403,
                0.9999997126313441,
                0.9999997617631184,
                0.9999993916406734,
                0.9999998802069444,
                0.999999554914842,
                0.9999997300423192,
                0.999999653367255
            ],
            [
                0.9999985406237794,
                0.9999988634357477,
                0.999997876620526,
                0.9999995262095551,
                7.73441946488886e-08,
                0.9999998144609645,
                0.9999982396561579,
                5.315789407685159e-08,
                6.144173869603344e-06,
                0.9999989322966213
            ],
            [
                4.139936066832438e-08,
                6.825602910433871e-08,
                2.699578096403948e-07,
                6.825602910433871e-08,
                4.691159887151251e-08,
                4.450852111155216e-07,
                5.3157830707696514e-08,
                1.855390576008354e-07,
                2.5110011880337063e-08,
                1.4449802095666915e-07
            ],
            [
                1.275191036933194e-07,
                5.315789407685159e-08,
                3.05902190458764e-07,
                6.023571320847322e-08,
                0.9999991148426479,
                3.05902263391829e-07,
                0.9999916019269751,
                0.9999969105044486,
                4.1399365603508136e-08,
                6.023579219579052e-08
            ],
            [
                0.9999995262093292,
                0.9999982396565777,
                0.999996499144756,
                0.9999998144609424,
                0.9999992188518559,
                0.9999852610180504,
                0.9999987901344612,
                0.9999993524050477,
                0.9999994284996213,
                0.9999993524051248
            ],
            [
                0.999999168471576,
                6.475949526020042e-07,
                0.9999980052700415,
                2.1024336609874897e-07,
                0.9999989969862708,
                7.338212429582604e-07,
                7.338213304363436e-07,
                0.9999984465016905,
                0.9999967112521124,
                6.475945666051092e-07
            ],
            [
                1.855390576008354e-07,
                3.224189323773857e-08,
                1.0677027427624903e-06,
                6.023577783447482e-08,
                3.22418970812682e-08,
                5.043476486924565e-07,
                3.927862470905692e-07,
                2.10243290909963e-07,
                5.715006514176113e-07,
                8.315279285370317e-07
            ],
            [
                6.825606978822427e-08,
                9.931193325852072e-08,
                2.5109999906960648e-08,
                9.93120161310289e-08,
                3.653485128944664e-08,
                7.73441946488886e-08,
                1.955569236151977e-08,
                4.691161005609407e-08,
                4.691159887151251e-08,
                0.9999977396754329
            ],
            [
                3.05902190458764e-07,
                1.147877359957198e-05,
                9.422447062270609e-07,
                1.2098661162023305e-06,
                6.825598842065202e-08,
                1.275190428875671e-07,
                1.2098653950656417e-06,
                4.5397852414783676e-05,
                0.9999993106388725,
                9.422447062240614e-07
            ],
            [
                0.9999945777790933,
                3.22418970812682e-08,
                0.999999607213753,
                2.3823702359290413e-07,
                0.9999996310114598,
                9.931187406410953e-08,
                1.8553903548231313e-07,
                1.855391239544352e-07,
                2.2159505132025125e-08,
                0.9999989322968758
            ],
            [
                0.9999999067050387,
                3.05902336324494e-07,
                0.9999994284993488,
                0.9999998461827322,
                0.9999982396572067,
                0.999999266179282,
                0.9999999006880076,
                0.9999999468421883,
                0.999999495652652,
                0.9999998874649051
            ],
            [
                0.9999997761971848,
                0.9999994956525319,
                0.9999998555019446,
                0.9999993916411085,
                0.9999987901338843,
                0.9999989322971304,
                0.9999995818811773,
                0.9999998362623334,
                0.9999972735287567,
                0.9999998874648246
            ],
            [
                9.422450432030903e-07,
                4.691160446380562e-08,
                9.422449308789479e-07,
                3.059022998581767e-07,
                1.760343633036322e-06,
                1.0677026154827912e-06,
                1.209865827752005e-06,
                2.699578096403948e-07,
                2.260324028443809e-06,
                6.825606165129312e-08
            ],
            [
                7.484626297687326e-05,
                1.7603440527286572e-06,
                0.9999930377462495,
                5.715002426486762e-07,
                1.6373766672994222e-07,
                3.9278629391427843e-07,
                8.939695238634211e-06,
                2.699578096403948e-07,
                6.825597214718257e-08,
                1.4449805540763184e-07
            ],
            [
                5.3157837044597743e-08,
                1.6373770576776313e-07,
                6.023571320847322e-08,
                0.9999998802069016,
                1.8553919030858602e-07,
                1.6373774480605869e-07,
                6.1441724046434924e-06,
                5.043475885696228e-07,
                2.6995784182140636e-07,
                2.1024341622426268e-07
            ],
            [
                0.9999975938979478,
                0.9999992661786697,
                0.9999957771680678,
                2.1024331597262577e-07,
                0.9999910602994373,
                1.7603440527286572e-06,
                0.9999945777803874,
                0.9999952149072203,
                0.9998415637085216,
                0.9999974387177899
            ],
            [
                2.1024341622426268e-07,
                0.9999985406232575,
                0.9999998257021006,
                0.9999997126315154,
                0.9999998642566381,
                0.9999978766217915,
                0.9999994956527122,
                0.9999977396754336,
                0.999999789756634,
                9.422448185510695e-07
            ],
            [
                0.9999998257021837,
                0.9999998642567351,
                0.999999887464838,
                0.9999997126313098,
                0.9999998555019619,
                0.9999998555020135,
                0.9999998024947272,
                0.9999997126313441,
                0.9999998461826405,
                0.9999999067051276
            ],
            [
                0.9999938558224738,
                0.9999994284994851,
                0.9999945777816824,
                0.9999869928715541,
                0.9999949062950023,
                3.059022998576899e-07,
                0.9999822214439326,
                0.9999993524052021,
                5.04347468323289e-07,
                0.9999992188513904
            ],
            [
                0.9999977396746257,
                1.994730672668496e-06,
                0.9999993524052021,
                0.9999996072136126,
                0.9999998461826405,
                0.9999999317440279,
                0.9999990577556312,
                0.9999998642566381,
                0.9999997897566589,
                0.9999997617631186
            ],
            [
                0.9999997463980427,
                0.9999999317439221,
                0.9999998144609424,
                0.9999998802069731,
                0.9999998461826222,
                0.9999987901347497,
                0.9999998362622747,
                0.9999999006879721,
                0.999999825702163,
                0.9999990577557432
            ],
            [
                0.9999957771670656,
                0.9999992661792823,
                0.9999987121049388,
                0.9999992661788449,
                0.9999949062962185,
                0.9999988634362901,
                6.023573475041126e-08,
                0.9999993524049706,
                0.9999991148429646,
                0.999999894282935
            ],
            [
                5.3157837044597743e-08,
                8.764254764749753e-08,
                0.9999986290429573,
                0.9999960330150336,
                0.999997097688017,
                5.04347468323289e-07,
                0.9999985406236054,
                0.9999986290426303,
                0.9999983463096265,
                0.9999977396746254
            ],
            [
                6.023569884718319e-08,
                5.3157811697009444e-08,
                1.1253509497883659e-07,
                3.653482080235082e-08,
                3.6534807736504303e-08,
                4.691162683297406e-08,
                3.224185864592658e-08,
                2.5110011880337063e-08,
                2.9023116391675407e-06,
                1.1861127080436108e-08
            ],
            [
                5.422218969895357e-06,
                1.0129987357517693e-05,
                3.7266383956509585e-06,
                0.9999997300423192,
                0.9999999067050054,
                6.1441767993788005e-06,
                4.1399365603508136e-08,
                1.522999403720043e-08,
                7.734418542875216e-08,
                3.653485564473625e-08
            ],
            [
                7.734426841017797e-08,
                0.9999998802069873,
                0.9999999226557317,
                0.9999998874648514,
                6.023579219579052e-08,
                0.9999974387168746,
                0.9999960330150327,
                0.99999995860059,
                0.9999998461826588,
                0.999999900688043
            ],
            [
                0.9999982396574169,
                0.9999992188517627,
                0.9999996072137062,
                0.9999993106390369,
                0.9999982396569976,
                0.9999996743688975,
                0.9999998802069159,
                0.9999993106389546,
                0.9999996072139403,
                1.2751899728311609e-07
            ],
            [
                9.931195693628605e-08,
                5.315784971839039e-08,
                2.215950249040774e-08,
                0.9999998874649051,
                3.653481209178873e-08,
                3.224184327183648e-08,
                3.653479467066246e-08,
                5.315781803390236e-08,
                1.4449807263312446e-07,
                0.9999999273418009
            ],
            [
                2.5109996913559987e-08,
                0.9999980052693287,
                0.9999991684717743,
                0.9999998874647307,
                0.9999997617629764,
                0.9999998257021421,
                0.9999997126314468,
                0.9999930377412639,
                6.825602910433871e-08,
                0.9999999006879838
            ],
            [
                0.9999994956524718,
                0.9999997300422226,
                0.9999986290426303,
                0.9999993106387084,
                0.999996033012669,
                0.9999993524048932,
                0.9999994631248682,
                0.99999862904214,
                0.9999978766215388,
                0.9999981261250641
            ],
            [
                0.9999916019299818,
                0.9999921107345991,
                1.275190276859705e-07,
                3.6534807736504303e-08,
                1.27519088491875e-07,
                1.4449795205457127e-07,
                7.734418542875216e-08,
                5.3157837044597743e-08,
                2.102434412875379e-07,
                3.653479031538012e-08
            ],
            [
                3.927862002654366e-07,
                0.9999998642567351,
                0.9999995262092163,
                0.9999998642566542,
                0.9999996072137062,
                0.9999998724809267,
                0.9999998257021422,
                0.9999995549148422,
                0.9999992661792821,
                0.9999982396574167
            ],
            [
                0.9999995818811274,
                0.9999998024946566,
                0.9999998257022045,
                0.9999998257022045,
                0.9999998461826038,
                0.9999986290424668,
                0.9999994284996212,
                0.9999994631251882,
                0.9999992661789323,
                0.9999996072137062
            ],
            [
                0.9999998942829224,
                1.8553910183674878e-07,
                0.9999996743687809,
                1.1253509497883659e-07,
                0.9999999530883564,
                0.9999996743688974,
                0.9999997617631468,
                4.6911638017556955e-08,
                0.999993037745414,
                0.9999998642566542
            ],
            [
                0.9999993106391191,
                0.9999993106390369,
                3.05902336324494e-07,
                0.9999981261241703,
                6.475945666063607e-07,
                0.9999974387168744,
                0.9999991148426479,
                3.059022998581767e-07,
                0.9999964991439181,
                0.9999986290423037
            ],
            [
                0.9999995262092163,
                0.999986992874644,
                0.9999998874649318,
                0.9999990577549571,
                0.9999975938965142,
                0.9999989969857925,
                0.9999991148428589,
                2.5110005893648856e-08,
                0.9999995549148951,
                0.9999852610197949
            ],
            [
                8.939700567094277e-06,
                2.1024339116168358e-07,
                8.7642558095602e-08,
                2.9023119851781017e-06,
                1.8553910183548312e-07,
                3.288749849529972e-06,
                2.382369667929001e-07,
                8.76424013786396e-08,
                7.734426841017797e-08,
                2.382370235933104e-07
            ],
            [
                1.125352291309328e-07,
                1.1253516205489029e-07,
                0.999996499146422,
                1.6373764721072816e-07,
                2.51099699735139e-08,
                5.315781803390236e-08,
                2.382368815916736e-07,
                0.9999985406230838,
                1.1253509497835043e-07,
                0.9999974387180959
            ],
            [
                0.9999998942830863,
                0.9999984465020609,
                0.9999993524052792,
                0.9999986290426303,
                0.9999996940977731,
                0.9999998362623137,
                0.9999970976873251,
                0.9999995818811773,
                0.999999814460854,
                0.9999994631248043
            ],
            [
                6.023578501491997e-08,
                3.466325384678894e-07,
                3.653482080235082e-08,
                6.023573475041126e-08,
                2.2159510415258326e-08,
                6.825600469412533e-08,
                2.2159478715835187e-08,
                1.1253526937656726e-07,
                4.1399365603508136e-08,
                1.8553905760062447e-07
            ],
            [
                1.275190884913241e-07,
                1.855390354818069e-07,
                0.9999970976866328,
                1.1253509497883659e-07,
                1.4449798650551755e-07,
                0.9999969105040809,
                0.9999967112509368,
                1.275190580890061e-07,
                7.734418542875216e-08,
                0.9999970976869789
            ],
            [
                0.9999999123575987,
                0.9999998362623723,
                0.9999998144608983,
                0.9999993524049703,
                0.9999999006880668,
                0.9999998802069587,
                0.9999997300423191,
                3.653479467066246e-08,
                0.9999999677581106,
                0.9999989322966211
            ],
            [
                0.9999972735297322,
                0.9999993524052792,
                0.9999938558261361,
                0.9999987901346054,
                0.9999977396765112,
                0.999999218851949,
                0.9999978766205261,
                0.9999987901338844,
                0.9999987121043243,
                0.9999989969856731
            ],
            [
                3.653482080235082e-08,
                6.023577783447482e-08,
                4.450852641717689e-07,
                7.73442776303243e-08,
                7.734418542875216e-08,
                8.764242227418718e-08,
                1.9947290081177566e-06,
                5.315780536011123e-08,
                5.043475284447896e-07,
                2.699578740032504e-07
            ]
        ]
    },
    {
        "q_id": "9925_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            41,
            43,
            44,
            45,
            46,
            47,
            48,
            50,
            51,
            52,
            53,
            55,
            56,
            57,
            59,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            78,
            79,
            80,
            81,
            82,
            83,
            85,
            87,
            88,
            90,
            91,
            92,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            103,
            105,
            106,
            108,
            109,
            110,
            111,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126
        ],
        "rewards": [
            [
                6.475947210046347e-07,
                8.315279285370317e-07,
                6.475947210046347e-07,
                7.338212429582604e-07,
                4.4508515805735777e-07,
                4.4508505193791187e-07,
                1.9947299593078385e-06,
                8.481104139717231e-05,
                2.382368247924618e-07,
                3.4663249714612693e-07
            ],
            [
                7.338209805200689e-07,
                2.902311639183378e-06,
                6.475949525981759e-07,
                1.99472900813862e-06,
                6.475951069985296e-07,
                1.0677024881980089e-06,
                3.4663278639738526e-07,
                1.7603434231705793e-06,
                1.3709575337078829e-06,
                2.902312331125353e-06
            ],
            [
                2.6995790618469934e-07,
                8.764254764749753e-08,
                5.315781803390236e-08,
                8.764249540862797e-08,
                2.382369951932796e-07,
                1.855391681906175e-07,
                2.10243290909724e-07,
                4.691162683297406e-08,
                1.4449795205472734e-07,
                3.927860597945825e-07
            ],
            [
                0.9999974387168777,
                8.939695238634211e-06,
                0.9999756997506362,
                0.9999970976890549,
                0.9999822214418405,
                1.0677029973219343e-06,
                6.962255419931625e-06,
                4.006369219393695e-05,
                1.4738985486506781e-05,
                1.8925157266089433e-05
            ],
            [
                2.6995784182140636e-07,
                4.450849988798682e-07,
                8.315280276607289e-07,
                6.475949526020042e-07,
                1.1253517547010071e-07,
                3.059022998576899e-07,
                1.2751910369275402e-07,
                1.8553919030708836e-07,
                2.3823682479181176e-07,
                1.8553903548113195e-07
            ],
            [
                9.422443692555439e-07,
                1.0677027427600627e-06,
                3.9278634073732336e-07,
                6.475949526020042e-07,
                6.475945666051092e-07,
                2.1024336609843824e-07,
                8.315281267861397e-07,
                2.699577774585891e-07,
                5.04347468323289e-07,
                3.466326211113502e-07
            ],
            [
                1.3709572068422585e-06,
                1.0677029973192638e-06,
                5.715004470295662e-07,
                3.059023727894942e-07,
                4.4508494582405734e-07,
                2.5612831266946347e-06,
                8.315277302788957e-07,
                8.315278294072958e-07,
                1.994730197090463e-06,
                5.043474081993875e-07
            ],
            [
                1.8553907971879076e-07,
                3.288750241561788e-06,
                6.82560779249779e-08,
                9.931193325852072e-08,
                6.1441746020359e-06,
                2.5612828213934817e-06,
                4.222832437798974e-06,
                1.30071315662049e-05,
                5.04347287955046e-07,
                2.699578096403948e-07
            ],
            [
                4.222831934286977e-06,
                5.144220753172505e-05,
                1.6701429808632785e-05,
                NaN,
                1.0677029973219343e-06,
                2.2603248367949354e-06,
                1.3709570434219446e-06,
                1.1478772230929451e-05,
                1.5534975693869924e-06,
                4.222832941193893e-06
            ],
            [
                8.315283250371857e-07,
                4.450851580555361e-07,
                1.6373772528581146e-07,
                5.04347528440776e-07,
                7.338213304316717e-07,
                1.3709572068522336e-06,
                2.3823688159069855e-07,
                1.6373766672821107e-07,
                6.475950297942253e-07,
                3.0590226339061185e-07
            ],
            [
                5.043475885696228e-07,
                1.6373774480605869e-07,
                1.8553907971855875e-07,
                3.927863875616689e-07,
                3.653482080235082e-08,
                3.927863407379485e-07,
                2.3823690999323465e-07,
                5.71500719545698e-07,
                9.931185038635267e-08,
                3.05902263391829e-07
            ],
            [
                1.4449800373065699e-07,
                2.902313023130843e-06,
                2.90231094723893e-06,
                1.5534971990169383e-06,
                2.5612819054133693e-06,
                2.260323758987159e-06,
                NaN,
                1.994730197090463e-06,
                1.1253525596134564e-07,
                5.715005151606823e-07
            ],
            [
                1.9947297215125433e-06,
                1.994729721518893e-06,
                3.120190765829341e-05,
                1.9947301970972664e-06,
                8.315277302841894e-07,
                3.466326211113502e-07,
                5.715005151606823e-07,
                1.209865827752005e-06,
                3.288748281329893e-06,
                6.475947210012481e-07
            ],
            [
                4.785093353940187e-06,
                2.2603245673443566e-06,
                4.222832437798974e-06,
                4.4508494582405734e-07,
                2.5612819054133693e-06,
                2.2603251062450327e-06,
                1.0677027427624903e-06,
                4.222833444590791e-06,
                4.450850519403407e-07,
                2.902312331170226e-06
            ],
            [
                8.939697369980456e-06,
                5.715006514176113e-07,
                1.30071315662049e-05,
                4.222832437798974e-06,
                6.144175334468545e-06,
                3.7266397283908927e-06,
                1.4738985486506781e-05,
                1.0129994602895546e-05,
                6.144176066901277e-06,
                4.222834954801051e-06
            ],
            [
                8.481105151274973e-05,
                4.785095635655362e-06,
                0.9999985406230849,
                0.00010889692232771249,
                7.33821330437595e-07,
                8.315277302841894e-07,
                0.9999970976873268,
                0.9999970976869805,
                0.9999985406239545,
                9.422450432014836e-07
            ],
            [
                3.535625914363812e-05,
                2.902312677137316e-06,
                1.1478768126057254e-05,
                1.4738987243236881e-05,
                1.3007123813382511e-05,
                NaN,
                9.422450431989127e-07,
                3.288749457432399e-06,
                4.785096776499213e-06,
                4.785093353940187e-06
            ],
            [
                1.8553919030826963e-07,
                1.1253518888531272e-07,
                1.1253516205489029e-07,
                7.338212429582604e-07,
                1.8553916819032217e-07,
                4.2228339479858295e-06,
                6.475947982037486e-07,
                1.855391239544352e-07,
                1.1253516205489029e-07,
                1.1253516205489029e-07
            ],
            [
                1.6373766672973748e-07,
                2.5612816000646084e-06,
                1.3709573702822306e-06,
                3.726639284103523e-06,
                4.4508510499849186e-07,
                2.382370235933104e-07,
                3.927863875616689e-07,
                6.475947981975644e-07,
                9.422447062294175e-07,
                5.043472278322555e-07
            ],
            [
                0.00013982210754460409,
                9.610241502683509e-05,
                3.2887506336235617e-06,
                2.260323758987159e-06,
                4.785095635655362e-06,
                2.2603248367949354e-06,
                0.9999969105062964,
                1.7603425837855082e-06,
                1.8925143729954285e-05,
                0.999996711251334
            ],
            [
                9.422448185510695e-07,
                5.043473480766399e-07,
                1.5534975693933505e-06,
                1.7603434231833873e-06,
                5.043476486915964e-07,
                5.715003107738556e-07,
                4.222832941193893e-06,
                7.338211554783522e-07,
                4.450848927637999e-07,
                1.2098659719757836e-06
            ],
            [
                0.9999962733620538,
                2.561281294760143e-06,
                4.785094494811783e-06,
                4.222834954801051e-06,
                0.9999970976866341,
                0.9999942280806647,
                1.892515049819277e-05,
                4.2228319344021954e-06,
                3.7266397283908927e-06,
                0.999957352547438
            ],
            [
                9.422448185534261e-07,
                4.22283545819819e-06,
                2.5612819054133693e-06,
                3.059021175261338e-07,
                4.450848927650143e-07,
                3.466326624336003e-07,
                0.999991601927003,
                1.2751899728311609e-07,
                1.8553914607267268e-07,
                2.3823690999323465e-07
            ],
            [
                2.6995771309523475e-07,
                3.9278615344178325e-07,
                1.27519088491875e-07,
                1.1253513522447425e-07,
                2.3823685319244518e-07,
                2.10243290909724e-07,
                2.1024339116168358e-07,
                1.2751899728311609e-07,
                1.6373772528704005e-07,
                2.561282516066741e-06
            ],
            [
                1.1478764021029928e-05,
                3.9278605979534166e-07,
                1.760342793638743e-06,
                6.825598842065202e-08,
                1.6373776432509826e-07,
                4.2228319344021954e-06,
                5.422217030747413e-06,
                4.785095065232451e-06,
                2.699576809143613e-07,
                5.715002426486762e-07
            ],
            [
                1.9947292459347367e-06,
                1.0677032518748838e-06,
                6.475951069985296e-07,
                2.902313369111213e-06,
                2.5612831267202583e-06,
                1.209866260432471e-06,
                1.3709572068522336e-06,
                7.889261645427538e-06,
                1.0677024881980089e-06,
                5.422217030781934e-06
            ],
            [
                0.9999996072138936,
                0.9999988634365613,
                0.9999988634365615,
                0.999997876622046,
                0.999998239656788,
                0.9999989969857929,
                0.9999980052698043,
                0.9999996533673791,
                0.9999964991460069,
                0.9999996743687423
            ],
            [
                7.338207180884785e-07,
                3.12019039369228e-05,
                1.892515501014656e-05,
                0.9999916019300326,
                2.9023119851781017e-06,
                5.422221555380179e-06,
                0.9999934595643499,
                5.144223206152219e-05,
                2.90231094723893e-06,
                8.481104138976795e-05
            ],
            [
                1.4738985486506781e-05,
                6.962257909842961e-06,
                6.605216832236121e-05,
                8.481102118021275e-05,
                0.9999985406241274,
                1.6701423836262173e-05,
                1.0129994602895546e-05,
                2.1444956084718052e-05,
                0.999997273528756,
                2.5612834320563895e-06
            ],
            [
                8.315284241650899e-07,
                7.338209805224048e-07,
                4.0063701745046735e-05,
                5.043474081993875e-07,
                5.04347468323289e-07,
                1.5534979397740895e-06,
                1.0677033791612137e-06,
                5.043474081993875e-07,
                1.3709573702822306e-06,
                1.6701415872659116e-05
            ],
            [
                5.422217030747413e-06,
                1.1478770862735993e-05,
                2.5612831267086116e-06,
                2.1444943302181958e-05,
                7.484620943415587e-05,
                2.4300249425247723e-05,
                1.0129995810463632e-05,
                5.144221366623174e-05,
                2.4300243631272052e-05,
                6.962254589978262e-06
            ],
            [
                3.288748281329893e-06,
                7.338209805240734e-07,
                2.382370235933104e-07,
                6.144177531811707e-06,
                1.760343213335281e-06,
                1.7603434231833873e-06,
                5.1442238195844654e-05,
                5.715003789046955e-07,
                0.000261190278863158,
                3.288747889284851e-06
            ],
            [
                6.475947210046347e-07,
                3.927863407379485e-07,
                3.9278610661902853e-07,
                1.994729483729522e-06,
                3.466327037553825e-07,
                5.043476486924565e-07,
                2.699578740032504e-07,
                1.370957860576702e-06,
                1.994730672675753e-06,
                1.855391239544352e-07
            ],
            [
                8.481102118700006e-05,
                1.9947299593078385e-06,
                3.0590237279085045e-07,
                0.9999977396748972,
                0.9999687980886837,
                0.9999987121050936,
                1.9947301970972664e-06,
                5.422218969858371e-06,
                7.889260704968913e-06,
                3.726637951387472e-06
            ],
            [
                1.0677032518785256e-06,
                4.6911638017556955e-08,
                1.7603432133296774e-06,
                5.422220262636381e-06,
                1.6373772528704005e-07,
                1.5534981249697903e-06,
                1.275190732904469e-07,
                4.222831934379152e-06,
                7.338213304316717e-07,
                1.0677026154730804e-06
            ],
            [
                1.760342793638743e-06,
                2.7535700950274782e-05,
                1.067703124601679e-06,
                0.99999603301409,
                1.7603438428800754e-06,
                1.2098659719757836e-06,
                2.382369951932796e-07,
                0.9999934595612203,
                0.001032231219821124,
                9.422447062294175e-07
            ],
            [
                1.5534975693601474e-06,
                8.315278294001114e-07,
                1.3007126914612648e-05,
                1.4738980215111302e-05,
                1.3709572068422585e-06,
                1.7603436330179102e-06,
                3.4663266243111764e-07,
                5.043476486915964e-07,
                6.475945666033422e-07,
                8.315280276607289e-07
            ],
            [
                6.962259569750576e-06,
                4.53978902983119e-05,
                1.6701427818034747e-05,
                1.012999460278499e-05,
                0.00023050671570525025,
                5.043474683220276e-07,
                5.422220909009474e-06,
                7.889262585814522e-06,
                2.753569110256289e-05,
                7.889263526345123e-06
            ],
            [
                2.2603242978665707e-06,
                8.315278294097538e-07,
                7.338213304363436e-07,
                5.422217677078203e-06,
                6.475948754012522e-07,
                3.2887478892683997e-06,
                3.7266406168624155e-06,
                3.2887478892504536e-06,
                6.144173869558639e-06,
                1.5534971990126997e-06
            ],
            [
                1.4449795205457127e-07,
                4.450848927658745e-07,
                7.338208055613267e-07,
                1.8553916819032217e-07,
                1.8553905760062447e-07,
                2.1024334103505245e-07,
                2.1024331597262577e-07,
                3.4663253846718004e-07,
                1.4738989000422955e-05,
                2.382368531929327e-07
            ],
            [
                3.4663253846718004e-07,
                8.315284241650899e-07,
                2.382369383923073e-07,
                2.699578096393206e-07,
                1.1253525596134564e-07,
                4.450850519403407e-07,
                8.315283250371857e-07,
                1.994729008145876e-06,
                6.475947982037486e-07,
                7.338211554783522e-07
            ],
            [
                7.338208930460318e-07,
                2.902312331170226e-06,
                3.059022998581767e-07,
                3.466326211105621e-07,
                5.715006514176113e-07,
                6.475946438055299e-07,
                6.47594952603035e-07,
                1.760343633036322e-06,
                5.715003789046955e-07,
                1.275190428875671e-07
            ],
            [
                6.962256249935742e-06,
                2.902312677137316e-06,
                2.2603234895372223e-06,
                1.0677024881980089e-06,
                3.2887482813149375e-06,
                2.4300252320622747e-05,
                0.999996033015511,
                0.9999989969855538,
                0.9999983463098234,
                2.902312677137316e-06
            ],
            [
                3.46632497145457e-07,
                6.9622537599680095e-06,
                3.2887478892683997e-06,
                2.430024942462891e-05,
                6.9622537599680095e-06,
                2.260324567337161e-06,
                1.670141786325573e-05,
                1.5534971990126997e-06,
                6.962255419868303e-06,
                0.0001584361792827627
            ],
            [
                4.450852111148132e-07,
                5.715004470243685e-07,
                NaN,
                1.760343003481596e-06,
                2.2603240284371276e-06,
                2.561282210729555e-06,
                5.715005151606823e-07,
                9.422445939032799e-07,
                3.726638839878908e-06,
                7.338213304363436e-07
            ],
            [
                5.422217030707961e-06,
                1.760343003481596e-06,
                2.5612812947508257e-06,
                1.9947297215125433e-06,
                4.2228329411708495e-06,
                8.315283250394546e-07,
                1.3709572068522336e-06,
                1.3007131566015624e-05,
                5.422221555380179e-06,
                7.484625403938018e-05
            ],
            [
                0.9999861539972265,
                0.9999970976890563,
                2.1024339116168358e-07,
                0.9999892166826898,
                1.4738976701652988e-05,
                6.962258739796719e-06,
                9.422445939054222e-07,
                5.422220262636381e-06,
                0.9999962733616146,
                4.450850519403407e-07
            ],
            [
                0.9999983463096266,
                0.9999955048173549,
                1.4449798650551755e-07,
                3.7266397283908927e-06,
                5.715002426460124e-07,
                0.9999938558254066,
                6.144175334468545e-06,
                6.1441746020359e-06,
                2.5612828213934817e-06,
                1.0677029973192638e-06
            ],
            [
                0.9999972735290833,
                0.999964643732589,
                4.22283545819819e-06,
                4.006370652067535e-05,
                2.5612828213934817e-06,
                0.9999989322970038,
                0.9999967112501535,
                2.2603253756956754e-06,
                0.9999983463104181,
                2.260324567337161e-06
            ],
            [
                6.144173869603344e-06,
                1.1478769494396542e-05,
                5.829125859775265e-05,
                8.93969950132721e-06,
                0.9999934595604709,
                1.8925148241493373e-05,
                7.48462183607529e-05,
                8.315279285370317e-07,
                1.994729483723626e-06,
                7.889261645427538e-06
            ],
            [
                1.3709572068478697e-06,
                7.338208055664991e-07,
                3.1201926253802263e-05,
                1.0677026154774503e-06,
                2.2603251061664e-06,
                1.7603440527222532e-06,
                3.9278634073732336e-07,
                NaN,
                1.8925143729954285e-05,
                4.450851580555361e-07
            ],
            [
                3.4663278639892215e-07,
                8.315278294114555e-07,
                4.450848927658745e-07,
                7.338212429582604e-07,
                1.6373762769138607e-07,
                2.382370235933104e-07,
                1.4449800373065699e-07,
                2.3823688159291947e-07,
                3.05902226923399e-07,
                1.1253509497835043e-07
            ],
            [
                1.760343003481596e-06,
                1.3007133116542802e-05,
                2.5612831267202583e-06,
                3.466326624322211e-07,
                6.144177531767002e-06,
                3.2887482812745586e-06,
                8.939697369882888e-06,
                7.338207180864763e-07,
                1.5534975693933505e-06,
                NaN
            ],
            [
                5.715003789046955e-07,
                2.6995774527718623e-07,
                3.927863875616689e-07,
                9.931198061405701e-08,
                1.1478769494542698e-05,
                3.059023727894942e-07,
                1.209865827752005e-06,
                1.637377643243723e-07,
                5.043472879540142e-07,
                3.4663249714612693e-07
            ],
            [
                2.699577774585891e-07,
                3.1201900218617364e-05,
                1.209865539295696e-06,
                1.8553907971855875e-07,
                3.059021175261338e-07,
                6.144173137170873e-06,
                4.450849988780466e-07,
                6.475947210031623e-07,
                2.3823688159291947e-07,
                1.0677027427624903e-06
            ],
            [
                6.475947210012481e-07,
                5.715004470313855e-07,
                1.2098661161982042e-06,
                4.222832941142044e-06,
                2.902311639183378e-06,
                1.1478764020883773e-05,
                3.2887502415438413e-06,
                9.422448185478557e-07,
                1.0677024881980089e-06,
                6.962257079775324e-06
            ],
            [
                6.475949526020042e-07,
                2.699578096403948e-07,
                3.2887502415767434e-06,
                1.9947304348862686e-06,
                7.889264466868659e-06,
                7.734415776836702e-08,
                1.2751901248454963e-07,
                1.5534975693979422e-06,
                2.699578096403948e-07,
                3.2887482813149375e-06
            ],
            [
                1.9947297215125433e-06,
                2.382370235933104e-07,
                2.3823682479181176e-07,
                1.637377448057981e-07,
                4.0063696969564425e-05,
                5.715005832886879e-07,
                3.059022269250683e-07,
                2.3823688159291947e-07,
                5.043474081993875e-07,
                5.422217030747413e-06
            ],
            [
                2.382369383923073e-07,
                1.8553903548231313e-07,
                2.102434162245973e-07,
                2.699578096403948e-07,
                3.4663278639892215e-07,
                3.466327037553825e-07,
                3.466325797896173e-07,
                2.3823696679327928e-07,
                1.6373764721072816e-07,
                2.102434412875379e-07
            ],
            [
                1.2098659719757836e-06,
                1.2098652508424818e-06,
                1.8553907971758842e-07,
                2.1024341622368903e-07,
                1.1253521571574156e-07,
                1.9947297215125433e-06,
                8.315277302841894e-07,
                6.475945666051092e-07,
                3.9278605979534166e-07,
                5.043474081993875e-07
            ],
            [
                8.315280276607289e-07,
                3.7266397283908927e-06,
                0.0002611902165612174,
                6.144172404693786e-06,
                1.670141786325573e-05,
                0.9999955048195052,
                3.288748673376478e-06,
                1.4738989000422955e-05,
                1.8925157266089433e-05,
                8.939700567094277e-06
            ],
            [
                0.9999724642991694,
                1.892515049819277e-05,
                0.9999980052707564,
                0.9999916019249765,
                1.5534973842076057e-06,
                0.9999756997535274,
                1.012999581057419e-05,
                7.889265407327733e-06,
                0.9999724642992257,
                0.999997739675165
            ],
            [
                0.9999999176674946,
                0.22270013366638422,
                1.6701425827133152e-05,
                4.539787947559951e-05,
                0.9999972735294067,
                0.9999852610198211,
                1.012998977264307e-05,
                1.30071315662049e-05,
                0.9999910603015729,
                0.999998126123724
            ],
            [
                1.8553919030858602e-07,
                1.3007133116732079e-05,
                6.475948754012522e-07,
                5.043476486924565e-07,
                5.043475885696228e-07,
                3.288747889284851e-06,
                3.059022269254856e-07,
                5.715003107767143e-07,
                3.120192625482384e-05,
                1.6373766672973748e-07
            ],
            [
                2.90231094723893e-06,
                0.9999975938976631,
                1.3709567165530083e-06,
                6.475946438055299e-07,
                1.5534977545886537e-06,
                2.5612834320563895e-06,
                0.9999861539971321,
                0.9999949062950056,
                0.9999981261241707,
                1.1478770862882149e-05
            ],
            [
                1.1253522913127183e-07,
                7.338210680021253e-07,
                2.699577774589574e-07,
                2.1024334103581732e-07,
                1.8553919030858602e-07,
                NaN,
                1.8553914607267268e-07,
                4.4508494582405734e-07,
                5.043475885696228e-07,
                3.05902190458764e-07
            ],
            [
                5.829127945202588e-05,
                2.4300252321904572e-05,
                7.338210680021253e-07,
                7.338207180898968e-07,
                0.9999949062943974,
                1.147877359957198e-05,
                2.753569110256289e-05,
                0.9999955048173541,
                0.9999982396569977,
                3.288749065423109e-06
            ],
            [
                2.1024331597262577e-07,
                3.7266397283908927e-06,
                6.475947982037486e-07,
                7.338207180898968e-07,
                1.994729721518893e-06,
                2.3823696679327928e-07,
                6.144176799334096e-06,
                1.6701421845057263e-05,
                7.338212429594283e-07,
                6.023571320847322e-08
            ],
            [
                2.561281600086738e-06,
                0.9999646437620714,
                0.9999646437451921,
                0.9999985406243026,
                1.994729483729522e-06,
                1.6373776432509826e-07,
                4.785094494811783e-06,
                0.9999997617631186,
                0.9999930377404419,
                1.3709568799919866e-06
            ],
            [
                0.00033534999118960975,
                1.760343213322473e-06,
                0.00012339458963849851,
                1.7603436330259153e-06,
                4.222831934379152e-06,
                4.785093353909723e-06,
                1.6701415872385704e-05,
                2.430024073399743e-05,
                1.3007131566015624e-05,
                7.889265407177056e-06
            ],
            [
                8.939700567004841e-06,
                1.0677032518785256e-06,
                4.2228319344021954e-06,
                1.067702870039777e-06,
                6.475945666051092e-07,
                7.338213304363436e-07,
                1.2098662604247682e-06,
                2.561281600076256e-06,
                4.785093924362895e-06,
                1.7603440527286572e-06
            ],
            [
                1.4738976701652988e-05,
                3.927863875616689e-07,
                1.760342793638743e-06,
                2.5612822107167428e-06,
                1.444980209564556e-07,
                3.466327037548308e-07,
                2.2603251062450327e-06,
                9.422444815814404e-07,
                4.450852111155216e-07,
                1.3709568799879344e-06
            ],
            [
                7.338210680021253e-07,
                1.5534984953552536e-06,
                7.889265407327733e-06,
                1.4738978458623327e-05,
                1.275190124842887e-07,
                1.994729483729522e-06,
                1.7603425837903113e-06,
                3.9278610661902853e-07,
                8.315277302857965e-07,
                3.9278634073732336e-07
            ],
            [
                2.1024334103581732e-07,
                9.931200429212718e-08,
                1.1253508156363576e-07,
                4.4508515805735777e-07,
                9.422444815814404e-07,
                7.338212429594283e-07,
                2.699578096403948e-07,
                5.715005832895975e-07,
                1.4449802095666915e-07,
                1.4449798650569826e-07
            ],
            [
                2.6995784182140636e-07,
                1.6373770576776313e-07,
                1.855391239544352e-07,
                1.2751908849167202e-07,
                1.8553910183607374e-07,
                3.4663274507713016e-07,
                1.3709578605542582e-06,
                2.3823690999290963e-07,
                6.475947982037486e-07,
                5.04347528446051e-07
            ],
            [
                2.3823693839325527e-07,
                1.27519088491875e-07,
                1.994729483729522e-06,
                2.699578740032504e-07,
                1.1253525596174225e-07,
                1.8553905760062447e-07,
                1.4449800373118268e-07,
                2.69957906184239e-07,
                8.939696304311336e-06,
                1.855391681906175e-07
            ],
            [
                8.939696304116203e-06,
                3.927862470899887e-07,
                7.338210680021253e-07,
                2.9023119851781017e-06,
                2.2603253756874524e-06,
                9.422445939002803e-07,
                1.370957860576702e-06,
                0.000709670556414641,
                2.5612819054028872e-06,
                3.466326211113502e-07
            ],
            [
                1.3709567165617364e-06,
                1.209865539295696e-06,
                3.4663274507713016e-07,
                1.067703124601679e-06,
                1.7603434231833873e-06,
                3.726637951387472e-06,
                1.4449802095666915e-07,
                5.715002426475718e-07,
                1.3709572068522336e-06,
                8.315277302857965e-07
            ],
            [
                5.422218322851817e-06,
                1.0677029973219343e-06,
                1.7603425837702984e-06,
                3.9278605979534166e-07,
                1.209866260432471e-06,
                5.715003789046955e-07,
                4.4508494582405734e-07,
                1.7603440527286572e-06,
                5.422219616228845e-06,
                4.450850519403407e-07
            ],
            [
                3.4663278639892215e-07,
                1.444979692800516e-07,
                3.927863407379485e-07,
                1.067703124601679e-06,
                6.475945666063607e-07,
                3.288749065423109e-06,
                5.043476486924565e-07,
                1.2751899728311609e-07,
                2.9023119851899796e-06,
                1.2098661162056318e-06
            ],
            [
                1.994729483729522e-06,
                0.9999974387184026,
                0.9999996310115483,
                0.9999983463106127,
                1.5534984953552536e-06,
                7.338208055680009e-07,
                0.999999218851391,
                2.5612819054133693e-06,
                2.2603253756956754e-06,
                1.7603434231833873e-06
            ],
            [
                3.288749457432399e-06,
                1.0677032518785256e-06,
                1.2098659719757836e-06,
                1.3709576971425944e-06,
                1.2098662604291696e-06,
                1.444980209564556e-07,
                9.422450432014836e-07,
                6.475950298011458e-07,
                1.5534977545886537e-06,
                1.3709567165579959e-06
            ],
            [
                1.855391681906175e-07,
                3.4663262111182307e-07,
                1.7603425837903113e-06,
                1.5534984953552536e-06,
                2.3823690999323465e-07,
                5.043476486924565e-07,
                3.9278620026686556e-07,
                2.5612819054133693e-06,
                3.726638839878908e-06,
                1.4449800373118268e-07
            ],
            [
                2.260324297853209e-06,
                8.939696304213768e-06,
                2.260324836776948e-06,
                4.785096776499213e-06,
                1.3709572068522336e-06,
                6.144174601991196e-06,
                1.8925155009767892e-05,
                4.222834451382849e-06,
                2.90231094723893e-06,
                1.9947292459347367e-06
            ],
            [
                1.275190276859705e-07,
                5.04347468323289e-07,
                4.450848927658745e-07,
                9.93118503859575e-08,
                1.6373776432509826e-07,
                1.4449807263312446e-07,
                6.47595107001401e-07,
                5.715006514176113e-07,
                1.8553910183607374e-07,
                1.855391681906175e-07
            ],
            [
                1.3007130015488633e-05,
                1.3709568799919866e-06,
                0.999998932297387,
                1.5534977545886537e-06,
                2.2603253756956754e-06,
                0.9999990577555201,
                7.338209805240734e-07,
                0.9999975938979525,
                0.9999969105051941,
                6.144174601991196e-06
            ],
            [
                5.043472879540142e-07,
                1.1478768126057254e-05,
                2.2603234895289998e-06,
                1.1478764021029928e-05,
                1.0129994602895546e-05,
                7.889266347715168e-06,
                1.4738981972323349e-05,
                1.3709576971425944e-06,
                4.22283545819819e-06,
                1.6701423836262173e-05
            ],
            [
                1.99472900813862e-06,
                2.9023119851635836e-06,
                7.734415776836702e-08,
                1.99472924590571e-06,
                7.734416698849138e-08,
                3.120192625278069e-05,
                7.889259764445822e-06,
                3.726639728348526e-06,
                1.0129987357158383e-05,
                9.610243789808358e-05
            ],
            [
                1.7603440527286572e-06,
                0.9999977396748954,
                6.962253760024999e-06,
                5.422220262636381e-06,
                3.1201922535494165e-05,
                5.829129334130764e-05,
                4.2228319344021954e-06,
                2.9023109472494878e-06,
                3.1201915096836145e-05,
                0.9999974387184019
            ],
            [
                1.012999581057419e-05,
                4.450852111155216e-07,
                1.9947304348862686e-06,
                1.444979692800516e-07,
                0.00037998443405181374,
                3.4663278639892215e-07,
                1.9947304348862686e-06,
                5.715002426486762e-07,
                5.715002426486762e-07,
                1.5534984953552536e-06
            ],
            [
                9.931185038635267e-08,
                1.0677026154806063e-06,
                9.422448185510695e-07,
                3.05902190458764e-07,
                1.994729721518893e-06,
                1.7603438428800754e-06,
                3.4663278639738526e-07,
                1.8553916819032217e-07,
                1.3709576971425944e-06,
                8.315279285370317e-07
            ],
            [
                8.764249540862797e-08,
                5.422221555340727e-06,
                9.422445939054222e-07,
                1.1253512180925583e-07,
                5.3157887739943563e-08,
                2.6995784182140636e-07,
                1.1253509497883659e-07,
                2.382368815932174e-07,
                4.450851580540182e-07,
                1.4449805540763184e-07
            ],
            [
                1.3709568799879344e-06,
                7.338209805224048e-07,
                1.4738976701411704e-05,
                1.994730434879465e-06,
                1.3709570434219446e-06,
                2.2603242978871282e-06,
                7.338211554783522e-07,
                1.553497754577351e-06,
                1.99472900813862e-06,
                5.715004470295662e-07
            ],
            [
                1.7603425837903113e-06,
                2.699578740032504e-07,
                4.450852111155216e-07,
                1.8553905760062447e-07,
                9.422450432030903e-07,
                4.4508515805735777e-07,
                1.27519088491875e-07,
                1.0677032518814388e-06,
                3.9278629391427843e-07,
                1.444979692800516e-07
            ],
            [
                9.422443692574719e-07,
                6.475946438055299e-07,
                0.0007096703882029484,
                0.0013250225116449087,
                8.481108184529756e-05,
                5.422220909009474e-06,
                1.9947299593078385e-06,
                2.4300249425247723e-05,
                3.9278605979534166e-07,
                5.422218969895357e-06
            ],
            [
                3.288749457469787e-06,
                1.2098662604291696e-06,
                6.144176799283803e-06,
                1.7603430034743913e-06,
                2.7535700949523498e-05,
                3.726637951367137e-06,
                1.7603434231833873e-06,
                1.9947299592933255e-06,
                NaN,
                1.6701421845057263e-05
            ],
            [
                0.9999986290423039,
                3.535626336201389e-05,
                0.9999991148430699,
                2.2603248367949354e-06,
                1.0677032518814388e-06,
                3.535626757653154e-05,
                1.5534981249736758e-06,
                1.2098656835252174e-06,
                4.539785783018247e-05,
                1.3709573702856596e-06
            ],
            [
                5.422218323487975e-06,
                1.275190580890061e-07,
                0.9999996940978462,
                0.9999972735294063,
                4.0063696969564425e-05,
                2.5612828213934817e-06,
                0.9999974387171804,
                0.9999995262093295,
                0.9999998024947273,
                2.430023204460668e-05
            ],
            [
                8.764254764780641e-08,
                8.7642558095602e-08,
                3.2241839428313264e-08,
                4.139941495546278e-08,
                6.023578501513224e-08,
                6.023569166654288e-08,
                2.1024336609874897e-07,
                8.76424013786396e-08,
                3.224184327183648e-08,
                9.93120161310289e-08
            ],
            [
                3.288750241561788e-06,
                1.1478768125911099e-05,
                3.466326211113502e-07,
                3.726639728370556e-06,
                0.00012339460439135077,
                1.0677027427525368e-06,
                1.0129993395217047e-05,
                0.00048785717971890487,
                5.422221555340727e-06,
                3.726638395634011e-06
            ],
            [
                1.1253506814842375e-07,
                7.338208055680009e-07,
                7.73441946488886e-08,
                8.939697369980456e-06,
                5.3157830707696514e-08,
                3.9278629391427843e-07,
                2.3823693839325527e-07,
                7.338208055680009e-07,
                1.1253506814842375e-07,
                1.012998977264307e-05
            ],
            [
                1.6373774480605869e-07,
                8.315281267882195e-07,
                1.275190732904469e-07,
                4.450852641737424e-07,
                3.2887506336235617e-06,
                7.33821330437595e-07,
                4.450852111148132e-07,
                5.043475885696228e-07,
                3.4663274507713016e-07,
                3.05902336324494e-07
            ],
            [
                0.9999993106387083,
                0.9999996072139404,
                0.9999997897567091,
                0.9999990577550695,
                0.9999989969860323,
                0.9999996072137062,
                0.9999987901343176,
                0.999999057755182,
                0.999999526209386,
                0.9999991148431757
            ],
            [
                6.475949526020042e-07,
                1.855391681906175e-07,
                3.4663274507713016e-07,
                8.315278294097538e-07,
                4.691162124067829e-08,
                2.561282210740037e-06,
                9.422443692527585e-07,
                2.561282210740037e-06,
                2.5612834320470717e-06,
                1.1478770862735993e-05
            ],
            [
                2.382370235922541e-07,
                3.2887502415438413e-06,
                5.4222183235249605e-06,
                1.3709567165617364e-06,
                2.2603234895289998e-06,
                1.994730672668496e-06,
                4.4508510499849186e-07,
                1.3709573702822306e-06,
                5.043472879525233e-07,
                3.9278624708775595e-07
            ]
        ]
    },
    {
        "q_id": "10188_mmlu_physics",
        "cot_ids": [
            0,
            1,
            3,
            4,
            6,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            17,
            18,
            19,
            20,
            21,
            22,
            25,
            27,
            28,
            30,
            31,
            32,
            34,
            35,
            36,
            37,
            39,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            53,
            55,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            99,
            100,
            102,
            106,
            107,
            108,
            109,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.466327037539638e-07,
                3.059021175247079e-07,
                4.450852641737424e-07,
                8.315283250371857e-07,
                1.2098652508347793e-06,
                7.338211554758494e-07,
                1.8553903548231313e-07,
                8.31528424162821e-07,
                7.338213304363436e-07,
                5.043476486902204e-07
            ],
            [
                1.3709575337078829e-06,
                9.422448185478557e-07,
                1.8925141473599938e-05,
                1.0677026154730804e-06,
                9.422447062202052e-07,
                2.2603242978871282e-06,
                1.0677028700363782e-06,
                2.9023116391675407e-06,
                8.315278294072958e-07,
                1.2098653950656417e-06
            ],
            [
                9.422450431989127e-07,
                1.3709567165579959e-06,
                6.9622595696935874e-06,
                9.422448185510695e-07,
                6.144172404738491e-06,
                3.9278615344178325e-07,
                6.144177531767002e-06,
                2.3823696679327928e-07,
                2.7535697667202906e-05,
                1.2098658277489788e-06
            ],
            [
                1.994729008145876e-06,
                1.3709567165617364e-06,
                8.315281267861397e-07,
                2.1024331597262577e-07,
                3.288750241561788e-06,
                1.275191036933194e-07,
                5.043475885696228e-07,
                0.9999938558239452,
                2.561281294760143e-06,
                1.067702870039777e-06
            ],
            [
                1.2751905808881762e-07,
                8.764247451307293e-08,
                1.275190884913241e-07,
                7.734423152941018e-08,
                3.0590237279085045e-07,
                9.931198061405701e-08,
                1.1253514863968147e-07,
                6.023572038912295e-08,
                9.931190958026426e-08,
                1.6373772528506686e-07
            ],
            [
                1.2098658277489788e-06,
                0.9999990577557437,
                0.9999952149038093,
                5.71500515159253e-07,
                0.999996910506309,
                1.994730197090463e-06,
                0.9999974387168779,
                0.9999978766215433,
                0.9999967112501574,
                0.9999916019250074
            ],
            [
                1.275190732904469e-07,
                8.315278294114555e-07,
                1.0677026154730804e-06,
                1.0677028700320085e-06,
                3.927863407379485e-07,
                8.315278294114555e-07,
                3.288748673360027e-06,
                9.422444815765128e-07,
                1.0677028700266676e-06,
                1.6373772528704005e-07
            ],
            [
                0.9999977396749,
                0.9999988634366974,
                0.9999969105051947,
                0.9999955048162926,
                0.9999987121047863,
                0.9999967112521171,
                1.4449805540763184e-07,
                0.9999960330122037,
                0.9999934595628,
                0.999997876620782
            ],
            [
                3.9278629391427843e-07,
                3.0590237279085045e-07,
                1.7603434231097403e-06,
                6.475945666051092e-07,
                8.315282259138311e-07,
                1.275190732904469e-07,
                1.2098653950551882e-06,
                5.71500515159253e-07,
                5.043476486915964e-07,
                1.5534971989809095e-06
            ],
            [
                4.785095635592258e-06,
                3.7266410611296085e-06,
                3.2887506335906595e-06,
                1.147877359957198e-05,
                1.7603436330091044e-06,
                1.3007128464961824e-05,
                1.4738985485997396e-05,
                1.6701421845361053e-05,
                1.760343213322473e-06,
                7.889262585886274e-06
            ],
            [
                8.315278294114555e-07,
                NaN,
                2.10243290909963e-07,
                3.059022998576899e-07,
                8.31528325040778e-07,
                4.785096206047877e-06,
                1.9947304348862686e-06,
                5.043476486915964e-07,
                6.475945666063607e-07,
                3.2887482813149375e-06
            ],
            [
                1.2098658277082653e-06,
                5.04347528446051e-07,
                1.2098659719232413e-06,
                1.2098653950656417e-06,
                6.475946437722523e-07,
                5.043474081993875e-07,
                6.475950298011458e-07,
                9.422449308716635e-07,
                5.043475284430694e-07,
                1.3709570434219446e-06
            ],
            [
                5.715003107767143e-07,
                6.475950298011458e-07,
                1.5534973842076057e-06,
                2.382370235922541e-07,
                3.466327863961242e-07,
                5.715003107767143e-07,
                2.3823688159291947e-07,
                1.444980209564556e-07,
                1.9947299593078385e-06,
                9.422442569315887e-07
            ],
            [
                9.93120161310289e-08,
                1.0677026154827912e-06,
                NaN,
                3.9278610661902853e-07,
                6.144175334468545e-06,
                1.637376862489725e-07,
                1.994729721518893e-06,
                3.059022269250683e-07,
                3.466327037553825e-07,
                1.2751901248454963e-07
            ],
            [
                5.04347287955046e-07,
                1.0129988565084915e-05,
                0.9999861539987784,
                2.382369951932796e-07,
                2.2603253756956754e-06,
                5.829126555256903e-05,
                4.450852641737424e-07,
                4.0063701745046735e-05,
                3.059022269254856e-07,
                0.9999785550413917
            ],
            [
                3.2887478892055875e-06,
                1.5534984953453635e-06,
                0.9998911030413614,
                1.4738985486506781e-05,
                4.785096206047877e-06,
                2.430025232128576e-05,
                2.5612816000646084e-06,
                1.6701423835624208e-05,
                1.9947299592933255e-06,
                1.3709576971425944e-06
            ],
            [
                1.275190276859705e-07,
                1.6373766672973748e-07,
                6.144172404738491e-06,
                2.10243290909724e-07,
                3.059021175261338e-07,
                2.6995784182183607e-07,
                7.338208930460318e-07,
                9.931189774187203e-08,
                1.8553919030858602e-07,
                1.209866260432471e-06
            ],
            [
                3.05902226923399e-07,
                2.2603248367949354e-06,
                2.561281294760143e-06,
                3.288749065423109e-06,
                3.9278634073732336e-07,
                8.939693107288474e-06,
                3.927862470899887e-07,
                1.8553916819032217e-07,
                2.561281294760143e-06,
                5.422217030747413e-06
            ],
            [
                2.102434412871794e-07,
                5.715007195431641e-07,
                0.9999942280799892,
                0.9999977396748988,
                5.4222183235249605e-06,
                3.2887494574518405e-06,
                1.994729008145876e-06,
                3.2887506336235617e-06,
                0.9999969105051972,
                5.715003789033962e-07
            ],
            [
                1.7603434231777837e-06,
                0.9999994631248044,
                0.9999822214547301,
                0.9999987121052474,
                0.9999955048195112,
                0.9999885212346807,
                0.9999983463098249,
                0.004070138508684598,
                0.999997593897663,
                0.9999977396759779
            ],
            [
                4.4508494582314646e-07,
                1.2751901248454963e-07,
                2.3823690999290963e-07,
                2.2603253756956754e-06,
                7.889266347715168e-06,
                3.059021175255426e-07,
                9.422450432014836e-07,
                4.222835458175145e-06,
                4.006371129776199e-05,
                1.892514598627448e-05
            ],
            [
                6.475947982002148e-07,
                7.338209805200689e-07,
                4.4508510499849186e-07,
                3.9278634073732336e-07,
                1.2098661161982042e-06,
                3.288748673376478e-06,
                2.3823685319244518e-07,
                6.144176799334096e-06,
                4.450848927658745e-07,
                5.715003789033962e-07
            ],
            [
                2.2603251062450327e-06,
                3.059022269250683e-07,
                1.2098661162056318e-06,
                5.715002426475718e-07,
                4.22283545819819e-06,
                1.0677024882009222e-06,
                6.475947210031623e-07,
                6.144173137126169e-06,
                1.3709576971463352e-06,
                5.043476486915964e-07
            ],
            [
                1.670141786325573e-05,
                0.9999981261250661,
                0.9999852610163267,
                8.939694172957213e-06,
                7.338209805240734e-07,
                7.338207180898968e-07,
                2.69957906184239e-07,
                1.444979692800516e-07,
                7.484621836619826e-05,
                3.9278629391427843e-07
            ],
            [
                1.0677032518785256e-06,
                3.059022269250683e-07,
                5.043475885674441e-07,
                1.637377448057981e-07,
                3.726638839878908e-06,
                5.715005832886879e-07,
                8.315283250394546e-07,
                2.561283432035425e-06,
                3.9278605979534166e-07,
                8.93969950132721e-06
            ],
            [
                9.93118503859575e-08,
                4.6911638017556955e-08,
                5.715002426486762e-07,
                1.2098661162056318e-06,
                1.6373774480535133e-07,
                1.5534984953552536e-06,
                2.9023112932177327e-06,
                2.1024331597262577e-07,
                9.422449308774482e-07,
                9.931190958076104e-08
            ],
            [
                9.422442569290178e-07,
                0.9999960330126723,
                4.785095065204162e-06,
                2.430024073461624e-05,
                1.7603434231777837e-06,
                1.1478765389368729e-05,
                0.9999985406234325,
                2.2603234895372223e-06,
                3.7266406168624155e-06,
                4.222834954778007e-06
            ],
            [
                8.315281267861397e-07,
                1.855391681898159e-07,
                3.05902263389638e-07,
                2.382369383923073e-07,
                2.102433410343832e-07,
                2.1024336609843824e-07,
                3.466327450756327e-07,
                1.4449798650417048e-07,
                1.8553910183607374e-07,
                2.699577774585891e-07
            ],
            [
                1.209866260432471e-06,
                1.4449805540740185e-07,
                3.927862470899887e-07,
                5.715002426486762e-07,
                2.1024326584639497e-07,
                1.4449803818215767e-07,
                2.699576809143613e-07,
                8.315281267861397e-07,
                3.9278634073732336e-07,
                2.6995771309523475e-07
            ],
            [
                0.9999945777810442,
                1.8925145985895816e-05,
                1.7603427936335396e-06,
                6.475950298011458e-07,
                1.3007133116542802e-05,
                1.8925157266089433e-05,
                0.9999993524054341,
                0.9999986290432851,
                0.000626334182010526,
                6.144173869603344e-06
            ],
            [
                2.5612819054133693e-06,
                2.902312677150514e-06,
                5.422219616265831e-06,
                2.561282516066741e-06,
                8.939699501416646e-06,
                2.5612812947508257e-06,
                8.315283250371857e-07,
                4.785096776499213e-06,
                2.382368247924618e-07,
                3.4663262110945863e-07
            ],
            [
                4.222832437798974e-06,
                2.260325106237323e-06,
                1.8553907971879076e-07,
                2.902312331170226e-06,
                3.466326211113502e-07,
                0.9999916019239806,
                6.475950298011458e-07,
                0.9999977396746293,
                1.275190732904469e-07,
                0.9999832985822427
            ],
            [
                1.2751899728286965e-07,
                5.043476486924565e-07,
                2.1024331597262577e-07,
                6.475949526020042e-07,
                3.466327450765785e-07,
                6.475950298011458e-07,
                3.059022998576899e-07,
                1.4449798650551755e-07,
                5.715003789033962e-07,
                9.422445939032799e-07
            ],
            [
                1.6701419853852583e-05,
                1.209865827752005e-06,
                5.422218969895357e-06,
                0.9999921107364986,
                8.315277302857965e-07,
                5.422217030781934e-06,
                7.484622728735096e-05,
                9.422444815814404e-07,
                6.475947982037486e-07,
                0.00010889693528247257
            ],
            [
                5.043472879525233e-07,
                2.561282210740037e-06,
                1.5534977545886537e-06,
                4.450849988811838e-07,
                2.699576809143613e-07,
                1.3709568799919866e-06,
                8.315279285351409e-07,
                NaN,
                1.5534984953510149e-06,
                5.04347287955046e-07
            ],
            [
                2.382369383923073e-07,
                6.023569884718319e-08,
                1.1253516205489029e-07,
                3.059022998576899e-07,
                2.1024339116082313e-07,
                1.8553905760024476e-07,
                1.8553910183607374e-07,
                8.315284241650899e-07,
                1.855391239544352e-07,
                5.715003789046955e-07
            ],
            [
                NaN,
                3.05902336324494e-07,
                2.699578096393206e-07,
                7.889266347786918e-06,
                6.475950298011458e-07,
                NaN,
                NaN,
                2.6995784182140636e-07,
                3.927862002663297e-07,
                2.6995784182140636e-07
            ],
            [
                2.102434412875379e-07,
                3.05902336324494e-07,
                1.3709568799919866e-06,
                1.4449807263312446e-07,
                1.8553903548231313e-07,
                1.9947301970972664e-06,
                7.338212429582604e-07,
                1.067703124601679e-06,
                8.764244316973974e-08,
                3.0590237279032884e-07
            ],
            [
                5.715005832886879e-07,
                1.6373774480605869e-07,
                3.4663274507713016e-07,
                2.260323758987159e-06,
                6.475947982037486e-07,
                7.73442776303243e-08,
                3.0590226339061185e-07,
                3.927862939126708e-07,
                2.902312331170226e-06,
                5.715007195431641e-07
            ],
            [
                1.4449803818215767e-07,
                3.288747889284851e-06,
                4.450850519403407e-07,
                5.715003107767143e-07,
                6.475950298011458e-07,
                9.422449308774482e-07,
                9.422448185534261e-07,
                2.3823693839325527e-07,
                6.475947982037486e-07,
                1.7603438428800754e-06
            ],
            [
                1.3007134667259441e-05,
                3.7266410611296085e-06,
                1.0129988564974359e-05,
                3.535626757524533e-05,
                2.5612819054028872e-06,
                8.939695238536645e-06,
                1.6701427818034747e-05,
                9.422448185510695e-07,
                1.3007126914435202e-05,
                2.561282210740037e-06
            ],
            [
                2.1024331597262577e-07,
                1.6373774480605869e-07,
                1.2751905808881762e-07,
                6.825602910433871e-08,
                0.9999945777784506,
                6.825606165129312e-08,
                6.825602910433871e-08,
                6.825602910433871e-08,
                7.73442776300517e-08,
                2.5109996913559987e-08
            ],
            [
                9.42244930862237e-07,
                2.902313023039776e-06,
                6.47594952595231e-07,
                8.31528126775552e-07,
                1.3709578605617394e-06,
                7.338208930391909e-07,
                1.99473067264854e-06,
                1.3709567165530083e-06,
                7.338213304196583e-07,
                7.338212429504183e-07
            ],
            [
                2.382370235933104e-07,
                6.475951069985296e-07,
                1.8553910183607374e-07,
                2.38237023590304e-07,
                2.1024344128488479e-07,
                3.927860597945825e-07,
                5.715003107767143e-07,
                1.5534975693933505e-06,
                1.2751905808881762e-07,
                3.927862002641863e-07
            ],
            [
                5.715004470272272e-07,
                1.0677024882009222e-06,
                1.0677026154806063e-06,
                1.067702870039777e-06,
                1.6373764720990908e-07,
                1.6373776432303203e-07,
                2.1024329090685577e-07,
                3.927862939113312e-07,
                3.4663262110945863e-07,
                3.0590226338838606e-07
            ],
            [
                1.0677032518785256e-06,
                1.2751910369310194e-07,
                6.475947210031623e-07,
                1.3709576971425944e-06,
                2.2603253756956754e-06,
                3.059022998576899e-07,
                2.2603237589676295e-06,
                1.0129994602895546e-05,
                2.902313023130843e-06,
                8.315280276626197e-07
            ],
            [
                5.043474082005342e-07,
                1.7603434231833873e-06,
                9.422448185510695e-07,
                1.4449805540740185e-07,
                2.382369667929001e-07,
                9.422443692555439e-07,
                5.715005832886879e-07,
                3.927862470899887e-07,
                3.466325384678894e-07,
                8.315284241650899e-07
            ],
            [
                3.059021175261338e-07,
                9.931189774187203e-08,
                1.3709576971463352e-06,
                1.8553910183607374e-07,
                2.1024331597262577e-07,
                1.275190884913241e-07,
                7.734418542875216e-08,
                9.422443692555439e-07,
                2.3823685318968256e-07,
                3.927862470899887e-07
            ],
            [
                6.475950298011458e-07,
                1.0677029973158649e-06,
                NaN,
                1.0677027427600627e-06,
                1.0677032518814388e-06,
                3.288749849498565e-06,
                1.3709570434122812e-06,
                3.4663262110803996e-07,
                1.760343213335281e-06,
                8.315282259138311e-07
            ],
            [
                1.6373770576776313e-07,
                4.785095065232451e-06,
                5.04347528446051e-07,
                1.7603432133296774e-06,
                2.902312331170226e-06,
                3.4663278639892215e-07,
                1.5534975693979422e-06,
                2.2603240284371276e-06,
                1.5534983101602148e-06,
                5.715002426486762e-07
            ],
            [
                3.288749457469787e-06,
                2.902312677137316e-06,
                3.0590215399183813e-07,
                3.2887482813149375e-06,
                4.4508494582405734e-07,
                1.1478769494250387e-05,
                4.450848927637999e-07,
                1.2098661162023305e-06,
                2.902312677137316e-06,
                2.2603234895289998e-06
            ],
            [
                5.422220262599396e-06,
                5.043475885674441e-07,
                2.260325106237323e-06,
                2.260325106237323e-06,
                NaN,
                2.260323758987159e-06,
                8.315277302841894e-07,
                1.0677027427600627e-06,
                1.2098653950692178e-06,
                9.422442569315887e-07
            ],
            [
                3.726637951367137e-06,
                4.785095065232451e-06,
                0.9999942280779266,
                0.9999969105062945,
                4.222833444590791e-06,
                1.8925141473978602e-05,
                0.9999988634364271,
                1.9947301970972664e-06,
                7.889263526345123e-06,
                0.9999970976880216
            ],
            [
                1.4449798650551755e-07,
                3.224187402001668e-08,
                6.475949526020042e-07,
                3.059022998576899e-07,
                2.3823690999290963e-07,
                4.1399365603508136e-08,
                2.6995771309523475e-07,
                2.8453360847779477e-08,
                3.466325384661554e-07,
                1.6373770576776313e-07
            ],
            [
                2.1024331597152624e-07,
                1.2098652508424818e-06,
                NaN,
                5.043476486924565e-07,
                6.962255419931625e-06,
                1.994729721518893e-06,
                2.102434412875379e-07,
                5.715005832886879e-07,
                1.4449803818215767e-07,
                1.6373768624837685e-07
            ],
            [
                0.9999970976866386,
                0.9999988634357494,
                0.9999978766207808,
                0.9999945777784589,
                0.9999987901338862,
                3.120192625482384e-05,
                1.1478764021029928e-05,
                0.9999986290429581,
                0.9999974387165713,
                8.315280276607289e-07
            ],
            [
                9.931195693628605e-08,
                1.8553919030858602e-07,
                2.382368815916736e-07,
                1.855391681898159e-07,
                3.927862939113312e-07,
                4.450852111148132e-07,
                7.734424996967756e-08,
                1.855391681898159e-07,
                3.466327450765785e-07,
                2.1024329090867228e-07
            ],
            [
                1.4449805540740185e-07,
                1.4449796927932878e-07,
                0.9999904837449258,
                1.1253512180925583e-07,
                8.764247451307293e-08,
                7.73441946488886e-08,
                6.825598028364134e-08,
                1.855391681906175e-07,
                1.855391681906175e-07,
                3.9278610661902853e-07
            ],
            [
                5.715005151606823e-07,
                3.059022269250683e-07,
                3.466326624336003e-07,
                9.931193325852072e-08,
                2.1024339116010604e-07,
                6.825606165129312e-08,
                4.450848927650143e-07,
                3.059023727894942e-07,
                3.05902336324494e-07,
                1.855391681898159e-07
            ],
            [
                3.927860597945825e-07,
                6.475945666051092e-07,
                8.315281267861397e-07,
                0.9999969105048188,
                2.1444950971601277e-05,
                1.3709573702822306e-06,
                1.994729008145876e-06,
                1.3709567165579959e-06,
                7.338212429582604e-07,
                3.288748281329893e-06
            ],
            [
                9.422449308774482e-07,
                3.927863407379485e-07,
                2.699577774589574e-07,
                5.043475885696228e-07,
                1.275190580890061e-07,
                1.855391681906175e-07,
                2.3823688159291947e-07,
                4.4508526417298334e-07,
                1.444979692800516e-07,
                1.2098659719788098e-06
            ],
            [
                9.931195693628605e-08,
                3.0590219045914655e-07,
                2.3823690999323465e-07,
                8.31528325040778e-07,
                1.994729483729522e-06,
                9.422445939054222e-07,
                8.315279285370317e-07,
                2.699578096403948e-07,
                6.47594952603035e-07,
                6.475950298021765e-07
            ],
            [
                3.059021175261338e-07,
                1.0677033791612137e-06,
                1.994729008145876e-06,
                2.561281600086738e-06,
                3.726639284144195e-06,
                3.726639284144195e-06,
                2.6995784182140636e-07,
                1.855391681906175e-07,
                2.3823682479292225e-07,
                9.422442569315887e-07
            ],
            [
                6.9622587396067566e-06,
                7.889261645269683e-06,
                4.785094494783494e-06,
                NaN,
                8.939697369785323e-06,
                2.430023783734196e-05,
                3.120190765625026e-05,
                4.222834954778007e-06,
                2.1444943301674863e-05,
                1.9947299592824403e-06
            ],
            [
                0.9999974387168767,
                3.05902336324494e-07,
                0.9999982396574179,
                0.9999991684716755,
                0.9999994284997576,
                0.9999994631251884,
                0.9999996940977732,
                0.9999994284996214,
                0.9999993106390372,
                0.9999994956524115
            ],
            [
                1.0677032518785256e-06,
                2.699578740032504e-07,
                1.209866260432471e-06,
                2.6995774527718623e-07,
                1.9947292459347367e-06,
                5.04347468323289e-07,
                3.2887506336235617e-06,
                1.1478772231232203e-05,
                3.9278605979534166e-07,
                3.4663266243308805e-07
            ],
            [
                3.927863875616689e-07,
                2.1024329090929374e-07,
                1.6373776432509826e-07,
                5.715002426475718e-07,
                4.450848927658745e-07,
                9.422450432014836e-07,
                5.043472278322555e-07,
                9.931186222523604e-08,
                2.102434162245973e-07,
                7.734415776836702e-08
            ],
            [
                3.9278605979534166e-07,
                6.475947210046347e-07,
                2.382369951932796e-07,
                9.931202796993203e-08,
                4.785095065232451e-06,
                1.6373774480605869e-07,
                1.4449807263312446e-07,
                1.0677029973219343e-06,
                1.4449807263312446e-07,
                2.1024334103581732e-07
            ],
            [
                6.825598028392069e-08,
                1.1253517547010071e-07,
                8.764249540862797e-08,
                7.338208055680009e-07,
                8.764246406483893e-08,
                1.6373762769138607e-07,
                1.1253513522447425e-07,
                1.1253520230052635e-07,
                1.275190124842887e-07,
                1.1253518888464745e-07
            ],
            [
                1.7603425837903113e-06,
                2.2603242978871282e-06,
                2.9023112932177327e-06,
                1.0677033791583005e-06,
                1.209865539295696e-06,
                1.209865539295696e-06,
                1.2098656835224664e-06,
                0.9999938558268809,
                4.4508510499849186e-07,
                1.0677029973219343e-06
            ],
            [
                NaN,
                5.144222593244026e-05,
                5.715005832886879e-07,
                1.994729483723626e-06,
                3.288747889284851e-06,
                9.422442569315887e-07,
                3.288749457469787e-06,
                1.9947304348862686e-06,
                7.338210680021253e-07,
                2.2603240284371276e-06
            ],
            [
                1.5534971990126997e-06,
                7.338207180898968e-07,
                NaN,
                2.2603253756956754e-06,
                8.764244316973974e-08,
                4.785093353940187e-06,
                2.10243290909724e-07,
                3.4663266243308805e-07,
                5.715006514176113e-07,
                3.466325797896173e-07
            ],
            [
                3.059022998576899e-07,
                3.466327037548308e-07,
                8.764242227418718e-08,
                1.994730672668496e-06,
                8.315277302841894e-07,
                1.444979692800516e-07,
                3.466325384661554e-07,
                9.422450431989127e-07,
                1.0677033791612137e-06,
                5.715003107738556e-07
            ],
            [
                NaN,
                2.699577774589574e-07,
                4.450850519409479e-07,
                NaN,
                3.466325797900508e-07,
                9.422443692574719e-07,
                7.338212429594283e-07,
                3.927860597945825e-07,
                2.699578740032504e-07,
                NaN
            ],
            [
                9.422445939032799e-07,
                3.53562549305363e-05,
                8.939693107190907e-06,
                1.0677028700422047e-06,
                1.7603438428800754e-06,
                0.999978555041456,
                3.726637951387472e-06,
                3.9278634073732336e-07,
                4.4508510499849186e-07,
                0.9999925887201465
            ],
            [
                3.4663266243111764e-07,
                4.785095635624897e-06,
                1.1253513522447425e-07,
                4.222834954778007e-06,
                3.7266406168827523e-06,
                6.9622587397397306e-06,
                5.043474081993875e-07,
                9.931199245228978e-08,
                3.927862470899887e-07,
                2.699577774585891e-07
            ],
            [
                1.5534984953510149e-06,
                0.9999885212319221,
                2.9023116391978967e-06,
                0.9999970976876744,
                0.999999428499349,
                0.9999970976873286,
                0.9999964991447563,
                2.3823688159291947e-07,
                0.9999861539971435,
                3.7266406168827523e-06
            ],
            [
                2.699577774585891e-07,
                2.2603253756956754e-06,
                8.315280276626197e-07,
                3.726638395611981e-06,
                9.422449308774482e-07,
                6.475951069855719e-07,
                1.0677026154806063e-06,
                3.927862002654366e-07,
                1.5534984953453635e-06,
                2.9023130231176453e-06
            ],
            [
                7.73442776300517e-08,
                8.7642516304188e-08,
                3.466326211113502e-07,
                7.734424996967756e-08,
                1.8553910183607374e-07,
                2.102433660979124e-07,
                5.715007195447234e-07,
                3.288748673376478e-06,
                5.043472879540142e-07,
                0.9999898700126507
            ],
            [
                2.2603251061458426e-06,
                2.2603242978871282e-06,
                1.2098652508424818e-06,
                9.422445939032799e-07,
                1.6701419853852583e-05,
                1.0129993395336818e-05,
                7.338207180838067e-07,
                1.994729721482609e-06,
                2.9023116391675407e-06,
                1.5534984953453635e-06
            ],
            [
                2.9023133690821773e-06,
                2.102434162245973e-07,
                1.7603434231705793e-06,
                4.222834451292594e-06,
                5.422220262636381e-06,
                1.2751905808881762e-07,
                1.5534984953453635e-06,
                2.5612812947508257e-06,
                1.994729721482609e-06,
                NaN
            ],
            [
                1.760343633031919e-06,
                1.5534971990126997e-06,
                6.475947210046347e-07,
                4.2228324377740105e-06,
                1.5534975693933505e-06,
                4.222835458148261e-06,
                2.2603240284371276e-06,
                3.726639728370556e-06,
                1.7603434231777837e-06,
                3.7266406168624155e-06
            ],
            [
                1.2098659719788098e-06,
                8.315281267882195e-07,
                5.4222183235249605e-06,
                4.22283545819819e-06,
                6.144176799334096e-06,
                1.0677032518785256e-06,
                3.7266406168827523e-06,
                1.9947301970972664e-06,
                1.2098659719788098e-06,
                1.3709572068522336e-06
            ],
            [
                1.6373766672821107e-07,
                2.1024334103352274e-07,
                3.927862002641863e-07,
                3.4663249714325014e-07,
                4.450849988780466e-07,
                5.715003107738556e-07,
                3.927862939126708e-07,
                1.855391681883394e-07,
                3.4663266243111764e-07,
                2.1024334103352274e-07
            ],
            [
                2.260323758987159e-06,
                8.315281267882195e-07,
                5.715004470326849e-07,
                2.1024339116168358e-07,
                2.6995790618469934e-07,
                2.902312677150514e-06,
                NaN,
                3.466327037553825e-07,
                4.450851049991497e-07,
                1.8553905759969634e-07
            ],
            [
                4.450852641737424e-07,
                9.422449308774482e-07,
                1.4449807263312446e-07,
                2.69957906184239e-07,
                1.012999218776902e-05,
                4.450852641737424e-07,
                2.6995790618350237e-07,
                1.5534973842076057e-06,
                4.222834954801051e-06,
                3.466327863983311e-07
            ],
            [
                1.6373776432509826e-07,
                9.931193325852072e-08,
                0.9999996940978826,
                5.04347468323289e-07,
                3.4663266243308805e-07,
                0.999999218851763,
                1.6373772528704005e-07,
                9.931189774187203e-08,
                4.450851049991497e-07,
                3.120191509592808e-05
            ],
            [
                1.1253506814842375e-07,
                4.4508494582314646e-07,
                6.023571320819244e-08,
                6.023571320847322e-08,
                1.1253520230052635e-07,
                3.927862470899887e-07,
                3.288749065406658e-06,
                1.8553907971855875e-07,
                1.2751904288710323e-07,
                6.475947982037486e-07
            ],
            [
                8.315277302857965e-07,
                NaN,
                3.4663274507713016e-07,
                NaN,
                8.315280276626197e-07,
                2.260325106237323e-06,
                5.715006514176113e-07,
                4.4508510499849186e-07,
                6.962259569750576e-06,
                5.043472278322555e-07
            ],
            [
                6.962257909842961e-06,
                1.2098652508424818e-06,
                3.4663249714612693e-07,
                NaN,
                1.0129994602895546e-05,
                5.04347468323289e-07,
                3.46632497145457e-07,
                7.338211554801876e-07,
                1.760343213335281e-06,
                8.315277302841894e-07
            ],
            [
                7.734414854823498e-08,
                2.699577774585891e-07,
                8.315284241650899e-07,
                1.4449805540740185e-07,
                5.715006514176113e-07,
                3.0590237279032884e-07,
                3.0590237279032884e-07,
                1.4449805540740185e-07,
                2.1024334103505245e-07,
                1.1253526937697666e-07
            ],
            [
                5.715003788993679e-07,
                3.059023727894942e-07,
                1.5534984953510149e-06,
                6.475946438055299e-07,
                1.6373768624837685e-07,
                8.315277302841894e-07,
                2.3823685319244518e-07,
                2.3823690999290963e-07,
                1.4449805540740185e-07,
                1.275190884913241e-07
            ]
        ]
    },
    {
        "q_id": "10139_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            38,
            97
        ],
        "rewards": [
            [
                0.9999999123575151,
                0.9999997761971582,
                9.422450432014836e-07,
                0.9999996072139404,
                0.999998863435748,
                0.9999996940976272,
                1.2098658277489788e-06,
                0.9999998642566381,
                0.9999998942829098,
                0.999999887464932
            ],
            [
                0.9999995549149484,
                0.999999266179108,
                0.9999977396749,
                0.9999992661790201,
                0.999999712631447,
                0.9999985406232603,
                0.9999957771660646,
                0.9999981261239487,
                0.9999992661791077,
                0.9999993916410368
            ],
            [
                1.553497384196656e-06,
                7.338208930460318e-07,
                7.338208055664991e-07,
                1.0677032518785256e-06,
                3.059022269250683e-07,
                8.315282259051341e-07,
                3.2887478892683997e-06,
                8.315280276580819e-07,
                1.5534981249697903e-06,
                5.71500719545698e-07
            ],
            [
                1.275191036933194e-07,
                5.4222183235249605e-06,
                2.102434412875379e-07,
                9.931187406410953e-08,
                1.444979692800516e-07,
                7.734418542875216e-08,
                9.931193325852072e-08,
                2.561281294760143e-06,
                3.4663249714612693e-07,
                1.8553919030858602e-07
            ],
            [
                0.9999998724809875,
                0.9999995262094423,
                0.9999994956524118,
                0.9999990577555194,
                0.9999993524050479,
                0.9999998802069587,
                0.9999999067050387,
                0.9999994284997579,
                0.9999998942828973,
                0.9999998362623529
            ],
            [
                0.9999982396565792,
                0.9999994631248046,
                0.9999993106388732,
                0.9999980052702809,
                0.9999982396561625,
                0.999998790134463,
                0.9999992188512979,
                0.9999990577549578,
                0.9999987901337413,
                0.9999993916408186
            ],
            [
                0.9999997761971049,
                0.999999880206916,
                0.9999998461826222,
                5.043472879504592e-07,
                0.9999997897567342,
                0.999999825702059,
                0.9999995818811275,
                0.9999997300422226,
                0.9999998144608541,
                0.9999995262092729
            ],
            [
                0.9999998144609424,
                0.9999994956527123,
                0.9999994284992808,
                0.9999982396567891,
                0.9999997761970782,
                1.5534975693979422e-06,
                0.9999984465024335,
                0.9999998144608098,
                0.9999990577555192,
                0.9999993916408185
            ],
            [
                0.999998446502433,
                0.999999114842965,
                0.9999989969856745,
                0.9999988634365621,
                0.9999993916408912,
                0.9999993916411092,
                0.99999773967463,
                0.9999994631247408,
                0.9999994956523518,
                0.9999994956525324
            ],
            [
                1.9947304348862686e-06,
                0.9999977396762465,
                0.9999982396563699,
                0.9999984465022471,
                0.9999990577555194,
                0.9999989969854345,
                0.9999995549147359,
                0.9999984465020632,
                0.9999995549148953,
                0.9999978766217928
            ],
            [
                0.9999998802069302,
                0.9999998642566381,
                0.9999998802069731,
                0.9999998942829981,
                0.9999993916410365,
                0.9999997761971049,
                0.9999999067049943,
                0.9999998942829225,
                0.9999998362623139,
                0.9999995262092166
            ],
            [
                0.9999994284994169,
                0.9999983463110067,
                0.9999994284996215,
                0.9999990577551823,
                0.9999974387184052,
                0.9999993106389553,
                0.9999993106387088,
                0.9999993916411812,
                0.9999995549147362,
                0.999999631011372
            ],
            [
                0.9999999067050943,
                0.9999993106389552,
                0.9999999226557685,
                1.0,
                0.999998996986272,
                0.9999998257020591,
                0.9999999273418789,
                0.9999998555020307,
                0.999999495652532,
                0.9999999530883508
            ],
            [
                0.9999998724809877,
                0.9999998874647574,
                0.9999996940976273,
                0.9999995549147892,
                0.9999998802068873,
                0.9999998461826223,
                0.9999998461826038,
                0.9999999226557778,
                0.9999998362623137,
                0.9999994956527726
            ],
            [
                1.0677029973192638e-06,
                1.8553914607128047e-07,
                5.043472879540142e-07,
                6.475950297971703e-07,
                5.043473480730849e-07,
                9.422445939002803e-07,
                5.043472879540142e-07,
                1.0677024881980089e-06,
                9.422443692555439e-07,
                3.059023727894942e-07
            ],
            [
                0.9999993106387907,
                0.9999982396559496,
                0.999998346309825,
                0.9999984465020624,
                0.9999983463096276,
                0.9999987121041715,
                0.008577486744252828,
                0.9999992661789326,
                0.9999997617630333,
                0.9999985406236068
            ],
            [
                0.9999998802069017,
                0.9999997761970515,
                0.999998996986271,
                0.9999986290421402,
                0.9999996743687423,
                3.9278610661902853e-07,
                0.9999997761970515,
                0.9999998461826956,
                0.999999802494633,
                0.9999998555019619
            ],
            [
                0.9999998555019962,
                0.9999992188519492,
                4.691162683297406e-08,
                0.9999993106387907,
                0.9999994956525919,
                6.144173137170873e-06,
                0.9999999358793868,
                0.9999998257021837,
                0.9999992661789323,
                6.962255419931625e-06
            ],
            [
                0.9999987121047851,
                0.9999995549147891,
                0.9999993916409639,
                0.9999992188518562,
                0.9999993106391194,
                0.9999997126313441,
                1.2098656835224664e-06,
                0.999999391640746,
                0.9999991148427539,
                0.999999526209499
            ],
            [
                0.9999997126314469,
                0.9999997761972117,
                0.9999994956527728,
                0.9999984465028028,
                0.9999985406237806,
                0.9999993916409636,
                0.99999921885167,
                0.9999996072136595,
                0.9999996072137065,
                0.9999994284997582
            ],
            [
                0.9999990577551825,
                0.9999996743686259,
                0.9999995818811775,
                0.9999994956527727,
                0.9999994956526526,
                0.9999992661790201,
                0.9999996072137064,
                0.99999967436882,
                0.9999984465020635,
                0.9999996310113722
            ],
            [
                1.4449807263312446e-07,
                1.4449800373065699e-07,
                1.2751901248454963e-07,
                2.3823682479181176e-07,
                9.931187406368048e-08,
                1.6373766672973748e-07,
                2.2603253756874524e-06,
                1.6373762769138607e-07,
                1.760343633031919e-06,
                4.4508510499849186e-07
            ],
            [
                0.9999999123574629,
                1.0,
                0.9999999397642079,
                0.9999999317439058,
                1.0,
                0.999999958600659,
                0.9999997300422226,
                0.9999999226557224,
                0.9999999468421124,
                0.9999999067050164
            ],
            [
                2.1024331597262577e-07,
                1.1253512180925583e-07,
                1.6373764721072816e-07,
                1.6373762769138607e-07,
                1.6373774480605869e-07,
                1.855391681906175e-07,
                1.4449798650551755e-07,
                1.2751902768612997e-07,
                1.6373764721039308e-07,
                5.715006514176113e-07
            ],
            [
                0.9999998802069874,
                0.9999998555019964,
                0.9999999067050165,
                0.9999999226557776,
                1.0,
                0.9999999067051055,
                0.9999997126314126,
                0.999999943413811,
                0.9999999226557131,
                0.9999999434137975
            ],
            [
                0.9999994284994171,
                0.9999997897565839,
                0.9999993106387907,
                0.9999974387174865,
                0.9999993916406735,
                1.5534973842076057e-06,
                0.9999994956524119,
                0.9999992661787579,
                0.9999991684715765,
                0.9999991684722704
            ],
            [
                0.9999998942829224,
                0.9999999586006048,
                0.9999999397642222,
                0.9999999006880431,
                1.0,
                0.9999999530883508,
                0.9999999586006098,
                0.9999999559306101,
                0.9999999397643011,
                1.0
            ],
            [
                0.9999994631251886,
                0.9999985406234336,
                0.999998446501692,
                0.9999982396569994,
                0.9999992188516704,
                0.9999987121043257,
                0.9999982396574195,
                0.9999987901337413,
                0.9999992188518567,
                0.9999986290431223
            ],
            [
                3.9278610661822475e-07,
                5.043475284430694e-07,
                5.715003788993679e-07,
                8.315282259117513e-07,
                1.6373774480535133e-07,
                1.8553910183607374e-07,
                2.3823685319244518e-07,
                2.6995771309523475e-07,
                3.927862470899887e-07,
                5.715002426475718e-07
            ],
            [
                0.9999995549150015,
                0.9999994631248685,
                0.9999993916407464,
                0.9999994956524718,
                0.9999996743688588,
                0.9999997463980731,
                0.9999995549149484,
                0.9999996310115482,
                0.9999982396569993,
                0.9999992188515769
            ],
            [
                2.1024339116010604e-07,
                1.8553919030858602e-07,
                1.444979692800516e-07,
                3.927862002641863e-07,
                8.7642516304188e-08,
                8.315283250371857e-07,
                9.931190958076104e-08,
                3.0590237279032884e-07,
                1.6373762769138607e-07,
                2.1024331597262577e-07
            ],
            [
                0.9999998642567353,
                0.9999998555019619,
                0.9999997300422871,
                0.9999996072137065,
                0.9999992661789326,
                0.9999994956527126,
                0.999999789756634,
                0.9999998642567028,
                0.9999998942829603,
                0.9999998362622943
            ],
            [
                0.9999995262094422,
                0.9999999586006245,
                1.0,
                0.9999999123575881,
                0.9999983463098234,
                1.0,
                0.999999958600659,
                0.9999999500627916,
                0.9999997463982241,
                1.0
            ],
            [
                0.9999996533672965,
                0.9999998724808964,
                0.9999997617629766,
                0.9999998461827322,
                0.9999998362622944,
                0.9999998461826405,
                0.9999998555019963,
                0.9999998461826956,
                0.999999746398073,
                0.9999993916410361
            ],
            [
                0.9999981261246181,
                0.9999981261237257,
                0.9999986290423044,
                0.9999987121041715,
                0.9999989969862714,
                0.9999989322972588,
                0.9999975938973767,
                0.9999992188513908,
                0.999999581881377,
                0.9999982396561601
            ],
            [
                0.9999988634366967,
                0.9999998024947273,
                0.9999987901337404,
                0.9999998461826588,
                0.9999998802069731,
                0.9999998024946802,
                0.9999992661787575,
                0.9999995549147891,
                0.99999926617867,
                0.999999495652592
            ],
            [
                0.9999997761970248,
                0.9999997463981938,
                0.9999987121046315,
                0.9999990577549572,
                0.9999980052705174,
                0.9999997897566592,
                0.999999846182714,
                0.9999998362622943,
                0.9999997761970248,
                0.9999967112505449
            ],
            [
                1.0,
                0.9999999317440116,
                0.9999996072139403,
                0.9999998802069302,
                0.9999996743686645,
                0.9999999006880312,
                0.9999992188517628,
                0.9999999559305839,
                8.764241182641775e-08,
                0.9999999226557131
            ],
            [
                0.999999776197185,
                0.9999993106387906,
                0.999999526209612,
                0.9999990577549576,
                0.9999998461826588,
                0.9999986290423053,
                0.9999997761970516,
                0.9999992188517632,
                0.9999994956525322,
                0.9999991684715764
            ],
            [
                0.9999997126315155,
                0.999999746398194,
                0.9999998024946801,
                0.9999998362622943,
                0.9999997463980429,
                0.9999994956527727,
                0.9999998257021007,
                0.9999994284994171,
                0.9999997126313099,
                0.9999997126315496
            ],
            [
                0.9999983463102177,
                0.999999917667475,
                0.9999998555020309,
                0.9999999226558054,
                5.043476486924565e-07,
                0.99999994341373,
                1.3709568799919866e-06,
                0.999999953088334,
                0.9999998874648648,
                0.9999998642566704
            ],
            [
                2.3823699519143784e-07,
                2.382370235933104e-07,
                3.05902117523595e-07,
                3.059022269250683e-07,
                2.6995790618252024e-07,
                1.4449800373065699e-07,
                0.999998126123724,
                4.4508526417298334e-07,
                1.8553914607128047e-07,
                2.3823682479181176e-07
            ],
            [
                0.9999988634360194,
                0.999999168471874,
                0.9999986290431222,
                0.9999983463102197,
                0.9999991684721717,
                0.9999992661786702,
                0.9999978766217941,
                5.8291293348093234e-05,
                0.9999970976880211,
                0.9999981261241719
            ],
            [
                0.9999994631248683,
                0.9999998461826589,
                0.9999987121044782,
                0.9999995818810777,
                0.9999997761971049,
                0.9999989322972581,
                0.999998446501692,
                0.9999993106388733,
                0.9999997617630618,
                0.9999981261252892
            ],
            [
                0.9999997761971049,
                0.9999998024946566,
                0.9999997126315496,
                0.9999995818810777,
                0.9999992188517632,
                0.9999997897567092,
                0.9999998461826406,
                0.9999998024947038,
                0.9999997761970515,
                0.999999526209273
            ],
            [
                0.9999998362623139,
                0.9999995549151076,
                0.9999993524052023,
                0.9999996743688199,
                1.0,
                0.9999994956524119,
                0.9999989322970035,
                0.9999994631248685,
                0.9999991148428592,
                0.9999991148427539
            ],
            [
                0.9999999397642582,
                1.4449798650551755e-07,
                9.931190958076104e-08,
                0.9999999123575255,
                9.931199245292204e-08,
                0.9999981261246176,
                0.9999999176675731,
                0.9999999006880431,
                0.9999999358793562,
                0.9999994956524719
            ],
            [
                0.9999898700066344,
                4.4508515805735777e-07,
                4.785093353940187e-06,
                1.2098656835224664e-06,
                2.382370235933104e-07,
                6.1441767993788005e-06,
                1.3709567165617364e-06,
                0.0001398220908991855,
                3.4663278639892215e-07,
                3.9278605979534166e-07
            ],
            [
                0.9999995818812772,
                0.9999993916406739,
                0.9999994631251249,
                0.9999993916406738,
                0.9999993524052025,
                0.9999996533672965,
                0.9999997761971852,
                0.9999995818811775,
                0.9999997463981939,
                0.9999996940976276
            ],
            [
                0.9999999715466289,
                0.9999999067050276,
                0.9999999273418443,
                0.9999998257020591,
                0.9999999434137975,
                0.9999995549147891,
                0.9999997617630618,
                0.9999997897566841,
                0.9999999397642653,
                0.9999993524052021
            ],
            [
                2.561281294760143e-06,
                1.3709567165617364e-06,
                5.043476486924565e-07,
                2.102434162245973e-07,
                NaN,
                3.4663278639892215e-07,
                3.059022998581767e-07,
                2.3823685319244518e-07,
                4.2228339479858295e-06,
                1.5534984953552536e-06
            ],
            [
                0.9999998724809268,
                0.9999996072139403,
                0.9999997761971849,
                0.9999996743688199,
                0.9999993106388728,
                0.9999994631247403,
                0.9999998555019447,
                0.9999997761971317,
                0.9999996743688975,
                0.9999993106391194
            ],
            [
                0.9999992188513913,
                0.9999992188515772,
                0.9999996310115921,
                0.9999987121050936,
                0.9999970976876744,
                0.9999978766223,
                0.9999982396574183,
                0.9999994631248047,
                0.9999970976876734,
                0.9999975938985253
            ],
            [
                0.9999996940977002,
                0.9999999358793639,
                0.9999997300422226,
                0.999999631011416,
                0.999999789756634,
                0.999999310639037,
                0.9999999067051276,
                0.999999631011328,
                0.9999997126313098,
                0.9999996940976638
            ],
            [
                0.9999949062944037,
                0.9999991684718738,
                0.9999989969856733,
                0.9999995549150015,
                0.9999992661788449,
                0.9999993524048942,
                0.9999987121046323,
                2.260324028427877e-06,
                0.9999982396572084,
                0.9999983463108096
            ],
            [
                1.1253524254650944e-07,
                3.0590219045914655e-07,
                1.444979692800516e-07,
                7.734415776836702e-08,
                9.422445938917108e-07,
                6.023578501513224e-08,
                1.637376862489725e-07,
                9.931185038635267e-08,
                1.275190124846946e-07,
                6.023577065381482e-08
            ],
            [
                0.9999995818813768,
                0.9999998942829981,
                0.9999998802069302,
                0.999999864256719,
                0.9999996533673376,
                0.9999998802068875,
                1.275190428875671e-07,
                0.9999938558254184,
                0.9999998257021422,
                0.9999998555019275
            ],
            [
                0.9999996072138937,
                0.9999993916411088,
                0.9999995549147364,
                0.9999994284994853,
                0.9999970976873273,
                0.9999994956527726,
                0.9999994956525322,
                0.999999554914789,
                0.999998629042958,
                0.9999992188519495
            ],
            [
                0.9999996533672137,
                0.9999995262093857,
                0.9999998024946802,
                0.9999998802069731,
                0.9999990577554069,
                0.9999998874648246,
                0.9999998555019446,
                0.999998126124395,
                0.9999997897566841,
                0.9999998802069874
            ],
            [
                1.4449795205429202e-07,
                1.6373768624837685e-07,
                1.4449807263287805e-07,
                9.931189774140912e-08,
                1.6373776432509826e-07,
                1.1253526937656726e-07,
                1.6373774480479287e-07,
                7.734414854823498e-08,
                1.4449800373065699e-07,
                3.653482951291499e-08
            ],
            [
                0.9999993106391192,
                0.9999994956527725,
                0.9999998802069587,
                0.9999998461826771,
                0.9999998724808964,
                0.9999997126315497,
                0.9999992661791074,
                0.9999998724809572,
                0.9999998362622943,
                0.9999998555019447
            ],
            [
                0.9999991684717746,
                0.9999996310114161,
                0.9999996310114603,
                0.9999992661787579,
                0.9999991148429649,
                0.9999987901341739,
                0.9999995262095555,
                0.9999996310115041,
                0.9999987901341737,
                0.9999991148432815
            ],
            [
                0.9999995262095551,
                1.0,
                0.999999607213753,
                0.9999999358794173,
                0.999999391640746,
                0.9999999468421249,
                1.0,
                0.9999998942830737,
                0.9999998724810027,
                0.9999996310113719
            ],
            [
                0.999999554914736,
                0.9999991148431759,
                0.9999993106387084,
                0.9999997126313099,
                0.9999991684721716,
                0.9999985406243027,
                0.999999607213847,
                0.9999969105066624,
                0.9999984465020625,
                0.9999981261246191
            ],
            [
                1.1253516205489029e-07,
                6.962258739796719e-06,
                0.9999998724808963,
                0.9999996940978461,
                2.10243290909724e-07,
                0.999999802494586,
                0.9999996533673376,
                1.1253512180925583e-07,
                2.3823696679327928e-07,
                0.9999996072137999
            ],
            [
                0.9999998144608098,
                0.999999581881327,
                0.999999894282935,
                0.9999998144609203,
                0.9999998024946095,
                0.9999997126314469,
                0.999999789756634,
                0.9999995549147893,
                0.9999996940976272,
                0.9999997617630901
            ],
            [
                0.9999993524052794,
                0.9999997463981637,
                0.999999428499758,
                0.999999168471775,
                0.9999994284994854,
                0.9999990577557439,
                0.9999993916408914,
                0.9999989322972583,
                0.9999994284995534,
                0.9999996940978826
            ],
            [
                0.9999987121041711,
                0.9999972735287596,
                0.9999987121050936,
                0.9999994631251884,
                0.9999992661791952,
                0.9999994956523517,
                9.422448185534261e-07,
                0.9999995549150545,
                0.9999993524049707,
                0.9999993106390372
            ],
            [
                0.9999997761971849,
                0.9999998555019619,
                0.9999994631249323,
                0.9999999067049942,
                0.999999894283061,
                0.999999864256719,
                0.9999998724808964,
                0.9999998257021007,
                0.9999996072136126,
                0.9999998802069445
            ],
            [
                3.1201907657271834e-05,
                6.962257909722651e-06,
                5.715003788993679e-07,
                1.012999218776902e-05,
                4.785093353940187e-06,
                4.785095635655362e-06,
                2.902312677137316e-06,
                5.043472879504592e-07,
                0.9999988634357484,
                3.726639284103523e-06
            ],
            [
                2.6995784182140636e-07,
                5.043472879540142e-07,
                0.9999994631250607,
                0.9999994631249965,
                0.9999995818813271,
                0.999999057755744,
                0.999999168471775,
                0.9999991148428592,
                0.9999997617631754,
                0.9999998144608983
            ],
            [
                4.0063682641226247e-05,
                5.715006514176113e-07,
                1.067703124601679e-06,
                1.4449802095666915e-07,
                0.9999983463106122,
                1.855390576008354e-07,
                3.9278629391427843e-07,
                0.9999998555019791,
                0.9999997463981032,
                0.9999993524049705
            ],
            [
                2.9023119851899796e-06,
                0.999999761763147,
                0.9999996940977368,
                0.9999996940978826,
                0.9999997463981637,
                0.9999998802068873,
                0.9999993916407462,
                0.9999998024946095,
                0.9999995818814267,
                0.9999993524053566
            ],
            [
                0.9999987901338864,
                0.9999972735307131,
                0.9999985406243033,
                0.9999989322972599,
                0.9999994631248044,
                0.999998446501692,
                0.999998126123951,
                0.9999992661786706,
                0.9999987901343188,
                0.9999955048179044
            ],
            [
                0.999999761763147,
                0.9999994956527124,
                0.999999631011328,
                0.9999981261243951,
                0.9999993916406736,
                0.9999997463981637,
                0.9999994956526523,
                0.9999993524052022,
                0.9999998942828973,
                0.999999653367255
            ],
            [
                3.0590237279032884e-07,
                3.9278634073732336e-07,
                3.466325797888292e-07,
                2.3823688159291947e-07,
                6.475950298011458e-07,
                2.3823682479292225e-07,
                6.475947210031623e-07,
                1.637377057673536e-07,
                2.561282210740037e-06,
                8.764242227418718e-08
            ],
            [
                2.3823693839290317e-07,
                4.785094494783494e-06,
                5.715006514074756e-07,
                2.6995771309523475e-07,
                3.927862002663297e-07,
                6.475949526020042e-07,
                5.829128639666634e-05,
                3.7266397283908927e-06,
                5.04347468323289e-07,
                2.6995771309523475e-07
            ],
            [
                0.9999994284994169,
                0.9999995549149483,
                0.9999990577550695,
                0.999999802494586,
                0.9999997761970515,
                0.9999994956525321,
                0.9999998555019275,
                0.9999998024945624,
                0.999999712631481,
                0.999999746398073
            ],
            [
                0.9999996743686644,
                1.6373766672888118e-07,
                1.0129993395336818e-05,
                0.9999999317439221,
                5.315781803390236e-08,
                2.6995768091310296e-07,
                3.927863407379485e-07,
                2.69957906184239e-07,
                1.1253520230052635e-07,
                2.902312331170226e-06
            ],
            [
                0.9999996310115039,
                0.9999998461827322,
                0.9999989322968762,
                0.9999995549149483,
                0.9999998362622552,
                0.9999988634361544,
                0.9999992188518559,
                3.927863875616689e-07,
                0.9999994631248684,
                0.9999996310114599
            ],
            [
                0.9999990577550705,
                0.9999981261237254,
                0.9999984465020635,
                0.9999969105055591,
                0.9999996072136129,
                0.9999983463108103,
                0.9999988634362907,
                0.9999994284996218,
                0.9999996310115922,
                0.9999995818813769
            ],
            [
                0.9999991684722705,
                0.9999998555019275,
                0.9999989322975129,
                0.9999998024945861,
                0.999999814460832,
                9.422445939054222e-07,
                0.9999994284996897,
                0.999998712104939,
                0.999999631011372,
                0.9999990577557447
            ],
            [
                0.9999999006881142,
                0.9999999586006245,
                0.9999999123575882,
                0.9999999317439627,
                0.9999999586006295,
                0.9999999397643156,
                0.999999554914842,
                1.0,
                0.999999927341801,
                0.9999999273418443
            ],
            [
                0.9999987121049401,
                0.9999978766220484,
                0.9999991684719735,
                0.9999993916410365,
                0.9999949062956173,
                0.9999993916408917,
                0.9999990577552946,
                0.999999218851857,
                0.999997876621037,
                0.9999995262094428
            ],
            [
                0.9999995262093861,
                0.9999992661786702,
                2.5612819054133693e-06,
                0.9999991684719729,
                0.9999990577556316,
                0.9999987121046331,
                0.9999988634362903,
                0.9999989969859128,
                0.9999987901341738,
                0.9999993524051254
            ],
            [
                2.561282516066741e-06,
                7.338211554783522e-07,
                8.315278294114555e-07,
                5.043476486915964e-07,
                4.785096776468749e-06,
                5.422220909009474e-06,
                5.715003107755449e-07,
                1.892515049819277e-05,
                3.466326624322211e-07,
                2.9023112932177327e-06
            ],
            [
                1.855391681906175e-07,
                0.999999266179195,
                1.4449802095666915e-07,
                0.9999980052702796,
                7.338212429594283e-07,
                1.4449803818215767e-07,
                0.9999999176674553,
                0.9999999226557224,
                1.2098656835224664e-06,
                4.139941002027314e-08
            ],
            [
                0.9999993106390374,
                4.2228334445658276e-06,
                1.012998977264307e-05,
                0.9999986290426306,
                0.999999057754958,
                0.9999991148428592,
                0.9999992188518563,
                1.0129993395336818e-05,
                0.999999057755632,
                0.9999980052707562
            ],
            [
                3.466325797888292e-07,
                4.450852641737424e-07,
                1.2751905808881762e-07,
                2.3823693839290317e-07,
                1.2751904288739315e-07,
                1.2751908849167202e-07,
                5.043475885674441e-07,
                7.734418542875216e-08,
                1.6373770576776313e-07,
                2.1024336609843824e-07
            ],
            [
                1.3709567165530083e-06,
                0.9999999226557409,
                0.9999999468421503,
                0.9999996310115039,
                0.9999999317440197,
                0.9999999273417663,
                1.0,
                0.9999997897566592,
                0.999999631011592,
                0.9999999697115587
            ],
            [
                0.999999554914736,
                NaN,
                0.9999994631247404,
                0.9999993916409639,
                0.9999992661786705,
                0.9999969105066633,
                0.9999982396574175,
                0.9999986290427948,
                0.9999984465026178,
                0.9999995549150545
            ],
            [
                0.9999960330126793,
                0.9999962733620552,
                0.9999980052693295,
                0.9999977396762484,
                0.9999986290423057,
                0.9999989969861529,
                0.9999987121049401,
                0.9999989969861528,
                0.9999982396565793,
                0.9999992188514845
            ],
            [
                0.9999995262094987,
                0.9999993524052021,
                0.9999996940978098,
                0.9999996743686257,
                0.9999989322968762,
                0.9999997463981636,
                2.144495352533148e-05,
                0.9999993106386263,
                0.9999996940978098,
                0.999999730042094
            ],
            [
                0.9999998024947038,
                0.99999995308839,
                1.0,
                0.9999998362622747,
                0.9999999067050276,
                1.0,
                1.0,
                0.9999998024947273,
                0.9999991148432813,
                1.0
            ],
            [
                0.9999993916411088,
                0.9999998024946332,
                0.9999998257021837,
                0.999999746398073,
                0.999999631011416,
                0.9999991684718738,
                0.9999998362622747,
                0.9999993916408186,
                0.999999526209273,
                0.9999998362623529
            ],
            [
                0.9999990577551823,
                0.999999789756609,
                0.9999998257021631,
                0.9999997897567093,
                0.9999994284994174,
                0.999999526209273,
                0.9999997126314127,
                0.9999999123575674,
                0.9999997300422226,
                0.9999996743688976
            ],
            [
                0.9999996072138001,
                0.9999993106392017,
                0.9999998144609646,
                0.9999992188514837,
                0.9999989322967491,
                0.9999989322971308,
                0.9999987901340291,
                0.9999995549148423,
                0.9999995818813271,
                0.9999993524052027
            ],
            [
                0.9999995262094987,
                0.9999998461827139,
                0.9999982396567886,
                0.9999997897565588,
                0.9999997617631186,
                0.9999998362623335,
                0.9999999226558054,
                0.9999997126313783,
                0.9999997126313441,
                0.999999218851856
            ],
            [
                2.6995784182140636e-07,
                1.2751908849167202e-07,
                2.699577774585891e-07,
                2.102433660979124e-07,
                3.059022998581767e-07,
                1.444980209564556e-07,
                2.699577774585891e-07,
                1.4449798650551755e-07,
                1.1253520230052635e-07,
                2.699577774585891e-07
            ],
            [
                0.9999996072138936,
                0.9999869928700229,
                0.9999997300421262,
                0.999999802494633,
                0.9999992188516699,
                0.9999998874647441,
                0.999999495652592,
                0.9999994631251885,
                0.9999997126315496,
                0.9999997300421261
            ],
            [
                1.2098661162056318e-06,
                0.9999991684720719,
                0.9999997897567342,
                0.9999984465026173,
                0.9999989322967487,
                0.9999977396746261,
                0.9999996743688586,
                5.715007195447234e-07,
                0.9999930377421123,
                0.9999991684721711
            ],
            [
                1.637377643243723e-07,
                1.6373764721039308e-07,
                1.1253509497883659e-07,
                1.6373766672821107e-07,
                8.764249540862797e-08,
                5.043472879540142e-07,
                1.1253518888531272e-07,
                1.6373764721072816e-07,
                7.734421308914719e-08,
                0.9999832985761912
            ],
            [
                1.1478765389368729e-05,
                6.475947210031623e-07,
                3.726637951367137e-06,
                8.315277302841894e-07,
                1.5534971990126997e-06,
                1.5534977545886537e-06,
                2.5612828213690224e-06,
                1.0677024881980089e-06,
                5.043472879525233e-07,
                2.9023133690980155e-06
            ],
            [
                0.999999631011372,
                0.9999998555019792,
                0.9999998461826772,
                0.9999998874649051,
                0.9999997897566841,
                0.9999996533673791,
                0.9999997126313783,
                0.9999997463981032,
                0.9999997617629766,
                0.9999998802069302
            ],
            [
                0.9999994284996216,
                0.9999977396751671,
                0.99999971263131,
                0.9999990577552952,
                0.9999996940976639,
                0.999999114843176,
                0.9999996310113283,
                0.9999989969860322,
                0.9999994284994174,
                0.9999988634362906
            ],
            [
                0.9999996940977003,
                0.9999998724809268,
                0.9999998024946567,
                0.999999789756684,
                0.999999872480942,
                0.9999997761970248,
                0.9999999067050498,
                0.9999992188514838,
                0.999999730042287,
                0.9999993106387907
            ],
            [
                0.9999996743688588,
                0.999999114843281,
                0.9999997897566841,
                0.9999996533673791,
                0.9999997897565839,
                0.9999985406239545,
                0.9999993524052797,
                0.9999986290431216,
                1.8925143728749452e-05,
                0.9999995818814268
            ],
            [
                0.9999987121043249,
                0.9999993524048932,
                0.9999975938979495,
                0.9999996072137999,
                0.9999977396759732,
                0.999998863436562,
                0.9999994284997575,
                0.999996711252116,
                0.9999987901346057,
                0.999998629043284
            ],
            [
                2.3823690999160957e-07,
                9.931189774187203e-08,
                1.8553903548231313e-07,
                1.637377448057981e-07,
                1.125352291309328e-07,
                9.931193325852072e-08,
                2.382370235933104e-07,
                9.931195693628605e-08,
                5.315786239218605e-08,
                2.1024341622426268e-07
            ],
            [
                0.9999996743687424,
                0.9999985406243028,
                0.9999987901337412,
                0.9999995549151076,
                0.9999995549150545,
                0.9999989322967495,
                0.999998996985913,
                0.9999984465020618,
                0.9999990577556317,
                0.9999995818812771
            ],
            [
                0.9999998942829477,
                0.9999995549149483,
                0.9999989322970031,
                0.9999999176674946,
                0.9999998144608981,
                0.9999999358793332,
                0.9999993916408185,
                0.999999922655787,
                0.9999999530884012,
                0.9999998942829602
            ],
            [
                0.9999997126314126,
                0.9999998461826223,
                5.715005832886879e-07,
                0.9999998362623138,
                0.9999998642566219,
                0.999999864256719,
                0.9999997897566841,
                0.9999998362623529,
                0.9999998724809875,
                0.9999998257020799
            ],
            [
                0.9999998362622357,
                0.9999999273417836,
                0.9999999176674553,
                0.9999993524052021,
                0.9999999176675535,
                0.9999998802069017,
                0.9999999273418443,
                0.9999996743688199,
                0.9999741325631464,
                0.9999999500628513
            ],
            [
                0.9999989969854345,
                0.9999997897566341,
                0.9999996310116359,
                0.9999994631249327,
                0.9999998257022046,
                0.9999994631247406,
                0.9999998724809117,
                0.9999992661790199,
                0.9999993916409637,
                0.9999996940977732
            ],
            [
                0.9999998461827139,
                0.9999997617630049,
                5.043473480766399e-07,
                0.9999993916408185,
                0.9999998144608762,
                0.9999998257021214,
                0.9999998144608983,
                0.999999825702163,
                0.9999997897565839,
                0.9999998362622553
            ],
            [
                0.999998446502617,
                0.9999989969857929,
                0.999999168471973,
                0.9999991684716756,
                0.999996499146847,
                0.9999993106386261,
                0.9999995262094422,
                2.382369667929001e-07,
                0.9999996533674617,
                0.9999997126315154
            ],
            [
                0.9999993106392018,
                0.9999988634358838,
                0.9999997617630334,
                1.0,
                0.9999986290424668,
                0.9999998642566381,
                0.9999987121047857,
                0.9999990577554071,
                3.0590222692437275e-07,
                0.9999993524049705
            ],
            [
                0.9999995818812775,
                0.9999997897566841,
                0.9999998362622748,
                0.9999992661792827,
                0.9999997300421907,
                0.9999997300421584,
                0.9999990577555194,
                0.9999997617631186,
                0.9999998461826223,
                0.9999994631247406
            ],
            [
                0.9999998461826956,
                0.9999998362622944,
                0.9999997300422548,
                0.9999998642567353,
                0.999999943413784,
                0.9999998874648245,
                0.9999996533674617,
                0.9999998802069445,
                0.9999997761971583,
                0.9999998642567028
            ],
            [
                9.422448185534261e-07,
                0.9999995818814267,
                0.9999990577555192,
                0.9999996072139403,
                0.9999995549148952,
                0.9999998555019275,
                0.9999998144608098,
                0.9999996743688199,
                0.9999991684722702,
                0.9999998802069445
            ],
            [
                0.9999988634366969,
                0.9999952149032449,
                1.370957860567974e-06,
                0.9999983463106138,
                0.999998863436428,
                0.9999993916408915,
                0.9999996072139404,
                0.9999988634365619,
                0.999999631011328,
                0.9999982396569994
            ],
            [
                7.338208055664991e-07,
                5.043476486915964e-07,
                2.1024341622426268e-07,
                3.059021175247079e-07,
                3.059022998576899e-07,
                2.3823699519225038e-07,
                1.6373764721039308e-07,
                2.699577774585891e-07,
                1.855391239544352e-07,
                8.315281267861397e-07
            ],
            [
                0.9999997897567343,
                0.999999789756659,
                0.9999998144608098,
                0.9999995549148952,
                0.999999776197025,
                0.999999391640746,
                0.9999998942829854,
                0.9999998362623335,
                0.9999998642566705,
                0.999999746398073
            ],
            [
                1.0,
                0.9999999677581067,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999995549150013,
                1.0,
                0.9999999123574836,
                1.0
            ],
            [
                0.9999993106387086,
                0.9999996310114162,
                0.999999887464838,
                0.9999998942829099,
                0.9999998461826406,
                0.9999999123575255,
                0.9999998555019963,
                0.9999998144608983,
                0.999999631011416,
                0.9999993106388729
            ],
            [
                0.9999999500628571,
                1.0,
                1.0,
                0.9999999586006393,
                0.9999999559306259,
                0.9999997126313098,
                0.9999994956525319,
                0.9999999530883732,
                1.0,
                0.9999996072139404
            ]
        ]
    },
    {
        "q_id": "10143_mmlu_physics",
        "cot_ids": [
            2,
            6,
            7,
            10,
            11,
            13,
            16,
            17,
            19,
            20,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            80,
            81,
            82,
            83,
            84,
            86,
            87,
            88,
            91,
            93,
            94,
            95,
            96,
            98,
            99,
            100,
            104,
            105,
            106,
            107,
            108,
            109,
            111,
            113,
            114,
            116,
            117,
            121,
            125,
            126,
            127
        ],
        "rewards": [
            [
                8.315282259138311e-07,
                1.2098653950656417e-06,
                2.1024331597262577e-07,
                1.5534973841895917e-06,
                9.422448185478557e-07,
                1.4449798650569826e-07,
                1.2098656835136636e-06,
                9.422444815726566e-07,
                8.315281267861397e-07,
                3.05902263391829e-07
            ],
            [
                1.8553907971855875e-07,
                4.450852641737424e-07,
                3.927862470816829e-07,
                2.699578740032504e-07,
                3.05902336324494e-07,
                1.6373774480605869e-07,
                4.222835458044565e-06,
                1.9947299593014888e-06,
                1.6373764721091427e-07,
                9.422448185534261e-07
            ],
            [
                8.315279285370317e-07,
                3.927863875616689e-07,
                2.6995790618350237e-07,
                2.699578740011634e-07,
                NaN,
                8.315278294114555e-07,
                5.715005832853093e-07,
                8.315281267861397e-07,
                3.9278634073625165e-07,
                2.382368815916736e-07
            ],
            [
                NaN,
                7.338212429582604e-07,
                8.315284241650899e-07,
                2.9023116392097746e-06,
                NaN,
                1.2098659719788098e-06,
                5.043475885674441e-07,
                6.475947982037486e-07,
                NaN,
                6.962257909842961e-06
            ],
            [
                8.315282259138311e-07,
                1.444980209564556e-07,
                2.2603251062450327e-06,
                2.3823688159291947e-07,
                2.3823688159291947e-07,
                1.7603430034867993e-06,
                3.466327037553825e-07,
                1.9947299593078385e-06,
                2.3823690999323465e-07,
                2.382368531929327e-07
            ],
            [
                2.3823685319320354e-07,
                NaN,
                1.209865827752005e-06,
                5.715002426486762e-07,
                NaN,
                1.8553910183674878e-07,
                2.3823685319320354e-07,
                2.10243290909963e-07,
                NaN,
                3.4663253846473677e-07
            ],
            [
                5.043472278280699e-07,
                3.466325797888292e-07,
                8.315283250371857e-07,
                2.3823693839290317e-07,
                1.4449798650551755e-07,
                3.059022269250683e-07,
                2.3823688159291947e-07,
                1.994730197071414e-06,
                2.382368531929327e-07,
                2.699578096393206e-07
            ],
            [
                4.450852641737424e-07,
                2.382370235933104e-07,
                NaN,
                2.6995784182140636e-07,
                4.450850519409479e-07,
                1.3709573702856596e-06,
                1.9947299593078385e-06,
                5.043475284468537e-07,
                4.222833444590791e-06,
                3.466327863983311e-07
            ],
            [
                3.466327037539638e-07,
                5.043473480777865e-07,
                1.2098658277451275e-06,
                8.315283250371857e-07,
                3.466327037548308e-07,
                5.04347528446051e-07,
                1.3709568799919866e-06,
                1.760342793638743e-06,
                3.9278615344178325e-07,
                5.715005832886879e-07
            ],
            [
                7.338208930391909e-07,
                2.1024341622368903e-07,
                7.338208055536515e-07,
                2.1024336609874897e-07,
                2.699577774585891e-07,
                1.5534979397740895e-06,
                3.466325797896173e-07,
                1.3709575337078829e-06,
                6.475947210012481e-07,
                2.6995790618350237e-07
            ],
            [
                2.69957906184239e-07,
                3.7266383955882547e-06,
                1.4449795205429202e-07,
                6.475945666051092e-07,
                2.3823693839290317e-07,
                5.715004470313855e-07,
                1.8553916819032217e-07,
                3.288750241410738e-06,
                1.6373762769138607e-07,
                6.475951069985296e-07
            ],
            [
                7.338209805133949e-07,
                1.0677033791612137e-06,
                1.3709567165530083e-06,
                5.043476486915964e-07,
                3.927863875584984e-07,
                5.043472278280699e-07,
                8.315278294072958e-07,
                5.043474683204221e-07,
                7.338209805200689e-07,
                7.338208930460318e-07
            ],
            [
                1.6373770576776313e-07,
                2.1024341622426268e-07,
                7.734416698849138e-08,
                1.4449800373065699e-07,
                1.6373774480605869e-07,
                1.6373776432509826e-07,
                1.4449802095666915e-07,
                2.382368815932174e-07,
                1.6373768624837685e-07,
                6.825606165129312e-08
            ],
            [
                5.04347528446051e-07,
                5.043475885674441e-07,
                3.46632497145457e-07,
                7.338207180864763e-07,
                3.927860597945825e-07,
                3.05902190458764e-07,
                3.4663249714451116e-07,
                8.315283250371857e-07,
                1.3709567165530083e-06,
                6.475947210031623e-07
            ],
            [
                6.023579219579052e-08,
                1.8553910183674878e-07,
                9.931185038635267e-08,
                5.315781803390236e-08,
                3.2241881707064475e-08,
                6.023571320847322e-08,
                6.825597214718257e-08,
                9.931200429212718e-08,
                6.023572038912295e-08,
                6.023572038912295e-08
            ],
            [
                4.222834954778007e-06,
                6.962255419931625e-06,
                1.9947292459347367e-06,
                5.422217030707961e-06,
                6.962256249885085e-06,
                6.475949526020042e-07,
                1.4738989000422955e-05,
                8.939697369980456e-06,
                3.9278605979534166e-07,
                3.7266392840781026e-06
            ],
            [
                3.9278629391427843e-07,
                8.315279285370317e-07,
                6.023568448589658e-08,
                1.275190732904469e-07,
                2.3823685319244518e-07,
                1.6373764721072816e-07,
                1.760343003481596e-06,
                2.69957906184239e-07,
                1.2751905808881762e-07,
                6.023568448589658e-08
            ],
            [
                5.71500515161527e-07,
                3.466327037553825e-07,
                NaN,
                4.4508515805735777e-07,
                3.4663249714612693e-07,
                2.3823696679327928e-07,
                1.275190428875671e-07,
                5.043475284468537e-07,
                9.93119806143167e-08,
                2.699577774589574e-07
            ],
            [
                5.043475284430694e-07,
                NaN,
                NaN,
                7.338210680032098e-07,
                1.5534975693979422e-06,
                NaN,
                NaN,
                1.0677026154827912e-06,
                NaN,
                1.3709575337159875e-06
            ],
            [
                2.3823696679327928e-07,
                6.475950298011458e-07,
                3.059021175261338e-07,
                3.4663253846718004e-07,
                1.4449798650551755e-07,
                7.338208930391909e-07,
                3.0590215399183813e-07,
                7.338211554783522e-07,
                5.422219616184461e-06,
                4.450848927650143e-07
            ],
            [
                1.5534975693869924e-06,
                1.4738980215593877e-05,
                8.315280276546789e-07,
                NaN,
                7.338209805224048e-07,
                6.605212894856585e-05,
                2.5612812947508257e-06,
                4.785095065171522e-06,
                3.2887506336235617e-06,
                3.927860597935108e-07
            ],
            [
                1.2098659719757836e-06,
                4.4508505193791187e-07,
                3.466327037548308e-07,
                4.450852111148132e-07,
                5.043472278280699e-07,
                4.450848927650143e-07,
                2.382370235922541e-07,
                3.0590226339061185e-07,
                3.059021904559123e-07,
                5.715002426439334e-07
            ],
            [
                2.2603253756956754e-06,
                3.927860597935108e-07,
                1.8553919030776337e-07,
                3.05902263389638e-07,
                2.6995771309210433e-07,
                3.927862470899887e-07,
                9.931194509683815e-08,
                3.4663249714451116e-07,
                1.4449802095609418e-07,
                1.8553907971855875e-07
            ],
            [
                3.059021175247079e-07,
                1.2098656835252174e-06,
                2.561282821402217e-06,
                4.4508515805735777e-07,
                NaN,
                2.9023116392097746e-06,
                1.0677027427600627e-06,
                9.422450432030903e-07,
                1.3709572068553509e-06,
                1.0677033791612137e-06
            ],
            [
                2.699577774585891e-07,
                3.0590237279032884e-07,
                5.715003107767143e-07,
                1.8553916819032217e-07,
                1.1253516205489029e-07,
                1.275190276859705e-07,
                5.04347468323289e-07,
                9.931190958076104e-08,
                1.6373776432509826e-07,
                1.444980209564556e-07
            ],
            [
                6.475947210046347e-07,
                5.715003789046955e-07,
                1.2098652508424818e-06,
                8.315281267882195e-07,
                7.338211554688417e-07,
                3.9278605979534166e-07,
                9.422444815679433e-07,
                1.3709568799919866e-06,
                2.2603242978377903e-06,
                1.9947290081286418e-06
            ],
            [
                5.71500515161527e-07,
                5.043474082012222e-07,
                1.0677024882009222e-06,
                1.6373772528704005e-07,
                4.4508515805735777e-07,
                3.059021175261338e-07,
                2.699578740032504e-07,
                3.9278629391427843e-07,
                3.4663262111182307e-07,
                4.4508515805735777e-07
            ],
            [
                8.315284241597959e-07,
                1.994729245917502e-06,
                1.2098659719601033e-06,
                2.9023109472244114e-06,
                1.3709572068422585e-06,
                9.422448185478557e-07,
                1.0677032518748838e-06,
                1.5534975693869924e-06,
                1.4738983729535602e-05,
                3.2887494574518405e-06
            ],
            [
                5.715006514176113e-07,
                6.475946438055299e-07,
                5.715003788993679e-07,
                2.382368247924618e-07,
                2.69957906184239e-07,
                8.315277302857965e-07,
                5.422220909009474e-06,
                8.315284241650899e-07,
                7.338208055680009e-07,
                5.043472278322555e-07
            ],
            [
                7.338207180898968e-07,
                3.05902190458764e-07,
                8.764247451307293e-08,
                2.3823699519290042e-07,
                5.71500515161527e-07,
                3.059021175261338e-07,
                1.275190732904469e-07,
                3.466325797888292e-07,
                NaN,
                1.8553910183674878e-07
            ],
            [
                1.8553916819032217e-07,
                6.475950298021765e-07,
                1.6373774480535133e-07,
                8.764241182605906e-08,
                1.4449800373065699e-07,
                9.422444815814404e-07,
                1.1253512180925583e-07,
                1.2098659719757836e-06,
                7.338209805240734e-07,
                3.288747889284851e-06
            ],
            [
                1.855391239544352e-07,
                9.422445939032799e-07,
                9.422445939054222e-07,
                3.466325797896173e-07,
                5.043476486924565e-07,
                1.209865539295696e-06,
                3.059022998576899e-07,
                9.422442569315887e-07,
                1.0677026154806063e-06,
                3.466327037548308e-07
            ],
            [
                6.475947210031623e-07,
                2.1024341622426268e-07,
                2.699578096393206e-07,
                7.338207180864763e-07,
                5.043475885674441e-07,
                5.715002426475718e-07,
                2.1024334103505245e-07,
                1.6373774480605869e-07,
                2.382368247924618e-07,
                8.315283250371857e-07
            ],
            [
                9.422447062270609e-07,
                2.90231094723893e-06,
                5.043472879540142e-07,
                8.315282259117513e-07,
                2.699576809143613e-07,
                8.315283250371857e-07,
                5.422221555380179e-06,
                7.338212429582604e-07,
                1.7603434231777837e-06,
                7.338209805224048e-07
            ],
            [
                1.637376862489725e-07,
                2.1024341622426268e-07,
                6.825602910433871e-08,
                2.6995771309523475e-07,
                9.931200429212718e-08,
                1.444979692800516e-07,
                6.825597214691097e-08,
                1.6373768624837685e-07,
                1.4449807263312446e-07,
                7.734424996967756e-08
            ],
            [
                2.5612819054028872e-06,
                2.9023119851781017e-06,
                2.561281600086738e-06,
                1.5534975693979422e-06,
                3.9278615344178325e-07,
                1.760342793638743e-06,
                3.288749457469787e-06,
                6.475945666063607e-07,
                1.4449796928021588e-07,
                2.902312677150514e-06
            ],
            [
                1.8553907971758842e-07,
                1.2751899728286965e-07,
                2.3823693839290317e-07,
                4.691161005609407e-08,
                7.734416698849138e-08,
                3.653482080235082e-08,
                1.6373770576776313e-07,
                6.825597214718257e-08,
                9.931190958076104e-08,
                1.4449803818156628e-07
            ],
            [
                5.04347528446051e-07,
                2.6995790618469934e-07,
                3.4663253846718004e-07,
                3.4663253846718004e-07,
                2.382369383923073e-07,
                3.466327450765785e-07,
                4.785094494783494e-06,
                1.5534975693869924e-06,
                3.466325797896173e-07,
                1.0677032518785256e-06
            ],
            [
                1.209865827752005e-06,
                3.059022269254856e-07,
                4.450850519409479e-07,
                1.275189972832538e-07,
                8.315284241665078e-07,
                2.6995771309523475e-07,
                1.6373766672994222e-07,
                1.3709572068553509e-06,
                6.023573475041126e-08,
                5.715006514176113e-07
            ],
            [
                3.927862002663297e-07,
                5.715002426486762e-07,
                2.102434412875379e-07,
                8.315278294097538e-07,
                1.2098656835252174e-06,
                1.370957860576702e-06,
                3.927863407379485e-07,
                7.338209805224048e-07,
                5.715005832853093e-07,
                5.043476486915964e-07
            ],
            [
                7.734424996967756e-08,
                1.8553907971855875e-07,
                7.889266347715168e-06,
                6.023574911170301e-08,
                1.4449800373065699e-07,
                4.691167716359673e-08,
                2.1024334103505245e-07,
                1.6373768624837685e-07,
                1.2751899728311609e-07,
                1.6373770576776313e-07
            ],
            [
                3.466327037553825e-07,
                6.47594875403829e-07,
                5.715006514176113e-07,
                3.927861534431675e-07,
                7.33821330437595e-07,
                8.315278294114555e-07,
                2.699578096403948e-07,
                3.466326624336003e-07,
                7.338209805240734e-07,
                5.043476486924565e-07
            ],
            [
                8.315283250371857e-07,
                1.0677031245990084e-06,
                NaN,
                4.450850519403407e-07,
                3.927863875584984e-07,
                5.715002426439334e-07,
                1.8925145985895816e-05,
                6.475951069985296e-07,
                7.338209805200689e-07,
                1.7603432133296774e-06
            ],
            [
                2.3823693839325527e-07,
                4.450852111148132e-07,
                1.3709572068522336e-06,
                2.1024331597262577e-07,
                3.9278634073732336e-07,
                6.475948754012522e-07,
                5.715003789046955e-07,
                1.6373770576776313e-07,
                5.715005832895975e-07,
                3.288748281329893e-06
            ],
            [
                1.012998977264307e-05,
                NaN,
                1.209865827752005e-06,
                2.382370235922541e-07,
                5.715002426460124e-07,
                9.422445939054222e-07,
                1.0677033791612137e-06,
                5.715003107767143e-07,
                3.4663274507713016e-07,
                7.889266347786918e-06
            ],
            [
                5.715005832895975e-07,
                5.715004470326849e-07,
                1.5534983101602148e-06,
                8.315279285012978e-07,
                1.0677024881980089e-06,
                5.04347348070562e-07,
                5.71500515159253e-07,
                5.715005832895975e-07,
                2.1024334103581732e-07,
                5.71500719545698e-07
            ],
            [
                5.043475885674441e-07,
                7.338209805224048e-07,
                1.2751899728311609e-07,
                7.338212429582604e-07,
                3.9278634073732336e-07,
                5.043472879525233e-07,
                7.338210680021253e-07,
                3.466327863983311e-07,
                5.715004470313855e-07,
                6.475945666051092e-07
            ],
            [
                1.8553907971855875e-07,
                3.059022998576899e-07,
                1.8553903548231313e-07,
                2.6995790618252024e-07,
                9.931190958026426e-08,
                1.0677026154774503e-06,
                1.2751899728286965e-07,
                2.10243290909724e-07,
                6.475948753965404e-07,
                3.466327037539638e-07
            ],
            [
                6.475946438055299e-07,
                1.2098656835252174e-06,
                5.71500719545698e-07,
                1.067703124601679e-06,
                6.962257079889302e-06,
                1.3709568799919866e-06,
                1.3709573702856596e-06,
                7.33821330437595e-07,
                NaN,
                NaN
            ],
            [
                6.475949526020042e-07,
                7.338207180898968e-07,
                3.9278605979534166e-07,
                6.825597214691097e-08,
                2.382370235922541e-07,
                1.5534971990169383e-06,
                2.6995774527718623e-07,
                8.764241182605906e-08,
                1.4449803818215767e-07,
                1.637377448057981e-07
            ],
            [
                6.475949525981759e-07,
                3.726641061058432e-06,
                2.9023133690980155e-06,
                6.475947209953583e-07,
                7.338211554783522e-07,
                7.338209805224048e-07,
                2.5612819054133693e-06,
                1.3709570434178922e-06,
                9.422444815792981e-07,
                1.0677028700363782e-06
            ],
            [
                4.1399375473868e-08,
                8.764245361752286e-08,
                6.825598842065202e-08,
                4.691167716359673e-08,
                7.734421308914719e-08,
                9.931189774187203e-08,
                4.691161005609407e-08,
                1.6373762769138607e-07,
                2.3823688159291947e-07,
                5.315784971839039e-08
            ],
            [
                6.023576347299818e-08,
                8.764244316973974e-08,
                2.1024331597262577e-07,
                2.382369951932796e-07,
                1.1253509497883659e-07,
                8.315281267882195e-07,
                1.4449803818215767e-07,
                1.6373774480605869e-07,
                1.8553919030858602e-07,
                9.422443692574719e-07
            ],
            [
                2.1024336609843824e-07,
                4.450851580555361e-07,
                2.2603242978665707e-06,
                3.4663253846718004e-07,
                8.315281267882195e-07,
                3.927860597935108e-07,
                6.475948754012522e-07,
                8.315280276580819e-07,
                3.466327037548308e-07,
                3.927860597945825e-07
            ],
            [
                6.475947210031623e-07,
                4.785095635624897e-06,
                1.209866260432471e-06,
                4.222831934379152e-06,
                1.3709572068522336e-06,
                1.9947299593014888e-06,
                5.715003789033962e-07,
                3.288748673376478e-06,
                2.260323758987159e-06,
                7.889259764445822e-06
            ],
            [
                6.47595107001401e-07,
                1.7603440527334603e-06,
                5.715002426486762e-07,
                NaN,
                9.422443692574719e-07,
                5.043475885696228e-07,
                3.9278629391427843e-07,
                1.0677027427624903e-06,
                1.0677028700363782e-06,
                3.927863875616689e-07
            ],
            [
                2.382369667929001e-07,
                1.6373772528704005e-07,
                9.931198061405701e-08,
                2.3823682479317953e-07,
                6.023576347299818e-08,
                4.4508515805735777e-07,
                6.825602910433871e-08,
                1.4449800373118268e-07,
                5.315789407666425e-08,
                3.059021904571643e-07
            ],
            [
                2.3823696679327928e-07,
                1.2751899728286965e-07,
                8.764247451307293e-08,
                5.71500719545698e-07,
                2.3823685319244518e-07,
                6.475946438055299e-07,
                9.93118503859575e-08,
                1.6373772528636992e-07,
                5.043473480777865e-07,
                2.699577774585891e-07
            ],
            [
                4.4508515805735777e-07,
                6.47595107001401e-07,
                2.699577452775239e-07,
                NaN,
                1.0677028700422047e-06,
                2.699577774589574e-07,
                2.6995784182183607e-07,
                5.715005832895975e-07,
                3.05902263391829e-07,
                5.043475885696228e-07
            ],
            [
                7.338209805200689e-07,
                1.2098661162056318e-06,
                3.288750241561788e-06,
                6.475947210046347e-07,
                1.8553919030858602e-07,
                9.422443692574719e-07,
                4.785093924362895e-06,
                3.059023727894942e-07,
                9.422442569334097e-07,
                9.422450431989127e-07
            ],
            [
                0.999996033014089,
                1.2751899728286965e-07,
                1.2751904288710323e-07,
                1.4449798650551755e-07,
                1.6373768624837685e-07,
                1.4449800373065699e-07,
                1.2751904288710323e-07,
                1.4449798650417048e-07,
                2.38237023590304e-07,
                1.4449805540585765e-07
            ],
            [
                1.2098659719788098e-06,
                6.962254589914941e-06,
                3.288749065436569e-06,
                3.7266410611296085e-06,
                4.785096776499213e-06,
                3.927862470899887e-07,
                1.2098656835252174e-06,
                NaN,
                1.0677032518748838e-06,
                5.715003107767143e-07
            ],
            [
                5.043476486915964e-07,
                1.0677027427624903e-06,
                1.4449800373065699e-07,
                1.5534975693979422e-06,
                1.2098661162056318e-06,
                4.450851049991497e-07,
                2.6995771309523475e-07,
                5.04347528446051e-07,
                NaN,
                2.90231094723893e-06
            ],
            [
                1.0677029973192638e-06,
                8.315281267882195e-07,
                3.927860597945825e-07,
                9.422444815495185e-07,
                5.043476486902204e-07,
                3.466326211113502e-07,
                8.315279285370317e-07,
                3.4663278639892215e-07,
                6.475950298011458e-07,
                7.338210679979539e-07
            ],
            [
                2.2603234895289998e-06,
                1.855391681906175e-07,
                2.1024339116168358e-07,
                1.8553914607267268e-07,
                7.338208055664991e-07,
                2.1024339116168358e-07,
                6.475950298011458e-07,
                3.059022998576899e-07,
                2.6995784182140636e-07,
                2.699576809143613e-07
            ],
            [
                0.9999985406234325,
                6.962256249821764e-06,
                1.8925152753790864e-05,
                0.9999955048184299,
                0.9999993524054341,
                2.5612812947240366e-06,
                0.9999990577556317,
                3.535624650150453e-05,
                0.9999974387184037,
                0.9999898700042144
            ],
            [
                1.7603432133296774e-06,
                4.2228329411708495e-06,
                8.31527928532683e-07,
                7.338209805200689e-07,
                8.315281267861397e-07,
                2.260324028427877e-06,
                7.338213304363436e-07,
                4.785093353940187e-06,
                3.927862470899887e-07,
                4.222833947960866e-06
            ],
            [
                1.637377057680051e-07,
                5.715003107767143e-07,
                5.043473480777865e-07,
                2.699578740032504e-07,
                3.4663274507713016e-07,
                4.4508494582405734e-07,
                8.315278294114555e-07,
                3.288750241561788e-06,
                1.1253516205489029e-07,
                2.382369951932796e-07
            ],
            [
                2.1024341622368903e-07,
                9.931202796993203e-08,
                7.338207180898968e-07,
                2.1024336609843824e-07,
                1.1253516205489029e-07,
                3.466327037548308e-07,
                8.315281267861397e-07,
                9.931186222523604e-08,
                3.059022998576899e-07,
                7.734416698849138e-08
            ],
            [
                2.902313369111213e-06,
                4.785095065232451e-06,
                1.9947292459347367e-06,
                1.0129995810463632e-05,
                NaN,
                7.889263526345123e-06,
                1.5534981249697903e-06,
                1.760343633031919e-06,
                1.012999218776902e-05,
                1.760342793638743e-06
            ],
            [
                2.382369951932796e-07,
                1.6373764720990908e-07,
                1.1253521571574156e-07,
                NaN,
                1.4449796927932878e-07,
                7.338209805240734e-07,
                1.4449805540700758e-07,
                8.764254764749753e-08,
                1.2751907329024393e-07,
                1.4449805540700758e-07
            ],
            [
                3.2887490653872164e-06,
                1.2098659719757836e-06,
                1.7603425837791042e-06,
                4.785096206076165e-06,
                3.726637951367137e-06,
                3.726638395611981e-06,
                6.475950298011458e-07,
                3.1201926253802263e-05,
                1.3709576971316842e-06,
                1.0677032518785256e-06
            ],
            [
                1.2098661161927025e-06,
                7.338210679909462e-07,
                1.5534971990126997e-06,
                2.2603242978778778e-06,
                1.5534981249574276e-06,
                9.422447062202052e-07,
                2.902311639073834e-06,
                4.785095635592258e-06,
                1.99472924590571e-06,
                1.7603425837606927e-06
            ],
            [
                1.0677029973219343e-06,
                1.7603438428800754e-06,
                5.04347528446051e-07,
                3.2887502415767434e-06,
                NaN,
                NaN,
                1.209866260432471e-06,
                7.338210679979539e-07,
                1.7603425837903113e-06,
                5.715005832886879e-07
            ],
            [
                1.0677024881683915e-06,
                5.043472879525233e-07,
                1.7603425837702984e-06,
                8.315284241401329e-07,
                1.0677031245905116e-06,
                1.8925143729575624e-05,
                1.994729721469003e-06,
                1.3709572068422585e-06,
                5.715003107738556e-07,
                2.3823693839154895e-07
            ],
            [
                NaN,
                3.653482951291499e-08,
                4.4508510499849186e-07,
                NaN,
                NaN,
                1.209865539298447e-06,
                1.147876812620341e-05,
                3.059022998576899e-07,
                3.059023727894942e-07,
                NaN
            ],
            [
                8.315284241665078e-07,
                1.637376862489725e-07,
                3.72663883989755e-06,
                3.4663262111182307e-07,
                NaN,
                3.05902190458764e-07,
                7.338208055680009e-07,
                3.466326624336003e-07,
                NaN,
                9.422450432030903e-07
            ],
            [
                5.715005151606823e-07,
                4.450848927650143e-07,
                5.715005151606823e-07,
                2.2603253756956754e-06,
                1.209866260432471e-06,
                5.715003789046955e-07,
                1.2098656835224664e-06,
                3.927862002663297e-07,
                8.315283250371857e-07,
                3.9278615344178325e-07
            ],
            [
                5.715005832895975e-07,
                8.315281267834927e-07,
                4.006369219393695e-05,
                1.9947304348703948e-06,
                3.0590237279085045e-07,
                1.275190580890061e-07,
                1.4449800373118268e-07,
                1.3709572068522336e-06,
                3.05902336324494e-07,
                1.6373774480605869e-07
            ],
            [
                5.715005151574337e-07,
                9.422445939032799e-07,
                2.260324836776948e-06,
                8.315277302841894e-07,
                1.3709568799879344e-06,
                1.7603427936263351e-06,
                5.715003107767143e-07,
                9.422448185534261e-07,
                1.9947297215043796e-06,
                1.994730434847717e-06
            ],
            [
                2.2603251061664e-06,
                3.288749457432399e-06,
                1.4738987243236881e-05,
                2.2603248367512505e-06,
                1.9947304348703948e-06,
                7.889266347636241e-06,
                9.422448185478557e-07,
                4.222834954687752e-06,
                2.2603251062013478e-06,
                3.726641061085547e-06
            ],
            [
                1.670141587208191e-05,
                1.994729008105057e-06,
                1.3709575337078829e-06,
                1.994729483694599e-06,
                4.222834451292594e-06,
                5.422219616026655e-06,
                7.3382080556433e-07,
                9.422442569208767e-07,
                2.2603237589676295e-06,
                2.260325375634003e-06
            ],
            [
                1.0677032518700286e-06,
                5.715005832853093e-07,
                1.125352291309328e-07,
                7.338210679979539e-07,
                3.466327037548308e-07,
                2.3823688159291947e-07,
                3.05902263391829e-07,
                1.1253518888531272e-07,
                8.764242227418718e-08,
                8.764241182641775e-08
            ],
            [
                NaN,
                3.4663278639892215e-07,
                NaN,
                2.6995771309523475e-07,
                6.9622595696935874e-06,
                5.043472879504592e-07,
                3.059022998576899e-07,
                4.2228319344021954e-06,
                1.5534981249697903e-06,
                1.855391239544352e-07
            ],
            [
                7.734418542875216e-08,
                1.2751904288739315e-07,
                5.715004470313855e-07,
                1.2751904288710323e-07,
                1.4449796927932878e-07,
                1.1253508156363576e-07,
                3.05902263391829e-07,
                1.444980209564556e-07,
                1.8553907971855875e-07,
                7.734416698849138e-08
            ],
            [
                3.466326211113502e-07,
                3.726638839878908e-06,
                3.466327863983311e-07,
                3.4663249714612693e-07,
                3.4663253846718004e-07,
                6.475947210031623e-07,
                7.338208055664991e-07,
                6.475947210046347e-07,
                9.422450432014836e-07,
                1.209866260432471e-06
            ],
            [
                3.927862470899887e-07,
                3.466327037553825e-07,
                9.422450431954847e-07,
                6.475947982037486e-07,
                3.0590237279032884e-07,
                3.0590237279032884e-07,
                3.059023727894942e-07,
                5.715004470313855e-07,
                2.1024339116168358e-07,
                3.4663257978780455e-07
            ],
            [
                6.475950298011458e-07,
                3.466325384678894e-07,
                1.1253513522391131e-07,
                3.0590237279032884e-07,
                6.023576347299818e-08,
                1.0677032518814388e-06,
                1.0677031245990084e-06,
                2.6995771309523475e-07,
                1.4449798650569826e-07,
                1.8553903548231313e-07
            ]
        ]
    },
    {
        "q_id": "9799_mmlu_physics",
        "cot_ids": [
            1,
            2,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            13,
            15,
            16,
            17,
            18,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            38,
            39,
            40,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            57,
            58,
            60,
            61,
            63,
            64,
            65,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                0.9999994631249322,
                8.764245361752286e-08,
                9.422449308748773e-07,
                3.4663278639892215e-07,
                8.939694172957213e-06,
                5.715003107755449e-07,
                1.0129987357407137e-05,
                2.902313369111213e-06,
                1.4738980215352592e-05,
                5.043472278322555e-07
            ],
            [
                1.3709568799592562e-06,
                2.9023116391477434e-06,
                8.315279285205827e-07,
                9.422444815409489e-07,
                1.2098653950656417e-06,
                1.0677032518785256e-06,
                2.561283126639892e-06,
                1.2098662604291696e-06,
                3.726641061085547e-06,
                1.2098653950656417e-06
            ],
            [
                8.939696304311336e-06,
                2.902311985146426e-06,
                3.7266410611296085e-06,
                8.315280276626197e-07,
                7.889261645355786e-06,
                7.889261645427538e-06,
                1.3007131566015624e-05,
                0.9999861539938175,
                1.5534983101602148e-06,
                1.012999098021058e-05
            ],
            [
                2.5612828213818346e-06,
                9.422450431989127e-07,
                1.0677032518785256e-06,
                1.2098652507957165e-06,
                1.2098653950606901e-06,
                2.2603248367656408e-06,
                3.9278615344178325e-07,
                9.422450432014836e-07,
                5.715005832886879e-07,
                5.7150044702099e-07
            ],
            [
                5.715005832886879e-07,
                1.0677027427569065e-06,
                8.315283250394546e-07,
                6.47595107001401e-07,
                6.475946438042047e-07,
                1.7603440527046419e-06,
                3.726639284125553e-06,
                2.6995790618469934e-07,
                3.927863407379485e-07,
                3.927863407379485e-07
            ],
            [
                6.9622587397397306e-06,
                5.04347287955046e-07,
                2.561281600076256e-06,
                7.338208055664991e-07,
                1.6701425825492673e-05,
                3.466326211113502e-07,
                1.5534979397790343e-06,
                2.5612831267086116e-06,
                4.785093924330255e-06,
                5.043472278322555e-07
            ],
            [
                9.422447062294175e-07,
                3.4663249714612693e-07,
                2.2603240284371276e-06,
                5.043476486915964e-07,
                3.466327037548308e-07,
                9.422449308774482e-07,
                1.0677032518814388e-06,
                3.72663883989755e-06,
                3.059021175261338e-07,
                9.422450432014836e-07
            ],
            [
                2.561282516042282e-06,
                2.5612812947380135e-06,
                1.5534981249397663e-06,
                2.902312677060767e-06,
                1.2098652508287273e-06,
                7.889265407177056e-06,
                2.2603234894560207e-06,
                1.5534975693488444e-06,
                4.785096206013061e-06,
                1.3709570434054234e-06
            ],
            [
                1.994729008145876e-06,
                1.9947301970972664e-06,
                7.338209805224048e-07,
                2.4300234941261454e-05,
                2.5612831267086116e-06,
                5.71500515159253e-07,
                3.2887494574518405e-06,
                6.475947210046347e-07,
                2.2603234895176927e-06,
                1.3709570434178922e-06
            ],
            [
                2.5612831267202583e-06,
                6.475946438042047e-07,
                4.785093353909723e-06,
                1.2098662604291696e-06,
                2.2603242978871282e-06,
                7.88926070489716e-06,
                1.4738981972323349e-05,
                3.726638839878908e-06,
                1.3709567165617364e-06,
                2.4300237837960777e-05
            ],
            [
                5.043476486924565e-07,
                1.067703124601679e-06,
                8.315281267882195e-07,
                2.2603234895372223e-06,
                2.1024331597288867e-07,
                1.067703124601679e-06,
                NaN,
                2.902312331170226e-06,
                2.2603253756956754e-06,
                1.0677027427624903e-06
            ],
            [
                2.3823688159291947e-07,
                2.2603253756956754e-06,
                2.3823682479292225e-07,
                2.6995774527718623e-07,
                1.8553903548231313e-07,
                3.927863875616689e-07,
                1.4449803818215767e-07,
                8.315284241650899e-07,
                9.931202796993203e-08,
                5.043473480777865e-07
            ],
            [
                0.9999938558276008,
                0.9999964991468431,
                0.9999877809283882,
                0.9999904837494679,
                0.9999852610128057,
                0.9999942280820437,
                0.9999955048173567,
                0.9999960330136168,
                0.999994228077912,
                0.9999962733593856
            ],
            [
                1.994730434879465e-06,
                4.0063682641226247e-05,
                2.144495608378187e-05,
                7.889261645269683e-06,
                5.144220753172505e-05,
                8.939700566907275e-06,
                1.9947299593014888e-06,
                2.430023494002383e-05,
                4.539785241263674e-05,
                6.962257079832313e-06
            ],
            [
                1.0677024882009222e-06,
                7.338208055664991e-07,
                1.9947299593014888e-06,
                1.7603438428564603e-06,
                1.5534975693933505e-06,
                1.7603425837855082e-06,
                8.315279285370317e-07,
                1.067702870039777e-06,
                1.0677026154619133e-06,
                8.315279285351409e-07
            ],
            [
                4.785092783519724e-06,
                5.043472278322555e-07,
                3.0590237279032884e-07,
                6.475947210031623e-07,
                9.422445939032799e-07,
                1.5534971990126997e-06,
                1.0677024882009222e-06,
                5.715006514167015e-07,
                7.338211554783522e-07,
                7.338213304363436e-07
            ],
            [
                1.7603440527286572e-06,
                3.059021175261338e-07,
                1.0677027427624903e-06,
                8.315277302857965e-07,
                6.14417313680765e-06,
                9.422445939032799e-07,
                6.144175334468545e-06,
                2.699578096403948e-07,
                1.0677033791612137e-06,
                7.338213304363436e-07
            ],
            [
                1.4738987243478167e-05,
                2.902311293147782e-06,
                2.5612819053166966e-06,
                1.7603430034743913e-06,
                6.144173869558639e-06,
                5.422217030747413e-06,
                8.93969950132721e-06,
                6.144174601879434e-06,
                7.484623620850474e-05,
                1.5534977545886537e-06
            ],
            [
                0.9999934595635653,
                NaN,
                0.9999977396748959,
                4.785096206076165e-06,
                6.962256249885085e-06,
                1.1478768126057254e-05,
                1.3007131566015624e-05,
                0.9999756997564224,
                0.9999972735297319,
                4.785092783519724e-06
            ],
            [
                1.4449805540763184e-07,
                5.715004470295662e-07,
                1.7603438428740716e-06,
                1.5534984953298217e-06,
                1.855391239547094e-07,
                6.475947210046347e-07,
                1.30071315662049e-05,
                5.043475885696228e-07,
                0.9999810748541337,
                0.9999930377429467
            ],
            [
                0.9999930377429627,
                1.1253516205489029e-07,
                3.059022998576899e-07,
                1.7603440527286572e-06,
                0.999941708706911,
                1.9947292459347367e-06,
                1.3709570434178922e-06,
                7.338209805240734e-07,
                0.9999955048184321,
                0.9999957771645492
            ],
            [
                1.4738987243478167e-05,
                6.144175334468545e-06,
                1.4738976701411704e-05,
                2.902313023130843e-06,
                6.962257909785973e-06,
                9.422450432014836e-07,
                1.2098661162056318e-06,
                3.2887502415438413e-06,
                5.8291251656508296e-05,
                7.889261645427538e-06
            ],
            [
                3.927860597945825e-07,
                1.892515501014656e-05,
                1.6373774480605869e-07,
                3.927863875616689e-07,
                5.04347287955046e-07,
                6.962257079889302e-06,
                3.05902190458764e-07,
                4.4508515805735777e-07,
                2.382369951932796e-07,
                3.9278605979534166e-07
            ],
            [
                4.785093924362895e-06,
                1.4738981972323349e-05,
                2.144495608424996e-05,
                7.338209805224048e-07,
                3.927863875616689e-07,
                5.422219616265831e-06,
                2.7535697667202906e-05,
                4.222833444590791e-06,
                0.9999945777784529,
                7.889262585886274e-06
            ],
            [
                4.0063687409856826e-05,
                9.610239209126842e-05,
                1.6701423835320418e-05,
                8.939696304213768e-06,
                1.0129990980100021e-05,
                4.78509563546605e-06,
                1.6701417862648148e-05,
                4.222833947932061e-06,
                3.288750241561788e-06,
                9.422444815792981e-07
            ],
            [
                2.2603234895289998e-06,
                1.9947292459347367e-06,
                1.5534983101549167e-06,
                4.4508515805735777e-07,
                1.2098658277451275e-06,
                2.902312331170226e-06,
                3.288748673360027e-06,
                3.2887506336086064e-06,
                1.994730672675753e-06,
                3.466325797900508e-07
            ],
            [
                0.9997040430088311,
                3.120190393794438e-05,
                6.144175334468545e-06,
                3.120190765625026e-05,
                0.9999942280772334,
                0.9999038975975149,
                3.726638839878908e-06,
                6.605214470327124e-05,
                0.000123394633832426,
                4.785092783519724e-06
            ],
            [
                2.5612825160562587e-06,
                8.315281267861397e-07,
                1.7603434231705793e-06,
                2.902310947208574e-06,
                1.5534973841895917e-06,
                5.043472879525233e-07,
                6.475947210012481e-07,
                1.2098655392871682e-06,
                1.3709578605617394e-06,
                1.5534981249496567e-06
            ],
            [
                9.422450431989127e-07,
                3.726638839878908e-06,
                1.9947292459347367e-06,
                1.994729008145876e-06,
                3.726639284144195e-06,
                6.475948754012522e-07,
                9.422448185510695e-07,
                3.288747889284851e-06,
                5.715004470313855e-07,
                1.3709573702822306e-06
            ],
            [
                0.9999992188515768,
                0.9999983463104168,
                5.422218323487975e-06,
                5.144223206414209e-05,
                0.999987780928472,
                0.9999925887210309,
                0.9999987121052464,
                0.9999969105059237,
                7.889266347786918e-06,
                2.1444950971601277e-05
            ],
            [
                0.999993459560438,
                0.999996910505186,
                1.275190124846946e-07,
                0.9999832985801821,
                4.450851580566494e-07,
                0.9999964991464226,
                0.9999892166890814,
                1.2751902768612997e-07,
                7.73442776303243e-08,
                9.931185038635267e-08
            ],
            [
                2.5612834320563895e-06,
                2.6995790618469934e-07,
                2.699578096403948e-07,
                1.2098652508424818e-06,
                1.0677033791612137e-06,
                6.144174601991196e-06,
                4.450850519403407e-07,
                4.450852111148132e-07,
                1.6701427817427163e-05,
                NaN
            ],
            [
                1.067703379154416e-06,
                1.3709568799823232e-06,
                6.144176799283803e-06,
                1.7603434231777837e-06,
                1.7603430034743913e-06,
                4.2228324377740105e-06,
                4.785094494783494e-06,
                NaN,
                6.9622537599680095e-06,
                1.0677032518785256e-06
            ],
            [
                5.043473480777865e-07,
                1.370957860576702e-06,
                6.47595107001401e-07,
                3.9278605979534166e-07,
                4.450848927658745e-07,
                1.2098652508424818e-06,
                3.927863875616689e-07,
                2.102434162245973e-07,
                1.0677028700422047e-06,
                5.422219616265831e-06
            ],
            [
                2.902312677150514e-06,
                1.7603434231833873e-06,
                3.72663883989755e-06,
                5.422220262636381e-06,
                1.0677032518814388e-06,
                6.475947210012481e-07,
                6.962257909785973e-06,
                6.962254589978262e-06,
                3.05902190458764e-07,
                1.7603434231833873e-06
            ],
            [
                7.734424996967756e-08,
                2.10243290909724e-07,
                2.6995774527718623e-07,
                0.9999925887227968,
                2.6995784182140636e-07,
                0.9999945777816855,
                6.475945666051092e-07,
                0.9999599362985427,
                0.9999904837483258,
                3.466325797896173e-07
            ],
            [
                4.4508510499849186e-07,
                1.0677032518814388e-06,
                5.715002426475718e-07,
                2.10243290909724e-07,
                4.450848927658745e-07,
                9.422447062294175e-07,
                7.338209805224048e-07,
                8.315277302841894e-07,
                5.715003107767143e-07,
                3.059022998581767e-07
            ],
            [
                2.102434162245973e-07,
                4.450848927658745e-07,
                2.69957906184239e-07,
                1.3709567165617364e-06,
                3.9278610661902853e-07,
                1.3709575337159875e-06,
                5.043472278322555e-07,
                2.5612819054133693e-06,
                3.466325797900508e-07,
                2.1024336609843824e-07
            ],
            [
                3.927863875616689e-07,
                NaN,
                1.0677027427600627e-06,
                1.4449802095666915e-07,
                1.275190580890061e-07,
                3.4663278639892215e-07,
                5.715006514176113e-07,
                1.0677033791612137e-06,
                2.90231094723893e-06,
                7.338209805224048e-07
            ],
            [
                0.9999960330155093,
                0.9999978766215388,
                0.9999987121047854,
                0.9999910603005144,
                6.144173137126169e-06,
                0.9999980052707564,
                0.9999957771655538,
                0.9999945777823281,
                0.9999546021480853,
                1.5534983101602148e-06
            ],
            [
                3.53562422882756e-05,
                0.000295957135427911,
                0.999990483748327,
                4.006370652067535e-05,
                0.9999949062925818,
                0.9999938558268744,
                0.9999516743565149,
                4.785094494783494e-06,
                0.9999938558246758,
                7.484623620850474e-05
            ],
            [
                1.994729008145876e-06,
                2.5612834320470717e-06,
                8.315279285351409e-07,
                6.962257909842961e-06,
                2.902312331170226e-06,
                2.90231094723893e-06,
                NaN,
                5.043476486915964e-07,
                2.753568453792444e-05,
                NaN
            ],
            [
                2.2603242978778778e-06,
                2.9023126771227976e-06,
                1.9947297215043796e-06,
                2.9023119851781017e-06,
                2.902311639183378e-06,
                2.7535681254804434e-05,
                3.7266388398585725e-06,
                3.288749457469787e-06,
                8.939699501132077e-06,
                3.288748281295496e-06
            ],
            [
                3.927861066170637e-07,
                6.475945666051092e-07,
                3.466325797896173e-07,
                3.9278605979208185e-07,
                1.2098661162056318e-06,
                3.4663266243111764e-07,
                3.9278634073732336e-07,
                2.5612828213934817e-06,
                1.0677029973192638e-06,
                7.338212429582604e-07
            ],
            [
                5.715004470313855e-07,
                3.927862939126708e-07,
                1.0677032518785256e-06,
                1.5534975693933505e-06,
                1.6701421845361053e-05,
                1.3709573702822306e-06,
                1.209866260432471e-06,
                1.760343003481596e-06,
                2.561282210740037e-06,
                4.450852111148132e-07
            ],
            [
                8.315281267882195e-07,
                1.0677029973219343e-06,
                6.475947210046347e-07,
                9.422445939002803e-07,
                3.05902336324494e-07,
                3.05902336324494e-07,
                5.715003789046955e-07,
                4.450852111155216e-07,
                5.043472278322555e-07,
                1.0677026154774503e-06
            ],
            [
                3.0590237279085045e-07,
                0.9999967112493701,
                0.9999910603058416,
                0.9999981261248412,
                0.9999969105062917,
                3.4663274507713016e-07,
                0.9999970976869793,
                2.902312677150514e-06,
                0.9999934595596668,
                0.9999960330155115
            ],
            [
                1.4449796928021588e-07,
                4.4508494582405734e-07,
                1.3709578605729614e-06,
                3.0590237279032884e-07,
                1.2751902768612997e-07,
                6.962257079889302e-06,
                6.475950298011458e-07,
                2.561282821402217e-06,
                4.450850519403407e-07,
                8.939695238634211e-06
            ],
            [
                6.144173869603344e-06,
                2.902313023130843e-06,
                1.6701419854156377e-05,
                6.962259569750576e-06,
                1.760343003481596e-06,
                1.0677031245990084e-06,
                5.04347528446051e-07,
                1.5534981249697903e-06,
                0.9999945777810404,
                7.889260704968913e-06
            ],
            [
                1.7603440527222532e-06,
                4.539785782605375e-05,
                1.3007134666644292e-05,
                1.5534975693707442e-06,
                6.475945666051092e-07,
                9.422444815765128e-07,
                1.0129987357158383e-05,
                9.61024493707659e-05,
                2.9023133690425823e-06,
                2.5612831267202583e-06
            ],
            [
                3.05902190458764e-07,
                1.5534975693933505e-06,
                3.059021175261338e-07,
                6.475947210012481e-07,
                4.785094494783494e-06,
                6.962256249885085e-06,
                2.382370235933104e-07,
                4.450848927658745e-07,
                5.04347468323289e-07,
                7.889264466725156e-06
            ],
            [
                2.382368531929327e-07,
                1.9947292459265734e-06,
                4.450848927650143e-07,
                4.2228339479858295e-06,
                2.382369951932796e-07,
                7.338209805240734e-07,
                7.889261645427538e-06,
                2.7535697667202906e-05,
                6.475945666051092e-07,
                4.4508510499737865e-07
            ],
            [
                8.939693107093343e-06,
                5.4222183234485234e-06,
                2.2603234895176927e-06,
                2.5612812947508257e-06,
                1.0677026154730804e-06,
                1.2098656835224664e-06,
                4.785093924330255e-06,
                6.475947982037486e-07,
                5.715003107738556e-07,
                1.2098653950656417e-06
            ],
            [
                7.889261645355786e-06,
                1.0677026154730804e-06,
                1.2098656835136636e-06,
                1.7603434231705793e-06,
                1.99472900813862e-06,
                4.006371129615879e-05,
                5.04347528446051e-07,
                4.222833947960866e-06,
                0.7057850278370112,
                3.927862939126708e-07
            ],
            [
                0.9999869928746524,
                0.999985261019809,
                3.927862470899887e-07,
                5.715003789046955e-07,
                7.338207180838067e-07,
                5.04347528446051e-07,
                0.9999982396572071,
                0.9999843104465584,
                1.760342793638743e-06,
                0.9999877809240015
            ],
            [
                4.691168275606451e-08,
                6.023577065381482e-08,
                4.139940508508409e-08,
                4.691168275606451e-08,
                4.691160446380562e-08,
                6.825601283086733e-08,
                6.825608606172863e-08,
                4.6911677163762064e-08,
                1.275189972832538e-07,
                6.825604537781398e-08
            ],
            [
                7.338213304363436e-07,
                5.043474081993875e-07,
                4.222834954778007e-06,
                7.338210680021253e-07,
                5.04347528446051e-07,
                1.7603434231777837e-06,
                5.715005151606823e-07,
                4.450848927650143e-07,
                1.5534979397790343e-06,
                5.715003789046955e-07
            ],
            [
                0.9999997300422869,
                0.999999931743971,
                0.9999997300421904,
                0.9999992661787577,
                0.9999921107374271,
                0.9999992661792827,
                0.9999995549149482,
                0.9999998257021837,
                0.9999998461827322,
                0.9999997761971048
            ],
            [
                1.6373764721072816e-07,
                9.422443692390473e-07,
                2.7535697666401535e-05,
                1.3709572068354007e-06,
                5.144221366623174e-05,
                1.5534975693933505e-06,
                2.90231094723893e-06,
                2.5612819054028872e-06,
                NaN,
                4.2228329411708495e-06
            ],
            [
                0.9999921107383676,
                0.9999996533672137,
                0.9999949062937897,
                0.9999982396572077,
                6.475949526020042e-07,
                0.9999843104484599,
                0.9999921107336626,
                6.475945666051092e-07,
                0.999915188949517,
                1.6373764721072816e-07
            ],
            [
                1.994729483723626e-06,
                1.9947292459347367e-06,
                1.994729008145876e-06,
                8.315282259138311e-07,
                1.0677026154806063e-06,
                1.9947304348703948e-06,
                1.1478772231232203e-05,
                5.043476486915964e-07,
                1.1478770862735993e-05,
                8.315283250394546e-07
            ],
            [
                0.9999925887219048,
                0.9999852610145723,
                0.9999771720056179,
                0.9999955048178951,
                3.05902336324494e-07,
                1.6373766672973748e-07,
                0.9999960330126729,
                0.9999910603058475,
                0.9999869928653616,
                0.9998911030657672
            ],
            [
                0.9999916019259856,
                2.382368531929327e-07,
                0.9999785550567378,
                3.9278610661902853e-07,
                0.9999942280779168,
                0.9999785550567619,
                0.9999964991455882,
                0.9999852610110213,
                0.9999957771660569,
                3.4663274507713016e-07
            ],
            [
                1.994729008145876e-06,
                1.994730672675753e-06,
                1.0677024881980089e-06,
                3.4663249714612693e-07,
                6.475950298011458e-07,
                6.475949526020042e-07,
                2.902313023130843e-06,
                1.670141985446017e-05,
                6.475946438055299e-07,
                7.338208055664991e-07
            ],
            [
                5.043472879540142e-07,
                1.5534984953552536e-06,
                5.04347468323289e-07,
                2.902312677150514e-06,
                1.2098658277451275e-06,
                3.466326211113502e-07,
                1.9947301970972664e-06,
                1.2098653950692178e-06,
                2.699578740032504e-07,
                6.475946438055299e-07
            ],
            [
                4.222834954778007e-06,
                8.315284241650899e-07,
                1.8553914607267268e-07,
                4.450852641737424e-07,
                1.994730197090463e-06,
                3.927862002663297e-07,
                1.7603427936183298e-06,
                2.1024334103581732e-07,
                1.1253526937697666e-07,
                6.475947210046347e-07
            ],
            [
                4.4508515805735777e-07,
                NaN,
                3.466326211113502e-07,
                1.5534983101602148e-06,
                3.288747889284851e-06,
                7.889261645427538e-06,
                1.5534983101602148e-06,
                0.00017952792358181245,
                6.475949526020042e-07,
                2.382370235933104e-07
            ],
            [
                6.962255419931625e-06,
                2.260325106237323e-06,
                2.2603242978871282e-06,
                8.315280276546789e-07,
                4.785093924362895e-06,
                2.9023133690980155e-06,
                6.144174601991196e-06,
                1.7603436330259153e-06,
                7.338209805224048e-07,
                2.144495608378187e-05
            ],
            [
                5.043476486915964e-07,
                3.466325797896173e-07,
                3.466325797896173e-07,
                5.043472278322555e-07,
                3.9278605979534166e-07,
                2.382369951932796e-07,
                3.466327037553825e-07,
                5.04347408197782e-07,
                5.043472278322555e-07,
                5.71500719545698e-07
            ],
            [
                3.288749849498565e-06,
                9.422450431860582e-07,
                2.9023133690980155e-06,
                1.5534975693933505e-06,
                9.422443692489024e-07,
                1.994729483680993e-06,
                8.315278294038928e-07,
                1.2098655392662613e-06,
                6.475948753991907e-07,
                2.2603237589676295e-06
            ],
            [
                0.9999972735284363,
                0.9999994284994174,
                0.9999972735297327,
                0.9999892166904826,
                2.9023126771227976e-06,
                0.9999970976890582,
                0.9999991684715773,
                0.9999987901346068,
                0.9999969105040865,
                0.9999957771670646
            ],
            [
                0.9999969105051886,
                1.300713156582635e-05,
                0.9999516743680937,
                0.9999916019269751,
                0.9999981261243966,
                0.9999960330126748,
                0.00012339460442007728,
                0.9999969105059239,
                1.0129989772532511e-05,
                0.9999151889693225
            ],
            [
                8.939693107093343e-06,
                4.450851580555361e-07,
                1.5534984953510149e-06,
                1.3709573702778664e-06,
                6.605216831803618e-05,
                7.484620944504663e-05,
                4.785093924362895e-06,
                2.2603237589779086e-06,
                1.7603430034743913e-06,
                1.7603434231777837e-06
            ],
            [
                1.5534981249496567e-06,
                1.9947292459347367e-06,
                4.4508510499849186e-07,
                8.315280276607289e-07,
                9.422448185510695e-07,
                7.338213304243302e-07,
                1.3709578605542582e-06,
                7.889263526345123e-06,
                0.9999962733616093,
                2.561282516042282e-06
            ],
            [
                1.5534984953453635e-06,
                1.209865539295696e-06,
                1.0677028700363782e-06,
                9.422447062270609e-07,
                6.475950298011458e-07,
                8.315284241650899e-07,
                6.475951070002966e-07,
                3.05902263391829e-07,
                1.7603438428800754e-06,
                3.059022998581767e-07
            ],
            [
                0.9999852610233262,
                1.0677026154806063e-06,
                4.450852111155216e-07,
                0.9999930377445927,
                0.9999952149049393,
                3.05902190458764e-07,
                0.9999962733620533,
                0.9999970976887101,
                2.260324567337161e-06,
                0.9999930377462534
            ],
            [
                0.9999960330136178,
                0.0001584361603779452,
                5.8291251656508296e-05,
                0.9999546021370467,
                1.5534973842076057e-06,
                1.3007126914435202e-05,
                0.9999832985722125,
                1.0677026154806063e-06,
                0.3775406617944891,
                0.9999339478320995
            ],
            [
                1.9947301970972664e-06,
                8.315279285351409e-07,
                2.561282210740037e-06,
                1.2098658277489788e-06,
                2.561281294760143e-06,
                1.5534981249697903e-06,
                2.2603242978871282e-06,
                0.00037998448677216,
                8.939693107288474e-06,
                0.9999097196136172
            ],
            [
                2.3823682479292225e-07,
                5.715006514167015e-07,
                3.059022269250683e-07,
                9.422450431989127e-07,
                2.3823682479292225e-07,
                3.466326624336003e-07,
                3.05902336324494e-07,
                8.315279285351409e-07,
                5.04347468323289e-07,
                8.315282259117513e-07
            ],
            [
                7.338207180898968e-07,
                0.9999599362893784,
                0.9999485577686138,
                8.315277302841894e-07,
                NaN,
                2.75356878194421e-05,
                0.9999379494751267,
                0.9999452402444418,
                6.144175334468545e-06,
                0.9999706884619735
            ],
            [
                6.144176799334096e-06,
                7.338213304363436e-07,
                3.4663278639892215e-07,
                1.994730434879465e-06,
                1.0129990979547237e-05,
                NaN,
                NaN,
                1.3709576971316842e-06,
                2.1444940743225995e-05,
                6.475949525981759e-07
            ],
            [
                5.715006514151423e-07,
                2.1024336609724313e-07,
                1.8553910183607374e-07,
                NaN,
                3.927862002641863e-07,
                2.3823693839290317e-07,
                3.059023727894942e-07,
                2.3823685319244518e-07,
                2.382368247924618e-07,
                1.0677028700363782e-06
            ],
            [
                2.430024652792821e-05,
                2.1444945858485726e-05,
                6.144173869379821e-06,
                7.889265407255982e-06,
                6.962256249821764e-06,
                7.88926446679691e-06,
                2.4300252320622747e-05,
                3.120190021759579e-05,
                3.1201922533564516e-05,
                2.902312677137316e-06
            ],
            [
                7.48462005130053e-05,
                0.9999930377437691,
                0.000626334108194004,
                0.9999962733589436,
                0.00017952798773269405,
                0.999997273528758,
                0.9999969105055566,
                1.8925157265710765e-05,
                0.9999972735303865,
                9.610246084344956e-05
            ],
            [
                4.222834451382849e-06,
                3.9278634073732336e-07,
                1.067702870039777e-06,
                4.785096776468749e-06,
                3.726638839878908e-06,
                2.9023116391978967e-06,
                9.422448185534261e-07,
                1.3709568799879344e-06,
                1.209865683518615e-06,
                3.288747889284851e-06
            ],
            [
                0.9999955048162846,
                1.1253525596174225e-07,
                9.931202796993203e-08,
                1.0129994602895546e-05,
                0.9999982396561592,
                0.9999998461826589,
                0.9999985406241287,
                0.9999997463981333,
                0.9999981261241717,
                0.9999972735300559
            ],
            [
                5.043472879540142e-07,
                5.715005151606823e-07,
                2.1024334103505245e-07,
                2.699577774585891e-07,
                1.0677033791612137e-06,
                3.4663249714612693e-07,
                2.561281600086738e-06,
                1.5534981249697903e-06,
                5.715006514167015e-07,
                5.043476486915964e-07
            ],
            [
                4.2228339479858295e-06,
                2.144495864059426e-05,
                3.726639728348526e-06,
                5.715005151606823e-07,
                8.939698435560267e-06,
                4.222834451355964e-06,
                7.889261645355786e-06,
                3.726639728348526e-06,
                8.315284241650899e-07,
                0.00017952800899965663
            ],
            [
                1.760343213335281e-06,
                2.382370235933104e-07,
                8.315278294114555e-07,
                3.466326211113502e-07,
                3.927862002663297e-07,
                1.067703124601679e-06,
                1.5534971990169383e-06,
                2.9023119851899796e-06,
                2.9023119851899796e-06,
                5.043476486924565e-07
            ],
            [
                2.1024341622426268e-07,
                9.422450431954847e-07,
                1.0677032518785256e-06,
                0.9999151889188076,
                1.76034300345598e-06,
                1.7603430034743913e-06,
                6.475945666051092e-07,
                8.315281267706361e-07,
                1.0677032518814388e-06,
                2.9023119851781017e-06
            ],
            [
                6.475950298011458e-07,
                0.9999852610216355,
                7.889261645427538e-06,
                2.90231094723893e-06,
                1.0677033791612137e-06,
                4.222834954778007e-06,
                2.260325106237323e-06,
                0.00010889693531733128,
                1.9947292459347367e-06,
                2.260325106237323e-06
            ],
            [
                2.9023109472244114e-06,
                1.9947299593014888e-06,
                4.222835458175145e-06,
                2.2603248367656408e-06,
                1.5534975693933505e-06,
                1.0129992187253088e-05,
                1.7603427936263351e-06,
                2.1444950971601277e-05,
                2.902312677137316e-06,
                1.7603427936263351e-06
            ],
            [
                9.422444815765128e-07,
                2.5612819054133693e-06,
                2.260324567337161e-06,
                2.260324028427877e-06,
                5.422221555380179e-06,
                1.0129988564845378e-05,
                8.939696304311336e-06,
                3.726639284144195e-06,
                3.927860597945825e-07,
                4.450848927650143e-07
            ],
            [
                5.715003789046955e-07,
                7.338209805240734e-07,
                2.9023116391675407e-06,
                1.0677032518748838e-06,
                1.30071315662049e-05,
                1.9947306726594253e-06,
                1.5534981249697903e-06,
                1.0677029973192638e-06,
                1.5534975693979422e-06,
                5.715003789046955e-07
            ],
            [
                0.9999957771670739,
                0.9999986290424702,
                3.288748673376478e-06,
                0.9999974387184137,
                0.9999972735307097,
                2.3823690999323465e-07,
                0.9999975938965179,
                0.9999972735303871,
                0.9999949062962303,
                1.5534979397790343e-06
            ],
            [
                0.9999993524048931,
                0.9999706884616136,
                0.9999967112493732,
                0.9999942280772354,
                0.9999934595604449,
                1.3007126914435202e-05,
                0.9999771720029089,
                0.9998601779624487,
                0.9999978766217933,
                0.9999983463106126
            ],
            [
                8.481106160734935e-05,
                2.90231094723893e-06,
                1.7603432133136672e-06,
                2.2603234895289998e-06,
                2.90231094723893e-06,
                2.5612831267202583e-06,
                4.0063677865600476e-05,
                5.422219616265831e-06,
                8.939697369882888e-06,
                4.2228339479858295e-06
            ],
            [
                3.927860597945825e-07,
                2.9023119851781017e-06,
                8.315278294072958e-07,
                0.99973880967601,
                1.9947297215125433e-06,
                1.3709567165530083e-06,
                3.535626335815526e-05,
                0.9999975938982424,
                0.9999810748473001,
                1.994730197090463e-06
            ],
            [
                5.043474683220276e-07,
                0.9997388096034562,
                5.422220909009474e-06,
                2.1444943302181958e-05,
                3.12019039369228e-05,
                3.535623807260338e-05,
                7.338212429562581e-07,
                1.4738976701411704e-05,
                4.2228329411708495e-06,
                2.5612812947508257e-06
            ],
            [
                4.450852111155216e-07,
                NaN,
                2.6995784182183607e-07,
                4.4508515805735777e-07,
                1.8553919030858602e-07,
                3.927863875616689e-07,
                5.04347528446051e-07,
                3.9278610661902853e-07,
                2.699578096403948e-07,
                1.3709575337016483e-06
            ],
            [
                2.2603251062270446e-06,
                4.785096205651846e-06,
                1.5534984952111384e-06,
                3.535623781947785e-05,
                5.422221555296344e-06,
                4.222835458148261e-06,
                1.7603427936079236e-06,
                4.785095064601411e-06,
                2.5612822106654943e-06,
                1.9947292458930106e-06
            ],
            [
                0.9999982396565785,
                0.9999952149055161,
                1.5534975693979422e-06,
                0.9999983463104153,
                0.9999955048168198,
                0.9999925887174977,
                0.999999114843387,
                0.9999983463104153,
                0.9999991684721715,
                0.9999984465018764
            ],
            [
                2.10243290909724e-07,
                3.2887478892683997e-06,
                1.3709575337078829e-06,
                8.315277302841894e-07,
                1.0677031245623505e-06,
                7.338209805240734e-07,
                2.1024336609843824e-07,
                9.422449308673789e-07,
                7.338208930265102e-07,
                1.7603436330091044e-06
            ],
            [
                2.9023116392097746e-06,
                1.275190428875671e-07,
                8.315277302857965e-07,
                1.1253506814842375e-07,
                1.1253510839355284e-07,
                7.338210680021253e-07,
                2.561281600086738e-06,
                1.994729721518893e-06,
                1.0677026154806063e-06,
                3.7266397283908927e-06
            ],
            [
                2.260324836787226e-06,
                7.338211554783522e-07,
                7.338213304363436e-07,
                1.3709568799879344e-06,
                0.9999869928700321,
                3.2887506336086064e-06,
                1.3709573702822306e-06,
                1.2098662604291696e-06,
                3.726638839878908e-06,
                1.994730672668496e-06
            ],
            [
                2.1444945858485726e-05,
                2.260325375664839e-06,
                2.2603234895176927e-06,
                1.2098655392871682e-06,
                2.9023116391675407e-06,
                3.2887478892504536e-06,
                1.5534984953453635e-06,
                3.288749849477628e-06,
                9.4224425692559e-07,
                4.222832941193893e-06
            ]
        ]
    },
    {
        "q_id": "9120_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999962733589421,
                2.382369667929001e-07,
                0.999996910506659,
                0.9999997463980124,
                2.6995768091383957e-07,
                9.422444815792981e-07,
                1.444980209564556e-07,
                0.9999994956524717,
                2.6995768091310296e-07,
                7.338213304316717e-07
            ],
            [
                0.9999938558275993,
                0.9999994956524717,
                0.9999987901346055,
                0.9999984465015055,
                0.9999967112497616,
                0.9999983463108099,
                0.9999991684717747,
                0.9999980052695667,
                0.9999996533674204,
                0.9999983463108093
            ],
            [
                0.9999038975978435,
                0.9999995818814266,
                0.9999981261239472,
                0.999999946842125,
                0.9999960330131431,
                0.9999996940978096,
                1.637377057673536e-07,
                6.825604537781398e-08,
                0.9999998461827139,
                0.9999998461826406
            ],
            [
                0.9999998874648379,
                0.999998346310218,
                0.9999994631251243,
                0.9999916019269763,
                0.9999999397642868,
                6.825608606148807e-08,
                0.9999996940977003,
                0.9999999500627798,
                0.9999999273418962,
                6.023569884718319e-08
            ],
            [
                0.9999991684718734,
                3.059022269250683e-07,
                1.4449805540740185e-07,
                0.9999995262092163,
                0.9999999865595934,
                1.8553905760024476e-07,
                2.6995774527657245e-07,
                1.855391239544352e-07,
                0.9999832985841574,
                1.2751905808881762e-07
            ],
            [
                4.785095065204162e-06,
                0.9999991684716755,
                0.9999998724809723,
                1.5534979397790343e-06,
                0.9999999397642939,
                0.9999999397642293,
                0.9999999226557224,
                0.9999998942830611,
                0.999985261018053,
                1.0
            ],
            [
                2.102433410343832e-07,
                9.422450431989127e-07,
                8.764247451307293e-08,
                3.059021539909339e-07,
                8.7642516304188e-08,
                0.9999998144608319,
                4.450852111148132e-07,
                2.3823690999290963e-07,
                1.8553919030826963e-07,
                0.9999991684717744
            ],
            [
                0.999999939764215,
                0.9999999067049943,
                0.9999999358794173,
                0.9999999634651879,
                0.999998996986271,
                0.9999998874648112,
                5.04347287955046e-07,
                4.222833444590791e-06,
                0.99999994341373,
                0.9999999176674553
            ],
            [
                0.999997097687671,
                0.9999970976890544,
                0.9999990577555189,
                0.9999910602994412,
                0.9999980052693291,
                0.9999949062931779,
                3.4663249714612693e-07,
                0.9999995818814267,
                0.9999970976866335,
                0.9999930377437609
            ],
            [
                2.382370235933104e-07,
                0.9999999067050387,
                0.999999825702059,
                0.9999999006881023,
                0.9999996940978096,
                1.444980209564556e-07,
                0.9999995262093293,
                0.9999997463981031,
                0.9999997300423192,
                0.9999992188519491
            ],
            [
                0.9999952149043693,
                0.9999991684720718,
                0.9999991684720718,
                0.9999998874647575,
                0.9999997126315496,
                0.9999985406237796,
                0.9999975938965152,
                0.9999998362622552,
                0.9999999067050943,
                0.9999999611088904
            ],
            [
                6.475951069932288e-07,
                0.9999975938979482,
                3.0590226338282174e-07,
                0.9999997300420939,
                0.9999869928668892,
                0.9999646437452016,
                0.9999995818812272,
                0.9999983463100203,
                7.889260704732132e-06,
                9.422444815409489e-07
            ],
            [
                0.9999930377429249,
                0.999998346310218,
                1.7603425837702984e-06,
                2.9023133690188264e-06,
                0.9999955048189606,
                0.9999921107336567,
                1.855391681906175e-07,
                0.9999852610180489,
                3.4663262110945863e-07,
                0.9999921107383624
            ],
            [
                0.9999995818813268,
                5.715007195447234e-07,
                0.99999879013374,
                0.9999995818813268,
                2.6995787400282076e-07,
                0.9999996940976636,
                1.4449800373098553e-07,
                0.9999998724809268,
                0.999998712104324,
                0.9999724643123477
            ],
            [
                0.9999969105051855,
                0.9999991684717743,
                0.9999999586006048,
                0.9999964991455874,
                0.9999986290424668,
                0.9999998555019447,
                0.9999999226558237,
                0.9999999067050943,
                0.9999993916408184,
                0.9999991684719727
            ],
            [
                0.9999998942828973,
                0.9999995262094987,
                0.9999997617630617,
                0.9999999123575672,
                0.999999607213753,
                0.9999998802069159,
                0.9999998461826222,
                0.999999631011328,
                1.1478769494250387e-05,
                0.9999998942829477
            ],
            [
                1.0,
                0.9999960330131442,
                1.8553907971855875e-07,
                0.9999999123575882,
                0.9999998461826222,
                0.9999999317439872,
                0.9999989969860319,
                3.0590222692437275e-07,
                9.931195693628605e-08,
                7.73441946488886e-08
            ],
            [
                0.9999999226558423,
                0.9999999067050943,
                0.9999999500628631,
                0.9999977396759727,
                0.9999999273417922,
                0.9999998724809572,
                0.9999977396746259,
                2.3823688159291947e-07,
                0.9999957771665581,
                0.9999997300423192
            ],
            [
                0.9999869928762042,
                1.0,
                0.9999998802069731,
                0.9999999697115877,
                0.9999910603037038,
                0.9999999500627917,
                1.0,
                0.999999802494633,
                0.9999999697115516,
                1.275190276859705e-07
            ],
            [
                3.059022998576899e-07,
                8.315281267834927e-07,
                3.927862939126708e-07,
                5.715007195447234e-07,
                4.450852111120808e-07,
                4.450848927650143e-07,
                3.927860597935108e-07,
                1.0677033791583005e-06,
                5.715007195431641e-07,
                7.338207180864763e-07
            ],
            [
                1.2098659719524008e-06,
                4.785094494750855e-06,
                1.3709573702722555e-06,
                4.0063706517323215e-05,
                5.715004470313855e-07,
                6.475947982002148e-07,
                1.7603440527286572e-06,
                3.9278634073625165e-07,
                5.715005151606823e-07,
                1.760344052714248e-06
            ],
            [
                0.9999984465016906,
                0.9999975938976615,
                7.734416698849138e-08,
                0.9999996940977732,
                5.04347287955046e-07,
                0.9999910603005078,
                0.9999930377454153,
                0.999999352405125,
                1.8553916819032217e-07,
                0.9999996940978826
            ],
            [
                1.4449805540763184e-07,
                0.9999999123575777,
                5.043472879540142e-07,
                0.9999999500628095,
                1.1253506814842375e-07,
                1.6373766672973748e-07,
                2.382369667929001e-07,
                2.3823690999290963e-07,
                0.999999761763147,
                0.9999998362623724
            ],
            [
                0.9999993524048932,
                4.1399365603508136e-08,
                0.9999898700126572,
                0.9999885212359991,
                0.9999992188518559,
                0.9999994631251243,
                0.999999730042126,
                3.466327450756327e-07,
                0.9999998024945624,
                0.9999996940977367
            ],
            [
                0.9999996533674204,
                0.9999967112505442,
                0.9999995549149482,
                0.9999952149049391,
                0.9999998024947273,
                5.043476486915964e-07,
                2.1024341622426268e-07,
                0.9999992188517628,
                0.9999997126315153,
                2.69957906184239e-07
            ],
            [
                0.9999997126314468,
                0.999999653367255,
                0.9999921107345974,
                0.9999986290432842,
                0.9999724642958198,
                3.288748281329893e-06,
                0.9999994631247402,
                0.9999945777823254,
                0.9999957771670618,
                0.999997876622298
            ],
            [
                0.9999999006880668,
                1.0,
                0.9999981261248412,
                2.1024326584639497e-07,
                0.999999855502048,
                0.999997876622298,
                0.9999997300422548,
                3.9278634073625165e-07,
                2.1024326584582131e-07,
                0.9999989322972576
            ],
            [
                0.9999996743688975,
                0.9999756997477076,
                0.9999993524049705,
                0.9999999226558238,
                0.999999653367503,
                0.9999997126314126,
                0.9999992661791072,
                0.9999989969857931,
                0.9999785550490916,
                0.9999999611088674
            ],
            [
                0.999978555046504,
                6.023573475041126e-08,
                5.043474683220276e-07,
                6.144173869603344e-06,
                1.637377448057981e-07,
                1.855391239544352e-07,
                1.1253514863968147e-07,
                0.9999997126315154,
                0.9999997300421261,
                0.9999980052695663
            ],
            [
                0.9999852610215536,
                0.9999993106389548,
                7.338209805240734e-07,
                2.102434162245973e-07,
                1.275190580884987e-07,
                3.466327037539638e-07,
                0.9999785550413981,
                3.288749065423109e-06,
                8.315282259138311e-07,
                2.699576809143613e-07
            ],
            [
                0.9999996310115039,
                6.023578501491997e-08,
                4.4508510499737865e-07,
                4.450852111100568e-07,
                1.1253521571574156e-07,
                0.9999974387171812,
                1.2751901248454963e-07,
                0.9999904837471898,
                0.9999992661791949,
                0.9999999006880431
            ],
            [
                7.734416698815724e-08,
                0.9999992661791072,
                2.3823702359290413e-07,
                0.9999998144608983,
                0.999999802494586,
                3.059022998569248e-07,
                0.9999967112509383,
                0.9999998257021837,
                0.9999984465020612,
                0.9999999067050943
            ],
            [
                0.999999310639119,
                0.9999970976883621,
                4.450848927650143e-07,
                1.444980726324838e-07,
                5.1442213657997754e-05,
                0.9999999732705507,
                0.9999996310115479,
                0.9999996940976638,
                3.059022998576899e-07,
                0.9999977396751643
            ],
            [
                0.9999996533673378,
                0.9999977396765121,
                2.260324567302214e-06,
                0.999989870006617,
                3.466324971415162e-07,
                5.4222183234485234e-06,
                0.9999996940976638,
                0.9999962733602735,
                0.9999975938965142,
                2.2603237589676295e-06
            ],
            [
                0.9999981261246176,
                1.4449802095609418e-07,
                0.9999998874648379,
                0.999999872480942,
                3.927862002663297e-07,
                0.9999930377445887,
                0.9999998642567351,
                0.9999938558276128,
                0.9999981261241709,
                0.9999994956527722
            ],
            [
                1.0,
                0.9999998257021007,
                0.9999975938965144,
                0.9999999317440279,
                0.9999989969855535,
                0.9999985406234317,
                0.9999852610162854,
                0.9999998461826954,
                0.999996499144336,
                0.9999998362623137
            ],
            [
                0.9999995818813767,
                0.9999988634362899,
                0.9999991684720718,
                0.9999997761972116,
                3.9278624708775595e-07,
                0.9999998942829225,
                0.999997876621539,
                0.9999987121041714,
                0.9999997126313098,
                4.1399410020127234e-08
            ],
            [
                0.9999969105040807,
                0.9999785550439584,
                0.9999984465018757,
                0.9999938558268685,
                0.9999970976880163,
                6.825598842035714e-08,
                5.315789407666425e-08,
                0.9999997463980729,
                1.8553916819032217e-07,
                0.9999977396759736
            ],
            [
                0.999999855501979,
                0.9999999358793867,
                0.9999998802069587,
                0.9999999273417922,
                0.9999994284992807,
                0.9999997897566089,
                0.9999998024946801,
                0.9999997897567342,
                0.9999986290427937,
                0.9999999677581028
            ],
            [
                0.9999994631251883,
                0.9999957771665589,
                0.9999998874649051,
                0.9999999358794174,
                0.9999998642567028,
                0.9999999176675829,
                0.9999999006881259,
                0.9999997617631469,
                0.9999990577555189,
                0.9999998024945624
            ],
            [
                0.9999997761972116,
                0.999999894283061,
                0.9999998802069159,
                0.9999998144608319,
                3.059021904580685e-07,
                0.9999999358793714,
                2.3823690999290963e-07,
                0.9999994284994169,
                0.9999998802069159,
                9.931185038635267e-08
            ],
            [
                0.9999999559306102,
                0.9999999656787324,
                0.9999996940978096,
                0.9999996743686257,
                0.9999995549150013,
                0.9999999123574419,
                0.999995504816281,
                8.764247451307293e-08,
                0.9999990577555188,
                0.9999994956527123
            ],
            [
                1.0,
                0.9999999634651574,
                0.9999998461826038,
                0.999997097688364,
                0.9999991148432811,
                0.9999999358793715,
                0.9999998555020307,
                0.999999789756609,
                0.9999999273418182,
                0.9999993106391194
            ],
            [
                0.9999999611088627,
                0.9999998724809724,
                0.9999998362622943,
                0.9999999123574524,
                6.962257079465052e-06,
                0.9999999226557962,
                0.999999976411355,
                6.14417313680765e-06,
                1.760343213322473e-06,
                0.9999987901346055
            ],
            [
                2.6995774527718623e-07,
                3.4663278639892215e-07,
                1.1253512180925583e-07,
                3.466325797896173e-07,
                0.9999934595635578,
                2.6995790618469934e-07,
                2.3823690999290963e-07,
                0.999999495652592,
                0.9999987121050922,
                0.9999994631251883
            ],
            [
                0.9999998942830863,
                0.9999992661788448,
                0.9999994631251883,
                4.4508494582405734e-07,
                8.315279285351409e-07,
                1.637377448057981e-07,
                0.9999969105040809,
                0.9999999468421756,
                0.9999998144609203,
                1.1253512180925583e-07
            ],
            [
                3.4663249714325014e-07,
                0.9999910602994483,
                0.9999904837505862,
                5.043475885674441e-07,
                2.6995790618252024e-07,
                1.5534975693979422e-06,
                3.059023727894942e-07,
                7.338209805200689e-07,
                3.2887506335906595e-06,
                0.9999964991439181
            ],
            [
                0.9999998024946566,
                0.9999999434137301,
                0.9999987901344616,
                0.9999993106387083,
                0.9999993916407459,
                0.9999999500627917,
                0.9999999634651793,
                0.9999999176675338,
                0.999999789756659,
                0.9999998362623334
            ],
            [
                1.1253520230052635e-07,
                1.855391239539711e-07,
                7.734423152941018e-08,
                1.6373762769138607e-07,
                2.382369951932796e-07,
                0.9999978766210326,
                5.715004470313855e-07,
                0.9999978766222986,
                2.5612825160562587e-06,
                0.9999974387180963
            ],
            [
                0.9999993916406735,
                1.4449798650551755e-07,
                8.939693107093343e-06,
                0.9999996310116359,
                0.9999990577550697,
                0.9999998362622358,
                0.9999994956527122,
                0.9999999317439465,
                0.9999995818813269,
                0.9999999468421059
            ],
            [
                0.9999995818811275,
                0.9999999226557224,
                0.9999998642566219,
                0.9999999226557869,
                0.9999999677581144,
                0.9999999656786792,
                0.9999998724809875,
                0.9999996940977002,
                0.9999996072136593,
                0.9999999123574628
            ],
            [
                1.8553907971855875e-07,
                0.999999939764258,
                0.9999999006880786,
                0.9999999397643156,
                0.9999999226557224,
                0.9999999358793714,
                0.9999999434137974,
                0.9999999273418009,
                0.9999998024946095,
                0.9999998257021214
            ],
            [
                1.6373768624837685e-07,
                0.9999998874648245,
                6.023572038912295e-08,
                7.734421308914719e-08,
                0.9999982396574171,
                0.9999955048173548,
                0.9999988634358834,
                1.8553903548231313e-07,
                5.315788140287312e-08,
                5.043472879540142e-07
            ],
            [
                3.05902190458764e-07,
                1.6373764721072816e-07,
                1.3709576971425944e-06,
                5.422218323487975e-06,
                3.726637951387472e-06,
                4.785094494750855e-06,
                4.4508526417298334e-07,
                0.9999904837517197,
                1.5534984953510149e-06,
                2.3823702359290413e-07
            ],
            [
                0.9999998724809875,
                0.9999962733589399,
                0.9999977396757033,
                0.9999986290432843,
                3.9278634073732336e-07,
                4.450849988780466e-07,
                0.9999972735307063,
                0.9999985406230836,
                0.9999741325629541,
                1.6373766672973748e-07
            ],
            [
                0.9999955048184241,
                6.475951069961737e-07,
                1.760343423160973e-06,
                0.9999992661786697,
                1.0677024881887838e-06,
                3.4663266243308805e-07,
                0.999998239656578,
                0.9999910602994421,
                1.855390354818069e-07,
                2.1024326584582131e-07
            ],
            [
                1.760343423160973e-06,
                7.73441946488886e-08,
                0.9999989969861514,
                0.9999977396757036,
                1.8553907971855875e-07,
                0.9999756997535193,
                0.9999992188515766,
                0.9999980052700418,
                0.9999151889897943,
                4.450851580540182e-07
            ],
            [
                0.9999998874647977,
                3.9278605979534166e-07,
                2.1024336609843824e-07,
                0.9999997300423191,
                0.9999960330150344,
                0.9999038975745108,
                1.125352291309328e-07,
                0.9999724643122878,
                0.9999970976883623,
                0.9999892166865111
            ],
            [
                0.9999999358794096,
                1.1253513522447425e-07,
                3.653479467066246e-08,
                0.9999998874648515,
                0.9999998461826772,
                2.6995768091383957e-07,
                0.9999999500628215,
                0.9999916019289768,
                0.9999999273417662,
                1.0
            ],
            [
                0.9999998555019619,
                0.9999938558246694,
                0.9999969105059222,
                0.9999998802069302,
                0.9999999123575151,
                0.9999998802069017,
                0.9999996743688586,
                0.9999999006880786,
                0.999999887464811,
                0.999994577781679
            ],
            [
                0.999999554914736,
                0.999999730042287,
                3.466327037548308e-07,
                0.9999942280792881,
                2.3823688159291947e-07,
                0.9999993524054337,
                2.3823693839290317e-07,
                0.9999997897565839,
                0.9999985406232581,
                2.1024334103505245e-07
            ],
            [
                3.653482080235082e-08,
                0.9999983463096263,
                1.275190276859705e-07,
                3.0590237279032884e-07,
                9.931199245292204e-08,
                3.9278638755992735e-07,
                0.9999996743688199,
                3.9278615344178325e-07,
                5.04347528446051e-07,
                1.1253514863968147e-07
            ],
            [
                0.9999975938979483,
                0.9999999697115516,
                0.9999998724809267,
                0.9999998257021837,
                0.9999998802069017,
                0.9999989322967485,
                1.2751910369275402e-07,
                0.9999997897567342,
                1.0,
                0.9999999468421947
            ],
            [
                0.999999894282935,
                2.1024336609843824e-07,
                2.699577774585891e-07,
                2.260324567337161e-06,
                0.9999999006881497,
                3.059022269250683e-07,
                0.9999999358793714,
                0.9999977396751643,
                0.9999998024946566,
                0.9999989969855535
            ],
            [
                2.260325106237323e-06,
                1.209866260432471e-06,
                0.9999960330131412,
                5.422218969895357e-06,
                1.8553919030858602e-07,
                3.0590237279085045e-07,
                5.715003107767143e-07,
                0.9999945777803869,
                2.260325106237323e-06,
                1.0
            ],
            [
                3.466326211113502e-07,
                0.9999921107402404,
                0.9999898700041968,
                8.764240137829087e-08,
                8.764243272157922e-08,
                3.05902190458764e-07,
                9.422445939054222e-07,
                0.9999991148433863,
                1.4449798650476187e-07,
                0.9999955048173529
            ],
            [
                5.043476486915964e-07,
                1.6373776432509826e-07,
                4.450852111148132e-07,
                1.444980209564556e-07,
                3.059022269250683e-07,
                7.338209805224048e-07,
                5.043475885674441e-07,
                9.931195693628605e-08,
                1.4449798650551755e-07,
                2.3823693839290317e-07
            ],
            [
                2.382369951932796e-07,
                3.4663249714612693e-07,
                0.9999945777816815,
                0.9999996533672137,
                0.9999999732705507,
                0.9999993106387083,
                0.9999994284993489,
                0.9999990577551819,
                0.9999962733620503,
                0.9999417087277357
            ],
            [
                0.999999825702059,
                2.1024331597262577e-07,
                6.825601283086733e-08,
                0.9999998942829728,
                7.338210680021253e-07,
                1.0,
                0.9999999123574419,
                0.9999999611088719,
                0.9999998724809116,
                0.9999995818811773
            ],
            [
                0.9999999273417922,
                0.9999991684719726,
                0.9999998942830358,
                0.9999997761970515,
                0.9999998461826038,
                0.9999999006880786,
                0.9999999067050053,
                2.1024331597262577e-07,
                0.9999996310114599,
                0.9999997126314125
            ],
            [
                1.6373764721072816e-07,
                0.9999810748562833,
                0.9999996072136593,
                2.10243290909724e-07,
                0.9999998642566219,
                0.9999998874649051,
                0.9999992661788448,
                0.9999995549150543,
                0.9999997126313784,
                0.9999999559306206
            ],
            [
                9.422448185435711e-07,
                3.4663249714451116e-07,
                2.6995771309523475e-07,
                2.6995777745711594e-07,
                9.422449308716635e-07,
                1.1253513522391131e-07,
                8.764240137829087e-08,
                2.102433410343832e-07,
                8.315277302788957e-07,
                3.059022998569248e-07
            ],
            [
                0.999999825702163,
                6.475946438042047e-07,
                0.999998005269328,
                0.9999991148427533,
                7.338207180864763e-07,
                0.9999869928653502,
                0.9999984465028016,
                0.9999992661791071,
                0.999999554914842,
                0.9999998942829602
            ],
            [
                0.9999998942830737,
                0.999999218851949,
                0.999998712104478,
                0.9999995818810776,
                3.535625493182252e-05,
                0.9999992661787573,
                0.9999998555019446,
                0.9999994631247402,
                0.9999999123575568,
                0.9999996533672963
            ],
            [
                2.3823690999160957e-07,
                1.0677026154619133e-06,
                9.931186222482958e-08,
                1.8553903548231313e-07,
                3.46632497145457e-07,
                1.8553905759969634e-07,
                5.04347348075149e-07,
                6.475947210031623e-07,
                8.315279285351409e-07,
                1.1253521571574156e-07
            ],
            [
                0.9999996310116358,
                0.9999998642566866,
                0.9999996743688199,
                0.9999998024946095,
                0.9999999273418095,
                0.9999997300422869,
                0.9999998802068873,
                0.9999995818814266,
                2.1024331597262577e-07,
                0.9999997897566089
            ],
            [
                1.1253506814797596e-07,
                0.9999981261250643,
                0.9999992661791073,
                3.9278638756099906e-07,
                3.059023363231725e-07,
                0.9999996072137062,
                2.102433159721477e-07,
                5.043476486902204e-07,
                8.315281267834927e-07,
                3.0590222692437275e-07
            ],
            [
                1.637377448057981e-07,
                0.9999949062937887,
                1.0,
                1.637377448057981e-07,
                0.9999998362623332,
                7.734416698849138e-08,
                0.9999999434137907,
                1.8553907971813685e-07,
                0.9999998362622552,
                0.9999930377429341
            ],
            [
                0.9999996533675031,
                0.9999998144609645,
                0.9999996940977003,
                0.9999810748450347,
                0.9999998555020481,
                0.9999151889691399,
                1.855391239544352e-07,
                0.9999996743686257,
                0.9999999434137435,
                0.9999995549150013
            ],
            [
                5.315789407666425e-08,
                4.450849988811838e-07,
                3.4663249714612693e-07,
                4.450849988798682e-07,
                3.059022998569248e-07,
                1.444980209564556e-07,
                9.422445939002803e-07,
                1.1253513522447425e-07,
                5.71500651413193e-07,
                0.9999998461826771
            ],
            [
                0.9999998724808964,
                1.0,
                0.9999998461826405,
                0.9999999530883955,
                0.9999999656786834,
                1.855391239547094e-07,
                0.9999998724809267,
                2.102433159721477e-07,
                0.9999999123575987,
                0.9999994956527122
            ],
            [
                6.825608606148807e-08,
                0.9999998874647977,
                0.9999999226557776,
                0.9999999611088487,
                0.9999997300421583,
                0.9999998362623723,
                1.2751908849167202e-07,
                0.999999653367255,
                0.9999999530883675,
                0.9999998642567028
            ],
            [
                6.825606165129312e-08,
                1.4449807263287805e-07,
                6.023572038912295e-08,
                9.931195693628605e-08,
                9.422445939032799e-07,
                1.275190276853036e-07,
                1.6373776432481905e-07,
                7.73441946488886e-08,
                2.699577774585891e-07,
                1.444980726324838e-07
            ],
            [
                0.9999977396748949,
                0.9999999067050498,
                0.9999988634358833,
                0.9999978766205262,
                0.9999038975655558,
                0.999986992874653,
                0.9999997897565838,
                0.9999998461826954,
                0.9999999123574942,
                5.04347528446051e-07
            ],
            [
                4.450852641717689e-07,
                1.7603438428740716e-06,
                0.9999987121047847,
                0.9999989322972578,
                2.2603251062450327e-06,
                5.422217030781934e-06,
                1.3709576971463352e-06,
                1.2098661162056318e-06,
                0.9999983463110061,
                0.9999980052702795
            ],
            [
                0.9999986290421399,
                1.637377057673536e-07,
                0.9999921107345988,
                0.9999756997651056,
                0.9999986290421402,
                0.9999977396765118,
                0.9999339478478283,
                0.9999869928762062,
                0.9999724643188183,
                1.1253521571574156e-07
            ],
            [
                0.9999994284992807,
                0.9999996940976638,
                0.999999057755631,
                0.9999999397642653,
                0.9999999697115588,
                0.9999998942829477,
                0.9999934595596641,
                0.9999999434138109,
                0.9999998461826038,
                0.9999997897566089
            ],
            [
                2.3823702359290413e-07,
                2.6995787400208416e-07,
                0.9999995262093292,
                1.637377643243723e-07,
                0.9999998362623138,
                0.9999998802069731,
                1.6373776432509826e-07,
                0.9999989322975122,
                1.1253520230052635e-07,
                0.9999993106387082
            ],
            [
                0.999996711251721,
                0.9999990577551818,
                0.9999981261248408,
                5.315781169679188e-08,
                1.6373768624837685e-07,
                0.99999963101146,
                0.999999814460876,
                1.8553907971855875e-07,
                2.102433410343832e-07,
                3.466327450756327e-07
            ],
            [
                0.9999998874647441,
                0.9999996743688198,
                0.9999998942829981,
                0.9999999559305628,
                0.9999999468421883,
                0.9999998461826038,
                0.9999999317439221,
                0.9999999611088766,
                0.999999814460854,
                0.9999999530883564
            ],
            [
                1.3709568799919866e-06,
                0.999996711251328,
                1.370957860576702e-06,
                1.9947299593078385e-06,
                2.902312677150514e-06,
                1.4738989000181669e-05,
                3.0590219045914655e-07,
                0.9999964991451703,
                0.9999974387168744,
                9.931193325852072e-08
            ],
            [
                0.9999997897565588,
                2.3823690999290963e-07,
                0.999999730042094,
                0.9999999067051499,
                3.466326211105621e-07,
                3.46632497145457e-07,
                0.9999999358794021,
                0.9999999123575464,
                9.931186222523604e-08,
                0.999997739675434
            ],
            [
                5.3157830707696514e-08,
                0.9999997300421904,
                4.450852111148132e-07,
                0.9999964991468411,
                7.734418542875216e-08,
                2.1024336609843824e-07,
                0.9999988634366963,
                4.4508494582314646e-07,
                4.139936066832438e-08,
                2.3823699519143784e-07
            ],
            [
                0.9999970976873265,
                1.6373770576776313e-07,
                0.9999970976887086,
                8.315281267861397e-07,
                0.9999980052698048,
                0.999996273361608,
                0.9999977396757042,
                2.561282516042282e-06,
                0.9999983463108095,
                0.9999916019239727
            ],
            [
                6.023573475041126e-08,
                0.9999970976890551,
                2.1024339116168358e-07,
                2.10243290909724e-07,
                1.1253514863968147e-07,
                3.653479467066246e-08,
                0.9999832985801913,
                0.9999957771675699,
                1.6373774480479287e-07,
                1.275190276859705e-07
            ],
            [
                0.9999993524048931,
                0.9999999697115515,
                0.9999832985702084,
                0.9999999434137841,
                0.9999999468421313,
                0.999999730042094,
                0.9999998362622358,
                0.9999998874648782,
                0.9999998724809116,
                0.9999877809254595
            ],
            [
                0.9999991148433867,
                0.9999974387165699,
                0.9999988634358834,
                1.275190580884987e-07,
                1.444979692800516e-07,
                2.102434412871794e-07,
                0.9999998362623138,
                0.9999997897565588,
                0.9999994956525319,
                1.637377057673536e-07
            ],
            [
                9.931196877517082e-08,
                0.9999756997506397,
                0.9999999611088904,
                1.2751908849167202e-07,
                1.275190276859705e-07,
                0.9999995262095551,
                0.9999999530883508,
                0.9999910603037098,
                0.9999998362622357,
                0.9999993916409634
            ],
            [
                0.9999972735307067,
                0.9999998024946801,
                0.9999999397642939,
                1.8553905760062447e-07,
                1.6373776432509826e-07,
                0.9999999500627798,
                6.475950298011458e-07,
                0.9999999559305576,
                0.9999999358793791,
                0.9999999317439627
            ],
            [
                2.6995771309523475e-07,
                5.043474683220276e-07,
                0.999993037740435,
                0.9999952149043676,
                1.855391239544352e-07,
                7.338210680002898e-07,
                9.931195693628605e-08,
                0.9999997761971849,
                3.9278610661902853e-07,
                0.9999998555019446
            ],
            [
                0.999999922655787,
                7.3382080556433e-07,
                0.9999999273418355,
                0.9999990577551818,
                0.9999999273418789,
                0.9999999397642436,
                3.466327450765785e-07,
                0.999999894282935,
                0.9999852610180443,
                9.931193325852072e-08
            ],
            [
                0.9999989322971302,
                0.9999996940978096,
                0.9999967112505452,
                0.9999869928761964,
                0.9999921107346005,
                3.927860597945825e-07,
                0.9999998257021837,
                0.9999997897565838,
                0.9999798543116211,
                0.9999995262093293
            ],
            [
                0.9999981261241704,
                0.9999952149037977,
                0.9999998144609645,
                8.315279285351409e-07,
                0.9999987121043243,
                2.6995780963846126e-07,
                0.9999930377462445,
                0.9999967112501519,
                0.999999653367503,
                0.9999967112505438
            ],
            [
                5.043472879540142e-07,
                2.6995768091383957e-07,
                1.9947294837154625e-06,
                3.05902190458764e-07,
                5.04347408197782e-07,
                3.4663266243308805e-07,
                2.3823696679230424e-07,
                3.059023363231725e-07,
                6.475951069985296e-07,
                2.6995774527657245e-07
            ],
            [
                0.9999998144609203,
                0.9999994631249961,
                0.999997273529731,
                0.9999994284994851,
                0.9999997463981938,
                0.9999989322967487,
                0.9999997463982241,
                0.9999999500628274,
                0.9999992661786699,
                0.9999999500627798
            ],
            [
                0.9999974387174853,
                1.4449803818215767e-07,
                0.9999942280799863,
                0.999999927341801,
                0.999954602142388,
                0.9999999358793485,
                0.9999417087556575,
                0.9999998555020307,
                0.9999981261239471,
                0.9999998942830862
            ],
            [
                0.9999991684721709,
                0.9999994631248682,
                0.999999391641036,
                0.9999989969855536,
                0.999995777165049,
                0.9999999123574732,
                0.9999993916408909,
                0.9999982396574169,
                3.9278634073625165e-07,
                0.9999988634364255
            ],
            [
                0.9999785550516355,
                0.9999996533674617,
                0.9999998802069159,
                0.9999999123575359,
                1.2751905808881762e-07,
                0.9999999559306259,
                0.9999861539971354,
                0.9999986290432844,
                0.9999904837505916,
                0.9999996533672137
            ],
            [
                0.9999992661789322,
                1.27519088491875e-07,
                2.10243290909724e-07,
                1.8925155009767892e-05,
                0.9999994956524717,
                1.1253506814842375e-07,
                0.9999993524048932,
                2.6995784182140636e-07,
                5.04347287955046e-07,
                0.9999993106387081
            ],
            [
                0.999999428499485,
                0.9999993916408185,
                0.9999993916408185,
                0.9999967112497602,
                0.9999985406237798,
                0.9999998461826038,
                0.9999994631247402,
                0.9999996940976639,
                0.9999996743687034,
                0.999999391641036
            ],
            [
                0.9999987121043246,
                0.9999949062943954,
                0.9999982396559484,
                0.9999984465018756,
                3.466325384661554e-07,
                6.023569884718319e-08,
                1.637377643243723e-07,
                7.734423152941018e-08,
                0.9999988634364254,
                9.931190958076104e-08
            ],
            [
                1.99473067264854e-06,
                1.0,
                0.9999999468421947,
                0.9999999067051388,
                0.9999999226557317,
                0.9999999273418788,
                0.999999864256719,
                0.9999999358794173,
                0.9999999500628036,
                0.9999998942830737
            ],
            [
                0.9999997463981333,
                0.9999997300421583,
                0.9999990577555187,
                0.9999999816291358,
                0.9999996533672965,
                0.9999999176674945,
                0.9999999067051388,
                0.9999998362622552,
                0.9999991684719727,
                7.734421308914719e-08
            ],
            [
                2.1024326584639497e-07,
                0.9999998257020798,
                0.9999989969855535,
                2.1024336609843824e-07,
                2.3823693839290317e-07,
                0.9999998257021421,
                1.8553905760062447e-07,
                0.9999999176675829,
                0.9999996072138935,
                5.04347287955046e-07
            ],
            [
                2.902312677137316e-06,
                3.927862939126708e-07,
                1.2751908849167202e-07,
                3.05902226923399e-07,
                1.0677032518785256e-06,
                2.260325375664839e-06,
                2.6995774527657245e-07,
                1.8553905760024476e-07,
                1.2098658277451275e-06,
                1.8553910183607374e-07
            ],
            [
                0.999999789756684,
                0.9999999586006146,
                0.9999999677581567,
                0.9999999715466392,
                0.9999999317439708,
                0.9999970976866341,
                0.9999998642567189,
                0.9999995262094422,
                3.927862002654366e-07,
                0.9999038975763035
            ],
            [
                4.450849458218309e-07,
                8.315279285351409e-07,
                5.715005832886879e-07,
                2.1024331597262577e-07,
                1.0677028700363782e-06,
                2.260324567302214e-06,
                2.260324836776948e-06,
                7.3382080556433e-07,
                2.3823690999160957e-07,
                1.760343213322473e-06
            ],
            [
                0.9999991148432811,
                1.0,
                0.9999998257020799,
                0.9999996072136593,
                0.9999996743688199,
                0.9999997463981334,
                0.9999990577555188,
                0.9999996533674618,
                0.99999976176309,
                0.9999996940976638
            ],
            [
                6.475951069961737e-07,
                0.9999994631249963,
                0.9998204720579069,
                0.9999994956525318,
                0.9999998874647307,
                0.9999986290421402,
                0.9999967112505442,
                0.9999999530883508,
                0.9999992661789323,
                0.9999997463981032
            ],
            [
                0.9999546021477209,
                0.9999810748427564,
                0.9999910603068968,
                3.2887502415767434e-06,
                0.9999945777784496,
                0.9999687980775512,
                1.0677027427624903e-06,
                0.9999993106388724,
                0.9999980052700413,
                0.9999980052707551
            ],
            [
                0.9999999732705379,
                0.9999987121043243,
                2.2603237589779086e-06,
                6.475951070002966e-07,
                0.9999885212346616,
                2.699577774585891e-07,
                0.9999996743687033,
                4.222835458148261e-06,
                0.9999990577550695,
                1.553498124964492e-06
            ],
            [
                0.9999999434137636,
                0.9999999559305839,
                1.0,
                0.9999996743687422,
                0.9999999067050388,
                0.999999953088334,
                0.9999999006881377,
                0.9999999358794097,
                0.9999999611088766,
                0.999999963465201
            ],
            [
                2.3823690999290963e-07,
                4.691162124067829e-08,
                0.9999930377445854,
                1.8553916819032217e-07,
                0.9999998362622943,
                0.9999984465022461,
                1.1253512180925583e-07,
                0.999999495652592,
                2.102434162245973e-07,
                2.1024336609843824e-07
            ],
            [
                0.9999998802069017,
                0.9999998642566866,
                0.9999999468420996,
                5.422221555380179e-06,
                0.9999998144609646,
                4.222832941193893e-06,
                0.9999982396574171,
                0.9999997300420939,
                0.9999998642566219,
                0.9999999397643154
            ],
            [
                0.9999997761971583,
                0.999968798096175,
                1.1253513522447425e-07,
                0.9999921107374299,
                1.6373770576776313e-07,
                0.999996273359386,
                0.999993037742097,
                2.1024339116082313e-07,
                0.999999554914789,
                0.9999998362623529
            ],
            [
                0.9999999500627857,
                0.9999994956523515,
                0.9999998874649318,
                0.999999746398073,
                0.9999998942828973,
                0.9999997300422548,
                0.9999999559305732,
                0.9999998024947273,
                3.0590237279032884e-07,
                1.3709576971242028e-06
            ],
            [
                2.1024344128584085e-07,
                0.9999991148427535,
                8.315281267800897e-07,
                1.209865539274514e-06,
                3.9278610661545617e-07,
                6.475948753991907e-07,
                0.9999546021314838,
                8.315283250343497e-07,
                3.4663249714325014e-07,
                4.785094494716039e-06
            ],
            [
                0.9999997463981939,
                0.9999996940977002,
                0.9999999067050832,
                1.2751899728286965e-07,
                0.9999999358794479,
                0.9999998144609645,
                1.1253520230052635e-07,
                0.9999996072136594,
                0.999997739675165,
                0.999999581881277
            ]
        ]
    },
    {
        "q_id": "9821_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            42,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            88,
            90,
            91,
            92,
            93,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                6.144177531767002e-06,
                1.0129987357287368e-05,
                1.4738989000422955e-05,
                2.430024073461624e-05,
                8.481103128838341e-05,
                2.1444945858485726e-05,
                0.00043055698927498215,
                0.9999938558239593,
                3.288749065406658e-06,
                6.605213682591808e-05
            ],
            [
                0.9999999317439221,
                1.0,
                0.9999999611089182,
                1.0,
                0.9999999500628393,
                0.9999999123575568,
                0.9999999397642437,
                0.9999999586006542,
                0.9999999006879958,
                0.9999999434137165
            ],
            [
                0.9999995818810777,
                0.9999996310113721,
                0.9999975938976619,
                0.9999996533674617,
                0.9999852610110692,
                1.0,
                1.0,
                0.9999988634360188,
                0.9999994284996896,
                0.9999995549150014
            ],
            [
                0.9999997463981939,
                0.9999998942829098,
                1.1253508156363576e-07,
                1.3709575337159875e-06,
                8.764254764780641e-08,
                9.931185038635267e-08,
                2.1024339116168358e-07,
                0.9999999317440116,
                0.9999997463981636,
                1.275190580890061e-07
            ],
            [
                0.9999998802069445,
                1.0,
                0.9999999273418269,
                0.9999997463980125,
                1.0,
                0.999998863436561,
                0.9999999434137637,
                1.7603440527334603e-06,
                0.9999999067050832,
                1.0
            ],
            [
                0.999999814460832,
                0.9999995549148422,
                0.9999998642566543,
                0.9999998362622748,
                0.9999998461826038,
                0.999999730042287,
                0.9999995818813768,
                0.9999984465028022,
                0.9999996533672963,
                0.999999846182604
            ],
            [
                6.475947210031623e-07,
                9.422442569315887e-07,
                2.382370235933104e-07,
                1.994729721518893e-06,
                4.450850519403407e-07,
                1.2098661162056318e-06,
                1.8553905760062447e-07,
                3.9278610661902853e-07,
                6.475947210046347e-07,
                4.222834954801051e-06
            ],
            [
                0.9999996072137531,
                0.9999998257021213,
                0.9999998024947273,
                0.9999998461827139,
                0.9999997761970781,
                0.9999994284995531,
                0.9999997897567091,
                0.9999997761971848,
                0.9999998257021837,
                0.999999730042287
            ],
            [
                6.47595107001401e-07,
                9.931186222523604e-08,
                9.422445939054222e-07,
                5.715006514176113e-07,
                3.9278629391427843e-07,
                2.3823690999323465e-07,
                4.450852641737424e-07,
                2.10243290909724e-07,
                2.3823682479292225e-07,
                7.338208055680009e-07
            ],
            [
                0.9999999226558238,
                0.9999999176675338,
                0.9999997617631469,
                0.9999998362622358,
                0.9999999006879957,
                1.0,
                0.9999999317439708,
                0.9999999500628036,
                0.9999999358793485,
                0.9999998555020135
            ],
            [
                0.9999952149055068,
                0.00023050677073686453,
                1.4738987243692646e-05,
                9.422448185534261e-07,
                8.481105151953705e-05,
                3.120192253651574e-05,
                1.0129993395447374e-05,
                5.4222202626709005e-06,
                6.47595107001401e-07,
                0.0001233946191424094
            ],
            [
                0.9999998362623334,
                0.9999998257021838,
                0.9999975938985243,
                0.9999998874649051,
                0.9999998144608098,
                0.9999998362623529,
                0.999999631011548,
                0.9999998874648917,
                0.9999998874649185,
                0.9999998257020591
            ],
            [
                3.4663262111182307e-07,
                2.1024336609874897e-07,
                0.9999998461826405,
                1.8553910183674878e-07,
                1.855391681906175e-07,
                0.9999998942830233,
                0.999999958600585,
                0.9999999500628095,
                3.05902336324494e-07,
                9.93120161310289e-08
            ],
            [
                3.4663278639892215e-07,
                1.8553914607267268e-07,
                1.3709572068553509e-06,
                4.4508515805735777e-07,
                8.764244316973974e-08,
                4.450852111155216e-07,
                2.699577774585891e-07,
                1.209865539298447e-06,
                2.699578740032504e-07,
                1.9947299593078385e-06
            ],
            [
                0.9999996072138935,
                0.9999997300422226,
                0.9999996940978096,
                0.9999994956524118,
                0.9999998724808964,
                0.999999814460876,
                0.9999993524053564,
                0.9999998642566543,
                0.9999995549151074,
                0.9999998362622748
            ],
            [
                0.9999994631250604,
                0.9999996533675031,
                0.9999990577549576,
                0.9999994631250604,
                0.9999991148433868,
                0.9999989322968765,
                0.9999995262093293,
                0.9999995262096119,
                0.9999988634357483,
                0.9999996072136595
            ],
            [
                0.9999998802069444,
                0.9999998362623138,
                0.9999999586006393,
                0.9999996940977368,
                0.9999998362622553,
                0.9999997126314126,
                0.9999999006880195,
                0.9999992661792821,
                0.9999999067050388,
                0.9999989969859121
            ],
            [
                0.9999998257022045,
                0.9999998724809723,
                0.9999999067050054,
                0.9999997463981033,
                0.9999996533674617,
                0.9999998942829225,
                0.9999998642567351,
                0.9999998802069587,
                0.9999995549147893,
                0.9999997463982242
            ],
            [
                0.9999996310116358,
                0.9999989969862709,
                0.9999969105051878,
                0.9999997126315153,
                0.9999994284993489,
                0.9999997300422226,
                0.9999998024946095,
                0.9999994631247403,
                0.9999996072139403,
                0.9999997897565588
            ],
            [
                0.9999998942830485,
                0.9999998802069587,
                0.9999997761970516,
                0.9999998555019447,
                0.9999997463980126,
                0.9999995818812272,
                0.9999998362623723,
                0.9999994956523516,
                0.9999998461826589,
                0.9999998144609203
            ],
            [
                0.9999998461827139,
                0.9999998724808963,
                0.9999997897566592,
                1.0,
                1.0,
                0.9999998257020591,
                0.999999900687984,
                1.0,
                0.9999998724809116,
                0.9999998362622553
            ],
            [
                0.9999998362622553,
                0.9999998362623334,
                0.9999989969856733,
                0.999999789756609,
                0.9999998874649051,
                0.9999998362622943,
                0.9999993524052794,
                0.9999998802069444,
                0.9999998724809419,
                0.9999998555020309
            ],
            [
                9.610240357303448e-05,
                8.939699501416646e-06,
                8.315278294114555e-07,
                2.699578096403948e-07,
                4.450850519403407e-07,
                3.4663278639892215e-07,
                2.5612819054133693e-06,
                2.1024339116168358e-07,
                3.927863875616689e-07,
                1.3709576971463352e-06
            ],
            [
                0.9999999176675632,
                0.9999996743688586,
                1.0,
                0.9999998555019446,
                1.0,
                0.9999998874647306,
                0.999999943413811,
                0.9999999317440198,
                0.9999998724809875,
                0.9999998024947273
            ],
            [
                1.4738981972564636e-05,
                1.9947297215125433e-06,
                1.3709570434178922e-06,
                4.222832437798974e-06,
                5.715007195447234e-07,
                4.785095065232451e-06,
                1.3709568799919866e-06,
                5.043473480777865e-07,
                6.475951069985296e-07,
                1.5534971990126997e-06
            ],
            [
                2.699577452775239e-07,
                1.637376862489725e-07,
                0.9999999434137975,
                0.9999997126314127,
                0.9999999397642868,
                0.9999999006880431,
                1.209865539298447e-06,
                5.043475885696228e-07,
                2.3823685319320354e-07,
                1.6373774480605869e-07
            ],
            [
                0.9999974387168769,
                0.9999977396762456,
                0.9999992188517627,
                0.9999988634364254,
                0.0007096705566623147,
                0.9999990577556318,
                0.9999981261243952,
                0.9999984465015055,
                0.9999996072136594,
                0.9999974387168761
            ],
            [
                0.9999999006881023,
                8.315277302857965e-07,
                0.9999999123575359,
                0.9999910602994421,
                0.9999998461826222,
                0.9999998874648112,
                0.9999998642566219,
                0.9999998942829098,
                0.9999999123575151,
                0.9999997617631184
            ],
            [
                1.5534971990126997e-06,
                2.90231094723893e-06,
                2.9023116392097746e-06,
                3.7266383956509585e-06,
                7.889264466868659e-06,
                1.6701423836262173e-05,
                8.939699501416646e-06,
                4.006367786720367e-05,
                3.72663883989755e-06,
                4.785094494811783e-06
            ],
            [
                0.9999994284992809,
                0.9999969105066622,
                0.9999988634366976,
                0.999983298576358,
                0.9999996310115481,
                0.9999986290426314,
                0.9999995262092167,
                0.9999989322971317,
                0.9999992661787578,
                0.9999991148427537
            ],
            [
                0.9999995549147362,
                0.9999996072137063,
                0.999999631011372,
                0.9999996940977733,
                0.9999988634358846,
                1.209865539295696e-06,
                0.9999985406243018,
                0.9999992188512975,
                0.999999352405357,
                0.9999992661792827
            ],
            [
                2.6995790618469934e-07,
                3.927863875616689e-07,
                2.3823696679327928e-07,
                2.699578740032504e-07,
                2.3823693839325527e-07,
                9.422450432030903e-07,
                2.3823690999323465e-07,
                5.043475885696228e-07,
                1.0677027427624903e-06,
                6.47595107001401e-07
            ],
            [
                7.338209805240734e-07,
                1.3709567165617364e-06,
                5.04347287955046e-07,
                3.466326211113502e-07,
                2.9023112932296107e-06,
                9.422443692574719e-07,
                7.338213304363436e-07,
                3.4663266243308805e-07,
                1.0677026154827912e-06,
                1.209865539298447e-06
            ],
            [
                8.76424013786396e-08,
                9.93120161310289e-08,
                1.8553919030858602e-07,
                6.825608606172863e-08,
                6.825598028392069e-08,
                0.9999996072136595,
                7.734428685047173e-08,
                0.9999990577554069,
                7.734426841017797e-08,
                7.338212429594283e-07
            ],
            [
                0.9999998642566866,
                0.999999789756609,
                0.999999846182604,
                0.999999789756659,
                0.9999998144609424,
                0.9999999176675436,
                0.9999998024946802,
                0.9999997463980125,
                0.9999998362622944,
                0.9999997897566341
            ],
            [
                0.9999990577552945,
                0.9999994284994854,
                0.9999977396765132,
                0.999998126124172,
                0.9999997463980126,
                0.9999996072136127,
                0.9999995262093296,
                0.999993037742135,
                0.9999996743688976,
                0.9999573525423555
            ],
            [
                0.9999949062931835,
                1.4449807263312446e-07,
                6.962255419931625e-06,
                1.9947301970972664e-06,
                7.889261645427538e-06,
                0.9999996743687035,
                1.0,
                0.9999989969859124,
                1.012999218776902e-05,
                3.927863407379485e-07
            ],
            [
                0.9999999006880075,
                0.9999998724809877,
                0.9999991148427538,
                0.9999996940976639,
                0.9999991148428592,
                0.9999996310115479,
                0.999999631011636,
                0.9999995549151076,
                0.9999994956525922,
                0.9999995262094424
            ],
            [
                0.9999989969857926,
                0.9999996940977732,
                0.9999987121052458,
                0.9999995262094986,
                0.9999997761970248,
                0.9999995262092164,
                0.9999998555019447,
                0.9999998724810027,
                0.9999995549150545,
                0.999999855502048
            ],
            [
                0.9999998461827322,
                0.9999998802069016,
                0.9999998802069302,
                0.9999998942829729,
                0.9999999530883787,
                0.9999999317439627,
                0.9999998024946095,
                0.9999987901347498,
                0.9999962733598294,
                0.9999998724809267
            ],
            [
                6.962257079775324e-06,
                6.144174601935314e-06,
                9.422449308673789e-07,
                1.14787708624228e-05,
                4.785094494750855e-06,
                1.0129987357158383e-05,
                4.222834451254188e-06,
                3.7266401726173067e-06,
                2.2603237589779086e-06,
                1.3709567165461505e-06
            ],
            [
                0.9999997761970516,
                0.9999996310114164,
                0.9999997126313784,
                0.9999997617629767,
                0.9999997617630901,
                0.9999996533672553,
                0.9999996743687811,
                0.9999997463981033,
                0.9999996940978462,
                0.9999997300421906
            ],
            [
                0.999999872480942,
                0.9999999067050165,
                0.9999998942829855,
                0.9999998642567028,
                0.999999789756609,
                0.9999999123575881,
                0.9999996533672139,
                0.9999998461827323,
                2.382368531929327e-07,
                0.9999978766210325
            ],
            [
                0.9999998874648112,
                0.9999999468421124,
                0.9999999176675829,
                0.9999997617631186,
                0.9999998942828972,
                0.9999997897565839,
                0.9999997126313098,
                0.9999997761970248,
                0.9999998942830485,
                0.9999989969860319
            ],
            [
                1.2098658277451275e-06,
                1.0677032518785256e-06,
                1.3709567165530083e-06,
                6.475949526020042e-07,
                2.5612819054028872e-06,
                3.726638839878908e-06,
                9.422449308748773e-07,
                4.539789029616496e-05,
                1.5534971990126997e-06,
                7.338209805224048e-07
            ],
            [
                1.0,
                1.0,
                0.999999894282935,
                0.9999999123575672,
                0.9999999067050165,
                0.999999906705061,
                0.9999999358793944,
                0.9999999067051055,
                0.999999894282935,
                0.9999998461827322
            ],
            [
                0.9999996310114161,
                0.9999998257021837,
                0.9999995818813768,
                0.999999814460832,
                0.9999997617630334,
                0.9999998461826405,
                0.9999997897567092,
                0.9999998362622553,
                0.9999997300422228,
                0.9999998144609646
            ],
            [
                0.9999998257021837,
                0.9999999123574942,
                0.9999999434137233,
                0.9999997463981939,
                0.9999999176675338,
                0.9999999067049943,
                0.9999999273418961,
                0.9999997126314811,
                0.9999997126314469,
                0.9999999176674651
            ],
            [
                2.699576809143613e-07,
                1.067703124601679e-06,
                1.5534973842076057e-06,
                1.2098659719788098e-06,
                3.0590237279085045e-07,
                0.9999994284997578,
                5.715005832895975e-07,
                7.33821330437595e-07,
                0.9999993524052023,
                1.0677029973219343e-06
            ],
            [
                0.9999999006881378,
                0.9999996072136127,
                0.999999953088334,
                0.9999998942829602,
                0.9999998257021628,
                0.9999999468421124,
                0.9999999226558054,
                0.9999998802069302,
                0.9999996072137064,
                0.9999999067050498
            ],
            [
                0.9999993106387083,
                0.999998446502802,
                0.9999987121041709,
                0.9999998257020798,
                0.9999957771650504,
                0.9999994631248683,
                0.9999985406236057,
                0.9999992188516698,
                0.9999991684720718,
                0.9999999317439627
            ],
            [
                0.9999861539988368,
                0.9999969105055624,
                0.9999983463100228,
                0.999998996985793,
                2.5612819053586272e-06,
                0.9999869928685282,
                0.9999982396572088,
                0.006692850072955687,
                0.9999982396561605,
                4.006368263437623e-05
            ],
            [
                0.9999996533672966,
                0.9999998642567028,
                7.734416698849138e-08,
                3.4663274507713016e-07,
                0.9999997761972117,
                0.9999995262092164,
                3.059022269254856e-07,
                2.1024336609874897e-07,
                5.043475885696228e-07,
                4.450850519403407e-07
            ],
            [
                0.9999998024946802,
                0.9999996533673791,
                0.9999996940978462,
                0.9999998362623334,
                0.9999995262095551,
                0.9999994284994169,
                0.9999998874649318,
                0.9999997617631753,
                0.9999998555019963,
                0.9999993524053564
            ],
            [
                5.715002426486762e-07,
                1.7603436330259153e-06,
                1.994729721518893e-06,
                6.47595107001401e-07,
                5.715003107767143e-07,
                1.0129989772412744e-05,
                7.338207180898968e-07,
                5.043475284468537e-07,
                8.315278294114555e-07,
                1.7603436330091044e-06
            ],
            [
                4.785096206076165e-06,
                5.144223819846456e-05,
                1.2098659719757836e-06,
                9.422449308774482e-07,
                3.120190765829341e-05,
                0.00026119043453447834,
                5.422217030781934e-06,
                7.338209805240734e-07,
                3.120191137762131e-05,
                3.7266397283908927e-06
            ],
            [
                0.9999991684722703,
                0.9999999123575256,
                2.1024326584582131e-07,
                0.9999990577549579,
                0.9999994956524119,
                0.9999957771645465,
                1.2098656835224664e-06,
                0.9999989969861519,
                0.9999988634358842,
                3.059022998576899e-07
            ],
            [
                0.9999998144608983,
                0.9999998642567351,
                0.9999999273418183,
                0.999999917667475,
                0.9999999067050499,
                0.9999997126313441,
                0.9999999006880076,
                0.999999864256719,
                0.9999999530883396,
                0.9999997126315154
            ],
            [
                1.125351083940518e-07,
                1.0677024882009222e-06,
                0.999996273360279,
                1.7603438428848787e-06,
                1.1478772231086046e-05,
                2.6995771309523475e-07,
                1.370957860576702e-06,
                3.059022269250683e-07,
                3.726638839878908e-06,
                0.999996499143925
            ],
            [
                0.9999999176674749,
                1.0,
                0.9999999586005851,
                0.9999999226557409,
                0.9999999434137637,
                0.9999998802068873,
                0.9999996533674204,
                0.9999999123575881,
                0.9999999226557132,
                0.9999997761971048
            ],
            [
                3.466326624336003e-07,
                3.0590219045914655e-07,
                1.6373766672994222e-07,
                1.4449796928021588e-07,
                1.4449795205472734e-07,
                1.855390576008354e-07,
                1.0677029973219343e-06,
                1.1253522913127183e-07,
                1.6373766672994222e-07,
                1.275190124846946e-07
            ],
            [
                7.338207180898968e-07,
                0.9999967112493738,
                5.04347287955046e-07,
                1.4449802095666915e-07,
                0.9999990577556318,
                2.3823688159291947e-07,
                0.9999822214482194,
                9.931186222523604e-08,
                2.2603251062450327e-06,
                1.0677026154806063e-06
            ],
            [
                0.9999998555019274,
                0.9999998362622943,
                0.9999998362622358,
                0.9999998144609645,
                0.9999998257020799,
                0.9999998874648112,
                0.9999998144608762,
                0.9999998257021838,
                0.9999998362622358,
                0.9999998362622747
            ],
            [
                0.9999997761970515,
                0.9999999273418269,
                0.999999653367255,
                0.9999998942829602,
                0.9999999634651661,
                0.999999922655787,
                0.999999922655787,
                0.9999999067051055,
                0.999999310638626,
                0.9999998362622943
            ],
            [
                0.999999310638626,
                0.9999999358793332,
                1.553497754577351e-06,
                0.9999989969855536,
                0.9999998724809267,
                0.9999998724808964,
                0.9999989322972578,
                1.0,
                3.726639284125553e-06,
                0.9999981261252878
            ],
            [
                2.1024339116168358e-07,
                3.9278629391427843e-07,
                1.8553910183674878e-07,
                5.043474082012222e-07,
                1.8553914607267268e-07,
                5.715006514176113e-07,
                3.4663249714612693e-07,
                0.9999997126313099,
                9.93120161310289e-08,
                6.47595107001401e-07
            ],
            [
                0.9999997617630333,
                0.9999998024947272,
                0.9999997300422547,
                0.9999998802069159,
                0.9999997761971315,
                0.9999998024946566,
                0.9999998024947037,
                0.9999998461826772,
                0.9999997761970516,
                0.9999997761970516
            ],
            [
                7.734428685047173e-08,
                2.10243290909963e-07,
                1.4449798650569826e-07,
                8.764253720001207e-08,
                1.855391239547094e-07,
                7.73442776303243e-08,
                4.4508515805735777e-07,
                7.734414854823498e-08,
                1.8553910183674878e-07,
                0.9999998724809571
            ],
            [
                1.0,
                0.9999999397642508,
                1.0,
                0.9999999530883675,
                0.9999999500628631,
                0.9999997463981939,
                1.0,
                0.9999999123575046,
                1.0,
                0.9999997897567092
            ],
            [
                1.5534973842030142e-06,
                1.9947299593014888e-06,
                3.2887502415243994e-06,
                4.78509278348926e-06,
                1.7603432133032607e-06,
                1.0129989772412744e-05,
                1.2098659719757836e-06,
                3.466325797900508e-07,
                2.6995784182183607e-07,
                3.7266383955882547e-06
            ],
            [
                7.88926070489716e-06,
                2.7535700949523498e-05,
                1.3007126914245925e-05,
                4.539786323732447e-05,
                7.889266347715168e-06,
                4.785092783454444e-06,
                7.88926070489716e-06,
                3.288749457469787e-06,
                1.4738989000422955e-05,
                5.422219616228845e-06
            ],
            [
                0.9999998874648112,
                0.9999998642566543,
                0.9999999067050388,
                0.9999999123575359,
                1.0,
                0.9999998942829981,
                0.9999999067050054,
                0.9999998555020136,
                0.9999998874649318,
                0.9999998942829099
            ],
            [
                0.9999992661792826,
                0.9999989322971319,
                0.9999977396765142,
                0.9999995262095556,
                0.999999391640964,
                0.9999972735300638,
                0.999999526209612,
                0.9999993106389554,
                0.9999994631249965,
                0.9999992188519498
            ],
            [
                0.9999998642566542,
                0.999999894282935,
                0.9999998555019275,
                0.9999998362623723,
                0.9999998362623723,
                0.9999998802068873,
                0.999999814460854,
                0.9999998942830485,
                0.9999998555019447,
                0.9999998257021422
            ],
            [
                0.9999999586006146,
                1.0,
                0.9999999530883228,
                0.9999997617631469,
                1.0,
                0.99999992265575,
                0.9999999434137637,
                0.9999999067050832,
                1.0,
                1.0
            ],
            [
                4.222835458148261e-06,
                0.00010889687038985114,
                1.5534979397677313e-06,
                0.9999991148427535,
                0.9999977396754348,
                1.994729483723626e-06,
                0.9999992661786701,
                3.1201907657271834e-05,
                1.1478765389368729e-05,
                1.760343003481596e-06
            ],
            [
                9.422442569315887e-07,
                2.260324836776948e-06,
                8.315278294072958e-07,
                1.1478766757561534e-05,
                3.12019039369228e-05,
                2.9023133690821773e-06,
                8.939700566801578e-06,
                2.902310947208574e-06,
                1.0677032518785256e-06,
                2.5612825160562587e-06
            ],
            [
                0.9999999468420997,
                0.9999999434138042,
                0.9999999273417923,
                0.9999999273418182,
                0.9999999397643083,
                0.9999998257021214,
                0.9999998461826222,
                0.9999998362622552,
                0.9999999123575464,
                1.0
            ],
            [
                0.9999997617630334,
                0.9999998144609425,
                0.9999998257021838,
                0.9999998144608983,
                0.9999998874647977,
                0.9999997126313098,
                0.9999997897566089,
                0.9999997761970516,
                0.9999998555020481,
                0.9999996072136126
            ],
            [
                3.059022269254856e-07,
                4.450850519409479e-07,
                2.699577452775239e-07,
                9.422450432030903e-07,
                3.9278629391427843e-07,
                1.3709575337159875e-06,
                0.9999998724809267,
                1.4449800373118268e-07,
                2.1024334103581732e-07,
                1.855391239547094e-07
            ],
            [
                0.9999957771670633,
                4.450850519403407e-07,
                0.9999996072138467,
                0.9999985406243018,
                0.9999985406234317,
                1.3709570434122812e-06,
                0.9999987121043247,
                7.338208055680009e-07,
                0.9999975938973765,
                9.422442569334097e-07
            ],
            [
                3.466325797900508e-07,
                3.466326624336003e-07,
                4.4508515805735777e-07,
                0.9999998362622552,
                3.0590219045914655e-07,
                1.4449795205472734e-07,
                3.466325384682834e-07,
                8.764254764780641e-08,
                8.7642526752214e-08,
                1.4449796928021588e-07
            ],
            [
                0.9999996310115479,
                0.9999999176674651,
                0.9999997761972116,
                0.9999996743687034,
                0.9999998461826406,
                0.999999674368781,
                0.9999998362622553,
                0.9999998362623138,
                0.9999998802069731,
                0.9999998724810027
            ],
            [
                0.999999218851484,
                0.9999996743686259,
                0.9999995549148954,
                0.9999990577550701,
                0.9999981261252888,
                0.9999994631248686,
                0.9999985406243027,
                0.999999712631447,
                0.9999996533672966,
                0.9999994956526523
            ],
            [
                0.9999998024946802,
                0.9999993916410361,
                0.999999802494586,
                0.999999168472171,
                0.9999999434137368,
                0.9999998461827322,
                0.9999999530883396,
                0.9999998724809268,
                0.9999996072137532,
                0.9999998555019275
            ],
            [
                0.9999998024946095,
                0.9999997761972116,
                0.9999998802069874,
                0.999999802494633,
                1.0,
                0.999999631011328,
                0.9999998461826038,
                0.9999997463982243,
                0.9999997617630901,
                0.9999998144609424
            ],
            [
                0.9999994284996215,
                0.9999967112493686,
                0.9999970976873245,
                0.999999168472072,
                1.6373770576776313e-07,
                0.9999980052702796,
                0.9999861540004185,
                2.699577774585891e-07,
                0.9999991148433867,
                0.9999995818811773
            ],
            [
                3.466325797900508e-07,
                7.338212429594283e-07,
                0.9999998024946801,
                0.9999983463108093,
                1.0,
                5.043475284468537e-07,
                2.3823685319320354e-07,
                0.999999789756609,
                3.9278620026686556e-07,
                9.931187406410953e-08
            ],
            [
                0.9999999397643156,
                0.9999998724809877,
                0.999999917667475,
                0.9999999317439058,
                0.999999939764258,
                0.9999999468421567,
                0.9999993916410364,
                0.9999998874649051,
                0.9999999273418183,
                0.999999864256719
            ],
            [
                1.0,
                0.9999999500628155,
                1.0,
                1.0,
                1.0,
                0.9999999358794249,
                0.9999999226558423,
                1.0,
                0.9999992188514835,
                0.9999999434137637
            ],
            [
                0.9999998144608983,
                0.999999958600585,
                0.9999999530883563,
                0.9999998555019619,
                0.9999996743686259,
                7.33821330437595e-07,
                0.9999998461827323,
                1.0,
                0.9999997897565589,
                0.9999999123575047
            ],
            [
                0.9999998144609646,
                0.9999994284995533,
                0.9999996940976275,
                0.9999998257021214,
                0.9999998257021214,
                0.9999998461826589,
                0.9999998461826222,
                0.9999995262094988,
                0.9999990577549575,
                0.9999998874647977
            ],
            [
                9.422442569315887e-07,
                1.9947301970972664e-06,
                1.209866260432471e-06,
                2.561282516066741e-06,
                7.338212429582604e-07,
                6.475946438055299e-07,
                8.315284241650899e-07,
                1.3709576971463352e-06,
                7.338208930460318e-07,
                9.422448185534261e-07
            ],
            [
                0.9999998874647977,
                1.0,
                0.9999999530883843,
                0.9999998724809571,
                0.9999999468421947,
                0.9999998362622747,
                1.0,
                0.9999994284995534,
                0.9999999176674749,
                0.9999997126314469
            ],
            [
                3.9278610661902853e-07,
                3.4663274507713016e-07,
                3.05902263391829e-07,
                1.0,
                1.27519088491875e-07,
                2.382369951932796e-07,
                0.9999999434137907,
                4.4508515805735777e-07,
                1.2751908849167202e-07,
                1.855391239547094e-07
            ],
            [
                5.71500515161527e-07,
                2.1024334103581732e-07,
                2.1024339116168358e-07,
                5.043475885696228e-07,
                2.1444948415296896e-05,
                7.734416698849138e-08,
                3.4663278639892215e-07,
                4.450851049991497e-07,
                4.4508515805735777e-07,
                1.1253525596174225e-07
            ],
            [
                7.338211554783522e-07,
                1.4449800373098553e-07,
                3.927862470899887e-07,
                1.9947297215125433e-06,
                8.315284241650899e-07,
                6.475949526020042e-07,
                3.059022269250683e-07,
                6.475947210012481e-07,
                3.059021175261338e-07,
                3.927860597945825e-07
            ],
            [
                2.9023116392097746e-06,
                2.561281294760143e-06,
                0.00013982210758122318,
                0.9999998642566219,
                1.3709567165617364e-06,
                5.829128640345195e-05,
                1.760342793638743e-06,
                6.47594952603035e-07,
                2.6995790618469934e-07,
                8.315278294114555e-07
            ],
            [
                0.9999998461826772,
                0.999999846182714,
                0.9999998942830737,
                0.9999998802069731,
                0.9999999176674749,
                0.9999999067049832,
                0.9999998362622357,
                0.9999998642566704,
                0.9999999273418443,
                0.9999997300421904
            ],
            [
                0.9999992188512982,
                0.9999987901341737,
                0.9999987121043261,
                0.00010889688339134737,
                0.9999992661788453,
                0.9999996743686648,
                0.9999992661787581,
                0.9999993916408914,
                0.9999991684719735,
                2.382368247924618e-07
            ],
            [
                2.260323758987159e-06,
                1.3709570434219446e-06,
                2.2603242978943238e-06,
                7.889259764517575e-06,
                3.2887494574832472e-06,
                2.5612834320563895e-06,
                1.3709567165617364e-06,
                6.962255419931625e-06,
                1.9947304348862686e-06,
                2.3823688159291947e-07
            ],
            [
                2.699576809143613e-07,
                0.9999969105059257,
                0.9999989322973852,
                0.9999996072137064,
                0.9999998802069302,
                0.9999998144609424,
                0.9999998802069302,
                0.9999991684721714,
                0.9999904837506286,
                0.9999998555020309
            ],
            [
                1.0,
                0.9999999273417662,
                0.9999999530883675,
                0.9999997300423191,
                0.9999998874647843,
                0.999999887464811,
                0.9999999358793867,
                0.9999998144608098,
                1.0,
                0.9999996533672137
            ],
            [
                8.939696304311336e-06,
                5.422218969895357e-06,
                4.006370652067535e-05,
                0.0013250223491237157,
                NaN,
                0.00037998444130376283,
                6.962255419931625e-06,
                0.9999942280806693,
                0.9999989969857936,
                1.3007133116732079e-05
            ],
            [
                1.2751899728311609e-07,
                5.715002426486762e-07,
                3.466326624336003e-07,
                4.785092783519724e-06,
                1.760342793638743e-06,
                6.023573475041126e-08,
                1.0677032518814388e-06,
                5.715003789046955e-07,
                1.4449807263312446e-07,
                1.067703124601679e-06
            ],
            [
                0.9999982396563699,
                6.1441767993788005e-06,
                0.0006263340798114444,
                3.05902263391829e-07,
                0.9999991684718741,
                1.4449807263312446e-07,
                1.209865827752005e-06,
                5.043475284468537e-07,
                5.043475885696228e-07,
                3.9278605979534166e-07
            ],
            [
                0.9999995549150545,
                3.2887506336235617e-06,
                0.9999988634361552,
                0.9999991684720722,
                0.9999996072138002,
                0.9999996310113283,
                0.9999996310113282,
                0.9999904837517344,
                0.9999975938965157,
                0.9999987901346066
            ],
            [
                9.931187406410953e-08,
                1.1253525596174225e-07,
                1.6373764721091427e-07,
                2.1024339116168358e-07,
                6.023579219579052e-08,
                0.9999996940977731,
                7.734428685047173e-08,
                0.9999998024946095,
                7.734425919002834e-08,
                0.9999998362623528
            ],
            [
                7.338208055664991e-07,
                4.450852641717689e-07,
                6.144172404738491e-06,
                1.1253516205489029e-07,
                8.315282259138311e-07,
                3.927862470899887e-07,
                3.9278610661822475e-07,
                4.4508494582405734e-07,
                2.5612831267202583e-06,
                5.04347468323289e-07
            ],
            [
                5.71500719545698e-07,
                7.338212429594283e-07,
                1.5534984953552536e-06,
                3.466326624336003e-07,
                7.338212429594283e-07,
                7.338210680032098e-07,
                5.043475885696228e-07,
                3.0590219045914655e-07,
                3.05902263391829e-07,
                4.450851049991497e-07
            ],
            [
                0.9999997897566089,
                0.9999998257021214,
                0.9999998802069017,
                0.9999993106387084,
                0.9999998461826406,
                0.9999999123575464,
                0.9999998362622358,
                0.9999998144608319,
                0.9999997617631469,
                0.9999996940978462
            ],
            [
                0.9999999123575672,
                0.9999998362622552,
                0.9999996940977367,
                0.9999998362623723,
                0.9999998874647977,
                0.9999998461826405,
                0.9999998642567028,
                0.9999997897566841,
                0.9999998555020309,
                0.9999998724810027
            ],
            [
                1.209865683518615e-06,
                1.4449807263312446e-07,
                2.6995784182140636e-07,
                1.9947304348332037e-06,
                8.315282259117513e-07,
                1.8553919030858602e-07,
                1.5534975693933505e-06,
                1.2751902768612997e-07,
                3.4663262110945863e-07,
                1.6373770576776313e-07
            ],
            [
                2.699578096403948e-07,
                5.715002426486762e-07,
                1.3709575337159875e-06,
                0.9999997463980428,
                2.699578740032504e-07,
                6.47594952603035e-07,
                2.382368815932174e-07,
                1.3709575337159875e-06,
                1.1253524254650944e-07,
                0.9999993106391193
            ],
            [
                6.144172404738491e-06,
                4.785093924389007e-06,
                1.275190732904469e-07,
                3.288749849529972e-06,
                3.466325797900508e-07,
                1.2098656835252174e-06,
                2.699577130960941e-07,
                1.4449807263312446e-07,
                6.47595107001401e-07,
                7.338212429594283e-07
            ],
            [
                0.9999998874647307,
                0.9999998724809267,
                0.9999995262093294,
                0.9999998362623334,
                0.9999993916411088,
                0.9999994284996213,
                0.9999997617631754,
                0.999999864256719,
                0.9999994631250604,
                0.9999998802068873
            ],
            [
                2.1024336609874897e-07,
                7.33821330437595e-07,
                9.422442569334097e-07,
                5.422220909009474e-06,
                6.475950298021765e-07,
                5.715006514176113e-07,
                8.315277302857965e-07,
                3.927862470905692e-07,
                1.9947292459406333e-06,
                2.2603251061458426e-06
            ],
            [
                0.9999995262093857,
                0.9999996533672137,
                0.999999802494586,
                0.9999998874648917,
                0.999999864256719,
                0.9999999006880668,
                0.9999998642566219,
                0.9999998555019963,
                0.9999998555019447,
                0.9999992661788449
            ]
        ]
    },
    {
        "q_id": "9819_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                9.931187406410953e-08,
                8.764254764749753e-08,
                2.102433159721477e-07,
                8.764247451307293e-08,
                6.023574911170301e-08,
                8.764255809528314e-08,
                3.6534807736504303e-08,
                9.931199245292204e-08,
                4.450850519403407e-07,
                1.4449798650551755e-07
            ],
            [
                6.825597214718257e-08,
                8.315280276626197e-07,
                1.5534971990169383e-06,
                7.734424074954332e-08,
                1.275190276859705e-07,
                4.139938534423022e-08,
                6.825598842065202e-08,
                7.734416698849138e-08,
                1.9947297215125433e-06,
                1.444979692800516e-07
            ],
            [
                0.9999999358793791,
                0.9999999500628155,
                0.9999999123574523,
                0.9999997300422547,
                0.9999998461826589,
                0.999999825702059,
                0.999996910505554,
                0.999999967758126,
                0.9999999123574628,
                0.9999999500628155
            ],
            [
                3.2887506336086064e-06,
                2.3823685319244518e-07,
                2.3823682479181176e-07,
                0.9999987901343169,
                1.444979692797559e-07,
                7.338212429582604e-07,
                9.422447062270609e-07,
                1.994730672668496e-06,
                2.699576809143613e-07,
                1.6373774480605869e-07
            ],
            [
                0.999999927341853,
                0.9999998144608319,
                0.9999993106388725,
                0.999999974890015,
                0.9999998802069302,
                0.9999998724808964,
                0.9999999559305995,
                0.9999999468421502,
                0.9999995262092727,
                1.0
            ],
            [
                0.9999993106387903,
                0.9999998144609645,
                0.9999996072136593,
                0.9999996072136593,
                0.9999994956525919,
                0.9999997897566089,
                0.9999998362623528,
                0.999999789756634,
                0.9999998555019963,
                0.9999997897565587
            ],
            [
                3.927862002663297e-07,
                7.338212429537553e-07,
                4.450848927637999e-07,
                1.9947297215043796e-06,
                3.4663253846718004e-07,
                5.715003789046955e-07,
                3.9278610661902853e-07,
                0.9999925887192527,
                5.715003107715166e-07,
                2.6995771309523475e-07
            ],
            [
                2.382369951932796e-07,
                2.6995784182140636e-07,
                1.6373764721072816e-07,
                2.6995784182183607e-07,
                6.475949526020042e-07,
                1.6373766672888118e-07,
                3.927862470899887e-07,
                1.6373770576776313e-07,
                2.6995774527718623e-07,
                5.715005151606823e-07
            ],
            [
                0.9999991684720716,
                2.3823696679327928e-07,
                0.9999938558254027,
                2.1024339116168358e-07,
                2.3823682479292225e-07,
                1.275190580890061e-07,
                1.1253508156363576e-07,
                1.275191036933194e-07,
                8.764254764780641e-08,
                8.7642558095602e-08
            ],
            [
                0.9999999677581413,
                0.999998996985912,
                0.9999996072138466,
                0.9999999611088904,
                0.9999993524050476,
                0.9999998362622358,
                0.999999802494633,
                0.9999996940978096,
                0.9999998942829854,
                0.999999931743979
            ],
            [
                0.9999998555019791,
                0.999999825702163,
                0.9999999397643154,
                0.9999999226557684,
                0.999999943413757,
                0.9999998362623528,
                0.9999999176674553,
                0.9999997126314125,
                0.9999999273418183,
                0.9999999226557408
            ],
            [
                1.209865683518615e-06,
                0.9999996743687422,
                4.4508505193932864e-07,
                0.999999057755631,
                2.3823696679230424e-07,
                0.9999996310115038,
                0.9999996072138466,
                0.9999995262093857,
                3.9278634073732336e-07,
                0.9999994631250603
            ],
            [
                0.9999987121046312,
                1.444979692800516e-07,
                1.1253526937656726e-07,
                7.889262585211807e-06,
                2.10243290909724e-07,
                2.3823685319244518e-07,
                2.1024334103352274e-07,
                4.22283545808297e-06,
                2.6995771309523475e-07,
                2.1024344128584085e-07
            ],
            [
                0.9999998024946566,
                0.9999999176675338,
                0.9999997761971848,
                0.9999998802069731,
                0.9999999006879721,
                0.999999939764215,
                0.999999802494633,
                0.999999931743979,
                0.999999931743979,
                0.999998346311006
            ],
            [
                0.9999989969855533,
                8.7642516304188e-08,
                0.9999998461826222,
                1.8553907971855875e-07,
                9.931192141964017e-08,
                0.9999898700126519,
                0.9999967112505436,
                0.9999986290429569,
                0.9999991684720716,
                0.9999999697115659
            ],
            [
                2.9023116391978967e-06,
                7.484621836619826e-05,
                0.9999970976887078,
                3.9278610661902853e-07,
                0.9999992661790196,
                3.535626336201389e-05,
                6.144175334468545e-06,
                1.760343213335281e-06,
                0.9999991148430697,
                0.9999994631247402
            ],
            [
                0.9999999006880194,
                0.9999999677581298,
                3.5356238071317175e-05,
                0.9999999358793867,
                0.9999995549147359,
                0.9999993916407459,
                0.9999998642567351,
                0.9999992188518558,
                0.9999995262095551,
                0.9999992661791947
            ],
            [
                0.9999992661791072,
                0.9999999273418875,
                0.9999998362623724,
                0.9999999226557316,
                0.9999999530883564,
                0.9999999358794021,
                0.9999999611088487,
                1.0,
                0.9999996310115039,
                0.9999999559306153
            ],
            [
                3.2241847115356483e-08,
                1.2751905808881762e-07,
                6.023574911170301e-08,
                2.1024326584639497e-07,
                4.450852111148132e-07,
                6.825604537781398e-08,
                9.931190958076104e-08,
                1.8553916819032217e-07,
                7.734414854823498e-08,
                6.475946438042047e-07
            ],
            [
                7.73442776303243e-08,
                1.2751904288739315e-07,
                0.9999989969860317,
                0.9999984465016905,
                1.8553919030858602e-07,
                1.1253525596174225e-07,
                8.76424013786396e-08,
                3.059021175261338e-07,
                2.382368247924618e-07,
                1.8553919030858602e-07
            ],
            [
                3.059021175261338e-07,
                1.6373762769138607e-07,
                7.338210680021253e-07,
                8.315278294114555e-07,
                3.4663278639892215e-07,
                1.760343213335281e-06,
                2.3823693839290317e-07,
                7.734416698849138e-08,
                4.450848927658745e-07,
                3.4663274507713016e-07
            ],
            [
                6.825598842065202e-08,
                3.65348425788669e-08,
                1.27519088491875e-07,
                0.999997876622298,
                0.9999985406232574,
                1.275190428875671e-07,
                6.825597214718257e-08,
                2.1024334103553052e-07,
                0.9999991684719726,
                2.3823688159291947e-07
            ],
            [
                0.9999996533672962,
                0.9999998024945624,
                0.9999987901343169,
                0.9999998362623138,
                0.9999998642566219,
                0.9999993916410359,
                0.9999996072137998,
                0.9999994956527722,
                0.9999996940977731,
                0.9999987121043241
            ],
            [
                1.994729245878497e-06,
                3.0590237279085045e-07,
                0.9999996940976272,
                1.4449798650551755e-07,
                2.902311639183378e-06,
                2.1024331597262577e-07,
                2.260324028306588e-06,
                0.9999998724809267,
                0.9999986290427936,
                0.9999987901343168
            ],
            [
                1.1253520230052635e-07,
                6.825598028392069e-08,
                6.023572038912295e-08,
                7.734416698849138e-08,
                8.76424013786396e-08,
                9.931187406410953e-08,
                2.1024339116082313e-07,
                1.1253506814842375e-07,
                9.93120161310289e-08,
                7.338208055680009e-07
            ],
            [
                0.9999997897565839,
                0.9999998802069587,
                0.999999607213753,
                0.9999999500627798,
                0.9999999317440198,
                0.9999998642566381,
                0.9999999123575046,
                0.999999825702059,
                0.9999999273418269,
                0.9999997617630049
            ],
            [
                0.9999921107374183,
                0.9999997761971049,
                0.9999993916411085,
                0.9999992188514834,
                0.9999997897565588,
                2.902311639183378e-06,
                7.338209805224048e-07,
                0.9999994631251883,
                0.999999653367503,
                0.9999993916409636
            ],
            [
                0.9999996940978826,
                0.9999998555019446,
                0.9999996743688975,
                0.9999997463981938,
                0.9999996940977003,
                0.9999992188518559,
                0.9999996533674202,
                0.9999998802069302,
                0.9999996940978461,
                0.9999995549151075
            ],
            [
                0.99999834631002,
                0.9999999006880194,
                0.9999993524049703,
                0.999999352405202,
                0.9999998362623723,
                0.9999998942828972,
                0.9999989969855535,
                0.9999996743686257,
                0.9999998642566219,
                0.9999991148429643
            ],
            [
                2.699576809143613e-07,
                8.764242227418718e-08,
                0.9999997617631184,
                2.561281294760143e-06,
                0.999993037746244,
                0.9999993106389546,
                1.1253509497883659e-07,
                1.1253508156363576e-07,
                2.699576809143613e-07,
                1.4449802095609418e-07
            ],
            [
                0.9999990577551816,
                2.3823696679327928e-07,
                0.999998932297003,
                0.999998932297003,
                4.450852641737424e-07,
                1.637376862489725e-07,
                0.9999998555019963,
                2.3823688159291947e-07,
                0.9999996310115479,
                1.4449802095666915e-07
            ],
            [
                0.9999990577550694,
                0.9999930377454134,
                0.9999957771675637,
                0.9999623635664731,
                0.9999942280813495,
                0.9999992661791947,
                5.043476486915964e-07,
                0.9999852610110147,
                0.9999989322968756,
                0.999998996985912
            ],
            [
                1.4449798650551755e-07,
                3.2887506336235617e-06,
                2.2603245673443566e-06,
                2.3823688159291947e-07,
                1.994730197090463e-06,
                9.931198061405701e-08,
                1.855391239544352e-07,
                1.3709575337159875e-06,
                0.9999885212277791,
                1.0677027427624903e-06
            ],
            [
                7.73442776303243e-08,
                5.715005832872586e-07,
                8.315277302841894e-07,
                2.382369951932796e-07,
                5.043475885674441e-07,
                6.825602910433871e-08,
                3.466325797888292e-07,
                2.260324567337161e-06,
                9.931193325852072e-08,
                6.475947982037486e-07
            ],
            [
                8.315279285351409e-07,
                9.422448185510695e-07,
                1.0677027427624903e-06,
                7.338211554801876e-07,
                2.5612819054028872e-06,
                6.475949526020042e-07,
                5.715002426460124e-07,
                2.3823690999290963e-07,
                3.4663278639892215e-07,
                8.315279285370317e-07
            ],
            [
                2.102434412871794e-07,
                2.102434412871794e-07,
                1.6373764721072816e-07,
                9.931189774187203e-08,
                1.4449795205429202e-07,
                1.275191036933194e-07,
                1.4449795205429202e-07,
                3.059021175255426e-07,
                1.8553919030708836e-07,
                1.0677032518700286e-06
            ],
            [
                5.715003107755449e-07,
                6.475949526003845e-07,
                1.6373772528704005e-07,
                2.1024336609843824e-07,
                5.043474082005342e-07,
                8.315282259138311e-07,
                1.637377057680051e-07,
                5.043474683220276e-07,
                3.927862470899887e-07,
                6.825598028392069e-08
            ],
            [
                0.999999931743979,
                0.9999999656786793,
                0.9999999530883452,
                0.9999999634651836,
                0.9999999358793714,
                0.9999999123575359,
                0.9999998461826405,
                0.9999999434137637,
                0.9999999500628393,
                0.999999712631344
            ],
            [
                0.9999993524051247,
                0.9999998874647709,
                0.9999991148427534,
                0.9999997126314468,
                0.9999997617629766,
                0.9999985406234323,
                0.999998932297385,
                0.999999554914789,
                0.9999996940978462,
                0.9999997463981032
            ],
            [
                0.9999993524052792,
                0.9999996940978095,
                0.999999802494586,
                0.999999802494633,
                0.9999995262096116,
                0.999999554914895,
                0.9999996310114159,
                0.9999997617629764,
                0.9999996310115038,
                0.9999999176674357
            ],
            [
                0.9999998257021213,
                9.931187406410953e-08,
                4.139936066832438e-08,
                3.224187402001668e-08,
                6.023568448589658e-08,
                9.931202796993203e-08,
                1.1253508156363576e-07,
                4.6911677163762064e-08,
                1.275190428875671e-07,
                7.734428685047173e-08
            ],
            [
                2.6995784182073116e-07,
                1.8553907971813685e-07,
                1.6373776432481905e-07,
                5.043472879540142e-07,
                3.05902190458764e-07,
                0.9999997300421261,
                2.6995771309523475e-07,
                9.931193325852072e-08,
                3.059022998576899e-07,
                3.05902190458764e-07
            ],
            [
                1.8553905760062447e-07,
                1.1253525596174225e-07,
                1.4738976701652988e-05,
                9.422447062270609e-07,
                6.475950298011458e-07,
                3.05902190458764e-07,
                1.99472900813862e-06,
                5.043476486915964e-07,
                4.4508510499849186e-07,
                3.9278615344178325e-07
            ],
            [
                1.1253525596174225e-07,
                9.931185038635267e-08,
                8.939695238333382e-06,
                1.8553907971855875e-07,
                7.73442776303243e-08,
                1.2751901248454963e-07,
                0.9999987901346054,
                2.6995771309523475e-07,
                9.931186222523604e-08,
                1.8553919030858602e-07
            ],
            [
                1.275190732904469e-07,
                1.7603434231833873e-06,
                3.46632497145457e-07,
                1.4449798650569826e-07,
                3.4663266242969896e-07,
                1.855391239544352e-07,
                7.734414854823498e-08,
                6.825598028392069e-08,
                2.1024326584639497e-07,
                2.699576809143613e-07
            ],
            [
                9.931190958076104e-08,
                7.734421308914719e-08,
                8.764245361752286e-08,
                9.931189774187203e-08,
                6.825601283086733e-08,
                1.6373762769138607e-07,
                2.382369667929001e-07,
                3.05902263389638e-07,
                7.734425918979532e-08,
                1.4449798650551755e-07
            ],
            [
                0.9999998724809874,
                0.9999980052698034,
                0.9999999123575046,
                0.9999996533672136,
                0.9999998362622358,
                0.999999057755631,
                0.9999995549150011,
                0.9999990577552941,
                0.9999984465016902,
                0.999999927341827
            ],
            [
                2.3823685319244518e-07,
                8.764242227418718e-08,
                1.4449803818215767e-07,
                1.4449798650551755e-07,
                1.6373772528677946e-07,
                4.1399365603508136e-08,
                2.1024339116082313e-07,
                2.6995774527657245e-07,
                2.69957906184239e-07,
                4.139935079796334e-08
            ],
            [
                2.102433159721477e-07,
                1.6373766672973748e-07,
                8.7642526752214e-08,
                0.9999977396748948,
                2.6995774527718623e-07,
                6.82560779249779e-08,
                6.023579219579052e-08,
                1.444979692797559e-07,
                9.931185038635267e-08,
                1.4449800373118268e-07
            ],
            [
                5.715005832886879e-07,
                0.9999995549149482,
                1.9947299592824403e-06,
                1.8925148241493373e-05,
                1.3709575337159875e-06,
                0.999999168471576,
                2.144494585801764e-05,
                0.9999960330155052,
                0.9999996533672136,
                0.9999996743687033
            ],
            [
                9.931185038635267e-08,
                1.4449803818215767e-07,
                0.9999999317439465,
                0.9999997617629764,
                0.9999998642566219,
                1.275190276859705e-07,
                0.9999998874648917,
                1.6373770576776313e-07,
                0.9999999123575359,
                0.9999988634358834
            ],
            [
                0.9999999397643083,
                0.9999998144608098,
                0.9999988634360187,
                0.9999996533673376,
                0.9999998024945624,
                0.9999998024947273,
                0.9999999176675632,
                0.9999994956525319,
                0.9999998461826038,
                0.9999996743688586
            ],
            [
                1.8553903548231313e-07,
                6.475949526003845e-07,
                7.338209805240734e-07,
                4.785095065232451e-06,
                1.1253512180925583e-07,
                2.1024334103505245e-07,
                4.450852641717689e-07,
                1.7603440527286572e-06,
                6.475950298011458e-07,
                4.450852111148132e-07
            ],
            [
                2.102434412875379e-07,
                5.315780536011123e-08,
                1.4449795205429202e-07,
                2.1024339116082313e-07,
                5.315780536011123e-08,
                8.764244316973974e-08,
                0.9999988634364252,
                2.8453371023563735e-08,
                3.0590237279085045e-07,
                4.139934092760465e-08
            ],
            [
                1.2751905808881762e-07,
                7.73441946488886e-08,
                9.931186222523604e-08,
                4.4508526417298334e-07,
                1.6373770576776313e-07,
                8.764247451307293e-08,
                1.6373776432509826e-07,
                1.4449798650551755e-07,
                2.102434412871794e-07,
                1.4449798650551755e-07
            ],
            [
                0.9999999006880312,
                0.9999999611088903,
                0.9999999764113295,
                0.9999999123575777,
                0.9999999611088719,
                0.9999999611089044,
                0.9999988634364252,
                0.9999988634357476,
                0.9999998461826038,
                0.99999992265575
            ],
            [
                1.2751905808881762e-07,
                2.382370235922541e-07,
                2.1024341622426268e-07,
                1.444979692800516e-07,
                1.067703124601679e-06,
                9.931198061405701e-08,
                2.1024336609843824e-07,
                1.8553910183607374e-07,
                2.1024339116082313e-07,
                7.734418542875216e-08
            ],
            [
                1.8553914607237736e-07,
                5.715006514167015e-07,
                0.99996879809982,
                2.6995784182183607e-07,
                1.1253520230052635e-07,
                6.825602910433871e-08,
                2.3823693839325527e-07,
                2.3823696679327928e-07,
                1.6373772528704005e-07,
                1.2751901248454963e-07
            ],
            [
                0.9999977396754338,
                3.9278610661822475e-07,
                0.9999984465016905,
                0.9999984465024311,
                2.3823702359290413e-07,
                5.043472278322555e-07,
                0.9999980052700415,
                3.466327450765785e-07,
                2.1024339116134898e-07,
                0.9999984465024313
            ],
            [
                4.4508494582405734e-07,
                3.05902263391829e-07,
                3.9278615344178325e-07,
                1.4449798650551755e-07,
                0.9999930377420954,
                1.760342793638743e-06,
                8.315281267882195e-07,
                1.8553903548231313e-07,
                2.699578740032504e-07,
                1.1253522913127183e-07
            ],
            [
                0.9999998555019446,
                0.9999925887183686,
                0.9999996310116358,
                0.9999992661791945,
                0.9999999317439059,
                0.9999986290423032,
                0.9999997300422869,
                0.9999996533674202,
                0.9999999634651574,
                0.999999927341801
            ],
            [
                0.999999730042287,
                0.9999994956525919,
                0.9999970976869784,
                0.9999994956527722,
                0.9999994284997575,
                0.9999997300423191,
                0.999999802494633,
                0.9999995549147891,
                0.9999990577555186,
                0.9999999530883844
            ],
            [
                0.9999992188512973,
                0.9999997300423192,
                0.9999994631251242,
                0.9999988634360188,
                0.9999996940978462,
                0.9999991148426479,
                0.9999980052695665,
                0.9999996743687422,
                0.9999987901344612,
                0.999999653367379
            ],
            [
                1.2751910369310194e-07,
                1.6373764721072816e-07,
                9.931187406410953e-08,
                2.6995771309523475e-07,
                1.1253520230052635e-07,
                3.059023363231725e-07,
                2.1024331597262577e-07,
                3.059022269250683e-07,
                1.4449798650551755e-07,
                1.275190276859705e-07
            ],
            [
                7.338207180884785e-07,
                8.764244316973974e-08,
                1.637377643243723e-07,
                5.043472879540142e-07,
                4.691159887151251e-08,
                2.1024326584639497e-07,
                6.825604537781398e-08,
                7.734416698849138e-08,
                6.825602910433871e-08,
                9.931196877517082e-08
            ],
            [
                0.9999994631247402,
                0.9999996072137999,
                0.9999997617630049,
                0.9999988634365606,
                0.9999983463108088,
                0.9999987121043242,
                0.9999991684722699,
                0.9999967112517197,
                4.4508510499737865e-07,
                5.043475885696228e-07
            ],
            [
                0.9999980052707548,
                0.999999057755294,
                0.9999993106392012,
                0.9999986290421399,
                0.9999969105044488,
                0.9999991684715762,
                0.9999852610145247,
                0.9999996072137064,
                0.9999987901338842,
                0.999999352405202
            ],
            [
                3.466327037548308e-07,
                5.043472278312808e-07,
                7.338209805240734e-07,
                9.422447062270609e-07,
                2.699577774585891e-07,
                3.466326624336003e-07,
                2.699577774585891e-07,
                4.4508505193932864e-07,
                4.4508526417298334e-07,
                1.4449807263312446e-07
            ],
            [
                0.9999998724809571,
                0.9999999358793409,
                0.9999998724809875,
                0.9999998724810027,
                0.9999998555020135,
                0.9999994631248043,
                0.9999999358794096,
                0.9999998555020307,
                0.9999999317440197,
                2.1024339116134898e-07
            ],
            [
                0.9999988634357477,
                1.760342793638743e-06,
                0.9999996533673378,
                0.9999960330131417,
                2.382370235933104e-07,
                1.637377448057981e-07,
                0.9999975938973744,
                4.222833948008874e-06,
                1.1253513522447425e-07,
                1.209865827752005e-06
            ],
            [
                7.338210680021253e-07,
                5.043474082005342e-07,
                1.8553905760062447e-07,
                3.059022269250683e-07,
                5.715005832886879e-07,
                3.0590237279032884e-07,
                0.9999934595635575,
                8.315278294114555e-07,
                7.338209805240734e-07,
                2.699576809143613e-07
            ],
            [
                3.4663266242969896e-07,
                9.931198061405701e-08,
                1.2751899728311609e-07,
                3.927860597945825e-07,
                2.6995790618350237e-07,
                8.315280276607289e-07,
                9.422449308716635e-07,
                3.0590215399183813e-07,
                8.764255809528314e-08,
                1.1253518888531272e-07
            ],
            [
                9.422442569290178e-07,
                6.144172404693786e-06,
                9.422449308774482e-07,
                0.9999999358794402,
                5.4222176771176554e-06,
                1.6373776432481905e-07,
                0.9999999006879838,
                0.9999921107364782,
                1.760343633031919e-06,
                1.0677026154806063e-06
            ],
            [
                0.9999999656786793,
                0.9999992188515765,
                0.9999999226558423,
                0.9999997617629764,
                0.9999999434138109,
                0.9999998802069016,
                0.9999997300421583,
                0.9999998642566542,
                0.9999999677581375,
                0.999999939764251
            ],
            [
                0.9999978766217913,
                2.3823682479292225e-07,
                3.288747889284851e-06,
                2.2603242978871282e-06,
                5.715002426486762e-07,
                1.6701415872385704e-05,
                0.9999989969854337,
                0.9999885212359884,
                0.999998005270041,
                4.785094494811783e-06
            ],
            [
                0.9999991684719726,
                0.9999994631249322,
                8.764241182641775e-08,
                0.999999825702059,
                1.8553914607267268e-07,
                1.1253520230052635e-07,
                0.999999825702059,
                1.4449798650551755e-07,
                1.275191036933194e-07,
                0.9999977396751643
            ],
            [
                1.4449803818215767e-07,
                1.27519088491875e-07,
                2.10243290909724e-07,
                1.6373764721072816e-07,
                0.9999986290429571,
                0.999999310639037,
                0.9999997126315154,
                0.9999982396574169,
                0.9999997126313098,
                9.93120161310289e-08
            ],
            [
                3.0590219045914655e-07,
                1.855391460719133e-07,
                3.927862002654366e-07,
                0.9999995262093857,
                0.9999997761972116,
                1.0677033791612137e-06,
                6.475945666063607e-07,
                1.637377448057981e-07,
                8.764243272157922e-08,
                4.4508515805735777e-07
            ],
            [
                0.999999802494633,
                0.9999989969860318,
                0.9999999434137772,
                0.999999931743914,
                0.9999998461826588,
                0.9999999006880549,
                0.9999996940976272,
                0.999999912357515,
                0.999999894282935,
                0.9999998555020135
            ],
            [
                3.927862002663297e-07,
                1.8553907971855875e-07,
                5.315781803390236e-08,
                6.023573475041126e-08,
                8.764247451307293e-08,
                9.422443692555439e-07,
                5.715006514167015e-07,
                2.1024336609874897e-07,
                2.3823702359290413e-07,
                8.764244316973974e-08
            ],
            [
                0.9999997761971315,
                2.382369951932796e-07,
                3.466327037553825e-07,
                0.9999978766215387,
                1.4449800373118268e-07,
                2.6995774527718623e-07,
                0.9999992188513902,
                0.9999962733620507,
                0.9999983463110063,
                0.9999989322972578
            ],
            [
                0.9999994284995531,
                0.9999996940978095,
                0.9999989322967487,
                0.9999992661789323,
                0.999999428499417,
                0.9999996533672963,
                0.99999800527028,
                0.9999995818810776,
                0.9999996072136125,
                0.9999994631251883
            ],
            [
                9.931185038635267e-08,
                2.6995774527718623e-07,
                8.7642558095602e-08,
                3.4663266243308805e-07,
                2.3823690999323465e-07,
                8.315277302857965e-07,
                2.69957906184239e-07,
                7.734415776836702e-08,
                1.1253512180925583e-07,
                2.1024331597288867e-07
            ],
            [
                0.9999994631249323,
                0.9999998802069017,
                0.9999985406234315,
                0.9999996072139403,
                0.9999991684722699,
                0.9999995549150011,
                0.9999991148432809,
                0.9999996940977002,
                0.9999995262096116,
                0.9999999067050276
            ],
            [
                2.3823696679230424e-07,
                0.9999989322972577,
                2.3823702359290413e-07,
                5.715005151606823e-07,
                3.9278610661822475e-07,
                6.475945666051092e-07,
                6.475949526003845e-07,
                0.9999991148431754,
                0.9999987121049385,
                0.999999554914789
            ],
            [
                2.3823690999323465e-07,
                0.9999991148426478,
                1.6373772528704005e-07,
                0.9999990577550694,
                5.715006514176113e-07,
                8.764241182641775e-08,
                1.6373774480605869e-07,
                0.9999993524048931,
                5.715006514176113e-07,
                3.05902336324494e-07
            ],
            [
                0.999999953088362,
                0.9999998024947037,
                0.9999999677581105,
                0.9999997300422226,
                0.9999999559305891,
                0.9999999317439383,
                0.9999999586005949,
                0.99999976176309,
                0.9999997126314126,
                0.9999998724809571
            ],
            [
                0.9999998874648245,
                0.9999999006880194,
                0.9999996533673376,
                0.9999999176675142,
                0.9999985406230835,
                0.999999927341827,
                0.9999991684722699,
                0.9999999176675044,
                0.9999997463982241,
                0.9999998362622943
            ],
            [
                0.9999999123574732,
                0.9999998362623332,
                0.9999999273418528,
                0.999999814460876,
                0.9999998461826222,
                0.9999994284992806,
                0.999999825702163,
                0.9999999317439708,
                0.9999989322971304,
                0.9999998024947272
            ],
            [
                2.1024326584639497e-07,
                2.90231094723893e-06,
                9.422447061876404e-07,
                1.2098652508287273e-06,
                8.315283249923769e-07,
                3.28875024125221e-06,
                1.5534981249397663e-06,
                1.5534977545497995e-06,
                1.1253521571574156e-07,
                1.6373762769138607e-07
            ],
            [
                0.9999997126315496,
                0.99999916847227,
                0.9999998257021422,
                0.9999998555020135,
                0.9999998642567028,
                0.9999998802069159,
                0.9999998874647709,
                0.999999887464838,
                0.9999994956527725,
                0.9999995549150543
            ],
            [
                1.1253512180925583e-07,
                9.422445939002803e-07,
                3.059022998576899e-07,
                4.139940508508409e-08,
                7.889259764445822e-06,
                1.0129992186939844e-05,
                1.4738983729294318e-05,
                1.2098658277489788e-06,
                8.7642558095602e-08,
                1.1253525596174225e-07
            ],
            [
                0.9999997761971049,
                0.9999994956527722,
                0.9999998555020135,
                0.9999998461827321,
                0.9999997617630332,
                5.422220262555012e-06,
                0.9999997761971582,
                0.9999998555019274,
                0.9999998724809571,
                0.9999996940977366
            ],
            [
                2.699578740032504e-07,
                9.931186222523604e-08,
                1.4449805540700758e-07,
                1.6373764721072816e-07,
                3.05902263391829e-07,
                1.4449803818215767e-07,
                7.338213304363436e-07,
                1.444979692800516e-07,
                1.2751901248454963e-07,
                1.444979692800516e-07
            ],
            [
                0.9999997300422547,
                2.699577774585891e-07,
                2.1024336609843824e-07,
                2.3823688159291947e-07,
                1.1253518888531272e-07,
                6.47595107001401e-07,
                9.931187406410953e-08,
                1.4449805540763184e-07,
                5.04347468323289e-07,
                2.1024326584639497e-07
            ],
            [
                1.2098652507957165e-06,
                8.315282258900085e-07,
                1.2098653950551882e-06,
                7.338210679949506e-07,
                2.102433410343832e-07,
                7.338210679949506e-07,
                8.315280276338815e-07,
                5.715005832872586e-07,
                1.067703379136937e-06,
                7.338207180761315e-07
            ],
            [
                0.9999998144608981,
                0.9999999656787243,
                0.9999998461826222,
                0.9999999500627916,
                0.9999999067049832,
                0.9999999715466528,
                0.9999997761971848,
                0.9999999656786956,
                0.9999999397642222,
                0.9999999586005949
            ],
            [
                3.927861534406222e-07,
                0.9999997126314468,
                0.9999992661791948,
                0.9999993524048931,
                0.9999992188512972,
                0.9999925887201345,
                0.9999982396565779,
                0.9999984465024313,
                0.9999989969855534,
                0.9999986290423036
            ],
            [
                1.1253512180925583e-07,
                3.466325797896173e-07,
                6.023574911170301e-08,
                9.931186222523604e-08,
                9.931187406410953e-08,
                1.209866260432471e-06,
                1.1253524254650944e-07,
                1.8553907971855875e-07,
                3.0590237279032884e-07,
                1.27519088491875e-07
            ],
            [
                3.0590226339061185e-07,
                0.9999995549150542,
                5.043474683220276e-07,
                2.6995774527577444e-07,
                3.9278610661902853e-07,
                6.023569884718319e-08,
                3.927860597945825e-07,
                1.855391681906175e-07,
                9.931202796993203e-08,
                3.0590237279032884e-07
            ],
            [
                1.3709572068354007e-06,
                4.5397868646614036e-05,
                9.422444815765128e-07,
                0.00010889693528247257,
                2.902312677137316e-06,
                5.043475885657239e-07,
                1.9947304348703948e-06,
                0.0001398221242266438,
                9.422449308673789e-07,
                6.475946438022905e-07
            ],
            [
                1.125352291309328e-07,
                2.6995784182140636e-07,
                1.855391460719133e-07,
                9.931187406410953e-08,
                1.6373770576776313e-07,
                1.27519088491875e-07,
                1.6373766672973748e-07,
                6.023571320847322e-08,
                2.382369667929001e-07,
                3.927862002663297e-07
            ],
            [
                1.067703124601679e-06,
                7.338209805240734e-07,
                1.6373770576776313e-07,
                0.9999970976890542,
                5.715005832895975e-07,
                3.466326211113502e-07,
                1.27519088491875e-07,
                0.9999960330136146,
                8.315280276626197e-07,
                1.4449805540763184e-07
            ],
            [
                0.9999998024946801,
                0.9999999273418096,
                0.9999999273418009,
                0.9999995549149482,
                0.9999999715466595,
                0.9999994631249323,
                1.0,
                0.9999998802069159,
                0.9999987901340286,
                0.9999997463980124
            ],
            [
                1.4449798650476187e-07,
                2.3823690999323465e-07,
                5.04347468323289e-07,
                1.1253526937656726e-07,
                1.1253509497835043e-07,
                1.4449795205429202e-07,
                2.1024326584582131e-07,
                0.9999996533673376,
                0.9999996743686644,
                0.9999993524048931
            ],
            [
                0.9999996940977732,
                0.9999980052702792,
                2.3823696679327928e-07,
                3.927863407379485e-07,
                0.9999994284993488,
                3.4663249714612693e-07,
                0.9999843104521681,
                1.0129990979694647e-05,
                0.9999992661786699,
                1.637377057680051e-07
            ],
            [
                2.2603234895372223e-06,
                1.5534975693979422e-06,
                0.9999938558261321,
                6.475946438055299e-07,
                5.715003107767143e-07,
                5.043473480777865e-07,
                5.043475885688201e-07,
                2.5612831267202583e-06,
                8.764241182641775e-08,
                5.715002426486762e-07
            ],
            [
                3.466327037548308e-07,
                0.9999921107365161,
                2.699578740032504e-07,
                0.9999975938979498,
                0.9999916019249706,
                2.3823693839325527e-07,
                3.059022269250683e-07,
                0.9999985406239539,
                2.3823685319244518e-07,
                5.715003107767143e-07
            ],
            [
                7.73442776303243e-08,
                1.4449798650551755e-07,
                0.9999999530883397,
                7.734421308914719e-08,
                6.825609419848033e-08,
                7.734414854823498e-08,
                1.8553919030858602e-07,
                6.023579219579052e-08,
                7.734415776836702e-08,
                7.734415776836702e-08
            ],
            [
                0.9999974387168751,
                0.9999997126314126,
                0.9999996940978462,
                0.9999997126315153,
                0.9999996310115918,
                0.9999997617630901,
                0.9999997463981334,
                0.9999998024946566,
                0.9999987121049385,
                0.9999994631249322
            ],
            [
                0.9999997126315496,
                6.475946438055299e-07,
                0.9999982396563681,
                0.999998629043284,
                0.9999993106388726,
                2.1024341622426268e-07,
                0.9999997761971049,
                1.067703124601679e-06,
                2.3823685319244518e-07,
                0.999999631011416
            ],
            [
                2.260325375677174e-06,
                4.785096776468749e-06,
                5.043472278312808e-07,
                5.04347408197782e-07,
                3.466327450756327e-07,
                3.2887506335906595e-06,
                1.5534981249574276e-06,
                1.2098661161982042e-06,
                5.715003107755449e-07,
                5.043476486915964e-07
            ],
            [
                0.9999998144608762,
                0.9999999123574941,
                0.9999997126313783,
                0.9999997300421261,
                0.9999998024946566,
                0.999997593898522,
                0.9999992661791072,
                0.9999994956525318,
                0.9999991684717744,
                0.9999997126313783
            ],
            [
                0.9999955048189602,
                0.9999991148431755,
                6.475947982037486e-07,
                5.315780536011123e-08,
                0.9999991684721709,
                0.999998446502061,
                0.9999986290424673,
                1.209865827752005e-06,
                1.1253508156363576e-07,
                5.043475885696228e-07
            ],
            [
                5.043475885674441e-07,
                4.139941495546278e-08,
                1.8553919030858602e-07,
                1.4449798650551755e-07,
                1.4449795205429202e-07,
                1.1253506814842375e-07,
                8.764247451307293e-08,
                1.1253508156363576e-07,
                1.4449800373065699e-07,
                1.1478769494542698e-05
            ],
            [
                1.0677027427600627e-06,
                1.3709576971379186e-06,
                0.9999995818810776,
                1.300713156582635e-05,
                2.2603234895289998e-06,
                8.315281267882195e-07,
                0.9999983463100202,
                8.315284241650899e-07,
                0.9999991684719726,
                5.043473480777865e-07
            ],
            [
                2.1024331597262577e-07,
                1.275190276859705e-07,
                1.637377057680051e-07,
                5.043472278322555e-07,
                1.275191036933194e-07,
                6.475946438055299e-07,
                2.699578740032504e-07,
                2.1024339116082313e-07,
                5.3157830707696514e-08,
                7.734428685047173e-08
            ],
            [
                1.275191036933194e-07,
                6.825600469412533e-08,
                9.93120161310289e-08,
                2.6995774527718623e-07,
                3.466327450765785e-07,
                1.2751907329024393e-07,
                0.9999980052698036,
                1.6373768624837685e-07,
                1.1253517547010071e-07,
                0.9999996310113279
            ],
            [
                5.043476486924565e-07,
                1.2751904288739315e-07,
                1.1253516205489029e-07,
                3.059021175261338e-07,
                3.059021175261338e-07,
                6.023569884718319e-08,
                9.422442569315887e-07,
                1.8553919030858602e-07,
                1.4449803818215767e-07,
                1.275190428875671e-07
            ],
            [
                0.9999984465016906,
                0.9999993524048931,
                0.9999998362622943,
                0.9999999358794326,
                0.9999994284992806,
                0.9999983463102173,
                0.999999825702163,
                0.9999997300422226,
                0.9999942280799741,
                0.9999999067050387
            ],
            [
                0.9999997463980729,
                0.999999631011504,
                0.9999998144608098,
                0.9999995818810777,
                0.9999998362622747,
                0.9999995549149482,
                0.99999976176309,
                0.9999994956527122,
                0.9999997300423191,
                0.9999995818810776
            ],
            [
                1.4449798650551755e-07,
                1.8553910183548312e-07,
                3.9278634073732336e-07,
                3.0590237279032884e-07,
                3.927862470899887e-07,
                5.715005832872586e-07,
                4.450848927650143e-07,
                6.475945666033422e-07,
                6.475947210031623e-07,
                4.450851580566494e-07
            ],
            [
                2.6995784182140636e-07,
                3.05902336324494e-07,
                0.9999985406243013,
                1.637377448057981e-07,
                1.855391239547094e-07,
                3.0590237279085045e-07,
                3.4663249714612693e-07,
                1.1253518888531272e-07,
                0.9999995262092727,
                0.9999995262093857
            ],
            [
                0.9999991148428587,
                1.1253506814842375e-07,
                1.637376862489725e-07,
                0.9999996072139402,
                0.9999992661789323,
                5.715005832895975e-07,
                0.9999993524049703,
                2.1024331597288867e-07,
                3.927863875616689e-07,
                0.9999989322975122
            ],
            [
                0.9999996743688586,
                0.9999996940976638,
                0.9999986290426301,
                5.043473480777865e-07,
                0.9999974387174851,
                6.475949526020042e-07,
                7.338209805224048e-07,
                0.9999987121041707,
                1.444980209564556e-07,
                1.2751902768612997e-07
            ],
            [
                6.023579219579052e-08,
                8.315280276607289e-07,
                1.3709568799879344e-06,
                1.7603427935967163e-06,
                1.2098658277264215e-06,
                6.475946437996402e-07,
                1.9947290081177566e-06,
                1.0677032518413822e-06,
                1.0677028700203557e-06,
                1.5534981249496567e-06
            ],
            [
                5.043472278312808e-07,
                7.73441946488886e-08,
                3.4663278639892215e-07,
                3.466327450765785e-07,
                3.05902263391829e-07,
                3.4663266243308805e-07,
                1.2751905808881762e-07,
                5.71500719545698e-07,
                3.059021175261338e-07,
                3.4663278639892215e-07
            ],
            [
                0.9999999611088672,
                0.9999998942829098,
                0.9999993916410359,
                0.9999999006880905,
                0.9999998257021006,
                0.999999955930589,
                0.9999997463982241,
                0.9999999586006344,
                0.9999999611088812,
                1.0
            ]
        ]
    },
    {
        "q_id": "9885_mmlu_physics",
        "cot_ids": [
            0,
            1,
            3,
            5,
            6,
            7,
            10,
            12,
            13,
            14,
            15,
            16,
            19,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            36,
            37,
            39,
            43,
            44,
            47,
            48,
            49,
            50,
            51,
            52,
            55,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            67,
            68,
            69,
            70,
            71,
            72,
            75,
            76,
            77,
            78,
            80,
            81,
            82,
            83,
            88,
            89,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            117,
            118,
            119,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                9.610238063677138e-05,
                5.422217030663578e-06,
                5.829124470169357e-05,
                7.484621835530752e-05,
                3.120190021759579e-05,
                4.785096776468749e-06,
                6.962259569630266e-06,
                1.1478770862735993e-05,
                2.4300246525983375e-05,
                1.9947290081177566e-06
            ],
            [
                2.753568781693781e-05,
                0.0008040859582641382,
                1.0129988563730593e-05,
                0.0002305066331008433,
                2.144494585747154e-05,
                0.0002959570293928509,
                1.994729483694599e-06,
                1.012999218752948e-05,
                NaN,
                0.00023050671560129052
            ],
            [
                9.610240358212368e-05,
                1.760343003481596e-06,
                1.7603436330179102e-06,
                3.0590237279032884e-07,
                1.5534971990126997e-06,
                7.338211554783522e-07,
                1.5534975693933505e-06,
                5.04347348075149e-07,
                9.422443692574719e-07,
                1.2098656835252174e-06
            ],
            [
                1.1478769494250387e-05,
                3.927862939126708e-07,
                2.5612819054028872e-06,
                2.902312677137316e-06,
                9.422448185510695e-07,
                1.6373762769138607e-07,
                3.288749065423109e-06,
                1.4738981972323349e-05,
                3.726639728370556e-06,
                5.04347468323289e-07
            ],
            [
                7.338209805224048e-07,
                1.7603434231777837e-06,
                9.422448185510695e-07,
                1.0129989772532511e-05,
                1.3709573702822306e-06,
                3.7266401726173067e-06,
                1.7603438428800754e-06,
                5.04347287955046e-07,
                9.422447062294175e-07,
                3.2887478892683997e-06
            ],
            [
                1.3709578605617394e-06,
                3.535625071602016e-05,
                6.144176066795103e-06,
                NaN,
                4.785095635624897e-06,
                7.889266347636241e-06,
                NaN,
                2.9023126771227976e-06,
                7.88926070489716e-06,
                3.5356267573959116e-05
            ],
            [
                2.5612819054028872e-06,
                1.3709567165530083e-06,
                5.422219616184461e-06,
                1.5534973842076057e-06,
                3.7266406168624155e-06,
                1.760343003481596e-06,
                6.962255419868303e-06,
                3.726638395611981e-06,
                7.889261645090304e-06,
                1.0129993395088066e-05
            ],
            [
                2.2603234895289998e-06,
                NaN,
                1.2098658277451275e-06,
                7.889266347636241e-06,
                2.7535691101761522e-05,
                NaN,
                3.726638839878908e-06,
                NaN,
                2.144494585801764e-05,
                NaN
            ],
            [
                4.785093353909723e-06,
                1.6701423836262173e-05,
                9.422447062202052e-07,
                1.6701429807964442e-05,
                6.144172404587612e-06,
                3.12019150949065e-05,
                4.0063706519072155e-05,
                0.00020342690093858216,
                1.3007134667259441e-05,
                1.1478766757404937e-05
            ],
            [
                2.430024652792821e-05,
                2.56128159999123e-06,
                1.670142383595838e-05,
                6.144176799283803e-06,
                1.8925155009767892e-05,
                1.9947301970813926e-06,
                NaN,
                NaN,
                NaN,
                1.0677027427600627e-06
            ],
            [
                1.3007126914245925e-05,
                1.0129995809929273e-05,
                4.222832437639588e-06,
                1.1478768124992398e-05,
                1.4738981971813965e-05,
                1.0129987357158383e-05,
                6.144173869312763e-06,
                1.9947306726358406e-06,
                1.3007134665934505e-05,
                2.561281294644835e-06
            ],
            [
                2.1444940745839484e-05,
                1.9947304348703948e-06,
                1.4738983729294318e-05,
                3.535624228698939e-05,
                3.120191881525687e-05,
                4.539789029616496e-05,
                1.8925148241872038e-05,
                1.012999460278499e-05,
                6.605212107553962e-05,
                5.829125860453825e-05
            ],
            [
                9.422442569290178e-07,
                1.0129989772532511e-05,
                1.0677033791612137e-06,
                2.260324836787226e-06,
                5.422218323487975e-06,
                5.715004470313855e-07,
                4.785092783519724e-06,
                1.8925150497848527e-05,
                2.902312677137316e-06,
                8.939695238536645e-06
            ],
            [
                8.939695237666677e-06,
                0.9996200154865084,
                1.6701421844753466e-05,
                6.144172404302622e-06,
                6.962259569313662e-06,
                2.4300252319296727e-05,
                3.120191881525687e-05,
                6.144173137014406e-06,
                1.4738980214280206e-05,
                3.726639728262097e-06
            ],
            [
                1.892514598469098e-05,
                1.6701421845057263e-05,
                8.315278294072958e-07,
                1.7603434231705793e-06,
                3.288750241561788e-06,
                1.760343003481596e-06,
                1.1478766757049986e-05,
                3.5356267573959116e-05,
                6.962259569484628e-06,
                1.8925157265710765e-05
            ],
            [
                3.288749457469787e-06,
                3.7266388398585725e-06,
                NaN,
                1.8925148241872038e-05,
                8.939693107093343e-06,
                1.6701425826525565e-05,
                1.2098658277451275e-06,
                1.760343633031919e-06,
                1.2098659719788098e-06,
                6.962256249885085e-06
            ],
            [
                6.1441731370702875e-06,
                2.9023116391675407e-06,
                NaN,
                3.5356238071317175e-05,
                3.726637951387472e-06,
                1.9947306726594253e-06,
                0.00012339456025847758,
                2.430023783734196e-05,
                2.4300246527309398e-05,
                2.902313023101807e-06
            ],
            [
                NaN,
                2.4300232043369055e-05,
                1.760343003481596e-06,
                2.5612831267202583e-06,
                6.144176066901277e-06,
                0.0001088969482847688,
                1.7603432133296774e-06,
                1.7603434231833873e-06,
                NaN,
                NaN
            ],
            [
                1.6701421843720577e-05,
                1.209865683518615e-06,
                1.8925145985104064e-05,
                1.2098656835136636e-06,
                1.370957860576702e-06,
                1.3007126914435202e-05,
                3.4663249714451116e-07,
                1.0677032518814388e-06,
                1.6701419852090592e-05,
                4.222834954778007e-06
            ],
            [
                NaN,
                5.422219616140078e-06,
                NaN,
                NaN,
                5.422218969769604e-06,
                5.422221555069497e-06,
                6.144174601935314e-06,
                0.001325022661688189,
                5.14422013945992e-05,
                6.605212103421139e-05
            ],
            [
                6.962253759581752e-06,
                6.962254589781966e-06,
                6.47594798194325e-07,
                4.785092783371756e-06,
                1.6701429808632785e-05,
                3.288750633545794e-06,
                8.481102115861673e-05,
                1.89251527534122e-05,
                1.01299946023704e-05,
                5.1442195260093975e-05
            ],
            [
                4.5397852414783676e-05,
                1.8925157264919016e-05,
                5.829127250060064e-05,
                4.222831934379152e-06,
                1.6701417862648148e-05,
                4.0063696966212295e-05,
                5.144222592420627e-05,
                0.0002611904032162952,
                4.222832941142044e-06,
                1.8925148241493373e-05
            ],
            [
                NaN,
                NaN,
                9.422450432014836e-07,
                1.2098653950692178e-06,
                8.315282259138311e-07,
                NaN,
                NaN,
                NaN,
                1.209866260432471e-06,
                7.889263526345123e-06
            ],
            [
                7.338208055664991e-07,
                3.53562633540394e-05,
                1.670142582682936e-05,
                3.120192253242944e-05,
                1.9947304348595095e-06,
                3.535626336072768e-05,
                1.6701421844753466e-05,
                5.144222593244026e-05,
                1.0677027427471959e-06,
                1.0129988564264954e-05
            ],
            [
                1.0677024881980089e-06,
                2.260325106237323e-06,
                2.1444943302181958e-05,
                2.7535694383279957e-05,
                8.939698435340743e-06,
                2.7535704231043113e-05,
                2.4300252320622747e-05,
                2.1444953527476883e-05,
                1.7603427936263351e-06,
                8.315281267861397e-07
            ],
            [
                7.484622727047031e-05,
                7.889265407004852e-06,
                3.12019225345861e-05,
                3.288749849477628e-06,
                7.338209805200689e-07,
                1.994729483705484e-06,
                1.5534979397592542e-06,
                6.962253759828703e-06,
                1.0677032518700286e-06,
                6.9622587396067566e-06
            ],
            [
                1.7603425837855082e-06,
                4.785096776499213e-06,
                NaN,
                2.5612831266946347e-06,
                NaN,
                1.994729008145876e-06,
                NaN,
                1.9947292459347367e-06,
                1.0677032518785256e-06,
                5.715003789046955e-07
            ],
            [
                2.430025232128576e-05,
                7.889260704818233e-06,
                4.785095635655362e-06,
                1.3709573702822306e-06,
                2.6995774527657245e-07,
                NaN,
                NaN,
                1.5534981249697903e-06,
                7.889261645355786e-06,
                1.0677027427600627e-06
            ],
            [
                3.12019039369228e-05,
                1.7603425837855082e-06,
                1.0677028700363782e-06,
                7.338209805170655e-07,
                8.481104138298063e-05,
                9.610242647154786e-05,
                9.610241500865668e-05,
                NaN,
                1.0677027427600627e-06,
                1.3709578605729614e-06
            ],
            [
                1.1478772230929451e-05,
                7.889264466725156e-06,
                1.012999097997104e-05,
                9.610246083366117e-05,
                2.144495864059426e-05,
                6.144176799227922e-06,
                3.2887486733420804e-06,
                3.535625071602016e-05,
                1.0129987357287368e-05,
                1.4738989000422955e-05
            ],
            [
                3.726641061109272e-06,
                4.4508505193791187e-07,
                1.7603425837791042e-06,
                5.043475885674441e-07,
                1.2098655392921197e-06,
                1.2098661161927025e-06,
                8.315277302747361e-07,
                4.785093924103951e-06,
                1.2098653950656417e-06,
                2.9023133690980155e-06
            ],
            [
                2.260324567337161e-06,
                1.3709572068422585e-06,
                7.338212429582604e-07,
                4.785095635592258e-06,
                1.0677027427624903e-06,
                3.72663883989755e-06,
                9.422449308774482e-07,
                7.338213304316717e-07,
                1.8925145985895816e-05,
                1.209866260432471e-06
            ],
            [
                5.829124470169357e-05,
                7.48462094227206e-05,
                2.5612812947077304e-06,
                9.4224425692559e-07,
                1.0677031245905116e-06,
                2.1444958640087166e-05,
                3.535624649610246e-05,
                6.144173869502757e-06,
                1.7603427936079236e-06,
                3.726639284125553e-06
            ],
            [
                6.144173869446876e-06,
                3.288748673295719e-06,
                5.4222202624563834e-06,
                3.288747889229516e-06,
                4.222833444506298e-06,
                5.422217030707961e-06,
                0.00010889693528247257,
                5.422217030663578e-06,
                4.785092783319532e-06,
                3.535623806720131e-05
            ],
            [
                2.1444940745371397e-05,
                6.962259569630266e-06,
                2.2603248367358324e-06,
                0.0003799844414474752,
                2.5612819054028872e-06,
                1.5534973841705173e-06,
                6.144175334418252e-06,
                1.0129993395336818e-05,
                4.222833947960866e-06,
                2.7535700948722127e-05
            ],
            [
                7.889259764445822e-06,
                NaN,
                4.450852111155216e-07,
                6.144175334468545e-06,
                5.715005151606823e-07,
                8.939700567004841e-06,
                3.059022269250683e-07,
                6.144177531767002e-06,
                5.422218323487975e-06,
                1.1478764020883773e-05
            ],
            [
                7.338211554801876e-07,
                4.785095065232451e-06,
                7.338213304363436e-07,
                3.288747889284851e-06,
                2.2603234895372223e-06,
                1.2098659719788098e-06,
                3.4663266243308805e-07,
                4.4508510499849186e-07,
                6.475945666063607e-07,
                3.0590237279085045e-07
            ],
            [
                3.288749457469787e-06,
                3.2887486733420804e-06,
                2.5612831267086116e-06,
                2.9023133690980155e-06,
                4.222833947960866e-06,
                4.539787947345257e-05,
                5.422219616228845e-06,
                9.422445939002803e-07,
                1.5534971990126997e-06,
                4.785094494750855e-06
            ],
            [
                6.144175334418252e-06,
                1.2098655392921197e-06,
                1.4738976700929127e-05,
                NaN,
                6.962259569630266e-06,
                0.0001398220242259832,
                8.481106161413668e-05,
                3.7266392840781026e-06,
                1.4738985486265496e-05,
                5.422217030614265e-06
            ],
            [
                6.144177531767002e-06,
                4.785092783519724e-06,
                1.8925145985895816e-05,
                7.889261645355786e-06,
                NaN,
                1.7603434231777837e-06,
                3.288750241561788e-06,
                NaN,
                7.889266347715168e-06,
                1.994729483723626e-06
            ],
            [
                7.889259764359722e-06,
                1.7603425837791042e-06,
                1.0129989772412744e-05,
                3.288748281295496e-06,
                1.994730672668496e-06,
                4.785096776394765e-06,
                NaN,
                5.82912516531155e-05,
                9.610242644358106e-05,
                1.473898372822193e-05
            ],
            [
                1.4738987243236881e-05,
                2.5612822106841303e-06,
                2.7535691097454142e-05,
                2.260323489490968e-06,
                1.892514372737249e-05,
                2.7535691097454142e-05,
                4.006368741670684e-05,
                7.88926540679677e-06,
                1.473897670007122e-05,
                2.1444940741392653e-05
            ],
            [
                1.3007126914245925e-05,
                4.539788488274408e-05,
                1.3007130015299356e-05,
                1.5534975693933505e-06,
                4.006367786224833e-05,
                NaN,
                6.96225873967641e-06,
                8.481101106463892e-05,
                5.144223205871514e-05,
                3.535624650150453e-05
            ],
            [
                1.5534983101602148e-06,
                2.260324836776948e-06,
                7.889259764359722e-06,
                8.315281267861397e-07,
                1.30071315662049e-05,
                1.3709570434178922e-06,
                5.4222176771176554e-06,
                5.422220262599396e-06,
                4.785094494750855e-06,
                3.7266401725935817e-06
            ],
            [
                1.0677028700266676e-06,
                6.962257079629686e-06,
                5.829127944184748e-05,
                4.785096776394765e-06,
                4.78509563550957e-06,
                1.7603427936183298e-06,
                4.785094494672519e-06,
                8.939695238211425e-06,
                3.7266383955882547e-06,
                1.670141786295194e-05
            ],
            [
                8.939700566801578e-06,
                8.315278293762888e-07,
                2.90231233114251e-06,
                1.5534975693792215e-06,
                4.222832437747125e-06,
                4.785094494783494e-06,
                3.72664061681327e-06,
                5.422220262599396e-06,
                7.338208930391909e-07,
                5.715006514105942e-07
            ],
            [
                1.0129995809929273e-05,
                4.222834451169694e-06,
                8.93969417199781e-06,
                1.1478764020372226e-05,
                3.726639728262097e-06,
                4.0063706517323215e-05,
                4.222831934202483e-06,
                5.422217030362759e-06,
                1.8925150497848527e-05,
                2.561283431942246e-06
            ],
            [
                1.0677028700266676e-06,
                1.012998977198894e-05,
                2.5612828213690224e-06,
                7.889265407177056e-06,
                2.561283431942246e-06,
                4.222833444467892e-06,
                1.1478765389222573e-05,
                5.422217030707961e-06,
                6.14417753171671e-06,
                5.422217030362759e-06
            ],
            [
                0.0001584361980907647,
                1.8925157264919016e-05,
                6.962256249821764e-06,
                4.0063682641226247e-05,
                1.1478765389222573e-05,
                9.610242648063708e-05,
                7.889260704818233e-06,
                2.5612819054028872e-06,
                NaN,
                1.892515501014656e-05
            ],
            [
                6.962258739796719e-06,
                1.5534979397790343e-06,
                6.144173869603344e-06,
                8.315283250394546e-07,
                2.5612825160562587e-06,
                1.2098662604291696e-06,
                6.144177531767002e-06,
                2.75356812556058e-05,
                3.288749065423109e-06,
                2.260323758987159e-06
            ],
            [
                4.222834954753043e-06,
                6.475946438042047e-07,
                1.3709570434219446e-06,
                1.5534983101602148e-06,
                7.889261645355786e-06,
                NaN,
                4.222831934379152e-06,
                NaN,
                1.3709567165579959e-06,
                4.222833444590791e-06
            ],
            [
                1.9947297215125433e-06,
                1.7603432133296774e-06,
                5.144223206152219e-05,
                5.715005151606823e-07,
                0.000123394633832426,
                2.90231094723893e-06,
                4.539785782605375e-05,
                3.2887502415438413e-06,
                1.9947299593014888e-06,
                8.481107172971651e-05
            ],
            [
                5.422218969895357e-06,
                5.715004470313855e-07,
                1.0677024882009222e-06,
                1.3709567165617364e-06,
                8.315281267882195e-07,
                3.9278634073732336e-07,
                1.670141985446017e-05,
                1.3709572068522336e-06,
                9.422443692555439e-07,
                9.422449308748773e-07
            ],
            [
                NaN,
                5.715004470295662e-07,
                NaN,
                NaN,
                3.120191509592808e-05,
                4.5397884884891014e-05,
                NaN,
                2.1444940745839484e-05,
                NaN,
                1.9947292459347367e-06
            ],
            [
                2.2603245673155757e-06,
                2.2603251062270446e-06,
                3.726639284103523e-06,
                8.939697369882888e-06,
                NaN,
                NaN,
                2.9023126771227976e-06,
                3.2887478892683997e-06,
                3.2887486733420804e-06,
                3.726637951387472e-06
            ],
            [
                4.222834954753043e-06,
                2.5612825160271407e-06,
                1.3709567165579959e-06,
                6.144176799334096e-06,
                NaN,
                1.300713001508642e-05,
                8.481104139717231e-05,
                NaN,
                8.315280276456036e-07,
                0.00029595699421718763
            ],
            [
                NaN,
                4.222832437747125e-06,
                5.422219616140078e-06,
                4.222834451355964e-06,
                NaN,
                5.422219616184461e-06,
                1.0129988564845378e-05,
                2.430024073333442e-05,
                8.939693107093343e-06,
                1.0129992187658463e-05
            ],
            [
                1.8925157265332104e-05,
                2.1444950970626095e-05,
                1.3007128464559612e-05,
                5.829125164632989e-05,
                6.962253759904688e-06,
                9.422449308673789e-07,
                0.00023050666056633585,
                5.422220908925639e-06,
                2.902312331125353e-06,
                3.288750241500471e-06
            ],
            [
                4.539788488274408e-05,
                3.120191881423529e-05,
                4.785093353874907e-06,
                9.42244256915735e-07,
                3.120191137455659e-05,
                3.726639728348526e-06,
                1.6701423834591316e-05,
                5.422217030747413e-06,
                1.9947290081286418e-06,
                4.785092783454444e-06
            ],
            [
                1.0129990980100021e-05,
                4.785092783454444e-06,
                8.939695238333382e-06,
                9.61024493798551e-05,
                3.5356254926549066e-05,
                NaN,
                1.7603436330091044e-06,
                3.288750241500471e-06,
                9.422444815765128e-07,
                4.785093924330255e-06
            ],
            [
                2.430023494002383e-05,
                2.9023119851266288e-06,
                2.7535704231844484e-05,
                5.422218969661113e-06,
                1.8925155009767892e-05,
                3.12019225345861e-05,
                1.8925143729575624e-05,
                1.76034300345598e-06,
                0.00013982212414933676,
                3.1201915093884926e-05
            ],
            [
                1.4738988998117324e-05,
                2.5612828213690224e-06,
                3.726638395527247e-06,
                1.1478770862067849e-05,
                4.539787947345257e-05,
                2.260323489490968e-06,
                5.422219616085833e-06,
                6.962257079275089e-06,
                5.422217030707961e-06,
                2.2603245672497918e-06
            ],
            [
                6.962259569750576e-06,
                NaN,
                3.726637951387472e-06,
                7.889262585886274e-06,
                NaN,
                3.288749457469787e-06,
                NaN,
                3.1201915093884926e-05,
                2.2603253756956754e-06,
                6.9622595696935874e-06
            ],
            [
                1.7603438428660665e-06,
                1.1478770862735993e-05,
                2.1444940744864302e-05,
                1.3007123813193233e-05,
                1.0129988564716393e-05,
                0.0001233945749646458,
                NaN,
                NaN,
                NaN,
                3.726637951387472e-06
            ],
            [
                2.561283432005142e-06,
                2.9023119851266288e-06,
                2.902311639073834e-06,
                3.7266401725935817e-06,
                4.222835458175145e-06,
                2.5612812947380135e-06,
                3.2887506334560605e-06,
                9.422448185510695e-07,
                2.2603245673279107e-06,
                1.994730672668496e-06
            ],
            [
                8.315284241665078e-07,
                1.2098656835252174e-06,
                7.889264466868659e-06,
                NaN,
                NaN,
                8.315278294114555e-07,
                5.043475284468537e-07,
                5.71500719545698e-07,
                6.962258739796719e-06,
                1.3709573702822306e-06
            ],
            [
                2.2603245673155757e-06,
                1.3007130015299356e-05,
                2.1444943301674863e-05,
                3.288749849477628e-06,
                1.6701421844753466e-05,
                1.0129993395088066e-05,
                NaN,
                NaN,
                6.144176066850984e-06,
                9.610246083366117e-05
            ],
            [
                2.561281600049467e-06,
                1.9947301970972664e-06,
                6.475949525981759e-07,
                6.962257909785973e-06,
                1.7603438428740716e-06,
                2.561282516042282e-06,
                7.889259764517575e-06,
                1.9947292458930106e-06,
                1.994729245917502e-06,
                1.5534973841895917e-06
            ],
            [
                2.753568453552033e-05,
                1.1478769493331685e-05,
                1.670141587174774e-05,
                3.535626757125808e-05,
                1.6701419853518415e-05,
                8.939697369785323e-06,
                1.1478770862255766e-05,
                8.93969950101825e-06,
                1.0129995809929273e-05,
                1.1478766757049986e-05
            ],
            [
                2.144495863958007e-05,
                2.7535684534618784e-05,
                2.144494585801764e-05,
                6.144176799283803e-06,
                0.0006263340334301912,
                1.4738985485997396e-05,
                4.539786864876098e-05,
                0.0013250224974724438,
                2.4300246526646385e-05,
                4.006367786720367e-05
            ],
            [
                6.144177531767002e-06,
                2.5612831267202583e-06,
                1.4738976701411704e-05,
                9.422448185510695e-07,
                3.72663883989755e-06,
                6.144176799334096e-06,
                2.9023126771227976e-06,
                1.012999460278499e-05,
                6.9622537599680095e-06,
                9.422443692555439e-07
            ],
            [
                0.0005527786821701399,
                6.962259569630266e-06,
                1.994729245917502e-06,
                2.2603242978778778e-06,
                1.3709576971379186e-06,
                NaN,
                2.2603237589676295e-06,
                NaN,
                1.7603440527222532e-06,
                2.561282516042282e-06
            ],
            [
                0.9999892166903939,
                2.90231094723893e-06,
                4.785094494783494e-06,
                1.3709570434178922e-06,
                5.715003107767143e-07,
                8.315282259138311e-07,
                1.9947304348862686e-06,
                6.144172404738491e-06,
                NaN,
                NaN
            ],
            [
                0.00010889688339134737,
                3.7266388398585725e-06,
                5.422218969818919e-06,
                1.0129989772532511e-05,
                6.1441731370702875e-06,
                1.4738980215352592e-05,
                8.481104138976795e-05,
                3.288748281295496e-06,
                6.144172404520556e-06,
                1.0129990980100021e-05
            ],
            [
                1.0129990980100021e-05,
                3.120191881616493e-05,
                4.0063677865600476e-05,
                1.3007134667259441e-05,
                6.962254589978262e-06,
                2.5612831267086116e-06,
                2.9023116391978967e-06,
                5.715005832886879e-07,
                NaN,
                5.71500515159253e-07
            ],
            [
                1.994729721518893e-06,
                2.9023116391978967e-06,
                1.3007133116542802e-05,
                2.260324836776948e-06,
                3.4663278639892215e-07,
                1.6701421844753466e-05,
                1.7603427936335396e-06,
                1.7603432133296774e-06,
                1.9947299593014888e-06,
                6.962259569750576e-06
            ],
            [
                1.2098661161927025e-06,
                1.5534984953453635e-06,
                1.994729245917502e-06,
                1.0677027427471959e-06,
                6.144173869558639e-06,
                3.726637951387472e-06,
                1.994729008105057e-06,
                1.7603440527046419e-06,
                1.0677026154730804e-06,
                3.7266388398585725e-06
            ],
            [
                2.260325106237323e-06,
                1.0677024881980089e-06,
                4.785092783519724e-06,
                1.067702870039777e-06,
                4.222833444590791e-06,
                2.9023133690980155e-06,
                3.726639284103523e-06,
                2.2603242978871282e-06,
                4.539787946932385e-05,
                1.067702870039777e-06
            ],
            [
                1.3709570434054234e-06,
                3.726638395611981e-06,
                1.8925141473599938e-05,
                5.715005151606823e-07,
                1.2098659719757836e-06,
                1.0677033791437343e-06,
                1.5534984953298217e-06,
                1.3709573702822306e-06,
                5.422220909009474e-06,
                4.539786865090791e-05
            ],
            [
                3.5356267573959116e-05,
                1.1478764020727177e-05,
                8.939693107190907e-06,
                5.4222202624563834e-06,
                1.147876812574406e-05,
                6.605214469029609e-05,
                2.5612834320214477e-06,
                4.7850933538313875e-06,
                NaN,
                6.962259569560613e-06
            ],
            [
                6.475948753991907e-07,
                3.7266401726173067e-06,
                1.4738981972323349e-05,
                7.889264466725156e-06,
                8.939698435657833e-06,
                2.260325106237323e-06,
                2.561282210729555e-06,
                1.5534971990126997e-06,
                7.889266347636241e-06,
                1.4738987243478167e-05
            ],
            [
                3.535625071602016e-05,
                5.829125860453825e-05,
                1.2098653950656417e-06,
                2.9023119851635836e-06,
                2.1444945858485726e-05,
                1.5534979397740895e-06,
                2.90231094723893e-06,
                1.3007133116542802e-05,
                4.785096206047877e-06,
                1.3007130015488633e-05
            ],
            [
                7.88926634755014e-06,
                1.5534981249697903e-06,
                8.481102118021275e-05,
                2.9023116391675407e-06,
                5.422219616228845e-06,
                1.7603425837791042e-06,
                8.939696304213768e-06,
                1.8925155009767892e-05,
                1.670142582682936e-05,
                2.75356845363217e-05
            ],
            [
                7.484623620850474e-05,
                2.260324836776948e-06,
                NaN,
                4.222834451355964e-06,
                5.829126554578343e-05,
                1.994729245917502e-06,
                8.939693107093343e-06,
                NaN,
                0.00010889688337946374,
                2.260325106237323e-06
            ],
            [
                4.78509563546605e-06,
                8.939696304116203e-06,
                7.88926446679691e-06,
                7.484622728190558e-05,
                3.726641061027928e-06,
                2.2603234895176927e-06,
                4.785096776468749e-06,
                NaN,
                4.785093353909723e-06,
                1.553497754577351e-06
            ],
            [
                1.5534971989907999e-06,
                1.9947306726213275e-06,
                1.7603438428564603e-06,
                1.994729008105057e-06,
                1.1478764020372226e-05,
                2.144494330116777e-05,
                1.5534971989907999e-06,
                1.2098653950551882e-06,
                1.2098653950551882e-06,
                1.0129993395088066e-05
            ],
            [
                3.726638839878908e-06,
                1.5534973842076057e-06,
                1.7603440527286572e-06,
                1.5534977545886537e-06,
                5.422217030747413e-06,
                1.994729008145876e-06,
                5.4222209089700225e-06,
                1.5534977545886537e-06,
                1.0129990980100021e-05,
                1.3709570434219446e-06
            ],
            [
                NaN,
                0.9999885212346397,
                0.9998204720137666,
                0.9999485578048546,
                0.9992903295453379,
                0.9999810748450114,
                5.144223206414209e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                8.315277302841894e-07,
                1.0677029973192638e-06,
                1.0129988564845378e-05,
                2.561283432035425e-06,
                1.4738989000422955e-05,
                NaN,
                6.962257079832313e-06,
                1.3709572068522336e-06,
                2.2603234895289998e-06,
                1.994729483705484e-06
            ],
            [
                2.90231233114251e-06,
                2.5612828213690224e-06,
                2.260325375664839e-06,
                1.2098658277451275e-06,
                1.3007131565613412e-05,
                2.5612819053586272e-06,
                1.0129993394959082e-05,
                2.144495352642369e-05,
                1.6701427817427163e-05,
                3.726639284103523e-06
            ],
            [
                3.288749065406658e-06,
                5.422217030614265e-06,
                2.1444943301674863e-05,
                NaN,
                2.561283126679493e-06,
                1.4738987242968784e-05,
                1.3007125363719486e-05,
                2.1444940744318203e-05,
                1.0129995810463632e-05,
                NaN
            ]
        ]
    },
    {
        "q_id": "9464_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                8.315284241650899e-07,
                7.734414854823498e-08,
                2.561282210740037e-06,
                1.5534984953552536e-06,
                7.338207180898968e-07,
                2.902312677150514e-06,
                NaN,
                3.927863875616689e-07,
                NaN,
                1.7603425837903113e-06
            ],
            [
                8.315283250305684e-07,
                9.422448185510695e-07,
                NaN,
                3.4663266243308805e-07,
                2.699578740032504e-07,
                9.422445939054222e-07,
                6.475950298011458e-07,
                4.450848927658745e-07,
                NaN,
                4.4508494582405734e-07
            ],
            [
                6.962255419868303e-06,
                NaN,
                NaN,
                5.043475885696228e-07,
                NaN,
                NaN,
                NaN,
                6.9622595696935874e-06,
                9.422447062294175e-07,
                NaN
            ],
            [
                6.023577065381482e-08,
                1.1253522913127183e-07,
                6.825608606172863e-08,
                2.699577774589574e-07,
                2.1444956084718052e-05,
                7.734416698849138e-08,
                1.067703379154416e-06,
                4.691160446380562e-08,
                5.315789407685159e-08,
                1.855391681906175e-07
            ],
            [
                3.927863407379485e-07,
                1.760342793638743e-06,
                1.5534983101393749e-06,
                7.889262585886274e-06,
                3.927860597945825e-07,
                1.3709572068522336e-06,
                6.962254589914941e-06,
                4.4508515805735777e-07,
                NaN,
                8.315280276626197e-07
            ],
            [
                9.422445939054222e-07,
                1.3709576971425944e-06,
                9.422448185510695e-07,
                5.043476486924565e-07,
                9.422449308774482e-07,
                NaN,
                3.466325797900508e-07,
                4.450852111155216e-07,
                3.46632497145457e-07,
                NaN
            ],
            [
                NaN,
                NaN,
                6.825606978822427e-08,
                NaN,
                4.4508515805735777e-07,
                7.734426841017797e-08,
                3.05902336324494e-07,
                NaN,
                NaN,
                1.855391681906175e-07
            ],
            [
                NaN,
                NaN,
                2.561282210740037e-06,
                7.338209805240734e-07,
                7.338208930460318e-07,
                8.315279285370317e-07,
                5.043472278322555e-07,
                1.3709568799919866e-06,
                5.715006514176113e-07,
                5.71500515161527e-07
            ],
            [
                8.315279285351409e-07,
                5.04347287955046e-07,
                1.3709573702856596e-06,
                2.699578096403948e-07,
                1.0677027427624903e-06,
                1.6701417863559525e-05,
                9.422447062294175e-07,
                8.315283250394546e-07,
                7.33821330437595e-07,
                2.3823688159291947e-07
            ],
            [
                2.102434412875379e-07,
                7.734425919002834e-08,
                NaN,
                1.4449800373118268e-07,
                7.734425919002834e-08,
                NaN,
                1.2751902768612997e-07,
                9.931200429212718e-08,
                3.466326624336003e-07,
                6.475946438055299e-07
            ],
            [
                1.855391681906175e-07,
                7.338209805240734e-07,
                NaN,
                NaN,
                5.71500515161527e-07,
                NaN,
                1.4449798650569826e-07,
                5.043473480777865e-07,
                3.4663274507713016e-07,
                NaN
            ],
            [
                1.9947301970972664e-06,
                1.7603430034867993e-06,
                8.939699501416646e-06,
                3.927863875616689e-07,
                1.2098662604291696e-06,
                NaN,
                5.043476486924565e-07,
                3.05902190458764e-07,
                4.222834954801051e-06,
                6.475947982037486e-07
            ],
            [
                NaN,
                NaN,
                1.637377057680051e-07,
                8.764254764780641e-08,
                9.93119806143167e-08,
                1.2098653950551882e-06,
                NaN,
                7.338211554758494e-07,
                9.422447062294175e-07,
                1.8553905760062447e-07
            ],
            [
                3.059022269250683e-07,
                3.0590237279032884e-07,
                5.043475885696228e-07,
                3.05902263391829e-07,
                1.637377057680051e-07,
                1.4449798650569826e-07,
                5.71500719545698e-07,
                1.6373776432509826e-07,
                4.4508515805735777e-07,
                2.3823693839325527e-07
            ],
            [
                9.422445939054222e-07,
                3.0590219045914655e-07,
                NaN,
                3.927863875616689e-07,
                NaN,
                0.9999852610215693,
                2.3823702359290413e-07,
                5.043474683240344e-07,
                2.6995784182183607e-07,
                NaN
            ],
            [
                5.3157811697009444e-08,
                NaN,
                2.3823690999323465e-07,
                6.023577783447482e-08,
                NaN,
                6.475950298011458e-07,
                6.47595107001401e-07,
                3.05902336324494e-07,
                1.2751910369343538e-07,
                1.067702870039777e-06
            ],
            [
                NaN,
                NaN,
                6.47595107001401e-07,
                NaN,
                NaN,
                1.2098652508424818e-06,
                NaN,
                1.0677027427624903e-06,
                NaN,
                4.785095635655362e-06
            ],
            [
                NaN,
                1.275190124846946e-07,
                2.1024339116168358e-07,
                1.6373766672994222e-07,
                NaN,
                2.3823690999323465e-07,
                2.10243290909963e-07,
                3.9278629391427843e-07,
                2.3823690999323465e-07,
                4.691167157146029e-08
            ],
            [
                0.9999967112517216,
                NaN,
                0.9999756997622153,
                0.9997694933196578,
                0.9999921107402551,
                1.2751902768612997e-07,
                1.1253522913127183e-07,
                6.023568448589658e-08,
                0.9999938558246713,
                0.9999964991468415
            ],
            [
                NaN,
                NaN,
                2.1024331597288867e-07,
                0.999991060304775,
                NaN,
                NaN,
                0.9999810748427546,
                NaN,
                1.0677032518700286e-06,
                NaN
            ],
            [
                1.994729483705484e-06,
                8.315280276626197e-07,
                2.9023119851781017e-06,
                3.4663274507713016e-07,
                NaN,
                6.475947210046347e-07,
                NaN,
                NaN,
                6.475950298021765e-07,
                2.2603242978871282e-06
            ],
            [
                NaN,
                NaN,
                6.144175334468545e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                5.715006514176113e-07,
                9.422448185534261e-07,
                NaN
            ],
            [
                6.475945666063607e-07,
                6.475950298011458e-07,
                2.90231094723893e-06,
                NaN,
                1.0677028700422047e-06,
                6.47595107001401e-07,
                6.475946438055299e-07,
                NaN,
                5.715005832895975e-07,
                1.7603425837903113e-06
            ],
            [
                NaN,
                1.1253509497883659e-07,
                1.3709576971463352e-06,
                5.422217030781934e-06,
                1.2751904288710323e-07,
                2.3823688159291947e-07,
                3.4663274507713016e-07,
                1.9947304348862686e-06,
                2.3823696679327928e-07,
                NaN
            ],
            [
                NaN,
                6.475947210046347e-07,
                NaN,
                1.0677029973219343e-06,
                1.5534984953552536e-06,
                NaN,
                7.338208055680009e-07,
                NaN,
                1.9947297215125433e-06,
                1.994729721518893e-06
            ],
            [
                2.1024334103581732e-07,
                5.04347528446051e-07,
                9.422443692574719e-07,
                1.1478765389368729e-05,
                NaN,
                2.6995790618469934e-07,
                1.0677027427624903e-06,
                7.338208930460318e-07,
                NaN,
                NaN
            ],
            [
                1.4449805540763184e-07,
                1.275190124846946e-07,
                NaN,
                4.785093924389007e-06,
                NaN,
                8.315281267882195e-07,
                NaN,
                NaN,
                4.4508515805735777e-07,
                NaN
            ],
            [
                NaN,
                0.9999251537376902,
                NaN,
                NaN,
                NaN,
                3.7266397283908927e-06,
                3.4663249714612693e-07,
                2.561281600086738e-06,
                NaN,
                3.05902336324494e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                1.275190580890061e-07,
                2.3823696679327928e-07,
                1.209865539295696e-06,
                NaN,
                NaN,
                1.2751902768612997e-07,
                NaN
            ],
            [
                7.338207180898968e-07,
                1.1253522913127183e-07,
                4.1399400149893274e-08,
                NaN,
                2.3823685319320354e-07,
                3.0590237279085045e-07,
                NaN,
                2.699578096403948e-07,
                3.535625914363812e-05,
                NaN
            ],
            [
                NaN,
                NaN,
                6.475947982037486e-07,
                1.2098653950692178e-06,
                6.475950298011458e-07,
                4.4508494582405734e-07,
                NaN,
                4.450849988811838e-07,
                NaN,
                4.450852111155216e-07
            ],
            [
                7.734425919002834e-08,
                9.422450432030903e-07,
                0.9999993916408184,
                1.8553907971879076e-07,
                4.785093924389007e-06,
                NaN,
                0.9999756997622171,
                6.47594875403829e-07,
                8.315280276626197e-07,
                5.043474082012222e-07
            ],
            [
                1.4449796928021588e-07,
                NaN,
                2.1024326584702836e-07,
                1.4449807263312446e-07,
                NaN,
                0.9999687980998311,
                2.699578740032504e-07,
                1.6373766672994222e-07,
                8.764247451307293e-08,
                8.764251630441717e-08
            ],
            [
                1.444979692797559e-07,
                1.4449800373065699e-07,
                NaN,
                NaN,
                5.715002426486762e-07,
                2.3823696679327928e-07,
                NaN,
                9.931189774187203e-08,
                2.6995771309523475e-07,
                2.382369951932796e-07
            ],
            [
                1.0677031245905116e-06,
                1.637377448057981e-07,
                8.315277302857965e-07,
                5.71500515159253e-07,
                NaN,
                5.043474683240344e-07,
                3.9278629391427843e-07,
                2.699576809143613e-07,
                1.5534971989258068e-06,
                NaN
            ],
            [
                NaN,
                0.9999339478477495,
                2.561281294760143e-06,
                NaN,
                7.338209805240734e-07,
                5.043476486924565e-07,
                1.209865827752005e-06,
                1.0677028700422047e-06,
                5.715006514176113e-07,
                NaN
            ],
            [
                NaN,
                1.9947301970972664e-06,
                8.939700567094277e-06,
                7.889266347715168e-06,
                3.9278629391427843e-07,
                2.561281294760143e-06,
                2.10243290909724e-07,
                NaN,
                NaN,
                2.5612834320563895e-06
            ],
            [
                1.0677028700422047e-06,
                5.715005832895975e-07,
                1.0677033791612137e-06,
                9.422445939054222e-07,
                2.9023133690980155e-06,
                7.338210680021253e-07,
                1.0677032518785256e-06,
                2.699577774589574e-07,
                1.0677027427624903e-06,
                6.475947982037486e-07
            ],
            [
                4.4508515805735777e-07,
                0.9999771720082986,
                0.9999810748495368,
                1.5534975693979422e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                2.2603251062450327e-06,
                NaN
            ],
            [
                7.338210680021253e-07,
                NaN,
                0.0007096703030032253,
                3.05902190458764e-07,
                6.023577783447482e-08,
                NaN,
                7.734421308914719e-08,
                NaN,
                NaN,
                9.931185038635267e-08
            ],
            [
                NaN,
                1.1253525596174225e-07,
                NaN,
                6.962257909842961e-06,
                NaN,
                2.2603253756956754e-06,
                3.9278629391427843e-07,
                0.9996646497403352,
                8.764253720001207e-08,
                NaN
            ],
            [
                2.6995784182183607e-07,
                0.9999485577619253,
                1.855390576008354e-07,
                NaN,
                3.0590237279085045e-07,
                NaN,
                1.5534971990169383e-06,
                1.147876812620341e-05,
                NaN,
                2.1024334103581732e-07
            ],
            [
                3.0590219045914655e-07,
                NaN,
                7.338208055680009e-07,
                1.8553914607267268e-07,
                NaN,
                NaN,
                2.2603245673443566e-06,
                9.931185038635267e-08,
                7.734415776836702e-08,
                NaN
            ],
            [
                1.5534979397829198e-06,
                NaN,
                NaN,
                9.422443692574719e-07,
                6.475945666063607e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                8.315280276626197e-07,
                2.753568453792444e-05,
                4.785096776499213e-06,
                1.6701423836262173e-05,
                3.9278610661902853e-07,
                1.3709568799879344e-06,
                1.1253512180925583e-07,
                2.9023133690980155e-06,
                5.715005151606823e-07,
                1.1478768126057254e-05
            ],
            [
                2.5612831267202583e-06,
                5.043476486924565e-07,
                7.889261645355786e-06,
                2.902313369111213e-06,
                NaN,
                NaN,
                1.7603430034867993e-06,
                7.338210680021253e-07,
                2.5612831267202583e-06,
                NaN
            ],
            [
                NaN,
                6.475947982037486e-07,
                1.1253506814842375e-07,
                6.475945666063607e-07,
                3.927863407379485e-07,
                3.9278605979534166e-07,
                2.3823696679327928e-07,
                4.4508515805735777e-07,
                4.450851049991497e-07,
                NaN
            ],
            [
                NaN,
                1.2098653950656417e-06,
                NaN,
                NaN,
                1.209866260432471e-06,
                3.535626757524533e-05,
                6.475945666063607e-07,
                NaN,
                NaN,
                1.99472900813862e-06
            ],
            [
                NaN,
                NaN,
                8.315280276626197e-07,
                1.9947299592933255e-06,
                1.3709576971379186e-06,
                4.450850519403407e-07,
                7.338209805240734e-07,
                NaN,
                NaN,
                3.288749849477628e-06
            ],
            [
                NaN,
                NaN,
                1.0677024882009222e-06,
                5.04347287955046e-07,
                1.6373766672973748e-07,
                7.338208930460318e-07,
                4.450852111155216e-07,
                8.315279285370317e-07,
                8.7642526752214e-08,
                1.2751902768612997e-07
            ],
            [
                NaN,
                9.93119806143167e-08,
                1.8553905760062447e-07,
                NaN,
                8.315278293762888e-07,
                NaN,
                NaN,
                NaN,
                1.3709573702822306e-06,
                NaN
            ],
            [
                1.9947301970972664e-06,
                NaN,
                NaN,
                NaN,
                2.5612831267202583e-06,
                7.338211554783522e-07,
                1.3709567165579959e-06,
                NaN,
                1.0677029973219343e-06,
                5.04347468323289e-07
            ],
            [
                0.9999987121047849,
                0.9999970976866319,
                0.9999977396754334,
                0.9999989322967484,
                0.99999211073648,
                0.999992588716602,
                8.315279285351409e-07,
                0.9999938558275973,
                0.9999997126314468,
                6.47594952603035e-07
            ],
            [
                NaN,
                NaN,
                1.2098656835224664e-06,
                5.71500719545698e-07,
                NaN,
                NaN,
                NaN,
                5.04347287955046e-07,
                5.043472278322555e-07,
                NaN
            ],
            [
                3.466325797900508e-07,
                NaN,
                NaN,
                1.2751902768612997e-07,
                NaN,
                3.466325797900508e-07,
                NaN,
                1.9947301970972664e-06,
                NaN,
                4.450852641737424e-07
            ],
            [
                3.7266397283908927e-06,
                4.4508515805735777e-07,
                NaN,
                NaN,
                0.9999898700078197,
                5.043472278322555e-07,
                0.999933947824066,
                0.0010322312213816892,
                2.902313023130843e-06,
                0.9999980052695662
            ],
            [
                8.764254764780641e-08,
                3.05902263391829e-07,
                8.764251630441717e-08,
                1.2751902768612997e-07,
                1.6373766672994222e-07,
                NaN,
                NaN,
                1.275190732904469e-07,
                1.1253525596174225e-07,
                6.475945666063607e-07
            ],
            [
                1.855391681906175e-07,
                3.288747889284851e-06,
                NaN,
                7.338212429594283e-07,
                4.785095065232451e-06,
                0.9998911031044508,
                NaN,
                3.9278634073732336e-07,
                0.999948557792614,
                0.9998204721007804
            ],
            [
                NaN,
                NaN,
                NaN,
                1.5534981249697903e-06,
                8.315277302857965e-07,
                NaN,
                4.785095635655362e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                1.3709575337159875e-06,
                1.994729008145876e-06,
                NaN,
                7.338210680021253e-07,
                8.939697370069891e-06,
                2.5612812947508257e-06,
                NaN,
                2.2603245673443566e-06,
                2.2603242978943238e-06,
                1.0677026154806063e-06
            ],
            [
                1.553497754583709e-06,
                5.715003107767143e-07,
                NaN,
                5.715006514176113e-07,
                1.067703379154416e-06,
                1.7603430034867993e-06,
                7.338207180898968e-07,
                NaN,
                3.466327037548308e-07,
                NaN
            ],
            [
                2.144495608424996e-05,
                1.994729721518893e-06,
                1.2098655392811161e-06,
                9.422443692555439e-07,
                NaN,
                6.475947982037486e-07,
                NaN,
                2.902312677150514e-06,
                3.2887478892683997e-06,
                1.760343213335281e-06
            ],
            [
                3.927862470899887e-07,
                9.422445939054222e-07,
                4.4508494582405734e-07,
                2.902313023130843e-06,
                9.422442569315887e-07,
                NaN,
                NaN,
                1.6701415872385704e-05,
                1.0677028700422047e-06,
                2.2603245673443566e-06
            ],
            [
                8.315279285351409e-07,
                4.450850519403407e-07,
                3.466325797896173e-07,
                2.1024339116168358e-07,
                2.10243290909963e-07,
                4.4508510499849186e-07,
                1.1253524254650944e-07,
                3.05902263391829e-07,
                3.059022998581767e-07,
                2.699578096403948e-07
            ],
            [
                9.422444815814404e-07,
                NaN,
                1.0677032518578904e-06,
                NaN,
                NaN,
                1.7603425837903113e-06,
                NaN,
                NaN,
                4.785094494811783e-06,
                6.475945666063607e-07
            ],
            [
                NaN,
                1.3007134667259441e-05,
                1.209866260432471e-06,
                7.338208055680009e-07,
                2.2603245673443566e-06,
                2.5612834320563895e-06,
                5.043476486924565e-07,
                NaN,
                5.043476486915964e-07,
                8.315284241650899e-07
            ],
            [
                1.209865827740176e-06,
                2.902312331170226e-06,
                NaN,
                NaN,
                5.715005832853093e-07,
                NaN,
                2.69957906184239e-07,
                1.3709568799919866e-06,
                1.3709572068522336e-06,
                2.1024326584639497e-07
            ],
            [
                NaN,
                0.9999339478792858,
                5.04347468323289e-07,
                2.699578096403948e-07,
                0.9999251537911474,
                0.9999921107402426,
                0.999974132569041,
                0.9999339478714219,
                0.999990483750585,
                NaN
            ],
            [
                3.0590237279085045e-07,
                1.994730672675753e-06,
                3.288747889284851e-06,
                1.5534981249574276e-06,
                NaN,
                9.422445939032799e-07,
                1.5534983101602148e-06,
                4.222832437798974e-06,
                NaN,
                8.315280276607289e-07
            ],
            [
                NaN,
                NaN,
                1.275190428875671e-07,
                9.931200429212718e-08,
                NaN,
                3.4663274507713016e-07,
                1.8553914607267268e-07,
                2.3823693839325527e-07,
                4.450852111155216e-07,
                1.8553910183674878e-07
            ],
            [
                6.962258739796719e-06,
                3.2887502415767434e-06,
                8.315284241650899e-07,
                3.72663883989755e-06,
                1.5534975693979422e-06,
                2.699576809143613e-07,
                8.315280276626197e-07,
                1.3709567165617364e-06,
                1.0677028700422047e-06,
                NaN
            ],
            [
                9.422445939002803e-07,
                2.2603253756874524e-06,
                5.043472879540142e-07,
                NaN,
                0.0,
                1.6373772528636992e-07,
                2.2603242978871282e-06,
                2.382368531929327e-07,
                1.8553919030858602e-07,
                1.2098653950716937e-06
            ],
            [
                NaN,
                9.422447062294175e-07,
                NaN,
                NaN,
                6.47595107001401e-07,
                1.209865827752005e-06,
                NaN,
                4.22283545819819e-06,
                1.2098656835224664e-06,
                7.338207180898968e-07
            ],
            [
                7.889261645427538e-06,
                7.338208930460318e-07,
                3.288749457469787e-06,
                5.422219616265831e-06,
                2.1444943302650045e-05,
                3.288749457469787e-06,
                5.715005151606823e-07,
                2.902312677150514e-06,
                1.994729008145876e-06,
                6.475950298011458e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                1.5534977545886537e-06,
                3.927863875616689e-07,
                3.927862002663297e-07,
                1.7603440527286572e-06,
                NaN,
                5.043475885674441e-07,
                NaN
            ],
            [
                NaN,
                7.338210680021253e-07,
                NaN,
                NaN,
                5.715003107767143e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                7.338207180898968e-07
            ],
            [
                2.3823690999323465e-07,
                2.3823685319320354e-07,
                0.9999485577803794,
                3.0590226339061185e-07,
                0.9982992775249203,
                NaN,
                1.6373764721091427e-07,
                3.05902263391829e-07,
                4.6911660386730734e-08,
                6.82560779249779e-08
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                3.2887506336235617e-06,
                NaN,
                NaN,
                1.275190124846946e-07,
                1.9947304348862686e-06,
                NaN
            ],
            [
                5.715004470334646e-07,
                NaN,
                3.288749849529972e-06,
                9.422442569334097e-07,
                NaN,
                NaN,
                1.209866260432471e-06,
                NaN,
                6.47595107001401e-07,
                6.475949526020042e-07
            ],
            [
                7.338207180898968e-07,
                1.994729721518893e-06,
                2.699576809143613e-07,
                1.855391681906175e-07,
                3.9278629391427843e-07,
                3.4663274507713016e-07,
                1.5534977545886537e-06,
                3.927863407379485e-07,
                9.422448185534261e-07,
                2.1024331597288867e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                6.47595107001401e-07,
                NaN,
                4.4508510499849186e-07
            ],
            [
                3.4663278639892215e-07,
                1.5534984953552536e-06,
                3.059022998581767e-07,
                1.4449800373118268e-07,
                8.315281267882195e-07,
                9.931189774187203e-08,
                1.209865827752005e-06,
                1.5534971990169383e-06,
                1.0677027427624903e-06,
                1.7603434231833873e-06
            ],
            [
                NaN,
                NaN,
                1.3709575337159875e-06,
                NaN,
                NaN,
                1.5534984953552536e-06,
                NaN,
                NaN,
                1.5534975693979422e-06,
                1.7603436330179102e-06
            ],
            [
                NaN,
                NaN,
                5.715002426486762e-07,
                3.726639284144195e-06,
                2.2603245673443566e-06,
                NaN,
                4.785095635655362e-06,
                8.939697370069891e-06,
                NaN,
                NaN
            ],
            [
                2.699577774589574e-07,
                NaN,
                1.637377057680051e-07,
                NaN,
                NaN,
                1.275190580890061e-07,
                1.1253524254650944e-07,
                NaN,
                9.422444815814404e-07,
                2.3823690999323465e-07
            ],
            [
                2.5612816000331606e-06,
                NaN,
                NaN,
                9.422450432030903e-07,
                5.043474683240344e-07,
                NaN,
                2.2603248367949354e-06,
                NaN,
                6.962257079889302e-06,
                8.315281267861397e-07
            ],
            [
                0.999988521230513,
                4.450852111155216e-07,
                0.999989870004196,
                NaN,
                3.53562422882756e-05,
                2.260324028443809e-06,
                0.9999952149072185,
                NaN,
                0.9999038975856193,
                1.855391239547094e-07
            ],
            [
                NaN,
                NaN,
                3.927863407379485e-07,
                NaN,
                NaN,
                9.422442569334097e-07,
                NaN,
                NaN,
                NaN,
                1.7603438428800754e-06
            ],
            [
                1.855391239547094e-07,
                NaN,
                7.338207180898968e-07,
                9.422447062294175e-07,
                2.5612834320563895e-06,
                NaN,
                1.7603430034867993e-06,
                1.2098659719788098e-06,
                3.4663274507713016e-07,
                1.3709567165617364e-06
            ],
            [
                6.144176799334096e-06,
                NaN,
                1.209865827752005e-06,
                5.715002426410745e-07,
                1.0677028700422047e-06,
                NaN,
                1.7603425837903113e-06,
                2.9023112932296107e-06,
                4.450852111148132e-07,
                6.475949525981759e-07
            ],
            [
                NaN,
                2.902311293147782e-06,
                1.5534979397790343e-06,
                1.2098656835224664e-06,
                NaN,
                9.422449308716635e-07,
                1.3007126912826352e-05,
                NaN,
                NaN,
                NaN
            ],
            [
                1.9947304348862686e-06,
                1.209866260432471e-06,
                NaN,
                1.5534975693979422e-06,
                2.5612812947508257e-06,
                9.422447062294175e-07,
                NaN,
                3.288748281329893e-06,
                5.043474683204221e-07,
                9.422444815814404e-07
            ],
            [
                8.7642516304188e-08,
                1.275191036933194e-07,
                2.382369951932796e-07,
                6.023579219579052e-08,
                7.734416698849138e-08,
                9.931185038635267e-08,
                9.931200429212718e-08,
                3.0590237279085045e-07,
                1.8553910183674878e-07,
                1.275190580890061e-07
            ],
            [
                5.715003789046955e-07,
                1.9947301970972664e-06,
                6.475947210046347e-07,
                3.466326211113502e-07,
                1.2098652508424818e-06,
                3.9278605979534166e-07,
                1.0677032518814388e-06,
                2.6995790618252024e-07,
                1.5534975693979422e-06,
                NaN
            ],
            [
                3.726638395611981e-06,
                2.5612831267202583e-06,
                7.889261645427538e-06,
                1.3709568799919866e-06,
                NaN,
                1.5534983101602148e-06,
                1.7603425837903113e-06,
                4.785095635655362e-06,
                4.222832437386106e-06,
                1.760342793638743e-06
            ],
            [
                0.9999970976866338,
                0.9999546021315899,
                9.422448185534261e-07,
                0.9999967112509377,
                NaN,
                0.9999987901340289,
                0.9999955048200335,
                0.9999981261237241,
                0.9999798543140564,
                0.9999989322975122
            ],
            [
                NaN,
                NaN,
                3.05902336324494e-07,
                1.30071315662049e-05,
                1.9947301970451086e-06,
                1.760343213335281e-06,
                NaN,
                2.2603253756874524e-06,
                NaN,
                NaN
            ],
            [
                2.902312331170226e-06,
                3.059021175261338e-07,
                1.209865539298447e-06,
                8.315277302857965e-07,
                1.2098653950692178e-06,
                4.450851580566494e-07,
                NaN,
                NaN,
                9.422443692574719e-07,
                7.33821330437595e-07
            ],
            [
                1.3709567165617364e-06,
                1.9947301970972664e-06,
                NaN,
                1.0677026154827912e-06,
                3.927863875616689e-07,
                1.7603425837903113e-06,
                6.475946438055299e-07,
                1.5534971990169383e-06,
                8.315282259138311e-07,
                1.2098656835252174e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                5.04347468323289e-07,
                9.422448185534261e-07,
                5.715006514176113e-07,
                NaN,
                0.9999885212291707,
                NaN,
                NaN
            ],
            [
                3.927863875616689e-07,
                NaN,
                3.9278605979534166e-07,
                1.2098661162056318e-06,
                8.315277302841894e-07,
                NaN,
                3.927863407379485e-07,
                3.927862002663297e-07,
                NaN,
                8.315279285351409e-07
            ],
            [
                1.275191036933194e-07,
                2.3823690999323465e-07,
                2.699576809143613e-07,
                NaN,
                5.043475885696228e-07,
                1.6373764721091427e-07,
                2.3823693839325527e-07,
                2.1024334103581732e-07,
                0.9999251537818837,
                2.1024339116168358e-07
            ],
            [
                7.338211554758494e-07,
                8.315280276626197e-07,
                5.715005151606823e-07,
                1.3709568799760888e-06,
                NaN,
                9.422443692574719e-07,
                NaN,
                1.209865539274514e-06,
                1.3709575337016483e-06,
                2.2603237589542675e-06
            ],
            [
                1.2098655392871682e-06,
                1.3709572068522336e-06,
                5.715003789046955e-07,
                9.422449308748773e-07,
                NaN,
                5.715006514176113e-07,
                3.059022269254856e-07,
                2.2603242978871282e-06,
                1.0677026154827912e-06,
                4.450848927658745e-07
            ],
            [
                7.338212429582604e-07,
                3.059022998576899e-07,
                NaN,
                3.466325797896173e-07,
                NaN,
                NaN,
                3.2887502415767434e-06,
                1.7603438428800754e-06,
                7.338213304363436e-07,
                5.715003789046955e-07
            ],
            [
                2.6995784182183607e-07,
                9.931185038635267e-08,
                1.0677033791583005e-06,
                9.422448185534261e-07,
                1.7603436330179102e-06,
                2.2603240284371276e-06,
                NaN,
                4.222833444506298e-06,
                6.475950298011458e-07,
                3.466327037553825e-07
            ],
            [
                9.422447062294175e-07,
                NaN,
                NaN,
                NaN,
                9.422442569334097e-07,
                NaN,
                1.2098659719788098e-06,
                1.3709573702778664e-06,
                NaN,
                1.9947292458930106e-06
            ],
            [
                6.962257909785973e-06,
                5.043474081993875e-07,
                2.5612834320563895e-06,
                2.902312677150514e-06,
                1.5534981249697903e-06,
                3.726639284144195e-06,
                8.315281267882195e-07,
                1.637377448057981e-07,
                7.338208055664991e-07,
                4.450852111155216e-07
            ],
            [
                1.1253517547010071e-07,
                6.023571320847322e-08,
                6.475946438055299e-07,
                NaN,
                1.4449803818215767e-07,
                NaN,
                1.5534971990126997e-06,
                2.1024334103581732e-07,
                NaN,
                4.4508515805735777e-07
            ],
            [
                1.067703124601679e-06,
                6.475946438055299e-07,
                NaN,
                NaN,
                NaN,
                2.6995790618469934e-07,
                8.315280276626197e-07,
                NaN,
                NaN,
                6.475945666063607e-07
            ],
            [
                NaN,
                4.4508515805735777e-07,
                1.760343213335281e-06,
                NaN,
                3.927863407379485e-07,
                NaN,
                1.209865827752005e-06,
                1.760343213335281e-06,
                3.9278610661902853e-07,
                NaN
            ],
            [
                1.3007128464961824e-05,
                1.994729008145876e-06,
                NaN,
                2.9023130230846496e-06,
                NaN,
                1.2098662604291696e-06,
                6.475947982037486e-07,
                9.422443692555439e-07,
                6.1441724046434924e-06,
                2.260325106237323e-06
            ],
            [
                1.0129988565084915e-05,
                5.144221980317192e-05,
                NaN,
                4.22283545819819e-06,
                1.5534973842076057e-06,
                NaN,
                0.9999898700066201,
                5.1442207537151994e-05,
                1.994729721518893e-06,
                NaN
            ],
            [
                1.1253524254650944e-07,
                9.93120161310289e-08,
                NaN,
                9.931186222523604e-08,
                2.1024326584702836e-07,
                NaN,
                NaN,
                6.023577065381482e-08,
                1.6373764721091427e-07,
                NaN
            ],
            [
                1.4449800373118268e-07,
                5.3157887739943563e-08,
                1.8553910183674878e-07,
                NaN,
                1.4449796928021588e-07,
                NaN,
                NaN,
                4.691159887151251e-08,
                NaN,
                2.10243290909963e-07
            ],
            [
                0.9999417087347935,
                1.3709573702822306e-06,
                NaN,
                NaN,
                3.72663883989755e-06,
                NaN,
                5.04347287955046e-07,
                0.999951674368114,
                1.0677026154827912e-06,
                7.338209805240734e-07
            ],
            [
                NaN,
                8.315281267882195e-07,
                5.715002426475718e-07,
                5.04347287955046e-07,
                3.4663249714612693e-07,
                5.71500651413193e-07,
                NaN,
                NaN,
                NaN,
                9.422450432014836e-07
            ],
            [
                1.1253508156363576e-07,
                1.9947299593078385e-06,
                3.288749457469787e-06,
                9.931189774187203e-08,
                1.637377057680051e-07,
                4.450852641737424e-07,
                5.71500719545698e-07,
                3.466326211113502e-07,
                1.6373764721072816e-07,
                3.059022269250683e-07
            ],
            [
                NaN,
                1.9947299593078385e-06,
                2.902311639183378e-06,
                2.561282210701601e-06,
                1.7603425837855082e-06,
                NaN,
                2.5612819054133693e-06,
                2.561281600086738e-06,
                NaN,
                1.994729483705484e-06
            ],
            [
                NaN,
                NaN,
                1.8553910183674878e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                8.315277302857965e-07,
                NaN,
                1.5534983101644536e-06,
                3.0590237279085045e-07,
                8.315284241665078e-07,
                1.6373776432509826e-07,
                6.144177531811707e-06,
                NaN,
                1.0677029973219343e-06,
                NaN
            ],
            [
                NaN,
                4.785092783519724e-06,
                1.8553914607267268e-07,
                2.902312677150514e-06,
                6.962254589978262e-06,
                NaN,
                NaN,
                1.5534979397740895e-06,
                7.734425919002834e-08,
                NaN
            ]
        ]
    },
    {
        "q_id": "9763_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999984465015054,
                0.9999991684718735,
                9.931200429181105e-08,
                0.9999992661789323,
                0.9999987121043246,
                0.9999785550567651,
                7.734423152941018e-08,
                0.9999997300420939,
                0.9999995818812272,
                1.4449807263287805e-07
            ],
            [
                0.9999982396561582,
                0.9999957771645457,
                0.999997273530707,
                0.9999998724809571,
                0.9999997126313098,
                0.9999992188512972,
                0.9999996072138467,
                0.9999974387171802,
                0.9999949062943935,
                0.9999990577552941
            ],
            [
                0.9999995818810777,
                1.4449803818156628e-07,
                8.764253719973308e-08,
                0.9999921107364788,
                0.9999987901346054,
                0.9999964991451716,
                2.9023133690637e-06,
                0.9999987121046313,
                0.9999987121043246,
                6.02357778338585e-08
            ],
            [
                1.1253520230052635e-07,
                1.1253514863968147e-07,
                5.043472879504592e-07,
                2.102433410343832e-07,
                0.9999978766205266,
                5.04347528446051e-07,
                0.9999991684715762,
                0.9999977396754341,
                0.9999998461827139,
                9.422442569290178e-07
            ],
            [
                0.999998446502061,
                0.9999990577557437,
                8.764255809528314e-08,
                2.3823693839290317e-07,
                0.9999993916406735,
                0.9999916019259771,
                2.6995784182140636e-07,
                0.9999994631248044,
                8.764247451307293e-08,
                1.8553916819032217e-07
            ],
            [
                7.73441946488886e-08,
                4.139934586278605e-08,
                1.8553910183649565e-07,
                4.691160446380562e-08,
                8.764243272157922e-08,
                2.8453354063983556e-08,
                6.825601283086733e-08,
                5.3157900413760374e-08,
                1.2751910369275402e-07,
                4.691164920214251e-08
            ],
            [
                0.9999952149066522,
                0.9999995818814266,
                0.9999994284993489,
                0.9999986290424671,
                8.764252675194995e-08,
                0.9999975938968022,
                0.9999942280792871,
                0.9999975938979495,
                0.9999993524054337,
                0.9999892166865054
            ],
            [
                4.691162683297406e-08,
                0.9999974387187074,
                4.691164920214251e-08,
                4.6911638017556955e-08,
                2.5109978953528905e-08,
                8.764244316973974e-08,
                5.3157818033672716e-08,
                0.9999982396574179,
                6.023573475041126e-08,
                9.931200429212718e-08
            ],
            [
                1.637377057673536e-07,
                7.734423152941018e-08,
                0.9999962733593857,
                4.6911638017556955e-08,
                1.444979692797559e-07,
                1.8553916819032217e-07,
                1.4449805540740185e-07,
                1.6373764721072816e-07,
                0.999998712104171,
                4.691162124067829e-08
            ],
            [
                0.9999983463100209,
                6.023569166629634e-08,
                0.9999990577555189,
                0.9999972735287583,
                0.9999989322970035,
                0.9999989322968761,
                0.9999994631247403,
                0.9999998555019963,
                1.855390354818069e-07,
                0.9999986290429583
            ],
            [
                0.9999993524053564,
                0.9999978766205266,
                6.825600469412533e-08,
                0.9999955048168189,
                0.9999985406239541,
                0.999993855822477,
                0.9999988634365616,
                1.275190580884987e-07,
                0.9999990577552941,
                0.9999877809269272
            ],
            [
                1.637377448057981e-07,
                1.6373770576776313e-07,
                1.8553907971758842e-07,
                1.1253512180925583e-07,
                1.8553905760024476e-07,
                7.734421308914719e-08,
                9.931196877517082e-08,
                3.46632497145457e-07,
                1.4449798650417048e-07,
                6.023571320847322e-08
            ],
            [
                0.9999970976887099,
                0.9999980052705179,
                0.9999992188515768,
                0.9999995549150544,
                0.9999945777797444,
                0.9999687980775964,
                0.9999934595643404,
                0.9999989969861515,
                0.9999925887166081,
                0.9999995818811774
            ],
            [
                0.9999969105051864,
                0.9999977396754344,
                0.9999980052707556,
                0.9999997761972116,
                0.9999994284996213,
                0.9999975938973753,
                0.9999997300422548,
                0.9999942280772252,
                0.9999339478635177,
                0.9999967112505469
            ],
            [
                3.466327863983311e-07,
                5.4222183234485234e-06,
                0.999997739675166,
                3.653482080235082e-08,
                0.9999980052709935,
                0.9999996940978827,
                9.422450431954847e-07,
                0.9999993524049705,
                0.9999990577555187,
                6.825601283086733e-08
            ],
            [
                0.9999994956525319,
                7.734421308914719e-08,
                0.9999998802069874,
                0.9999991684718743,
                0.9999995818813767,
                0.9999986290427939,
                0.9999962733616103,
                0.9999994284993489,
                0.9999975938985227,
                0.9999989322975124
            ],
            [
                0.999997593896515,
                0.9999934595643434,
                0.9999998555019619,
                0.9999852610127832,
                0.999995504818426,
                0.9999989969856732,
                0.9999986290432843,
                0.9999996533672139,
                0.9999988634365616,
                1.1253525596174225e-07
            ],
            [
                6.825604537781398e-08,
                6.023577065324986e-08,
                4.691164920214251e-08,
                5.315787506598473e-08,
                0.9999945777823279,
                8.764249540862797e-08,
                4.69116100558914e-08,
                1.6373764720849438e-07,
                9.931189774187203e-08,
                1.2751905808881762e-07
            ],
            [
                0.9999992188517631,
                0.9999980052709933,
                0.9999982396561593,
                0.9999995818811774,
                0.9999987121049388,
                0.9999993106387904,
                0.9999982396574175,
                0.9999997761971848,
                0.9999986290432844,
                0.9999983463106122
            ],
            [
                1.444980209564556e-07,
                7.734421308914719e-08,
                0.999999218851856,
                0.9999998362623529,
                0.9999998642567028,
                0.9999997463981637,
                0.9999995818814266,
                0.9999995818814266,
                0.9999993524053566,
                9.931190958076104e-08
            ],
            [
                0.9999982396574175,
                0.9999991684716755,
                0.9999993524052794,
                0.9999993106392014,
                0.9999957771655508,
                0.9999993916409636,
                0.9999991148431756,
                2.2603234895053587e-06,
                0.9999987901346055,
                0.999994577779743
            ],
            [
                0.9999832985841555,
                0.9999952149066496,
                0.9999997463981032,
                0.9999993524049705,
                0.9999993106392013,
                0.9999985406239537,
                0.9999978766220452,
                0.9999991684720718,
                0.9999990577552942,
                0.9999989969860319
            ],
            [
                1.2098661162023305e-06,
                0.9999989969856732,
                0.9999969105055543,
                0.9999983463108092,
                1.444980209564556e-07,
                0.999992110733665,
                8.764240137829087e-08,
                6.023572038882162e-08,
                0.9999962733611631,
                0.9999977396748956
            ],
            [
                0.9999975938970884,
                0.9999949062925734,
                0.9999996743687034,
                6.023574193105671e-08,
                0.9999997126313441,
                0.9999990577551822,
                0.9999952149043706,
                0.9999988634361545,
                0.9999934595596603,
                0.9999974387174868
            ],
            [
                0.9999998642566219,
                8.764254764780641e-08,
                0.9999998942830233,
                0.999999495652592,
                0.9999955048162832,
                1.275190276859705e-07,
                0.9999991684715763,
                0.9999960330155081,
                0.9999974387180953,
                6.825598842035714e-08
            ],
            [
                0.9999957771670637,
                4.691165479443628e-08,
                0.999769493342368,
                0.9999994631248044,
                0.9999898700066191,
                0.9999974387171808,
                0.9999921107402471,
                0.9999785550567479,
                0.999990483743784,
                2.3823696679230424e-07
            ],
            [
                0.9999987121041714,
                0.9999938558224772,
                0.9999987901346057,
                9.931199245292204e-08,
                1.444980209564556e-07,
                0.9999987121044784,
                0.9999992661786699,
                0.9999994284995533,
                0.999999428499417,
                0.9999930377421038
            ],
            [
                1.8553905760024476e-07,
                1.4449798650551755e-07,
                6.825598842035714e-08,
                1.6373770576776313e-07,
                1.6373770576776313e-07,
                6.144172404380855e-06,
                7.734416698849138e-08,
                0.9999898700078305,
                8.7642516304188e-08,
                6.023578501491997e-08
            ],
            [
                0.9999982396563679,
                0.999998005270756,
                0.9999885212359978,
                0.9999982396574175,
                0.999998446501691,
                0.9999996072138467,
                0.9999993524052794,
                0.9999989322972577,
                0.9999952149032285,
                0.9999994956527725
            ],
            [
                0.9999995262094423,
                0.9999921107374246,
                0.9999998024947273,
                0.9999980052709941,
                0.9999987121041709,
                0.9999998724809875,
                0.999999802494633,
                0.9999994631249327,
                6.825604537781398e-08,
                0.999999310638955
            ],
            [
                0.9999997463981939,
                0.9999989322966214,
                0.9999970976883626,
                0.9999998555020307,
                0.9999989969856735,
                0.999998239656788,
                0.9999983463096267,
                0.9999987901344616,
                0.9999997897566341,
                0.9999989322970034
            ],
            [
                0.9999978766223001,
                0.9999957771645431,
                0.9999998362622358,
                0.999999789756634,
                0.9999993106392013,
                0.9999996310114161,
                0.9999996072136594,
                0.9999995818811773,
                0.9999980052700438,
                0.9999994631248044
            ],
            [
                8.764244316973974e-08,
                4.6911638017556955e-08,
                5.3157837044597743e-08,
                2.1024339116134898e-07,
                8.764244316973974e-08,
                1.1253513522447425e-07,
                1.8553907971855875e-07,
                3.0590215399183813e-07,
                1.1253506814797596e-07,
                7.734425918979532e-08
            ],
            [
                9.931190958076104e-08,
                0.9999990577556312,
                0.9999988634362903,
                0.999999218851763,
                0.9999996743688587,
                0.9999967112509383,
                0.999999631011636,
                0.9999949062968237,
                0.9999986290423037,
                0.9999983463102183
            ],
            [
                0.9999978766215388,
                0.9999955048194968,
                0.9999989969854339,
                0.9999998724810027,
                0.9999952149043684,
                0.9999938558224736,
                0.9999989969861512,
                9.931199245292204e-08,
                0.9999991148430699,
                0.9999984465022466
            ],
            [
                5.315786872908501e-08,
                4.6911660386730734e-08,
                8.764247451307293e-08,
                8.764250585640737e-08,
                6.825606165129312e-08,
                4.691166597901517e-08,
                1.444980381819277e-07,
                1.1253524254615121e-07,
                6.825600469412533e-08,
                5.3157811697009444e-08
            ],
            [
                0.9999998461826954,
                0.9999985406239543,
                8.764249540862797e-08,
                0.9999982396565782,
                0.9999977396748959,
                0.9999998024947272,
                0.9999898700102583,
                0.9999988634357482,
                4.691162124067829e-08,
                0.9999994284995531
            ],
            [
                0.9999986290421411,
                0.9999997761971849,
                0.9999843104446996,
                1.1253524254615121e-07,
                0.9999991684717746,
                0.9999957771645479,
                0.9999996072136595,
                0.9999981261252878,
                0.9999977396765122,
                0.9999993106392014
            ],
            [
                0.9999997126315497,
                0.999999789756609,
                0.9999992661789323,
                0.9999992188512974,
                0.9999998362622358,
                0.9999916019269807,
                0.9999930377429326,
                0.9999993916406735,
                2.1024326584582131e-07,
                0.9999991684718738
            ],
            [
                0.9999962733602766,
                0.9999970976887087,
                0.9999980052709931,
                0.9999994956527123,
                0.9999981261241715,
                0.9999991684720719,
                0.9999877809181769,
                0.9999843104559147,
                0.9999988634361551,
                1.2751910369310194e-07
            ],
            [
                0.9999974387184011,
                0.9999151889190678,
                4.691167716359673e-08,
                0.9999978766215394,
                0.9999989969856733,
                0.9999970976869789,
                0.9999974387171802,
                9.931194509740267e-08,
                0.9999990577549572,
                0.9999955048189635
            ],
            [
                0.9999990577554069,
                0.999998239656997,
                0.9999994956523515,
                0.9999990577552943,
                0.999999428499349,
                0.9999992661788449,
                0.9999984465015049,
                0.9999986290431209,
                0.99999911484307,
                0.9999989969855536
            ],
            [
                8.76424013786396e-08,
                6.023572038912295e-08,
                4.139941495546278e-08,
                8.764242227418718e-08,
                0.9999987121050925,
                9.931195693628605e-08,
                8.764245361752286e-08,
                6.023572038912295e-08,
                2.5110011880337063e-08,
                7.734418542875216e-08
            ],
            [
                5.315786239218605e-08,
                0.9999992661788448,
                0.9999987901341728,
                0.999998996986032,
                0.9999998642567351,
                0.9999995262095552,
                0.9999997463981636,
                1.2751899728286965e-07,
                0.9999997300421904,
                0.9999996743688199
            ],
            [
                0.9999977396757042,
                0.9999998024946332,
                0.9999995262095552,
                0.9999994956523515,
                0.9999996940977732,
                0.9999986290421398,
                0.9999993106392013,
                0.9999998802069587,
                0.9999921107393097,
                0.9999969105044488
            ],
            [
                4.139938534423022e-08,
                7.734425918979532e-08,
                2.8453323536912213e-08,
                7.734424074954332e-08,
                1.4449798650551755e-07,
                6.825598842065202e-08,
                1.2751901248454963e-07,
                1.444979692800516e-07,
                3.6534807736504303e-08,
                1.4449798650476187e-07
            ],
            [
                0.9999991148430701,
                8.764247451307293e-08,
                0.9999987121047854,
                0.9999995549149483,
                0.9999989322968762,
                0.9999997463981334,
                0.9999952149032297,
                0.9999989969854342,
                0.999998996985434,
                0.999992588719253
            ],
            [
                1.4449805540763184e-07,
                1.1253514863909295e-07,
                6.962256249758443e-06,
                2.9023126771227976e-06,
                0.9999984465015056,
                3.927862470890063e-07,
                1.5534973842030142e-06,
                4.222834954753043e-06,
                8.764255809528314e-08,
                1.9947299592933255e-06
            ],
            [
                6.023578501491997e-08,
                0.9999949062962147,
                0.999997273529407,
                1.2751910369275402e-07,
                0.9999998144609203,
                0.9999877809225471,
                0.999988521233257,
                0.9999785550439698,
                0.9999960330155072,
                0.999999887464771
            ],
            [
                0.9999978766205264,
                0.9999955048189606,
                0.9999999226557408,
                0.9999938558239392,
                0.9999993524052795,
                0.999999554914842,
                0.9999998362622357,
                0.9999983463098241,
                0.9999983463108097,
                1.1253521571574156e-07
            ],
            [
                0.9999993916406736,
                4.450849988811838e-07,
                6.02357921955714e-08,
                0.9999989322966215,
                0.9999980052695665,
                0.9999942280786048,
                0.9999992188517631,
                0.9999988634358837,
                1.275190276859705e-07,
                0.9999987901338845
            ],
            [
                0.9999997617630617,
                1.1253506814797596e-07,
                0.9999942280779109,
                0.9999983463102177,
                0.9999993524054336,
                0.9999942280779146,
                0.9999993106391193,
                0.9999995262094987,
                1.4449805540740185e-07,
                0.9999974387180987
            ],
            [
                9.93118503859575e-08,
                0.9999955048184312,
                6.02357921955714e-08,
                0.9999952149043717,
                0.9999986290423034,
                0.9999992661788448,
                0.9999981261243943,
                0.9999785550516325,
                0.9999998461826405,
                0.999999114842648
            ],
            [
                0.9999988634357481,
                0.9999982396572087,
                3.224187402001668e-08,
                0.9999989969855536,
                0.9999975938985227,
                0.9999981261241714,
                0.9999994284995533,
                0.9999997300423191,
                0.9999982396572092,
                0.9999987121046323
            ],
            [
                0.9999994631250605,
                0.9999991148428589,
                0.9999981261237242,
                0.9999982396572079,
                0.9999986290426315,
                0.9999974387165687,
                0.9999977396765122,
                7.73441946488886e-08,
                9.931194509740267e-08,
                0.9999994284996896
            ],
            [
                0.9999995262094422,
                0.9999997300421263,
                NaN,
                0.9999998642566543,
                0.9999992661790199,
                0.999999789756659,
                0.9999980052707563,
                0.9999998144608098,
                0.9999996743686257,
                0.9999967112505469
            ],
            [
                0.9999986290431208,
                0.999991601924979,
                0.9999995549150544,
                0.9999980052698042,
                0.9999984465024314,
                0.9999972735290827,
                0.999998540623258,
                0.9999957771675634,
                6.02357921955714e-08,
                5.315786239218605e-08
            ],
            [
                0.9999942280786038,
                0.9999921107383679,
                0.9999994631249964,
                0.9999989322971305,
                0.9999990577557435,
                0.9999852610198035,
                6.825609419823202e-08,
                0.9999987121050922,
                0.9999989322975129,
                0.9999945777829752
            ],
            [
                9.931190958076104e-08,
                6.023576347299818e-08,
                6.023569166654288e-08,
                9.931189774187203e-08,
                6.825604537781398e-08,
                3.224185864592658e-08,
                4.691162124067829e-08,
                9.931190958076104e-08,
                4.139939521459479e-08,
                6.825606978801862e-08
            ],
            [
                3.059022269250683e-07,
                3.9278634073625165e-07,
                2.6995790618252024e-07,
                3.927862470899887e-07,
                1.6373776432509826e-07,
                3.0590215399183813e-07,
                1.8553907971855875e-07,
                1.4449802095609418e-07,
                2.6995774527718623e-07,
                1.553498124964492e-06
            ],
            [
                1.8553905760024476e-07,
                0.9999996072138936,
                0.99999854062378,
                0.9999989969859128,
                0.9999989322971311,
                3.2887482813149375e-06,
                0.9999985406236068,
                0.9999962733593877,
                0.9999998144608541,
                0.9999969105062925
            ],
            [
                6.475950298011458e-07,
                0.9999955048194996,
                0.9999993916409636,
                0.9999994631249325,
                0.9999998555019446,
                9.422445939032799e-07,
                0.9999991684718738,
                0.9999938558232072,
                0.99999911484307,
                0.9999996072137531
            ],
            [
                0.9999989322971307,
                0.9999962733593869,
                0.9999994631248044,
                0.9999986290429576,
                0.9999994956524118,
                0.999999057755182,
                0.9999970976883628,
                6.825606165129312e-08,
                0.9999970976876708,
                1.444979692797559e-07
            ],
            [
                0.9999981261239476,
                4.450852111135988e-07,
                0.999998932297258,
                1.0677028700320085e-06,
                4.785092783454444e-06,
                4.22283545808297e-06,
                1.4449798650417048e-07,
                6.962254589781966e-06,
                1.3709573702778664e-06,
                2.90231233114251e-06
            ],
            [
                0.9999984465016907,
                0.9999989322967485,
                0.9999999006881497,
                0.9999998942829477,
                0.9999984465020608,
                0.9999964991460054,
                0.9999983463110066,
                0.9999992661791073,
                0.9999997463981938,
                0.9999998461826588
            ],
            [
                0.999999931743979,
                9.931187406410953e-08,
                0.9999997897565588,
                0.9999985406232578,
                0.9999989969859124,
                8.764255809528314e-08,
                0.9999990577550696,
                0.9999995818812771,
                0.9999942280786001,
                0.9999995549147891
            ],
            [
                0.999999802494586,
                6.475947982022763e-07,
                0.9999994956524718,
                0.9999986290429578,
                1.2098662604126641e-06,
                0.9999994631249324,
                0.9999998555020481,
                0.9999990577550699,
                0.9999995262094987,
                0.9999975938970889
            ],
            [
                9.931193325852072e-08,
                0.9999994956526522,
                5.315787506598473e-08,
                0.9999993106388727,
                0.9999964991439183,
                0.9999991148426481,
                0.9999869928669095,
                0.9999996072138936,
                8.764243272157922e-08,
                0.9999991684715764
            ],
            [
                0.9999997126313442,
                0.9999974387171819,
                0.9999997300421904,
                0.9999993106386268,
                0.9999996743686259,
                0.9999996533673376,
                0.9999993916408911,
                0.9999964991460059,
                0.9999993524049706,
                8.764253719973308e-08
            ],
            [
                0.9999984465018762,
                5.315787506598473e-08,
                0.9999964991443369,
                0.9999960330136171,
                0.9999977396751646,
                0.9999934595635628,
                0.9999991684722703,
                0.9999960330155077,
                0.999999391640746,
                1.637377643243723e-07
            ],
            [
                0.9999995549148422,
                0.9999996743686259,
                0.9999991148432811,
                1.9947306726049992e-06,
                2.6995784182073116e-07,
                0.9999822214524219,
                0.9999724642991473,
                0.9999978766212859,
                0.9999949062956097,
                0.9999910603058371
            ],
            [
                0.999998790134173,
                0.9999998461827322,
                0.999999789756634,
                0.9999995262094422,
                0.9999998642567351,
                1.0,
                0.9999994631250604,
                2.6995790618252024e-07,
                0.9999994631248683,
                0.9999987121041707
            ],
            [
                3.466325384661554e-07,
                3.927861066170637e-07,
                7.3382080556433e-07,
                1.855391239539711e-07,
                1.855391239539711e-07,
                7.734426840938659e-08,
                6.475945666033422e-07,
                1.1253525596055243e-07,
                1.4449798650417048e-07,
                1.8553905760024476e-07
            ],
            [
                0.9999949062937875,
                0.9999978766217925,
                0.9999957771650472,
                0.999998005269806,
                0.9999984465024314,
                0.99999911484307,
                0.999992588720141,
                0.9999991684715762,
                0.9999999176674553,
                0.9999967112513299
            ],
            [
                0.9999996072136126,
                0.9999990577552942,
                0.9999983463106124,
                0.9999975938982355,
                0.9999996743688975,
                0.9999957771670647,
                0.999997438717181,
                0.9999977396762422,
                0.9999992188519491,
                0.9999974387165704
            ],
            [
                0.9999785550567555,
                0.9999987121043248,
                0.9999992188513904,
                0.9999898700054198,
                0.999996910505186,
                0.9999978766210325,
                0.9999998555019619,
                0.9999989969855535,
                0.9999981261248411,
                9.931189774187203e-08
            ],
            [
                1.275190580884987e-07,
                0.9999921107355405,
                7.734423152941018e-08,
                0.9999962733598307,
                1.4449798650551755e-07,
                0.9999972735284319,
                9.931189774187203e-08,
                0.9999921107402451,
                0.9999994284994852,
                0.9999997761971049
            ],
            [
                6.825606165129312e-08,
                1.2751905808881762e-07,
                3.6534807736504303e-08,
                7.73442776300517e-08,
                4.6911598871325847e-08,
                9.931202796884815e-08,
                1.2751899728286965e-07,
                1.4449805540651476e-07,
                3.653485128931788e-08,
                4.1399375473868e-08
            ],
            [
                0.9999984465028026,
                0.9999996072137999,
                0.9999945777803908,
                6.825605351455307e-08,
                0.9999975938979495,
                0.999998346310021,
                8.764242227418718e-08,
                0.9999945777823274,
                0.9999980052707553,
                0.9999916019289776
            ],
            [
                0.999999776197025,
                0.999999631011416,
                0.9999998257021422,
                0.9999975938979493,
                0.9999994284997575,
                0.9999916019299893,
                0.9999993916409637,
                0.9999993106389549,
                0.9999852610110153,
                0.9999996310113721
            ],
            [
                4.6911660386730734e-08,
                6.825608606148807e-08,
                6.023574911170301e-08,
                1.1253525596055243e-07,
                5.315785605498567e-08,
                7.734424996967756e-08,
                1.8553919030708836e-07,
                7.734419464850171e-08,
                5.315783704433184e-08,
                6.825604537781398e-08
            ],
            [
                0.9999992188517628,
                0.9999987121044787,
                0.9999843104503227,
                0.9999975938965157,
                0.9999995262096119,
                0.9999993106386262,
                0.9999986290421405,
                0.9999991684722702,
                5.315784971839039e-08,
                0.9999993524051249
            ],
            [
                3.288749849498565e-06,
                0.9999977396757049,
                0.9999985406230839,
                2.3823702359290413e-07,
                0.9999980052695666,
                0.9999996072137063,
                0.9999960330140886,
                0.9999996533673379,
                0.9999990577556311,
                0.999998712104171
            ],
            [
                0.9999998874647977,
                0.9999975938982355,
                0.9999945777823281,
                0.999999935879425,
                0.9999998642566219,
                0.9999952149066509,
                0.9999993106392013,
                0.9999996072136594,
                0.9999998024945624,
                0.9999996743688975
            ],
            [
                0.9999993106388729,
                0.9999975938979501,
                0.9999997463981334,
                0.9999986290432842,
                0.9999982396561583,
                7.734421308914719e-08,
                0.9999972735294068,
                0.9999599362889732,
                9.93118503859575e-08,
                0.9999991684718736
            ],
            [
                6.82560128305259e-08,
                8.764242227380856e-08,
                6.82560128305259e-08,
                1.4449800373065699e-07,
                3.2241881707064475e-08,
                1.637377643243723e-07,
                3.4663257978780455e-07,
                1.2751905808881762e-07,
                1.1253510839355284e-07,
                9.931193325852072e-08
            ],
            [
                2.845334049639656e-08,
                8.764249540862797e-08,
                8.764255809528314e-08,
                1.1253512180925583e-07,
                1.444979692797559e-07,
                1.1253509497883659e-07,
                9.931195693628605e-08,
                5.3157811697009444e-08,
                1.275190276859705e-07,
                0.9999985406241275
            ],
            [
                0.9999990577556311,
                0.999999057755631,
                0.9999999358793639,
                0.9999989322972579,
                6.144174601991196e-06,
                0.9999999732705729,
                0.9999997897567342,
                0.9999988634365609,
                0.9999999500627738,
                0.9999978766220452
            ],
            [
                4.139934586278605e-08,
                6.825601283086733e-08,
                8.764247451307293e-08,
                3.653483822348123e-08,
                7.73441946488886e-08,
                6.825606165129312e-08,
                4.691162124067829e-08,
                2.1024331597262577e-07,
                7.73442776303243e-08,
                6.023573475041126e-08
            ],
            [
                9.931199245322124e-08,
                3.059022998576899e-07,
                1.8553905760062447e-07,
                1.4449802095609418e-07,
                3.0590237279032884e-07,
                6.023573475041126e-08,
                2.382370235922541e-07,
                5.715007195447234e-07,
                1.1253520230052635e-07,
                1.8553907971855875e-07
            ],
            [
                0.9999983463102179,
                0.9999996072137999,
                0.9999981261241708,
                0.9999969105066622,
                9.931188590255539e-08,
                0.9999987901337405,
                0.9999994956526521,
                0.9999995818813768,
                0.9999982396563692,
                0.9999987901343176
            ],
            [
                0.9999998024947272,
                1.1253517547010071e-07,
                1.4449807263287805e-07,
                0.9999996072138466,
                0.9999997126314468,
                0.9999998874649185,
                0.9999992661792823,
                0.9999998555020307,
                0.9999991684718738,
                0.9999990577554067
            ],
            [
                0.9999994631247404,
                0.9999997897567092,
                1.8553905760024476e-07,
                0.9999964991460054,
                0.9999987121046315,
                0.9999996533673791,
                0.9999957771650465,
                0.9999991684720719,
                0.9999987901343178,
                0.9999988634362899
            ],
            [
                1.275190124842887e-07,
                4.691162683297406e-08,
                1.8553916819032217e-07,
                4.139936066832438e-08,
                2.6995784182140636e-07,
                8.764245361752286e-08,
                1.8553907971855875e-07,
                3.653482951291499e-08,
                1.4449798650476187e-07,
                6.825602910433871e-08
            ],
            [
                0.9999997463980729,
                0.9999986290426306,
                0.9999970976869796,
                6.023571320847322e-08,
                0.9999962733607186,
                0.9999983463098236,
                0.9999957771675652,
                0.9999991684722702,
                0.9999994284997578,
                0.9999957771675687
            ],
            [
                0.9999892166916545,
                0.99999787662078,
                0.9999990577554068,
                0.9999991684722702,
                0.9999904837471827,
                0.9999995262093858,
                0.9999978766215393,
                6.825598842035714e-08,
                0.9999980052709933,
                0.9999832985782134
            ],
            [
                1.8553919030708836e-07,
                0.9999989322967487,
                0.9999960330155101,
                0.9999975938968033,
                6.023569166629634e-08,
                0.999997438716877,
                0.9999962733602746,
                1.1253506814797596e-07,
                0.9999984465018767,
                0.9999983463106119
            ],
            [
                0.9999945777784554,
                0.9999599362935956,
                9.931202796957073e-08,
                0.9999898700078277,
                0.9999980052700419,
                0.9999993524050478,
                6.825609419823202e-08,
                0.9999885212291533,
                0.9999945777803926,
                0.9999980052707557
            ],
            [
                0.99999886343629,
                0.9999991148433867,
                0.99999926617902,
                0.9999972735303825,
                0.9999986290427941,
                0.9999992661789324,
                0.9999989322971305,
                6.825605351455307e-08,
                0.9999996072136594,
                0.9999991148432812
            ],
            [
                0.9999869928715556,
                0.9999898700126542,
                0.9999997463981334,
                0.99999385582394,
                0.9999982396559496,
                7.734418542875216e-08,
                0.9999938558276014,
                4.139938534423022e-08,
                5.043473480766399e-07,
                0.9999987121046315
            ],
            [
                0.9999993916411085,
                7.73441946488886e-08,
                0.9999991148429646,
                0.9999969105055545,
                0.9999977396748962,
                0.9999991148428593,
                0.9999991148433868,
                0.9999994631251244,
                0.9999967112517214,
                0.9999992661789324
            ],
            [
                4.1399365603508136e-08,
                2.845334049639656e-08,
                0.9999978766217941,
                5.3157830707696514e-08,
                4.139939521459479e-08,
                4.139934586278605e-08,
                0.9999985406243025,
                6.023576347299818e-08,
                4.139941495546278e-08,
                0.999999730042094
            ],
            [
                0.9999986290424677,
                0.9999980052700419,
                0.9999969105051861,
                0.9999984465022466,
                0.9999987901346056,
                0.9999996533672137,
                0.999998126123724,
                0.9999756997680279,
                6.825602910433871e-08,
                0.9999991684719727
            ],
            [
                0.9999995818813269,
                0.9999996940978096,
                0.9999991684715762,
                0.9999982396565774,
                0.9999984465022459,
                0.9999985406232579,
                9.931193325852072e-08,
                0.9999989969861515,
                0.9999989322967487,
                0.9999987901346055
            ],
            [
                0.999981074854035,
                0.9999989969856732,
                0.9999989322966213,
                4.139936066813141e-08,
                2.1024326584505647e-07,
                0.9999998802069017,
                5.043474081993875e-07,
                0.9999993916409634,
                0.9999993524050478,
                0.9999993524049703
            ],
            [
                1.444980209564556e-07,
                0.9999921107355466,
                0.999989216690366,
                1.2751905808881762e-07,
                0.999999730042287,
                0.9999998802069159,
                8.764247451307293e-08,
                8.764249540862797e-08,
                6.023577065363335e-08,
                1.275190580884987e-07
            ],
            [
                6.023577065363335e-08,
                0.9999991148429646,
                0.9999988634364263,
                0.9999987121049387,
                0.9999994284993489,
                0.9999987901340287,
                0.9999957771645454,
                0.9999990577552946,
                0.9999995818811276,
                0.9999985406241282
            ],
            [
                0.9999984465024326,
                0.9999980052705176,
                0.9999995818811774,
                0.9999986290429579,
                5.315786239218605e-08,
                0.9999952149066486,
                0.9999985406234321,
                0.9999987901341734,
                1.1253510839355284e-07,
                0.9999994284996896
            ],
            [
                0.9999967112521131,
                0.9999987901346054,
                1.275190276853036e-07,
                0.9999964991451707,
                0.9999964991451714,
                0.9999986290432842,
                0.9999892166839436,
                0.9999885212318904,
                0.9999861539954765,
                0.999985261012779
            ],
            [
                0.9999983463110067,
                0.9999998642566543,
                0.9999988634360188,
                0.9999985406239538,
                0.9999995818810776,
                0.9999990577552943,
                0.9999989969861516,
                0.9999972735284306,
                4.6911604463613627e-08,
                0.9999962733607191
            ],
            [
                2.102433159721477e-07,
                0.9999987901338845,
                4.4508526417298334e-07,
                0.9999843104540428,
                9.931198061405701e-08,
                3.9278634073625165e-07,
                0.9999990577557435,
                3.927862002654366e-07,
                0.9999995549148951,
                1.1253516205489029e-07
            ],
            [
                0.9999996743686645,
                0.9999996310114598,
                0.9999997897565839,
                0.9999998257021422,
                0.999999607213753,
                0.999994906295609,
                0.9999980052700417,
                0.9999987121049387,
                0.9999989969855535,
                0.9999989969856734
            ],
            [
                0.9999980052695671,
                1.855391239539711e-07,
                0.9999997300422229,
                0.9999991148433864,
                0.9999975938976615,
                0.9999992188518563,
                0.9999934595627804,
                0.9999994631251243,
                9.931196877517082e-08,
                0.999996273361608
            ],
            [
                0.9999998144609203,
                0.9999991684722702,
                4.69116268327394e-08,
                0.9999985406234321,
                0.9999989322970033,
                0.9999970976880174,
                0.9999942280779108,
                0.9999987901337404,
                0.9999982396559485,
                0.9999990577552942
            ],
            [
                9.931188590255539e-08,
                4.139935079796334e-08,
                4.6911677163762064e-08,
                8.764247451307293e-08,
                5.315786239218605e-08,
                3.224186633297071e-08,
                1.2751899728286965e-07,
                1.8553903548231313e-07,
                1.2751901248454963e-07,
                6.023571320847322e-08
            ],
            [
                0.9999997897566841,
                0.9999998724810027,
                0.9999985406236058,
                0.9999986290421402,
                0.9999995818811276,
                0.9999822214503171,
                0.9999974387180965,
                0.9999991684722704,
                7.734421308914719e-08,
                0.999998346310021
            ],
            [
                0.9999994631248044,
                0.9999981261252878,
                0.9999960330126706,
                0.9999996533675031,
                0.9999991684715761,
                9.931195693628605e-08,
                0.9999970976883615,
                0.9999994284996895,
                0.9999989969861515,
                0.9999885212346337
            ],
            [
                7.734424996967756e-08,
                4.691162683297406e-08,
                7.734416698849138e-08,
                1.1253517547010071e-07,
                6.023572038912295e-08,
                6.825602910433871e-08,
                6.825602910433871e-08,
                1.1253512180925583e-07,
                1.6373776432481905e-07,
                1.4449807263312446e-07
            ],
            [
                0.9999980052700423,
                0.9999985406236057,
                0.9999996940977731,
                0.9999998461827322,
                0.999994906293182,
                0.9999987121044781,
                0.9999998461826956,
                0.9999938558268688,
                0.9999994631251883,
                0.9999989322973851
            ],
            [
                0.9999974387187082,
                0.9999995818811276,
                0.9999980052695667,
                2.1024344128584085e-07,
                0.9999996743688975,
                0.9999962733620524,
                0.999987780922555,
                0.9999994956527724,
                0.9999982396559487,
                0.9999994631248045
            ],
            [
                9.422444815726566e-07,
                4.222834954687752e-06,
                0.9999989322970034,
                0.9999996940978462,
                0.9999995262093858,
                0.9999993916406734,
                7.734416698815724e-08,
                0.999999266178845,
                0.9999974387168753,
                0.9999975938979483
            ],
            [
                1.855391681906175e-07,
                9.931187406410953e-08,
                1.8553907971855875e-07,
                9.931195693628605e-08,
                1.2751905808881762e-07,
                1.27519088491875e-07,
                1.4449807263312446e-07,
                1.1253509497883659e-07,
                1.8553907971855875e-07,
                1.275191036933194e-07
            ],
            [
                0.9999957771675667,
                0.9999960330136183,
                0.9999993916408185,
                0.9999925887227913,
                0.9999981261246176,
                0.9999964991455901,
                0.9999741325721059,
                0.9999997463982241,
                0.9999997126315497,
                0.9999993524053565
            ],
            [
                0.9999987901338845,
                0.9999991148431756,
                0.9999991684722703,
                0.9999962733616071,
                0.9999991684717746,
                6.825598028364134e-08,
                0.999999391640746,
                0.9999977396762435,
                0.9999996940978462,
                0.9999756997651715
            ],
            [
                1.8553905760062447e-07,
                7.734421308914719e-08,
                1.1253512180925583e-07,
                8.764242227418718e-08,
                5.315783704433184e-08,
                6.825602910433871e-08,
                6.825609419823202e-08,
                6.023572038912295e-08,
                6.023569884718319e-08,
                9.931193325852072e-08
            ],
            [
                0.9999885212277801,
                0.9999981261246176,
                6.023573475041126e-08,
                0.9999964991468402,
                0.9999869928715501,
                0.9999997126313783,
                0.9999960330150338,
                0.9999985406243016,
                0.9999992188515765,
                0.9999991684718736
            ],
            [
                NaN,
                0.9999945777823328,
                0.9999990577551822,
                0.9999975938985224,
                0.9999992661792824,
                0.9999993524054337,
                0.999999674368781,
                0.9999996533674204,
                0.9999994284996895,
                0.9999994284997576
            ],
            [
                0.9999967112521162,
                0.9999990577552943,
                0.9999892166903643,
                0.9999969105048191,
                NaN,
                0.9999983463110067,
                0.9999997126314126,
                0.9999989322967492,
                5.315786239218605e-08,
                0.9999962733611655
            ]
        ]
    },
    {
        "q_id": "9710_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.999999917667573,
                0.9999999317439546,
                0.9999999176674848,
                0.9999999226557592,
                0.9999998802069159,
                0.9999999358794479,
                0.9999999123575881,
                0.9999999559305944,
                0.9999998874647977,
                0.9999999176674454
            ],
            [
                1.0,
                0.9999998874647307,
                0.9999999226557316,
                0.999999943413784,
                0.9999999176675239,
                1.0,
                0.9999999176675829,
                0.999999946842125,
                0.9999998942830863,
                0.9999999006881259
            ],
            [
                0.9999999358794096,
                0.9999999358793409,
                0.9999999434137232,
                0.9999994956523515,
                0.9999998802069444,
                1.0,
                0.9999999176675436,
                0.9999998362622943,
                1.0,
                0.9999999273418356
            ],
            [
                0.999999825702163,
                1.0,
                0.9999999358793333,
                0.9999999611088672,
                0.9999999468421693,
                0.9999999586006542,
                1.0,
                1.0,
                0.9999998724809419,
                0.9999999559305943
            ],
            [
                1.0,
                0.9999998942830737,
                0.9999999500628215,
                0.9999999006880549,
                0.9999998461826589,
                0.9999999358794021,
                0.9999998874647709,
                0.9999998461826222,
                0.9999998724810027,
                0.9999998461826772
            ],
            [
                0.9999998942829351,
                0.9999998642567353,
                0.9999996072138001,
                0.9999998362622747,
                0.9999997463980729,
                1.0,
                0.9999993916407462,
                0.9999996533674617,
                0.9999997761971849,
                0.9999999067049831
            ],
            [
                1.0,
                0.9999999226558054,
                0.999999922655833,
                0.9999999123574942,
                0.999999802494586,
                0.9999999559305943,
                0.9999999273418182,
                0.9999999500628274,
                0.9999998802068873,
                0.999999943413757
            ],
            [
                1.4449803818215767e-07,
                1.4449796928021588e-07,
                1.4449800373118268e-07,
                1.444980209564556e-07,
                9.931200429212718e-08,
                3.2887502415767434e-06,
                2.3823696679327928e-07,
                1.2751904288710323e-07,
                3.05902263391829e-07,
                8.764247451307293e-08
            ],
            [
                0.9999999226557776,
                0.9999995262095551,
                1.0,
                0.9999998461826038,
                0.9999998942830358,
                0.9999998362622552,
                0.9999997463981939,
                0.9999999176675534,
                0.9999999226558515,
                0.9999998942829602
            ],
            [
                0.999999814460832,
                0.999999927341775,
                0.9999998642566219,
                0.9999999067050498,
                0.999999864256719,
                0.9999999067050832,
                0.9999998555019791,
                0.9999999176675142,
                0.9999996743686259,
                0.9999998461826956
            ],
            [
                0.999999391641036,
                0.999999653367379,
                0.9999998642566219,
                0.9999997897567342,
                0.9999998257021007,
                0.9999997761972116,
                0.9999996310114159,
                0.999999581881277,
                0.9999996533673378,
                0.9999996310115039
            ],
            [
                0.9999999067050498,
                0.9999999123575881,
                0.9999998724809724,
                0.9999999468421693,
                1.0,
                0.9999998724809115,
                0.9999998874647574,
                0.999999917667475,
                0.9999998942829477,
                1.0
            ],
            [
                8.31528424151477e-07,
                6.1441731370702875e-06,
                8.939696304116203e-06,
                5.04347348075149e-07,
                5.715004470272272e-07,
                6.962256249758443e-06,
                3.2887482812506295e-06,
                4.450852111120808e-07,
                7.338211554725124e-07,
                5.043475284430694e-07
            ],
            [
                0.9999998874647307,
                0.9999999226558146,
                0.9999998144608541,
                0.9999999067050165,
                0.9999999226557131,
                0.9999999226557408,
                0.9999998555019446,
                0.9999998802069874,
                0.9999998942829477,
                1.0
            ],
            [
                0.9999999226558515,
                0.9999999317440035,
                0.9999998874649051,
                0.9999998802069588,
                0.9999998642567351,
                0.9999999559305944,
                0.9999999397643083,
                0.9999999176674357,
                0.999999814460832,
                0.9999999176674357
            ],
            [
                0.9999999358794402,
                0.9999999226557685,
                0.9999999397642293,
                0.9999999468421313,
                0.9999999226557778,
                0.9999999006879957,
                0.9999999358793867,
                0.999999961108858,
                0.9999999273418615,
                0.9999999273418182
            ],
            [
                1.0,
                0.999999581881327,
                0.999999554914842,
                0.9999999006880668,
                0.9999998257020799,
                0.9999998942830737,
                0.9999998802069731,
                0.9999999176674848,
                0.9999999226557501,
                0.9999998942828973
            ],
            [
                0.9999998942830485,
                0.9999998362623139,
                0.999999927341801,
                0.9999999273418703,
                0.9999998642566543,
                1.0,
                0.9999998362623138,
                0.999999931743914,
                0.9999998942830862,
                0.9999999226558238
            ],
            [
                0.9999999226558238,
                2.1024344128584085e-07,
                0.9999999123575151,
                4.450852641717689e-07,
                0.9999999317439383,
                0.9999995262094422,
                1.7603440527222532e-06,
                0.999998863436019,
                0.9999992661786701,
                0.9999997761970515
            ],
            [
                0.9999998802069302,
                0.9999998461827139,
                0.9999999226558515,
                0.9999999176675534,
                0.9999999123575151,
                0.9999997463981938,
                0.9999999067051499,
                0.9999999358794096,
                0.9999996072137063,
                0.9999999176674357
            ],
            [
                0.9999999067051499,
                0.9999999317440035,
                0.9999999358793791,
                0.9999998555020481,
                0.9999999397642294,
                0.9999999397642437,
                0.9999999468421124,
                0.9999999123574523,
                0.9999998724809875,
                0.9999999317439058
            ],
            [
                0.9999999006881023,
                0.9999999317440034,
                0.9999999358794097,
                0.9999998461826589,
                0.9999998362622943,
                0.9999996940977367,
                1.0,
                0.999999776197185,
                0.9999999176674848,
                0.9999996533674204
            ],
            [
                4.785092783519724e-06,
                4.2228329411708495e-06,
                6.9622595696935874e-06,
                5.043474081993875e-07,
                0.9999969105040811,
                4.222831934379152e-06,
                1.9947304348862686e-06,
                1.0677032518785256e-06,
                1.3007130015299356e-05,
                1.7603425837606927e-06
            ],
            [
                0.9999984465028021,
                0.9999996743687424,
                0.999999761763005,
                0.9999985406243022,
                0.9999991148429646,
                3.927863875616689e-07,
                0.9999993916408911,
                0.9999985406230838,
                0.9999987901341727,
                8.939698435560267e-06
            ],
            [
                0.9999997126314811,
                0.9999998802069159,
                0.9999998461827322,
                0.9999964991451712,
                0.9999999067050609,
                0.9999999317440197,
                0.9999998642566704,
                0.9999988634366962,
                0.9999991684719727,
                0.9999998144609203
            ],
            [
                0.9999999067051388,
                0.9999999397642724,
                0.9999998642567028,
                0.9999997617631469,
                0.9999998257021214,
                0.9999999611089043,
                0.9999996743688586,
                0.9999998942830863,
                0.99999976176309,
                0.9999999358793332
            ],
            [
                3.4663278639892215e-07,
                0.9991959140616583,
                3.9278629391427843e-07,
                8.315280276626197e-07,
                1.2098661162056318e-06,
                5.043472278322555e-07,
                1.2098659719788098e-06,
                5.71500719545698e-07,
                1.6373776432509826e-07,
                3.927863875616689e-07
            ],
            [
                0.9999998362622552,
                0.9999996743687422,
                1.0,
                1.0,
                0.999999922655833,
                0.9999997300421583,
                1.0,
                0.999999963465201,
                0.9999998362623723,
                0.9999999656786792
            ],
            [
                0.9999998874648917,
                0.9999998362623137,
                0.999999730042287,
                0.9999998802069159,
                0.9999999176675632,
                0.9999997761971849,
                0.9999994631248683,
                0.9999996072139402,
                0.9999998724809723,
                0.9999998724810027
            ],
            [
                0.9999996072136128,
                0.9999998555019274,
                0.9999999226558054,
                0.9999998802069874,
                0.999999825702163,
                0.9999999317439954,
                0.9999999123574629,
                0.9999998555020136,
                0.999999730042094,
                0.9999999500628334
            ],
            [
                0.9999996533674617,
                1.0,
                0.9999999176675535,
                0.9999999317440279,
                0.999999761763005,
                0.9999998555019446,
                0.9999999176674552,
                0.9999999226557684,
                7.73441946488886e-08,
                0.9999999397642939
            ],
            [
                0.9999999273418355,
                0.9999998555020136,
                0.9999994284997575,
                0.9999999397643156,
                0.9999997897567342,
                0.9999998874648783,
                0.9999996743688199,
                1.0,
                0.9999999006880431,
                0.9999998362623335
            ],
            [
                0.9999999006881497,
                0.9999999434137841,
                0.9999999273418095,
                0.9999998362622943,
                0.9999999397642436,
                0.9999998257021421,
                0.9999999273418009,
                0.9999999123575359,
                0.9999999468420996,
                1.0
            ],
            [
                1.0,
                0.9999993524053566,
                0.9999995262092729,
                0.9999998362623723,
                0.999999554914736,
                0.9999998802069874,
                0.9999997897566842,
                0.9999999067050276,
                0.9999995549149483,
                0.9999996072136593
            ],
            [
                0.9999999226557224,
                0.9999999006880668,
                0.9999995549151075,
                0.9999996940976639,
                1.0,
                0.9999999067051499,
                0.9999998942828973,
                0.9999998724809724,
                0.9999999634651531,
                0.9999998874649184
            ],
            [
                0.9999997761971849,
                0.9999997300421583,
                0.9999999500628214,
                0.9999999611089043,
                1.0,
                1.0,
                1.0,
                0.9999998724809723,
                0.9999998874648648,
                0.9999998874648112
            ],
            [
                0.9999996940978826,
                0.9999999006881497,
                0.999999939764258,
                1.0,
                0.9999998942828972,
                0.9999999317439954,
                0.9999998802069731,
                0.9999999317439059,
                0.9999999067050499,
                9.931188590255539e-08
            ],
            [
                0.9999999434137368,
                0.9999998942829098,
                0.9999996940977003,
                0.9999999273418095,
                0.9999999500627739,
                0.999999887464838,
                0.9999998461826589,
                0.9999997761971849,
                0.9999998555019274,
                0.9999994631247404
            ],
            [
                0.9999998802068873,
                0.9999995818813269,
                0.9999991684720718,
                0.9999999530883508,
                0.9999998874649318,
                0.9999995818813767,
                0.9999999559306206,
                0.9999997126314811,
                0.9999999434138043,
                0.9999998461827139
            ],
            [
                0.9999998874648514,
                0.9999999677581567,
                0.9999999500628036,
                1.0,
                0.9999999358793485,
                0.9999999123574523,
                0.9999999358794021,
                1.0,
                0.9999999586006196,
                0.999999939764215
            ],
            [
                0.9999999273417836,
                0.9999999226557961,
                0.99999976176309,
                0.9999999226558238,
                0.9999997761970515,
                0.9999996743688586,
                0.9999996310114159,
                0.9999996533673791,
                1.1253520230052635e-07,
                0.9999998942830358
            ],
            [
                1.0,
                0.9999998942829854,
                0.9999999123575046,
                1.0,
                0.9999999273418876,
                1.0,
                0.9999999358794249,
                0.9999999176675338,
                0.9999997897567091,
                0.9999997761971583
            ],
            [
                0.9999999500628571,
                0.9999998642566219,
                0.9999998802069159,
                0.9999998802069731,
                0.9999998802069731,
                0.9999999317439221,
                0.999999927341853,
                0.9999999273418876,
                0.9999999067050609,
                0.9999999067050943
            ],
            [
                0.9999999559305786,
                1.0,
                0.9999999500627917,
                0.9999998144609424,
                0.9999999530883341,
                0.9999997300420939,
                1.0,
                0.9999999500628393,
                0.9999999697115443,
                0.9999999778405133
            ],
            [
                0.9999999067051276,
                0.9999999397643156,
                0.9999999176674651,
                0.9999998642566381,
                0.9999997761970515,
                0.9999998362623723,
                0.9999999123574836,
                0.9999999397642796,
                0.9999999006881023,
                0.9999999123574523
            ],
            [
                0.9999996940977367,
                0.9999999468421503,
                0.9999999500628214,
                0.9999998642567351,
                0.999999900688043,
                0.9999999006880785,
                0.9999999273417922,
                0.9999998257021422,
                0.9999998642566704,
                0.9999999273418875
            ],
            [
                0.999999946842125,
                0.9999998724809115,
                0.9999999530883564,
                0.9999999530883843,
                0.9999997126313099,
                0.9999999397642797,
                0.9999993524050478,
                1.0,
                0.9999997897567092,
                0.9999999397642437
            ],
            [
                0.9999998874647307,
                0.9999998874648648,
                0.9999997761971048,
                0.9999999434137368,
                0.9999999226558515,
                0.9999998724809419,
                1.0,
                0.9999998802068873,
                0.9999999397642796,
                0.9999999176675634
            ],
            [
                0.9999998802069731,
                0.9999999123574523,
                0.9999999530883843,
                0.999999927341801,
                0.9999996072138466,
                0.9999999176675143,
                0.9999999176675829,
                0.999999943413784,
                0.9999999317440278,
                0.9999999226558238
            ],
            [
                0.9999998024945624,
                0.9999998942830737,
                0.9999999006879721,
                0.9999998362623723,
                0.9999999123574524,
                0.9999999677581028,
                0.9999998642567351,
                0.9999999634651878,
                0.9999998257020798,
                0.9999999397642437
            ],
            [
                0.9999999358793944,
                1.0,
                0.9999999559305733,
                0.9999996743686647,
                0.9999999176675634,
                0.99999995308839,
                0.9999999358794402,
                0.9999995262095553,
                0.9999997300422548,
                0.9999998024945624
            ],
            [
                1.0,
                0.9999997897565839,
                0.9999994631249324,
                1.0,
                0.9999999500628453,
                0.999999917667475,
                0.9999999176674946,
                3.05902190458764e-07,
                0.999999894282935,
                0.9999999273418443
            ],
            [
                0.9999997126315499,
                0.9999999273417662,
                0.9999998802069731,
                0.9999999358794479,
                0.9999998461826406,
                0.9999999176675044,
                0.9999998257021837,
                0.999999912357442,
                0.9999999358794021,
                0.9999999434137233
            ],
            [
                0.9999995818814266,
                0.9999916019289765,
                0.9999998802069017,
                0.9999998144609424,
                0.9999998362623723,
                0.9999998024946802,
                0.9999983463096266,
                0.999999855502048,
                0.9999980052705174,
                0.9999996743688586
            ],
            [
                0.9999999067050832,
                0.9999998461826771,
                0.9999998362622943,
                0.9999998461827139,
                0.9999998461827138,
                0.9999998874647978,
                0.9999999176675044,
                0.9999999358794402,
                0.999999931743979,
                0.9999997897566842
            ],
            [
                8.315281267861397e-07,
                1.3709570434178922e-06,
                5.71500515159253e-07,
                4.450852111100568e-07,
                8.315281267861397e-07,
                8.315278294097538e-07,
                3.0590237279032884e-07,
                2.2603240284371276e-06,
                0.9999955048200324,
                1.2098659719757836e-06
            ],
            [
                0.9999999273417923,
                1.0,
                0.9999998257021006,
                1.0,
                0.9999999067050165,
                0.9999999226558515,
                0.9999995818813269,
                0.9999998144608983,
                0.9999998874649051,
                0.9999999226557592
            ],
            [
                1.0,
                0.9999999434137435,
                0.9999998874647977,
                1.0,
                0.9999999434137367,
                1.0,
                0.9999999006880668,
                0.9999998257021422,
                0.9999990577552943,
                0.9999999067049942
            ],
            [
                0.9999999273418616,
                0.9999999559306206,
                0.9999997126313441,
                0.9999999559306312,
                1.0,
                0.9999999586006394,
                0.9999999226557224,
                0.9999999317439954,
                0.9999998642567028,
                0.9999999500627857
            ],
            [
                0.9999999226557131,
                0.9999998942830862,
                0.9999999317439058,
                0.9999999358794479,
                0.9999999273418442,
                1.0,
                0.999999943413757,
                0.9999998461826222,
                0.9999999397642437,
                0.9999999317439872
            ],
            [
                0.9999999397642653,
                1.0,
                0.9999999468421186,
                0.9999999530883508,
                0.9999998642567351,
                0.9999999067050276,
                1.0,
                0.9999999067050609,
                0.9999999067051054,
                0.999999887464771
            ],
            [
                0.9999999500628513,
                0.9999999273417749,
                1.0,
                1.0,
                0.9999999358794173,
                0.9999998257021422,
                0.9999999123575359,
                0.9999999176674749,
                0.9999999434137637,
                1.0
            ],
            [
                1.0,
                0.9999999273418443,
                1.0,
                0.9999997463980427,
                1.0,
                0.9999999273418703,
                0.999999939764258,
                1.0,
                1.0,
                0.9999999434137773
            ],
            [
                0.9999999176675044,
                0.9999999468420996,
                0.9999999123574836,
                0.9999999226557962,
                0.9999998942829854,
                0.9999998362622943,
                0.999999855501962,
                0.9999997617630901,
                0.9999999226558515,
                0.9999998555019274
            ],
            [
                0.9999998461827139,
                0.9999998362623139,
                1.0,
                0.9999999434137907,
                0.9999998257021213,
                1.0,
                0.9999997897567092,
                1.0,
                0.9999999273418789,
                0.9999996743688975
            ],
            [
                0.9999998942829099,
                0.9999995818812771,
                1.0,
                0.9999999397642724,
                0.9999998461826954,
                0.9999999273418528,
                0.9999999123574628,
                0.9999999500627857,
                0.9999999123575464,
                0.9999993106392014
            ],
            [
                0.9999997300422226,
                0.9999998874648246,
                0.9999998555019619,
                0.999999789756609,
                0.9999998874648246,
                0.9999998461826223,
                0.999999864256719,
                0.9999998144608319,
                0.9999997463980125,
                0.9999998942830485
            ],
            [
                0.9999999434137233,
                0.9999998874649051,
                0.9999998257021213,
                0.9999997617630049,
                0.9999998942829602,
                0.9999998555019791,
                0.9999998555019275,
                0.9999998642566381,
                0.9999997126313099,
                0.9999999226557409
            ],
            [
                0.999999789756659,
                0.999999880206916,
                0.9999998942829981,
                0.9999998461826772,
                0.9999996310115482,
                0.9999994631250606,
                0.9999997897565589,
                0.9999998362622944,
                0.9999997761970516,
                0.9999997897567342
            ],
            [
                0.9999997300422226,
                0.9999996072136127,
                0.9999996743686645,
                0.9999998461826038,
                0.9999998257021422,
                0.9999998555019446,
                0.9999998362622944,
                0.9999998144608983,
                0.999999931743971,
                0.9999999317439872
            ],
            [
                0.9999998257020591,
                0.9999997761972116,
                0.9999999434137637,
                0.9999998874648246,
                0.9999999317440197,
                0.9999998461826956,
                0.9999998257020799,
                0.9999998874648515,
                0.999999846182604,
                0.9999995549148424
            ],
            [
                2.69957906184239e-07,
                2.102433159721477e-07,
                3.288749065423109e-06,
                1.8553916819032217e-07,
                6.962257079832313e-06,
                1.6373772528581146e-07,
                6.962258739796719e-06,
                6.962255419804982e-06,
                0.9999997617631469,
                8.7642516304188e-08
            ],
            [
                0.9999999358793639,
                0.9999997897566841,
                0.9999999226558054,
                0.9999997761971582,
                0.9999998362622552,
                0.9999999500627857,
                0.999999906705061,
                0.9999998942829098,
                0.9999999123574838,
                0.9999996940976638
            ],
            [
                0.9999999123574419,
                0.9999992188514837,
                0.9999998362623334,
                1.3709570434122812e-06,
                0.9999999317439059,
                0.9999998942829729,
                0.9999997126314126,
                0.9999992188513905,
                0.9999996743688587,
                0.9999999397642653
            ],
            [
                0.9999999006881497,
                0.9999999123575359,
                0.9999999317439221,
                0.999999927341801,
                1.0,
                0.999999931743914,
                0.9999999273418615,
                0.9999999358794173,
                0.999999946842182,
                1.0
            ],
            [
                0.9999997761970248,
                0.9999992188515766,
                0.9999998942830485,
                0.9999991148427535,
                0.9999992661792821,
                0.999999802494586,
                0.9999999226558054,
                0.9999992661791947,
                0.9999994284993488,
                0.9999992188518559
            ],
            [
                3.53562549305363e-05,
                1.8553916819032217e-07,
                7.338210680021253e-07,
                7.338208055664991e-07,
                1.8553910183607374e-07,
                8.315278294114555e-07,
                3.05902336324494e-07,
                1.5534975693979422e-06,
                8.939700567094277e-06,
                2.102433159721477e-07
            ],
            [
                1.0,
                0.9999999586006048,
                1.0,
                1.0,
                0.9999999176674357,
                1.0,
                1.0,
                0.999999953088362,
                1.0,
                1.0
            ],
            [
                8.764247451307293e-08,
                8.764253719973308e-08,
                9.931194509740267e-08,
                2.3823693839290317e-07,
                6.825602910433871e-08,
                1.444980381819277e-07,
                1.4449802095609418e-07,
                1.1253520230052635e-07,
                8.7642516304188e-08,
                9.931194509740267e-08
            ],
            [
                0.9999998724808964,
                0.9999999006880904,
                0.9999998874648782,
                1.0,
                0.9999999226558054,
                0.9999998642566219,
                0.9999999123574942,
                0.999999825702163,
                0.9999999317439465,
                0.9999999634651792
            ],
            [
                0.9999999176674749,
                0.999999746398073,
                0.9999998362623724,
                0.9999998874649318,
                0.9999999226557592,
                0.9999998724808964,
                0.9999996533674202,
                0.9999999397642725,
                0.9999998802069731,
                0.9999999067049831
            ],
            [
                0.999999958600659,
                0.9999999123574629,
                0.9999999559305787,
                0.9999999434137098,
                0.9999998024945861,
                1.0,
                1.0,
                0.9999999434137367,
                0.9999999500628513,
                0.9999998144609202
            ],
            [
                0.9999999123574523,
                0.9999992188517629,
                0.9999991148429644,
                0.9999998555020307,
                0.9999999358794021,
                0.999999872480942,
                0.9999999067051388,
                0.9999999176674553,
                0.9999991148433867,
                0.9999998555019274
            ],
            [
                0.9999999176675142,
                0.9999999273418703,
                0.9999999500627976,
                0.9999998942830358,
                0.9999999434137232,
                0.9999999317439384,
                0.9999996310115479,
                0.9999998942829225,
                0.9999999358793639,
                0.9999999434137098
            ],
            [
                0.9999997463980124,
                0.9999998724809267,
                0.9999996072136594,
                0.9999997463981939,
                0.9999998144608098,
                0.9999997761970516,
                0.9999997617630617,
                0.9999999468421186,
                0.9999999123575672,
                0.9999996533674204
            ],
            [
                0.999999352405202,
                0.9999999358794021,
                0.9999999500628155,
                0.9999999677581606,
                0.9999997617630332,
                0.9999995818812272,
                0.9999996072136594,
                0.9999999123575359,
                0.9999999397643012,
                0.9999999559305787
            ],
            [
                0.9999998461826588,
                6.825604537781398e-08,
                0.9999998362622943,
                0.9999997463981939,
                9.931202796957073e-08,
                0.9999997463981939,
                0.999999653367503,
                0.9999999176675338,
                0.9999999500627917,
                0.9999999586006542
            ],
            [
                3.927862002663297e-07,
                4.785095065204162e-06,
                1.6701427817730953e-05,
                0.9999992188514835,
                2.902311639183378e-06,
                3.0590237279032884e-07,
                2.2603234895289998e-06,
                3.46632497145457e-07,
                0.9999938558239364,
                0.9999972735287569
            ],
            [
                0.9999999067049943,
                0.9999999500627916,
                0.9999999358793791,
                0.9999997463982242,
                1.0,
                1.0,
                0.9999998024946566,
                0.9999999634652009,
                1.0,
                0.999999963465201
            ],
            [
                1.0,
                0.9999999530883955,
                0.9999999358793791,
                0.9999999273418961,
                0.9999999434137975,
                0.9999999226557132,
                1.0,
                1.0,
                0.9999998144608099,
                0.9999999226557501
            ],
            [
                0.9999999226557961,
                0.9999999586006344,
                0.9999998942829981,
                0.9999998802069587,
                0.9999999530883508,
                0.9999999273418269,
                0.9999999468421312,
                0.9999999006880312,
                0.9999992661789323,
                0.9999999434137571
            ],
            [
                0.9999999273418096,
                0.9999999006880431,
                0.9999998461826588,
                0.9999999176674652,
                0.9999994284996213,
                0.9999999530883397,
                0.9999999397643083,
                0.9999995818810776,
                0.9999996743686257,
                0.9999999067050387
            ],
            [
                0.9999999468421567,
                0.9999998461826222,
                0.9999995549148951,
                0.9999999397642293,
                1.0,
                0.9999997300421583,
                1.5534981249697903e-06,
                0.9999999123574942,
                0.9999997126313098,
                1.0
            ],
            [
                0.999999391640746,
                0.999999943413811,
                1.0,
                0.9999998874648112,
                1.0,
                0.9999993916409636,
                0.9999999176674454,
                0.9999997617630616,
                0.9999999006879957,
                0.9999997463981032
            ],
            [
                0.9999999500628155,
                0.9999999397642725,
                1.0,
                0.9999999006880904,
                0.9999998942830233,
                0.9999998874648649,
                3.927862939126708e-07,
                0.9999999273418095,
                0.9999982396565775,
                0.9999998942829981
            ],
            [
                0.9999999434137165,
                0.9999996940976638,
                0.9999999176675338,
                1.0,
                0.9999998802069017,
                0.9999998724809268,
                0.9999996940977367,
                0.9999999468421693,
                0.9999998461826772,
                0.999999864256719
            ],
            [
                0.9999997617631754,
                0.9999996940977733,
                0.9999998024946802,
                0.9999998802069445,
                0.9999998362622748,
                0.9999997617631186,
                0.9999996533674619,
                0.9999996072136128,
                0.9999990577554069,
                0.9999998724809723
            ],
            [
                0.9999999067050832,
                0.9999999067051165,
                0.9999999317439954,
                0.9999998555020135,
                1.0,
                1.0,
                0.9999996743688975,
                0.9999998642566543,
                0.999999927341775,
                0.9999999226557224
            ],
            [
                0.9999999226557501,
                0.9999998802069159,
                0.9999998144609203,
                0.9999996743686645,
                1.0,
                0.9999999397643083,
                0.9999999067050832,
                0.999999730042094,
                1.0,
                1.0
            ],
            [
                0.9999997300421262,
                0.999999927341853,
                0.9999998257022045,
                1.0,
                0.999999922655787,
                0.9999999273418961,
                1.0,
                0.9999998802068873,
                0.9999999067050831,
                0.999999887464932
            ],
            [
                0.9999996310113721,
                1.3709570434178922e-06,
                0.9999998724809572,
                7.338209805240734e-07,
                1.7603438428740716e-06,
                4.785096206047877e-06,
                0.9999996310115039,
                0.9999993106392014,
                0.9999994284994851,
                1.0677027427569065e-06
            ],
            [
                0.9999999067049832,
                0.9999997300421904,
                0.9999999530883675,
                1.0,
                0.9999999434137705,
                0.9999999559306154,
                0.9999998874647709,
                0.999999391640891,
                0.9999999006879958,
                0.999999917667475
            ],
            [
                0.9999998724809571,
                0.9999998461826223,
                0.999999887464838,
                0.9999999123575777,
                4.785092783519724e-06,
                4.785096776468749e-06,
                1.0677032518814388e-06,
                2.5612816000145246e-06,
                1.3709573702778664e-06,
                2.5612825160562587e-06
            ],
            [
                0.9999998555020481,
                0.9999997463980427,
                0.9999996743687034,
                0.9999998362622358,
                0.9999998024947038,
                0.9999996940978096,
                0.9999999123575255,
                0.9999998362622553,
                0.9999998362622748,
                0.999999814460854
            ],
            [
                0.9999998802069587,
                1.0,
                0.9999999176675143,
                0.9999999397642365,
                0.9999999317440279,
                0.9999998257020798,
                0.9999999317439058,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999123574838,
                0.9999998555020309,
                0.9999999358794479,
                0.9999999226558054,
                0.9999993106386262,
                0.9999997463980428,
                0.9999989322971304,
                0.9999998642566381,
                0.9999993524053568,
                0.9999999226557225
            ],
            [
                0.9999998144609424,
                0.9999999006880549,
                0.9999998362622943,
                0.999999917667524,
                5.043473480777865e-07,
                0.9999999176674651,
                0.9999999317440197,
                0.9999999226558146,
                0.9999999434137773,
                0.9999996743686257
            ],
            [
                1.0,
                0.9999998802069159,
                0.999999653367255,
                0.9999999176674454,
                1.0,
                0.999999917667475,
                0.9999998362622943,
                0.9999999176674945,
                0.9999999559305943,
                0.9999999586006393
            ],
            [
                0.9999997126315496,
                0.999998346309824,
                0.999999761763005,
                0.9999997300422547,
                0.9999992661787577,
                0.9999998874649185,
                0.9999998555019274,
                0.9999982396561587,
                0.9999991684722701,
                0.9999998942829602
            ],
            [
                0.9999997761971317,
                0.9999998461826957,
                0.9999998642566704,
                0.9999998874649318,
                0.9999998144608762,
                0.999999927341775,
                0.9999998874649318,
                0.9999998874648648,
                0.9999999226558238,
                0.999999927341827
            ],
            [
                0.9999998874648782,
                0.9999995262093293,
                1.0,
                0.9999999317440279,
                0.9999998942830106,
                0.999999931743971,
                0.9999999358794326,
                0.9999998942829602,
                0.9999999586006098,
                0.9999999273418095
            ],
            [
                1.0,
                0.9999999176674651,
                0.9999999358794479,
                0.9999999123574942,
                0.9999996940977732,
                0.9999998257021422,
                0.9999998461826956,
                1.0,
                1.0,
                0.999999931743979
            ],
            [
                1.0,
                0.9999999067050498,
                0.9999998874648246,
                0.9999999358794021,
                0.9999999067050054,
                0.9999999123575151,
                0.9999999273417662,
                0.9999997300421261,
                0.9999999226557224,
                0.9999999317439383
            ],
            [
                0.9999999226558515,
                0.9999998362623529,
                0.9999999434137367,
                0.9999998724809875,
                0.9999995262095551,
                0.99999995308839,
                0.9999999468421693,
                0.9999999434137907,
                0.9999996743688588,
                0.9999997300423192
            ],
            [
                0.9999996310114599,
                0.9999993916408185,
                1.0,
                1.0,
                0.9999999397643083,
                0.9999999397643011,
                0.9999999317440116,
                0.999999825702059,
                1.0,
                0.9999999226557961
            ],
            [
                0.9999986290426306,
                0.9999999006879721,
                0.9999998642566704,
                0.9999999656787161,
                0.9999999067050832,
                0.9999999067050609,
                0.9999986290424668,
                0.9999998802069731,
                0.999999802494586,
                0.9999996940977732
            ],
            [
                0.9999999397643083,
                0.9999999358793562,
                0.9999999006879721,
                1.0,
                1.0,
                0.9999998461827139,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999998144609646,
                0.9999999176675044,
                0.9999999226557593,
                0.999999946842144,
                0.9999998724809419,
                0.9999998802069587,
                0.9999995818811774,
                0.9999999006880668,
                0.9999997126313441,
                0.999999789756609
            ],
            [
                0.9999998257021837,
                0.9999998724809724,
                1.0,
                0.999999872480942,
                0.9999999067050498,
                0.9999999123575046,
                0.9999999317440116,
                0.9999998874649051,
                0.9999998144609646,
                1.0
            ],
            [
                7.889266347636241e-06,
                2.4300243630653244e-05,
                5.043472278322555e-07,
                2.5612819054133693e-06,
                3.288749065423109e-06,
                7.889263526345123e-06,
                1.067702615468225e-06,
                3.2887482813149375e-06,
                1.3007134667070165e-05,
                5.422219616184461e-06
            ],
            [
                0.9999998461826406,
                0.9999999006880905,
                0.9999999358794174,
                0.9999998555019791,
                0.9999999067050276,
                0.9999999006880549,
                0.9999998555019447,
                0.9999994631251243,
                0.9999999226557776,
                0.9999999226557593
            ],
            [
                4.4508510499849186e-07,
                3.0590215399183813e-07,
                3.466327037553825e-07,
                3.059021175261338e-07,
                1.0677031245953668e-06,
                3.466325797888292e-07,
                1.4449800373065699e-07,
                2.2603234895372223e-06,
                3.466327863983311e-07,
                2.3823696679230424e-07
            ],
            [
                0.9999999358794327,
                0.9999999764113634,
                0.9999999634651487,
                0.9999999500628334,
                0.9999990577552941,
                0.9999998942830862,
                0.9999998555020307,
                0.9999998555019618,
                1.0,
                0.9999999559306049
            ],
            [
                0.9999999358793867,
                0.9999998362623137,
                0.9999999317439464,
                0.999999894283061,
                0.9999999317440197,
                0.9999998257021423,
                0.9999999176675731,
                0.9999999273417922,
                0.9999998724808964,
                0.9999999397643156
            ],
            [
                8.764245361752286e-08,
                1.6373764721039308e-07,
                1.6373764721039308e-07,
                1.1253513522447425e-07,
                7.338210679979539e-07,
                3.466326211113502e-07,
                1.1253517547010071e-07,
                1.4449798650551755e-07,
                1.1253513522447425e-07,
                1.300713156582635e-05
            ],
            [
                1.0,
                0.9999999176674454,
                0.9999999559305839,
                0.9999997617631753,
                1.0,
                1.0,
                0.9999998642566867,
                0.9999999397642437,
                1.0,
                0.9999998642566543
            ]
        ]
    },
    {
        "q_id": "9260_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            39,
            42,
            43,
            44,
            45,
            46,
            48,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            104,
            105,
            106,
            108,
            109,
            111,
            112,
            113,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.699578096403948e-07,
                2.1024334103581732e-07,
                3.4663249714612693e-07,
                1.855391239547094e-07,
                NaN,
                2.382369951932796e-07,
                2.699577452775239e-07,
                2.561281294760143e-06,
                5.043474081993875e-07,
                1.6373772528704005e-07
            ],
            [
                1.3007130015488633e-05,
                6.144173869558639e-06,
                1.209865539295696e-06,
                1.6373762769034363e-07,
                9.422442569315887e-07,
                6.144177531767002e-06,
                1.209865827740176e-06,
                1.300713156582635e-05,
                9.422444815792981e-07,
                6.475948753965404e-07
            ],
            [
                6.47594875403829e-07,
                7.338212429594283e-07,
                6.475945666063607e-07,
                3.9278605979534166e-07,
                2.699578096403948e-07,
                6.475945666063607e-07,
                8.315284241665078e-07,
                7.338211554813555e-07,
                2.699577774585891e-07,
                1.3709575337159875e-06
            ],
            [
                5.043474683204221e-07,
                9.422443692555439e-07,
                1.760342793638743e-06,
                4.450851580555361e-07,
                3.0590237279032884e-07,
                5.043476486915964e-07,
                6.9622587397397306e-06,
                1.3709570433885908e-06,
                3.0590237279032884e-07,
                3.7266406168827523e-06
            ],
            [
                1.89251527534122e-05,
                3.726639284144195e-06,
                6.962256249885085e-06,
                2.5612828213934817e-06,
                1.5534984953453635e-06,
                1.0129995810343862e-05,
                1.0677028700363782e-06,
                2.9023123311583482e-06,
                5.043472879525233e-07,
                1.9947297214944016e-06
            ],
            [
                0.9999995262096116,
                0.9999996310115039,
                0.9999969105059232,
                0.9999994631249322,
                0.9999996533673375,
                0.9999930377437595,
                0.9999982396574172,
                0.9999985406241276,
                0.9999988634362897,
                0.9999992188513902
            ],
            [
                4.222834954778007e-06,
                1.5534977545886537e-06,
                6.475947209918244e-07,
                4.785095635592258e-06,
                7.338208055664991e-07,
                9.422443692446175e-07,
                3.927860597935108e-07,
                1.994729721482609e-06,
                1.7603425837903113e-06,
                1.994730434879465e-06
            ],
            [
                1.370957860576702e-06,
                6.144173869558639e-06,
                1.994729483729522e-06,
                1.5534975693979422e-06,
                2.561282210740037e-06,
                6.962255419931625e-06,
                1.209866260432471e-06,
                2.90231094723893e-06,
                9.422450431989127e-07,
                1.760343213335281e-06
            ],
            [
                2.5612834320214477e-06,
                1.3709572068422585e-06,
                1.3709572068272963e-06,
                2.9023126771227976e-06,
                8.315281267834927e-07,
                2.5612812947508257e-06,
                1.370957860567974e-06,
                2.561281600049467e-06,
                4.450851580540182e-07,
                7.889264466725156e-06
            ],
            [
                1.2751904288710323e-07,
                2.3823702359290413e-07,
                3.0590226339061185e-07,
                2.1024326584582131e-07,
                3.059021539909339e-07,
                3.05902263389638e-07,
                2.3823690999160957e-07,
                7.338210680002898e-07,
                3.927862002663297e-07,
                6.475948754012522e-07
            ],
            [
                0.9998911030651161,
                1.7603425837903113e-06,
                4.785094494811783e-06,
                3.288748281329893e-06,
                2.902312331170226e-06,
                1.9947299593078385e-06,
                1.994729008145876e-06,
                1.994729721518893e-06,
                3.2887506336235617e-06,
                4.222834451403972e-06
            ],
            [
                1.6373766672973748e-07,
                3.059022269250683e-07,
                1.4449795205429202e-07,
                2.382370235922541e-07,
                2.6995774527718623e-07,
                2.3823690999290963e-07,
                1.444980209564556e-07,
                3.9278610661902853e-07,
                2.6995784182140636e-07,
                5.04347528446051e-07
            ],
            [
                1.9947297215043796e-06,
                6.144175334367959e-06,
                6.144173869379821e-06,
                1.5534981249697903e-06,
                9.422447062202052e-07,
                8.939699501416646e-06,
                1.067702615468225e-06,
                6.144175334418252e-06,
                5.043472879540142e-07,
                8.315277302841894e-07
            ],
            [
                1.7603425837791042e-06,
                2.2603242978778778e-06,
                1.3007131565613412e-05,
                4.78509392429544e-06,
                3.2887486733420804e-06,
                1.9947297215125433e-06,
                2.2603245673155757e-06,
                1.1478769494083349e-05,
                1.0129995810463632e-05,
                1.9947299592824403e-06
            ],
            [
                3.4663266243308805e-07,
                5.04347588554027e-07,
                1.7603425837855082e-06,
                5.715003789046955e-07,
                2.9023116391675407e-06,
                5.715005151574337e-07,
                0.999512142908496,
                6.475945666051092e-07,
                1.994730434879465e-06,
                9.422444815495185e-07
            ],
            [
                1.2098653950656417e-06,
                3.72663883989755e-06,
                2.2603245673279107e-06,
                1.855391239544352e-07,
                1.9947299593014888e-06,
                7.338211554783522e-07,
                6.1441767993788005e-06,
                9.931193325852072e-08,
                2.9023116391978967e-06,
                7.338207180898968e-07
            ],
            [
                0.9999986290421404,
                0.9999984465028022,
                0.9999995818814266,
                0.9999998362623138,
                0.9999998362622943,
                0.9999996310113279,
                0.9999994284997576,
                0.9999998144608981,
                0.9999998024945624,
                0.9999995549147891
            ],
            [
                2.1024336609724313e-07,
                1.6373774480479287e-07,
                2.6995790618469934e-07,
                1.8553903548113195e-07,
                1.1253520229983549e-07,
                1.6373762769034363e-07,
                2.3823685319174098e-07,
                3.0590237279032884e-07,
                1.2751904288710323e-07,
                2.1024336609638268e-07
            ],
            [
                0.9999998257021837,
                0.9999991684721711,
                0.9999998555019618,
                0.9999997300423191,
                0.9999999006880786,
                0.9999998362623138,
                0.9999987901344616,
                0.9999998024946566,
                0.9999986290427941,
                0.9999998942830358
            ],
            [
                0.9999985406234317,
                0.9999982396565781,
                0.9999969105055558,
                0.9999960330155095,
                0.9999985406236062,
                0.9999955048173556,
                0.9999996533672963,
                0.9999998257021628,
                0.9999990577552945,
                0.999999761763147
            ],
            [
                4.785093353940187e-06,
                7.338208055664991e-07,
                3.288748281329893e-06,
                2.561282210729555e-06,
                1.994730434879465e-06,
                3.7266388398585725e-06,
                3.927862002641863e-07,
                7.338212429562581e-07,
                1.9947292459347367e-06,
                1.209865683518615e-06
            ],
            [
                2.561281600086738e-06,
                NaN,
                9.422448185534261e-07,
                1.3709575337159875e-06,
                6.475945666063607e-07,
                5.715005832895975e-07,
                3.466327037548308e-07,
                3.059022269254856e-07,
                1.7603425837903113e-06,
                1.4449805540740185e-07
            ],
            [
                4.450852111148132e-07,
                7.338208055664991e-07,
                5.043472278322555e-07,
                1.3709572068522336e-06,
                5.04347468323289e-07,
                3.927862470899887e-07,
                9.422447062294175e-07,
                5.04347468323289e-07,
                2.382368531929327e-07,
                1.0677026154806063e-06
            ],
            [
                0.9999995818813768,
                0.9999998802069445,
                0.9999995262094988,
                0.9999996743687034,
                0.9999996743687422,
                0.9999992188517629,
                0.999999789756609,
                0.9999987121044781,
                0.9999978766217923,
                0.9999998724809723
            ],
            [
                1.4449795205472734e-07,
                1.4449805540740185e-07,
                2.699578740032504e-07,
                1.8553903548231313e-07,
                1.4449796928021588e-07,
                NaN,
                1.4449802095666915e-07,
                3.466326624336003e-07,
                5.715002426486762e-07,
                1.27519088491875e-07
            ],
            [
                1.6373766672973748e-07,
                0.9999997300422548,
                0.9999977396751646,
                1.8553905760024476e-07,
                8.315284241650899e-07,
                0.9999999586006542,
                0.9999997300421261,
                1.444980726324838e-07,
                1.4449800373065699e-07,
                1.637377448057981e-07
            ],
            [
                NaN,
                1.5534983101393749e-06,
                3.7266397283908927e-06,
                4.4508515805735777e-07,
                1.0677026154730804e-06,
                1.0677024882009222e-06,
                7.889263526266196e-06,
                3.9278615344178325e-07,
                1.2098658277451275e-06,
                1.3709575337159875e-06
            ],
            [
                7.338208055664991e-07,
                3.726639728370556e-06,
                6.475947210012481e-07,
                6.962257079775324e-06,
                1.6701421844753466e-05,
                1.7603430034439723e-06,
                1.7603432133136672e-06,
                2.1444940745371397e-05,
                9.610239211853606e-05,
                1.2098655392811161e-06
            ],
            [
                1.0677033791612137e-06,
                1.0677027427600627e-06,
                4.785095635655362e-06,
                2.5612831267202583e-06,
                1.0677031245990084e-06,
                1.1478772231086046e-05,
                2.2603234895289998e-06,
                1.0677024881980089e-06,
                1.9947292459347367e-06,
                3.7266397283908927e-06
            ],
            [
                0.9999995262092728,
                0.999996499144338,
                0.999999631011592,
                0.9999987901347502,
                0.9999996533674206,
                0.9999980052707561,
                0.9999983463102188,
                0.9999995549147892,
                0.9999972735294063,
                0.9999996940977367
            ],
            [
                2.382368531929327e-07,
                2.561281600049467e-06,
                9.422445939032799e-07,
                2.69957906184239e-07,
                1.760344052714248e-06,
                3.927862470899887e-07,
                2.1024326584639497e-07,
                1.3709570433786157e-06,
                1.7603438428800754e-06,
                2.4300252321904572e-05
            ],
            [
                1.5534977545886537e-06,
                4.2228334445658276e-06,
                1.4738976701652988e-05,
                1.8925157266089433e-05,
                3.288748281329893e-06,
                1.6701425827133152e-05,
                1.7603438428800754e-06,
                1.0677029973219343e-06,
                7.889265407327733e-06,
                4.22283545819819e-06
            ],
            [
                0.999989870010308,
                1.3709575336947905e-06,
                6.962253759752719e-06,
                5.715005151574337e-07,
                1.3709575337078829e-06,
                1.7603427936263351e-06,
                0.9997965729621007,
                6.475950297971703e-07,
                1.2098661161927025e-06,
                6.962257079629686e-06
            ],
            [
                0.9999977396754354,
                0.9999984465018767,
                0.9999987121049391,
                0.9999962733607215,
                0.9999916019279816,
                0.9999955048173536,
                NaN,
                0.9989677690848492,
                0.9999980052707554,
                2.3823699519290042e-07
            ],
            [
                0.9999989322967494,
                9.422443692555439e-07,
                1.2098652508424818e-06,
                7.338212429582604e-07,
                0.9999996533674205,
                0.9999993106388726,
                2.902313023130843e-06,
                2.260325106237323e-06,
                2.2603234895289998e-06,
                6.144172404693786e-06
            ],
            [
                0.999999789756659,
                0.9999998642566866,
                0.9999977396746258,
                0.9999998362623529,
                0.9999964991451705,
                0.9999995818811275,
                0.99999879013374,
                0.9999998724808964,
                0.9999996743686257,
                0.999999825702059
            ],
            [
                0.9999981261241714,
                0.9999970976869792,
                0.9999988634362901,
                0.9999952149032283,
                0.9999969105044505,
                0.9999741325784764,
                0.9999987901343174,
                0.9999988634357486,
                7.338212429582604e-07,
                0.9999988634357486
            ],
            [
                1.7603434231705793e-06,
                NaN,
                6.962256249885085e-06,
                NaN,
                3.726639284144195e-06,
                5.715005832895975e-07,
                2.5612825160562587e-06,
                1.2098655392921197e-06,
                NaN,
                2.2603253756956754e-06
            ],
            [
                7.338212429537553e-07,
                0.9999996940977367,
                0.9999983463098235,
                0.9999993524052793,
                0.9999991148430699,
                0.9999998362623332,
                0.9999949062931826,
                0.999993459562003,
                0.9999986290431205,
                0.9999996310114599
            ],
            [
                6.475949526020042e-07,
                1.0677028700363782e-06,
                1.2751904288710323e-07,
                3.9278634073732336e-07,
                1.4449796927932878e-07,
                2.699578096393206e-07,
                3.9278624708775595e-07,
                1.1253509497883659e-07,
                5.715007195447234e-07,
                7.338211554801876e-07
            ],
            [
                1.760343213335281e-06,
                1.7603438428740716e-06,
                3.288749849529972e-06,
                2.1024344128584085e-07,
                2.5612819054133693e-06,
                2.5612819054133693e-06,
                1.0677028700422047e-06,
                7.338207180864763e-07,
                1.2098653950656417e-06,
                7.338213304363436e-07
            ],
            [
                3.288750241561788e-06,
                6.144173869603344e-06,
                0.9999904837483401,
                5.422217030747413e-06,
                5.043472879540142e-07,
                0.9999949062950035,
                5.043475885674441e-07,
                8.939694172867777e-06,
                7.338212429562581e-07,
                9.422445939032799e-07
            ],
            [
                8.315283250371857e-07,
                5.715005832872586e-07,
                8.315277302788957e-07,
                2.2603237589542675e-06,
                7.338209805224048e-07,
                1.3709576970949014e-06,
                4.450852111135988e-07,
                2.2603248367512505e-06,
                1.0677027427600627e-06,
                1.370956716529941e-06
            ],
            [
                2.2603234895372223e-06,
                0.999991601924971,
                0.9999998461826405,
                0.9999877809210995,
                2.260324836776948e-06,
                0.9999970976873266,
                0.9999993106388728,
                0.9999969105066607,
                0.9999930377404436,
                1.994730434879465e-06
            ],
            [
                0.9999994956527724,
                0.9999989969857925,
                0.9999989322975124,
                0.9999983463100212,
                0.9999964991460057,
                0.9999981261252877,
                0.9999992188517628,
                0.9999987901337402,
                0.999998712104939,
                0.9999989969856732
            ],
            [
                1.0677028700320085e-06,
                3.927862470899887e-07,
                1.2098656835224664e-06,
                7.338208055579897e-07,
                3.05902226923399e-07,
                9.422445939002803e-07,
                7.338212429464139e-07,
                7.3382080556433e-07,
                5.715003788993679e-07,
                8.315283250371857e-07
            ],
            [
                1.4738981972323349e-05,
                2.2603242978871282e-06,
                3.288749457469787e-06,
                8.315281267861397e-07,
                2.5612819054133693e-06,
                1.7603432133296774e-06,
                1.7603436330259153e-06,
                2.2603234895176927e-06,
                1.9947292459347367e-06,
                6.475945666051092e-07
            ],
            [
                5.043476486924565e-07,
                1.5534975693979422e-06,
                7.338209805240734e-07,
                2.2603242978778778e-06,
                2.2603240284371276e-06,
                2.902313369111213e-06,
                5.715005832886879e-07,
                5.715003107767143e-07,
                1.5534973842076057e-06,
                3.927862470899887e-07
            ],
            [
                2.6995790618350237e-07,
                5.715005832886879e-07,
                1.1253525596134564e-07,
                3.7266410611296085e-06,
                3.927860597945825e-07,
                3.927862002663297e-07,
                1.7603438428800754e-06,
                7.338210680021253e-07,
                2.69957906184239e-07,
                2.6995790618469934e-07
            ],
            [
                0.9999993524052794,
                0.9999991148428592,
                0.9999995549150544,
                0.99999926617902,
                0.9999994284996896,
                0.999999631011328,
                0.9999997300422548,
                0.999989216683938,
                0.9999993916410362,
                0.9999993916410361
            ],
            [
                3.288748281295496e-06,
                1.9947297214182054e-06,
                2.260324028372372e-06,
                5.04347468323289e-07,
                2.561282516042282e-06,
                1.0677027427600627e-06,
                9.422444815765128e-07,
                1.9947292459265734e-06,
                1.7603430034655858e-06,
                1.553497754577351e-06
            ],
            [
                0.9999998555019791,
                1.0,
                0.9999955048168166,
                0.9999993524051247,
                0.999991601927975,
                0.9999997463981031,
                0.9999969105040806,
                0.9999992188512972,
                0.9999998942829225,
                0.999998126123947
            ],
            [
                2.102434412871794e-07,
                1.1253525596174225e-07,
                4.450851049991497e-07,
                NaN,
                1.637376862489725e-07,
                1.855391239547094e-07,
                1.4449795205472734e-07,
                9.93120161310289e-08,
                NaN,
                1.2751910369343538e-07
            ],
            [
                8.764247451307293e-08,
                7.73441946488886e-08,
                1.2751905808881762e-07,
                1.1253525596174225e-07,
                1.8553919030826963e-07,
                9.931193325852072e-08,
                6.023578501491997e-08,
                1.275191036933194e-07,
                1.6373768624837685e-07,
                1.4449805540763184e-07
            ],
            [
                0.9999995262095551,
                0.9999996310113719,
                0.9999993916408911,
                0.999994228080665,
                0.9999994631249962,
                0.9999996072139403,
                0.99999916847227,
                0.9999994284994851,
                0.9999992188519489,
                0.999999428499417
            ],
            [
                7.338208930391909e-07,
                7.338208055664991e-07,
                1.2098662604049616e-06,
                6.475945665900901e-07,
                1.7603440527286572e-06,
                2.2603234895289998e-06,
                4.222834954778007e-06,
                1.0677026154774503e-06,
                8.315278294001114e-07,
                5.043474683204221e-07
            ],
            [
                4.785093353940187e-06,
                3.288748673376478e-06,
                9.422448185534261e-07,
                1.9947299593078385e-06,
                0.9999916019239802,
                0.9999991684721713,
                4.222834954778007e-06,
                0.9999885212319063,
                9.422444815792981e-07,
                2.90231094723893e-06
            ],
            [
                0.9999995818812771,
                0.9999964991455902,
                0.9999982396574192,
                0.9999989322975128,
                0.9999993106386263,
                0.9999985406241282,
                0.9999995549147891,
                0.9999925887183827,
                0.9999945777829773,
                0.9999985406230841
            ],
            [
                3.4663266242969896e-07,
                5.043472879504592e-07,
                6.962257079705671e-06,
                3.726638395634011e-06,
                9.422448185534261e-07,
                2.2603245673279107e-06,
                1.9947290081177566e-06,
                8.31528424162821e-07,
                1.7603432133136672e-06,
                8.939697369785323e-06
            ],
            [
                2.5612819054133693e-06,
                0.9999869928684724,
                1.0677026154806063e-06,
                4.450848927650143e-07,
                9.422442569290178e-07,
                2.2603242978871282e-06,
                2.5612819054028872e-06,
                9.422450432014836e-07,
                6.144173137126169e-06,
                1.2098656835224664e-06
            ],
            [
                1.9947294837154625e-06,
                3.927862002641863e-07,
                5.422218969818919e-06,
                9.422447062270609e-07,
                1.0677024881829577e-06,
                5.422219616228845e-06,
                3.7266406168624155e-06,
                5.422219616228845e-06,
                2.75356878194421e-05,
                1.0129995810343862e-05
            ],
            [
                1.760342793638743e-06,
                4.222834451403972e-06,
                1.7603425837903113e-06,
                6.1441767993788005e-06,
                7.338210680021253e-07,
                1.3709575337159875e-06,
                6.47595107001401e-07,
                4.785095635655362e-06,
                1.3709572068522336e-06,
                5.829127250060064e-05
            ],
            [
                0.9999998874647977,
                0.9999999273418703,
                8.315281267861397e-07,
                0.999998005270994,
                0.9999994956524717,
                0.999999653367379,
                0.9999998642566219,
                0.9999997897566589,
                0.9999993106388726,
                0.9999998642566219
            ],
            [
                0.9999910603069023,
                0.9999955048200335,
                0.9999984465024316,
                0.9999974387171806,
                0.9999957771655523,
                0.99999823965658,
                0.9999898700066201,
                0.9999970976890556,
                0.9999989322968765,
                0.9999984465026174
            ],
            [
                0.9999984465024316,
                0.9999987901338844,
                0.9999985406230841,
                0.9999987121052455,
                0.9999998144609424,
                0.9999977396754335,
                5.04347287955046e-07,
                0.9999983463102178,
                2.1024339116168358e-07,
                0.9999998642566704
            ],
            [
                4.450848927650143e-07,
                3.059021175261338e-07,
                4.2228329411708495e-06,
                2.2603234895289998e-06,
                3.466327450765785e-07,
                1.0677029973158649e-06,
                3.466326624322211e-07,
                3.466326624336003e-07,
                9.422448185510695e-07,
                3.466327037553825e-07
            ],
            [
                0.9999983463102181,
                0.9999970976873258,
                0.9999989969861514,
                0.9999975938970889,
                0.9999972735287564,
                0.9999970976866337,
                0.9999990577557434,
                0.999999391640964,
                0.9999869928653489,
                0.9999975938970888
            ],
            [
                3.120191509592808e-05,
                5.422218323487975e-06,
                1.4738976701411704e-05,
                4.450852111148132e-07,
                1.0677032518785256e-06,
                1.8925150497848527e-05,
                3.726637951387472e-06,
                3.120192625278069e-05,
                2.7535704231844484e-05,
                9.422450431989127e-07
            ],
            [
                3.9278605979208185e-07,
                3.927862002663297e-07,
                3.466327037548308e-07,
                6.47595107001401e-07,
                3.466325797888292e-07,
                3.4663249714451116e-07,
                5.043474081993875e-07,
                3.059022998576899e-07,
                1.2751908849167202e-07,
                6.475950297993789e-07
            ],
            [
                2.902311293147782e-06,
                8.315277302788957e-07,
                2.9023119851266288e-06,
                3.7266410611296085e-06,
                4.785096206047877e-06,
                2.260325375664839e-06,
                6.144176066795103e-06,
                2.902312331170226e-06,
                1.7603434231833873e-06,
                4.2228329411708495e-06
            ],
            [
                1.5534975693869924e-06,
                1.7603430034867993e-06,
                2.144495097113319e-05,
                8.315284241650899e-07,
                1.2098662604291696e-06,
                1.3709568799823232e-06,
                4.785094494783494e-06,
                1.209865683518615e-06,
                6.475949526020042e-07,
                5.422219616265831e-06
            ],
            [
                1.067702615468225e-06,
                1.2098658277451275e-06,
                4.4508505193791187e-07,
                5.043472879504592e-07,
                5.043472879504592e-07,
                7.338209805133949e-07,
                9.422443692446175e-07,
                1.0677032518748838e-06,
                1.3007126914245925e-05,
                9.422445938861406e-07
            ],
            [
                7.338212429537553e-07,
                1.2098653950551882e-06,
                1.5534975693792215e-06,
                1.3709576971242028e-06,
                6.144173137126169e-06,
                0.9999810748433138,
                2.753569110256289e-05,
                2.144494585801764e-05,
                1.6701429808632785e-05,
                1.012999460278499e-05
            ],
            [
                0.9999999176675829,
                0.9999949062931808,
                0.9999995262092164,
                0.9999999176675338,
                0.9999993106387906,
                0.9999957771680692,
                0.9999995549148951,
                6.962254589978262e-06,
                0.9999995262092728,
                0.9999993916408185
            ],
            [
                5.8291251656508296e-05,
                7.338211554783522e-07,
                2.5612822107167428e-06,
                1.7603432133296774e-06,
                8.315277302788957e-07,
                3.2887478892683997e-06,
                1.1478770862589836e-05,
                4.222834451355964e-06,
                2.902313369111213e-06,
                1.0129987357407137e-05
            ],
            [
                2.260324028404236e-06,
                8.939700566565793e-06,
                1.637377448057981e-07,
                5.04347287955046e-07,
                3.059022269250683e-07,
                1.4449805540763184e-07,
                2.6995774527718623e-07,
                1.7603427936263351e-06,
                2.382369667929001e-07,
                3.7266406168827523e-06
            ],
            [
                1.4449798650551755e-07,
                3.059022998581767e-07,
                1.4449795205472734e-07,
                1.1253512180925583e-07,
                1.8553905760062447e-07,
                4.450850519403407e-07,
                1.4449795205472734e-07,
                1.6373774480605869e-07,
                8.76424013786396e-08,
                1.6373764721072816e-07
            ],
            [
                6.475945666051092e-07,
                3.4663266243308805e-07,
                1.5534984953453635e-06,
                2.382368815932174e-07,
                5.043474081993875e-07,
                4.450851580555361e-07,
                3.927860597935108e-07,
                1.2098653950716937e-06,
                3.927860597945825e-07,
                3.9278634073732336e-07
            ],
            [
                3.0590219045914655e-07,
                1.637376862489725e-07,
                5.715006514176113e-07,
                9.422442569334097e-07,
                1.855391681906175e-07,
                4.4508515805735777e-07,
                1.209865827752005e-06,
                8.31528325040778e-07,
                4.4508515805735777e-07,
                9.931195693628605e-08
            ],
            [
                0.9999997761971582,
                0.9999978766212854,
                0.9999995818812272,
                0.9999986290421402,
                0.9999995262094987,
                0.9999989322967484,
                0.9999989969862709,
                0.9999988634357478,
                0.9999996743687034,
                0.9999993524049705
            ],
            [
                NaN,
                1.209865539295696e-06,
                1.7603430034655858e-06,
                2.2603253756956754e-06,
                3.288748281329893e-06,
                2.902312677137316e-06,
                4.2228339479858295e-06,
                1.994729483723626e-06,
                1.7603438428800754e-06,
                1.3709576971425944e-06
            ],
            [
                1.9947292459347367e-06,
                1.9947304348862686e-06,
                1.2098662604291696e-06,
                3.7266397283908927e-06,
                2.5612831267202583e-06,
                0.9999984465026165,
                8.939700567094277e-06,
                6.962258739796719e-06,
                5.715003107767143e-07,
                3.2887506336235617e-06
            ],
            [
                8.315284241597959e-07,
                2.561281600086738e-06,
                3.535624649893211e-05,
                2.5612819054028872e-06,
                1.2098662604291696e-06,
                1.3709570434054234e-06,
                1.9947299592933255e-06,
                1.994729008145876e-06,
                1.7603425837855082e-06,
                2.2603245673443566e-06
            ],
            [
                0.9999981261239501,
                5.144222592963322e-05,
                0.9999972735284347,
                5.422219616265831e-06,
                1.6701425827133152e-05,
                4.222834954778007e-06,
                4.2228339479858295e-06,
                0.9999989322975134,
                3.726639284125553e-06,
                0.9999983463106137
            ],
            [
                0.999999653367255,
                0.9999989322971305,
                0.9999997126313099,
                0.999999730042287,
                0.9999998555020307,
                0.9999985406236056,
                0.9999984465016905,
                0.9999982396565781,
                0.9999994284997576,
                0.9999996072139403
            ],
            [
                2.102434412875379e-07,
                7.889259764517575e-06,
                5.71500515161527e-07,
                1.4449807263312446e-07,
                7.338207180898968e-07,
                3.0590237279085045e-07,
                6.475946438055299e-07,
                9.931186222523604e-08,
                1.209866260432471e-06,
                1.6373776432509826e-07
            ],
            [
                6.962255419728997e-06,
                1.0677024881829577e-06,
                1.4738987243236881e-05,
                7.889261645427538e-06,
                1.1478770862735993e-05,
                2.753568782024347e-05,
                9.422443692489024e-07,
                6.962257909785973e-06,
                4.785096776468749e-06,
                1.2098661162023305e-06
            ],
            [
                3.05902117523595e-07,
                3.466325797888292e-07,
                6.475951069985296e-07,
                2.1024326584639497e-07,
                6.475946438055299e-07,
                6.475945666051092e-07,
                3.92786293909545e-07,
                6.475950298011458e-07,
                3.9278610661545617e-07,
                2.260324836787226e-06
            ],
            [
                1.3709575337016483e-06,
                6.9622587396067566e-06,
                1.0677032518748838e-06,
                2.2603245673155757e-06,
                4.785093353909723e-06,
                1.2098659719716573e-06,
                1.2098658277451275e-06,
                1.0677028700320085e-06,
                1.0677029973158649e-06,
                1.9947301970813926e-06
            ],
            [
                1.7603438428740716e-06,
                9.422450432014836e-07,
                1.0677024881980089e-06,
                4.785092783519724e-06,
                4.450848927650143e-07,
                8.315281267861397e-07,
                3.7266410611296085e-06,
                1.0677028700363782e-06,
                2.5612828213818346e-06,
                2.2603234895176927e-06
            ],
            [
                0.9999985406241279,
                0.9999993106387083,
                0.9999981261239472,
                0.9999997761971849,
                0.9999967112513286,
                0.9999998362623723,
                0.99999911484307,
                0.9999997126314126,
                0.9999995818810777,
                0.9999995262095551
            ],
            [
                1.0677024881980089e-06,
                3.4663262110945863e-07,
                1.7603427936335396e-06,
                3.0590237279085045e-07,
                1.9947299593014888e-06,
                5.715007195447234e-07,
                1.5534975693979422e-06,
                6.144173137126169e-06,
                1.0677029973192638e-06,
                4.450848927650143e-07
            ],
            [
                8.315281267882195e-07,
                2.5612831267202583e-06,
                4.450851580540182e-07,
                3.4663249714325014e-07,
                5.043475885688201e-07,
                3.927861066170637e-07,
                8.31527928532683e-07,
                6.47595107001401e-07,
                5.715002426486762e-07,
                8.315284241650899e-07
            ],
            [
                1.8553907971855875e-07,
                1.8553910183674878e-07,
                2.902312677150514e-06,
                9.931195693628605e-08,
                2.10243290909963e-07,
                1.8553905760062447e-07,
                1.275190276853036e-07,
                2.1024344128660572e-07,
                1.4449800373118268e-07,
                3.4663278639892215e-07
            ],
            [
                4.22283545795623e-06,
                1.994729721436347e-06,
                6.962254589978262e-06,
                1.3709576971061233e-06,
                2.7535700950274782e-05,
                1.3007128464961824e-05,
                5.422220262599396e-06,
                4.785094494672519e-06,
                3.2887506334560605e-06,
                4.222833947932061e-06
            ],
            [
                9.931198061405701e-08,
                3.4663266243308805e-07,
                2.699576809143613e-07,
                2.699577774585891e-07,
                6.475950298021765e-07,
                9.422445939054222e-07,
                2.3823702359290413e-07,
                3.05902263391829e-07,
                8.764245361752286e-08,
                2.699577452775239e-07
            ],
            [
                1.0677028700422047e-06,
                1.7603440527334603e-06,
                9.422444815814404e-07,
                9.422450432030903e-07,
                8.315278294114555e-07,
                4.22283545819819e-06,
                7.338208055680009e-07,
                3.927863875616689e-07,
                3.9278620026686556e-07,
                9.422450432030903e-07
            ],
            [
                0.9999989969857926,
                0.9999964991455885,
                0.9999975938982363,
                0.9999898700042158,
                0.999999802494633,
                0.9999978766212857,
                0.999999391641036,
                0.9999970976873251,
                0.999991601930982,
                4.006368741670684e-05
            ],
            [
                8.315280276456036e-07,
                9.422445939002803e-07,
                1.0677032518785256e-06,
                1.0677028700053041e-06,
                1.0677032518578904e-06,
                8.315277302788957e-07,
                1.3709576971425944e-06,
                9.422443692489024e-07,
                1.5534979397500702e-06,
                1.2098659719232413e-06
            ],
            [
                1.994729008145876e-06,
                1.5534983101602148e-06,
                6.475949526020042e-07,
                9.422442569315887e-07,
                1.2098659719757836e-06,
                5.715007195447234e-07,
                1.0677026154806063e-06,
                2.5612812947380135e-06,
                8.315283250394546e-07,
                1.9947297215125433e-06
            ],
            [
                3.927861534406222e-07,
                4.4508505193791187e-07,
                8.315280276626197e-07,
                4.785092783519724e-06,
                2.1444940745839484e-05,
                5.04347528446051e-07,
                1.5534977545886537e-06,
                6.475947210046347e-07,
                3.2887506336086064e-06,
                2.75356812556058e-05
            ],
            [
                0.999998005269329,
                0.9999988634358834,
                0.999999114842648,
                0.9999986290426307,
                0.999996499144338,
                0.9999994284993489,
                0.9999987121052458,
                0.999998346309824,
                0.9999993524053564,
                0.9999970976869786
            ],
            [
                1.2098662604049616e-06,
                1.855391239539711e-07,
                2.102432658440048e-07,
                2.3823690999160957e-07,
                1.4449802095609418e-07,
                6.475951069932288e-07,
                3.927861066170637e-07,
                2.1024339116082313e-07,
                2.3823693839057394e-07,
                6.475947981975644e-07
            ],
            [
                1.2098652508424818e-06,
                1.209865827752005e-06,
                2.2603251062450327e-06,
                2.1444956084718052e-05,
                9.422443692555439e-07,
                5.71500719545698e-07,
                1.067703124601679e-06,
                6.144176066901277e-06,
                2.5612834320563895e-06,
                1.370957860576702e-06
            ],
            [
                0.9999978766220446,
                4.450852111148132e-07,
                3.059021175261338e-07,
                0.9999987901337403,
                0.9999970976890542,
                0.9999952149043693,
                0.9999981261243943,
                3.9278638755992735e-07,
                0.9999981261250644,
                0.9999599363128584
            ],
            [
                7.889260704732132e-06,
                4.4508510499849186e-07,
                4.222832437639588e-06,
                2.5612828213690224e-06,
                1.4738983729294318e-05,
                1.0677032518748838e-06,
                1.0677026154774503e-06,
                4.222831934379152e-06,
                2.561283432035425e-06,
                1.5534975693869924e-06
            ],
            [
                0.9999977396757046,
                0.9999970976883641,
                0.9999975938976648,
                0.9999993524052029,
                0.9999962733602774,
                4.4508505193932864e-07,
                1.4738978458382043e-05,
                0.9999832985762269,
                0.9999986290429586,
                0.9999980052707564
            ],
            [
                0.9999945777803984,
                0.9999996072138468,
                0.9999992188514836,
                0.9999982396561601,
                0.9999949062944026,
                0.9999964991455892,
                0.9999993106388728,
                0.9999994284994854,
                0.9999996072136126,
                0.00015843627371237145
            ],
            [
                3.059022998576899e-07,
                9.931190958076104e-08,
                2.3823690999290963e-07,
                3.466325797888292e-07,
                2.69957906184239e-07,
                3.927862002641863e-07,
                1.4449795205429202e-07,
                0.9999985406241281,
                7.734421308914719e-08,
                2.102434162245973e-07
            ],
            [
                1.2098658277451275e-06,
                2.561281600086738e-06,
                3.2887482813149375e-06,
                1.7603436329714805e-06,
                1.5534979397394734e-06,
                1.994730672668496e-06,
                1.2098658277335738e-06,
                1.0677033791583005e-06,
                6.47594720987407e-07,
                4.450852111135988e-07
            ],
            [
                0.999999814460876,
                0.999998712104171,
                0.9999998802069731,
                0.9999993524050477,
                0.9999997300421583,
                0.9999998555019274,
                0.9999988634358835,
                0.9999998555019446,
                0.9999994631247403,
                0.9999992188518559
            ]
        ]
    },
    {
        "q_id": "10063_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.4663249714612693e-07,
                1.5534983101602148e-06,
                3.9278624708775595e-07,
                5.715004470313855e-07,
                7.338209805170655e-07,
                1.4449805540763184e-07,
                3.466326624336003e-07,
                2.699578096403948e-07,
                5.715003788993679e-07,
                3.466325797896173e-07
            ],
            [
                0.999876605469696,
                0.9999485577987188,
                0.9999972735284304,
                4.450852641737424e-07,
                0.9999967112505433,
                0.9999910603026332,
                0.9989677689397166,
                0.9998911030780946,
                0.9999938558275995,
                0.9999869928761992
            ],
            [
                2.699576809143613e-07,
                1.444980209564556e-07,
                0.9999546021260537,
                0.9999687980924183,
                0.9999687980924327,
                2.561282210740037e-06,
                8.764243272157922e-08,
                1.855391239539711e-07,
                2.3823688159291947e-07,
                0.9999599363126906
            ],
            [
                0.9999417087554069,
                0.9999599363079218,
                0.999985261012773,
                3.05902226923399e-07,
                0.9992903296267812,
                0.9999646437409275,
                6.475945666063607e-07,
                0.9999898700102381,
                0.9999921107393,
                0.9999038975737738
            ],
            [
                0.9999646437409301,
                5.043475885674441e-07,
                6.475948754012522e-07,
                8.31528424162821e-07,
                6.144173869379821e-06,
                7.338213304363436e-07,
                5.043475885696228e-07,
                3.9278634073625165e-07,
                0.9999646437451416,
                1.7603425837606927e-06
            ],
            [
                5.715004470295662e-07,
                1.8553907971855875e-07,
                3.9278605979534166e-07,
                0.9999646437409323,
                1.209865683518615e-06,
                0.999981074856284,
                0.9999952149049366,
                0.999968798096167,
                0.9999417087069492,
                2.102433410343832e-07
            ],
            [
                7.3382080556433e-07,
                4.450849988811838e-07,
                1.7603432133032607e-06,
                7.338210680002898e-07,
                1.0677026154619133e-06,
                1.4449805540740185e-07,
                3.927860597945825e-07,
                0.9999724642958329,
                9.422448185388577e-07,
                7.338210680002898e-07
            ],
            [
                0.9998911031170745,
                1.5534981249697903e-06,
                0.999959936298309,
                0.999983298578164,
                0.9999251537996787,
                0.9998766053812794,
                0.9999546021314575,
                4.222832437798974e-06,
                0.99990389758532,
                0.99990389759675
            ],
            [
                2.2603242978665707e-06,
                1.7603430034743913e-06,
                7.889266346287306e-06,
                1.994729959224386e-06,
                8.315277302701984e-07,
                4.222832940942332e-06,
                6.475947982002148e-07,
                9.422443692489024e-07,
                4.22283193393364e-06,
                5.043475284430694e-07
            ],
            [
                0.9999151889188076,
                1.3709570433885908e-06,
                1.3709568799760888e-06,
                1.1478765389065974e-05,
                6.475945666033422e-07,
                0.9999687980812777,
                0.9999724642991191,
                1.209865683518615e-06,
                1.55349775456958e-06,
                1.9947299592933255e-06
            ],
            [
                2.699577774585891e-07,
                0.9999984465016905,
                3.4663266243111764e-07,
                1.4449802095609418e-07,
                2.3823696679230424e-07,
                3.9278634073625165e-07,
                0.9999989322973849,
                0.9999997761971848,
                1.4449802095609418e-07,
                1.637377643243723e-07
            ],
            [
                0.999964643749356,
                8.315284241650899e-07,
                0.9999921107345964,
                0.9999810748562833,
                1.4449798650476187e-07,
                0.9997388096933677,
                1.3709567165617364e-06,
                0.9993736659143955,
                0.9999038976198183,
                0.9999885212346191
            ],
            [
                0.9999546021260729,
                1.9947292459347367e-06,
                0.9999251537462094,
                0.9998766053667189,
                1.9947292459406333e-06,
                1.7603434231833873e-06,
                0.9999687980886923,
                3.927862002606139e-07,
                2.699578740032504e-07,
                0.999989870009027
            ],
            [
                0.999941708727773,
                0.9999852610215588,
                2.6995768091383957e-07,
                0.9999962733602737,
                0.9999952149049374,
                1.5534979397740895e-06,
                0.9999945777829728,
                0.999983298584149,
                3.927862002606139e-07,
                0.9999724643056498
            ],
            [
                2.102433410343832e-07,
                0.9999038976198842,
                0.9999417087556092,
                0.9999904837449168,
                4.4508494582405734e-07,
                1.275190124842887e-07,
                9.422443692555439e-07,
                8.315282259138311e-07,
                2.9023109472244114e-06,
                2.1024336609843824e-07
            ],
            [
                0.9999724643089399,
                0.999975699756419,
                0.9999832985722086,
                2.69957906184239e-07,
                9.422442569315887e-07,
                0.9999898700102348,
                0.9999852610233173,
                5.715005151606823e-07,
                0.9999599363126939,
                5.715005832886879e-07
            ],
            [
                2.6995784181551376e-07,
                2.6995771309523475e-07,
                0.9999916019269736,
                0.9999955048189612,
                0.9999869928684512,
                0.999990483748318,
                2.1024334103352274e-07,
                0.9999785550516154,
                0.9999869928731,
                0.9999964991468402
            ],
            [
                1.0129987357407137e-05,
                5.04347348075149e-07,
                6.475946438055299e-07,
                8.315281267882195e-07,
                4.450849458200093e-07,
                0.9996646497725129,
                1.444979692797559e-07,
                7.338212429562581e-07,
                2.102433159721477e-07,
                1.855391239544352e-07
            ],
            [
                7.338209805200689e-07,
                3.288748281329893e-06,
                3.0590237278838124e-07,
                1.0677028700422047e-06,
                7.338212429582604e-07,
                2.699578740032504e-07,
                0.9999898700114452,
                7.338210679979539e-07,
                1.275190580890061e-07,
                1.1253513522391131e-07
            ],
            [
                0.999997273530706,
                0.9999989969855534,
                0.9999930377462449,
                1.6373764720849438e-07,
                0.999999495652652,
                0.9999967112513283,
                0.9999952149066488,
                0.9999975938968011,
                0.9999995262096116,
                0.99999879013374
            ],
            [
                5.715005832886879e-07,
                4.4508515805199415e-07,
                0.9999339478241169,
                0.9999687980812496,
                0.9999810748450194,
                0.9999724643023973,
                0.9999756997592939,
                0.9999646437578229,
                6.475949525919915e-07,
                2.1024344128488479e-07
            ],
            [
                3.1201907657271834e-05,
                9.931192141912081e-08,
                3.466325384661554e-07,
                1.275190884913241e-07,
                2.3823682479181176e-07,
                3.4663266243111764e-07,
                1.4449798650476187e-07,
                1.8553907971855875e-07,
                2.1024326584582131e-07,
                2.699576809143613e-07
            ],
            [
                3.059023363190688e-07,
                1.2751901248338985e-07,
                1.6373766672888118e-07,
                5.04347648680129e-07,
                1.6373768624837685e-07,
                3.466326211105621e-07,
                1.4449798650476187e-07,
                1.8553919030858602e-07,
                1.8553919030776337e-07,
                9.931198061405701e-08
            ],
            [
                0.999995214905508,
                0.9999974387171802,
                0.9999981261237239,
                0.9999987121047849,
                0.999997876622045,
                6.475948753965404e-07,
                0.9999852610162928,
                0.999994577781682,
                0.9999997897567091,
                0.9999962733593859
            ],
            [
                9.422448185534261e-07,
                1.6373774480404828e-07,
                8.315279285149107e-07,
                0.9999251537997663,
                0.9999646437535782,
                0.9999898700066148,
                0.9999687980775047,
                3.2887502415767434e-06,
                0.9993736658272439,
                0.9999921107374203
            ],
            [
                1.1253524254615121e-07,
                1.6373776432481905e-07,
                1.855391018347238e-07,
                3.059021539909339e-07,
                1.8553905760024476e-07,
                2.1024326584639497e-07,
                1.1253506814797596e-07,
                1.8553905760024476e-07,
                8.764249540862797e-08,
                7.338211554725124e-07
            ],
            [
                5.715003107767143e-07,
                2.260325375664839e-06,
                1.0677032518748838e-06,
                9.422443692527585e-07,
                0.9999599362983309,
                3.2887486733420804e-06,
                1.0677032518700286e-06,
                3.0590226339061185e-07,
                2.382370235922541e-07,
                3.059021175247079e-07
            ],
            [
                4.222831934202483e-06,
                5.04347528440776e-07,
                6.475951069932288e-07,
                2.3823685319244518e-07,
                1.8553907971758842e-07,
                4.4508515805199415e-07,
                7.338211554725124e-07,
                4.450849458200093e-07,
                5.715003788993679e-07,
                3.9278610661545617e-07
            ],
            [
                2.102434162245973e-07,
                0.9999810748450237,
                1.7603425837855082e-06,
                9.422443692527585e-07,
                0.9999646437577704,
                0.9999785550516119,
                0.999968798077524,
                0.9999417087346256,
                7.338211554758494e-07,
                0.9999885212359875
            ],
            [
                0.9999852610110153,
                0.9999910603047691,
                0.9999898700090272,
                0.9999756997593048,
                7.484622728190558e-05,
                9.422448185534261e-07,
                0.9999485577619253,
                0.9999756997534923,
                0.999959936288801,
                0.999978555043942
            ],
            [
                5.715002426475718e-07,
                1.0677027427569065e-06,
                5.715002426460124e-07,
                1.1253521571574156e-07,
                2.3823702359290413e-07,
                1.855391239544352e-07,
                2.1024339116082313e-07,
                1.6373776432481905e-07,
                3.4663253846718004e-07,
                3.9278638756099906e-07
            ],
            [
                1.275190884913241e-07,
                9.931190958076104e-08,
                5.04347468323289e-07,
                7.338213304363436e-07,
                4.4508510499849186e-07,
                4.450849458179853e-07,
                3.927862470861484e-07,
                2.102434162245973e-07,
                0.00010889689631124415,
                1.444979692800516e-07
            ],
            [
                1.8553910183607374e-07,
                3.4663249714451116e-07,
                2.1024326584639497e-07,
                1.444980209564556e-07,
                7.734423152941018e-08,
                6.023571320847322e-08,
                8.764249540862797e-08,
                6.825602910433871e-08,
                1.2751899728286965e-07,
                2.1024326584639497e-07
            ],
            [
                0.9999985406237794,
                0.9999485577681464,
                0.9999988634362896,
                0.9999991684715761,
                0.9999991148433864,
                0.9999989322971303,
                0.9999990577551817,
                0.9999984465016905,
                0.9999977396754334,
                2.38237023590304e-07
            ],
            [
                0.9999724642991294,
                0.9999852610127759,
                3.927863875616689e-07,
                0.9999892166903653,
                5.422220262636381e-06,
                7.338213304363436e-07,
                4.4508526417298334e-07,
                0.9999038976085394,
                4.450849988811838e-07,
                0.9999885212346259
            ],
            [
                3.7266397283908927e-06,
                2.3823690999160957e-07,
                0.999891103104283,
                0.9986749773909964,
                1.209866260432471e-06,
                3.46632497145457e-07,
                2.1024326584582131e-07,
                2.6995771309523475e-07,
                5.043475885674441e-07,
                2.3823682479181176e-07
            ],
            [
                3.927861066170637e-07,
                3.4663266243111764e-07,
                8.7642516304188e-08,
                1.8553905760024476e-07,
                3.059023727894942e-07,
                9.422443692446175e-07,
                2.1024334103505245e-07,
                2.6995790618350237e-07,
                2.3823685319244518e-07,
                6.475947210012481e-07
            ],
            [
                8.764245361708445e-08,
                7.734415776805048e-08,
                1.5381735953331146e-07,
                1.1253514863909295e-07,
                1.4449800373065699e-07,
                6.02357778338585e-08,
                9.931201612997889e-08,
                1.1253514863909295e-07,
                2.3823690999063455e-07,
                1.2751907328949007e-07
            ],
            [
                7.734421308914719e-08,
                1.76034300345598e-06,
                3.466325384661554e-07,
                1.8553905760024476e-07,
                1.2098653950551882e-06,
                0.9999962733616059,
                0.9999921107345983,
                2.3823688159237777e-07,
                0.9999877809269064,
                7.734418542875216e-08
            ],
            [
                3.059023727869902e-07,
                3.927862002641863e-07,
                3.9278634073098236e-07,
                2.6995774527577444e-07,
                1.8553907971758842e-07,
                1.1253509497835043e-07,
                8.764241182605906e-08,
                8.315281267800897e-07,
                2.38237023590304e-07,
                3.927862939126708e-07
            ],
            [
                3.0590226339061185e-07,
                5.715004470313855e-07,
                2.382369667929001e-07,
                2.6995787400282076e-07,
                2.561281600086738e-06,
                1.8553919030858602e-07,
                1.6373764721039308e-07,
                6.475949526020042e-07,
                1.2751904288617538e-07,
                2.3823688159291947e-07
            ],
            [
                2.3823685319244518e-07,
                0.9999985406230838,
                0.999876605426583,
                0.9999485577987836,
                0.9999930377445859,
                0.999998863435748,
                0.9997965729318293,
                0.9999832985702207,
                0.9999546021152503,
                0.9999869928715528
            ],
            [
                1.2098656835136636e-06,
                5.04347348075149e-07,
                5.422217677078203e-06,
                4.450849988798682e-07,
                0.9999810748562918,
                0.9999987901338842,
                0.9999921107355383,
                8.315282259117513e-07,
                1.0677032518785256e-06,
                1.275190884913241e-07
            ],
            [
                3.9278624708775595e-07,
                5.715006514151423e-07,
                2.5612819053166966e-06,
                0.9998911030522912,
                5.715002426460124e-07,
                7.338210679979539e-07,
                7.734416698815724e-08,
                8.315284241650899e-07,
                1.855391681898159e-07,
                1.6373766672888118e-07
            ],
            [
                2.1024329090867228e-07,
                3.9278638755456876e-07,
                5.04347528431602e-07,
                2.1024334103581732e-07,
                2.1024334102979404e-07,
                8.31527730252048e-07,
                5.715007195384861e-07,
                3.0590237278532086e-07,
                4.450851580540182e-07,
                1.3709576971425944e-06
            ],
            [
                5.71500719545698e-07,
                1.8553914607128047e-07,
                1.0677033791612137e-06,
                5.043473480777865e-07,
                3.9278610661902853e-07,
                1.2751899728311609e-07,
                2.699578096403948e-07,
                7.338213304363436e-07,
                0.9999892166890747,
                0.9999785550465158
            ],
            [
                2.382370235933104e-07,
                0.9999869928684462,
                0.9999885212346264,
                6.825604537781398e-08,
                0.9999977396746248,
                0.9999485577865206,
                0.9999485577804146,
                7.734421308914719e-08,
                0.999972464312219,
                0.9999981261246175
            ],
            [
                2.699576809143613e-07,
                5.71500651413193e-07,
                0.9999251537641438,
                0.9999987901346051,
                1.3709576971463352e-06,
                1.994729721518893e-06,
                8.764246406483893e-08,
                0.9999945777803856,
                2.3823690999160957e-07,
                0.9999756997593034
            ],
            [
                0.9999756997593156,
                0.9999599362935525,
                4.1399350797784484e-08,
                1.4449802095609418e-07,
                0.9999945777790947,
                0.9999962733593846,
                3.9278634073732336e-07,
                0.9999988634360188,
                3.4663266243111764e-07,
                0.9999785550567586
            ],
            [
                6.475945666063607e-07,
                1.3709576971463352e-06,
                6.023574911170301e-08,
                1.855391681906175e-07,
                1.370957860576702e-06,
                4.450850519403407e-07,
                1.1253525596174225e-07,
                3.05902263391829e-07,
                2.3823696679327928e-07,
                2.102434162245973e-07
            ],
            [
                4.4508515805199415e-07,
                6.475947210012481e-07,
                5.04347348070562e-07,
                5.043475885674441e-07,
                5.04347287955046e-07,
                2.6995774527718623e-07,
                7.338213304283347e-07,
                1.760343213335281e-06,
                2.10243290909724e-07,
                1.0677033791612137e-06
            ],
            [
                0.9999967112493677,
                0.999981074849527,
                5.715003789046955e-07,
                0.9999852610233173,
                0.9999832985702092,
                0.99989110307831,
                0.9999756997564098,
                1.637377643243723e-07,
                0.9999687980849624,
                0.999978555041387
            ],
            [
                9.422443692446175e-07,
                0.9999724643122112,
                1.8553912395262116e-07,
                2.902312677150514e-06,
                0.9999957771660531,
                3.9278605979208185e-07,
                4.450848927658745e-07,
                0.9994472214583611,
                9.422448185534261e-07,
                8.315280276626197e-07
            ],
            [
                0.999985261016286,
                0.9999952149043669,
                0.9999251537730296,
                0.9999756997650951,
                0.999981074858544,
                0.999985261018045,
                0.9997965729567377,
                5.043474081993875e-07,
                0.9999546021476836,
                0.9999962733602739
            ],
            [
                0.9999646437493943,
                2.6995771309523475e-07,
                0.9999885212318835,
                6.475947209918244e-07,
                1.5534975693601474e-06,
                2.699577774585891e-07,
                3.059021175247079e-07,
                4.691162683297406e-08,
                2.102433410343832e-07,
                3.059023727894942e-07
            ],
            [
                7.734418542875216e-08,
                8.764243272157922e-08,
                0.9999964991468407,
                0.9999646437578475,
                0.9999687980961285,
                2.3823699519143784e-07,
                0.9999910603069053,
                0.9998601778948764,
                5.043474683220276e-07,
                3.05902263389638e-07
            ],
            [
                4.450849988798682e-07,
                0.9999969105040797,
                7.73442776300517e-08,
                3.466325797888292e-07,
                1.6373776432481905e-07,
                4.450851580540182e-07,
                6.023569884692295e-08,
                0.06754669160889748,
                2.3823682479181176e-07,
                9.931199245292204e-08
            ],
            [
                0.9999251537377806,
                9.931198061405701e-08,
                1.2751901248454963e-07,
                1.444979692797559e-07,
                0.9997388097593934,
                1.4449802095609418e-07,
                0.9999687980738157,
                1.6373772528677946e-07,
                0.9999869928761931,
                3.05902190458764e-07
            ],
            [
                2.3823682479292225e-07,
                1.8553919030708836e-07,
                2.6995790618252024e-07,
                1.855391239547094e-07,
                1.6373774480479287e-07,
                3.927862470861484e-07,
                1.8553914607128047e-07,
                3.059021175247079e-07,
                8.315277302747361e-07,
                3.059023363207381e-07
            ],
            [
                0.9999151889591206,
                1.3709573702822306e-06,
                4.450850519403407e-07,
                0.9999810748472919,
                0.9999546021206779,
                0.9999785550490493,
                1.8553905760062447e-07,
                7.734425918979532e-08,
                0.9999945777816803,
                0.9999485577619706
            ],
            [
                9.422449308748773e-07,
                9.42244256915735e-07,
                4.450849988811838e-07,
                1.5534979397740895e-06,
                2.2603237589676295e-06,
                1.7603436329714805e-06,
                6.475946437996402e-07,
                1.5534971989992774e-06,
                9.422443692527585e-07,
                1.3709573702647743e-06
            ],
            [
                7.73441946488886e-08,
                9.93118503859575e-08,
                2.102433159721477e-07,
                8.764244316933122e-08,
                2.3823702359290413e-07,
                1.275190580884987e-07,
                1.2098652508424818e-06,
                3.7266401726359486e-06,
                5.043476486883855e-07,
                7.338208930460318e-07
            ],
            [
                3.466325797896173e-07,
                5.715003788993679e-07,
                1.7603434231705793e-06,
                3.059021175247079e-07,
                6.475947981975644e-07,
                3.466327450765785e-07,
                3.059023363221292e-07,
                4.450852111148132e-07,
                8.315277302857965e-07,
                2.382369383923073e-07
            ],
            [
                0.9999785550541597,
                1.5534984953552536e-06,
                0.9999251537997412,
                6.1441746020359e-06,
                0.9997965729786599,
                1.5534984953552536e-06,
                2.102433410343832e-07,
                9.931192141912081e-08,
                1.9947304348862686e-06,
                0.9999339478555221
            ],
            [
                0.9999546021206279,
                0.9999970976883626,
                0.9999852610198027,
                0.9999485577864872,
                0.9999687980775139,
                0.9997040429759201,
                0.9999417087276351,
                0.9999785550439503,
                0.999981074854043,
                0.9999869928715533
            ],
            [
                2.102433410343832e-07,
                0.999915188959313,
                0.999991601926974,
                3.9278605979534166e-07,
                0.9999921107393033,
                0.9999485577804041,
                8.315277302841894e-07,
                5.043474081993875e-07,
                0.9999869928653489,
                1.6373766672973748e-07
            ],
            [
                6.023569166629634e-08,
                1.4449798650551755e-07,
                1.444980209564556e-07,
                6.825606165129312e-08,
                6.47594566597747e-07,
                9.93120161306789e-08,
                6.023574911170301e-08,
                3.466327037512053e-07,
                5.3157830707696514e-08,
                1.855391239539711e-07
            ],
            [
                2.2603251062270446e-06,
                1.2098652508347793e-06,
                2.699579061812927e-07,
                2.699577774585891e-07,
                3.05902226923399e-07,
                5.04347528440776e-07,
                7.338213304283347e-07,
                3.4663249714325014e-07,
                5.715002426460124e-07,
                4.450848927650143e-07
            ],
            [
                5.04347348075149e-07,
                3.927860597945825e-07,
                3.9278638755456876e-07,
                4.450851580540182e-07,
                3.05902117523595e-07,
                2.3823702359290413e-07,
                5.04347348075149e-07,
                1.1253506814797596e-07,
                3.288750633545794e-06,
                7.338213304316717e-07
            ],
            [
                4.450849988758202e-07,
                3.4663249714325014e-07,
                1.4449805540651476e-07,
                1.6373766672888118e-07,
                2.1024341622297196e-07,
                3.9278629390240027e-07,
                7.338213304196583e-07,
                3.4663266242969896e-07,
                1.0677024881829577e-06,
                1.7603432132784448e-06
            ],
            [
                5.043475284430694e-07,
                8.764241182605906e-08,
                1.855391681891831e-07,
                2.699577774560111e-07,
                1.4449798650476187e-07,
                3.05902117523595e-07,
                1.4449798650417048e-07,
                7.734416698815724e-08,
                3.4663274507713016e-07,
                2.699577774560111e-07
            ],
            [
                0.999989216691663,
                5.043474081931949e-07,
                1.6373770576683237e-07,
                7.338207180601138e-07,
                5.04347588554027e-07,
                6.475951069755593e-07,
                7.338208930315157e-07,
                3.9278605979011705e-07,
                4.450852641656969e-07,
                3.927862470816829e-07
            ],
            [
                1.1253520229983549e-07,
                1.0677031245623505e-06,
                3.0590233632400716e-07,
                3.9278638755671223e-07,
                6.412059033372598e-08,
                1.1253514863909295e-07,
                2.1024344128584085e-07,
                9.931192141912081e-08,
                1.2751902768478173e-07,
                1.2751910369275402e-07
            ],
            [
                2.3823699519290042e-07,
                2.1024336609874897e-07,
                0.9999687980961444,
                7.338212429537553e-07,
                2.6995790618469934e-07,
                1.6373768624837685e-07,
                1.2751905808881762e-07,
                0.9995694429160199,
                1.994729483694599e-06,
                0.9998911030522912
            ],
            [
                5.715004470295662e-07,
                3.466325797888292e-07,
                1.8553919030776337e-07,
                0.999985261019809,
                0.9999417087347015,
                0.9999646437493857,
                0.9999832985841483,
                0.9999646437620748,
                5.043472879504592e-07,
                3.4663249714612693e-07
            ],
            [
                6.475950298011458e-07,
                5.04347468323289e-07,
                2.2603234895053587e-06,
                1.1253513522447425e-07,
                1.2098652508424818e-06,
                3.4663266243111764e-07,
                3.05902190458764e-07,
                9.422445939002803e-07,
                2.3823702359290413e-07,
                1.7603425837855082e-06
            ],
            [
                2.6995790618252024e-07,
                2.3823685319244518e-07,
                3.927863407379485e-07,
                1.444980209564556e-07,
                3.288749457469787e-06,
                4.450849988811838e-07,
                2.1024331597152624e-07,
                1.0677028700422047e-06,
                8.764248496035163e-08,
                7.338208930460318e-07
            ],
            [
                0.9999339478556144,
                3.059021175247079e-07,
                6.475947982022763e-07,
                0.9999339478556071,
                2.1024341622426268e-07,
                0.9999646437619825,
                0.9999810748563055,
                0.9999687980998219,
                0.9999756997506258,
                6.475950298011458e-07
            ],
            [
                5.715002426486762e-07,
                4.4508526417014975e-07,
                9.422444815628016e-07,
                6.023576347299818e-08,
                2.699576809143613e-07,
                7.734428685019034e-08,
                1.1253513522447425e-07,
                6.023572038912295e-08,
                4.691162683297406e-08,
                1.1253518888531272e-07
            ],
            [
                5.715006514105942e-07,
                5.3157818033672716e-08,
                1.7603438428740716e-06,
                9.931198061405701e-08,
                6.144175334468545e-06,
                1.637377448057981e-07,
                8.764254764749753e-08,
                2.3823702359290413e-07,
                8.7642516304188e-08,
                3.059023727894942e-07
            ],
            [
                0.9999974387184017,
                0.9999981261246179,
                0.9999996533675031,
                0.9999985406243014,
                0.9999997617631753,
                5.715004470295662e-07,
                0.9999987901347497,
                0.9999938558254008,
                0.9999962733593859,
                0.9999977396759732
            ],
            [
                1.2098655392871682e-06,
                6.475946437996402e-07,
                0.9999869928731,
                4.450849458200093e-07,
                0.9999599363223128,
                6.475950297942253e-07,
                5.715005151550947e-07,
                0.9998601779606158,
                2.1024341622368903e-07,
                0.9997040429446882
            ],
            [
                2.1024334103553052e-07,
                1.8553919030826963e-07,
                1.2751901248454963e-07,
                1.2751910369310194e-07,
                2.3823682479292225e-07,
                5.715003107755449e-07,
                1.8553919030858602e-07,
                1.4449805540763184e-07,
                1.8553910183649565e-07,
                8.7642558095602e-08
            ],
            [
                0.9999832985841457,
                0.9999785550413917,
                1.4449795205429202e-07,
                0.9999993524051248,
                6.023574911170301e-08,
                0.9998766053833514,
                0.9999724643057092,
                2.1024329090929374e-07,
                0.9999996310116359,
                2.3823702359290413e-07
            ],
            [
                5.715004470295662e-07,
                1.6373774480535133e-07,
                3.059023727894942e-07,
                3.4663249714325014e-07,
                3.4663266243111764e-07,
                5.04347528440776e-07,
                8.764241182605906e-08,
                5.043472879525233e-07,
                1.1253513522391131e-07,
                6.023576347299818e-08
            ],
            [
                1.2098658277451275e-06,
                2.3823682479181176e-07,
                6.475945666033422e-07,
                7.338212429562581e-07,
                3.0590226338838606e-07,
                1.0677028700266676e-06,
                1.5534981249574276e-06,
                1.994729245917502e-06,
                8.315277302788957e-07,
                2.9023116391477434e-06
            ],
            [
                8.481108182431855e-05,
                0.9999417087485492,
                1.8553903548231313e-07,
                0.9999417087416371,
                4.4508510499849186e-07,
                5.715002426486762e-07,
                4.222832437798974e-06,
                0.9999810748540378,
                0.9999852610162943,
                0.999978555059289
            ],
            [
                9.422443692489024e-07,
                8.315282259051341e-07,
                3.9278634073732336e-07,
                2.6995768091383957e-07,
                3.466327863983311e-07,
                4.450850519403407e-07,
                3.05902190458764e-07,
                8.315277302819205e-07,
                5.715004470272272e-07,
                5.04347468323289e-07
            ],
            [
                2.6995768091310296e-07,
                1.855391018347238e-07,
                0.9999964991455879,
                1.4449798650476187e-07,
                2.699577774585891e-07,
                1.6373768624837685e-07,
                3.466327037539638e-07,
                8.315279285351409e-07,
                0.9999904837483158,
                8.764249540862797e-08
            ],
            [
                2.699579061798195e-07,
                3.927862470861484e-07,
                0.9999771720083207,
                3.0590215398829087e-07,
                8.764242227380856e-08,
                2.699576809143613e-07,
                1.2751910369275402e-07,
                8.315281267800897e-07,
                1.1253514863909295e-07,
                1.2751910369310194e-07
            ],
            [
                9.931198061405701e-08,
                1.1253525596055243e-07,
                1.637377057673536e-07,
                3.4663266242969896e-07,
                6.825608606148807e-08,
                8.315277302841894e-07,
                3.466326624205564e-07,
                1.6373774480535133e-07,
                6.475945665800774e-07,
                2.9023112929973233e-06
            ],
            [
                0.9999969105055532,
                3.05902190458764e-07,
                0.999968798092389,
                4.450852111135988e-07,
                9.422447062294175e-07,
                2.6995777745711594e-07,
                8.315277302841894e-07,
                3.9278615344178325e-07,
                1.4449798650476187e-07,
                0.999968798092373
            ],
            [
                1.1253506814797596e-07,
                3.9278634073732336e-07,
                3.05902117523595e-07,
                3.4663249714325014e-07,
                9.931199245292204e-08,
                6.475945666051092e-07,
                1.0677032518748838e-06,
                0.9999546021098682,
                1.2751902768478173e-07,
                1.4449798650476187e-07
            ],
            [
                1.1253520230052635e-07,
                0.9999417087415159,
                2.699577774585891e-07,
                1.275190580884987e-07,
                1.4449805540740185e-07,
                1.2751910369275402e-07,
                8.764240137829087e-08,
                2.3823682479292225e-07,
                1.637377643243723e-07,
                2.1024331597262577e-07
            ],
            [
                3.0590237279032884e-07,
                0.00048785723841530726,
                2.102434162245973e-07,
                0.9999417087485492,
                3.9278634073098236e-07,
                8.315277302841894e-07,
                1.6373764721072816e-07,
                0.9999417087346832,
                3.059022269250683e-07,
                0.999968798096135
            ],
            [
                5.04347348075149e-07,
                9.931198061405701e-08,
                2.6995790618252024e-07,
                1.8553910183607374e-07,
                1.2098656835136636e-06,
                3.4663249714325014e-07,
                4.450851049941403e-07,
                8.764241182605906e-08,
                5.715006514151423e-07,
                5.043475885674441e-07
            ],
            [
                3.4663249714325014e-07,
                3.0590215398829087e-07,
                1.4449803818107344e-07,
                3.9278629390507954e-07,
                2.1024331597152624e-07,
                3.4663266242969896e-07,
                7.338213304283347e-07,
                5.715004470243685e-07,
                3.4663249714325014e-07,
                2.3823690999063455e-07
            ],
            [
                2.6995784182073116e-07,
                0.9999724643089319,
                2.7535681254003062e-05,
                0.9999898700078178,
                1.0129993395336818e-05,
                6.60521683089055e-05,
                0.9999756997650764,
                1.4449798650476187e-07,
                0.999876605426039,
                0.9999724643187882
            ],
            [
                5.043475885696228e-07,
                3.927862470899887e-07,
                1.7603430034743913e-06,
                0.9999852610110174,
                0.9991959140863509,
                0.00020342707066267436,
                2.144495097113319e-05,
                3.4663249714325014e-07,
                3.0590237279032884e-07,
                4.450851049959619e-07
            ],
            [
                1.444980209556342e-07,
                2.6995774527577444e-07,
                3.466327037548308e-07,
                1.0677029973192638e-06,
                0.9999980052693286,
                3.0590237278838124e-07,
                4.4508505193386385e-07,
                1.855391018347238e-07,
                6.475947981975644e-07,
                9.931193325852072e-08
            ],
            [
                0.999988521226415,
                3.4663278639892215e-07,
                2.1024326584639497e-07,
                8.764241182605906e-08,
                1.6373762769138607e-07,
                5.715003789017068e-07,
                5.043475885674441e-07,
                1.0677027427525368e-06,
                3.059021904571643e-07,
                5.715003788993679e-07
            ],
            [
                7.73441946488886e-08,
                1.2098662604247682e-06,
                3.059021539909339e-07,
                3.059023363231725e-07,
                7.734424074954332e-08,
                5.315784971839039e-08,
                3.059022998569248e-07,
                0.9999785550439746,
                0.9999339478791605,
                2.1024331597262577e-07
            ],
            [
                8.315277302857965e-07,
                2.102433410343832e-07,
                6.475950298021765e-07,
                2.3823702359290413e-07,
                1.8553910183607374e-07,
                2.382370235933104e-07,
                1.8553903548231313e-07,
                4.450852641717689e-07,
                3.466327450756327e-07,
                1.1253514863909295e-07
            ],
            [
                8.315281267882195e-07,
                2.6995777745711594e-07,
                2.5612828213934817e-06,
                1.4449805540585765e-07,
                1.3709572068522336e-06,
                1.760343213335281e-06,
                0.9999974387171804,
                1.2098659719757836e-06,
                1.637377448057981e-07,
                5.715005832886879e-07
            ],
            [
                3.9278605979534166e-07,
                0.9997965729316813,
                0.9999417087276458,
                0.9999599363078789,
                1.5534973842076057e-06,
                0.9999724643089305,
                0.9999910602994398,
                0.999891103065284,
                0.9999546021314433,
                2.902312677137316e-06
            ],
            [
                3.9278615344178325e-07,
                3.05902263389638e-07,
                2.6995768091310296e-07,
                7.338209805170655e-07,
                1.2751908849088918e-07,
                5.71500719531729e-07,
                1.855391018347238e-07,
                2.102433410343832e-07,
                2.3823693839057394e-07,
                3.059021904580685e-07
            ],
            [
                1.994730197090463e-06,
                1.1253513522447425e-07,
                5.715003107767143e-07,
                1.2751899728286965e-07,
                4.222832437798974e-06,
                2.3823699519290042e-07,
                6.475946438055299e-07,
                1.6373764721072816e-07,
                8.764245361752286e-08,
                8.315281267882195e-07
            ],
            [
                1.4449796927932878e-07,
                9.931192141912081e-08,
                1.1253508156317518e-07,
                1.6373766672888118e-07,
                3.466325797888292e-07,
                1.1253514863909295e-07,
                1.4449796927932878e-07,
                1.1253518888531272e-07,
                1.2751904288710323e-07,
                2.102433660979124e-07
            ],
            [
                7.338208055664991e-07,
                5.715003107767143e-07,
                9.422448185534261e-07,
                5.715003789046955e-07,
                4.4508515805199415e-07,
                7.338210680021253e-07,
                3.288748281329893e-06,
                1.7603427936335396e-06,
                0.9999724643089417,
                0.999995214906078
            ],
            [
                2.3823690999160957e-07,
                0.9999724643023933,
                0.9999916019269748,
                0.9999785550464995,
                0.9999646437367234,
                0.9999925887210236,
                8.7642516304188e-08,
                0.9999957771675664,
                1.2751899728286965e-07,
                0.9999771719920033
            ],
            [
                1.855391018347238e-07,
                1.7603432133032607e-06,
                2.1444943292703185e-05,
                1.6373766672973748e-07,
                2.561282210562998e-06,
                1.553497199007048e-06,
                5.043476486902204e-07,
                1.0677029973219343e-06,
                7.338213304283347e-07,
                1.9947292458930106e-06
            ],
            [
                0.9999852610145252,
                2.3823696679327928e-07,
                1.994729721518893e-06,
                1.3709578605729614e-06,
                0.9999546021205913,
                0.9999785550413892,
                1.2751905808881762e-07,
                5.715006514176113e-07,
                0.9999962733602737,
                2.561281600086738e-06
            ],
            [
                6.475945666033422e-07,
                6.475945666051092e-07,
                2.1024326584639497e-07,
                1.4449805540700758e-07,
                5.043474683204221e-07,
                6.023576347299818e-08,
                3.059021904543821e-07,
                7.734424996967756e-08,
                2.3823702359290413e-07,
                2.3823702359138736e-07
            ],
            [
                4.4508515805199415e-07,
                6.475947982022763e-07,
                0.9999910603037054,
                1.125352291309328e-07,
                5.043472879525233e-07,
                3.05902117523595e-07,
                0.9998911031300673,
                9.422445939054222e-07,
                0.9999038975967276,
                0.9998766054113544
            ],
            [
                2.6995771309523475e-07,
                1.6373764721039308e-07,
                8.764247451307293e-08,
                2.102433410343832e-07,
                3.4663249714451116e-07,
                5.315788140287312e-08,
                1.275190124842887e-07,
                1.8553903548231313e-07,
                1.444979692800516e-07,
                1.637377057673536e-07
            ],
            [
                3.4663266242969896e-07,
                3.059021175247079e-07,
                2.6995790618350237e-07,
                1.4449803817969355e-07,
                3.4663274507713016e-07,
                3.7266406168403854e-06,
                1.8553910183548312e-07,
                2.6995777745711594e-07,
                2.1024331597152624e-07,
                5.043474081931949e-07
            ],
            [
                1.0677024881887838e-06,
                1.9947306726594253e-06,
                1.9947304348595095e-06,
                5.715006514105942e-07,
                2.2603237589028734e-06,
                1.9947306726049992e-06,
                1.1478764020372226e-05,
                2.5612822106421996e-06,
                2.9023126767360923e-06,
                2.1444945853375776e-05
            ],
            [
                1.444980209564556e-07,
                1.855391681898159e-07,
                2.6995784182073116e-07,
                7.734423152941018e-08,
                2.6995777745711594e-07,
                1.275190276853036e-07,
                1.2751905808881762e-07,
                1.1253506814797596e-07,
                2.6995774527657245e-07,
                1.1253516205489029e-07
            ],
            [
                2.382368815916736e-07,
                7.338210680021253e-07,
                5.043475284430694e-07,
                1.8553905759969634e-07,
                1.3709567165617364e-06,
                1.760343633031919e-06,
                1.4449805540740185e-07,
                6.962256249885085e-06,
                2.260324836787226e-06,
                1.2098656835136636e-06
            ],
            [
                7.338209805240734e-07,
                4.450849458200093e-07,
                2.382369667892166e-07,
                3.466327863961242e-07,
                1.8553905759969634e-07,
                1.553497754577351e-06,
                1.8553910183607374e-07,
                2.3823702359138736e-07,
                1.6373766672821107e-07,
                2.1024341622368903e-07
            ],
            [
                2.1024326584639497e-07,
                0.999964643745125,
                0.9999646437325255,
                0.9999151889792813,
                1.5534983101478522e-06,
                1.4449805540740185e-07,
                1.4449798650569826e-07,
                2.102433410343832e-07,
                5.043475885674441e-07,
                2.6995768091310296e-07
            ],
            [
                0.9999885212264173,
                0.9998204719947799,
                0.9999945777784471,
                6.475950298011458e-07,
                0.9999785550593056,
                1.275190884903093e-07,
                0.9999810748450114,
                5.422220262636381e-06,
                0.9999599363174894,
                0.9999546021261142
            ],
            [
                1.275190276859705e-07,
                0.9999546021369493,
                0.9999251537554551,
                4.4508494582405734e-07,
                0.9999646437410106,
                1.6373770576776313e-07,
                0.9999646437578412,
                3.0590237279032884e-07,
                0.9999885212359879,
                1.6373770576776313e-07
            ],
            [
                0.9999955048168163,
                3.466324971415162e-07,
                1.7603434231385591e-06,
                3.9278624708775595e-07,
                3.4663262110945863e-07,
                0.9999910602994387,
                3.4663249714325014e-07,
                2.2603234895053587e-06,
                4.450849458200093e-07,
                8.31527928532683e-07
            ],
            [
                7.338208055680009e-07,
                0.9999785550541659,
                0.00020342692517810748,
                1.444980209564556e-07,
                0.9999756997477116,
                0.9998911030521376,
                0.9999898700066079,
                0.9998415637082289,
                0.99989110313024,
                0.9999852610110103
            ],
            [
                0.9999485577618926,
                0.9999810748517829,
                0.9999898700054036,
                0.9999898700126502,
                0.9999599362935825,
                0.9999852610180403,
                1.275190276859705e-07,
                0.9999869928731012,
                0.9999930377404351,
                2.1024339116082313e-07
            ],
            [
                0.9999852610127665,
                3.0590215399183813e-07,
                0.9999885212359904,
                1.6373764721072816e-07,
                0.9999898700054105,
                3.4663278639892215e-07,
                1.275190884913241e-07,
                0.9999945777790956,
                1.2751904288710323e-07,
                1.8553907971758842e-07
            ],
            [
                1.8553910183548312e-07,
                0.9997694932044838,
                1.4449802095609418e-07,
                0.9997965730035299,
                1.6373766672821107e-07,
                3.4663262110945863e-07,
                2.3823682479181176e-07,
                2.1024344128584085e-07,
                0.9999756997506123,
                2.3823690999063455e-07
            ]
        ]
    },
    {
        "q_id": "9222_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            88,
            89,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.7603434231777837e-06,
                1.9947294837154625e-06,
                1.3709572068522336e-06,
                4.222832941193893e-06,
                2.561282516066741e-06,
                2.2603234895289998e-06,
                5.043475885674441e-07,
                3.288748673360027e-06,
                9.422450432014836e-07,
                3.2887478892683997e-06
            ],
            [
                6.9622537599680095e-06,
                3.7266397283908927e-06,
                1.5534979397740895e-06,
                1.9947297215125433e-06,
                4.450848927658745e-07,
                1.3709572068478697e-06,
                1.553497754583709e-06,
                2.5612819054133693e-06,
                9.422450431989127e-07,
                2.902311639183378e-06
            ],
            [
                2.561283432035425e-06,
                1.1478773599425825e-05,
                4.222833444467892e-06,
                2.9023133690637e-06,
                2.1444940745371397e-05,
                4.006370652067535e-05,
                4.785095635655362e-06,
                2.2603242978665707e-06,
                3.7266406167827664e-06,
                1.553498124964492e-06
            ],
            [
                3.7266392840781026e-06,
                2.430023204460668e-05,
                5.71500719545698e-07,
                8.315280276580819e-07,
                2.260325106237323e-06,
                4.450850519403407e-07,
                1.0677031245953668e-06,
                1.5534984953453635e-06,
                2.2603237589779086e-06,
                NaN
            ],
            [
                2.6995784182140636e-07,
                1.5534971990126997e-06,
                3.927860597945825e-07,
                1.7603440527286572e-06,
                2.69957906184239e-07,
                5.715005832886879e-07,
                1.0677029973219343e-06,
                5.04347528446051e-07,
                5.715007195431641e-07,
                6.475947210031623e-07
            ],
            [
                4.4508494582405734e-07,
                1.9947299593014888e-06,
                2.6995774527718623e-07,
                NaN,
                6.475947982037486e-07,
                5.715003789033962e-07,
                3.466326624336003e-07,
                2.5612819054028872e-06,
                2.6995784182140636e-07,
                6.144174601991196e-06
            ],
            [
                5.715003789046955e-07,
                8.315282259089153e-07,
                5.71500719545698e-07,
                9.422442569315887e-07,
                1.3709575337159875e-06,
                2.1024341622426268e-07,
                8.31528424151477e-07,
                5.71500515161527e-07,
                5.715005151606823e-07,
                2.382369383923073e-07
            ],
            [
                5.422220909009474e-06,
                6.962255419931625e-06,
                1.670142383595838e-05,
                1.994730197090463e-06,
                6.475947210012481e-07,
                9.422442569315887e-07,
                2.9023112932045342e-06,
                4.450850519403407e-07,
                8.315284241650899e-07,
                1.2098659719757836e-06
            ],
            [
                3.288748281295496e-06,
                4.450849458200093e-07,
                2.9023112932177327e-06,
                1.2098653950656417e-06,
                1.8925155009767892e-05,
                2.5612825160271407e-06,
                1.3709576971242028e-06,
                4.450850519403407e-07,
                3.2887482813149375e-06,
                1.0129994602895546e-05
            ],
            [
                1.2098656835224664e-06,
                2.6995784182140636e-07,
                5.043472278322555e-07,
                5.04347528446051e-07,
                2.3823693839290317e-07,
                7.338210679949506e-07,
                2.10243290909724e-07,
                3.927860597945825e-07,
                3.4663278639892215e-07,
                3.927862470899887e-07
            ],
            [
                1.5534975693933505e-06,
                4.222834954753043e-06,
                NaN,
                8.939694172867777e-06,
                NaN,
                5.422220262636381e-06,
                4.2228334445658276e-06,
                NaN,
                2.2603242978871282e-06,
                6.962256249885085e-06
            ],
            [
                1.760343633031919e-06,
                1.9947299593078385e-06,
                2.90231094723893e-06,
                6.475947982037486e-07,
                5.043476486915964e-07,
                8.93969950132721e-06,
                9.422442569315887e-07,
                3.288748673360027e-06,
                2.561281600086738e-06,
                7.338208930443633e-07
            ],
            [
                9.422443692527585e-07,
                1.553497754583709e-06,
                3.9278634073732336e-07,
                9.422442569097361e-07,
                1.0677029973192638e-06,
                4.222835458148261e-06,
                1.0677033791437343e-06,
                1.2098652508391807e-06,
                2.561282821352716e-06,
                3.7266410611296085e-06
            ],
            [
                2.1444958640087166e-05,
                NaN,
                8.939697369671496e-06,
                2.9023126771227976e-06,
                NaN,
                4.222834954607099e-06,
                4.785095065132354e-06,
                5.422219616140078e-06,
                1.8925143728301937e-05,
                1.1478769494083349e-05
            ],
            [
                NaN,
                1.7603425837855082e-06,
                3.7266388398585725e-06,
                7.338212429582604e-07,
                1.3709573702822306e-06,
                6.475949526020042e-07,
                NaN,
                3.7266406168827523e-06,
                1.3007126914435202e-05,
                1.2098659719757836e-06
            ],
            [
                8.939699501229642e-06,
                NaN,
                1.4738983729294318e-05,
                4.785095065132354e-06,
                2.7535691100960147e-05,
                1.99473067264854e-06,
                3.288749457409966e-06,
                2.902310947208574e-06,
                8.481105149855805e-05,
                1.4738980215111302e-05
            ],
            [
                6.475949526020042e-07,
                1.0677033791583005e-06,
                1.3709575337159875e-06,
                NaN,
                5.043476486915964e-07,
                1.0677026154806063e-06,
                3.288747889229516e-06,
                9.422447062294175e-07,
                1.3709572068522336e-06,
                6.962253760024999e-06
            ],
            [
                9.42244256915735e-07,
                2.5612834320214477e-06,
                4.222832941193893e-06,
                5.043472278322555e-07,
                1.0677032518814388e-06,
                1.7603436330259153e-06,
                5.715005151606823e-07,
                8.315281267882195e-07,
                1.0,
                1.2098658277489788e-06
            ],
            [
                2.382369667929001e-07,
                1.0677026154806063e-06,
                2.1024339116168358e-07,
                7.338212429582604e-07,
                2.3823699519290042e-07,
                7.338208055680009e-07,
                7.338209805200689e-07,
                3.9278610661902853e-07,
                2.561281294760143e-06,
                7.338211554783522e-07
            ],
            [
                1.7603430034743913e-06,
                1.8925143729575624e-05,
                1.012999218776902e-05,
                1.5534981249697903e-06,
                1.370957860576702e-06,
                1.2098661162023305e-06,
                1.9947297215043796e-06,
                1.2098656835136636e-06,
                8.315281267861397e-07,
                1.2098653950656417e-06
            ],
            [
                1.3709572068522336e-06,
                6.962257079832313e-06,
                6.144176799283803e-06,
                6.962259569630266e-06,
                4.222834451355964e-06,
                4.785093353909723e-06,
                8.939696304213768e-06,
                2.2603248367656408e-06,
                3.7266401726173067e-06,
                1.0129987357287368e-05
            ],
            [
                8.315283250371857e-07,
                3.466327037548308e-07,
                5.715003107738556e-07,
                1.0677027427600627e-06,
                1.3709568799919866e-06,
                2.430024652854702e-05,
                4.450849988811838e-07,
                2.902312677137316e-06,
                6.475945666063607e-07,
                1.0129989772532511e-05
            ],
            [
                3.7266410611465547e-06,
                9.422445939054222e-07,
                3.120191881616493e-05,
                5.715005832853093e-07,
                1.9947304348595095e-06,
                4.0063701745046735e-05,
                1.2098655392871682e-06,
                3.927862002625787e-07,
                1.3709575337159875e-06,
                1.9947306726594253e-06
            ],
            [
                NaN,
                1.209866260432471e-06,
                NaN,
                5.043472879540142e-07,
                2.10243290909963e-07,
                5.043474683240344e-07,
                NaN,
                1.3709570434250617e-06,
                5.71500515159253e-07,
                3.0590215399246414e-07
            ],
            [
                5.422221555340727e-06,
                8.939699501132077e-06,
                4.4508494582314646e-07,
                2.7535700949523498e-05,
                3.1201922533564516e-05,
                1.3007131566015624e-05,
                6.144175334418252e-06,
                2.260325106237323e-06,
                1.0677027427471959e-06,
                3.288749457383046e-06
            ],
            [
                3.466326211105621e-07,
                4.4508494582405734e-07,
                1.637377643243723e-07,
                1.0677026154806063e-06,
                6.475945666033422e-07,
                3.927862002663297e-07,
                8.939696304002375e-06,
                3.2887506336235617e-06,
                6.475947210031623e-07,
                2.260324567337161e-06
            ],
            [
                2.902312677150514e-06,
                6.475945666051092e-07,
                1.5534977545886537e-06,
                7.338210679979539e-07,
                3.0590237278838124e-07,
                2.561282516066741e-06,
                5.043472879540142e-07,
                1.209865539295696e-06,
                4.4508510499849186e-07,
                3.9278634073732336e-07
            ],
            [
                1.209865539295696e-06,
                2.7535694383279957e-05,
                NaN,
                1.7603438428800754e-06,
                5.422220262636381e-06,
                5.043475885674441e-07,
                8.315277302857965e-07,
                4.450850519403407e-07,
                5.422217030614265e-06,
                4.785095635592258e-06
            ],
            [
                1.5534983101644536e-06,
                NaN,
                0.0001398220407330551,
                1.209865827752005e-06,
                3.288749849529972e-06,
                8.939696304311336e-06,
                8.939696304311336e-06,
                3.726639284144195e-06,
                3.726637951387472e-06,
                2.2603245673443566e-06
            ],
            [
                6.475945666051092e-07,
                9.422448185510695e-07,
                9.422444815792981e-07,
                5.715005832886879e-07,
                3.4663249714612693e-07,
                3.9278638755992735e-07,
                2.3823690999323465e-07,
                5.043474683220276e-07,
                7.889261645427538e-06,
                2.2603251062270446e-06
            ],
            [
                1.5534975693979422e-06,
                7.338209805240734e-07,
                9.422444815814404e-07,
                1.7603432133296774e-06,
                5.715003789017068e-07,
                2.699577452775239e-07,
                3.0590237279032884e-07,
                1.067702870039777e-06,
                4.450852641737424e-07,
                8.315282259117513e-07
            ],
            [
                3.288749457469787e-06,
                1.1478770862735993e-05,
                6.475948754012522e-07,
                9.422445939054222e-07,
                1.2098659719716573e-06,
                8.939693107288474e-06,
                8.315277302841894e-07,
                8.315277302841894e-07,
                1.3709567165579959e-06,
                1.9947299592824403e-06
            ],
            [
                2.144495608424996e-05,
                9.422443692555439e-07,
                8.315282259009745e-07,
                7.338212429504183e-07,
                2.6995790618350237e-07,
                3.535626336072768e-05,
                3.9278634073625165e-07,
                2.2603251062270446e-06,
                5.715003107715166e-07,
                1.7603438428800754e-06
            ],
            [
                NaN,
                1.3709573702822306e-06,
                1.3709568799919866e-06,
                1.7603438428848787e-06,
                6.475947210046347e-07,
                1.0677029973192638e-06,
                6.475947210031623e-07,
                7.338211554813555e-07,
                4.450848927658745e-07,
                1.3709573702856596e-06
            ],
            [
                1.3709575337159875e-06,
                5.715002426475718e-07,
                1.9947301970972664e-06,
                8.939698432202356e-06,
                2.9023133690980155e-06,
                1.2098655392811161e-06,
                4.785096776499213e-06,
                1.5534975693933505e-06,
                2.561282210740037e-06,
                6.475947982037486e-07
            ],
            [
                5.4222202626709005e-06,
                NaN,
                1.3709570434178922e-06,
                3.288749457469787e-06,
                2.6995774527718623e-07,
                3.9278634073732336e-07,
                1.6373770576776313e-07,
                1.5534971990126997e-06,
                5.715005151606823e-07,
                2.5612834320563895e-06
            ],
            [
                2.5612819054133693e-06,
                2.2603251062270446e-06,
                1.2098655392921197e-06,
                3.7266401726173067e-06,
                9.422445939032799e-07,
                1.9947299593014888e-06,
                NaN,
                1.994729483723626e-06,
                1.0677027427600627e-06,
                1.5534977545886537e-06
            ],
            [
                5.422218323399208e-06,
                1.760343423160973e-06,
                4.785094494576774e-06,
                2.902313023063532e-06,
                3.288749457383046e-06,
                4.222831934248571e-06,
                2.9023109471689794e-06,
                1.553498495281783e-06,
                4.785092783371756e-06,
                2.5612819053399912e-06
            ],
            [
                5.043474683204221e-07,
                5.043472879525233e-07,
                5.043472879525233e-07,
                4.450851049941403e-07,
                5.715004470313855e-07,
                9.422448185510695e-07,
                9.4224425692559e-07,
                6.47594952595231e-07,
                4.450849988811838e-07,
                2.699578740011634e-07
            ],
            [
                1.3709567165530083e-06,
                2.2603242978778778e-06,
                1.553498495338299e-06,
                1.7603438428740716e-06,
                2.5612816000646084e-06,
                3.288748673319648e-06,
                1.99472900813862e-06,
                3.535625493182252e-05,
                7.889261645427538e-06,
                1.1478764021029928e-05
            ],
            [
                6.475947210031623e-07,
                1.2098661162056318e-06,
                2.2603242978665707e-06,
                1.760343423160973e-06,
                7.338212429504183e-07,
                1.3709576971316842e-06,
                1.5534983101602148e-06,
                9.422449308716635e-07,
                1.7603434231505666e-06,
                1.370956716529941e-06
            ],
            [
                1.6701429808298613e-05,
                1.3709576971379186e-06,
                2.5612828213934817e-06,
                1.3709572068272963e-06,
                1.994730434879465e-06,
                9.422442569315887e-07,
                1.2098655392871682e-06,
                3.288750241561788e-06,
                4.785096206013061e-06,
                4.2228324377740105e-06
            ],
            [
                5.043473480777865e-07,
                1.8925157266089433e-05,
                8.315280276626197e-07,
                7.338207180601138e-07,
                2.4300237838535383e-05,
                1.5534975693979422e-06,
                6.962255419931625e-06,
                1.670141985446017e-05,
                NaN,
                8.315280276626197e-07
            ],
            [
                9.422448185510695e-07,
                4.4508515805735777e-07,
                2.6995784182183607e-07,
                2.1024341622426268e-07,
                5.71500719545698e-07,
                2.699578096403948e-07,
                5.715003789046955e-07,
                3.4663278639892215e-07,
                5.043476486924565e-07,
                9.422447062294175e-07
            ],
            [
                5.715005151606823e-07,
                9.422445939002803e-07,
                5.715003789046955e-07,
                5.715003789046955e-07,
                6.144173869603344e-06,
                2.2603242978871282e-06,
                4.222835458175145e-06,
                2.2603242978871282e-06,
                5.715002426486762e-07,
                5.04347468323289e-07
            ],
            [
                7.338210680021253e-07,
                6.475948754028718e-07,
                1.2098659719788098e-06,
                NaN,
                3.4663249714612693e-07,
                3.059022998581767e-07,
                8.315281267882195e-07,
                6.47595107001401e-07,
                1.4449802095666915e-07,
                9.422445939032799e-07
            ],
            [
                2.6995790618350237e-07,
                8.315281267834927e-07,
                8.315278294072958e-07,
                6.475948754012522e-07,
                NaN,
                3.0590215399183813e-07,
                1.5534975693933505e-06,
                1.0677032518748838e-06,
                7.338213304363436e-07,
                5.4222176771176554e-06
            ],
            [
                1.8553910183674878e-07,
                5.715003789046955e-07,
                NaN,
                4.2228319344021954e-06,
                1.7603438428740716e-06,
                1.8553907971855875e-07,
                6.475950298011458e-07,
                9.931199245322124e-08,
                3.927863407379485e-07,
                5.715005832886879e-07
            ],
            [
                1.8553903548231313e-07,
                7.338208930391909e-07,
                5.04347348070562e-07,
                2.902312677137316e-06,
                9.422445939032799e-07,
                6.475951069985296e-07,
                6.475945666051092e-07,
                NaN,
                4.450850519403407e-07,
                7.338209805224048e-07
            ],
            [
                5.043476486924565e-07,
                1.637377057673536e-07,
                8.315284241650899e-07,
                1.2751902768612997e-07,
                3.927860597945825e-07,
                2.2603234895289998e-06,
                3.726638839806038e-06,
                1.9947297215125433e-06,
                8.315277302857965e-07,
                9.422449308716635e-07
            ],
            [
                0.9999991684720722,
                0.9999996072136127,
                0.9999989322970039,
                0.999998126124618,
                0.9999995549150545,
                0.9999984465022471,
                0.9999972735284329,
                0.9999992188513906,
                0.9999995549148422,
                0.9999996310115479
            ],
            [
                1.5534977545886537e-06,
                1.209865539295696e-06,
                8.939695238634211e-06,
                8.315279285351409e-07,
                7.338209805224048e-07,
                8.315284241650899e-07,
                3.05902190458764e-07,
                9.422445939032799e-07,
                5.043473480777865e-07,
                3.927862470899887e-07
            ],
            [
                NaN,
                1.4449807263312446e-07,
                NaN,
                3.9278605979534166e-07,
                1.3709572068553509e-06,
                4.4508526417298334e-07,
                2.6995774527718623e-07,
                1.637377057680051e-07,
                NaN,
                NaN
            ],
            [
                9.422442569315887e-07,
                4.450851580555361e-07,
                7.338213304363436e-07,
                2.2603240284371276e-06,
                4.785092783519724e-06,
                3.059021175247079e-07,
                4.450849458218309e-07,
                2.3823702359290413e-07,
                9.422447062270609e-07,
                1.0129987357407137e-05
            ],
            [
                1.9947301970972664e-06,
                1.760343213335281e-06,
                9.422450432014836e-07,
                8.939696304311336e-06,
                3.466327037539638e-07,
                1.3007130015677909e-05,
                2.902313023130843e-06,
                4.450851580555361e-07,
                3.726638839878908e-06,
                2.1024344128660572e-07
            ],
            [
                2.3823696679327928e-07,
                9.422447062294175e-07,
                7.889265407255982e-06,
                NaN,
                NaN,
                4.450850519403407e-07,
                9.422445939032799e-07,
                NaN,
                4.4508510499849186e-07,
                1.067703124601679e-06
            ],
            [
                9.422445939032799e-07,
                3.466326211113502e-07,
                1.3709576971463352e-06,
                1.760343213335281e-06,
                6.475950298011458e-07,
                9.422444815792981e-07,
                6.144172404738491e-06,
                4.4508494582405734e-07,
                5.715005151606823e-07,
                4.450849988811838e-07
            ],
            [
                6.144175334468545e-06,
                1.5534977545886537e-06,
                5.04347468323289e-07,
                3.9278620026686556e-07,
                1.6701415872385704e-05,
                1.6373776432509826e-07,
                1.2098659719757836e-06,
                9.422443692555439e-07,
                4.450850519403407e-07,
                6.962255419931625e-06
            ],
            [
                4.785092783519724e-06,
                8.315279285351409e-07,
                1.3709576971316842e-06,
                2.5612831267202583e-06,
                7.338211554783522e-07,
                4.222831934379152e-06,
                1.7603438428740716e-06,
                8.315277302841894e-07,
                4.785096776499213e-06,
                3.059021175261338e-07
            ],
            [
                1.5534975693933505e-06,
                2.9023109472244114e-06,
                3.7266406168827523e-06,
                3.726638839878908e-06,
                3.7266406168624155e-06,
                1.994729008145876e-06,
                3.7266388398585725e-06,
                0.000626334177018984,
                4.222834451355964e-06,
                2.9023112932177327e-06
            ],
            [
                NaN,
                2.9023112932177327e-06,
                3.9278605979534166e-07,
                1.8925143729954285e-05,
                1.2098653950656417e-06,
                NaN,
                NaN,
                1.1478765389222573e-05,
                2.561281600086738e-06,
                4.450852111148132e-07
            ],
            [
                2.699577774585891e-07,
                1.7603432133296774e-06,
                6.962254589781966e-06,
                3.466327450765785e-07,
                5.04347528446051e-07,
                6.47594798194325e-07,
                5.04347528446051e-07,
                5.043472278322555e-07,
                4.222832941193893e-06,
                3.9278610661902853e-07
            ],
            [
                1.3709573702822306e-06,
                2.9023130231176453e-06,
                2.2603242978665707e-06,
                6.475945666051092e-07,
                1.3709576971425944e-06,
                8.315278294072958e-07,
                1.3709568799823232e-06,
                2.561283432035425e-06,
                1.3709570434178922e-06,
                9.422448185510695e-07
            ],
            [
                3.535624228698939e-05,
                7.889260704818233e-06,
                1.0129987357287368e-05,
                3.120190393590123e-05,
                NaN,
                5.422220908925639e-06,
                5.043476486915964e-07,
                4.785093924330255e-06,
                1.5534983101602148e-06,
                5.422220262555012e-06
            ],
            [
                3.288748673376478e-06,
                5.04347468323289e-07,
                1.0677029973219343e-06,
                8.315279285351409e-07,
                NaN,
                1.3709575337159875e-06,
                4.2228334445658276e-06,
                NaN,
                5.422217677152175e-06,
                2.2603251062450327e-06
            ],
            [
                4.450852111148132e-07,
                3.288749457469787e-06,
                1.3709567165617364e-06,
                3.927862939136532e-07,
                0.9999798543021179,
                NaN,
                6.475950298021765e-07,
                9.422445939054222e-07,
                1.0129993395336818e-05,
                NaN
            ],
            [
                2.382368531929327e-07,
                NaN,
                1.5534977545886537e-06,
                2.90231094723893e-06,
                0.8933094096048377,
                7.338209805200689e-07,
                NaN,
                2.9023112932177327e-06,
                2.902312677150514e-06,
                4.222834954801051e-06
            ],
            [
                2.2603234895372223e-06,
                1.5534984953510149e-06,
                9.422443692574719e-07,
                1.4738976701652988e-05,
                5.715005832886879e-07,
                4.222834451382849e-06,
                1.0677029973192638e-06,
                1.5534971989696065e-06,
                6.144172404693786e-06,
                1.7603440527286572e-06
            ],
            [
                1.209865827740176e-06,
                4.785093353940187e-06,
                1.2098662604291696e-06,
                1.994729008145876e-06,
                9.422444815765128e-07,
                3.288749065423109e-06,
                6.144172404693786e-06,
                9.422448185534261e-07,
                1.2098659719788098e-06,
                1.7603427936335396e-06
            ],
            [
                NaN,
                2.5612812947380135e-06,
                NaN,
                NaN,
                8.315280276546789e-07,
                6.962257909722651e-06,
                1.1478770862735993e-05,
                4.785096776468749e-06,
                7.3382080556433e-07,
                3.726639728370556e-06
            ],
            [
                1.9947306726594253e-06,
                2.260324297853209e-06,
                1.5534971989907999e-06,
                3.726639284103523e-06,
                2.9023133690425823e-06,
                2.1024331597262577e-07,
                2.5612819053166966e-06,
                2.561282210701601e-06,
                1.994730434816876e-06,
                1.3709575337078829e-06
            ],
            [
                3.288749065423109e-06,
                7.338210680021253e-07,
                2.382368531929327e-07,
                1.5534971990126997e-06,
                NaN,
                0.9997965729797639,
                1.7603430034867993e-06,
                1.994729483729522e-06,
                9.422443692555439e-07,
                7.889260704818233e-06
            ],
            [
                6.962259569484628e-06,
                5.422219616140078e-06,
                9.422443692555439e-07,
                1.2098659719788098e-06,
                1.0677032518785256e-06,
                NaN,
                2.561283126679493e-06,
                3.288750241500471e-06,
                8.315281267861397e-07,
                4.006369696286016e-05
            ],
            [
                2.699577774585891e-07,
                1.9947297215043796e-06,
                6.144176066901277e-06,
                NaN,
                3.7266397283908927e-06,
                1.2098661161927025e-06,
                9.4224425692559e-07,
                7.338209805224048e-07,
                1.209865827752005e-06,
                3.9278605979534166e-07
            ],
            [
                4.222835458148261e-06,
                1.2098656835224664e-06,
                1.8925152753790864e-05,
                5.043475885688201e-07,
                2.3823688159291947e-07,
                2.1024339116168358e-07,
                2.1024331597262577e-07,
                7.338212429582604e-07,
                8.939696304213768e-06,
                NaN
            ],
            [
                1.209865827740176e-06,
                2.7535697666401535e-05,
                5.04347468323289e-07,
                2.902310947190096e-06,
                1.5534981249574276e-06,
                3.7266406168827523e-06,
                5.04347348075149e-07,
                2.9023133690821773e-06,
                1.3709567165579959e-06,
                2.6995790618350237e-07
            ],
            [
                7.734416698849138e-08,
                2.10243290909724e-07,
                1.4449798650569826e-07,
                9.931200429212718e-08,
                1.8553907971758842e-07,
                1.9947294837154625e-06,
                1.1253524254650944e-07,
                1.994729483729522e-06,
                8.764249540862797e-08,
                2.382368531929327e-07
            ],
            [
                5.715005832886879e-07,
                1.3709573702822306e-06,
                5.715005832886879e-07,
                2.561281600086738e-06,
                7.338209805224048e-07,
                1.3709570434178922e-06,
                1.9947297215125433e-06,
                6.475947210031623e-07,
                2.2603242978871282e-06,
                2.2603242978871282e-06
            ],
            [
                4.785092783519724e-06,
                2.902310947208574e-06,
                2.56128159999123e-06,
                4.22283545819819e-06,
                3.726638395634011e-06,
                1.7603438428660665e-06,
                6.962254589851619e-06,
                1.5534983101602148e-06,
                1.0677028700363782e-06,
                1.994730434879465e-06
            ],
            [
                4.222834954778007e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                4.450852111155216e-07,
                2.5612812947508257e-06,
                1.3007123813193233e-05,
                9.931199245322124e-08,
                1.0677024881980089e-06
            ],
            [
                1.7603430034867993e-06,
                3.288749065423109e-06,
                2.5612828213934817e-06,
                7.338210680021253e-07,
                3.2887506336235617e-06,
                NaN,
                1.2098653950656417e-06,
                9.422442569097361e-07,
                6.144173869603344e-06,
                NaN
            ],
            [
                2.2603234895289998e-06,
                9.422442569315887e-07,
                1.3007123812980299e-05,
                1.0129987357287368e-05,
                1.8925148241872038e-05,
                9.422444815792981e-07,
                6.9622537599680095e-06,
                1.3709575337016483e-06,
                1.3709572068522336e-06,
                4.006371129615879e-05
            ],
            [
                5.043475284468537e-07,
                5.04347468323289e-07,
                2.699578096403948e-07,
                1.4449798650551755e-07,
                1.5534981249697903e-06,
                3.927863875616689e-07,
                3.0590237279032884e-07,
                6.475950298021765e-07,
                NaN,
                6.47594952603035e-07
            ],
            [
                4.222835458148261e-06,
                NaN,
                1.7603434231777837e-06,
                1.3709568799919866e-06,
                1.2098658277451275e-06,
                2.1024334103581732e-07,
                6.475947210031623e-07,
                1.2098658277489788e-06,
                1.3709576971379186e-06,
                1.9947301970813926e-06
            ],
            [
                3.927862002663297e-07,
                2.7535704232595768e-05,
                4.4508526417298334e-07,
                2.6995774527718623e-07,
                6.475948754012522e-07,
                6.962253760024999e-06,
                3.288749849529972e-06,
                6.475947982037486e-07,
                1.5534975693933505e-06,
                5.04347468323289e-07
            ],
            [
                3.9278629391427843e-07,
                8.315282259138311e-07,
                1.067702870039777e-06,
                2.1444940745839484e-05,
                6.9622587397397306e-06,
                8.315281267882195e-07,
                6.9622595696935874e-06,
                9.422444815765128e-07,
                7.338207180838067e-07,
                2.5612834320470717e-06
            ],
            [
                1.0677032518700286e-06,
                1.994730434879465e-06,
                5.04347468323289e-07,
                1.209865827740176e-06,
                9.422448185478557e-07,
                1.5534971990126997e-06,
                3.7266388396128453e-06,
                1.0677028700363782e-06,
                2.5612834320214477e-06,
                7.338209805200689e-07
            ],
            [
                2.5612834320470717e-06,
                8.315281267861397e-07,
                1.99472900813862e-06,
                8.939700567004841e-06,
                1.2098662604291696e-06,
                6.475948754012522e-07,
                6.96225873967641e-06,
                5.422219616265831e-06,
                1.5534973842076057e-06,
                2.5612834320470717e-06
            ],
            [
                1.9947301970972664e-06,
                3.059022269250683e-07,
                5.715002426486762e-07,
                9.422444815765128e-07,
                5.829128639666634e-05,
                1.2098658277489788e-06,
                2.9023112932177327e-06,
                7.338212429562581e-07,
                4.785093353940187e-06,
                6.475951069985296e-07
            ],
            [
                5.043474081993875e-07,
                8.315281267861397e-07,
                1.2098659719757836e-06,
                5.043475885696228e-07,
                8.315281267882195e-07,
                4.450850519403407e-07,
                6.144177531811707e-06,
                3.7266401726359486e-06,
                5.715003789046955e-07,
                7.338210679979539e-07
            ],
            [
                9.422450432014836e-07,
                1.99472900813862e-06,
                5.04347348075149e-07,
                8.315277302841894e-07,
                6.475947210031623e-07,
                3.466327037539638e-07,
                1.7603425837855082e-06,
                7.338210680002898e-07,
                1.0677029973158649e-06,
                5.043473480777865e-07
            ],
            [
                7.338207180898968e-07,
                3.0590219045914655e-07,
                1.5534983101644536e-06,
                5.04347287955046e-07,
                5.043475284468537e-07,
                7.889261645427538e-06,
                2.382370235933104e-07,
                8.315277302857965e-07,
                8.31528325040778e-07,
                8.315277302857965e-07
            ],
            [
                8.939696304311336e-06,
                2.9023116392097746e-06,
                6.962253760024999e-06,
                1.9947294837154625e-06,
                1.2098655392921197e-06,
                8.315277302788957e-07,
                1.4449800373118268e-07,
                2.5612819054133693e-06,
                1.5534979397740895e-06,
                1.994729483705484e-06
            ],
            [
                3.927862470899887e-07,
                1.7603436330259153e-06,
                2.90231094723893e-06,
                1.209865539295696e-06,
                8.315277302841894e-07,
                1.2098652508424818e-06,
                1.2098652508391807e-06,
                3.0590237279032884e-07,
                1.994729959270648e-06,
                1.553497199007048e-06
            ],
            [
                1.7603430034743913e-06,
                9.422449308673789e-07,
                1.760343003481596e-06,
                6.475949525981759e-07,
                2.2603237589676295e-06,
                8.939696304213768e-06,
                1.3709570434178922e-06,
                3.7266410611296085e-06,
                1.0677032518748838e-06,
                1.0677024881980089e-06
            ],
            [
                9.422444815814404e-07,
                7.889263526345123e-06,
                1.9947299593078385e-06,
                1.7603427936335396e-06,
                3.288749457469787e-06,
                1.9947292459347367e-06,
                1.2098661162056318e-06,
                NaN,
                3.2887498495150166e-06,
                3.288749457469787e-06
            ],
            [
                1.209866260432471e-06,
                5.04347468323289e-07,
                3.9278610661902853e-07,
                1.3709576971463352e-06,
                3.288749849529972e-06,
                1.3709572068522336e-06,
                1.0677028700422047e-06,
                3.927862002663297e-07,
                4.450852641737424e-07,
                5.04347468323289e-07
            ],
            [
                2.2603245673443566e-06,
                2.10243290909963e-07,
                1.760343213335281e-06,
                NaN,
                6.825597214718257e-08,
                1.3709570434250617e-06,
                2.699578096393206e-07,
                NaN,
                NaN,
                NaN
            ],
            [
                9.422445939054222e-07,
                6.475950298011458e-07,
                4.5397884884891014e-05,
                3.927862939126708e-07,
                8.315281267834927e-07,
                4.0063682641226247e-05,
                1.5534975693869924e-06,
                8.315277302857965e-07,
                6.962257079775324e-06,
                2.561283432035425e-06
            ],
            [
                8.315284241650899e-07,
                1.0677029973219343e-06,
                3.288749457469787e-06,
                5.715005832886879e-07,
                2.753568453792444e-05,
                1.0677032518814388e-06,
                2.144494841482881e-05,
                1.5534983101602148e-06,
                8.939698435560267e-06,
                1.3709576971425944e-06
            ],
            [
                6.47594952603035e-07,
                6.475947982037486e-07,
                8.315280276626197e-07,
                7.734423152941018e-08,
                NaN,
                1.7603440527286572e-06,
                8.315277302857965e-07,
                3.059021175261338e-07,
                5.04347287955046e-07,
                1.8925143729162536e-05
            ],
            [
                2.5612816000646084e-06,
                1.5534983101644536e-06,
                1.012999218776902e-05,
                3.726637951387472e-06,
                2.90231233114251e-06,
                1.5534981249697903e-06,
                2.561283432005142e-06,
                1.6701425827133152e-05,
                1.994729483723626e-06,
                3.726639284125553e-06
            ],
            [
                2.6995784182183607e-07,
                3.466326211113502e-07,
                1.6373764721072816e-07,
                2.1024334103505245e-07,
                3.726639284144195e-06,
                1.2751901248391176e-07,
                1.2751904288710323e-07,
                4.4508510499849186e-07,
                2.3823682479181176e-07,
                3.9278634073732336e-07
            ],
            [
                1.0677027427624903e-06,
                5.715002426486762e-07,
                1.370956716529941e-06,
                1.7603425837702984e-06,
                3.9278605979534166e-07,
                3.927863875616689e-07,
                2.9023119851899796e-06,
                9.422443692489024e-07,
                9.422442569097361e-07,
                4.222833948008874e-06
            ],
            [
                5.043473480777865e-07,
                9.422443692555439e-07,
                5.715006514176113e-07,
                NaN,
                NaN,
                7.338209805240734e-07,
                1.760342793638743e-06,
                3.2887502415767434e-06,
                3.288749065423109e-06,
                2.5612828213934817e-06
            ],
            [
                1.0677032518814388e-06,
                1.209866260432471e-06,
                6.144172404738491e-06,
                NaN,
                5.715006514167015e-07,
                4.4508510499849186e-07,
                4.785095065232451e-06,
                6.475950298011458e-07,
                4.785096776499213e-06,
                1.9947292459347367e-06
            ],
            [
                9.422445939032799e-07,
                1.3007133116732079e-05,
                1.7603434231777837e-06,
                1.0677028700363782e-06,
                3.288748673376478e-06,
                1.3709576971379186e-06,
                NaN,
                5.422217030781934e-06,
                7.338207180898968e-07,
                1.3007126914435202e-05
            ],
            [
                5.4222209089700225e-06,
                NaN,
                1.9947304348862686e-06,
                2.902312331170226e-06,
                3.0590237279032884e-07,
                3.059022998581767e-07,
                6.475945666051092e-07,
                4.4508505193791187e-07,
                1.0677032518785256e-06,
                1.760343633031919e-06
            ],
            [
                2.260324028427877e-06,
                7.338209805200689e-07,
                1.760344052693435e-06,
                1.2098653950656417e-06,
                1.7603425837702984e-06,
                9.422450432014836e-07,
                1.5534975693869924e-06,
                9.42244930862237e-07,
                1.0677032518748838e-06,
                1.9947301970972664e-06
            ],
            [
                3.927863875616689e-07,
                1.7603430034867993e-06,
                3.288749065423109e-06,
                6.962257909842961e-06,
                5.043472278322555e-07,
                1.6701421845057263e-05,
                NaN,
                2.10243290909724e-07,
                1.760343213335281e-06,
                NaN
            ],
            [
                4.539785782605375e-05,
                8.939696304311336e-06,
                1.553497754577351e-06,
                1.0677028700363782e-06,
                7.889265407255982e-06,
                3.7266397283908927e-06,
                8.315283250343497e-07,
                1.5534977545886537e-06,
                1.760343213322473e-06,
                3.0590215399183813e-07
            ],
            [
                9.422448185534261e-07,
                1.8925148241872038e-05,
                4.785096206076165e-06,
                0.9999977396759753,
                2.144495864059426e-05,
                0.9999970976873326,
                8.315278294114555e-07,
                2.2603240284371276e-06,
                4.450848927658745e-07,
                5.71500719545698e-07
            ],
            [
                0.00010889696111673426,
                6.475950298011458e-07,
                7.338207180864763e-07,
                8.315277302841894e-07,
                1.3709567165579959e-06,
                7.338211554783522e-07,
                3.2887490653109436e-06,
                6.475947210046347e-07,
                4.450849458218309e-07,
                2.561282516042282e-06
            ],
            [
                2.5612819054133693e-06,
                1.5534984953552536e-06,
                1.5534979397740895e-06,
                7.889264466868659e-06,
                5.715003788993679e-07,
                1.994730197090463e-06,
                2.5612819053586272e-06,
                1.370957860567974e-06,
                1.0677032518700286e-06,
                1.5534984953199313e-06
            ],
            [
                1.6373772528704005e-07,
                2.9023119851899796e-06,
                2.1024336609874897e-07,
                6.475947210031623e-07,
                1.5534979397829198e-06,
                3.0590237279085045e-07,
                5.043475284468537e-07,
                7.338208055680009e-07,
                1.0677027427624903e-06,
                NaN
            ],
            [
                1.2098652508424818e-06,
                5.715007195447234e-07,
                2.5612831267202583e-06,
                5.715007195384861e-07,
                8.315284241650899e-07,
                5.715005832886879e-07,
                8.315281267861397e-07,
                1.2098652508287273e-06,
                2.260324028427877e-06,
                1.3709568799760888e-06
            ],
            [
                3.2887506336086064e-06,
                3.726639728370556e-06,
                1.4738989000422955e-05,
                2.2603242978778778e-06,
                9.422449308748773e-07,
                3.288748281329893e-06,
                5.4222176771176554e-06,
                7.338211554783522e-07,
                3.72664061681327e-06,
                2.5612834320470717e-06
            ],
            [
                5.043475885674441e-07,
                3.9278605979534166e-07,
                1.4738987242968784e-05,
                1.0677032518748838e-06,
                3.059021904571643e-07,
                1.7603425837903113e-06,
                1.0677024881980089e-06,
                9.422450431989127e-07,
                1.0677029973158649e-06,
                2.2603234895289998e-06
            ]
        ]
    },
    {
        "q_id": "9252_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            13,
            14,
            15,
            16,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            60,
            61,
            62,
            63,
            64,
            66,
            67,
            68,
            70,
            71,
            75,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                5.715005832895975e-07,
                3.466327037553825e-07,
                1.1478765389368729e-05,
                4.222832941193893e-06,
                1.0677028700422047e-06,
                2.3823696679327928e-07,
                3.288748281329893e-06,
                1.209865539298447e-06,
                1.2098656835252174e-06,
                1.994729008151319e-06
            ],
            [
                5.04347468323289e-07,
                5.043472278322555e-07,
                9.422448185478557e-07,
                2.382369667929001e-07,
                6.475948754012522e-07,
                1.209865539295696e-06,
                5.043473480777865e-07,
                3.9278634073625165e-07,
                3.4663266243308805e-07,
                3.466325797896173e-07
            ],
            [
                1.3709570434178922e-06,
                3.726638395611981e-06,
                1.5534973842076057e-06,
                5.04347468323289e-07,
                1.209865827740176e-06,
                2.2603240283888175e-06,
                2.2603242978871282e-06,
                8.315282259138311e-07,
                5.043475284447896e-07,
                1.3709570434219446e-06
            ],
            [
                3.0590237279032884e-07,
                8.764245361752286e-08,
                2.382369951932796e-07,
                2.382369667929001e-07,
                2.1024331597262577e-07,
                1.4449805540740185e-07,
                1.8553914607267268e-07,
                3.059022998576899e-07,
                3.059022998576899e-07,
                1.27519088491875e-07
            ],
            [
                6.475949526020042e-07,
                4.4508510499849186e-07,
                3.2887506336235617e-06,
                3.4663249714612693e-07,
                1.0677032518785256e-06,
                1.5534975693979422e-06,
                3.927862470899887e-07,
                3.0590226339137693e-07,
                8.315284241650899e-07,
                NaN
            ],
            [
                7.734425918979532e-08,
                1.637377057673536e-07,
                2.699577774585891e-07,
                2.3823688159291947e-07,
                1.2751904288710323e-07,
                3.224187402001668e-08,
                7.734416698815724e-08,
                8.764244316973974e-08,
                1.275190580884987e-07,
                1.2751905808881762e-07
            ],
            [
                1.7603425837855082e-06,
                2.6995774527657245e-07,
                5.715003107755449e-07,
                3.927862470899887e-07,
                7.338209805240734e-07,
                2.6995784182140636e-07,
                3.4663278639265633e-07,
                5.043473480777865e-07,
                2.1024336609843824e-07,
                3.927862002654366e-07
            ],
            [
                1.0677032518814388e-06,
                5.04347468323289e-07,
                3.9278610661902853e-07,
                1.209865539295696e-06,
                7.338208930421943e-07,
                2.90231094723893e-06,
                1.0677029973192638e-06,
                2.2603237589779086e-06,
                2.2603240284371276e-06,
                1.3709572068522336e-06
            ],
            [
                3.059022998581767e-07,
                3.288750241561788e-06,
                2.3823682479292225e-07,
                1.067703124601679e-06,
                3.05902190458764e-07,
                3.466326211113502e-07,
                1.9947299593014888e-06,
                6.605216832236121e-05,
                1.4738978458382043e-05,
                3.4663278639892215e-07
            ],
            [
                6.475951069985296e-07,
                4.450848927650143e-07,
                3.4663262110945863e-07,
                9.4224425692559e-07,
                3.927860597945825e-07,
                3.0590215399183813e-07,
                8.315281267834927e-07,
                2.1024336609843824e-07,
                7.338207180864763e-07,
                3.0590237279032884e-07
            ],
            [
                3.2887482812745586e-06,
                1.5534975693933505e-06,
                1.3007134667070165e-05,
                4.785093924362895e-06,
                5.715003107755449e-07,
                6.605214469462115e-05,
                7.338209805224048e-07,
                1.0677029973192638e-06,
                1.7603427936263351e-06,
                9.422442569315887e-07
            ],
            [
                2.102434412871794e-07,
                1.6373762769138607e-07,
                7.734416698849138e-08,
                1.4449798650551755e-07,
                7.338211554783522e-07,
                2.3823696679230424e-07,
                2.382369667929001e-07,
                1.4449807263312446e-07,
                7.73441946488886e-08,
                2.6995774527718623e-07
            ],
            [
                3.4663274507713016e-07,
                2.382370235933104e-07,
                3.059022998576899e-07,
                8.7642516304188e-08,
                3.05902190458764e-07,
                2.699577774585891e-07,
                6.475948754028718e-07,
                2.699578740032504e-07,
                3.9278610661902853e-07,
                9.931190958076104e-08
            ],
            [
                3.288748673376478e-06,
                2.3823682479292225e-07,
                1.8553905760062447e-07,
                9.422445939054222e-07,
                8.315281267882195e-07,
                1.8553910183674878e-07,
                2.3823693839325527e-07,
                2.699576809143613e-07,
                1.6373774480605869e-07,
                9.422444815814404e-07
            ],
            [
                3.288749849529972e-06,
                4.4508494582314646e-07,
                7.338208055680009e-07,
                1.5534973842076057e-06,
                1.2098662604291696e-06,
                1.760343003481596e-06,
                NaN,
                9.422445939032799e-07,
                2.6995771309523475e-07,
                1.9947290081177566e-06
            ],
            [
                1.0677024881980089e-06,
                9.422449308716635e-07,
                8.315277302841894e-07,
                1.067702870039777e-06,
                1.5534984953510149e-06,
                6.475947210031623e-07,
                2.2603242978871282e-06,
                6.475950298011458e-07,
                0.9999970976876763,
                1.3709567165579959e-06
            ],
            [
                3.4663266242969896e-07,
                3.9278615344178325e-07,
                2.1024334103352274e-07,
                3.466327037539638e-07,
                5.715006514105942e-07,
                1.2751904288710323e-07,
                2.6995768091310296e-07,
                1.6373774480535133e-07,
                3.466325384661554e-07,
                4.450852641656969e-07
            ],
            [
                1.760342793583908e-06,
                3.288750241500471e-06,
                1.5534973841895917e-06,
                1.5534984953453635e-06,
                5.4222176771176554e-06,
                4.222831934352267e-06,
                2.5612819054133693e-06,
                1.3007123813382511e-05,
                5.422220908876325e-06,
                2.4300234940642642e-05
            ],
            [
                1.5534984953510149e-06,
                3.288747889284851e-06,
                3.2887482813149375e-06,
                6.9622587397397306e-06,
                3.288749065423109e-06,
                2.5612812947508257e-06,
                4.785096206076165e-06,
                1.7603440527286572e-06,
                NaN,
                1.5534975693933505e-06
            ],
            [
                3.059022269250683e-07,
                8.315280276607289e-07,
                2.3823688159291947e-07,
                2.1024341622426268e-07,
                1.3709567165617364e-06,
                1.6373774480605869e-07,
                1.0677033791612137e-06,
                2.102434412875379e-07,
                4.450848927650143e-07,
                2.6995790618469934e-07
            ],
            [
                1.2751905808881762e-07,
                6.475946438042047e-07,
                3.927861066170637e-07,
                3.9278634073732336e-07,
                3.05902117523595e-07,
                2.102434412875379e-07,
                2.6995777745711594e-07,
                1.855391681906175e-07,
                2.1024329090929374e-07,
                4.450851580540182e-07
            ],
            [
                3.726638395611981e-06,
                2.1444940745839484e-05,
                3.1201926253802263e-05,
                4.2228324377164004e-06,
                1.4738976700929127e-05,
                1.2098659719757836e-06,
                2.260325375634003e-06,
                1.0129988564099116e-05,
                2.561283432005142e-06,
                3.2887498493983645e-06
            ],
            [
                6.962256249885085e-06,
                4.222831934379152e-06,
                7.338209805200689e-07,
                4.785092783519724e-06,
                3.9278624708775595e-07,
                1.553498124964492e-06,
                1.7603427936183298e-06,
                2.5612816000646084e-06,
                2.2603234895372223e-06,
                9.422445939032799e-07
            ],
            [
                7.338210680021253e-07,
                1.6373768624837685e-07,
                5.04347648686092e-07,
                1.2751908849088918e-07,
                7.338210680021253e-07,
                1.8553905760062447e-07,
                8.315280276607289e-07,
                6.475948753991907e-07,
                4.450849988798682e-07,
                6.475950297993789e-07
            ],
            [
                4.1399375473868e-08,
                2.3823696679230424e-07,
                1.1253510839355284e-07,
                1.1253506814797596e-07,
                4.691160446380562e-08,
                9.931190958076104e-08,
                1.1253518888464745e-07,
                1.4449802095609418e-07,
                3.6534807736504303e-08,
                1.855391239544352e-07
            ],
            [
                1.7603438428660665e-06,
                3.466325797896173e-07,
                5.715007195431641e-07,
                5.043474683204221e-07,
                3.927862939126708e-07,
                5.715006514151423e-07,
                4.450852111148132e-07,
                3.0590237279032884e-07,
                1.0677028700363782e-06,
                1.8553903548231313e-07
            ],
            [
                5.715007195431641e-07,
                3.288747889284851e-06,
                2.9023112932296107e-06,
                2.5612831267086116e-06,
                3.2887482811908074e-06,
                1.2098653950692178e-06,
                NaN,
                2.5612828213934817e-06,
                7.338211554783522e-07,
                1.8925148242250705e-05
            ],
            [
                1.3709576971425944e-06,
                1.5534983101478522e-06,
                1.2098659719716573e-06,
                1.3709570434178922e-06,
                8.315281267882195e-07,
                5.715003788993679e-07,
                1.6373762769138607e-07,
                1.6373770576776313e-07,
                2.6995790618469934e-07,
                1.2751908849167202e-07
            ],
            [
                5.715007195447234e-07,
                5.04347348075149e-07,
                3.927862002654366e-07,
                2.102433410343832e-07,
                2.3823682479181176e-07,
                1.275190732904469e-07,
                9.422443692555439e-07,
                2.102433410343832e-07,
                1.1253510839355284e-07,
                8.764249540862797e-08
            ],
            [
                1.3709578604981489e-06,
                3.927860597945825e-07,
                8.315278294001114e-07,
                7.338210679949506e-07,
                6.475946438022905e-07,
                5.715002426460124e-07,
                7.3382080556433e-07,
                1.3709573702566696e-06,
                7.338210680021253e-07,
                1.994729008145876e-06
            ],
            [
                3.7266397283908927e-06,
                7.338207180898968e-07,
                2.2603234895372223e-06,
                2.2603253756956754e-06,
                2.561281600086738e-06,
                2.1444953527944967e-05,
                2.260324567337161e-06,
                4.450848927658745e-07,
                6.962259569750576e-06,
                7.338209805240734e-07
            ],
            [
                5.715005151606823e-07,
                1.5534979397790343e-06,
                1.0677024882009222e-06,
                1.2098658277489788e-06,
                3.4663266243308805e-07,
                2.2603240284371276e-06,
                6.475947210046347e-07,
                8.315281267882195e-07,
                1.9947304348862686e-06,
                1.3709576971425944e-06
            ],
            [
                2.6995790618469934e-07,
                2.1024339116082313e-07,
                0.0035936023379814406,
                7.338212429594283e-07,
                3.9278620026686556e-07,
                1.9947299593078385e-06,
                3.466327037553825e-07,
                9.931185038635267e-08,
                1.1253506814842375e-07,
                2.6995774527718623e-07
            ],
            [
                2.382369667929001e-07,
                2.6995774527718623e-07,
                8.481103128838341e-05,
                9.931189774187203e-08,
                3.059022998581767e-07,
                1.275190124842887e-07,
                1.6373766672973748e-07,
                3.46632497145457e-07,
                1.994729008151319e-06,
                1.444980209564556e-07
            ],
            [
                6.144176066901277e-06,
                1.7603438428800754e-06,
                2.9023116391978967e-06,
                1.7603425837791042e-06,
                3.0590237279085045e-07,
                4.4508505193932864e-07,
                1.7603438428800754e-06,
                1.7603440527286572e-06,
                1.209865539295696e-06,
                6.962257909785973e-06
            ],
            [
                8.315283250371857e-07,
                9.422442569290178e-07,
                9.422448185534261e-07,
                5.043474081993875e-07,
                7.338213304363436e-07,
                1.5534981249697903e-06,
                2.1024326584639497e-07,
                6.475947982022763e-07,
                7.338212429562581e-07,
                2.260324836776948e-06
            ],
            [
                7.889263526345123e-06,
                1.5534973842030142e-06,
                9.422447062270609e-07,
                3.2887506336235617e-06,
                5.144223206152219e-05,
                9.422450432014836e-07,
                4.222835458175145e-06,
                1.5534984953453635e-06,
                4.222832941142044e-06,
                6.475945666033422e-07
            ],
            [
                6.47594952603035e-07,
                1.1253508156363576e-07,
                1.8553919030858602e-07,
                2.3823688159291947e-07,
                3.9278605979534166e-07,
                2.3823702359290413e-07,
                2.3823690999323465e-07,
                2.1024331597262577e-07,
                2.5612834320563895e-06,
                2.3823685319244518e-07
            ],
            [
                6.475947982002148e-07,
                7.338210680002898e-07,
                5.71500515159253e-07,
                5.4222176771176554e-06,
                4.450852111148132e-07,
                5.715003107715166e-07,
                9.422445939032799e-07,
                8.315282259089153e-07,
                1.3007123813193233e-05,
                2.5612828213818346e-06
            ],
            [
                2.6995774527577444e-07,
                7.3382080556433e-07,
                1.2098662604291696e-06,
                3.059022998581767e-07,
                5.715003789017068e-07,
                9.422443692446175e-07,
                2.6995771309523475e-07,
                5.043474081993875e-07,
                3.466327037539638e-07,
                NaN
            ],
            [
                5.715005832886879e-07,
                3.288747889284851e-06,
                1.0677029973192638e-06,
                3.466327863983311e-07,
                1.2098658277489788e-06,
                1.370957860576702e-06,
                6.475947981975644e-07,
                1.2098653950656417e-06,
                8.315279285351409e-07,
                1.0677032518785256e-06
            ],
            [
                6.475945666063607e-07,
                3.927862470899887e-07,
                7.338210680021253e-07,
                2.902312677150514e-06,
                3.466325797896173e-07,
                2.382369951932796e-07,
                9.422447062294175e-07,
                3.4663278639892215e-07,
                2.102434162245973e-07,
                5.04347528446051e-07
            ],
            [
                4.450849988811838e-07,
                4.2228339479858295e-06,
                8.315284241597959e-07,
                3.466327037539638e-07,
                3.9278624708775595e-07,
                4.4508505193386385e-07,
                1.8553910183607374e-07,
                6.475947210046347e-07,
                6.475949526020042e-07,
                8.315281267861397e-07
            ],
            [
                5.715002426486762e-07,
                NaN,
                1.4449805540763184e-07,
                9.422444815814404e-07,
                8.315280276626197e-07,
                9.422449308774482e-07,
                1.9947299592933255e-06,
                9.610244938894432e-05,
                5.043474683204221e-07,
                3.05902190458764e-07
            ],
            [
                1.3709573702856596e-06,
                1.5534984953552536e-06,
                1.5534973842076057e-06,
                1.1253508156363576e-07,
                4.4508515805735777e-07,
                2.1024336609874897e-07,
                5.715005832895975e-07,
                1.0677029973219343e-06,
                3.466327037553825e-07,
                2.6995784182183607e-07
            ],
            [
                NaN,
                1.2098658277335738e-06,
                1.55349775456958e-06,
                9.422442569208767e-07,
                1.5534977545603963e-06,
                7.338210679979539e-07,
                2.5612828213352452e-06,
                4.450848927650143e-07,
                1.7603432132784448e-06,
                1.0677027427525368e-06
            ],
            [
                3.0590215399183813e-07,
                5.043472879540142e-07,
                6.475945666051092e-07,
                6.475947210031623e-07,
                2.6995774527718623e-07,
                3.466325797888292e-07,
                5.715005832853093e-07,
                2.6995780963846126e-07,
                3.059022998576899e-07,
                2.6995774527657245e-07
            ],
            [
                1.8553919030858602e-07,
                2.699577774585891e-07,
                3.4663274507713016e-07,
                2.1024339116134898e-07,
                2.1024341622426268e-07,
                2.1024336609843824e-07,
                3.927862002663297e-07,
                2.1024336609843824e-07,
                5.715003789046955e-07,
                2.3823690999290963e-07
            ],
            [
                5.715005151574337e-07,
                3.288748281295496e-06,
                8.315281267861397e-07,
                2.2603234895289998e-06,
                6.962257909722651e-06,
                7.338210680002898e-07,
                1.3709575337078829e-06,
                1.7603434231705793e-06,
                5.715006514105942e-07,
                7.338208930443633e-07
            ],
            [
                8.315278294097538e-07,
                4.450849988811838e-07,
                1.0677029973114952e-06,
                5.043475284468537e-07,
                1.0677026154806063e-06,
                1.3709576971425944e-06,
                5.043472278299047e-07,
                2.699578740032504e-07,
                9.422447062294175e-07,
                1.6373776432509826e-07
            ],
            [
                9.422442569290178e-07,
                9.422442569290178e-07,
                6.475947982002148e-07,
                9.422445938917108e-07,
                1.8553907971758842e-07,
                1.3709575337078829e-06,
                1.9947299592407137e-06,
                6.475948754012522e-07,
                7.889262585886274e-06,
                3.05902226923399e-07
            ],
            [
                1.5534983101549167e-06,
                1.3709575336947905e-06,
                1.0677027427166074e-06,
                2.260323489490968e-06,
                1.7603434231777837e-06,
                4.78509563546605e-06,
                1.7603427936263351e-06,
                1.9947292459347367e-06,
                7.338213304316717e-07,
                9.422442569208767e-07
            ],
            [
                2.5612831267202583e-06,
                1.9947292459347367e-06,
                1.0677033791495609e-06,
                1.7603427936079236e-06,
                1.3709573702822306e-06,
                1.994730434879465e-06,
                3.288748281329893e-06,
                1.7603430034655858e-06,
                9.422449308716635e-07,
                3.288748673319648e-06
            ],
            [
                6.023569166654288e-08,
                6.023569166654288e-08,
                4.139935079796334e-08,
                5.315781803390236e-08,
                3.9278634073625165e-07,
                8.764245361752286e-08,
                3.466327037553825e-07,
                1.444980209564556e-07,
                6.023577065381482e-08,
                1.4449796928021588e-07
            ],
            [
                3.466325384661554e-07,
                NaN,
                4.450848927650143e-07,
                1.8925157266089433e-05,
                3.0590226339061185e-07,
                4.450852111135988e-07,
                9.422450431989127e-07,
                1.0677029973192638e-06,
                9.422448185478557e-07,
                3.05902336324494e-07
            ],
            [
                5.043476486924565e-07,
                5.715006514167015e-07,
                8.315281267861397e-07,
                6.475950298011458e-07,
                1.5534984953510149e-06,
                2.699576809143613e-07,
                8.315284241650899e-07,
                2.6995768091310296e-07,
                3.466325797896173e-07,
                5.715002426486762e-07
            ],
            [
                1.4449795205472734e-07,
                6.47595107001401e-07,
                3.466325384661554e-07,
                1.4449796928021588e-07,
                1.4449798650551755e-07,
                4.785095065232451e-06,
                1.8553919030858602e-07,
                3.466326211113502e-07,
                3.0590237279085045e-07,
                7.734423152941018e-08
            ],
            [
                2.260324836787226e-06,
                3.059022998576899e-07,
                3.05902190458764e-07,
                3.927862470899887e-07,
                1.7603434231833873e-06,
                5.043472879525233e-07,
                3.9278638755992735e-07,
                2.6995771309523475e-07,
                5.422217030288788e-06,
                6.144173869558639e-06
            ],
            [
                5.043472278322555e-07,
                4.222833444590791e-06,
                2.6995774527718623e-07,
                1.209865827752005e-06,
                1.209865827752005e-06,
                7.338208930460318e-07,
                9.422445939054222e-07,
                7.338211554801876e-07,
                5.04347468323289e-07,
                2.5612819054133693e-06
            ],
            [
                4.691162124067829e-08,
                2.3823702359290413e-07,
                2.1024326584639497e-07,
                1.209866260432471e-06,
                2.1024326584582131e-07,
                1.994730672675753e-06,
                2.1024331597262577e-07,
                9.931185038635267e-08,
                5.715005151606823e-07,
                2.382370235933104e-07
            ],
            [
                1.4449807263287805e-07,
                2.102434162245973e-07,
                1.1253509497883659e-07,
                3.0590237279032884e-07,
                5.715007195431641e-07,
                7.734415776836702e-08,
                5.3157837044597743e-08,
                1.1253506814842375e-07,
                7.734416698849138e-08,
                1.1253524254615121e-07
            ],
            [
                2.1024334103505245e-07,
                2.3823688159291947e-07,
                3.927862002663297e-07,
                8.315277302857965e-07,
                6.475949526020042e-07,
                2.699578740032504e-07,
                3.05902117523595e-07,
                2.6995784182073116e-07,
                5.715006514176113e-07,
                5.04347528446051e-07
            ],
            [
                1.2751908849167202e-07,
                2.3823690999323465e-07,
                2.69957906184239e-07,
                1.4449798650417048e-07,
                6.825598842035714e-08,
                1.275190124842887e-07,
                1.1253520229983549e-07,
                1.6373766672888118e-07,
                3.4663249714612693e-07,
                5.043475284430694e-07
            ],
            [
                1.1253520230052635e-07,
                8.764242227418718e-08,
                7.73441946488886e-08,
                2.1024334103505245e-07,
                1.855391239544352e-07,
                1.1253520230052635e-07,
                1.4449798650551755e-07,
                1.8553919030776337e-07,
                9.931193325852072e-08,
                1.275190276859705e-07
            ],
            [
                3.059022998581767e-07,
                2.699578096403948e-07,
                1.6373772528704005e-07,
                1.2751901248454963e-07,
                0.9999983463096267,
                5.04347287955046e-07,
                1.3709575337159875e-06,
                2.699576809143613e-07,
                2.699578740032504e-07,
                1.4449807263312446e-07
            ],
            [
                8.939693107288474e-06,
                6.475946438055299e-07,
                1.0677032518785256e-06,
                2.3823693839290317e-07,
                2.3823702359290413e-07,
                6.475948754028718e-07,
                3.927862470899887e-07,
                5.715007195447234e-07,
                6.475947210031623e-07,
                6.475948754028718e-07
            ],
            [
                3.2887506335906595e-06,
                1.7603427936263351e-06,
                4.785094494672519e-06,
                1.2098652508287273e-06,
                1.3709573702647743e-06,
                8.315281267834927e-07,
                1.0677033791495609e-06,
                1.9947304348595095e-06,
                1.7603436330091044e-06,
                5.422217677028889e-06
            ],
            [
                2.7535700948722127e-05,
                6.475947981975644e-07,
                3.4663249714325014e-07,
                1.0677029973158649e-06,
                6.475947209918244e-07,
                5.71500515151976e-07,
                1.7603430034743913e-06,
                5.715003788993679e-07,
                3.9278605979208185e-07,
                3.46632497145457e-07
            ],
            [
                5.422221555340727e-06,
                5.422218969818919e-06,
                1.0129993395217047e-05,
                1.2098662604291696e-06,
                7.889262585814522e-06,
                1.4738981972323349e-05,
                6.962257909785973e-06,
                7.889261645427538e-06,
                2.561281600076256e-06,
                2.2603242978871282e-06
            ],
            [
                3.726638839878908e-06,
                3.927863407379485e-07,
                1.637377057680051e-07,
                0.005220125093864345,
                1.760343213335281e-06,
                2.1024339116168358e-07,
                1.7603436330259153e-06,
                2.382369667929001e-07,
                1.2098658277489788e-06,
                2.10243290909724e-07
            ],
            [
                3.4663249714451116e-07,
                1.0677027427600627e-06,
                3.726638395634011e-06,
                5.043472879525233e-07,
                1.2098658277264215e-06,
                3.927862002641863e-07,
                2.2603234895289998e-06,
                2.1024334103505245e-07,
                9.422450431954847e-07,
                9.422450431989127e-07
            ],
            [
                5.043474683204221e-07,
                3.466327863961242e-07,
                5.715006514167015e-07,
                4.785096206076165e-06,
                5.715007195410849e-07,
                1.5534975693933505e-06,
                4.4508510499849186e-07,
                3.0590215399183813e-07,
                1.3709575337016483e-06,
                8.315283250371857e-07
            ],
            [
                4.4508526417298334e-07,
                2.6995784182183607e-07,
                2.6995784182183607e-07,
                9.422444815792981e-07,
                3.059022998576899e-07,
                6.962254589978262e-06,
                5.043476486915964e-07,
                5.422218969895357e-06,
                7.338211554801876e-07,
                1.067703124601679e-06
            ],
            [
                9.422449308716635e-07,
                1.370957860567974e-06,
                7.338208055664991e-07,
                5.715003789017068e-07,
                6.475951069961737e-07,
                2.3823702359138736e-07,
                8.31528424162821e-07,
                3.927862939126708e-07,
                8.315277302788957e-07,
                9.4224425692559e-07
            ],
            [
                1.0677027427569065e-06,
                7.889261645427538e-06,
                1.209865827740176e-06,
                7.338209805240734e-07,
                1.7603436330179102e-06,
                7.338210680021253e-07,
                1.0677026154619133e-06,
                3.288748673376478e-06,
                3.4663249714451116e-07,
                1.5534975693979422e-06
            ],
            [
                3.466325797896173e-07,
                1.444979692800516e-07,
                6.825609419848033e-08,
                1.3709573702722555e-06,
                3.7266406168403854e-06,
                1.067703124601679e-06,
                1.8553914607267268e-07,
                1.2751899728311609e-07,
                2.5612828213690224e-06,
                1.8553905760062447e-07
            ],
            [
                8.764251630441717e-08,
                2.6995771309523475e-07,
                4.450852111155216e-07,
                9.422448185534261e-07,
                1.8553910183674878e-07,
                1.855390354818069e-07,
                4.450850519403407e-07,
                3.9278629391427843e-07,
                5.043475885696228e-07,
                2.102434162245973e-07
            ],
            [
                5.715005832872586e-07,
                1.5534979397740895e-06,
                1.0677027427600627e-06,
                1.067703379154416e-06,
                3.9278605979208185e-07,
                1.067703379154416e-06,
                1.3709576971425944e-06,
                1.2098659719757836e-06,
                4.4508510499737865e-07,
                1.7603425837855082e-06
            ],
            [
                1.6373772528704005e-07,
                1.760342793638743e-06,
                2.3823693839325527e-07,
                6.475946438055299e-07,
                1.8553914607267268e-07,
                8.764242227418718e-08,
                2.10243290909724e-07,
                1.8553905760062447e-07,
                5.715006514176113e-07,
                2.3823682479292225e-07
            ],
            [
                2.69957906184239e-07,
                8.764245361752286e-08,
                2.699577774585891e-07,
                5.043472278322555e-07,
                2.6995774527718623e-07,
                3.059022998576899e-07,
                1.637377057680051e-07,
                1.1253513522447425e-07,
                2.1024341622426268e-07,
                2.3823690999290963e-07
            ],
            [
                2.3823685319244518e-07,
                1.8553916819032217e-07,
                5.715003789033962e-07,
                1.5534979397677313e-06,
                2.3823690999160957e-07,
                1.8553907971855875e-07,
                2.6995784182183607e-07,
                3.927863875616689e-07,
                2.5612812947380135e-06,
                8.939695238439078e-06
            ],
            [
                1.1253525596134564e-07,
                1.6373774480535133e-07,
                5.71500242637956e-07,
                9.422450431860582e-07,
                1.6373762769138607e-07,
                1.444980209564556e-07,
                3.4663249714451116e-07,
                3.0590215399183813e-07,
                2.6995768091310296e-07,
                1.9947294836483373e-06
            ],
            [
                6.475950298021765e-07,
                2.1024334103581732e-07,
                8.315277302857965e-07,
                3.4663266243308805e-07,
                1.8553919030858602e-07,
                9.422448185534261e-07,
                4.450850519403407e-07,
                1.4449798650551755e-07,
                3.927860597945825e-07,
                7.338209805240734e-07
            ],
            [
                3.466326624336003e-07,
                9.422450432030903e-07,
                3.05902263391829e-07,
                1.994729008145876e-06,
                1.2751899728311609e-07,
                1.0677033791612137e-06,
                1.5534975693979422e-06,
                9.422447062294175e-07,
                5.043476486924565e-07,
                1.1253512180925583e-07
            ],
            [
                2.699577774585891e-07,
                3.9278615344178325e-07,
                2.1024331597262577e-07,
                1.553498124964492e-06,
                3.466326211113502e-07,
                3.059022269250683e-07,
                2.699576809143613e-07,
                2.382369951932796e-07,
                3.9278610661902853e-07,
                3.4663266243308805e-07
            ],
            [
                5.04347287955046e-07,
                2.6995771309523475e-07,
                7.338208055664991e-07,
                9.422444815814404e-07,
                3.726639284144195e-06,
                3.05902336324494e-07,
                4.4508494582405734e-07,
                2.9023112932177327e-06,
                2.382370235933104e-07,
                9.931193325852072e-08
            ],
            [
                1.637377057673536e-07,
                6.475948753991907e-07,
                2.3823690999290963e-07,
                1.3709575337159875e-06,
                3.05902190458764e-07,
                5.715005151606823e-07,
                2.3823702359290413e-07,
                1.4449798650551755e-07,
                1.9947299593078385e-06,
                1.855391239547094e-07
            ],
            [
                7.338208930421943e-07,
                7.889266347715168e-06,
                6.475948754028718e-07,
                7.338210680002898e-07,
                8.315283250394546e-07,
                5.715003789046955e-07,
                7.338213304316717e-07,
                1.7603427936263351e-06,
                5.715003789046955e-07,
                1.4449805540763184e-07
            ],
            [
                2.1024336609843824e-07,
                1.6373770576776313e-07,
                5.043472879540142e-07,
                2.3823699519143784e-07,
                2.699578096393206e-07,
                2.6995790618252024e-07,
                2.3823699519290042e-07,
                2.382368247924618e-07,
                2.1024336609724313e-07,
                4.450851049959619e-07
            ],
            [
                1.5534979397740895e-06,
                3.059022998576899e-07,
                1.067702870039777e-06,
                1.0677029973219343e-06,
                5.043474082005342e-07,
                4.4508494582314646e-07,
                2.1024336609874897e-07,
                1.7603430034867993e-06,
                7.33821330437595e-07,
                1.2098658277489788e-06
            ],
            [
                3.059021175261338e-07,
                1.3709576971463352e-06,
                1.2098659719788098e-06,
                1.370957860576702e-06,
                3.059022269250683e-07,
                NaN,
                5.715006514176113e-07,
                1.760343633031919e-06,
                4.4508510499849186e-07,
                1.994729483729522e-06
            ],
            [
                1.637377448057981e-07,
                1.6373766672973748e-07,
                1.994730197071414e-06,
                2.69957906184239e-07,
                2.699578740032504e-07,
                1.0677032518748838e-06,
                6.475945666051092e-07,
                2.5612822107167428e-06,
                1.4449807263312446e-07,
                1.994730434879465e-06
            ],
            [
                2.1024341622368903e-07,
                1.2098662604291696e-06,
                5.043474683204221e-07,
                3.4663262110945863e-07,
                2.6995790618469934e-07,
                3.4663266243308805e-07,
                4.450848927658745e-07,
                5.043476486915964e-07,
                3.927863875616689e-07,
                3.0590237279085045e-07
            ],
            [
                5.043472879504592e-07,
                5.043474081993875e-07,
                1.8553919030776337e-07,
                4.4508510499849186e-07,
                2.6995771309523475e-07,
                4.450852641717689e-07,
                5.043475284430694e-07,
                2.90231094723893e-06,
                1.3709576971379186e-06,
                3.9278605979208185e-07
            ],
            [
                1.5534977545886537e-06,
                3.72663883989755e-06,
                1.9947301970972664e-06,
                1.8553905760062447e-07,
                8.315280276626197e-07,
                2.1024339116168358e-07,
                1.1253508156363576e-07,
                2.902313369111213e-06,
                9.422445939054222e-07,
                1.5534971990169383e-06
            ],
            [
                7.338211554783522e-07,
                7.3382080556433e-07,
                1.067703124601679e-06,
                3.466326211105621e-07,
                1.760343003481596e-06,
                2.5612825160562587e-06,
                5.71500515159253e-07,
                1.9947290081286418e-06,
                8.315280276607289e-07,
                1.5534983101602148e-06
            ],
            [
                1.444980381819277e-07,
                7.338212429582604e-07,
                1.8553905760062447e-07,
                4.4508510499849186e-07,
                1.4449798650551755e-07,
                1.637377057680051e-07,
                1.1253524254615121e-07,
                2.6995784182183607e-07,
                0.00017952792355046838,
                1.6373772528704005e-07
            ],
            [
                4.450850519403407e-07,
                5.04347468323289e-07,
                9.422445939032799e-07,
                5.71500515159253e-07,
                5.715003107715166e-07,
                5.715003789033962e-07,
                2.382368815916736e-07,
                7.338208055664991e-07,
                2.382369667929001e-07,
                3.927862939126708e-07
            ],
            [
                4.006370174344354e-05,
                4.450851049959619e-07,
                1.4738976701411704e-05,
                8.315281267861397e-07,
                9.422449308748773e-07,
                5.043472278299047e-07,
                1.2098653950551882e-06,
                4.785094494750855e-06,
                2.9023112932045342e-06,
                5.715003107738556e-07
            ],
            [
                2.1024334103553052e-07,
                3.466327450765785e-07,
                3.0590215399183813e-07,
                9.422444815792981e-07,
                8.315283250394546e-07,
                3.466325384661554e-07,
                5.715002426475718e-07,
                1.370957860576702e-06,
                5.715006514176113e-07,
                8.315283250371857e-07
            ],
            [
                6.475945666051092e-07,
                3.0590215399183813e-07,
                1.067703124601679e-06,
                7.338208055664991e-07,
                9.422445939032799e-07,
                3.466326211113502e-07,
                6.475948754012522e-07,
                1.5534979397740895e-06,
                1.9947292459347367e-06,
                1.9947301970972664e-06
            ],
            [
                7.338212429594283e-07,
                6.475950297993789e-07,
                2.10243290909724e-07,
                1.1253525596174225e-07,
                1.6373770576776313e-07,
                2.3823702359290413e-07,
                2.1024331597262577e-07,
                3.05902336324494e-07,
                5.043475885696228e-07,
                9.931198061405701e-08
            ],
            [
                3.059021539909339e-07,
                1.6373762769138607e-07,
                3.0590226339061185e-07,
                6.475947210046347e-07,
                2.5612834320563895e-06,
                1.1253509497835043e-07,
                5.043472278280699e-07,
                5.715007195431641e-07,
                3.466326624322211e-07,
                3.9278605979208185e-07
            ],
            [
                1.2098661161789477e-06,
                1.760343633031919e-06,
                7.338210680002898e-07,
                1.7603425837791042e-06,
                1.3709570434122812e-06,
                9.422449308748773e-07,
                8.315282259117513e-07,
                3.466327037553825e-07,
                9.422449308748773e-07,
                8.315283250371857e-07
            ],
            [
                2.902312677150514e-06,
                9.422442569315887e-07,
                5.715005151606823e-07,
                7.338210680021253e-07,
                1.9947304348862686e-06,
                4.222834954778007e-06,
                1.0677033791612137e-06,
                1.3709572068522336e-06,
                2.2603242978871282e-06,
                5.715003789046955e-07
            ],
            [
                1.1253518888531272e-07,
                1.2751902768568054e-07,
                9.931187406410953e-08,
                1.8553919030858602e-07,
                1.275190884913241e-07,
                7.734421308914719e-08,
                2.1024326584639497e-07,
                9.931195693628605e-08,
                7.734418542875216e-08,
                1.1253518888531272e-07
            ],
            [
                1.5534975693933505e-06,
                1.3709570434178922e-06,
                4.785093924362895e-06,
                8.315282259138311e-07,
                1.4738981972564636e-05,
                9.422450432014836e-07,
                1.760343213335281e-06,
                1.2098656835224664e-06,
                6.9622587397397306e-06,
                2.2603242978871282e-06
            ],
            [
                3.0590215399183813e-07,
                1.2098656835224664e-06,
                1.9947299592933255e-06,
                9.42244256915735e-07,
                2.2603240284371276e-06,
                1.5534981249697903e-06,
                7.338210680021253e-07,
                4.4508505193932864e-07,
                9.422442569315887e-07,
                1.2098661161982042e-06
            ]
        ]
    },
    {
        "q_id": "9206_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.006371129615879e-05,
                5.422217030747413e-06,
                2.561281600086738e-06,
                5.043472879540142e-07,
                2.902312677150514e-06,
                1.012999218776902e-05,
                3.726637951387472e-06,
                5.422217677152175e-06,
                3.927863875616689e-07,
                2.1444953527944967e-05
            ],
            [
                4.450850519403407e-07,
                1.2098652508424818e-06,
                1.3709576971463352e-06,
                3.059021175261338e-07,
                4.2228339479858295e-06,
                1.5534971990169383e-06,
                1.637377057680051e-07,
                2.699578740032504e-07,
                4.450848927637999e-07,
                4.450848927658745e-07
            ],
            [
                6.475950298011458e-07,
                1.760343213335281e-06,
                2.6995790618469934e-07,
                2.3823702359290413e-07,
                0.9999892166852283,
                3.2887506336235617e-06,
                1.855391239544352e-07,
                2.382368531929327e-07,
                0.9999925887192559,
                3.9278610661902853e-07
            ],
            [
                0.9999861539938241,
                4.0063677865600476e-05,
                7.889259764445822e-06,
                0.99999160192397,
                0.9999921107355472,
                0.0001088969482847688,
                3.927862939126708e-07,
                1.5534983101549167e-06,
                0.9999925887227953,
                0.9999925887192515
            ],
            [
                1.0677032518814388e-06,
                8.764245361752286e-08,
                2.382370235933104e-07,
                5.4222176771176554e-06,
                3.46632497145457e-07,
                1.8553914607267268e-07,
                1.4449795205457127e-07,
                1.0677033791612137e-06,
                1.275190580890061e-07,
                3.9278605979534166e-07
            ],
            [
                2.5612831267202583e-06,
                7.338212429582604e-07,
                8.315280276626197e-07,
                3.059023363221292e-07,
                2.102434412875379e-07,
                6.475947981904966e-07,
                1.067703379154416e-06,
                5.043476486915964e-07,
                6.475946438022905e-07,
                6.475951069932288e-07
            ],
            [
                0.9999852610180512,
                0.9999930377404472,
                0.9999885212346517,
                0.9999987901344625,
                0.9998204720608219,
                0.9999921107365065,
                0.9999925887201496,
                0.9999892166890969,
                0.99999385582615,
                0.9999938558232117
            ],
            [
                NaN,
                6.144176799283803e-06,
                5.144220140002614e-05,
                3.120191509592808e-05,
                1.1478770862589836e-05,
                1.3007123813193233e-05,
                3.726641061109272e-06,
                6.144173137126169e-06,
                7.889259764517575e-06,
                1.1478770862735993e-05
            ],
            [
                0.9999960330131434,
                0.9999972735294069,
                0.9999910603047808,
                0.9999877809211096,
                0.9999970976883635,
                0.999996711250153,
                0.9999945777823321,
                0.9999810748563384,
                0.9999964991460069,
                0.9999852610215811
            ],
            [
                1.4738989000181669e-05,
                0.9999930377429326,
                0.9999898700066161,
                0.999989216685237,
                0.9999892166865287,
                0.9999957771680709,
                5.043472278322555e-07,
                0.9999942280772237,
                0.9999938558232185,
                0.9999546021158509
            ],
            [
                0.9999687980887261,
                0.9999151889499515,
                0.9999957771660555,
                0.9999916019299796,
                0.9999798543044017,
                0.9999877809181873,
                0.999994228080665,
                1.994730197090463e-06,
                1.0677029973192638e-06,
                0.0010322308308802928
            ],
            [
                1.209865827740176e-06,
                0.00026119027866556703,
                3.726641061027928e-06,
                1.370957860567974e-06,
                1.7603438428740716e-06,
                1.5534979397740895e-06,
                1.3007125363719486e-05,
                0.001700722111595075,
                2.2603242978665707e-06,
                5.715003788993679e-07
            ],
            [
                4.4508494582405734e-07,
                1.8553916819032217e-07,
                2.382369951932796e-07,
                3.466326624336003e-07,
                1.2751901248454963e-07,
                1.370957860576702e-06,
                5.715005832886879e-07,
                2.3823699519290042e-07,
                2.699576809143613e-07,
                8.315284241650899e-07
            ],
            [
                1.3709567165579959e-06,
                5.715003107767143e-07,
                3.05902336324494e-07,
                3.927863875616689e-07,
                3.927863875616689e-07,
                3.2887482813149375e-06,
                5.04347287955046e-07,
                2.699578740032504e-07,
                2.3823690999290963e-07,
                1.6373768624837685e-07
            ],
            [
                1.0677024882029858e-06,
                3.927862470905692e-07,
                3.7266397283908927e-06,
                6.47595107001401e-07,
                0.9999832985781775,
                4.222834451403972e-06,
                6.475949526020042e-07,
                0.9998415638035205,
                0.999993037741267,
                1.7603438428740716e-06
            ],
            [
                NaN,
                7.889261645427538e-06,
                8.939700567094277e-06,
                3.72663883989755e-06,
                NaN,
                8.315284241665078e-07,
                NaN,
                NaN,
                1.7603425837903113e-06,
                5.422221555414699e-06
            ],
            [
                0.9999921107355437,
                0.9999930377404366,
                0.9999930377404355,
                0.9999938558261402,
                6.605213682591808e-05,
                0.9999938558268698,
                0.9999960330155072,
                4.0063682641226247e-05,
                2.4300249425247723e-05,
                0.9999945777803906
            ],
            [
                3.7266401726359486e-06,
                0.999970688447856,
                3.466327037548308e-07,
                4.4508510499849186e-07,
                0.9999925887201513,
                1.4449803818215767e-07,
                1.444980209564556e-07,
                0.9999646437580925,
                0.9999972735300586,
                5.043472879540142e-07
            ],
            [
                5.043472278322555e-07,
                1.8553907971855875e-07,
                1.6373768624837685e-07,
                3.059021175261338e-07,
                3.927862939126708e-07,
                1.6373774480535133e-07,
                1.125352291309328e-07,
                5.315784971839039e-08,
                3.4663266243308805e-07,
                1.6373762769138607e-07
            ],
            [
                1.994730672675753e-06,
                1.5534979397790343e-06,
                7.338208055664991e-07,
                1.6701427818034747e-05,
                3.0590215399183813e-07,
                5.715005832886879e-07,
                NaN,
                5.043472879540142e-07,
                3.927862470899887e-07,
                3.288748281329893e-06
            ],
            [
                0.9999485577867159,
                0.9999822214460907,
                0.9999869928700238,
                0.9999724643156515,
                0.999972464308996,
                0.9999885212319031,
                0.9999869928731182,
                0.9999904837517314,
                0.9999921107336678,
                0.9999925887219091
            ],
            [
                2.102434162245973e-07,
                3.927862002654366e-07,
                1.5534973842076057e-06,
                2.1024334103505245e-07,
                1.3709567165617364e-06,
                1.4449800373065699e-07,
                2.699577774585891e-07,
                9.422447062294175e-07,
                2.260323758987159e-06,
                6.475945666051092e-07
            ],
            [
                5.043476486915964e-07,
                3.059022269250683e-07,
                2.6995784182140636e-07,
                2.3823699519290042e-07,
                2.382368531929327e-07,
                2.3823699519290042e-07,
                8.315282259138311e-07,
                1.3709575337078829e-06,
                1.444980209564556e-07,
                1.5534983101602148e-06
            ],
            [
                0.999981074856302,
                3.0590237279032884e-07,
                0.9999892166865099,
                1.209865539295696e-06,
                0.9999885212264212,
                0.9999832985702197,
                7.338212429582604e-07,
                1.3709572068522336e-06,
                6.475945666051092e-07,
                1.5534981249697903e-06
            ],
            [
                4.4508515805735777e-07,
                9.931190958076104e-08,
                2.6995790618469934e-07,
                7.338208930460318e-07,
                2.1024334103581732e-07,
                5.043472278322555e-07,
                4.450848927658745e-07,
                9.422443692574719e-07,
                5.043476486924565e-07,
                2.699578096403948e-07
            ],
            [
                0.9999646437578412,
                1.4738978458382043e-05,
                0.9999810748450335,
                0.9999957771660568,
                0.9999898700102499,
                1.3709568799879344e-06,
                0.999986992876213,
                0.9999810748563167,
                0.9999810748540663,
                0.999970688465084
            ],
            [
                1.6373768624837685e-07,
                3.059021175261338e-07,
                3.059022998576899e-07,
                3.05902263391829e-07,
                2.382370235933104e-07,
                1.6373764721072816e-07,
                1.6373776432509826e-07,
                3.059021175261338e-07,
                6.023577783447482e-08,
                8.764245361752286e-08
            ],
            [
                4.450848927658745e-07,
                8.7642516304188e-08,
                7.73442776300517e-08,
                1.27519088491875e-07,
                1.4449805540763184e-07,
                2.69957906184239e-07,
                1.2751899728311609e-07,
                5.3157837044597743e-08,
                6.825601283086733e-08,
                8.764244316973974e-08
            ],
            [
                0.9999977396762434,
                0.9999916019249726,
                0.9999942280806664,
                0.9998601779126386,
                0.9999832985801901,
                0.9999785550439878,
                0.999989216682655,
                0.9999925887219043,
                0.9999982396561587,
                0.9999957771670643
            ],
            [
                0.9999970976876709,
                0.9999942280806707,
                8.939698435657833e-06,
                0.9999904837460566,
                0.9999930377412766,
                0.9999832985783181,
                0.9999852610128068,
                0.9999904837471909,
                1.7603425837855082e-06,
                5.043472278322555e-07
            ],
            [
                5.715006514151423e-07,
                2.69957906184239e-07,
                5.715004470313855e-07,
                3.9278615344178325e-07,
                3.059023727894942e-07,
                1.6373764720990908e-07,
                4.450851580555361e-07,
                7.338212429537553e-07,
                3.466327863983311e-07,
                1.2098662604291696e-06
            ],
            [
                1.855391681906175e-07,
                5.043475885696228e-07,
                9.931195693628605e-08,
                2.102434162245973e-07,
                2.1024334103581732e-07,
                9.93120161310289e-08,
                9.93120161310289e-08,
                1.1253526937697666e-07,
                1.2098661162056318e-06,
                2.2603251062450327e-06
            ],
            [
                1.067703379154416e-06,
                5.04347468323289e-07,
                2.699577774585891e-07,
                2.5612831266946347e-06,
                1.3007134666431358e-05,
                2.3823693839290317e-07,
                7.338210680021253e-07,
                3.9278634073732336e-07,
                6.475946438055299e-07,
                5.715005832886879e-07
            ],
            [
                3.0590237279032884e-07,
                1.5534979397740895e-06,
                5.043476486915964e-07,
                8.31528424162821e-07,
                5.04347528446051e-07,
                1.2098661162056318e-06,
                5.4222176771176554e-06,
                1.0677026154806063e-06,
                5.043472879540142e-07,
                3.0590237279085045e-07
            ],
            [
                NaN,
                3.288748673376478e-06,
                7.338208930460318e-07,
                3.05902190458764e-07,
                2.5612819054133693e-06,
                1.3709576971463352e-06,
                5.043472278322555e-07,
                3.726639728370556e-06,
                1.0677029973219343e-06,
                5.422218969895357e-06
            ],
            [
                4.450850519403407e-07,
                6.475947210031623e-07,
                2.382369383923073e-07,
                5.043472879525233e-07,
                3.927862002641863e-07,
                4.785095635655362e-06,
                3.46632497145457e-07,
                2.382369951932796e-07,
                2.1024331597262577e-07,
                6.475948754012522e-07
            ],
            [
                3.059022998576899e-07,
                1.2751907329024393e-07,
                8.764249540862797e-08,
                9.931189774187203e-08,
                1.8553910183607374e-07,
                3.0590215399183813e-07,
                3.9278615344178325e-07,
                5.043475885674441e-07,
                8.7642516304188e-08,
                3.059022269250683e-07
            ],
            [
                1.275190580890061e-07,
                1.1253526937697666e-07,
                1.8553919030858602e-07,
                7.734416698849138e-08,
                1.275190732904469e-07,
                7.734414854823498e-08,
                6.825602910433871e-08,
                9.931199245322124e-08,
                1.6373764721072816e-07,
                8.76424013786396e-08
            ],
            [
                7.33821330437595e-07,
                1.4449805540740185e-07,
                1.2751899728286965e-07,
                5.71500719545698e-07,
                6.825598028364134e-08,
                9.931187406368048e-08,
                1.637377643243723e-07,
                2.699578096393206e-07,
                9.931199245292204e-08,
                2.3823685319244518e-07
            ],
            [
                6.962254589781966e-06,
                9.422448185510695e-07,
                9.422450431989127e-07,
                1.5534984953453635e-06,
                1.5534979397790343e-06,
                2.902313023101807e-06,
                2.2603234895289998e-06,
                3.288748281295496e-06,
                5.043472278280699e-07,
                1.994730434879465e-06
            ],
            [
                1.994729483729522e-06,
                1.7603434231833873e-06,
                5.043472278322555e-07,
                5.71500515161527e-07,
                2.1444943302181958e-05,
                1.8553910183674878e-07,
                3.4663274507713016e-07,
                9.422447062294175e-07,
                4.4508494582405734e-07,
                4.785095065232451e-06
            ],
            [
                9.422444815814404e-07,
                3.9278634073732336e-07,
                5.043472879540142e-07,
                3.9278634073732336e-07,
                8.315279285351409e-07,
                1.2098655392871682e-06,
                5.715002426486762e-07,
                5.715003107767143e-07,
                1.2098661162056318e-06,
                7.338208930391909e-07
            ],
            [
                0.9998204720381968,
                0.9999975938982364,
                0.9999967112501542,
                0.9999957771655582,
                0.9999960330136201,
                0.9999756997477216,
                0.9999964991447544,
                0.9999925887219023,
                0.9999974387174867,
                2.9023112932177327e-06
            ],
            [
                8.93969950132721e-06,
                2.902312331125353e-06,
                3.9278615344178325e-07,
                3.4663253846718004e-07,
                8.315280276546789e-07,
                2.144494585801764e-05,
                8.315284241597959e-07,
                7.484620050755993e-05,
                2.6995784182140636e-07,
                3.927862939126708e-07
            ],
            [
                1.0677032518785256e-06,
                3.120191509592808e-05,
                1.7603434231777837e-06,
                1.7603425837855082e-06,
                5.04347528446051e-07,
                3.726639728370556e-06,
                1.9947297215043796e-06,
                9.422445939032799e-07,
                5.715005151606823e-07,
                4.450852111148132e-07
            ],
            [
                1.5534973841705173e-06,
                NaN,
                1.0677028700363782e-06,
                3.927863875616689e-07,
                1.0677032518785256e-06,
                7.338209805224048e-07,
                8.315279285351409e-07,
                1.0677027427525368e-06,
                7.338211554783522e-07,
                2.6995784182183607e-07
            ],
            [
                2.699577774585891e-07,
                5.715005832827105e-07,
                1.5534981249574276e-06,
                5.043474081993875e-07,
                8.315278294097538e-07,
                4.450849988811838e-07,
                6.475951069985296e-07,
                1.0677024881980089e-06,
                5.715003107755449e-07,
                4.450848927650143e-07
            ],
            [
                1.637377448057981e-07,
                2.102434412875379e-07,
                2.69957906184239e-07,
                2.9023116392097746e-06,
                1.6373768624837685e-07,
                1.6373768624837685e-07,
                1.444980209564556e-07,
                2.699577774585891e-07,
                2.1024326584639497e-07,
                2.6995771309523475e-07
            ],
            [
                0.0,
                1.4449805540700758e-07,
                NaN,
                4.222832941193893e-06,
                2.9023119851781017e-06,
                1.2098653950656417e-06,
                7.338212429582604e-07,
                2.102434162220159e-07,
                1.7603427936335396e-06,
                4.450848927637999e-07
            ],
            [
                1.5534981249697903e-06,
                5.04347287955046e-07,
                2.5612828213934817e-06,
                4.222834451382849e-06,
                8.939700567004841e-06,
                3.7266406168827523e-06,
                4.2228324377740105e-06,
                1.0129988564974359e-05,
                1.3709570434178922e-06,
                1.7603425837855082e-06
            ],
            [
                1.30071315662049e-05,
                3.4663278639892215e-07,
                1.1253508156363576e-07,
                2.6995790618469934e-07,
                2.382369951932796e-07,
                7.889262585886274e-06,
                2.10243290909724e-07,
                2.561282210740037e-06,
                1.6373774480605869e-07,
                1.275190428875671e-07
            ],
            [
                8.315280276626197e-07,
                3.927862002654366e-07,
                9.422450431989127e-07,
                2.3823699519290042e-07,
                4.4508510499849186e-07,
                5.715005832886879e-07,
                9.422443692555439e-07,
                3.466327450765785e-07,
                1.2098653950692178e-06,
                6.962254589914941e-06
            ],
            [
                9.422445939032799e-07,
                3.059022998576899e-07,
                2.260324028427877e-06,
                0.999992110734605,
                0.9999916019279796,
                7.889265407177056e-06,
                7.889266347715168e-06,
                0.9999822214439745,
                6.475945666051092e-07,
                8.481101106463892e-05
            ],
            [
                0.9999925887166051,
                0.9999885212318956,
                0.9999921107336776,
                0.9999904837517486,
                0.999992588719258,
                0.9999942280806658,
                0.9999952149032294,
                0.9999785550542664,
                0.9999892166852354,
                0.9999573525321421
            ],
            [
                8.315280276626197e-07,
                1.994729008145876e-06,
                3.927862470899887e-07,
                4.222832941193893e-06,
                1.3709568799919866e-06,
                2.561281600076256e-06,
                3.059022269250683e-07,
                1.2751908849167202e-07,
                1.2098659719757836e-06,
                7.734419464850171e-08
            ],
            [
                1.2098662604291696e-06,
                2.260325375677174e-06,
                1.5534975693933505e-06,
                1.553497754577351e-06,
                5.043472879540142e-07,
                7.338212429582604e-07,
                6.475949526003845e-07,
                1.0677024882009222e-06,
                3.2887506336086064e-06,
                1.8925157264471508e-05
            ],
            [
                1.6373770576776313e-07,
                1.7603430034867993e-06,
                NaN,
                1.0677024882009222e-06,
                3.726637951387472e-06,
                1.209865827752005e-06,
                1.5534975693979422e-06,
                1.0129993395336818e-05,
                3.05902190458764e-07,
                1.8553905760062447e-07
            ],
            [
                6.475949525981759e-07,
                3.927862470899887e-07,
                4.450849988798682e-07,
                3.059021175247079e-07,
                9.422448185510695e-07,
                2.2603248366762157e-06,
                4.785095635655362e-06,
                3.927862002641863e-07,
                1.994729008145876e-06,
                7.338208930391909e-07
            ],
            [
                1.0677027427600627e-06,
                5.422221555380179e-06,
                3.927860597945825e-07,
                5.422221555380179e-06,
                6.1441746020359e-06,
                2.144495608424996e-05,
                5.715007195447234e-07,
                7.338213304363436e-07,
                5.715003107767143e-07,
                1.3709568799919866e-06
            ],
            [
                3.05902336324494e-07,
                2.102434162245973e-07,
                3.059021175261338e-07,
                1.855391239544352e-07,
                4.4508494582405734e-07,
                1.855391239547094e-07,
                1.4449798650551755e-07,
                9.931200429212718e-08,
                1.444979692800516e-07,
                2.6995790618469934e-07
            ],
            [
                1.5534981249697903e-06,
                2.90231094723893e-06,
                9.422448185510695e-07,
                2.2603234895289998e-06,
                5.422219616184461e-06,
                1.1478769494542698e-05,
                7.889264466639056e-06,
                8.93969843573914e-06,
                9.422447062294175e-07,
                1.4738981972564636e-05
            ],
            [
                4.450849988811838e-07,
                4.450849458179853e-07,
                1.8553914607267268e-07,
                1.067703124601679e-06,
                1.0677029973192638e-06,
                2.3823702359290413e-07,
                3.9278615344178325e-07,
                3.9278615344178325e-07,
                9.422450431989127e-07,
                5.043476486915964e-07
            ],
            [
                1.0129988564716393e-05,
                5.422218969818919e-06,
                2.561281905390075e-06,
                1.760344052714248e-06,
                2.2603242978665707e-06,
                6.475947210046347e-07,
                1.012999097997104e-05,
                2.5612831267202583e-06,
                1.3709575337078829e-06,
                1.1478764021029928e-05
            ],
            [
                7.734421308914719e-08,
                5.715002426486762e-07,
                2.9023119851899796e-06,
                1.994730672668496e-06,
                0.9999945777797397,
                6.47595107001401e-07,
                3.4663262111182307e-07,
                0.9999724643155167,
                1.2098662604291696e-06,
                4.222831934379152e-06
            ],
            [
                1.2098659719788098e-06,
                6.475949526020042e-07,
                0.9998415638035205,
                0.9999339478321592,
                0.9998415637665546,
                1.370957860576702e-06,
                0.9999687980849824,
                0.9999687980849583,
                0.9999798543164069,
                0.9999771720055962
            ],
            [
                4.4508494582405734e-07,
                1.209865827752005e-06,
                4.4508494582405734e-07,
                5.043472879504592e-07,
                1.370957860576702e-06,
                NaN,
                2.902312331170226e-06,
                1.0677029973219343e-06,
                1.209866260432471e-06,
                1.9947301970972664e-06
            ],
            [
                0.9999938558268688,
                0.9999869928700065,
                0.9999861539905149,
                NaN,
                0.9999892166865171,
                0.9999955048194987,
                0.9999885212332714,
                0.9999852610127886,
                0.9999869928715687,
                0.9999942280813533
            ],
            [
                3.05902190458764e-07,
                1.760343003481596e-06,
                3.05902190458764e-07,
                1.5534971990169383e-06,
                1.7603440527286572e-06,
                3.05902190458764e-07,
                3.466327863983311e-07,
                2.382369951932796e-07,
                4.4508494582405734e-07,
                2.2603251062450327e-06
            ],
            [
                2.5612819054133693e-06,
                1.5534977545886537e-06,
                8.764247451307293e-08,
                6.962256249885085e-06,
                3.9278634073732336e-07,
                2.902313369111213e-06,
                4.450852111135988e-07,
                3.466327863983311e-07,
                3.4663249714612693e-07,
                1.5534983101602148e-06
            ],
            [
                2.561281905390075e-06,
                1.2098655392871682e-06,
                8.315281267834927e-07,
                2.9023133690821773e-06,
                1.2098661161927025e-06,
                1.3709573702722555e-06,
                9.422444815628016e-07,
                1.6701419854156377e-05,
                6.962257909722651e-06,
                5.043472278280699e-07
            ],
            [
                1.7603432133136672e-06,
                1.0677024881980089e-06,
                9.422448185510695e-07,
                1.2098655392871682e-06,
                3.7266406168624155e-06,
                2.5612812947380135e-06,
                3.2887498494551953e-06,
                2.1444953526969788e-05,
                2.5612828213818346e-06,
                8.315279285351409e-07
            ],
            [
                3.927863875616689e-07,
                2.1024334103581732e-07,
                7.338210680021253e-07,
                9.422447062294175e-07,
                1.5534975693979422e-06,
                6.47595107001401e-07,
                1.994729483729522e-06,
                2.561282516066741e-06,
                5.422217030747413e-06,
                7.889266347786918e-06
            ],
            [
                2.2603234895289998e-06,
                4.2228319344021954e-06,
                1.3709567165579959e-06,
                9.422445939032799e-07,
                8.315284241560147e-07,
                4.785093924362895e-06,
                2.7535697667202906e-05,
                1.3709567165461505e-06,
                2.5612812947380135e-06,
                2.260324836787226e-06
            ],
            [
                6.023573475041126e-08,
                2.8453364239757298e-08,
                6.825604537781398e-08,
                7.73441946488886e-08,
                4.69116100558914e-08,
                1.2751904288710323e-07,
                1.637377448057981e-07,
                6.825606165129312e-08,
                8.764244316973974e-08,
                3.2241889394209404e-08
            ],
            [
                7.338212429582604e-07,
                8.315278294097538e-07,
                5.422217677152175e-06,
                6.144176799334096e-06,
                1.994730197090463e-06,
                6.144172404693786e-06,
                1.6373764721072816e-07,
                1.3007133116732079e-05,
                1.8553919030826963e-07,
                3.726639284144195e-06
            ],
            [
                1.370957860576702e-06,
                2.382369951932796e-07,
                3.466326211113502e-07,
                6.475947982037486e-07,
                4.450848927658745e-07,
                2.9023119851781017e-06,
                1.4449805540700758e-07,
                2.5612819054133693e-06,
                5.043476486924565e-07,
                1.275190732904469e-07
            ],
            [
                0.9999925887219128,
                0.9999843104521847,
                0.9999910603005183,
                0.999987780919657,
                0.9999869928669113,
                0.9999877809196625,
                0.9999898700102468,
                0.9999972735297327,
                0.999996033013145,
                0.9999810748450274
            ],
            [
                4.222835458148261e-06,
                3.466325797896173e-07,
                1.5534975693979422e-06,
                3.927860597945825e-07,
                7.338207180864763e-07,
                5.715007195447234e-07,
                1.0677029973158649e-06,
                9.422450431989127e-07,
                1.6373770576776313e-07,
                5.715007195447234e-07
            ],
            [
                6.475947210012481e-07,
                1.2098662604247682e-06,
                2.430023783530873e-05,
                4.785092783454444e-06,
                8.315278294072958e-07,
                3.288748673295719e-06,
                2.902311639183378e-06,
                2.9023109472244114e-06,
                3.7266406168403854e-06,
                1.7603432133136672e-06
            ],
            [
                9.422442569315887e-07,
                3.7266410611296085e-06,
                2.9023109472244114e-06,
                1.209865539295696e-06,
                6.475947982037486e-07,
                3.7266406168827523e-06,
                3.726638839878908e-06,
                1.2098662604291696e-06,
                3.0590237279085045e-07,
                7.338207180884785e-07
            ],
            [
                4.691162124067829e-08,
                0.9999942280779118,
                0.9999869928746524,
                0.9999955048162821,
                0.9999967112517221,
                0.99998615399217,
                0.999992110739305,
                0.9999942280772269,
                0.9999983463106124,
                0.9999904837494579
            ],
            [
                3.466327863983311e-07,
                9.931193325852072e-08,
                9.931190958076104e-08,
                6.825598028392069e-08,
                1.8553916819032217e-07,
                6.825602910433871e-08,
                1.1253513522447425e-07,
                1.2751904288710323e-07,
                1.6373768624837685e-07,
                1.855391681898159e-07
            ],
            [
                0.9998601779112308,
                3.9278634073732336e-07,
                5.043476486915964e-07,
                5.715006514176113e-07,
                2.1024329090929374e-07,
                8.315280276626197e-07,
                3.466327863961242e-07,
                6.475947210012481e-07,
                7.338209805200689e-07,
                0.9998911031306013
            ],
            [
                6.9622587397397306e-06,
                1.7603434231777837e-06,
                1.3709575337078829e-06,
                4.450848927637999e-07,
                8.939694172770212e-06,
                0.00015843617923435387,
                1.4738980215111302e-05,
                1.9947297215043796e-06,
                1.0677031245905116e-06,
                1.760343003481596e-06
            ],
            [
                3.9278605979534166e-07,
                1.760343213335281e-06,
                7.338212429582604e-07,
                4.450848927658745e-07,
                5.715002426486762e-07,
                9.422447062294175e-07,
                5.043475885696228e-07,
                9.422447062294175e-07,
                3.466327037548308e-07,
                2.6995774527718623e-07
            ],
            [
                2.260324836696773e-06,
                1.3709575337078829e-06,
                7.338209805200689e-07,
                2.9023116391477434e-06,
                5.715004470313855e-07,
                1.994729245917502e-06,
                1.2098655392871682e-06,
                1.7603432133136672e-06,
                1.2098662604126641e-06,
                2.260325375664839e-06
            ],
            [
                6.475947210031623e-07,
                4.785095065204162e-06,
                2.6995784182140636e-07,
                NaN,
                1.9947299593078385e-06,
                6.475947210031623e-07,
                1.3709567165617364e-06,
                3.927862002663297e-07,
                5.715006514151423e-07,
                1.9947292459347367e-06
            ],
            [
                6.825602910433871e-08,
                3.9278629391427843e-07,
                1.855391681906175e-07,
                3.9278629391427843e-07,
                1.444979692800516e-07,
                1.0677027427600627e-06,
                8.939699501416646e-06,
                5.043476486924565e-07,
                3.059021175261338e-07,
                9.931193325852072e-08
            ],
            [
                1.2098652508424818e-06,
                1.5534973842076057e-06,
                1.3709567165617364e-06,
                1.760342793638743e-06,
                6.475950298011458e-07,
                5.043473480777865e-07,
                2.102434162245973e-07,
                1.8553919030858602e-07,
                5.715002426486762e-07,
                8.315279285370317e-07
            ],
            [
                3.466327863983311e-07,
                3.9278605979534166e-07,
                3.466326624336003e-07,
                2.3823688159291947e-07,
                7.338208055664991e-07,
                5.043472278322555e-07,
                7.338208930460318e-07,
                5.715005832886879e-07,
                1.3709572068522336e-06,
                4.450850519403407e-07
            ],
            [
                5.422217030747413e-06,
                1.2098653950656417e-06,
                2.5612812947508257e-06,
                2.9023112932177327e-06,
                2.4300243630653244e-05,
                8.315281267834927e-07,
                3.288748281329893e-06,
                8.939693107190907e-06,
                1.2098653950656417e-06,
                1.209865539295696e-06
            ],
            [
                0.999994906293788,
                0.9999962733616071,
                0.9999974387168747,
                0.9999949062943949,
                0.999997273529407,
                0.9999967112505456,
                0.9999945777784516,
                0.9999984465028021,
                0.9999978766222981,
                0.9999981261252884
            ],
            [
                0.9999945777829765,
                0.999978555051669,
                1.8553907971855875e-07,
                5.04347528446051e-07,
                0.9999771720111373,
                0.9999934595627876,
                NaN,
                7.338212429582604e-07,
                0.9999843104447108,
                1.1253525596134564e-07
            ],
            [
                1.3007130015677909e-05,
                2.5612825160562587e-06,
                1.8925148241493373e-05,
                6.144172404693786e-06,
                1.3709576971425944e-06,
                3.120191509592808e-05,
                1.3007130015299356e-05,
                2.561282210729555e-06,
                5.715005151606823e-07,
                4.006369219393695e-05
            ],
            [
                0.9999339478716209,
                0.9999810748450133,
                0.9999832985781792,
                0.9999885212264173,
                0.9999934595620018,
                0.9999785550413917,
                0.9999934595612175,
                0.9999952149032261,
                0.9999861539905098,
                3.288749457469787e-06
            ],
            [
                0.9999687980776175,
                6.144173137170873e-06,
                2.2603248367949354e-06,
                1.0129987357517693e-05,
                1.5534984953552536e-06,
                3.927863875616689e-07,
                2.9023119851899796e-06,
                4.785094494811783e-06,
                2.6995790618469934e-07,
                6.475945666063607e-07
            ],
            [
                5.715005832872586e-07,
                5.715003788993679e-07,
                2.1024339116082313e-07,
                9.422449308716635e-07,
                9.422449308748773e-07,
                2.1024336609843824e-07,
                2.6995771309523475e-07,
                8.315282259089153e-07,
                3.0590237279032884e-07,
                6.825601283086733e-08
            ],
            [
                9.931199245228978e-08,
                5.3157830707696514e-08,
                1.1253518888531272e-07,
                8.76424013786396e-08,
                6.825598028392069e-08,
                7.734414854823498e-08,
                8.7642516304188e-08,
                7.73441946488886e-08,
                7.734418542875216e-08,
                9.931198061405701e-08
            ],
            [
                8.315279285370317e-07,
                0.9999623635531126,
                1.4449807263312446e-07,
                3.059021175261338e-07,
                8.7642516304188e-08,
                3.466327863983311e-07,
                1.4449795205429202e-07,
                0.9999925887201485,
                2.1024334103505245e-07,
                2.382370235933104e-07
            ],
            [
                3.4663278639892215e-07,
                9.422447062294175e-07,
                4.450851580555361e-07,
                1.3709570434178922e-06,
                3.9278615344178325e-07,
                3.466327863983311e-07,
                3.0590237279032884e-07,
                3.0590237279032884e-07,
                8.939696304311336e-06,
                1.7603427936335396e-06
            ],
            [
                5.043474081993875e-07,
                8.315280276626197e-07,
                NaN,
                3.9278610661902853e-07,
                4.222834451382849e-06,
                6.144176066901277e-06,
                5.71500719545698e-07,
                3.466325797896173e-07,
                1.8925152753790864e-05,
                5.829128640005915e-05
            ],
            [
                2.102434162245973e-07,
                1.0677028700422047e-06,
                3.466326624336003e-07,
                1.27519088491875e-07,
                4.4508494582405734e-07,
                9.422444815814404e-07,
                2.9023116392097746e-06,
                6.47595107001401e-07,
                1.4738980215593877e-05,
                3.288748673376478e-06
            ],
            [
                1.1253517547010071e-07,
                9.931196877517082e-08,
                1.6373764721072816e-07,
                9.931199245292204e-08,
                1.6373766672973748e-07,
                6.023573475041126e-08,
                2.3823693839325527e-07,
                2.1024331597262577e-07,
                1.1253508156363576e-07,
                4.691161005609407e-08
            ],
            [
                4.4508494582405734e-07,
                7.338208055664991e-07,
                5.04347528446051e-07,
                5.043472879540142e-07,
                5.043474081993875e-07,
                1.0677032518785256e-06,
                6.475945666051092e-07,
                4.222831934321543e-06,
                1.994730197090463e-06,
                3.466325797896173e-07
            ],
            [
                9.931189774187203e-08,
                7.734421308914719e-08,
                1.8553910183607374e-07,
                8.764249540862797e-08,
                2.6995790618350237e-07,
                1.4449805540740185e-07,
                6.825601283086733e-08,
                1.6373762769138607e-07,
                1.4449805540740185e-07,
                1.125352291309328e-07
            ],
            [
                0.999981074858559,
                4.4508515805735777e-07,
                8.315282259138311e-07,
                3.9278629391427843e-07,
                2.1024334103505245e-07,
                4.4508510499849186e-07,
                3.4663249714612693e-07,
                1.4738983729535602e-05,
                1.4449807263312446e-07,
                1.7603430034867993e-06
            ],
            [
                1.5534971990126997e-06,
                7.338210680021253e-07,
                4.2228329411708495e-06,
                1.6373766672973748e-07,
                0.9999203270200164,
                0.9999771719920015,
                3.2887506336086064e-06,
                3.059022998576899e-07,
                6.144174601991196e-06,
                5.715003789046955e-07
            ],
            [
                1.6373768624837685e-07,
                1.4449803818215767e-07,
                1.8553903548231313e-07,
                1.6373776432509826e-07,
                1.8553903548231313e-07,
                2.1024331597262577e-07,
                1.275190732904469e-07,
                NaN,
                8.315283250371857e-07,
                1.1253512180925583e-07
            ],
            [
                1.0677029973192638e-06,
                1.0677029973219343e-06,
                1.067703124601679e-06,
                4.22283545819819e-06,
                1.5534975693933505e-06,
                3.4663249714612693e-07,
                1.5534983101602148e-06,
                1.1478772231086046e-05,
                3.288748281329893e-06,
                1.7603440527286572e-06
            ],
            [
                2.699577774585891e-07,
                0.999968798085026,
                0.9999667858093734,
                0.9999516743738669,
                0.0004878571792647741,
                0.9999785550439931,
                1.0677029973192638e-06,
                0.9999741325783549,
                0.9999339478401125,
                3.726637951387472e-06
            ],
            [
                4.450852641737424e-07,
                2.3823690999323465e-07,
                5.3157900413760374e-08,
                7.338208930460318e-07,
                1.370957860576702e-06,
                7.734421308914719e-08,
                7.338208930460318e-07,
                1.1253512180925583e-07,
                2.3823696679327928e-07,
                6.825604537781398e-08
            ],
            [
                3.4663278639892215e-07,
                1.8553919030858602e-07,
                2.699577774585891e-07,
                5.715003107755449e-07,
                6.475949526020042e-07,
                NaN,
                2.2603237589779086e-06,
                8.764242227418718e-08,
                9.422450431989127e-07,
                7.338208055664991e-07
            ],
            [
                2.1024336609843824e-07,
                1.1478764020883773e-05,
                2.561281600086738e-06,
                3.466326211113502e-07,
                1.275190580890061e-07,
                1.4449798650551755e-07,
                2.3823696679327928e-07,
                9.931187406410953e-08,
                1.6373776432509826e-07,
                2.102434412875379e-07
            ],
            [
                1.3709570434219446e-06,
                4.785095635624897e-06,
                1.0129995810463632e-05,
                3.288749457469787e-06,
                1.5534984953510149e-06,
                1.0677031245990084e-06,
                1.5534979397740895e-06,
                1.5534981249697903e-06,
                1.5534971990126997e-06,
                6.144172404693786e-06
            ],
            [
                2.6995774527718623e-07,
                4.450848927658745e-07,
                1.3709576971463352e-06,
                3.059022998569248e-07,
                2.90231094723893e-06,
                6.475946438055299e-07,
                3.927862470899887e-07,
                1.9947292459347367e-06,
                1.4449805540740185e-07,
                4.450848927658745e-07
            ],
            [
                3.9278615344178325e-07,
                2.561282210740037e-06,
                7.338212429582604e-07,
                6.475947210046347e-07,
                3.0590237279085045e-07,
                5.715005832895975e-07,
                3.927860597945825e-07,
                2.3823693839290317e-07,
                3.9278629391427843e-07,
                1.6373770576776313e-07
            ],
            [
                1.2098653950480359e-06,
                4.4508494582314646e-07,
                5.04347528446051e-07,
                7.338211554783522e-07,
                2.699576809143613e-07,
                1.553498495281783e-06,
                4.450850519403407e-07,
                1.8553916819032217e-07,
                7.338207180864763e-07,
                1.5534981248528732e-06
            ],
            [
                1.4449800373118268e-07,
                1.012999460278499e-05,
                6.475945666051092e-07,
                5.422221555380179e-06,
                2.1444940745839484e-05,
                1.1478766757561534e-05,
                1.7603430034743913e-06,
                3.7266406168624155e-06,
                1.2098659719757836e-06,
                1.2098661162023305e-06
            ],
            [
                1.1253509497883659e-07,
                3.2887506336235617e-06,
                1.4449798650551755e-07,
                4.22283545819819e-06,
                1.2751901248454963e-07,
                3.05902190458764e-07,
                2.699576809143613e-07,
                2.1024331597262577e-07,
                2.699577774585891e-07,
                2.699578740032504e-07
            ]
        ]
    },
    {
        "q_id": "9692_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999991684720722,
                0.999999776197105,
                0.9999993106386262,
                0.9999993916411813,
                0.9999990577549576,
                0.9999999226558146,
                0.9999993106387906,
                0.9999998461826038,
                0.9999998144608319,
                0.9999986290431212
            ],
            [
                0.9999985406237808,
                0.9999960330122166,
                0.9999980052698065,
                0.9999992661789328,
                8.939696304311336e-06,
                0.9999989969856743,
                3.535625071730638e-05,
                1.1478768126057254e-05,
                0.9999995549150543,
                0.9999921107346292
            ],
            [
                0.9999998461827139,
                0.9999995549147891,
                0.9999991684722702,
                0.9999998724809877,
                0.9999998555019447,
                0.9999994631249963,
                0.9999996940978462,
                0.999999864256719,
                0.9999985406230841,
                0.9999999358793944
            ],
            [
                1.0129990979842057e-05,
                0.9999989969857944,
                0.9999988634365615,
                4.4508526417298334e-07,
                0.9999962733598388,
                2.6995774527718623e-07,
                1.0677029973192638e-06,
                1.4738983729535602e-05,
                4.785095635624897e-06,
                0.0005527786831992013
            ],
            [
                0.9999975938973813,
                1.9947292459347367e-06,
                1.5534971990126997e-06,
                0.999999114843177,
                1.3007128465151102e-05,
                0.9999993524054342,
                1.6701425827133152e-05,
                3.288748673360027e-06,
                1.0129989772412744e-05,
                0.9999987121052477
            ],
            [
                0.9999995549148422,
                0.9999995818811773,
                0.9999997463981939,
                0.9999991684716755,
                0.999997876621033,
                0.9999992188519492,
                0.9999987901341731,
                0.9999988634362901,
                0.9999997300423191,
                0.9999994956525319
            ],
            [
                0.9999986290424674,
                0.9999978766222991,
                0.9999993106390372,
                3.9278605979534166e-07,
                1.760343213335281e-06,
                0.9999990577551823,
                3.4663278639892215e-07,
                0.9999993106392013,
                0.9999981261248427,
                0.9999992188512975
            ],
            [
                0.9999957771645467,
                0.9999998362622747,
                0.9999996533672965,
                0.9999974387177912,
                0.9999992661791951,
                0.9999987121046318,
                0.9999991148429646,
                0.9999996072137062,
                0.9999981261237242,
                0.9999945777791002
            ],
            [
                2.5612831267202583e-06,
                0.9999997300421584,
                1.0,
                0.999999789756634,
                0.9999998942830233,
                0.9999995818811276,
                0.9999984465016909,
                0.999999631011416,
                0.9999993106392014,
                0.9999982396567881
            ],
            [
                0.9999992188514841,
                2.4300243631890864e-05,
                8.939693107288474e-06,
                0.9999992188518564,
                1.0677032518785256e-06,
                0.999999114843387,
                0.9999997463981637,
                1.855391681906175e-07,
                0.999998712104325,
                0.9999991684718741
            ],
            [
                0.9999998802069017,
                0.999999526209499,
                0.9999989969857932,
                0.9999994284995533,
                0.9999989322975129,
                0.9999984465022478,
                0.9999998802069159,
                3.7266401726359486e-06,
                0.9999991684720718,
                1.0677026154806063e-06
            ],
            [
                0.9999960330140929,
                0.9999990577556314,
                0.9999996310115039,
                0.9999994956526523,
                0.9999997463981334,
                0.9999995549151076,
                0.9999991684715761,
                0.9999980052709934,
                0.9999993524049706,
                0.9999989322966216
            ],
            [
                0.00023050674322105578,
                3.1201922535494165e-05,
                6.475945666051092e-07,
                2.7535691103314177e-05,
                6.962257909785973e-06,
                1.6373776432481905e-07,
                2.260324567337161e-06,
                2.6995774527718623e-07,
                5.8291265555961825e-05,
                2.9023116392097746e-06
            ],
            [
                0.9999991148433868,
                0.999999057755519,
                0.9999987121046315,
                0.9999992661787575,
                0.9999989969859124,
                0.9999992661788449,
                0.9999989969854345,
                0.9999978766217926,
                0.999999761763147,
                0.9999991684717744
            ],
            [
                2.1024331597262577e-07,
                2.1024331597262577e-07,
                6.023573475041126e-08,
                1.2751899728286965e-07,
                1.8553919030858602e-07,
                1.1253509497883659e-07,
                1.4449798650551755e-07,
                4.450852641737424e-07,
                2.382369383923073e-07,
                2.10243290909724e-07
            ],
            [
                1.6373770576776313e-07,
                2.6995771309523475e-07,
                2.3823685319244518e-07,
                2.3823693839154895e-07,
                4.450852111100568e-07,
                1.637377448057981e-07,
                3.059021175247079e-07,
                1.8553905760024476e-07,
                5.043475284430694e-07,
                5.715007195431641e-07
            ],
            [
                4.006367786720367e-05,
                6.1441746020359e-06,
                2.753568453792444e-05,
                3.726638839878908e-06,
                1.0129994602895546e-05,
                3.120191137659974e-05,
                4.450852111148132e-07,
                6.962257079832313e-06,
                6.144173869603344e-06,
                0.00017952792358181245
            ],
            [
                3.466327037539638e-07,
                2.1024339116134898e-07,
                1.855391239544352e-07,
                3.4663249714612693e-07,
                1.3709573702822306e-06,
                3.927862002663297e-07,
                4.4508510499849186e-07,
                4.4508510499849186e-07,
                3.9278634073625165e-07,
                2.6995774527718623e-07
            ],
            [
                2.382369951932796e-07,
                6.475945666063607e-07,
                2.2603251062450327e-06,
                5.715003789046955e-07,
                3.927862002663297e-07,
                0.9999970976873263,
                7.338210680021253e-07,
                3.059022998581767e-07,
                1.2098661162056318e-06,
                0.9999996072139404
            ],
            [
                0.9999987901337402,
                0.9999993916406736,
                0.999999746398194,
                3.466327037548308e-07,
                0.9999992188515767,
                4.450852641717689e-07,
                0.9999998724809268,
                0.999999554914736,
                0.9999997617631753,
                0.9999998642567028
            ],
            [
                1.2098659719757836e-06,
                4.785094494783494e-06,
                0.9999957771675717,
                2.561281294760143e-06,
                0.9999975938982386,
                7.338213304363436e-07,
                8.315282259138311e-07,
                4.450850519403407e-07,
                0.9999991684722704,
                1.3709570434178922e-06
            ],
            [
                0.9999994631248683,
                0.9999999006880075,
                0.9999992661788449,
                0.9999992188515766,
                0.9999990577556311,
                0.9999985406241281,
                0.9999991684715764,
                0.9999998362622943,
                0.999999802494586,
                0.9999993916411085
            ],
            [
                0.9999989969856732,
                0.9999998362623138,
                0.9999991148430705,
                1.1253509497883659e-07,
                0.9999989969855542,
                0.9999998257021007,
                0.9999999006880904,
                0.9999991684716756,
                0.9999994284996213,
                0.9999997463981334
            ],
            [
                6.962256249885085e-06,
                0.9999988634361551,
                4.785092783519724e-06,
                1.3007134667259441e-05,
                3.7266406168624155e-06,
                6.9622595696935874e-06,
                1.012999098021058e-05,
                5.715005832853093e-07,
                1.2098652508424818e-06,
                1.0677028700363782e-06
            ],
            [
                0.999999266179195,
                0.9999997463981032,
                0.9999992661792824,
                5.715003789046955e-07,
                0.9999985406234326,
                1.2098659719757836e-06,
                1.6373774480605869e-07,
                0.9999994631248045,
                0.9999997761971049,
                0.9999996072137063
            ],
            [
                0.9999998144608762,
                0.9999998642566381,
                0.9999995262093858,
                0.9999998362623723,
                0.999999825702163,
                0.9999998874649185,
                0.9999997761971583,
                0.9999996940977732,
                0.9999992188515766,
                0.9999988634357484
            ],
            [
                1.370957860576702e-06,
                0.9999991148429647,
                0.9999996072137531,
                0.9999998024945624,
                0.9999996072137531,
                0.9999997761971849,
                0.9999995549151075,
                0.999997438716573,
                5.715003789046955e-07,
                0.9999998362623138
            ],
            [
                0.9999992661786709,
                0.9999988634365612,
                0.9999993916410362,
                0.9999996072139403,
                0.9999993524052023,
                0.9999989969861525,
                0.999999057755295,
                0.9999998024947273,
                0.9999989969859134,
                0.9999993524052795
            ],
            [
                8.481108183851022e-05,
                0.9999952149055441,
                1.5534981249697903e-06,
                5.715003789046955e-07,
                2.2603242978871282e-06,
                3.1201922535494165e-05,
                8.939698435657833e-06,
                5.715003789033962e-07,
                2.2603242978871282e-06,
                2.5612828213818346e-06
            ],
            [
                2.90231094723893e-06,
                1.6701421845361053e-05,
                2.90231094723893e-06,
                1.892514373029853e-05,
                0.9999969105055591,
                3.120191137762131e-05,
                0.9999980052705186,
                0.9999987121049404,
                0.9999988634365621,
                3.726639728370556e-06
            ],
            [
                0.9999994284992809,
                0.9999995818812273,
                0.9999998642567028,
                2.1024339116134898e-07,
                0.9999993524053566,
                0.9999998555019619,
                0.9999998724809572,
                0.9999996743688587,
                0.9999997761971584,
                0.9999997761971315
            ],
            [
                0.9999999226557132,
                0.9999998642566543,
                0.9999999123575986,
                0.9999998144609203,
                0.9999999358793409,
                0.9999999434137773,
                0.9999999006880431,
                0.9999999006880312,
                1.0,
                0.9999957771675675
            ],
            [
                0.999999581881277,
                0.9999997126313783,
                0.999999653367255,
                0.9999997126313441,
                0.9999998362623334,
                0.9999997897567343,
                1.0,
                0.9999986290423034,
                0.9999998555019275,
                0.9999998555020135
            ],
            [
                0.9999998362622944,
                0.9999989969859129,
                0.999999746398073,
                0.9999999123575255,
                0.9999991148428594,
                0.9999997617631753,
                0.9999998942829477,
                0.9999992188514837,
                0.9999992188515768,
                0.9999995549151076
            ],
            [
                0.999998790133741,
                8.315284241597959e-07,
                0.9999997761970248,
                0.9999989969857932,
                0.9999991684718739,
                0.999998790134462,
                0.9999992188519496,
                0.9999998144609646,
                0.9999998144608541,
                1.9947292459265734e-06
            ],
            [
                NaN,
                7.889262585886274e-06,
                3.466325797896173e-07,
                1.8553907971855875e-07,
                9.422444815814404e-07,
                1.8553910183674878e-07,
                8.315279285370317e-07,
                3.927863407379485e-07,
                2.260324567337161e-06,
                1.994729721518893e-06
            ],
            [
                0.9999992661790208,
                0.999999495652472,
                0.9999992661789335,
                0.9999994631251247,
                0.9999987901344637,
                0.9999995549149483,
                0.9999975938970935,
                0.9999992661791954,
                0.9999987901343185,
                0.9999993524052803
            ],
            [
                0.9999999067050054,
                0.9999998555019446,
                0.9999992661787575,
                0.9999999273418355,
                0.9999987121043244,
                0.9999995549147891,
                0.9999991684720719,
                0.9999949062968219,
                0.9999994631249323,
                0.9999993106387084
            ],
            [
                5.715005832853093e-07,
                4.4508494582405734e-07,
                8.93969950132721e-06,
                5.715007195431641e-07,
                1.3709572068422585e-06,
                1.3709567165617364e-06,
                0.9999974387171827,
                0.9999972735294086,
                7.338212429582604e-07,
                1.0677024881980089e-06
            ],
            [
                0.9999970976873361,
                0.9999978766215447,
                0.9999962733589521,
                0.9999978766205316,
                0.9999977396751724,
                0.9999983463104204,
                0.9999982396565815,
                0.9999974387165806,
                0.9999975938982392,
                0.9999990577555213
            ],
            [
                2.2603251062450327e-06,
                0.9999990577552947,
                0.9999982396574191,
                0.9999989969855543,
                1.5534973842076057e-06,
                0.9999904837449372,
                4.785094494811783e-06,
                0.999998863436291,
                2.561281294760143e-06,
                0.9999986290432851
            ],
            [
                2.6995780963846126e-07,
                2.3823690999323465e-07,
                3.927863407379485e-07,
                1.637376862478556e-07,
                1.855391239544352e-07,
                3.466325797888292e-07,
                1.4449798650551755e-07,
                9.931190958076104e-08,
                5.715005832886879e-07,
                3.466325797888292e-07
            ],
            [
                0.9999998257021422,
                0.9999996072136126,
                0.9999996940978096,
                0.999999894282935,
                0.9999997463981636,
                0.9999995262093292,
                0.9999992188512976,
                0.9999994956527725,
                0.9999997300422226,
                0.9999995549150544
            ],
            [
                0.9999997463981334,
                0.9999996743686647,
                0.9999995818814267,
                0.9999986290421408,
                0.9999996743686259,
                0.9999994284994852,
                0.9999986290423039,
                0.9999978766210326,
                0.9999999067050388,
                5.715005151606823e-07
            ],
            [
                0.9999997897565839,
                0.9999999273418356,
                0.999998629042794,
                0.9999999067050943,
                0.9999997761970781,
                0.999999922655833,
                0.9999996743688975,
                0.9999996940976273,
                0.9999998555019619,
                0.9999998144608098
            ],
            [
                0.9999996072136593,
                0.9999999226557592,
                0.9999998555020135,
                0.999984310455914,
                1.4738980215593877e-05,
                0.999996273361164,
                9.422449308748773e-07,
                0.9999977396748954,
                0.9999975938982347,
                0.9999970976873246
            ],
            [
                0.9999989322972579,
                0.9999977396754338,
                0.9999982396569976,
                0.9999994631251242,
                0.9999997463981334,
                0.9999997126315154,
                0.9999985406232579,
                0.9999998724809875,
                0.9999999123574419,
                0.9999994631247403
            ],
            [
                0.9999994631251246,
                0.9999992188516701,
                0.9999988634357484,
                5.04347287955046e-07,
                0.9999993916411816,
                0.9999989322973861,
                0.999998446501879,
                0.9999989969855545,
                2.2603251062450327e-06,
                0.9999985406230846
            ],
            [
                1.7603434231833873e-06,
                1.2098653950606901e-06,
                0.999995504818427,
                4.222832941193893e-06,
                1.012998977264307e-05,
                6.144173869603344e-06,
                2.902313369111213e-06,
                3.288748281329893e-06,
                5.715004470313855e-07,
                0.9999975938976626
            ],
            [
                0.9999967112509376,
                1.994730434879465e-06,
                6.475947982037486e-07,
                3.927860597945825e-07,
                2.6995790618469934e-07,
                6.475947210046347e-07,
                5.715002426460124e-07,
                2.9023116392097746e-06,
                1.7603440527286572e-06,
                2.2603251062450327e-06
            ],
            [
                0.9999996940977003,
                1.0677028700422047e-06,
                0.9999995818810776,
                0.9999996743688199,
                0.9999995262093293,
                0.9999994956524717,
                0.9999994284997579,
                0.9999989322968764,
                0.9999972735284328,
                0.9999994284994169
            ],
            [
                0.9999999226557131,
                0.9999998802069016,
                0.9999998362622943,
                0.9999994284995533,
                0.9999997761970248,
                0.9999995262093292,
                0.9999999006881142,
                0.9999998942830737,
                1.0,
                0.9999999358793791
            ],
            [
                0.9999998144608984,
                0.9999993916409637,
                0.9999987901340291,
                0.9999993106389551,
                0.9999995262092728,
                0.999998863436697,
                0.9999978766207823,
                0.999999746398073,
                1.1253509497883659e-07,
                0.9999991148426481
            ],
            [
                0.9999974387187093,
                0.9999983463096288,
                1.370957860567974e-06,
                0.9999962733598472,
                1.9947299592933255e-06,
                0.9999967112509384,
                3.288748673360027e-06,
                0.9999955048195097,
                0.9999985406243028,
                0.9999983463096285
            ],
            [
                0.9999988634366967,
                0.9999995818813271,
                0.9999992188519493,
                0.9999986290424676,
                0.9999997761971849,
                0.9999990577550699,
                0.9999995549148423,
                0.9999993106386262,
                0.9999983463100212,
                0.9999997761971315
            ],
            [
                9.422448185435711e-07,
                0.999999391641181,
                9.4224425692559e-07,
                3.7266406168403854e-06,
                0.9999990577552941,
                0.9999964991451706,
                0.9999986290427936,
                0.999998005269804,
                0.9999995262095551,
                1.637377448057981e-07
            ],
            [
                0.9999955048168181,
                0.9999991684722702,
                0.9999996940977369,
                0.9999997463981032,
                0.9999982396565783,
                0.9999996743687424,
                0.9999982396572088,
                0.9999983463106134,
                0.9999972735303856,
                0.9999998362622747
            ],
            [
                0.9999999006881023,
                0.9999997463981636,
                0.9999995549151076,
                0.9999997126314469,
                0.9999987121052456,
                0.9999997761970781,
                0.9999996533673378,
                0.9999986290421408,
                0.9999992661787575,
                0.9999997463980124
            ],
            [
                1.1253512180925583e-07,
                1.0677028700422047e-06,
                4.222834954801051e-06,
                4.539788488687281e-05,
                0.0001233946191424094,
                3.7266410611465547e-06,
                3.535626336201389e-05,
                1.6701427818338537e-05,
                7.889260704968913e-06,
                9.422448185534261e-07
            ],
            [
                0.9999822214503116,
                1.3709576971379186e-06,
                0.999998629042794,
                0.9999993916410359,
                0.9999994631251242,
                2.1024334103505245e-07,
                0.9999987901347501,
                0.99998778092109,
                0.9999998144608541,
                2.1024336609843824e-07
            ],
            [
                0.9999998555019446,
                0.9999996533673376,
                0.9999993106392017,
                0.9999994284995535,
                0.999999855501979,
                0.9999991684719733,
                0.9999994284994854,
                0.9999992661792826,
                0.9999993524051252,
                0.9999994284997578
            ],
            [
                1.3007123813382511e-05,
                0.9999985406243049,
                0.00012339463384858465,
                4.785096206013061e-06,
                0.9999974387174914,
                5.829127945202588e-05,
                0.9999980052693346,
                0.9999993524054346,
                6.144176799334096e-06,
                7.338211554783522e-07
            ],
            [
                0.9999991148429649,
                0.9999997463981334,
                0.9999991148428593,
                0.9999994956525321,
                0.999999789756634,
                0.9999945777810407,
                0.9999998802069731,
                0.9999991148431756,
                1.5534981249697903e-06,
                5.043476486924565e-07
            ],
            [
                1.5534979397740895e-06,
                2.9023112930949896e-06,
                1.0129993395336818e-05,
                0.9999984465015055,
                0.9999993916411811,
                0.9999952149032252,
                3.9278615344267634e-07,
                1.5534984953453635e-06,
                5.043475885696228e-07,
                0.9999994284996894
            ],
            [
                0.9999992661788452,
                0.9999995818811277,
                0.9999949062943979,
                0.9999991684718739,
                0.9999989969861517,
                0.9999995549148422,
                0.9999997300421262,
                0.9999997897565588,
                0.9999984465022481,
                0.999999825702163
            ],
            [
                0.9999985406232582,
                0.999998346310022,
                0.9999987901347505,
                0.9999991148431759,
                0.9999980052707566,
                0.9999987901347505,
                0.9999989322970035,
                0.9999992661786701,
                0.9999898700054447,
                0.9999992661790201
            ],
            [
                0.9999945777784647,
                0.9999993524052021,
                0.9999998461826589,
                0.9999993106390372,
                0.9999998461827322,
                0.9999992661787575,
                0.9999998555020307,
                0.9999996940977004,
                0.999999802494633,
                0.9999997126315155
            ],
            [
                0.9999991684717748,
                0.9999997617629764,
                0.9999984465018775,
                0.9999999273417923,
                0.9999989969862714,
                0.9999996072139404,
                0.9999985406232589,
                0.9999987121050931,
                0.9999996072138937,
                0.9999991148426483
            ],
            [
                0.9999981261250646,
                0.9999984465024317,
                0.9999985406239539,
                0.9999991684715763,
                1.4738978458382043e-05,
                0.9999995549148952,
                0.9999998362622747,
                2.699578740032504e-07,
                0.9999983463106132,
                0.9999991684718738
            ],
            [
                0.9999992188518559,
                0.9999993106387906,
                0.9999967112513287,
                0.9999983463110065,
                0.9999997761971049,
                0.9999992661790197,
                0.9999982396565779,
                0.999999391640891,
                0.9999989969859123,
                0.9999974387174864
            ],
            [
                0.9999999468421313,
                0.9999996940978098,
                0.9999998461827139,
                0.9999993916408186,
                0.9999992661788448,
                0.9999999006879958,
                0.9999996743688586,
                0.999999730042287,
                0.9999998144608762,
                0.9999997897565588
            ],
            [
                2.1024334103581732e-07,
                3.927863875616689e-07,
                2.1024336609874897e-07,
                1.8553919030858602e-07,
                1.0677029973219343e-06,
                1.0677026154827912e-06,
                1.1253525596174225e-07,
                2.699576809143613e-07,
                5.71500719545698e-07,
                2.699577774589574e-07
            ],
            [
                3.059022269254856e-07,
                7.889266347786918e-06,
                1.5534984953552536e-06,
                5.043475885696228e-07,
                7.889265407327733e-06,
                5.043476486924565e-07,
                3.927860597935108e-07,
                5.043474081993875e-07,
                2.5612834320563895e-06,
                3.288747889284851e-06
            ],
            [
                0.9999981261252877,
                0.9999983463106122,
                0.9999942280779113,
                0.9999975938970884,
                0.9999997761972117,
                0.9999993524049706,
                0.9999995549151075,
                0.9999974387171804,
                0.9999998874648782,
                0.9999978766205265
            ],
            [
                0.9999977396751654,
                0.9999974387184021,
                0.999998540624302,
                0.9999983463110067,
                1.8553905760062447e-07,
                0.9999984465015059,
                0.9999975938979497,
                0.9999983463104154,
                0.9999969105044507,
                0.9999988634357478
            ],
            [
                2.1024339116168358e-07,
                0.9999974387174883,
                0.9999981261241725,
                0.9999892166890969,
                4.450848927658745e-07,
                5.715005151606823e-07,
                5.422220262636381e-06,
                1.370957860576702e-06,
                1.9947292459347367e-06,
                0.9999925887227963
            ],
            [
                4.450848927658745e-07,
                1.4738983729535602e-05,
                1.8553914607267268e-07,
                2.5612834320563895e-06,
                0.0002611903722932978,
                2.2603248367949354e-06,
                1.0129988565084915e-05,
                1.4738980215593877e-05,
                7.338208055680009e-07,
                8.939700567094277e-06
            ],
            [
                1.8925143729954285e-05,
                3.2887498495150166e-06,
                1.99472900813862e-06,
                1.3709567165617364e-06,
                0.9999843104559367,
                6.962257909842961e-06,
                3.535625071859258e-05,
                3.120190393896595e-05,
                5.715002426486762e-07,
                7.338208930460318e-07
            ],
            [
                0.9999996072139404,
                0.9999993524052794,
                0.9999992661789324,
                0.9999998461827322,
                0.9999998642567351,
                0.9999998555020307,
                0.9999994284992808,
                0.9999998724809572,
                0.9999991684717747,
                0.9999994631248684
            ],
            [
                0.9999998802069731,
                0.999999789756609,
                0.9999997126314126,
                0.9999994631247409,
                0.9999998144609203,
                0.9999997761971849,
                0.9999997617630617,
                0.9999998024946095,
                0.9999987901343173,
                0.9999998555019619
            ],
            [
                1.4449798650551755e-07,
                1.8553907971855875e-07,
                1.444979692800516e-07,
                1.6373770576776313e-07,
                1.1253520230052635e-07,
                2.699578740032504e-07,
                5.04347348075149e-07,
                3.466327037548308e-07,
                1.8553919030858602e-07,
                4.450852111148132e-07
            ],
            [
                0.9999964991443374,
                0.9999996743688199,
                0.9999993916406735,
                0.9999982396574182,
                0.9999995262093294,
                5.04347287955046e-07,
                0.9999981261250656,
                0.9999984465026172,
                0.00020342692526097766,
                0.9999981261248423
            ],
            [
                0.9999992661792831,
                0.9999996940977733,
                0.999999761763005,
                0.9999996533673791,
                0.9999997897567092,
                0.9999995549150545,
                0.9999994631248051,
                0.9999995818811277,
                5.043472879540142e-07,
                0.9999978766212894
            ],
            [
                0.9999991148427548,
                2.260324567337161e-06,
                4.450851580566494e-07,
                4.4508505193932864e-07,
                0.9999921107365285,
                0.9999960330145719,
                2.9023116391978967e-06,
                0.999995504818433,
                0.9999945777823587,
                1.3709572068522336e-06
            ],
            [
                0.9999972735307081,
                5.715005832872586e-07,
                0.9999987121049397,
                0.9999972735307092,
                9.422448185534261e-07,
                0.9999972735287589,
                0.9999991148426486,
                0.9999967112521155,
                0.9999972735294095,
                0.9999934595643645
            ],
            [
                0.9999993524050477,
                0.9999997300422226,
                0.9999980052700416,
                0.9999998802069587,
                0.9999997300421904,
                2.699577452775239e-07,
                0.9999997126313098,
                3.0590219045914655e-07,
                0.9999998642566542,
                4.222833948008874e-06
            ],
            [
                1.0,
                0.9999999358794249,
                0.9999997897565589,
                0.9999998724808963,
                0.9999998874648917,
                1.0,
                0.9999998024946802,
                1.0,
                1.0,
                0.9999995549151075
            ],
            [
                0.9999990577557447,
                0.9999998461826223,
                0.9999994956525321,
                2.1024334103581732e-07,
                0.9999998362622552,
                0.999999168471973,
                0.9999998874648379,
                5.715005151606823e-07,
                0.999999880206916,
                0.9999994631248044
            ],
            [
                0.999999114842648,
                0.9999974387174867,
                0.9999987121052463,
                1.5534977545886537e-06,
                0.9999988634360188,
                0.9999975938979497,
                0.9999996072138936,
                0.9999992188515768,
                0.9999988634365612,
                0.9999989969854343
            ],
            [
                1.855391239547094e-07,
                2.1024339116168358e-07,
                1.6373776432509826e-07,
                8.764244316973974e-08,
                1.4449805540763184e-07,
                1.0677029973219343e-06,
                2.1024334103581732e-07,
                2.3823688159237777e-07,
                2.102434162245973e-07,
                5.043472278322555e-07
            ],
            [
                0.9999945777816855,
                0.9999980052693292,
                0.999998790134606,
                0.9999985406243028,
                0.999993037741278,
                0.9999997126313441,
                0.9999981261243952,
                0.999997739675166,
                0.9999992188515766,
                0.9999997463980124
            ],
            [
                0.9999993916411817,
                5.043472278322555e-07,
                0.9999993106386263,
                0.9999990577549573,
                0.9999991148429648,
                0.9999994956525924,
                0.9999980052705185,
                0.9999995549151076,
                0.999996910505555,
                0.9999975938979506
            ],
            [
                0.9999998942830485,
                0.999999526209273,
                0.999999631011636,
                0.999999776197025,
                0.9999995818812272,
                0.9999993106390371,
                0.9999998942829603,
                1.0677026154730804e-06,
                0.9999995549148951,
                0.999999802494586
            ],
            [
                0.9999995549147365,
                0.9999998024946801,
                0.999998932297004,
                1.0,
                0.9999998461826222,
                0.9999994956526522,
                0.9999998942830863,
                0.999999730042287,
                1.0,
                0.9999999358793562
            ],
            [
                0.999998446502061,
                0.9999981261241717,
                0.9999978766215393,
                0.999998996985434,
                0.9999985406234319,
                1.2098653950692178e-06,
                0.9999989322966217,
                0.9999955048168209,
                0.9999989322967487,
                0.9999967112501525
            ],
            [
                0.9999990577556325,
                2.2603240284371276e-06,
                8.315280276626197e-07,
                5.422217030747413e-06,
                1.1478765389368729e-05,
                1.30071315662049e-05,
                0.9999986290429582,
                5.715007195431641e-07,
                8.939698435657833e-06,
                1.0129988564974359e-05
            ],
            [
                4.450848927637999e-07,
                3.288750241561788e-06,
                5.144221366623174e-05,
                4.450848927621807e-07,
                1.7603434231777837e-06,
                7.338213304363436e-07,
                1.0129995810463632e-05,
                3.1201900218617364e-05,
                6.962255419931625e-06,
                7.338207180864763e-07
            ],
            [
                2.6995790618350237e-07,
                6.475947982037486e-07,
                3.927861066170637e-07,
                2.6995771309523475e-07,
                2.6995784182140636e-07,
                2.102433660979124e-07,
                1.8553903548231313e-07,
                2.3823685319244518e-07,
                2.382369667929001e-07,
                1.637377057680051e-07
            ],
            [
                0.9999998461826954,
                0.9999999468421884,
                0.999999789756659,
                0.9999999397643083,
                0.9999998024947038,
                0.9999998724809419,
                0.9999997617630333,
                0.9999999634651705,
                0.9999999358794174,
                0.9999998144608319
            ],
            [
                2.3823682479292225e-07,
                1.8553919030826963e-07,
                1.4449800373118268e-07,
                3.0590237279032884e-07,
                9.931186222523604e-08,
                9.931187406410953e-08,
                2.3823685319244518e-07,
                1.444980209564556e-07,
                2.6995784182140636e-07,
                9.931190958076104e-08
            ],
            [
                0.9999962733616093,
                5.043472278312808e-07,
                0.9999975938976631,
                0.9999986290424677,
                0.9999991684715762,
                0.9999991684722707,
                0.9999996743686259,
                0.9999996072136595,
                0.9999983463100232,
                0.9999992661790201
            ],
            [
                0.999998996986271,
                0.9999955048168184,
                0.9999988634364255,
                0.9999998257021422,
                0.9999987901338849,
                0.9999997126313784,
                0.9999997761970248,
                0.9999997463981335,
                0.9999995549149482,
                0.9999998144608098
            ],
            [
                0.9999995549147361,
                0.9999998144609425,
                0.9999995549151075,
                0.9999992188518566,
                0.9999996940977731,
                0.999997273528757,
                0.9999996072137063,
                2.2603234895372223e-06,
                0.9999995818811775,
                0.9999991148433872
            ],
            [
                0.9999989969855543,
                0.9999993916408191,
                0.9999984465028042,
                0.9999982396563697,
                0.9999989322973867,
                0.9999995818813769,
                0.9999996072137534,
                0.9999992188512983,
                0.9999994631249329,
                0.9999986290427945
            ],
            [
                0.9999991684718736,
                0.9999993524050478,
                0.9999993916408909,
                0.9999984465018759,
                0.9999977396748956,
                0.9999997463982241,
                0.9999977396751658,
                0.9999982396569977,
                0.999998346310021,
                0.9999990577554065
            ],
            [
                0.9999993916408915,
                0.9999989969861519,
                0.9999989322967487,
                0.9999998144608983,
                0.999999631011548,
                0.999999631011548,
                0.999999554914736,
                0.9999977396746282,
                0.9999994956524119,
                0.9999994631247405
            ],
            [
                0.9999972735300583,
                0.9999992661789326,
                1.6373774480605869e-07,
                0.9999998144609424,
                0.9999972735287571,
                0.9999964991439227,
                0.9999991684716756,
                0.9999975938968085,
                0.999998996986032,
                0.999998346310614
            ],
            [
                0.999998346310415,
                0.9999982396559484,
                0.9999989969857926,
                0.99999345956044,
                1.3007126914435202e-05,
                0.9999986290427939,
                0.9999986290423036,
                0.9999975938985227,
                0.9999949062956095,
                0.9999975938985232
            ],
            [
                0.9999987121046315,
                0.9999993106389548,
                0.9999983463104163,
                0.9999972735284323,
                0.9999993106390371,
                0.9999992188518559,
                0.9999997761970781,
                0.9999987901347499,
                1.3709568799879344e-06,
                0.9999996072136594
            ],
            [
                0.9999972735290836,
                4.222832941193893e-06,
                0.9999987121052459,
                0.9999989969859125,
                2.561282516066741e-06,
                0.9999978766222997,
                1.8925141473978602e-05,
                0.9999975938979496,
                0.9999984465024323,
                6.962254589978262e-06
            ],
            [
                0.9999997126314814,
                0.999999864256719,
                0.999999761763147,
                0.9999994631247406,
                0.9999987901343191,
                0.9999994631251246,
                0.9999993916407465,
                0.9999996743686648,
                0.9999998024947039,
                0.9999995818812274
            ],
            [
                7.73441946488886e-08,
                0.9999972735300571,
                0.9999996533672137,
                0.9999988634365609,
                0.9999997126313783,
                0.9999987901338845,
                0.9999974387168751,
                0.999997876622298,
                0.9999724643089892,
                0.9999975938985217
            ],
            [
                0.9999996072136126,
                0.9999984465015057,
                0.999999391640746,
                0.9999985406237799,
                0.9999977396754351,
                0.9999974387187086,
                0.9999975938968013,
                0.999999168472072,
                0.9999991148428592,
                0.9999977396765125
            ],
            [
                2.6995790618469934e-07,
                3.466325797896173e-07,
                3.0590226339061185e-07,
                0.999997097686981,
                0.9999964991455897,
                0.9999993916411812,
                0.9999987121041708,
                0.9999981261250641,
                0.9999991684719726,
                3.05902336324494e-07
            ],
            [
                0.99999862904214,
                0.99999691050666,
                0.9999983463096267,
                0.9999984465026164,
                0.9999960330150405,
                0.9999983463098235,
                0.9999986290426305,
                0.9999921107364859,
                2.3823696679230424e-07,
                0.9999978766215394
            ],
            [
                0.9999994284995539,
                0.9999995549147365,
                0.999999218851764,
                0.9999987901338859,
                0.9999996940976275,
                0.9999995818812276,
                0.9999988634365634,
                0.9999990577556322,
                0.9999995549150017,
                0.9999994631248693
            ],
            [
                0.9999993106391195,
                0.9999997761972116,
                0.9999998024946095,
                0.9999989969857932,
                0.9999996072136594,
                0.999998932297004,
                0.9999994956527124,
                0.9999996533672963,
                0.9999992661790201,
                0.9999988634365615
            ],
            [
                1.0129989772532511e-05,
                7.889266347786918e-06,
                4.4508510499849186e-07,
                0.9999980052695663,
                0.9999977396765113,
                3.12019150949065e-05,
                1.5534975693979422e-06,
                3.466326211113502e-07,
                2.144495608424996e-05,
                0.9999967112517207
            ],
            [
                0.9999998802069445,
                0.9999988634364259,
                0.9999991148427535,
                0.9999997300422548,
                0.9999993524052795,
                0.9999998802069445,
                0.9999989969854343,
                0.99999926617867,
                0.9999993106390374,
                0.999999631011548
            ],
            [
                0.9999993524048938,
                0.9999983463098259,
                2.5612834320470717e-06,
                0.9999982396559509,
                0.9999987121049393,
                0.9999967112509492,
                0.9999974387184075,
                0.999998629042958,
                0.999999581881327,
                0.9999981261239489
            ],
            [
                0.9999985406241281,
                0.9999991148427535,
                2.6995790618350237e-07,
                2.1024326584582131e-07,
                0.9999991148430702,
                0.9999992661791949,
                0.9999945777810356,
                2.382369667929001e-07,
                0.9999993106389549,
                0.9999989969854343
            ],
            [
                0.9999994631251883,
                0.9999989322967491,
                0.999999495652532,
                0.9999993106392014,
                0.9999996940978827,
                0.9999991684720718,
                2.3823696679327928e-07,
                0.999999855502048,
                2.3823688159291947e-07,
                0.999999266178845
            ],
            [
                1.067703379154416e-06,
                9.610241502683509e-05,
                2.2603237589676295e-06,
                7.338212429562581e-07,
                0.9999952149049428,
                2.1024326584639497e-07,
                4.450852111148132e-07,
                3.05902117523595e-07,
                3.927861066170637e-07,
                1.9947299592933255e-06
            ]
        ]
    },
    {
        "q_id": "9456_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999991148431762,
                0.9999996533672139,
                0.9999991148427537,
                0.9999997126314126,
                0.9999996533672137,
                1.0,
                0.9999998024947273,
                0.9999992661787575,
                0.9999998942830359,
                0.9999996533674206
            ],
            [
                0.9999998802069874,
                0.9999999176674553,
                0.9999999732705506,
                0.9999993106386261,
                0.999999825702163,
                0.9999998024946332,
                0.999999825702163,
                0.9999998257021213,
                0.9999998642566543,
                0.9999998144608319
            ],
            [
                0.9999997126314811,
                0.9999997300421262,
                0.9999998257021837,
                0.9999993916411812,
                0.9999982396569994,
                0.9999998874647307,
                0.999999814460876,
                0.9999998642566381,
                0.999999761763147,
                0.9999921107336678
            ],
            [
                0.9999999530883283,
                1.0,
                0.9999999176674652,
                0.9999999586006493,
                1.0,
                0.9999998461826222,
                0.9999994631247404,
                0.9999999434137637,
                0.9999999559305524,
                0.9999998555019619
            ],
            [
                1.0,
                0.9999994956524719,
                0.99999995308839,
                0.9999999358794326,
                0.9999999006880076,
                0.9999997897566592,
                1.0,
                0.999999846182604,
                0.9999996310114598,
                0.9999997463980427
            ],
            [
                0.9999998642566543,
                0.999999927341827,
                1.0,
                0.9999997617629764,
                0.9999998724809268,
                0.9999999067050943,
                0.9999997897566841,
                0.9999999500628513,
                0.9999996940976639,
                0.9999994631247403
            ],
            [
                0.9999996533673793,
                0.9999993916410364,
                0.9999992188513909,
                0.99999971263131,
                0.9999996072137532,
                0.9999998555019274,
                0.9999998642566866,
                0.999999631011636,
                0.9999998144609424,
                0.9999997617629766
            ],
            [
                0.9999992188515767,
                0.9999996743686259,
                0.999999495652532,
                0.9999993916407461,
                0.9999995262094423,
                0.999999495652532,
                0.999999607213753,
                0.9999992661790198,
                0.9999999226557224,
                0.9999998724809875
            ],
            [
                0.9999991684719737,
                0.9999987901347499,
                2.430025232247918e-05,
                0.9999995262092163,
                0.9999997897565839,
                0.9999997897567343,
                0.9999992661792826,
                0.9999991148432815,
                2.7535691103314177e-05,
                0.9999997617630901
            ],
            [
                0.9999995818813766,
                0.9999999226557592,
                0.9999999317439303,
                0.9999999468421122,
                0.9999999530883955,
                0.9999999176674552,
                0.9999998642566543,
                0.9999992661787575,
                0.9999999273417662,
                0.9999998362622553
            ],
            [
                0.9999999468421946,
                0.9999991684722701,
                0.9999998874649318,
                0.9999992188514837,
                0.999998863436561,
                0.9999994631247403,
                0.9999999530883564,
                0.9999999006880431,
                0.9999985406232585,
                0.9999998802069017
            ],
            [
                0.9999998802069873,
                0.9999998724809723,
                0.9999990577550699,
                0.9999998144608762,
                0.9999991148432813,
                0.9999999006880785,
                0.9999993524051252,
                0.9999998257020591,
                0.9999989969854343,
                0.999999218851577
            ],
            [
                0.9999999500627977,
                0.999999391641036,
                0.9999998642566219,
                0.9999993916407464,
                1.0,
                0.9999999634651704,
                0.9999998802069445,
                0.9999998802069159,
                0.999999943413811,
                0.9999998555019963
            ],
            [
                0.999999631011636,
                0.9999997463981939,
                0.9999998555020307,
                0.9999999559305576,
                0.999999730042255,
                0.9999999123574732,
                0.999999352405125,
                1.0,
                1.0,
                0.9999998942830233
            ],
            [
                0.9999998257021837,
                0.9999996310114598,
                0.999999730042094,
                0.9999998257021007,
                0.9999990577552946,
                0.9999957771650508,
                0.999999789756634,
                0.9999996743687034,
                0.9999998024946801,
                0.9999994956523515
            ],
            [
                0.9999998555019792,
                0.9999996533672139,
                0.9999990577550705,
                0.9999997617630335,
                0.9999998461826956,
                0.9999997463980731,
                0.999999218851763,
                0.999999802494586,
                0.9999996310114162,
                0.9999994284993492
            ],
            [
                0.9999998024945624,
                0.9999993106387906,
                0.9999996743688976,
                0.9999998257021422,
                0.9999994631249327,
                0.9999998257021007,
                0.9999992661792826,
                0.9999995818813767,
                0.9999994284994851,
                0.9999997761970516
            ],
            [
                0.9999997126314812,
                0.9999997617630334,
                0.999999746398073,
                0.9999998461827139,
                0.9999998642566867,
                0.9999996072138001,
                0.9999998362623724,
                0.9999996940976275,
                0.9999998144608763,
                0.9999997300421263
            ],
            [
                0.9999996072139405,
                0.9999993524049706,
                0.999998005270995,
                0.9999993524052022,
                0.9999985406234325,
                0.9999994956524719,
                0.9999993524048933,
                0.9999991684722707,
                0.9999992661786704,
                0.9999991684721716
            ],
            [
                1.0,
                0.9999998461826037,
                0.9999998802069587,
                0.9999999358794402,
                0.9999999434137098,
                0.9999992188514835,
                0.9999997463980428,
                1.0,
                0.9999999067050165,
                0.9999999586006394
            ],
            [
                0.9999989969859124,
                0.9999997126313785,
                0.9999992188515772,
                0.9999991684720723,
                0.9999994956525321,
                0.9999991684718741,
                0.9999997126314127,
                0.9999992188515768,
                0.9999995262092165,
                0.9999990577549573
            ],
            [
                0.9999997897567342,
                0.9999994956524719,
                0.9999997617630334,
                0.9999997300422548,
                0.9999999226557778,
                0.9999995262092728,
                0.9999993524049706,
                0.9999995818812273,
                0.9999997463980125,
                0.999999391640746
            ],
            [
                0.9999997463981334,
                0.9999994284997578,
                0.9999996072138936,
                0.9999996940977004,
                0.9999998362623138,
                0.9999994956527725,
                0.9999994284996214,
                0.9999998802069874,
                0.9999997761971583,
                0.9999992188517629
            ],
            [
                0.9999999123575465,
                0.9999993106390371,
                0.9999999067051054,
                0.999999310638626,
                0.9999993524052793,
                0.9999997761971848,
                0.9999998461826038,
                0.9999995818814266,
                0.9999999067050943,
                0.9999997897566592
            ],
            [
                0.9999999530884011,
                1.0,
                0.9999999397642222,
                0.9999998144609425,
                1.0,
                1.0,
                0.9999995818812272,
                0.9999996072136126,
                0.9999997761971849,
                1.0
            ],
            [
                0.9999998555019963,
                0.9999998802069017,
                0.9999992661791073,
                0.999999653367503,
                0.9999999067049831,
                0.9999998257021838,
                0.9999994631249323,
                0.9999998144608098,
                0.9999999067050387,
                0.9999998144608983
            ],
            [
                0.999999922655833,
                0.9999998461826589,
                1.0,
                0.9999997126313441,
                0.999999789756659,
                0.9999991148431759,
                0.9999998802069587,
                0.999999825702059,
                0.9999999273418183,
                1.0
            ],
            [
                0.999999391640746,
                0.9999996072139404,
                0.9999998362623334,
                0.9999998802069302,
                0.9999998724809268,
                0.9999999067050498,
                0.999999694097664,
                0.9999998461827322,
                0.9999998724808964,
                0.9999988634364257
            ],
            [
                0.9999999273418616,
                0.9999998555020135,
                0.9999999468421946,
                0.9999995818813769,
                0.9999997897566592,
                0.9999999358794402,
                0.9999996310115041,
                0.9999997897566842,
                0.9999999176675535,
                0.9999998942830862
            ],
            [
                0.9999999123575046,
                0.9999997463980427,
                0.9999999434137098,
                0.9999994631251243,
                0.999999900687984,
                0.9999999500628036,
                0.9999999397642293,
                0.9999999006880786,
                0.999999961108909,
                0.9999997897567343
            ],
            [
                0.9999996072138935,
                0.9999998024946095,
                0.9999998257020798,
                0.9999999273418095,
                0.9999991148433868,
                0.9999998024947037,
                0.9999985406232587,
                0.9999997617630901,
                0.9999996072138936,
                0.9999996533672966
            ],
            [
                0.99999916847227,
                0.999999554914789,
                0.9999999611088672,
                0.9999998874648379,
                0.9999999434137098,
                1.0,
                0.9999999468421946,
                0.9999992661788449,
                0.9999989969861515,
                0.999999653367503
            ],
            [
                0.9999992661788448,
                1.0,
                1.0,
                0.9999998874647307,
                0.9999997300422548,
                0.9999996533673378,
                1.0,
                0.999999961108858,
                0.9999993524051249,
                0.9999999530883787
            ],
            [
                0.9999993916409637,
                0.9999998362623334,
                0.9999994956527726,
                0.9999998144609205,
                0.9999998802069731,
                0.9999999123574628,
                0.99999926617867,
                0.9999998461826588,
                0.9999998942829603,
                0.9999982396572076
            ],
            [
                0.9999994956523517,
                0.9999994956527726,
                0.9999995549149483,
                0.9999995549147892,
                0.9999996743686647,
                0.9999996072137062,
                0.9999998802069874,
                0.9999998144608762,
                0.9999997463980125,
                0.99999967436882
            ],
            [
                0.9999997617631753,
                0.9999996743688199,
                0.9999999067050388,
                0.9999999123574942,
                0.999999927341853,
                0.9999997617629766,
                0.9999997761971583,
                0.9999997617630617,
                0.9999998024946802,
                0.9999997617630049
            ],
            [
                1.0,
                0.9999994956527725,
                0.9999999358793944,
                0.9999999397642796,
                0.999999927341801,
                0.9999999397642868,
                0.9999997463981334,
                0.9999999273418876,
                0.999998996985434,
                0.999999789756659
            ],
            [
                0.9999992661787577,
                0.9999995818810777,
                0.9999969105048219,
                0.9999998362622747,
                0.9999994956523517,
                0.9999992661790201,
                0.9999997463981939,
                0.9999993524048935,
                0.9999998942830233,
                0.9999978766223007
            ],
            [
                0.9999994284995533,
                0.9999998362622747,
                0.9999999067050276,
                0.9999993106386261,
                1.0,
                1.0,
                0.9999998642567028,
                0.9999997761971317,
                0.9999997463980729,
                0.9999999317440198
            ],
            [
                0.9999999123574942,
                0.9999993524052024,
                0.9999997463980125,
                0.9999997126313098,
                0.9999998555020307,
                0.9999990577550696,
                0.9999997300421906,
                0.999999057754958,
                0.9999997463980125,
                0.9999957771665625
            ],
            [
                0.9999997126315154,
                0.9999997126313784,
                0.9999999226558238,
                0.9999996533673376,
                0.9999998942829225,
                0.9999998642566219,
                0.9999993106390371,
                0.9999999317439058,
                0.9999999317439384,
                0.9999996940978098
            ],
            [
                0.999999653367379,
                1.0,
                0.999999631011548,
                0.9999997897567342,
                0.9999998724809571,
                0.9999998257021007,
                0.9999996743687034,
                0.9999994956527123,
                0.9999998942829855,
                0.9999997463981334
            ],
            [
                0.9999995262094988,
                0.9999995549148953,
                0.9999988634364257,
                0.9999996072137532,
                0.999999526209499,
                0.9999994631250605,
                0.9999983463106128,
                0.9999998362622553,
                0.9999997463980126,
                0.999999776197185
            ],
            [
                0.9999996533673791,
                0.9999998802068873,
                0.9999985406234331,
                0.9999999468421693,
                0.999999776197025,
                0.9999997300421904,
                0.9999999500628394,
                0.999999114843281,
                0.9999999317439547,
                0.9999993524049708
            ],
            [
                0.9999995262092164,
                0.9999977396751658,
                0.9999996072139403,
                0.9999994956524118,
                0.999999526209273,
                0.9999998024947273,
                0.9999978766205271,
                0.9999996940977003,
                0.9999967112493716,
                0.9999997126314811
            ],
            [
                0.9999998362623137,
                0.9999998724809723,
                0.9999982396569975,
                0.9999994284997576,
                0.9999994284997576,
                0.9999992661787575,
                0.9999989322968763,
                0.9999998144609424,
                0.9999992661789324,
                0.9999993916409637
            ],
            [
                0.9999997617631469,
                0.999999391640891,
                0.9999977396748956,
                0.9999995818813767,
                0.9999987901341728,
                0.9999999006879957,
                0.9999995549148423,
                0.999999825702059,
                0.999999310638626,
                0.9999994284996896
            ],
            [
                0.9999993106388727,
                0.9999998257020798,
                0.9999998724809724,
                0.9999997761971583,
                0.9999998144608762,
                0.9999999006881378,
                0.9999989322966213,
                0.9999998642566219,
                0.9999999123575777,
                0.9999998461826405
            ],
            [
                0.9999998724808964,
                0.9999998144608984,
                0.9999999006879721,
                0.9999999006880076,
                0.999999927341827,
                0.9999991148430702,
                0.9999996310114159,
                0.9999995818811276,
                0.9999964991464233,
                0.9999998144608762
            ],
            [
                0.9999998724809116,
                0.9999996072136127,
                0.9999999067051277,
                0.9999994284992807,
                0.9999996533675031,
                0.9999994284994171,
                0.9999993106388726,
                0.9999998144608319,
                0.9999999358793867,
                0.9999989322970031
            ],
            [
                0.9999994284994852,
                0.9999993916408185,
                0.9999985406243018,
                0.9999991684716754,
                0.9999996940978826,
                0.9999991684716754,
                0.9999989969859125,
                0.9999988634362899,
                0.9999994631251242,
                0.9999997897566841
            ],
            [
                0.9999998802069874,
                0.9999998802068873,
                0.9999998555020135,
                0.9999999500628215,
                0.9999999397642437,
                0.9999999067050832,
                0.9999999500627739,
                0.9999999226558423,
                0.9999999176675535,
                0.9999999226558515
            ],
            [
                0.9999998642566219,
                0.9999998802069159,
                0.999999428499485,
                0.9999992188519491,
                0.9999993916411086,
                0.9999995818811774,
                0.9999993106387083,
                0.9999999226557501,
                0.9999993524052793,
                0.9999997761972116
            ],
            [
                0.9999999434137232,
                0.9999999559305524,
                0.9999993916410362,
                0.9999990577550697,
                0.9999993106392013,
                0.9999998942828973,
                0.9999999273418876,
                0.9999998642566867,
                0.999999554914736,
                1.0
            ],
            [
                0.9999995818812273,
                0.9999998724809419,
                0.9999995818810776,
                0.9999998874647441,
                0.9999999468421567,
                0.999999912357442,
                0.999999961108858,
                0.9999999317440035,
                1.0,
                0.9999998555019791
            ],
            [
                0.9999997617630049,
                0.9999997617630333,
                0.9999999176675142,
                0.999999864256719,
                0.999999789756609,
                0.9999991148431755,
                0.9999997463980427,
                0.9999987901347499,
                0.9999996940977732,
                0.9999996072136593
            ],
            [
                1.012999218776902e-05,
                1.0677032518785256e-06,
                7.889263526345123e-06,
                7.338208055664991e-07,
                3.9278615344178325e-07,
                1.067703379154416e-06,
                1.1478764020727177e-05,
                6.475951069961737e-07,
                3.4663249714451116e-07,
                0.00017952805197501883
            ],
            [
                0.9999996072136597,
                0.9999996743688975,
                0.9999996940978462,
                0.9999994956523517,
                0.99999971263131,
                0.9999997300421263,
                0.9999993916409636,
                0.9999999006880314,
                0.9999990577550705,
                0.9999997300421263
            ],
            [
                0.9999999006879958,
                0.9999996310115918,
                0.9999992661790198,
                0.9999984465028018,
                0.9999999358793791,
                0.9999984465015059,
                0.9999998724808963,
                0.9999996743688199,
                0.999999872480942,
                0.9999993106387906
            ],
            [
                0.9999997300421262,
                0.9999990577554068,
                0.9999998724810027,
                0.9999998144608763,
                0.9999997463981637,
                0.9999993524049708,
                0.9999996940978099,
                0.9999998724808963,
                0.9999997300421584,
                0.9999994956526524
            ],
            [
                0.9999995818814266,
                0.9999994284992807,
                0.9999998362622357,
                0.9999986290431209,
                0.9999994956527123,
                0.9999989969854343,
                0.9999988634358834,
                0.9999989969861516,
                0.9999987121047852,
                0.9999998024947037
            ],
            [
                1.0,
                0.9999998144609203,
                0.9999995549147892,
                0.9999995262092164,
                0.9999998874647307,
                0.9999998257022045,
                0.9999997761970782,
                0.9999999397642366,
                0.9999997463981637,
                0.9999993106387906
            ],
            [
                0.9999988634357485,
                0.9999996072137063,
                0.9999984465026174,
                0.9999996310116359,
                0.9999997463981335,
                0.9999988634365611,
                0.9999996072136126,
                0.9999998024946566,
                0.9999992188514836,
                0.999998629042794
            ],
            [
                0.9999988634358836,
                0.9999999067050943,
                0.9999999067050943,
                0.9999995262094422,
                0.9999999176675142,
                0.9999993106391193,
                0.9999998362623723,
                0.9999998874648112,
                0.9999999067050165,
                0.999999631011328
            ],
            [
                0.9999991684716755,
                0.9999974387171818,
                0.9999995262095555,
                0.999999825702163,
                0.9999997463980126,
                0.9999981261246176,
                0.9999996743687812,
                0.9999995262095551,
                0.9999997300420941,
                0.9999996533673791
            ],
            [
                0.999999802494633,
                0.9999998024946801,
                0.9999996072138936,
                0.9999997300422228,
                0.9999995549147891,
                0.9999998642566381,
                0.99999963101146,
                0.9999978766212863,
                0.9999998024946802,
                0.9999997617631184
            ],
            [
                0.999999746398073,
                0.9999997300421261,
                0.9999999123575674,
                0.9999989322967487,
                0.9999995818813768,
                0.9999998555019446,
                0.9999998724809116,
                0.9999999468421503,
                0.9999998144608319,
                0.9999987121041714
            ],
            [
                0.999999927341853,
                0.9999998802069731,
                0.9999998555020307,
                0.9999999530884012,
                0.9999998942828972,
                0.9999999468421756,
                0.9999999434137773,
                0.9999999006881023,
                0.9999996743688976,
                0.9999994284997576
            ],
            [
                3.535626335944147e-05,
                4.5397868646614036e-05,
                1.4738976700929127e-05,
                1.6701419853852583e-05,
                3.535624228698939e-05,
                0.9999990577555193,
                6.144172404520556e-06,
                0.009708478406571778,
                4.222835458148261e-06,
                3.7266397283231055e-06
            ],
            [
                0.9999998362622943,
                0.9999998257021838,
                0.9999998642567351,
                0.9999994631250603,
                0.9999999273417922,
                0.9999999397643083,
                0.9999998874648112,
                0.9999994956523516,
                0.9999999226557778,
                0.9999997617630901
            ],
            [
                0.9999998362622944,
                0.999999730042287,
                0.9999998802069731,
                0.9999999468421313,
                0.9999999067050165,
                0.9999998724809115,
                0.9999993524054336,
                0.9999998802069159,
                0.9999998802069874,
                0.9999986290431208
            ],
            [
                0.9999992661792824,
                0.9999998724809875,
                0.9999999559305681,
                0.9999999397642869,
                0.9999997300422226,
                0.9999989969857928,
                0.9999994631251242,
                0.9999998642567028,
                0.9999999006880786,
                0.9999998555019274
            ],
            [
                1.0,
                0.9999999123575255,
                0.9999996533673791,
                0.9999999358793562,
                0.9999998642566219,
                0.9999999317439873,
                0.9999998724809875,
                0.9999997897567342,
                0.9999997761971049,
                0.9999999500628394
            ],
            [
                0.9999998362622358,
                0.9999992661789326,
                0.9999998257021007,
                0.9999999358794173,
                0.9999991684718735,
                0.9999999317440198,
                0.9999998257020798,
                0.9999998144609645,
                0.9999999317440198,
                0.9999992661791949
            ],
            [
                0.9999982396561587,
                1.0,
                0.9999999273417923,
                1.0,
                0.9999999317439873,
                0.9999999586006443,
                1.0,
                0.9999999397642725,
                0.9999999500628394,
                0.999999814460854
            ],
            [
                0.9999999358794173,
                0.9999998642566866,
                0.9999999586006592,
                0.9999996533673791,
                0.9999993916409635,
                0.999999581881327,
                0.9999999123575151,
                0.9999997463981335,
                0.9999999634651878,
                0.9999999559305839
            ],
            [
                0.9999987121043249,
                0.9999999123574942,
                0.999999927341775,
                0.9999998642566866,
                1.0,
                0.999999939764251,
                0.999999114842648,
                1.0,
                0.9999999586006344,
                0.9999995549150544
            ],
            [
                0.9999998802069873,
                0.9999999176675044,
                0.9999999067050831,
                0.9999984465020615,
                0.9999996533674618,
                0.9999997617631753,
                0.9999991684722701,
                0.9999997617629766,
                0.9999998257022045,
                1.0
            ],
            [
                0.9999997761971582,
                0.999999674368781,
                0.9999995262093858,
                0.9999991148428591,
                0.9999998362623723,
                0.9999992188515766,
                0.9999972735297313,
                0.9999987901338844,
                0.9999995549151075,
                0.9999972735300572
            ],
            [
                0.9999989322971308,
                0.9999999123574942,
                0.9999995818813769,
                0.9999994956527726,
                0.999999057755519,
                0.9999998461826038,
                0.9999986290431215,
                0.9999996533673379,
                0.9999997300422228,
                0.9999999226557778
            ],
            [
                0.9999999500627857,
                0.9999992188515766,
                1.0,
                0.9999999067050387,
                0.9999998555020135,
                0.9999999176675632,
                0.9999998724809723,
                0.9999977396762427,
                0.9999990577552942,
                0.9999997897565588
            ],
            [
                0.9999993106392018,
                0.9999998024946332,
                0.9999995549150014,
                0.99999926617867,
                0.9999995818814267,
                0.9999991148427536,
                0.9999996072137532,
                0.9999985406241279,
                0.9999984465020614,
                0.9999993524048937
            ],
            [
                0.9999997897566842,
                0.9999999273418615,
                0.999999864256719,
                0.9999998874647709,
                0.9999998724809267,
                0.9999999067050054,
                0.9999999006881023,
                0.9999998724809723,
                0.9999999176674848,
                0.9999998024945624
            ],
            [
                0.9999998461827139,
                1.0,
                0.9999996940978826,
                0.9999999176675829,
                0.9999995262093293,
                0.9999989322975124,
                0.9999999611088904,
                1.0,
                0.999999631011328,
                1.0
            ],
            [
                0.999999802494633,
                0.999998346309825,
                0.9999998555019791,
                0.9999987121052457,
                0.9999984465026172,
                0.9999994284994171,
                0.999999631011548,
                0.9999997300423192,
                0.9999998724809419,
                0.999999391640891
            ],
            [
                0.9999997126314811,
                0.9999999559305787,
                0.9999996072139404,
                0.9999991148430702,
                0.9999982396559481,
                0.9999999434137098,
                0.9999999123574941,
                0.9999998461826405,
                0.9999999500627798,
                0.9999999634651617
            ],
            [
                0.9999999500627739,
                0.9999998144608983,
                0.9999998461826222,
                0.9999996310116359,
                0.9999998461826038,
                0.9999998144608319,
                0.9999987901340288,
                0.9999999397642293,
                0.9999993916408911,
                0.9999998642566866
            ],
            [
                0.9999987121046322,
                0.9999987901347506,
                0.00012339460442007728,
                0.9999993524052797,
                1.7603436330259153e-06,
                0.9999981261239481,
                0.9999962733594008,
                0.999998540623608,
                0.999998932296622,
                0.9999982396569986
            ],
            [
                0.999999939764258,
                0.9999999434137165,
                0.9999993106388726,
                0.9999999067050387,
                1.0,
                0.9999999468421883,
                0.9999999317439627,
                0.999999802494586,
                0.9999993916411812,
                0.9999999006881142
            ],
            [
                0.9999997126313441,
                0.9999999067050832,
                0.9999986290423034,
                1.0,
                0.9999998874648112,
                0.999999776197025,
                0.9999994284997578,
                0.9999991148430702,
                0.9999991148428593,
                0.9999997126314469
            ],
            [
                0.9999993106391192,
                0.9999996940977368,
                0.9999993916406735,
                0.9999996310113721,
                0.9999994284996216,
                0.9999994631251886,
                0.9999996310113721,
                0.9999993524054339,
                0.9999996743686647,
                0.9999997300420941
            ],
            [
                0.9999996940976276,
                0.9999995262092165,
                0.999999114843176,
                0.9999997126314812,
                0.9999996533675031,
                0.9999994956525321,
                0.9999998802069587,
                0.9999996940978462,
                0.9999998362622748,
                0.9999994956525321
            ],
            [
                0.999999631011372,
                0.9999995818813269,
                0.9999998257020799,
                0.9999998362623529,
                0.9999977396748964,
                0.9999996072137064,
                1.0,
                0.9999995262092728,
                0.999999802494633,
                0.999999631011636
            ],
            [
                0.9999997300421906,
                0.9999991148433868,
                0.9999987121043247,
                0.9999998642567351,
                0.9999998555020307,
                0.9999998942830737,
                0.9999997761971583,
                0.9999998555020481,
                0.9999997126313441,
                0.9999998942829351
            ],
            [
                0.999999855501979,
                0.9999996072136595,
                0.9999998024945624,
                0.9999998362622553,
                0.9999997761971583,
                0.9999998024945624,
                0.999999802494586,
                0.9999992188514842,
                0.9999999123574629,
                0.9999997300421904
            ],
            [
                0.9999996940978096,
                0.999999653367338,
                0.9999996940976273,
                0.9999996533675031,
                0.9999997300423191,
                0.9999998724808963,
                0.9999996072138936,
                0.9999998942830106,
                0.999999887464838,
                0.9999994284993489
            ],
            [
                0.9999999123575568,
                0.9999994284993489,
                0.9999999468420996,
                0.9999993524051248,
                0.999999802494633,
                0.9999999530883228,
                0.9999993524053569,
                0.9999992661791073,
                0.9999990577551819,
                0.9999999176675143
            ],
            [
                0.9999999468421122,
                0.9999995549151076,
                1.0,
                0.9999998144609203,
                1.0,
                0.9999996743687422,
                0.9999997897566592,
                1.0,
                0.9999998874647575,
                0.9999998874648379
            ],
            [
                0.9999997617631753,
                0.9999997300422548,
                0.999999939764215,
                0.9999997463981031,
                0.9999997617631753,
                0.9999999226558054,
                0.9999999317440116,
                0.99999911484307,
                0.9999998642566704,
                0.9999998144609205
            ],
            [
                0.9999999317440117,
                0.999999894282935,
                1.0,
                1.0,
                1.0,
                0.999998932296876,
                0.999998629042631,
                0.999999802494586,
                0.9999996743686257,
                0.9999999067050721
            ],
            [
                0.9999995818814266,
                0.9999996743687424,
                0.9999996533672965,
                0.9999997761970516,
                0.9999978766215433,
                0.9999998874648917,
                0.9999991684719727,
                0.9999984465028019,
                0.9999998024946801,
                0.9999995262093858
            ],
            [
                0.9999997126313099,
                0.9999999468421313,
                0.999999674368781,
                0.999999789756684,
                0.9999996072136126,
                0.9999992661791073,
                0.9999998874648112,
                0.9999998144608762,
                0.9999991148429644,
                0.9999991148429646
            ],
            [
                0.9999998257020593,
                0.9999996743687422,
                0.999999712631344,
                0.9999998362623529,
                0.9999998555019619,
                0.9999998257021838,
                0.9999998362622944,
                0.9999997463981636,
                0.9999993106389551,
                0.9999998144608983
            ],
            [
                0.999999607213753,
                0.9999990577552947,
                0.9999998555020135,
                0.999999927341827,
                0.9999999176675634,
                0.9999998942829981,
                0.9999999067051055,
                0.9999998362623138,
                0.9999998555019619,
                0.9999998461827139
            ],
            [
                0.9999996940977369,
                0.9999997617629766,
                0.9999996533674206,
                0.999999653367214,
                0.9999998144608319,
                0.9999997463980731,
                0.9999995549147364,
                0.9999996533672966,
                0.9999998724809116,
                0.9999990577555193
            ],
            [
                0.9999999611088534,
                1.0,
                0.9999997617631753,
                0.9999996743688199,
                0.9999994284996214,
                1.0,
                0.9999999434137773,
                0.9999999468421059,
                0.9999998461826772,
                0.9999992661787575
            ],
            [
                0.9999997126314127,
                0.9999999358794096,
                0.9999998024946096,
                0.9999999067051499,
                0.9999999123575465,
                0.9999999317440116,
                0.9999998144608762,
                0.9999999530883843,
                0.9999999559306101,
                0.9999999500627739
            ],
            [
                0.9999998362622358,
                0.9999996743688586,
                0.9999995818812273,
                0.999999939764251,
                0.9999999530883955,
                0.9999999500627798,
                0.9999998257021007,
                0.9999998461826222,
                0.9999996072137999,
                0.9999990577552943
            ],
            [
                0.9999992661789326,
                0.9999997463981032,
                0.9999981261252894,
                0.9999984465018766,
                0.9999991148429649,
                0.9999998144608762,
                0.9999969105066606,
                0.9999984465020618,
                0.9999998024945624,
                0.9999992188514838
            ],
            [
                0.9999999006881378,
                0.9999996072136594,
                0.9999998024946096,
                0.9999998802069587,
                0.9999998461826956,
                0.9999998802069587,
                0.9999997126313099,
                0.9999999397642222,
                1.0,
                0.9999998942829855
            ],
            [
                0.9999988634358843,
                0.9999998874648648,
                0.9999999226557408,
                0.9999993106388727,
                0.99999994341373,
                0.9999996743687035,
                0.9999997897566089,
                0.9999998874647977,
                0.9999999500628453,
                0.9999996940978462
            ],
            [
                0.9999997300423191,
                0.9999993916410365,
                0.9999996310115039,
                0.9999989322966224,
                0.9999996940978462,
                0.9999994631249323,
                0.9999997761972116,
                0.9999997463980427,
                0.999999864256719,
                0.9999994284994171
            ],
            [
                0.9999999530883508,
                0.9999990577552946,
                0.999999428499349,
                0.9999994956524116,
                0.9999992188512973,
                0.9999994956526522,
                0.9999998874647843,
                0.9999995262094423,
                0.9999996940978826,
                0.9999993106390371
            ],
            [
                0.9999997463980428,
                0.999999825702163,
                0.999999917667475,
                0.9999999067050387,
                0.9999997897567342,
                0.9999999176675535,
                0.9999987901338844,
                0.9999997300422548,
                0.9999997897565589,
                0.9999987121052456
            ],
            [
                0.9999995262092729,
                0.999999789756659,
                0.9999995262092729,
                0.9999993524054337,
                0.9999997300423192,
                0.9999998362622748,
                0.9999992188515768,
                0.9999995818811275,
                0.999999653367379,
                0.999999581881327
            ],
            [
                0.9999996940978826,
                0.999999802494633,
                0.9999994284997575,
                0.9999985406237797,
                0.9999996310115041,
                0.9999994631251883,
                0.999999391640746,
                0.9999998144609646,
                0.9999996072137999,
                0.9999997463981334
            ],
            [
                0.9999998555019447,
                0.9999992188512973,
                0.999999218851856,
                0.9999999123575674,
                0.9999999611088997,
                0.9999999397642078,
                0.9999997300421262,
                0.9999987121047859,
                0.9999993524053568,
                0.9999998874648514
            ],
            [
                0.9999996533675031,
                0.999995777166561,
                0.9999998555019619,
                0.9999994631251243,
                0.9999990577551818,
                0.9999969105051866,
                0.9999998257020798,
                0.9999999123574524,
                0.9999998144609203,
                0.9999992661792826
            ],
            [
                1.0,
                1.0,
                0.9999999500627739,
                0.9999998874648783,
                0.999999653367338,
                0.9999997463982242,
                0.999999631011504,
                0.9999998724809875,
                0.9999999358794326,
                0.99999994341373
            ],
            [
                0.9999998461827322,
                0.9999999586006048,
                0.9999999226557684,
                0.9999977396746261,
                0.9999999317439954,
                1.0,
                0.9999998144609646,
                1.0,
                0.9999994284994851,
                0.999999730042094
            ],
            [
                0.9999993916411811,
                0.9999998461826772,
                0.9999998461826772,
                0.9999997126313441,
                0.9999995262093293,
                0.999999746398073,
                0.9999994284994851,
                0.9999998555019274,
                0.9999998802068873,
                0.9999999434137434
            ],
            [
                0.9999987121046315,
                0.9999999500628394,
                1.0,
                0.9999995818810777,
                0.999999939764215,
                0.9999994284997576,
                0.9999998942830737,
                0.9999981261237244,
                0.9999999358794096,
                1.0
            ],
            [
                0.9999982396567888,
                0.9999988634357486,
                0.9999996743686259,
                0.9999993916408911,
                0.99999963101146,
                0.9999993106387906,
                0.9999996940977004,
                0.9999995262095553,
                0.9999996310113721,
                0.9999997897567342
            ],
            [
                0.9999995818812776,
                0.9999995262096122,
                0.9999995262093861,
                0.9999978766207813,
                0.9999980052707582,
                0.9999992188515768,
                0.9999993106386271,
                0.9999994631249968,
                0.9999993916409641,
                0.9999983463100236
            ],
            [
                0.9999997761970781,
                0.999998996985434,
                0.9999998724809723,
                0.9999994284994169,
                0.99999926617867,
                0.9999998802069017,
                0.999999946842182,
                0.9999995818810777,
                0.999999310639037,
                0.9999996533674617
            ],
            [
                0.9999997126315497,
                0.9999987121050918,
                0.9999978766222981,
                0.999999961108909,
                0.9999993916408186,
                0.9999977396746259,
                0.9999977396757037,
                0.9999987901338846,
                0.9999984465022461,
                0.9999998144608098
            ],
            [
                0.9999999273418442,
                0.9999994284993489,
                0.999999776197025,
                1.0,
                0.9999995549149483,
                0.9999997126315497,
                0.9999998874648649,
                0.9999996072138936,
                0.9999993106386261,
                0.9999994956527724
            ],
            [
                0.9999996533673792,
                0.9999987121047862,
                0.9999996533672137,
                0.9999998874647575,
                0.9999999067051054,
                0.9999998144609205,
                0.9999996743687422,
                0.9999994956523515,
                0.9999992188513903,
                0.999999495652532
            ]
        ]
    },
    {
        "q_id": "10133_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            4,
            5,
            7,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            27,
            30,
            31,
            32,
            36,
            37,
            38,
            39,
            41,
            42,
            43,
            44,
            45,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            66,
            67,
            69,
            70,
            71,
            72,
            73,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            106,
            107,
            109,
            110,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                9.422444815765128e-07,
                3.726639284125553e-06,
                6.475947981975644e-07,
                2.3823688159237777e-07,
                1.0677028700363782e-06,
                1.1478769494542698e-05,
                3.9278634073732336e-07,
                3.726638839878908e-06,
                3.2887482813149375e-06,
                1.8925157264919016e-05
            ],
            [
                1.0677026154806063e-06,
                5.715004470295662e-07,
                8.315281267861397e-07,
                1.5534984953552536e-06,
                5.715003789033962e-07,
                8.315280276607289e-07,
                5.043475284430694e-07,
                1.30071315662049e-05,
                7.338207180884785e-07,
                8.31528424162821e-07
            ],
            [
                4.222831934379152e-06,
                3.927860597945825e-07,
                5.422218969858371e-06,
                1.0677029973192638e-06,
                2.902313023130843e-06,
                3.288750241561788e-06,
                1.994729008145876e-06,
                2.6995774527577444e-07,
                7.338211554783522e-07,
                8.315279285351409e-07
            ],
            [
                5.715002426486762e-07,
                1.4449807263312446e-07,
                1.1478765389368729e-05,
                NaN,
                3.05902263391829e-07,
                6.144172404738491e-06,
                1.0677028700422047e-06,
                6.475945666063607e-07,
                9.931202796993203e-08,
                1.1253525596174225e-07
            ],
            [
                8.315283250371857e-07,
                1.2098653950656417e-06,
                9.422450432014836e-07,
                5.715007195431641e-07,
                1.5534979397740895e-06,
                5.715003107755449e-07,
                2.9023119851781017e-06,
                5.043474683204221e-07,
                1.7603438428740716e-06,
                2.5612816000646084e-06
            ],
            [
                2.2603251061664e-06,
                9.422444815563743e-07,
                1.5534983101393749e-06,
                2.9023133690821773e-06,
                1.5534977545603963e-06,
                1.3709568799879344e-06,
                1.0677027427471959e-06,
                2.561282516042282e-06,
                4.2228344508893285e-06,
                2.2603251061664e-06
            ],
            [
                4.450852111135988e-07,
                4.450851049959619e-07,
                1.5534981249697903e-06,
                5.04347468323289e-07,
                3.927862470899887e-07,
                8.315278294114555e-07,
                1.0677026154806063e-06,
                1.5534971990169383e-06,
                1.0677033791612137e-06,
                3.4663262110945863e-07
            ],
            [
                4.450848927658745e-07,
                3.2887486732000038e-06,
                1.7603430034151537e-06,
                9.422444815679433e-07,
                2.260324028427877e-06,
                2.699576809107705e-07,
                1.3709570433536782e-06,
                NaN,
                9.422447062270609e-07,
                5.422217676200406e-06
            ],
            [
                6.475947982002148e-07,
                6.475948754012522e-07,
                2.6995771309523475e-07,
                9.93120161306789e-08,
                2.6995774527718623e-07,
                8.764241182641775e-08,
                1.4449795205429202e-07,
                8.315282259089153e-07,
                1.3709575336947905e-06,
                3.927862939126708e-07
            ],
            [
                2.1444945858953813e-05,
                1.7603425837903113e-06,
                7.889266347786918e-06,
                5.422218969895357e-06,
                6.144177531811707e-06,
                2.699577774589574e-07,
                1.4738981972564636e-05,
                3.927863407379485e-07,
                1.670141985446017e-05,
                7.734415776836702e-08
            ],
            [
                2.2603251062450327e-06,
                9.422442569208767e-07,
                4.4508510499849186e-07,
                1.9947292459406333e-06,
                1.5534984953552536e-06,
                2.1024331597262577e-07,
                6.475949526003845e-07,
                1.8553919030858602e-07,
                1.8925148241872038e-05,
                3.2887502415767434e-06
            ],
            [
                4.785095635624897e-06,
                1.4738989000422955e-05,
                7.338207180864763e-07,
                5.829127250060064e-05,
                1.3709567165579959e-06,
                3.288749849498565e-06,
                1.994729483723626e-06,
                1.4738987243236881e-05,
                5.043472879540142e-07,
                1.2098659719716573e-06
            ],
            [
                4.222834451355964e-06,
                8.315281267861397e-07,
                8.315281267800897e-07,
                1.0677032518748838e-06,
                4.4508505193791187e-07,
                1.0677032518700286e-06,
                1.9947304348332037e-06,
                1.0677027427340866e-06,
                9.422443692489024e-07,
                1.2098656835136636e-06
            ],
            [
                1.1478768126057254e-05,
                0.0006263342578673952,
                0.00012339463381806274,
                2.1444950971601277e-05,
                2.7535700950274782e-05,
                3.535625914749675e-05,
                3.535625493182252e-05,
                0.01243165108186472,
                0.00010889694829665246,
                0.0040701371760450186
            ],
            [
                2.430024652854702e-05,
                1.6701415872659116e-05,
                1.473898900066424e-05,
                0.9999852610180593,
                8.315277302857965e-07,
                0.9999885212277887,
                2.753568453792444e-05,
                5.144221366623174e-05,
                6.605215257630029e-05,
                1.4738989000422955e-05
            ],
            [
                5.043476486902204e-07,
                2.6995790618350237e-07,
                6.475945666051092e-07,
                9.422448185534261e-07,
                1.0677027427600627e-06,
                7.338213304363436e-07,
                5.715006514167015e-07,
                8.315282259138311e-07,
                1.0677032518814388e-06,
                1.209865683518615e-06
            ],
            [
                4.1399410020127234e-08,
                3.224186633297071e-08,
                8.764245361708445e-08,
                8.764249540862797e-08,
                1.275190884913241e-07,
                4.139934092743992e-08,
                1.1253521571574156e-07,
                5.3157830707696514e-08,
                1.2751910369310194e-07,
                9.931195693628605e-08
            ],
            [
                2.10243290909724e-07,
                4.450851049959619e-07,
                3.9278624708775595e-07,
                3.059022269250683e-07,
                1.637377448057981e-07,
                3.927860597935108e-07,
                2.9023119850527192e-06,
                5.043475885674441e-07,
                2.699578096393206e-07,
                3.059021904571643e-07
            ],
            [
                3.726640172503764e-06,
                9.422449308716635e-07,
                5.422217030362759e-06,
                3.2887498494282754e-06,
                2.9023112931873767e-06,
                4.785095635624897e-06,
                2.2603248366762157e-06,
                2.561281905390075e-06,
                3.288749849477628e-06,
                4.0063682639477306e-05
            ],
            [
                1.1478770862735993e-05,
                2.260324567337161e-06,
                4.785096206047877e-06,
                2.9023119851781017e-06,
                9.422448185510695e-07,
                1.553498495338299e-06,
                3.927862002654366e-07,
                7.338209805224048e-07,
                7.889259764445822e-06,
                5.715003107755449e-07
            ],
            [
                2.9023126771227976e-06,
                2.5612812947508257e-06,
                2.9023130231176453e-06,
                7.889262585814522e-06,
                1.3709573702566696e-06,
                1.2098661161789477e-06,
                1.2098659719524008e-06,
                1.2098656834922064e-06,
                1.760343423160973e-06,
                3.726640616748873e-06
            ],
            [
                9.422450432014836e-07,
                4.4508494582405734e-07,
                5.422221555380179e-06,
                5.04347468318358e-07,
                7.88926446679691e-06,
                2.102434412871794e-07,
                2.9023133690980155e-06,
                5.043472879504592e-07,
                6.475951069755593e-07,
                1.9947299593014888e-06
            ],
            [
                3.0590237279085045e-07,
                9.931189774187203e-08,
                2.1024336609874897e-07,
                2.699578096393206e-07,
                2.1024334103505245e-07,
                1.6373770576776313e-07,
                9.931193325852072e-08,
                2.1024329090929374e-07,
                2.9023119850527192e-06,
                3.927862470899887e-07
            ],
            [
                2.75356812556058e-05,
                8.315281267800897e-07,
                7.338207180884785e-07,
                1.9947304348862686e-06,
                1.2098652508424818e-06,
                1.3709567165617364e-06,
                4.785094494811783e-06,
                2.382369383923073e-07,
                1.9947292459347367e-06,
                8.315284241650899e-07
            ],
            [
                5.04347528446051e-07,
                6.475948754012522e-07,
                1.0677027427600627e-06,
                6.1441746017453204e-06,
                2.260324836787226e-06,
                6.475950298011458e-07,
                1.0677027427600627e-06,
                8.315283250371857e-07,
                1.2098652508424818e-06,
                7.338211554783522e-07
            ],
            [
                6.605213682159303e-05,
                5.422221555380179e-06,
                9.610242648972629e-05,
                2.5612812947508257e-06,
                2.1444945858485726e-05,
                2.4300237837960777e-05,
                4.0063696969564425e-05,
                6.1441767993788005e-06,
                2.4300237837960777e-05,
                0.00037998457744365543
            ],
            [
                1.4449805540740185e-07,
                3.9278610661902853e-07,
                3.9278615344178325e-07,
                4.450852111135988e-07,
                2.2603242978871282e-06,
                6.475947982037486e-07,
                3.466327037553825e-07,
                3.0590215399183813e-07,
                1.8553910183607374e-07,
                1.6373770576683237e-07
            ],
            [
                0.9999861539954817,
                NaN,
                0.9999892166903769,
                0.9982992773717388,
                3.0590219045914655e-07,
                0.9999892166890945,
                0.9999916019280032,
                0.9999756997478787,
                0.9999843104484885,
                0.9999898700090616
            ],
            [
                6.144176799283803e-06,
                1.7603436329978976e-06,
                4.222833444590791e-06,
                1.3709575336947905e-06,
                1.5534975693869924e-06,
                1.9947306726594253e-06,
                5.422219616228845e-06,
                1.760343003481596e-06,
                7.338212429582604e-07,
                3.927862002663297e-07
            ],
            [
                5.71500651413193e-07,
                4.450851580555361e-07,
                5.04347348075149e-07,
                2.3823693839290317e-07,
                7.338209805224048e-07,
                5.715002426460124e-07,
                7.338213304316717e-07,
                3.927862939126708e-07,
                1.8553919030858602e-07,
                9.422448185510695e-07
            ],
            [
                3.726638839878908e-06,
                1.5534975693933505e-06,
                1.7603432133136672e-06,
                1.1478770862735993e-05,
                4.222831934379152e-06,
                4.785095635592258e-06,
                1.9947299592933255e-06,
                3.7266410611296085e-06,
                1.9947299592933255e-06,
                1.994730672668496e-06
            ],
            [
                0.9999964991455912,
                0.9999930377462478,
                5.715006514151423e-07,
                0.9999599363083415,
                2.430024652854702e-05,
                0.9999452402179054,
                0.9999945777803957,
                5.422217677152175e-06,
                0.9999599363128352,
                0.9999869928669192
            ],
            [
                3.2887486733420804e-06,
                2.382368247924618e-07,
                5.4222183234485234e-06,
                5.715007195353674e-07,
                1.3007133116542802e-05,
                1.3709572068272963e-06,
                1.9947304348703948e-06,
                2.5612822106841303e-06,
                1.2751904288739315e-07,
                2.902313368860448e-06
            ],
            [
                5.715005832676369e-07,
                4.4508526417014975e-07,
                8.315284241650899e-07,
                0.9999921107374274,
                2.561281905376098e-06,
                1.7603440527046419e-06,
                2.6995790618350237e-07,
                1.8553910183607374e-07,
                3.059021904571643e-07,
                1.0129993395088066e-05
            ],
            [
                3.4663249714451116e-07,
                0.9999910603047901,
                0.9999921107365012,
                2.1024334103352274e-07,
                1.067702615468225e-06,
                0.9999771720003197,
                0.9999934595604496,
                1.2098659719788098e-06,
                7.338209805224048e-07,
                0.9999921107374379
            ],
            [
                1.3709578605617394e-06,
                1.994729008105057e-06,
                9.422448185510695e-07,
                4.78509563550957e-06,
                8.939700566801578e-06,
                3.726638839878908e-06,
                2.260323489490968e-06,
                2.260324297853209e-06,
                3.059022998576899e-07,
                7.338211554783522e-07
            ],
            [
                6.96225873967641e-06,
                4.785092783454444e-06,
                NaN,
                8.315279285351409e-07,
                4.785096776394765e-06,
                4.785096776468749e-06,
                1.0129993393319151e-05,
                5.8291286393273546e-05,
                5.422221555340727e-06,
                8.939693107190907e-06
            ],
            [
                7.338211554783522e-07,
                3.288749849529972e-06,
                1.3709575337159875e-06,
                2.1444943302650045e-05,
                2.561281294760143e-06,
                6.962259569750576e-06,
                1.892515049819277e-05,
                2.382369383923073e-07,
                1.0677026154774503e-06,
                1.370957860576702e-06
            ],
            [
                8.31528126775552e-07,
                1.0677032518748838e-06,
                9.422447062240614e-07,
                1.2098661161927025e-06,
                1.7603434231777837e-06,
                1.2098655392871682e-06,
                7.889261645427538e-06,
                7.338209805200689e-07,
                1.0677028700363782e-06,
                4.222834954778007e-06
            ],
            [
                0.001501182342066647,
                5.715003789033962e-07,
                1.5534977545886537e-06,
                0.9999949062950051,
                1.2098653950403334e-06,
                1.994729008145876e-06,
                1.8553910183607374e-07,
                1.9947290080905435e-06,
                0.9999969105051865,
                5.043472879525233e-07
            ],
            [
                8.315277302788957e-07,
                3.4663266243111764e-07,
                5.04347468318358e-07,
                3.288749065423109e-06,
                5.715004470243685e-07,
                9.422444815726566e-07,
                5.04347348070562e-07,
                1.0677032518700286e-06,
                3.0590237278838124e-07,
                7.338211554688417e-07
            ],
            [
                1.0129992186202796e-05,
                5.715004470295662e-07,
                1.7603436329978976e-06,
                3.2887502413389517e-06,
                6.605214469462115e-05,
                1.5534979397677313e-06,
                2.9023130228840374e-06,
                1.1478772231086046e-05,
                3.2887478889034873e-06,
                4.22283545795623e-06
            ],
            [
                2.3823699519290042e-07,
                2.382369951932796e-07,
                2.3823685319244518e-07,
                4.450851580555361e-07,
                2.382369951932796e-07,
                3.0590237279032884e-07,
                7.338212429582604e-07,
                3.466327037539638e-07,
                2.1024331597066579e-07,
                2.6995784182140636e-07
            ],
            [
                2.3823702359290413e-07,
                6.475949526020042e-07,
                2.102434412875379e-07,
                2.902312331170226e-06,
                NaN,
                1.2098659719788098e-06,
                4.785094494783494e-06,
                8.315277302841894e-07,
                2.9023116392097746e-06,
                2.6995790618350237e-07
            ],
            [
                1.7603427936079236e-06,
                2.5612828213690224e-06,
                2.4300252320622747e-05,
                1.1478768126057254e-05,
                1.994729483705484e-06,
                1.994729008105057e-06,
                5.422221555296344e-06,
                3.2887490653647836e-06,
                8.315281267834927e-07,
                2.902312331125353e-06
            ],
            [
                3.0590215398829087e-07,
                2.9023116392097746e-06,
                1.9947301970972664e-06,
                4.450849458200093e-07,
                NaN,
                1.1478770862882149e-05,
                5.422217677152175e-06,
                8.315277302841894e-07,
                2.102434162245973e-07,
                1.994729483729522e-06
            ],
            [
                2.69957906184239e-07,
                1.0677032518785256e-06,
                1.0677026154806063e-06,
                2.10243290909724e-07,
                NaN,
                9.422450432014836e-07,
                2.3823702359290413e-07,
                2.699577774585891e-07,
                9.422444815792981e-07,
                3.059022269250683e-07
            ],
            [
                9.422448185510695e-07,
                1.9947299593014888e-06,
                5.043472879540142e-07,
                3.9278634073732336e-07,
                2.6995784182140636e-07,
                2.382369951932796e-07,
                8.315279285351409e-07,
                3.7266406168827523e-06,
                2.69957906184239e-07,
                4.450849458179853e-07
            ],
            [
                1.0677032518814388e-06,
                8.315280276399315e-07,
                1.5534975693869924e-06,
                1.2098659719757836e-06,
                5.715003107767143e-07,
                7.338210679949506e-07,
                7.338208930315157e-07,
                1.9947306726213275e-06,
                1.553497754583709e-06,
                2.2603253755476615e-06
            ],
            [
                0.9999949062956103,
                9.93120161310289e-08,
                0.9999852610198142,
                8.939696304311336e-06,
                4.78509278348926e-06,
                5.422219616265831e-06,
                2.1444940745839484e-05,
                0.0015011823441606264,
                4.785094494783494e-06,
                3.288748673360027e-06
            ],
            [
                4.2228324377164004e-06,
                0.9999930377462466,
                0.9999980052700437,
                6.47594798194325e-07,
                8.315281267800897e-07,
                0.9999916019269867,
                0.9999599362984571,
                0.9999869928653725,
                0.9999957771680735,
                0.9999910603015881
            ],
            [
                1.5534981249574276e-06,
                1.55349775456958e-06,
                1.5534984953199313e-06,
                1.2098653950480359e-06,
                3.0590215399183813e-07,
                5.422220262636381e-06,
                1.5534979397740895e-06,
                8.315282259117513e-07,
                2.2603237589542675e-06,
                6.475947981975644e-07
            ],
            [
                1.1478770862735993e-05,
                1.3709570433979422e-06,
                1.2098652508347793e-06,
                9.422447062202052e-07,
                1.4738983729053029e-05,
                3.726641061027928e-06,
                4.785096776394765e-06,
                1.5534975693792215e-06,
                1.7603434231505666e-06,
                1.067702615468225e-06
            ],
            [
                1.1253513522447425e-07,
                2.699577774585891e-07,
                3.4663274507713016e-07,
                5.04347468323289e-07,
                6.825601283086733e-08,
                1.6373768624837685e-07,
                2.9023126770343703e-06,
                2.1024334103505245e-07,
                2.699577774585891e-07,
                8.315278294114555e-07
            ],
            [
                9.931200429181105e-08,
                3.9278634073625165e-07,
                2.1024336609843824e-07,
                1.8553914607267268e-07,
                2.1024329090929374e-07,
                2.3823690999160957e-07,
                2.102433410343832e-07,
                2.3823682479181176e-07,
                2.6995768091310296e-07,
                2.382370235922541e-07
            ],
            [
                2.561281600076256e-06,
                1.0677024881829577e-06,
                5.422218323487975e-06,
                1.0129990980100021e-05,
                3.120192625175911e-05,
                2.2603234895289998e-06,
                1.994729483630195e-06,
                4.222831934379152e-06,
                2.9023126771227976e-06,
                2.9023112932045342e-06
            ],
            [
                2.5612831267202583e-06,
                1.3709572068522336e-06,
                6.605213682159303e-05,
                2.2603234895289998e-06,
                0.0109869427115529,
                1.2098661162056318e-06,
                6.962257909785973e-06,
                4.450849458200093e-07,
                1.0129990979842057e-05,
                2.90231094723893e-06
            ],
            [
                3.2887486731641103e-06,
                1.7603434231241496e-06,
                4.450852111148132e-07,
                7.338209805240734e-07,
                7.889261645427538e-06,
                5.043475885674441e-07,
                2.2603240284371276e-06,
                1.3709567165617364e-06,
                6.1441724046434924e-06,
                4.222831934352267e-06
            ],
            [
                8.315284241650899e-07,
                4.4508505193791187e-07,
                9.422448185510695e-07,
                5.715003789017068e-07,
                3.288750241561788e-06,
                2.5612828213934817e-06,
                1.2098656835224664e-06,
                8.315278294038928e-07,
                6.475947982002148e-07,
                6.475947982002148e-07
            ],
            [
                4.006371128945452e-05,
                0.9999038976107585,
                0.9999706884723386,
                2.902310947208574e-06,
                0.9998977001240837,
                7.88925976418034e-06,
                0.9999485577621218,
                0.9999251538006246,
                0.9999296881587274,
                0.00017952803042334226
            ],
            [
                8.939700566289352e-06,
                NaN,
                3.5356267573959116e-05,
                4.78509563546605e-06,
                1.012999218776902e-05,
                2.144495863958007e-05,
                1.3007133116542802e-05,
                3.72664061681327e-06,
                6.962259569630266e-06,
                4.222833947960866e-06
            ],
            [
                1.3709572068422585e-06,
                2.2603251061664e-06,
                1.9947304348703948e-06,
                2.260325375634003e-06,
                3.288749849477628e-06,
                8.315284241560147e-07,
                3.2887490653408545e-06,
                1.994729483705484e-06,
                4.222834954514924e-06,
                2.9023126770343703e-06
            ],
            [
                6.475950298011458e-07,
                1.2098659719788098e-06,
                3.927862470899887e-07,
                6.475950298011458e-07,
                7.338210680021253e-07,
                8.315284241650899e-07,
                6.475947982037486e-07,
                3.059021539909339e-07,
                3.0590237279032884e-07,
                5.715005832886879e-07
            ],
            [
                2.2603242978871282e-06,
                7.338212429504183e-07,
                1.3007125363719486e-05,
                8.939694172770212e-06,
                3.9278615344178325e-07,
                5.043475284430694e-07,
                4.785096776468749e-06,
                2.4300249425247723e-05,
                7.338212429537553e-07,
                7.338211554783522e-07
            ],
            [
                1.9947297215125433e-06,
                2.561283126728994e-06,
                0.999998863436561,
                1.4449798650476187e-07,
                1.9947292459347367e-06,
                5.144223819041771e-05,
                2.3823702359290413e-07,
                2.6995790618469934e-07,
                1.209865827740176e-06,
                1.553497384196656e-06
            ],
            [
                9.422444815814404e-07,
                4.222833444590791e-06,
                4.785096206076165e-06,
                2.699577774585891e-07,
                3.4663278639892215e-07,
                0.0001233946191424094,
                2.1444950971601277e-05,
                8.315284241665078e-07,
                1.2098659719788098e-06,
                3.927862470899887e-07
            ],
            [
                5.422220909009474e-06,
                3.726641061109272e-06,
                0.0001398221406320077,
                3.2887494574518405e-06,
                6.605216831371112e-05,
                5.715005832853093e-07,
                0.00010889692230394521,
                1.3007126914435202e-05,
                2.260323758987159e-06,
                0.9999339478325571
            ],
            [
                6.475947210031623e-07,
                1.0677029973192638e-06,
                6.475949526020042e-07,
                1.2098658277451275e-06,
                7.889265407255982e-06,
                1.0129995810463632e-05,
                1.7603436330259153e-06,
                1.209865539295696e-06,
                8.315282259117513e-07,
                2.5612812947508257e-06
            ],
            [
                NaN,
                8.764241182641775e-08,
                3.927862939126708e-07,
                1.637377448057981e-07,
                1.4449795205429202e-07,
                3.927863407379485e-07,
                1.4449798650551755e-07,
                1.275190124846946e-07,
                3.466325384678894e-07,
                3.059022269250683e-07
            ],
            [
                5.715005832827105e-07,
                6.475950298011458e-07,
                1.4738978458382043e-05,
                1.0677026154730804e-06,
                1.3709575337078829e-06,
                1.5534979397790343e-06,
                7.338211554783522e-07,
                7.338208930391909e-07,
                1.9947292459265734e-06,
                7.338209805200689e-07
            ],
            [
                6.475949526003845e-07,
                1.0677026154806063e-06,
                6.144172404738491e-06,
                6.144173869603344e-06,
                1.0677033791583005e-06,
                6.962259569750576e-06,
                1.3709572068522336e-06,
                3.7266406168827523e-06,
                3.7266401726173067e-06,
                2.260323758987159e-06
            ],
            [
                2.5612831266608576e-06,
                1.2098655392871682e-06,
                8.939693107093343e-06,
                1.3709570434054234e-06,
                6.144177531767002e-06,
                3.726639728348526e-06,
                1.2098658277264215e-06,
                1.6701421845057263e-05,
                1.2098655392662613e-06,
                2.9023116391978967e-06
            ],
            [
                4.222832437798974e-06,
                9.931195693628605e-08,
                6.962258739796719e-06,
                1.0677024882009222e-06,
                2.1024336609843824e-07,
                2.9023116392097746e-06,
                2.10243290909724e-07,
                5.715005151606823e-07,
                1.855391239544352e-07,
                3.7266397283908927e-06
            ],
            [
                1.067703124601679e-06,
                3.927863407379485e-07,
                1.3709576971463352e-06,
                2.902312677150514e-06,
                1.0677028700422047e-06,
                1.2098656835252174e-06,
                3.466326624336003e-07,
                NaN,
                7.734415776836702e-08,
                3.059022269254856e-07
            ],
            [
                3.0590215399183813e-07,
                2.382370235933104e-07,
                0.9999952149049423,
                0.9999982396567884,
                0.9999957771645488,
                0.9999921107383718,
                1.5534981249697903e-06,
                8.315284241650899e-07,
                9.422445939054222e-07,
                0.9999949062968272
            ],
            [
                7.338208930391909e-07,
                2.6995771309523475e-07,
                3.927860597935108e-07,
                1.1478770862735993e-05,
                5.71500719531729e-07,
                3.05902190458764e-07,
                4.222835458175145e-06,
                5.04347287955046e-07,
                3.0590215398829087e-07,
                6.475947209953583e-07
            ],
            [
                8.939698435657833e-06,
                8.315280276546789e-07,
                5.715003107755449e-07,
                1.0677026154806063e-06,
                5.715005832886879e-07,
                3.7266397283231055e-06,
                2.3823699519035448e-07,
                1.5534977545603963e-06,
                8.939696304213768e-06,
                1.994730197071414e-06
            ],
            [
                2.90231233114251e-06,
                4.006368263612517e-05,
                2.260325375677174e-06,
                2.902312677104321e-06,
                9.42244256915735e-07,
                4.785095635592258e-06,
                1.0129988564974359e-05,
                1.5534984953298217e-06,
                1.7603430034655858e-06,
                1.7603427936079236e-06
            ],
            [
                1.5534983101602148e-06,
                4.4508494582405734e-07,
                2.2603234895176927e-06,
                1.9947304348595095e-06,
                6.475946438055299e-07,
                2.2603251061849014e-06,
                3.288749457469787e-06,
                8.939693106987645e-06,
                4.222835458117536e-06,
                1.2098661161927025e-06
            ],
            [
                3.0590237279032884e-07,
                1.1253518888531272e-07,
                1.6373766672973748e-07,
                2.561281294760143e-06,
                1.8553905760062447e-07,
                1.300712536408621e-05,
                6.47595107001401e-07,
                7.338207180898968e-07,
                1.6373766672973748e-07,
                3.4663249714612693e-07
            ],
            [
                3.726638395415398e-06,
                4.785093353940187e-06,
                1.7603438428460541e-06,
                4.222834451169694e-06,
                9.422450431989127e-07,
                1.3709572068272963e-06,
                1.5534975693601474e-06,
                2.5612831266608576e-06,
                2.5612825160271407e-06,
                1.5534977545497995e-06
            ],
            [
                1.0677024881980089e-06,
                7.338212429537553e-07,
                3.288748673376478e-06,
                3.726638395634011e-06,
                3.288747889229516e-06,
                1.6701429808632785e-05,
                1.6701417863559525e-05,
                2.7535704229340197e-05,
                1.2098661162056318e-06,
                1.994730672675753e-06
            ],
            [
                1.0677026154806063e-06,
                5.043472879540142e-07,
                1.444979692800516e-07,
                2.902313023063532e-06,
                3.466327450765785e-07,
                6.825608606172863e-08,
                1.275190732904469e-07,
                1.1253512180925583e-07,
                8.315282259009745e-07,
                9.931199245322124e-08
            ],
            [
                1.1478772231086046e-05,
                5.422218969858371e-06,
                1.3007130015299356e-05,
                1.3709572068422585e-06,
                2.902313369111213e-06,
                1.4738983729294318e-05,
                7.338210679979539e-07,
                1.30071315662049e-05,
                2.144495608424996e-05,
                5.422218323487975e-06
            ],
            [
                1.1478769494542698e-05,
                2.10243290909724e-07,
                2.699577774585891e-07,
                5.043475885696228e-07,
                9.931186222523604e-08,
                0.006692851840624735,
                3.46632497145457e-07,
                3.466326211113502e-07,
                3.9278605979534166e-07,
                6.144172404738491e-06
            ],
            [
                5.715003107767143e-07,
                7.338213304363436e-07,
                3.288749065423109e-06,
                3.4663266243308805e-07,
                3.9278634073732336e-07,
                1.2098661162056318e-06,
                1.3709576971463352e-06,
                3.9278634073732336e-07,
                9.422443692574719e-07,
                3.059022998576899e-07
            ],
            [
                1.6701419854156377e-05,
                4.539788488885459e-05,
                3.535624650279074e-05,
                3.1201907657271834e-05,
                1.0129994602895546e-05,
                3.120191881616493e-05,
                6.962253760024999e-06,
                3.535626757524533e-05,
                4.222834954801051e-06,
                2.9023119851899796e-06
            ],
            [
                6.962254589851619e-06,
                2.561282210740037e-06,
                2.561281294644835e-06,
                4.450849988811838e-07,
                6.962254589528684e-06,
                6.1441760661636525e-06,
                9.4224425692559e-07,
                7.338212429504183e-07,
                2.260324297702111e-06,
                4.7850950648799385e-06
            ],
            [
                9.422443692489024e-07,
                2.9023119851635836e-06,
                3.288750633569722e-06,
                1.3709575337078829e-06,
                8.939694172867777e-06,
                2.2603251062270446e-06,
                4.222834954753043e-06,
                1.2098662604247682e-06,
                1.3709570434122812e-06,
                1.3709573702722555e-06
            ],
            [
                9.931187406410953e-08,
                7.734415776836702e-08,
                2.102434162245973e-07,
                4.22283545819819e-06,
                1.9947292459406333e-06,
                1.147876812620341e-05,
                6.962258739796719e-06,
                6.962257079889302e-06,
                2.6995790618469934e-07,
                1.9947292459406333e-06
            ],
            [
                2.9023119851781017e-06,
                NaN,
                6.144177531767002e-06,
                1.8925141473599938e-05,
                8.939700567004841e-06,
                1.370957860567974e-06,
                NaN,
                4.785096776468749e-06,
                1.7603434231777837e-06,
                7.889265407177056e-06
            ],
            [
                1.3709572068478697e-06,
                6.47594798194325e-07,
                6.144176799334096e-06,
                2.5612822107167428e-06,
                6.962255419804982e-06,
                NaN,
                1.0677029973158649e-06,
                1.9947297215125433e-06,
                2.902310947208574e-06,
                2.5612831267202583e-06
            ],
            [
                4.4508494582314646e-07,
                4.4508494582405734e-07,
                NaN,
                3.9278615344267634e-07,
                8.315282259089153e-07,
                1.0677032518785256e-06,
                7.338207180884785e-07,
                1.760343003481596e-06,
                3.05902190458764e-07,
                5.043476486915964e-07
            ],
            [
                5.043472278312808e-07,
                2.561282516066741e-06,
                3.726639728370556e-06,
                4.4508494582314646e-07,
                1.0677031245990084e-06,
                5.144220140264605e-05,
                1.0677032518814388e-06,
                9.422449308748773e-07,
                1.892515501014656e-05,
                2.9023119851781017e-06
            ],
            [
                4.222832941072913e-06,
                1.3007134667259441e-05,
                8.315281267834927e-07,
                7.338211554783522e-07,
                3.927862470861484e-07,
                1.7603432133136672e-06,
                1.1478768126057254e-05,
                4.450851580555361e-07,
                1.9947297215125433e-06,
                1.8925152753790864e-05
            ],
            [
                4.222832437798974e-06,
                1.0129995810463632e-05,
                1.5534984953453635e-06,
                1.5534984953510149e-06,
                2.902311639183378e-06,
                1.3709578605729614e-06,
                2.902312677137316e-06,
                2.9023126771227976e-06,
                1.0129995810463632e-05,
                1.3709568799919866e-06
            ],
            [
                1.0677028700266676e-06,
                1.3709568799760888e-06,
                4.785095065204162e-06,
                2.5612831263929686e-06,
                2.902312330965655e-06,
                2.9023119851781017e-06,
                7.338212429562581e-07,
                8.315280276505193e-07,
                1.5534971989427613e-06,
                1.0677028700266676e-06
            ],
            [
                0.9999916019309815,
                5.04347468323289e-07,
                0.999994906296216,
                9.422445939032799e-07,
                0.9999869928684474,
                3.0590237279032884e-07,
                8.315277302857965e-07,
                1.7603438428740716e-06,
                0.9999930377429253,
                5.422220262636381e-06
            ],
            [
                5.829127250060064e-05,
                1.7603425837903113e-06,
                4.785095065204162e-06,
                2.260325375634003e-06,
                9.422443692527585e-07,
                7.338207180898968e-07,
                1.0677024881980089e-06,
                6.144173137126169e-06,
                0.9996646499407574,
                3.7266410611296085e-06
            ],
            [
                1.855391239544352e-07,
                6.962257909722651e-06,
                3.2887482813149375e-06,
                3.288749849498565e-06,
                1.6701423836262173e-05,
                2.90231094723893e-06,
                1.30071315662049e-05,
                7.88926446679691e-06,
                1.0129995810463632e-05,
                0.9997965730042994
            ],
            [
                6.825606165129312e-08,
                1.0677032518814388e-06,
                8.764247451307293e-08,
                1.4738978458623327e-05,
                4.222832437798974e-06,
                1.147876812620341e-05,
                8.315278294114555e-07,
                2.6995790618252024e-07,
                1.9947297215125433e-06,
                1.4449795205429202e-07
            ]
        ]
    },
    {
        "q_id": "9668_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            7,
            8,
            9,
            10,
            11,
            13,
            14,
            15,
            17,
            18,
            19,
            20,
            21,
            23,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            71,
            73,
            74,
            75,
            77,
            79,
            80,
            81,
            82,
            83,
            84,
            87,
            88,
            89,
            90,
            91,
            92,
            94,
            95,
            97,
            98,
            100,
            101,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.6995790618469934e-07,
                1.6373772528704005e-07,
                1.2098661162023305e-06,
                2.6995774527718623e-07,
                1.3709572068522336e-06,
                9.422450432014836e-07,
                1.4449798650551755e-07,
                1.370957860576702e-06,
                2.102434162245973e-07,
                0.9999949062956199
            ],
            [
                5.715003107755449e-07,
                4.4508494582314646e-07,
                3.927862470899887e-07,
                8.315281267861397e-07,
                6.475946437996402e-07,
                6.475948754012522e-07,
                2.699578096393206e-07,
                5.043472879540142e-07,
                2.3823693839290317e-07,
                3.466327037548308e-07
            ],
            [
                3.288749065423109e-06,
                0.9999983463104168,
                0.999996711249766,
                0.9999988634361547,
                0.9999975938979523,
                1.4738981972564636e-05,
                0.9999970976873297,
                0.9999972735303841,
                2.1024329090781183e-07,
                0.999996910505186
            ],
            [
                1.7603440527286572e-06,
                6.825608606172863e-08,
                1.2098659719788098e-06,
                5.715003789046955e-07,
                1.4449803818215767e-07,
                1.6373766672994222e-07,
                1.3709576971463352e-06,
                2.1024339116168358e-07,
                9.931200429212718e-08,
                1.855391681906175e-07
            ],
            [
                1.0677032518814388e-06,
                6.475947982037486e-07,
                3.7266410611296085e-06,
                2.902313023130843e-06,
                6.475946438055299e-07,
                2.6995774527718623e-07,
                2.90231094723893e-06,
                1.0677032518814388e-06,
                1.5534979397790343e-06,
                1.3709573702822306e-06
            ],
            [
                3.726639284144195e-06,
                3.7266401726359486e-06,
                1.6701417863559525e-05,
                1.209865539295696e-06,
                2.2603251062450327e-06,
                6.1441767993788005e-06,
                0.9999904837449674,
                4.4508510499849186e-07,
                7.338208055680009e-07,
                6.144177531811707e-06
            ],
            [
                7.734415776836702e-08,
                1.5534983101644536e-06,
                1.3709573702822306e-06,
                3.4663274507713016e-07,
                1.1253506814797596e-07,
                1.8553903548231313e-07,
                3.9278605979534166e-07,
                9.422448185510695e-07,
                3.466325797900508e-07,
                2.699578740032504e-07
            ],
            [
                3.120192625482384e-05,
                2.4300243631890864e-05,
                0.999860177960923,
                1.5534983101602148e-06,
                7.338208930460318e-07,
                1.2098653950692178e-06,
                1.892515049819277e-05,
                0.9999785550491147,
                0.9999980052693286,
                0.9999977396754354
            ],
            [
                2.699577774585891e-07,
                1.5534975693869924e-06,
                1.444980209564556e-07,
                4.4508494582405734e-07,
                9.422447062202052e-07,
                1.553498124964492e-06,
                2.1024326584639497e-07,
                1.7603438428740716e-06,
                2.102434412875379e-07,
                3.927862002663297e-07
            ],
            [
                1.2098652508424818e-06,
                3.288749065423109e-06,
                2.2603240284371276e-06,
                8.315284241650899e-07,
                7.338212429582604e-07,
                2.260324567337161e-06,
                8.315279285351409e-07,
                1.760343213335281e-06,
                5.422219616265831e-06,
                7.338209805240734e-07
            ],
            [
                0.9999485577991725,
                0.9999898700126756,
                4.691168275606451e-08,
                9.422447062294175e-07,
                0.9993736657763083,
                2.5612812947508257e-06,
                2.75356812556058e-05,
                9.422449308748773e-07,
                1.0677024882009222e-06,
                5.043473480777865e-07
            ],
            [
                1.7603427936335396e-06,
                0.9999452402112377,
                2.6995774527718623e-07,
                3.927862002663297e-07,
                5.715003789046955e-07,
                3.726637951387472e-06,
                1.9947301970972664e-06,
                2.75356812556058e-05,
                0.9999885212264715,
                1.994729483723626e-06
            ],
            [
                2.10243290909724e-07,
                3.05902190458764e-07,
                5.715003107767143e-07,
                5.043472278322555e-07,
                1.3709576971463352e-06,
                6.475950298011458e-07,
                5.715004470326849e-07,
                1.4449805540700758e-07,
                2.382369383923073e-07,
                1.1253513522447425e-07
            ],
            [
                0.9999995818811774,
                0.9999992188519495,
                0.9999991684717751,
                0.9986749778517555,
                0.9999983463100216,
                0.9999987121052463,
                0.9999989322973853,
                0.9975273765194719,
                0.9999984465022471,
                0.9999955048173617
            ],
            [
                0.9999822214528755,
                2.430024073461624e-05,
                0.999992110740268,
                0.9999982396569999,
                5.4222183235249605e-06,
                2.5612819054133693e-06,
                0.9999485577809627,
                0.9999970976876761,
                6.144172404738491e-06,
                0.9999296881502049
            ],
            [
                5.043473480766399e-07,
                0.998299277823377,
                5.043474683220276e-07,
                1.8553919030858602e-07,
                2.561282210729555e-06,
                1.209865539295696e-06,
                3.059022269250683e-07,
                9.931195693628605e-08,
                1.0677033791612137e-06,
                4.450850519403407e-07
            ],
            [
                1.1253516205489029e-07,
                1.4449802095666915e-07,
                3.9278634073732336e-07,
                1.1253525596174225e-07,
                3.4663249714612693e-07,
                1.8553916819032217e-07,
                1.275190580890061e-07,
                1.8553919030858602e-07,
                1.1253513522447425e-07,
                3.059022269250683e-07
            ],
            [
                0.9999964991464251,
                0.9999877809269793,
                0.9999957771660679,
                0.9999822214418433,
                0.9999925887210267,
                0.9999949062950164,
                5.715006514176113e-07,
                0.9999485577932336,
                0.9999938558254176,
                1.2098659719757836e-06
            ],
            [
                7.338208930460318e-07,
                3.9278610661902853e-07,
                3.0590219045914655e-07,
                5.71500719545698e-07,
                1.209865827752005e-06,
                1.2098656835252174e-06,
                6.475945666063607e-07,
                3.927863407379485e-07,
                9.422443692574719e-07,
                NaN
            ],
            [
                3.0590237279032884e-07,
                1.9947301970972664e-06,
                1.0677028700422047e-06,
                1.2098662604291696e-06,
                6.962255419931625e-06,
                2.902312677137316e-06,
                8.939699501229642e-06,
                8.315281267882195e-07,
                NaN,
                9.422444815814404e-07
            ],
            [
                0.0001795280091563771,
                NaN,
                9.61024150359243e-05,
                8.764254764780641e-08,
                4.5397874064161706e-05,
                1.6373772528704005e-07,
                4.450852111155216e-07,
                0.00023050666077090176,
                1.4738976701652988e-05,
                NaN
            ],
            [
                1.994729483729522e-06,
                7.338211554813555e-07,
                4.785093924389007e-06,
                1.994729483729522e-06,
                3.7266383956509585e-06,
                3.466326624336003e-07,
                8.31528325040778e-07,
                1.0677026154827912e-06,
                5.043475284468537e-07,
                1.553497754592186e-06
            ],
            [
                5.422220262636381e-06,
                1.9947301970972664e-06,
                0.9840936063055303,
                3.726639284144195e-06,
                0.9999724643024414,
                3.72663883989755e-06,
                3.2887502415767434e-06,
                1.3709572068522336e-06,
                3.2887502415767434e-06,
                5.715003107767143e-07
            ],
            [
                0.9999960330140903,
                0.999992110738376,
                8.315281267861397e-07,
                5.043476486902204e-07,
                7.338212429582604e-07,
                7.3382080556433e-07,
                7.338208930460318e-07,
                3.0590237279032884e-07,
                6.475948754012522e-07,
                9.422444815792981e-07
            ],
            [
                0.9999852610233401,
                0.9999977396762428,
                0.9999955048162857,
                3.4663249714612693e-07,
                0.9999984465024317,
                7.338208055680009e-07,
                1.2098659719788098e-06,
                1.0677027427600627e-06,
                0.9999938558268775,
                0.9999983463108102
            ],
            [
                2.1444948415296896e-05,
                0.9996646500174255,
                0.9890130584522431,
                NaN,
                0.9975273768864361,
                0.0001398220575534256,
                0.0031726830309918535,
                6.1441746020359e-06,
                2.1024336609874897e-07,
                0.9998766054558517
            ],
            [
                NaN,
                NaN,
                9.931186222523604e-08,
                1.1253518888531272e-07,
                5.04347287955046e-07,
                8.7642558095602e-08,
                1.8553919030826963e-07,
                2.699576809143613e-07,
                1.4449807263325588e-07,
                5.715002426486762e-07
            ],
            [
                1.637377448057981e-07,
                1.4449798650569826e-07,
                7.338213304283347e-07,
                6.144174601991196e-06,
                0.9999417087209559,
                6.475945666051092e-07,
                0.9998601778943047,
                3.288748673376478e-06,
                0.9993736659787389,
                1.2098661162056318e-06
            ],
            [
                7.734415776836702e-08,
                5.043475885696228e-07,
                6.475950298011458e-07,
                8.315277302788957e-07,
                2.6995784182140636e-07,
                1.2098658277489788e-06,
                8.315277302841894e-07,
                8.315281267882195e-07,
                8.764245361752286e-08,
                3.9278638756099906e-07
            ],
            [
                1.3709568799919866e-06,
                1.760343213335281e-06,
                4.450848927650143e-07,
                3.466325797888292e-07,
                2.1024339116168358e-07,
                7.338213304363436e-07,
                2.382369383923073e-07,
                NaN,
                3.9278615344178325e-07,
                4.450851580540182e-07
            ],
            [
                7.338208930460318e-07,
                1.855391681906175e-07,
                1.2098652508424818e-06,
                1.5534975693979422e-06,
                1.6373776432509826e-07,
                3.0590237279085045e-07,
                8.315277302788957e-07,
                3.466326624336003e-07,
                4.4508515805735777e-07,
                NaN
            ],
            [
                1.8553903548231313e-07,
                8.764247451307293e-08,
                0.9999771720110866,
                1.3709575337159875e-06,
                7.889262585886274e-06,
                NaN,
                1.1253512180925583e-07,
                5.04347287955046e-07,
                1.8553907971855875e-07,
                0.99999048375173
            ],
            [
                1.4449798650569826e-07,
                2.6995784182183607e-07,
                9.931187406410953e-08,
                2.102434162245973e-07,
                1.8553910183674878e-07,
                2.3823690999323465e-07,
                2.1024339116168358e-07,
                1.855391681906175e-07,
                6.825609419848033e-08,
                3.0590237279085045e-07
            ],
            [
                3.4663262111182307e-07,
                4.222834954753043e-06,
                1.0677033791612137e-06,
                2.260323758987159e-06,
                3.288749849529972e-06,
                4.222831934202483e-06,
                3.288748281295496e-06,
                NaN,
                8.315278294114555e-07,
                3.927863407379485e-07
            ],
            [
                0.9999949062931962,
                0.9999942280779223,
                0.9999967112497674,
                0.9999957771670764,
                0.9999379494910078,
                0.9999952149043831,
                7.889262585886274e-06,
                0.9999952149072328,
                0.9999452402246553,
                0.9999949062925865
            ],
            [
                1.5534981249736758e-06,
                2.260325106237323e-06,
                NaN,
                3.466326624336003e-07,
                3.927863875616689e-07,
                3.9278615344178325e-07,
                1.209865827752005e-06,
                NaN,
                1.5534975693979422e-06,
                2.753569110256289e-05
            ],
            [
                1.6373770576776313e-07,
                1.4449802095609418e-07,
                1.855391681898159e-07,
                2.10243290909724e-07,
                2.3823682479292225e-07,
                1.6373766672821107e-07,
                2.69957906184239e-07,
                2.382369383923073e-07,
                4.4508494582405734e-07,
                2.3823685319244518e-07
            ],
            [
                1.9947297215125433e-06,
                0.9999869928654022,
                1.0677027427600627e-06,
                0.9999942280806738,
                1.0677027427600627e-06,
                0.9999687980814791,
                1.5534973842076057e-06,
                1.1253526937697666e-07,
                3.9278634073732336e-07,
                2.1024341622368903e-07
            ],
            [
                1.370957860576702e-06,
                4.4508515805735777e-07,
                1.9947299593078385e-06,
                4.4508494582405734e-07,
                NaN,
                2.2603248367949354e-06,
                1.2098656835224664e-06,
                7.338210680021253e-07,
                3.05902336324494e-07,
                7.338207180898968e-07
            ],
            [
                8.315278294097538e-07,
                1.5534983101602148e-06,
                NaN,
                7.33821330437595e-07,
                9.422443692574719e-07,
                9.422442569290178e-07,
                NaN,
                5.715003789046955e-07,
                1.067703124601679e-06,
                3.4663278639892215e-07
            ],
            [
                0.02595735832806066,
                2.7535694385633984e-05,
                NaN,
                6.475948754012522e-07,
                0.999796572955767,
                NaN,
                0.3486451217982255,
                0.9999546021259933,
                0.0021827164154266344,
                0.9999599363174894
            ],
            [
                0.9999994631251883,
                0.9999980052705181,
                0.9999832985742226,
                0.9999938558254093,
                0.9999916019289924,
                0.9999985406243018,
                6.1441746020359e-06,
                0.9999921107365017,
                0.9999898700066336,
                0.9999339478791676
            ],
            [
                2.382368531929327e-07,
                2.699576809143613e-07,
                2.699577774589574e-07,
                6.475945666051092e-07,
                9.422442569290178e-07,
                2.6995790618469934e-07,
                1.7603430034867993e-06,
                3.4663249714612693e-07,
                2.3823690999290963e-07,
                2.1024341622426268e-07
            ],
            [
                6.475945666063607e-07,
                3.927862470899887e-07,
                2.2603234895372223e-06,
                NaN,
                1.5534981249697903e-06,
                5.715007195447234e-07,
                9.422443692555439e-07,
                6.475947982037486e-07,
                2.3823696679327928e-07,
                2.69957906184239e-07
            ],
            [
                0.9999969105048206,
                0.9999969105059281,
                0.9999967112493711,
                0.9999991148433868,
                0.9999989322975131,
                0.9999972735287593,
                1.855391681906175e-07,
                0.9999984465026175,
                3.059022998581767e-07,
                0.9999985406237808
            ],
            [
                9.422443692555439e-07,
                1.1253525596174225e-07,
                7.734425918979532e-08,
                3.05902190458764e-07,
                1.4449807263312446e-07,
                1.8553905760062447e-07,
                2.699578740032504e-07,
                1.6373770576776313e-07,
                3.059022998576899e-07,
                9.931195693628605e-08
            ],
            [
                2.902312331170226e-06,
                2.902312331170226e-06,
                0.9953904279616417,
                6.144175334468545e-06,
                3.72663883989755e-06,
                8.939693107288474e-06,
                4.785095635655362e-06,
                8.939696304311336e-06,
                4.4508515805735777e-07,
                1.1478770862735993e-05
            ],
            [
                6.475945666063607e-07,
                1.5534975693979422e-06,
                3.927863407379485e-07,
                1.0677028700422047e-06,
                7.338210680021253e-07,
                1.3709567165617364e-06,
                7.338207180898968e-07,
                NaN,
                1.3709568799919866e-06,
                NaN
            ],
            [
                2.5612831267202583e-06,
                5.4222183235249605e-06,
                1.2098653950656417e-06,
                2.5612828213934817e-06,
                8.939696304311336e-06,
                3.288748673360027e-06,
                5.043476486915964e-07,
                2.9023112932177327e-06,
                2.2603234895372223e-06,
                1.994729483729522e-06
            ],
            [
                9.422445939054222e-07,
                0.3775406687981454,
                3.9278605979534166e-07,
                6.475946438055299e-07,
                5.043473480777865e-07,
                4.4508494582405734e-07,
                9.422444815814404e-07,
                2.902312331170226e-06,
                5.043476486924565e-07,
                2.1024334103581732e-07
            ],
            [
                5.04347528446051e-07,
                3.2887494574518405e-06,
                6.475950298011458e-07,
                1.5534984953510149e-06,
                3.927863875616689e-07,
                3.9278605979534166e-07,
                5.715003789033962e-07,
                2.902312331170226e-06,
                1.7603425837903113e-06,
                1.8553905760062447e-07
            ],
            [
                6.144176066901277e-06,
                2.902312677137316e-06,
                8.315277302841894e-07,
                1.3007126914612648e-05,
                2.6995771309523475e-07,
                2.2603251062450327e-06,
                4.450852111155216e-07,
                9.422443692574719e-07,
                NaN,
                2.1024336609843824e-07
            ],
            [
                6.475951069985296e-07,
                1.7603425837855082e-06,
                5.715003789033962e-07,
                6.475949526020042e-07,
                4.450850519403407e-07,
                5.715007195447234e-07,
                7.338207180864763e-07,
                8.315281267882195e-07,
                1.7603436330259153e-06,
                6.475949526020042e-07
            ],
            [
                0.9999993106392014,
                0.9999978766212889,
                0.9999945777803938,
                0.9999993524052795,
                0.9999970976880196,
                3.466327450756327e-07,
                0.9999985406239542,
                0.9999986290431214,
                0.999997876621288,
                0.9999991148432813
            ],
            [
                NaN,
                2.699578740032504e-07,
                1.892514598627448e-05,
                2.561281294760143e-06,
                3.466326624336003e-07,
                0.00010889687041282619,
                2.5612834320563895e-06,
                3.288747889284851e-06,
                4.450850519409479e-07,
                3.059022269254856e-07
            ],
            [
                5.715003107755449e-07,
                9.422445939054222e-07,
                4.450852111155216e-07,
                1.6373764721072816e-07,
                4.222834451382849e-06,
                1.4738987243478167e-05,
                1.209865539295696e-06,
                1.209865827752005e-06,
                4.222834954778007e-06,
                6.475949526020042e-07
            ],
            [
                7.338209805224048e-07,
                5.043474081993875e-07,
                6.475945666051092e-07,
                5.715003107755449e-07,
                8.315278294072958e-07,
                5.04347528446051e-07,
                5.715002426475718e-07,
                5.715005832886879e-07,
                2.382368815916736e-07,
                6.475951069985296e-07
            ],
            [
                0.9890130563978902,
                1.209866260432471e-06,
                0.9999706884722537,
                0.9940889316143973,
                4.785096776499213e-06,
                8.481102118021275e-05,
                7.338208055664991e-07,
                0.999986153992242,
                6.475947982037486e-07,
                0.9999861539971698
            ],
            [
                1.5534977545886537e-06,
                4.785096206076165e-06,
                1.0677026154774503e-06,
                6.962257079889302e-06,
                6.962257909842961e-06,
                6.60521210841897e-05,
                1.147877359957198e-05,
                3.927863407379485e-07,
                1.2098653950656417e-06,
                2.2603248367949354e-06
            ],
            [
                3.059021175261338e-07,
                1.637377643243723e-07,
                2.3823702359290413e-07,
                5.043473480777865e-07,
                1.8553905760062447e-07,
                1.637377643243723e-07,
                1.125352291309328e-07,
                1.8553919030858602e-07,
                2.102434412875379e-07,
                2.6995774527718623e-07
            ],
            [
                1.3709573702822306e-06,
                1.3709572068422585e-06,
                2.1024331597288867e-07,
                1.9947290081286418e-06,
                9.931187406410953e-08,
                6.475950297993789e-07,
                1.9947299593078385e-06,
                7.338209805224048e-07,
                1.553497384196656e-06,
                1.6373764721072816e-07
            ],
            [
                2.699578096393206e-07,
                2.382368531929327e-07,
                3.288750241561788e-06,
                3.2887502415438413e-06,
                0.9999949062956169,
                7.338207180864763e-07,
                2.1024341622426268e-07,
                3.0590215399183813e-07,
                0.9999706884615766,
                1.0129995810463632e-05
            ],
            [
                4.222834954280646e-06,
                8.315280276607289e-07,
                3.9278634073732336e-07,
                1.5534975693933505e-06,
                1.3709567165579959e-06,
                3.2887482812745586e-06,
                1.3709567165617364e-06,
                2.902312331170226e-06,
                1.760342793583908e-06,
                4.222834954607099e-06
            ],
            [
                3.726637951387472e-06,
                4.2228339479858295e-06,
                0.9999892166878476,
                2.5612828213690224e-06,
                1.3709572068522336e-06,
                5.422219616265831e-06,
                0.9999945777823351,
                8.481107172292919e-05,
                1.994729008145876e-06,
                0.9999967112505482
            ],
            [
                1.4449798650551755e-07,
                9.931186222523604e-08,
                2.561281294760143e-06,
                8.315279285351409e-07,
                4.22283545819819e-06,
                2.90231233114251e-06,
                1.5534981249697903e-06,
                5.715005151606823e-07,
                3.927863875616689e-07,
                6.475946438055299e-07
            ],
            [
                1.1253513522447425e-07,
                4.1399375473868e-08,
                3.653482080235082e-08,
                1.275190428875671e-07,
                1.855391681898159e-07,
                9.931187406410953e-08,
                8.76424013786396e-08,
                6.023576347315567e-08,
                5.3157811697009444e-08,
                9.931202796993203e-08
            ],
            [
                NaN,
                2.902312677150514e-06,
                5.715004470313855e-07,
                2.1024331597262577e-07,
                0.9999667857937159,
                4.450852111148132e-07,
                6.475950298011458e-07,
                1.0677029973219343e-06,
                4.785096206076165e-06,
                2.382370235933104e-07
            ],
            [
                1.0677032518814388e-06,
                1.7603425837903113e-06,
                3.9278605979534166e-07,
                3.0590233632400716e-07,
                7.338208930460318e-07,
                2.902312677150514e-06,
                5.715005832886879e-07,
                1.6373766672973748e-07,
                6.475947982037486e-07,
                5.043472278322555e-07
            ],
            [
                6.47594566597747e-07,
                4.450851580540182e-07,
                4.450849988811838e-07,
                5.043474081993875e-07,
                5.715007195410849e-07,
                5.043475885634304e-07,
                4.4508505193386385e-07,
                3.9278610661902853e-07,
                7.338208055613267e-07,
                6.475950297993789e-07
            ],
            [
                2.699576809143613e-07,
                2.3823696679327928e-07,
                1.27519088491875e-07,
                9.422447062294175e-07,
                1.2751902768612997e-07,
                3.927863875616689e-07,
                6.47595107001401e-07,
                5.04347287955046e-07,
                2.1024336609843824e-07,
                3.059022269250683e-07
            ],
            [
                1.2751908849167202e-07,
                5.3157837044597743e-08,
                2.69957906184239e-07,
                1.855391239544352e-07,
                1.4449805540763184e-07,
                7.734416698849138e-08,
                1.6373770576776313e-07,
                1.275190580890061e-07,
                1.2751901248454963e-07,
                2.102434162245973e-07
            ],
            [
                NaN,
                1.0129987357517693e-05,
                7.338213304316717e-07,
                1.7603436330259153e-06,
                6.144173869603344e-06,
                5.715006514105942e-07,
                2.90231094723893e-06,
                5.043475885674441e-07,
                3.2887478892683997e-06,
                3.7266410611296085e-06
            ],
            [
                2.902313369111213e-06,
                5.04347468323289e-07,
                1.3709575337159875e-06,
                2.260324836787226e-06,
                5.71500515161527e-07,
                5.715003789046955e-07,
                4.785094494811783e-06,
                1.209865827752005e-06,
                NaN,
                3.288747889284851e-06
            ],
            [
                2.1444950613748295e-05,
                3.2887506336235617e-06,
                1.994729008145876e-06,
                1.9947301970972664e-06,
                1.994729008145876e-06,
                1.3709568799919866e-06,
                2.2603234895372223e-06,
                3.4663274507713016e-07,
                4.4508515805735777e-07,
                2.2603251062450327e-06
            ],
            [
                3.726638839878908e-06,
                2.2603253756956754e-06,
                1.9947304348862686e-06,
                NaN,
                1.0677024882009222e-06,
                1.0677032518785256e-06,
                3.466325384678894e-07,
                2.9023133690980155e-06,
                7.889263526345123e-06,
                9.422445939054222e-07
            ],
            [
                2.699578740032504e-07,
                4.4508510499849186e-07,
                1.1253522913127183e-07,
                1.4449805540763184e-07,
                1.7603434231833873e-06,
                2.382369951932796e-07,
                8.315278294114555e-07,
                4.450850519403407e-07,
                3.927862002663297e-07,
                1.0677027427600627e-06
            ],
            [
                1.012999098021058e-05,
                2.4300243631890864e-05,
                3.4663278639892215e-07,
                1.6701421845361053e-05,
                1.855391239547094e-07,
                1.1253525596174225e-07,
                5.4222183235249605e-06,
                1.4449803818215767e-07,
                0.999796573003814,
                1.012999098021058e-05
            ],
            [
                4.450851049959619e-07,
                0.9999982396570005,
                5.043473480777865e-07,
                3.288749457469787e-06,
                0.9999945777803968,
                0.9999934595620315,
                2.2603234895372223e-06,
                1.5534973842076057e-06,
                1.3709570434178922e-06,
                2.5612828213934817e-06
            ],
            [
                3.9278629391427843e-07,
                2.699576809143613e-07,
                1.8553905760062447e-07,
                3.9278605979534166e-07,
                4.450850519403407e-07,
                1.855391239547094e-07,
                3.46632497145457e-07,
                2.382369951932796e-07,
                2.10243290909724e-07,
                5.043473480777865e-07
            ],
            [
                8.315277302841894e-07,
                1.2751899728286965e-07,
                2.699578096403948e-07,
                9.931193325852072e-08,
                8.315278294097538e-07,
                7.338207180884785e-07,
                1.2098652508424818e-06,
                1.067702870039777e-06,
                9.422450432014836e-07,
                1.553497199007048e-06
            ],
            [
                2.561281905390075e-06,
                2.9023133690821773e-06,
                2.2603237589542675e-06,
                1.012999581021488e-05,
                7.338209805200689e-07,
                2.9023116391675407e-06,
                8.939697369785323e-06,
                2.902312331125353e-06,
                6.962259569484628e-06,
                0.0001233945603033627
            ],
            [
                3.466325797896173e-07,
                2.6995790618469934e-07,
                2.699577774585891e-07,
                7.338208055664991e-07,
                0.9999969105055584,
                1.444979692800516e-07,
                5.71500515159253e-07,
                3.059022998576899e-07,
                1.6373762769138607e-07,
                3.0590237279032884e-07
            ],
            [
                NaN,
                1.0677033791612137e-06,
                NaN,
                6.47594952603035e-07,
                1.637376862489725e-07,
                4.450850519403407e-07,
                2.699576809143613e-07,
                NaN,
                1.5534983101602148e-06,
                2.699577774589574e-07
            ],
            [
                9.422448185534261e-07,
                0.9999987901340291,
                1.7603438428800754e-06,
                5.715005151606823e-07,
                3.4663274507713016e-07,
                8.315284241665078e-07,
                1.0677026154806063e-06,
                2.260323758987159e-06,
                1.0677029973219343e-06,
                5.04347528446051e-07
            ],
            [
                5.043475885696228e-07,
                0.9999785550440244,
                NaN,
                0.9999904837460691,
                1.2098659719788098e-06,
                1.3709572068478697e-06,
                0.9999921107374254,
                5.715007195447234e-07,
                0.9999843104559085,
                1.5534971990126997e-06
            ],
            [
                4.785095065232451e-06,
                3.4663278639892215e-07,
                0.9999898700078382,
                6.9622537599680095e-06,
                0.9999938558239487,
                1.9947299593078385e-06,
                9.4224425692559e-07,
                0.9999980052705192,
                5.715004470313855e-07,
                9.422449308748773e-07
            ],
            [
                3.466326624336003e-07,
                2.1024334103505245e-07,
                4.4508515805735777e-07,
                1.4449805540700758e-07,
                1.3709576971463352e-06,
                9.422442569334097e-07,
                2.3823693839325527e-07,
                1.6373762769138607e-07,
                3.466326624336003e-07,
                1.4449800373065699e-07
            ],
            [
                2.699578096403948e-07,
                2.3823693839325527e-07,
                8.315278294114555e-07,
                5.715004470326849e-07,
                2.9023119851781017e-06,
                2.1024341622426268e-07,
                4.4508515805735777e-07,
                NaN,
                8.315277302857965e-07,
                3.466326624336003e-07
            ],
            [
                3.0590219045914655e-07,
                9.931202796993203e-08,
                1.2751902768612997e-07,
                8.764253720001207e-08,
                1.3709572068522336e-06,
                1.4449795205472734e-07,
                6.023577065381482e-08,
                3.726641061109272e-06,
                1.9947301970972664e-06,
                9.422443692489024e-07
            ],
            [
                5.715003789033962e-07,
                1.2098661161789477e-06,
                2.902312677137316e-06,
                1.9947299593014888e-06,
                1.553497754577351e-06,
                7.48462005189952e-05,
                2.561283432035425e-06,
                1.0129992187400498e-05,
                2.9023119851635836e-06,
                3.288749065423109e-06
            ],
            [
                0.9999962733616208,
                0.9999982396574177,
                0.9999974387184052,
                2.2603242978871282e-06,
                1.5534979397592542e-06,
                0.9999916019290066,
                0.9999949062931898,
                0.9999964991447668,
                0.9999949062925794,
                0.9999955048163
            ],
            [
                NaN,
                7.338208930460318e-07,
                2.144494585747154e-05,
                7.889264466725156e-06,
                7.484626294256741e-05,
                6.962257909842961e-06,
                NaN,
                3.059022998576899e-07,
                1.3709575337016483e-06,
                3.0590237279085045e-07
            ],
            [
                2.9023126771227976e-06,
                1.2098662604247682e-06,
                1.0677028700130727e-06,
                1.9947297215043796e-06,
                1.5534975693792215e-06,
                1.7603427936079236e-06,
                1.067702615468225e-06,
                8.315281267861397e-07,
                1.8925143729575624e-05,
                2.561282210729555e-06
            ],
            [
                1.994729008151319e-06,
                NaN,
                1.0677026154774503e-06,
                6.47595107001401e-07,
                8.31528126775552e-07,
                2.260325106237323e-06,
                9.93120161310289e-08,
                2.5612828213818346e-06,
                5.043473480777865e-07,
                1.0677031245953668e-06
            ],
            [
                4.222834954778007e-06,
                3.2887490653872164e-06,
                9.4224425692559e-07,
                2.260324567337161e-06,
                1.3709573702647743e-06,
                3.7266406168624155e-06,
                2.260323489490968e-06,
                NaN,
                2.9023119851781017e-06,
                5.715002426486762e-07
            ],
            [
                5.043473480777865e-07,
                3.4663249714612693e-07,
                0.9999687980812931,
                2.2603234895372223e-06,
                0.9999485577989785,
                0.9999151889593648,
                0.999948557762058,
                0.99999649914559,
                0.9999964991447537,
                0.9999785550439568
            ],
            [
                8.315280276607289e-07,
                8.315277302819205e-07,
                4.785093924389007e-06,
                2.10243290909724e-07,
                3.7266406168827523e-06,
                1.444979692800516e-07,
                1.5534977545886537e-06,
                1.8553919030858602e-07,
                3.653482080235082e-08,
                8.315277302857965e-07
            ],
            [
                2.5612819054133693e-06,
                4.785094494783494e-06,
                7.889263526345123e-06,
                0.9999798543141724,
                2.4300252321904572e-05,
                8.939693107288474e-06,
                0.9999573525227659,
                5.422218969895357e-06,
                1.670141786295194e-05,
                0.9999573525120168
            ],
            [
                1.3709576971463352e-06,
                5.043476486924565e-07,
                6.47595107001401e-07,
                1.2098656835224664e-06,
                1.0677027427624903e-06,
                4.785094494811783e-06,
                7.338209805224048e-07,
                6.47595107001401e-07,
                3.9278610661902853e-07,
                5.715005832895975e-07
            ]
        ]
    },
    {
        "q_id": "10284_mmlu_physics",
        "cot_ids": [
            0,
            1,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            16,
            17,
            18,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            90,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.9023119851899796e-06,
                NaN,
                1.760342793638743e-06,
                3.9278620026686556e-07,
                NaN,
                4.450848927658745e-07,
                6.47595107001401e-07,
                1.3709572068522336e-06,
                5.71500515161527e-07,
                9.422445939054222e-07
            ],
            [
                NaN,
                6.475947210031623e-07,
                NaN,
                1.209865539295696e-06,
                4.450850519403407e-07,
                2.9023116391978967e-06,
                3.927862939126708e-07,
                1.3709575337159875e-06,
                5.043475284468537e-07,
                4.450852111148132e-07
            ],
            [
                9.422448185534261e-07,
                7.338207180898968e-07,
                5.043475885696228e-07,
                6.475947210031623e-07,
                2.2603234895372223e-06,
                1.209865539295696e-06,
                NaN,
                2.699578096403948e-07,
                5.04347468323289e-07,
                1.9947301970972664e-06
            ],
            [
                5.422219616265831e-06,
                1.0677027427600627e-06,
                3.2887506336235617e-06,
                8.315279285370317e-07,
                6.475947982037486e-07,
                4.222835458148261e-06,
                2.2603242978871282e-06,
                1.9947301970972664e-06,
                8.315282259138311e-07,
                NaN
            ],
            [
                NaN,
                2.382369951932796e-07,
                3.726639284144195e-06,
                2.561281294760143e-06,
                5.043475885696228e-07,
                1.7603425837903113e-06,
                5.71500719545698e-07,
                2.6995790618469934e-07,
                2.699578740032504e-07,
                2.5612819054028872e-06
            ],
            [
                1.5534975693933505e-06,
                6.962259569750576e-06,
                1.5534983101602148e-06,
                1.760343213335281e-06,
                1.2098658277451275e-06,
                2.561281294760143e-06,
                7.338211554783522e-07,
                6.475950298011458e-07,
                1.2098652508424818e-06,
                1.5534977545886537e-06
            ],
            [
                NaN,
                NaN,
                1.7603434231777837e-06,
                1.5534979397790343e-06,
                1.1478770862735993e-05,
                4.222834954753043e-06,
                5.4222209089700225e-06,
                NaN,
                1.7603438428800754e-06,
                6.1441746020359e-06
            ],
            [
                6.475948754012522e-07,
                9.422443692574719e-07,
                7.338207180898968e-07,
                1.5534975693979422e-06,
                NaN,
                3.9278605979534166e-07,
                8.315282259138311e-07,
                6.47595107001401e-07,
                3.05902263391829e-07,
                1.5534984953552536e-06
            ],
            [
                NaN,
                1.370957860576702e-06,
                7.33821330437595e-07,
                8.315284241650899e-07,
                8.315277302857965e-07,
                3.288748673319648e-06,
                4.4508515805735777e-07,
                NaN,
                NaN,
                NaN
            ],
            [
                1.994729721518893e-06,
                5.715003789046955e-07,
                1.3709575337159875e-06,
                7.338213304363436e-07,
                NaN,
                5.043473480777865e-07,
                NaN,
                9.422444815814404e-07,
                2.5612819054133693e-06,
                1.0677028700422047e-06
            ],
            [
                1.0677028700422047e-06,
                1.0677029973219343e-06,
                8.315277302841894e-07,
                1.3709570434219446e-06,
                4.450852111155216e-07,
                3.927863407379485e-07,
                4.539787406217992e-05,
                6.475945666063607e-07,
                NaN,
                5.043473480777865e-07
            ],
            [
                1.0677024882009222e-06,
                1.0677031245990084e-06,
                6.475945666051092e-07,
                4.0063696966212295e-05,
                1.5534971990169383e-06,
                6.475945666063607e-07,
                1.0677032518748838e-06,
                6.144177531767002e-06,
                1.7603432133296774e-06,
                3.7266410611296085e-06
            ],
            [
                1.2098653950692178e-06,
                7.338209805240734e-07,
                7.338208055664991e-07,
                4.450848927658745e-07,
                1.3709573702822306e-06,
                8.315283250371857e-07,
                4.785096206076165e-06,
                2.561282516066741e-06,
                4.450848927658745e-07,
                1.209866260432471e-06
            ],
            [
                6.962259569750576e-06,
                9.422443692555439e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                1.5534983101644536e-06,
                NaN,
                1.209865539298447e-06,
                2.9023119851781017e-06
            ],
            [
                1.994730434879465e-06,
                1.2098653950656417e-06,
                2.2603251062450327e-06,
                1.9947299593078385e-06,
                3.7266410611296085e-06,
                6.144177531660828e-06,
                1.7603430034867993e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                6.47595107001401e-07,
                NaN,
                NaN,
                7.338208930460318e-07,
                NaN,
                5.043475885696228e-07,
                5.715002426486762e-07,
                NaN,
                5.04347468323289e-07,
                NaN
            ],
            [
                5.715005151606823e-07,
                5.715003107755449e-07,
                1.7603434231833873e-06,
                3.9278610661902853e-07,
                NaN,
                NaN,
                2.699578740032504e-07,
                6.962254589978262e-06,
                NaN,
                1.067703124601679e-06
            ],
            [
                1.760343213335281e-06,
                1.760343213335281e-06,
                6.962258739796719e-06,
                5.4222183235249605e-06,
                5.4222183235249605e-06,
                1.2098661162056318e-06,
                7.889266347786918e-06,
                1.300712536408621e-05,
                6.475948754012522e-07,
                2.2603248367949354e-06
            ],
            [
                1.067703124601679e-06,
                6.475947210046347e-07,
                6.475947210046347e-07,
                5.715003789046955e-07,
                9.422445939054222e-07,
                NaN,
                NaN,
                6.475950298011458e-07,
                8.315280276626197e-07,
                5.715003789046955e-07
            ],
            [
                6.475950298011458e-07,
                9.422445939054222e-07,
                7.889265407004852e-06,
                1.0677032518814388e-06,
                1.5534981249697903e-06,
                1.5534975693979422e-06,
                1.209866260432471e-06,
                1.3709572068478697e-06,
                1.2098662604291696e-06,
                6.962255419931625e-06
            ],
            [
                1.5534971990126997e-06,
                8.939696304311336e-06,
                5.043474683204221e-07,
                6.144176799334096e-06,
                NaN,
                4.450848927658745e-07,
                3.466325797896173e-07,
                2.2603234895176927e-06,
                3.7266406168624155e-06,
                3.466325797896173e-07
            ],
            [
                1.760342793638743e-06,
                1.2098656835252174e-06,
                6.144175334468545e-06,
                1.994729483729522e-06,
                NaN,
                3.2887506336235617e-06,
                NaN,
                NaN,
                2.699578740032504e-07,
                4.785094494783494e-06
            ],
            [
                7.338208930460318e-07,
                6.475947210012481e-07,
                9.422450432014836e-07,
                2.561283432035425e-06,
                NaN,
                4.222834451355964e-06,
                1.760343003481596e-06,
                1.2098658277489788e-06,
                1.9947292459265734e-06,
                8.315283250371857e-07
            ],
            [
                2.5612819054028872e-06,
                4.785092783519724e-06,
                6.144172404693786e-06,
                4.785096776468749e-06,
                1.7603434231833873e-06,
                NaN,
                4.785096776468749e-06,
                3.2887478892683997e-06,
                1.4738983729294318e-05,
                1.0129995810463632e-05
            ],
            [
                2.2603248367949354e-06,
                NaN,
                5.715002426475718e-07,
                9.422449308774482e-07,
                1.209866260432471e-06,
                1.2098662604192665e-06,
                2.561282210740037e-06,
                1.7603440527286572e-06,
                1.3709570434178922e-06,
                1.2098659719757836e-06
            ],
            [
                6.144177531767002e-06,
                NaN,
                3.726637951387472e-06,
                3.288749065406658e-06,
                5.043474081993875e-07,
                2.902313023130843e-06,
                NaN,
                4.222835458175145e-06,
                6.475947210031623e-07,
                4.450848927658745e-07
            ],
            [
                1.473898900066424e-05,
                5.715006514176113e-07,
                6.475947210031623e-07,
                1.0677032518748838e-06,
                1.4738980215593877e-05,
                3.7266401726359486e-06,
                2.2603234895289998e-06,
                4.2228339479858295e-06,
                1.3709567165530083e-06,
                NaN
            ],
            [
                1.0677028700422047e-06,
                5.422217677152175e-06,
                NaN,
                2.2603237589779086e-06,
                1.3709576971425944e-06,
                2.3823685319320354e-07,
                1.9947292459347367e-06,
                NaN,
                NaN,
                1.994730197090463e-06
            ],
            [
                9.422444815792981e-07,
                1.0677026154806063e-06,
                4.785093924330255e-06,
                NaN,
                7.338210679979539e-07,
                1.9947299593014888e-06,
                2.561282821402217e-06,
                1.2098656835224664e-06,
                9.422443692489024e-07,
                NaN
            ],
            [
                2.2603234895372223e-06,
                1.7603438428800754e-06,
                0.9999916019289823,
                1.9947299593078385e-06,
                8.315279285370317e-07,
                NaN,
                9.422447062294175e-07,
                NaN,
                1.3709576971463352e-06,
                NaN
            ],
            [
                3.466326211113502e-07,
                3.927862939126708e-07,
                3.466327037553825e-07,
                NaN,
                1.5534984953552536e-06,
                7.338208055680009e-07,
                1.8553919030858602e-07,
                1.5534983101644536e-06,
                9.422444815814404e-07,
                1.2098659719788098e-06
            ],
            [
                NaN,
                9.422442569290178e-07,
                2.2603251062270446e-06,
                4.785093924330255e-06,
                1.0677027427569065e-06,
                1.2098661162056318e-06,
                7.88926070489716e-06,
                2.260325375677174e-06,
                1.5534981249697903e-06,
                2.902313369111213e-06
            ],
            [
                NaN,
                3.9278629391427843e-07,
                1.760342793638743e-06,
                NaN,
                1.6373764721091427e-07,
                2.1024336609843824e-07,
                1.9947297215125433e-06,
                NaN,
                3.466325797900508e-07,
                3.288749457469787e-06
            ],
            [
                4.4508510499849186e-07,
                1.370957860576702e-06,
                2.902312331170226e-06,
                2.2603251062450327e-06,
                9.422447062294175e-07,
                6.47595107001401e-07,
                6.475947210046347e-07,
                1.2098656835252174e-06,
                NaN,
                1.0677032518814388e-06
            ],
            [
                1.7603436330259153e-06,
                3.927862002663297e-07,
                4.5397884884891014e-05,
                6.144173869603344e-06,
                0.0013250224948536187,
                3.288749457469787e-06,
                5.715003789017068e-07,
                4.450848927650143e-07,
                9.422448185478557e-07,
                NaN
            ],
            [
                1.0677027427525368e-06,
                2.102434162245973e-07,
                1.5534981249697903e-06,
                1.275190580890061e-07,
                1.2098656835224664e-06,
                NaN,
                3.726637951387472e-06,
                1.3709575337125585e-06,
                2.102434162245973e-07,
                2.5612819054028872e-06
            ],
            [
                1.0677029973192638e-06,
                7.338212429582604e-07,
                1.209865827752005e-06,
                1.5534975693979422e-06,
                1.0677024882009222e-06,
                1.7603436330259153e-06,
                7.338207180864763e-07,
                1.9947292459265734e-06,
                2.2603251062450327e-06,
                9.422442569208767e-07
            ],
            [
                7.338212429582604e-07,
                5.043472879540142e-07,
                1.3709567165617364e-06,
                5.715005151606823e-07,
                NaN,
                2.3823688159291947e-07,
                6.962257909842961e-06,
                9.422450432014836e-07,
                NaN,
                7.338208930460318e-07
            ],
            [
                5.715003789046955e-07,
                3.7266406168827523e-06,
                2.902313023039776e-06,
                3.7266401725681614e-06,
                5.422219616085833e-06,
                1.7603436330179102e-06,
                8.93969736955767e-06,
                2.9023130230846496e-06,
                5.422217677078203e-06,
                1.7603436329978976e-06
            ],
            [
                7.338212429582604e-07,
                NaN,
                NaN,
                1.7603436330259153e-06,
                1.2751902768612997e-07,
                8.315277302841894e-07,
                2.902312331170226e-06,
                7.338209805224048e-07,
                6.475947982037486e-07,
                6.475946438055299e-07
            ],
            [
                1.7603425837791042e-06,
                1.067702870039777e-06,
                NaN,
                2.902313369111213e-06,
                9.422442569290178e-07,
                2.260324567337161e-06,
                8.315280276626197e-07,
                9.422448185534261e-07,
                1.5534981249697903e-06,
                1.9947292459347367e-06
            ],
            [
                4.222831934202483e-06,
                9.422450431989127e-07,
                1.209865539295696e-06,
                1.7603436330259153e-06,
                6.475946438022905e-07,
                7.338209805170655e-07,
                1.9947299593014888e-06,
                1.9947299593014888e-06,
                9.422449308716635e-07,
                1.55349775456958e-06
            ],
            [
                3.726638395611981e-06,
                3.288749457469787e-06,
                2.902312331170226e-06,
                3.288748281329893e-06,
                NaN,
                2.5612812947508257e-06,
                NaN,
                1.209866260432471e-06,
                3.726638395611981e-06,
                3.726638395634011e-06
            ],
            [
                NaN,
                9.422448185534261e-07,
                2.6995790618469934e-07,
                3.9278610661902853e-07,
                NaN,
                5.715002426486762e-07,
                1.5534984953552536e-06,
                NaN,
                1.3709572068522336e-06,
                NaN
            ],
            [
                7.338210680021253e-07,
                1.370957860576702e-06,
                2.2603253756956754e-06,
                1.0677027427624903e-06,
                NaN,
                2.699578096403948e-07,
                3.726638839878908e-06,
                6.475945666063607e-07,
                7.338213304363436e-07,
                1.760342793638743e-06
            ],
            [
                1.994729008145876e-06,
                9.422450432014836e-07,
                1.760342793638743e-06,
                9.422447062294175e-07,
                1.2098652508424818e-06,
                NaN,
                6.475947982037486e-07,
                1.2098653950656417e-06,
                2.6995784182140636e-07,
                8.315283250394546e-07
            ],
            [
                1.0,
                NaN,
                NaN,
                3.059022998581767e-07,
                2.699578096403948e-07,
                5.71500719545698e-07,
                3.9278610661902853e-07,
                6.47595107001401e-07,
                5.043475885696228e-07,
                NaN
            ],
            [
                5.043476486924565e-07,
                5.043476486924565e-07,
                NaN,
                4.450848927650143e-07,
                3.927863407379485e-07,
                5.043476486924565e-07,
                5.715005832886879e-07,
                1.209866260432471e-06,
                NaN,
                5.715005151606823e-07
            ],
            [
                1.2098659719788098e-06,
                6.47595107001401e-07,
                NaN,
                2.9023116392097746e-06,
                3.2887478892683997e-06,
                1.0677032518814388e-06,
                6.962257909842961e-06,
                1.9947292459347367e-06,
                1.5534973842076057e-06,
                NaN
            ],
            [
                2.2603242978871282e-06,
                5.715005151606823e-07,
                3.4663274507713016e-07,
                8.315279285351409e-07,
                6.475945666063607e-07,
                8.315279285370317e-07,
                2.9023119851781017e-06,
                2.2603251062450327e-06,
                NaN,
                4.785096206076165e-06
            ],
            [
                NaN,
                1.5534983101644536e-06,
                5.422221555414699e-06,
                NaN,
                NaN,
                NaN,
                7.889260704968913e-06,
                1.0677028700422047e-06,
                1.7603432133296774e-06,
                3.726639284144195e-06
            ],
            [
                3.05902336324494e-07,
                1.5534984953510149e-06,
                6.144176066901277e-06,
                7.338208930443633e-07,
                1.3709568799919866e-06,
                NaN,
                6.475950298021765e-07,
                2.2603234895372223e-06,
                1.5534971990126997e-06,
                6.962254589978262e-06
            ],
            [
                3.9278605979534166e-07,
                3.927862002663297e-07,
                1.2098655392871682e-06,
                3.466326624322211e-07,
                3.927862939126708e-07,
                1.2098653950656417e-06,
                8.315281267861397e-07,
                8.315278294072958e-07,
                9.422447062202052e-07,
                3.059021175261338e-07
            ],
            [
                8.315277302841894e-07,
                4.785095065232451e-06,
                1.2098652508424818e-06,
                6.9622537599680095e-06,
                3.726639284144195e-06,
                1.0677029973219343e-06,
                NaN,
                1.0677026154806063e-06,
                1.7603425837903113e-06,
                0.9999910603058416
            ],
            [
                9.422444815814404e-07,
                NaN,
                1.7603434231833873e-06,
                0.0,
                NaN,
                NaN,
                2.561282210740037e-06,
                3.7266383956509585e-06,
                1.067703124601679e-06,
                NaN
            ],
            [
                1.4449798650569826e-07,
                9.422443692574719e-07,
                NaN,
                3.059022998581767e-07,
                3.059022998581767e-07,
                NaN,
                9.422445939054222e-07,
                NaN,
                1.3709575337159875e-06,
                5.715003789046955e-07
            ],
            [
                1.30071315662049e-05,
                1.5534983101602148e-06,
                NaN,
                NaN,
                NaN,
                2.2603248367949354e-06,
                8.315283250371857e-07,
                8.315283250371857e-07,
                5.04347287955046e-07,
                9.422442569315887e-07
            ],
            [
                3.288748673360027e-06,
                3.288749457469787e-06,
                2.561282210740037e-06,
                5.043472879540142e-07,
                3.726639284144195e-06,
                1.7603434231777837e-06,
                NaN,
                NaN,
                8.315279285370317e-07,
                NaN
            ],
            [
                7.338208055680009e-07,
                3.059022269254856e-07,
                1.3709567165617364e-06,
                1.5534981249736758e-06,
                8.315278294114555e-07,
                4.7850933539684755e-06,
                3.059022998581767e-07,
                5.715003107767143e-07,
                9.422442569315887e-07,
                1.209866260432471e-06
            ],
            [
                7.338208055680009e-07,
                4.222832437747125e-06,
                1.4738989000422955e-05,
                1.1478770862882149e-05,
                3.9278634073732336e-07,
                5.04347468323289e-07,
                5.043473480777865e-07,
                2.3823696679327928e-07,
                1.209865827752005e-06,
                6.475947210046347e-07
            ],
            [
                2.9023116391978967e-06,
                2.9023133690821773e-06,
                1.0677032518814388e-06,
                3.2887506335906595e-06,
                1.067703379154416e-06,
                6.962255419804982e-06,
                8.315278294097538e-07,
                1.5534979397740895e-06,
                1.7603436330259153e-06,
                9.422444815726566e-07
            ],
            [
                1.994729483694599e-06,
                NaN,
                1.76034300345598e-06,
                8.315284241650899e-07,
                1.2098655392871682e-06,
                NaN,
                1.3709567165461505e-06,
                NaN,
                5.4222183235249605e-06,
                1.5534979397677313e-06
            ],
            [
                NaN,
                3.927862470905692e-07,
                5.715002426460124e-07,
                NaN,
                5.043476486924565e-07,
                NaN,
                1.1478770862882149e-05,
                1.2098656835252174e-06,
                2.3823690999323465e-07,
                3.466326211113502e-07
            ],
            [
                NaN,
                6.144172404738491e-06,
                7.88926446679691e-06,
                6.144176799334096e-06,
                9.422442569315887e-07,
                1.7603425837791042e-06,
                3.7266401725681614e-06,
                NaN,
                1.2098662604291696e-06,
                1.553498124964492e-06
            ],
            [
                1.3709573702822306e-06,
                1.2098652508391807e-06,
                3.726638839878908e-06,
                3.726639728370556e-06,
                1.7603425837606927e-06,
                2.561282516066741e-06,
                6.962254589851619e-06,
                5.715006514176113e-07,
                3.288748673376478e-06,
                1.994730197090463e-06
            ],
            [
                1.0677027427600627e-06,
                3.726637951367137e-06,
                NaN,
                1.2098652508391807e-06,
                5.422217030747413e-06,
                2.5612831267202583e-06,
                4.785096776433933e-06,
                1.3709576971425944e-06,
                9.422445939002803e-07,
                1.2098656835136636e-06
            ],
            [
                4.450852641737424e-07,
                1.0677029973219343e-06,
                4.450850519409479e-07,
                1.2098662604291696e-06,
                2.102434162245973e-07,
                7.338208055680009e-07,
                3.059022998581767e-07,
                7.338208055680009e-07,
                8.315280276626197e-07,
                2.3823690999323465e-07
            ],
            [
                NaN,
                1.2098652508424818e-06,
                NaN,
                NaN,
                NaN,
                4.222833444590791e-06,
                NaN,
                2.260323758987159e-06,
                6.144172404738491e-06,
                1.9947304348862686e-06
            ],
            [
                9.422444815814404e-07,
                NaN,
                NaN,
                6.144175334468545e-06,
                3.9278605979534166e-07,
                1.2098656835224664e-06,
                NaN,
                6.475948754012522e-07,
                5.043476486924565e-07,
                2.6995784182183607e-07
            ],
            [
                3.9278629391427843e-07,
                NaN,
                1.444980209564556e-07,
                5.715005832886879e-07,
                4.450850519409479e-07,
                1.3709575337159875e-06,
                1.0677024882029858e-06,
                1.760342793638743e-06,
                1.0677026154827912e-06,
                1.6373770576776313e-07
            ],
            [
                5.04347528446051e-07,
                NaN,
                1.994730672668496e-06,
                1.3709572068522336e-06,
                1.0677027427600627e-06,
                6.475949526020042e-07,
                5.715003107715166e-07,
                3.7266401726359486e-06,
                7.338211554783522e-07,
                3.726639284144195e-06
            ],
            [
                7.338207180898968e-07,
                6.475947210046347e-07,
                3.726639284144195e-06,
                1.0677027427624903e-06,
                NaN,
                8.315277302857965e-07,
                3.059022269254856e-07,
                5.71500515161527e-07,
                1.2098653950716937e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                2.902312677150514e-06,
                6.475948754028718e-07,
                NaN,
                1.209865539298447e-06,
                4.450848927658745e-07,
                1.3007126914612648e-05
            ],
            [
                1.994729483723626e-06,
                1.3709573702778664e-06,
                1.9947292459406333e-06,
                7.338210680002898e-07,
                9.422442569290178e-07,
                8.315284241650899e-07,
                2.5612812947508257e-06,
                3.53562549329801e-05,
                3.288749065423109e-06,
                5.422217030781934e-06
            ],
            [
                2.9023119851781017e-06,
                2.5612828213934817e-06,
                1.3709573702778664e-06,
                8.315279285351409e-07,
                2.902313023130843e-06,
                2.5612828213934817e-06,
                1.5534975693979422e-06,
                6.962255419868303e-06,
                1.7603434231777837e-06,
                4.222834954778007e-06
            ],
            [
                4.785096776499213e-06,
                8.315283250394546e-07,
                7.338208055680009e-07,
                5.715005832886879e-07,
                6.144173869603344e-06,
                1.5534983101644536e-06,
                1.5534971990169383e-06,
                1.7603438428800754e-06,
                5.422217677152175e-06,
                3.288748281329893e-06
            ],
            [
                1.3709575337159875e-06,
                5.715003107767143e-07,
                2.2603240284371276e-06,
                NaN,
                5.422219616265831e-06,
                NaN,
                7.338209805240734e-07,
                1.5534981249697903e-06,
                2.9023126771227976e-06,
                1.4738983729294318e-05
            ],
            [
                NaN,
                1.0677032518814388e-06,
                2.90231094723893e-06,
                2.26032402841657e-06,
                1.9947292459347367e-06,
                1.3709576971425944e-06,
                1.5534977545886537e-06,
                1.9947301970972664e-06,
                2.2603242978871282e-06,
                5.422217030747413e-06
            ],
            [
                1.3709567165579959e-06,
                2.9023130230846496e-06,
                2.2603253756956754e-06,
                1.0129988564974359e-05,
                6.475948754028718e-07,
                1.9947304348862686e-06,
                1.7603432133296774e-06,
                NaN,
                1.0677027427600627e-06,
                1.3709575337159875e-06
            ],
            [
                1.2098652508287273e-06,
                9.422448185435711e-07,
                2.561283432035425e-06,
                1.5534971990126997e-06,
                7.338212429562581e-07,
                2.260324567302214e-06,
                1.3709567165579959e-06,
                1.2098659719757836e-06,
                1.3709570434178922e-06,
                1.7603436329978976e-06
            ],
            [
                1.760342793638743e-06,
                2.699577130960941e-07,
                1.3709567165617364e-06,
                2.90231094723893e-06,
                6.475947982037486e-07,
                NaN,
                9.422448185534261e-07,
                3.288749457469787e-06,
                9.422445939054222e-07,
                NaN
            ],
            [
                2.3823702359290413e-07,
                2.6995771309523475e-07,
                1.1253525596174225e-07,
                5.715006514176113e-07,
                2.1024334103581732e-07,
                1.855391239547094e-07,
                NaN,
                2.699578096403948e-07,
                1.8553907971879076e-07,
                6.47594952603035e-07
            ],
            [
                2.561282210729555e-06,
                NaN,
                6.1441724046434924e-06,
                2.2603237589676295e-06,
                2.561282516066741e-06,
                3.288749065423109e-06,
                1.5534975693979422e-06,
                7.889259764445822e-06,
                2.2603240284371276e-06,
                1.9947299592933255e-06
            ],
            [
                2.382368815932174e-07,
                4.450852111155216e-07,
                3.05902336324494e-07,
                2.382368531929327e-07,
                1.275190580890061e-07,
                5.715003107767143e-07,
                3.9278610661902853e-07,
                3.059022998576899e-07,
                4.450852641737424e-07,
                2.902313023101807e-06
            ],
            [
                5.422217676200406e-06,
                7.338208055664991e-07,
                1.0677029973158649e-06,
                NaN,
                7.889262585814522e-06,
                1.5534979397677313e-06,
                6.962255419868303e-06,
                2.2603242978665707e-06,
                NaN,
                1.0677027427600627e-06
            ],
            [
                1.5534971990169383e-06,
                3.2887502415767434e-06,
                3.05902263391829e-07,
                9.422444815814404e-07,
                6.475947982037486e-07,
                9.422447062270609e-07,
                3.0590237279032884e-07,
                3.927861534431675e-07,
                1.3709576971463352e-06,
                1.0677027427624903e-06
            ],
            [
                1.067702870039777e-06,
                NaN,
                6.475947210031623e-07,
                7.338208930443633e-07,
                5.043474081993875e-07,
                1.7603436330259153e-06,
                8.315284241650899e-07,
                7.338208055680009e-07,
                1.3709575337125585e-06,
                9.422448185510695e-07
            ],
            [
                2.3823685319320354e-07,
                NaN,
                8.315284241650899e-07,
                5.043472278322555e-07,
                3.927863875616689e-07,
                3.466327037553825e-07,
                NaN,
                2.902312331170226e-06,
                1.3709567165617364e-06,
                8.315279285370317e-07
            ],
            [
                5.715007195447234e-07,
                2.561283432035425e-06,
                6.475949526003845e-07,
                1.760343003481596e-06,
                NaN,
                NaN,
                NaN,
                1.3709575337078829e-06,
                2.1444953526969788e-05,
                1.7603427936335396e-06
            ],
            [
                NaN,
                1.7603425837791042e-06,
                2.561283432035425e-06,
                7.33821330437595e-07,
                NaN,
                NaN,
                NaN,
                9.422449308673789e-07,
                5.715006514176113e-07,
                NaN
            ],
            [
                3.4663266242969896e-07,
                4.4508505193791187e-07,
                1.9947294837154625e-06,
                6.475945666033422e-07,
                1.3709575337078829e-06,
                2.902311639183378e-06,
                2.260324567337161e-06,
                8.315278294097538e-07,
                1.147876949310201e-05,
                2.1444943300075563e-05
            ],
            [
                3.05902336324494e-07,
                NaN,
                5.715003789017068e-07,
                2.2603234895372223e-06,
                7.338207180898968e-07,
                NaN,
                5.422217677152175e-06,
                NaN,
                2.561281600086738e-06,
                NaN
            ],
            [
                1.9947304348862686e-06,
                7.889263526266196e-06,
                1.3007125363908762e-05,
                2.9023130231176453e-06,
                4.785096776499213e-06,
                2.5612816000646084e-06,
                1.3709572068522336e-06,
                1.553498495338299e-06,
                1.3709572068522336e-06,
                1.9947297215125433e-06
            ],
            [
                3.288749457469787e-06,
                1.2098659719757836e-06,
                1.994729008145876e-06,
                1.2098656835224664e-06,
                4.78509392429544e-06,
                1.370957860567974e-06,
                3.7266401726173067e-06,
                1.9947297215125433e-06,
                3.288747889284851e-06,
                1.3709567165579959e-06
            ],
            [
                9.422443692555439e-07,
                6.475951070002966e-07,
                7.338210680002898e-07,
                3.288749065423109e-06,
                6.47595107001401e-07,
                5.715005151606823e-07,
                9.422443692574719e-07,
                6.47595107001401e-07,
                1.994729008145876e-06,
                1.0129989772532511e-05
            ],
            [
                7.338210679979539e-07,
                3.927862470899887e-07,
                NaN,
                3.2887506336235617e-06,
                5.715003789046955e-07,
                5.04347528446051e-07,
                4.450850519403407e-07,
                1.0677027427600627e-06,
                1.5534979397740895e-06,
                2.5612812947508257e-06
            ],
            [
                1.370957860576702e-06,
                9.422450432014836e-07,
                5.715006514176113e-07,
                2.9023119851899796e-06,
                6.475946438055299e-07,
                1.209866260432471e-06,
                5.043476486924565e-07,
                NaN,
                5.422220262505697e-06,
                1.209866260432471e-06
            ],
            [
                9.422449308748773e-07,
                NaN,
                5.422218323487975e-06,
                7.338207180898968e-07,
                1.5534975693979422e-06,
                1.5534981249697903e-06,
                2.5612831267202583e-06,
                2.9023119851781017e-06,
                6.1441767993788005e-06,
                7.889262585886274e-06
            ],
            [
                1.994729483729522e-06,
                9.422447062294175e-07,
                NaN,
                9.422443692574719e-07,
                1.637376862489725e-07,
                1.994729483729522e-06,
                3.288749849529972e-06,
                NaN,
                1.7603425837903113e-06,
                1.209865539298447e-06
            ],
            [
                6.47595107001401e-07,
                1.5534979397829198e-06,
                2.2603245673443566e-06,
                8.315277302857965e-07,
                1.3709575337159875e-06,
                1.2098659719788098e-06,
                4.222834451403972e-06,
                NaN,
                4.4508515805735777e-07,
                NaN
            ],
            [
                1.3709572068522336e-06,
                8.315284241650899e-07,
                5.043475885696228e-07,
                2.3823688159291947e-07,
                0.9999945777784582,
                5.715005832886879e-07,
                5.715003107767143e-07,
                1.3709572068522336e-06,
                2.90231094723893e-06,
                7.338209805240734e-07
            ],
            [
                1.2098662604291696e-06,
                1.2098659719716573e-06,
                3.288749065423109e-06,
                3.7266383956509585e-06,
                NaN,
                1.7603430034743913e-06,
                1.760343003481596e-06,
                1.2098659719716573e-06,
                1.3709576971425944e-06,
                1.30071315662049e-05
            ],
            [
                6.47594952603035e-07,
                3.9278634073732336e-07,
                4.450850519403407e-07,
                5.043475885696228e-07,
                5.043472278322555e-07,
                1.855391239547094e-07,
                8.315282259138311e-07,
                8.315277302857965e-07,
                8.315280276626197e-07,
                9.422445939054222e-07
            ],
            [
                3.7266410611296085e-06,
                1.5534979397740895e-06,
                7.338208055664991e-07,
                3.7266383955882547e-06,
                NaN,
                1.0677027427471959e-06,
                2.90231094723893e-06,
                5.715004470313855e-07,
                7.338213304363436e-07,
                2.260325106237323e-06
            ],
            [
                1.3709573702822306e-06,
                3.4663278639892215e-07,
                1.7603430034867993e-06,
                5.04347468323289e-07,
                4.4508515805735777e-07,
                NaN,
                1.5534973842076057e-06,
                5.71500719545698e-07,
                4.450851049991497e-07,
                NaN
            ],
            [
                1.5534971990169383e-06,
                NaN,
                1.209865539295696e-06,
                NaN,
                NaN,
                2.2603234895372223e-06,
                5.043475885696228e-07,
                NaN,
                3.288747889229516e-06,
                2.9023109471689794e-06
            ],
            [
                1.5534977545497995e-06,
                3.726638839878908e-06,
                6.144176799283803e-06,
                1.9947294837154625e-06,
                3.2887502415438413e-06,
                1.2098655392921197e-06,
                1.2098656835224664e-06,
                2.9023133690980155e-06,
                1.7603425837702984e-06,
                2.902312677137316e-06
            ],
            [
                2.5612819054133693e-06,
                1.067703124601679e-06,
                1.5534984953552536e-06,
                1.5534973842076057e-06,
                1.0677026154806063e-06,
                1.3709576971463352e-06,
                1.3709572068522336e-06,
                1.994729483729522e-06,
                1.3709567165617364e-06,
                5.043476486924565e-07
            ],
            [
                NaN,
                4.450852641737424e-07,
                NaN,
                1.0677027427624903e-06,
                6.475946438055299e-07,
                4.785093353940187e-06,
                4.4508494582405734e-07,
                3.05902263391829e-07,
                NaN,
                NaN
            ],
            [
                4.222832437798974e-06,
                1.3709575337016483e-06,
                1.5534983101602148e-06,
                3.288748673376478e-06,
                7.889263526345123e-06,
                2.9023133690980155e-06,
                1.9947304348703948e-06,
                3.726637951387472e-06,
                2.2603245673279107e-06,
                1.994730672668496e-06
            ],
            [
                1.370957860576702e-06,
                8.315281267834927e-07,
                2.699577774589574e-07,
                NaN,
                6.962256249885085e-06,
                8.315279285370317e-07,
                2.902312677150514e-06,
                NaN,
                9.422447062294175e-07,
                NaN
            ],
            [
                2.5612834320563895e-06,
                4.450848927658745e-07,
                9.422445939032799e-07,
                NaN,
                NaN,
                5.04347287955046e-07,
                3.9278610661902853e-07,
                9.422442569334097e-07,
                5.715002426486762e-07,
                1.3709575337159875e-06
            ],
            [
                NaN,
                9.422442569290178e-07,
                3.2887486732358968e-06,
                5.715005832872586e-07,
                1.9947299593014888e-06,
                1.2098662604291696e-06,
                1.0129993395336818e-05,
                NaN,
                1.553497199007048e-06,
                4.222834954778007e-06
            ],
            [
                1.7603427936183298e-06,
                NaN,
                NaN,
                1.5534977545886537e-06,
                1.7603427936335396e-06,
                NaN,
                1.5534973842076057e-06,
                NaN,
                2.2603242978778778e-06,
                NaN
            ],
            [
                1.209866260432471e-06,
                3.927863875616689e-07,
                1.0677029973219343e-06,
                NaN,
                1.2098659719757836e-06,
                3.05902263391829e-07,
                5.043472278322555e-07,
                8.315279285370317e-07,
                NaN,
                5.04347468323289e-07
            ],
            [
                5.715003107767143e-07,
                1.370957860576702e-06,
                1.2098652508424818e-06,
                9.4224425692559e-07,
                1.147877359957198e-05,
                8.315279285370317e-07,
                NaN,
                2.5612834320563895e-06,
                NaN,
                7.338207180898968e-07
            ],
            [
                1.0677027427525368e-06,
                1.0677024881980089e-06,
                9.422442569315887e-07,
                1.0677032518814388e-06,
                6.475947982002148e-07,
                4.4508494582314646e-07,
                NaN,
                1.067702870039777e-06,
                9.422443692555439e-07,
                2.902312677150514e-06
            ]
        ]
    },
    {
        "q_id": "10098_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.067702615468225e-06,
                0.999991060300516,
                3.4663257978780455e-07,
                0.9999921107393112,
                0.9999964991468411,
                1.0129989772532511e-05,
                2.260324297853209e-06,
                5.422220262555012e-06,
                0.9999869928715501,
                0.9998911031173945
            ],
            [
                9.422447062202052e-07,
                8.315280276626197e-07,
                1.760343633031919e-06,
                1.760343423160973e-06,
                6.962259569750576e-06,
                1.5534983101602148e-06,
                5.043472879525233e-07,
                5.715003107767143e-07,
                0.9998766053963412,
                0.9999969105048165
            ],
            [
                0.99999457778039,
                0.9999861539971072,
                0.999997739675434,
                1.994729245917502e-06,
                0.9999967112521128,
                0.9999910603069027,
                0.9999970976887085,
                1.9947299593014888e-06,
                0.9999980052695664,
                0.9999925887219037
            ],
            [
                0.9999962733589404,
                0.9999945777797414,
                6.144173137170873e-06,
                0.999981074851787,
                1.9947294837154625e-06,
                3.927862939126708e-07,
                0.999995504819497,
                9.422448185510695e-07,
                1.4738983729535602e-05,
                5.715005832853093e-07
            ],
            [
                1.5534983101602148e-06,
                5.71500719545698e-07,
                1.8553903548231313e-07,
                5.043472879540142e-07,
                1.3709576971425944e-06,
                3.9278605979534166e-07,
                1.6373772528704005e-07,
                1.2098662604291696e-06,
                6.475950298011458e-07,
                4.450852111148132e-07
            ],
            [
                2.382369383923073e-07,
                1.4449800373118268e-07,
                0.9999885212359899,
                5.04347528446051e-07,
                0.9999974387180955,
                0.9998204720140016,
                0.9999942280772208,
                0.9999970976890534,
                0.9999967112497598,
                0.9999921107383599
            ],
            [
                5.043472879540142e-07,
                3.288749065423109e-06,
                2.5612812947508257e-06,
                7.338209805224048e-07,
                8.315284241650899e-07,
                5.715003107755449e-07,
                0.9999938558246686,
                5.043474081993875e-07,
                1.2098659719757836e-06,
                1.0677033791612137e-06
            ],
            [
                6.962257079832313e-06,
                5.422219616265831e-06,
                0.9998911031045381,
                0.9999687980998683,
                0.999995214906079,
                0.9999785550541752,
                2.9023133690980155e-06,
                0.9999962733616068,
                0.9999972735297309,
                3.726639728370556e-06
            ],
            [
                2.5612819054133693e-06,
                0.9999978766220446,
                0.9999988634358834,
                0.9999964991451703,
                0.9999983463102173,
                0.9999993524048932,
                0.9999964991464221,
                0.9999885212332523,
                0.9999599362983708,
                0.9999987121052454
            ],
            [
                0.9999975938976621,
                0.9999978766205264,
                0.9999985406230835,
                0.9999967112521128,
                0.9999982396569972,
                0.9999724643089597,
                0.9999910603069,
                0.9999983463104148,
                0.9999989322972574,
                0.9999978766217922
            ],
            [
                4.450850519360903e-07,
                9.422449308748773e-07,
                0.9999724643122326,
                6.475947210046347e-07,
                1.0677031245953668e-06,
                4.450852111148132e-07,
                4.450852111135988e-07,
                8.315281267834927e-07,
                1.2098662604291696e-06,
                9.422444815765128e-07
            ],
            [
                3.2887502415438413e-06,
                0.9999417087209483,
                0.9999898700078178,
                1.4738983729535602e-05,
                0.9999898700126536,
                0.9999785550516178,
                1.1253518888531272e-07,
                6.962257909785973e-06,
                0.9999910603037038,
                0.9999916019249706
            ],
            [
                0.9999910603026374,
                0.9999989322970031,
                0.9999930377404342,
                0.9999687980738071,
                0.9999985406243017,
                0.9999987901340285,
                0.999997438718401,
                1.5534981249574276e-06,
                1.2098659719716573e-06,
                5.04347528446051e-07
            ],
            [
                1.9947304348703948e-06,
                0.9999977396762422,
                0.9999983463106118,
                4.222835458117536e-06,
                0.9999339478555154,
                0.9999885212359866,
                0.9999251537998262,
                0.9999992188518559,
                0.9999984465015054,
                0.9999949062962141
            ],
            [
                0.9999921107393,
                0.9999967112509358,
                0.9999964991460042,
                2.5612812947508257e-06,
                0.9999930377437539,
                0.9999925887210174,
                6.475950298011458e-07,
                0.9999975938979478,
                2.9023130231176453e-06,
                5.04347287955046e-07
            ],
            [
                3.927860597945825e-07,
                0.9999910603037075,
                0.999981074856302,
                0.9999993524051248,
                0.9999974387184019,
                0.9999993106390371,
                5.422220262636381e-06,
                0.99999911484307,
                5.043474081993875e-07,
                0.999989216690361
            ],
            [
                5.043474081993875e-07,
                0.9999983463108089,
                0.9999952149055075,
                1.0677031245990084e-06,
                0.999984310446555,
                0.9999992661788449,
                0.9999417087071218,
                1.5534983101393749e-06,
                0.9999977396754334,
                0.9999969105044489
            ],
            [
                1.5534975693933505e-06,
                2.561281905390075e-06,
                2.1444953526969788e-05,
                1.9947301970813926e-06,
                1.760343213335281e-06,
                7.338212429504183e-07,
                1.2098662604291696e-06,
                7.338209805200689e-07,
                3.9278634073098236e-07,
                9.422444815765128e-07
            ],
            [
                1.5534984953453635e-06,
                3.927860597945825e-07,
                8.481107172971651e-05,
                6.475948754012522e-07,
                3.726638839878908e-06,
                1.012998977264307e-05,
                1.0677027427600627e-06,
                2.5612819054028872e-06,
                3.2887498495150166e-06,
                1.5534971990126997e-06
            ],
            [
                1.0129993395088066e-05,
                4.0063682641226247e-05,
                1.300713156582635e-05,
                1.5534975693792215e-06,
                2.902313023101807e-06,
                5.71500651413193e-07,
                1.067703379154416e-06,
                7.338213304283347e-07,
                7.484625403938018e-05,
                9.422450431989127e-07
            ],
            [
                1.2098661161927025e-06,
                0.999997438718401,
                0.9999981261246175,
                9.422447062270609e-07,
                7.338207180864763e-07,
                0.9999994284996895,
                0.999998239656158,
                0.9999993916406734,
                0.9999930377429255,
                9.422449308748773e-07
            ],
            [
                6.475947210012481e-07,
                6.144175334172377e-06,
                3.2887502413389517e-06,
                1.6701427818034747e-05,
                2.902313023063532e-06,
                5.715004470313855e-07,
                4.222832941072913e-06,
                8.315279285205827e-07,
                1.3709576971061233e-06,
                3.726638395611981e-06
            ],
            [
                2.260323758939877e-06,
                5.829127250399344e-05,
                8.315283250371857e-07,
                2.5612815999423112e-06,
                2.902313023101807e-06,
                1.8925145985895816e-05,
                6.962254589781966e-06,
                5.422221555340727e-06,
                6.962256249758443e-06,
                8.939693107288474e-06
            ],
            [
                0.9999852610110228,
                0.999998446502061,
                0.9999974387174857,
                1.2098662604291696e-06,
                0.9999985406239539,
                0.9999832985821511,
                0.9999974387165693,
                0.9999885212264065,
                0.9999957771650468,
                0.9999930377445851
            ],
            [
                0.9999885212277796,
                0.9999987901338846,
                0.9999962733602751,
                0.9999925887219003,
                0.9999957771675652,
                0.9999904837517176,
                0.9999925887183686,
                0.9999975938985227,
                0.9999843104428208,
                0.9999974387180959
            ],
            [
                0.9999969105040803,
                0.9999921107374189,
                7.338212429504183e-07,
                4.450850519403407e-07,
                2.1024331597262577e-07,
                1.209866260432471e-06,
                4.785094494750855e-06,
                7.338208930391909e-07,
                0.9999885212291443,
                3.9278615344178325e-07
            ],
            [
                0.9994472213270271,
                0.9999832985801683,
                0.9999974387187063,
                0.9999975938979495,
                0.9999898700066219,
                0.9999955048194962,
                0.9999984465018763,
                0.9999921107346011,
                0.9999957771680704,
                0.9999989322973851
            ],
            [
                9.422447062202052e-07,
                4.006369219233375e-05,
                6.144176799283803e-06,
                0.9999980052700423,
                0.9999910603026405,
                5.043476486902204e-07,
                2.1444943301674863e-05,
                0.9999960330140886,
                0.9999981261243943,
                5.422218969858371e-06
            ],
            [
                0.9999964991464233,
                0.9999974387180959,
                0.9999952149055108,
                0.9999916019259733,
                0.9999798543092,
                0.9999952149049397,
                0.9999942280779128,
                0.9999949062931808,
                1.7603440527286572e-06,
                0.9999930377404357
            ],
            [
                0.9999994956527123,
                0.999999168472171,
                0.9999985406232579,
                0.9999990577552943,
                0.9999977396746268,
                0.9999972735294067,
                0.9999993106392013,
                1.3709567165579959e-06,
                0.999997273530383,
                0.999998932297258
            ],
            [
                2.902312677137316e-06,
                0.9999942280785977,
                2.5612819054028872e-06,
                6.144177531767002e-06,
                5.043474683204221e-07,
                1.3709570433979422e-06,
                0.9999687980738157,
                0.9999877809283733,
                3.726638395415398e-06,
                0.99999691050666
            ],
            [
                7.88925976418034e-06,
                2.2603234895289998e-06,
                0.9999952149043676,
                0.9999934595619979,
                0.9999546021422797,
                0.9999942280779106,
                1.2098659719757836e-06,
                5.422217030495909e-06,
                0.9999832985841393,
                1.7603430034655858e-06
            ],
            [
                8.315282259138311e-07,
                1.0677028700266676e-06,
                8.315281267861397e-07,
                1.0677027427600627e-06,
                1.012999218776902e-05,
                4.450852111148132e-07,
                8.315284241650899e-07,
                1.4449798650551755e-07,
                4.2228334445370225e-06,
                8.939696304311336e-06
            ],
            [
                3.288747889284851e-06,
                0.9999892166852222,
                0.9999967112501543,
                2.902312677137316e-06,
                4.450849988758202e-07,
                0.9999955048173531,
                7.338209805224048e-07,
                0.9999985406241279,
                0.9999921107402459,
                1.2751907329024393e-07
            ],
            [
                1.5534971990126997e-06,
                0.9999934595596622,
                0.9999934595643382,
                1.9947306726594253e-06,
                1.9947292459347367e-06,
                1.2098656835224664e-06,
                2.9023126771227976e-06,
                1.0677032518748838e-06,
                1.3007123813382511e-05,
                8.315282259117513e-07
            ],
            [
                3.7266379513162962e-06,
                4.222833947960866e-06,
                1.994730197071414e-06,
                7.338213304283347e-07,
                4.785096776468749e-06,
                7.88926446679691e-06,
                8.939696304213768e-06,
                5.4222215550004564e-06,
                7.88926446679691e-06,
                0.9999485577926047
            ],
            [
                2.3823685319244518e-07,
                1.7603425837855082e-06,
                0.999995777165049,
                6.475947982002148e-07,
                0.9999904837471815,
                5.043476486915964e-07,
                8.315281267834927e-07,
                1.7603438428740716e-06,
                2.5612819054028872e-06,
                1.9947306726594253e-06
            ],
            [
                6.475951069932288e-07,
                1.6373766672973748e-07,
                1.3709567165617364e-06,
                5.043472278322555e-07,
                9.422445939032799e-07,
                4.4508510499849186e-07,
                1.6373776432509826e-07,
                2.6995784182140636e-07,
                1.3709567165617364e-06,
                3.288749849529972e-06
            ],
            [
                4.785094494783494e-06,
                9.422447062240614e-07,
                4.006369219393695e-05,
                9.422442569315887e-07,
                4.222833444590791e-06,
                1.4738978458140753e-05,
                4.785095065132354e-06,
                2.5612819054028872e-06,
                1.760344052714248e-06,
                2.2603242978871282e-06
            ],
            [
                9.422448185510695e-07,
                3.726639728370556e-06,
                8.315281267834927e-07,
                7.338209805240734e-07,
                1.760343213322473e-06,
                3.7266410611296085e-06,
                4.222834954753043e-06,
                5.043472879525233e-07,
                1.0677024881980089e-06,
                5.144223206414209e-05
            ],
            [
                3.7266383956509585e-06,
                0.9999957771665581,
                5.1442207537151994e-05,
                0.9999974387187072,
                8.315281267834927e-07,
                1.2098656835224664e-06,
                2.260324836776948e-06,
                0.9999892166839363,
                3.288750241561788e-06,
                0.9999991148429644
            ],
            [
                3.9278610661902853e-07,
                8.939695238439078e-06,
                4.450852111148132e-07,
                6.475947210031623e-07,
                1.2098658277451275e-06,
                3.059022998576899e-07,
                0.9999955048168172,
                0.9999877809181684,
                0.9999832985841526,
                1.0677032518748838e-06
            ],
            [
                0.999999168472072,
                0.9999339478401038,
                0.9999945777823261,
                6.962256249885085e-06,
                0.9999969105066595,
                0.9999962733598305,
                0.9999955048194976,
                0.9999986290421407,
                0.9999485577742193,
                0.9999981261246174
            ],
            [
                0.9999982396559483,
                0.9999970976869783,
                0.9999898700066134,
                7.338211554783522e-07,
                2.2603240284371276e-06,
                0.9999885212332581,
                0.9999985406243016,
                1.7603432133296774e-06,
                7.338213304316717e-07,
                0.9999952149055076
            ],
            [
                0.9999756997506015,
                0.9999904837449101,
                4.450851580555361e-07,
                3.4663266242969896e-07,
                5.715003788993679e-07,
                0.9999892166852228,
                4.4508505193791187e-07,
                0.999941708706956,
                0.9999921107346029,
                0.9995121429445142
            ],
            [
                0.9999975938985225,
                0.9999969105059232,
                0.9999977396757027,
                0.9999151889904138,
                0.9999994956524116,
                0.9999986290432843,
                0.9999995818812771,
                6.475950297942253e-07,
                0.9999990577554064,
                0.9999978766220449
            ],
            [
                0.9999995262095551,
                0.9999952149066486,
                0.9999977396762422,
                0.9999992188513902,
                0.9999994631248682,
                0.9999984465016902,
                0.9999969105066585,
                0.999999554914789,
                0.9999978766222978,
                0.9999910603026345
            ],
            [
                0.9999987901346056,
                0.9999938558261332,
                0.9999869928746445,
                0.9999942280799738,
                2.9023112932177327e-06,
                0.9999885212346271,
                3.466327037548308e-07,
                1.5534971990126997e-06,
                0.9999955048178889,
                0.9999993524048933
            ],
            [
                0.9999885212332488,
                2.7535691101761522e-05,
                4.2228334445658276e-06,
                9.422443692555439e-07,
                0.999989870009027,
                0.9999687980998565,
                5.422217030747413e-06,
                1.4738987243478167e-05,
                1.5534975693869924e-06,
                0.9999916019239689
            ],
            [
                0.9999938558261346,
                5.043475284430694e-07,
                0.9999994284996214,
                0.9999967112521136,
                0.9999975938979486,
                1.5534977545886537e-06,
                0.9999969105055541,
                5.422220262636381e-06,
                5.043472879540142e-07,
                0.9999967112513283
            ],
            [
                0.9999942280792871,
                0.9999877809196293,
                4.2228339479858295e-06,
                1.9947292459347367e-06,
                5.422220909009474e-06,
                0.9999989322968759,
                0.9999969105055541,
                7.484622728735096e-05,
                0.9999892166916526,
                1.9947304348703948e-06
            ],
            [
                0.9999975938965141,
                6.475949525981759e-07,
                9.422450431989127e-07,
                9.422442569315887e-07,
                3.4663249714612693e-07,
                0.9999756997680279,
                6.475945666051092e-07,
                2.260325106237323e-06,
                4.2228334445658276e-06,
                1.3709568799919866e-06
            ],
            [
                9.422450432014836e-07,
                0.9999930377462435,
                0.9999921107336572,
                3.927863407379485e-07,
                0.9999934595604383,
                0.9999930377437539,
                0.9999925887174854,
                0.9999898700090257,
                0.9999921107402394,
                5.715005151606823e-07
            ],
            [
                0.9999945777829718,
                0.9999982396561585,
                0.999998346310809,
                0.9999949062931789,
                0.9999942280792856,
                0.9999952149049386,
                0.9999989322973851,
                0.999998629042631,
                0.9999949062962145,
                0.9999974387171804
            ],
            [
                0.9999993106387081,
                0.99999211073648,
                0.9999990577557434,
                0.9999982396572072,
                1.2098659719757836e-06,
                0.999995214907218,
                0.9999960330126686,
                0.9999986290426303,
                0.9999938558246689,
                0.9999986290426306
            ],
            [
                5.043476486915964e-07,
                1.5534983101393749e-06,
                8.315283250371857e-07,
                1.0129994602895546e-05,
                1.3709567165530083e-06,
                3.0590229985296015e-07,
                1.3709568799919866e-06,
                6.144173869558639e-06,
                3.2887478892683997e-06,
                9.422447062270609e-07
            ],
            [
                4.4508515805199415e-07,
                1.5534973841895917e-06,
                2.5612825160562587e-06,
                2.260325375664839e-06,
                1.3709568799760888e-06,
                5.715003107755449e-07,
                1.2098655392811161e-06,
                1.5534975693869924e-06,
                1.9947304348703948e-06,
                2.561281600049467e-06
            ],
            [
                0.9999974387180958,
                0.9999942280820402,
                0.9999955048184258,
                1.2098652508424818e-06,
                0.9999949062931797,
                0.9999962733598291,
                0.9999938558275995,
                0.9999942280799741,
                0.9999981261239471,
                2.5612812947508257e-06
            ],
            [
                0.999989216682655,
                1.2098655392811161e-06,
                0.9999987121050921,
                0.9999942280792846,
                0.9999952149072207,
                0.9999986290426303,
                0.999996273361164,
                0.9999957771665575,
                0.9999964991443366,
                0.9999990577549572
            ],
            [
                0.9999980052700415,
                1.4738985486265496e-05,
                0.9999985406232578,
                0.9999916019269736,
                2.260324836776948e-06,
                0.9999991684715762,
                0.9999986290427937,
                1.4738989000181669e-05,
                0.9999989969854345,
                0.9999885212359959
            ],
            [
                0.999998126123947,
                3.059022998576899e-07,
                4.222833444590791e-06,
                7.338213304283347e-07,
                3.9278610661366994e-07,
                0.9999991148433864,
                0.9999969105055535,
                0.9999987901338845,
                0.9999972735290801,
                0.9999964991468419
            ],
            [
                6.144176799334096e-06,
                0.9999921107393033,
                6.475947210046347e-07,
                5.422221555414699e-06,
                1.3709567165530083e-06,
                0.9999945777790947,
                8.315278294072958e-07,
                4.222833947897496e-06,
                0.9999974387184014,
                0.9999910603005155
            ],
            [
                0.9999978766205269,
                6.475946437996402e-07,
                0.9999989969855537,
                0.9999952149066496,
                0.9999991148429649,
                0.9999952149049397,
                3.4663278639738526e-07,
                0.9999955048178925,
                0.9999910603005058,
                0.9999989322966216
            ],
            [
                0.999841563784807,
                1.2098659719757836e-06,
                5.043472879525233e-07,
                0.9999969105044485,
                0.9999975938985222,
                5.043474683204221e-07,
                4.785094494783494e-06,
                4.450851580555361e-07,
                0.9999945777823291,
                0.9999898700126507
            ],
            [
                1.0129993395217047e-05,
                1.1478769494396542e-05,
                4.785092783454444e-06,
                8.315283250371857e-07,
                2.144495608424996e-05,
                0.9999546021206425,
                0.9999962733593863,
                1.4738981972323349e-05,
                4.006369219233375e-05,
                6.605212895289091e-05
            ],
            [
                1.7603438428740716e-06,
                0.9999869928700044,
                1.994730197090463e-06,
                0.9999974387165697,
                0.9999983463110069,
                1.9947292459347367e-06,
                9.422444815765128e-07,
                0.9999785550593302,
                1.760343003481596e-06,
                0.999991060304774
            ],
            [
                0.9999983463098239,
                0.9999898700054043,
                0.9999978766205264,
                0.999997273530381,
                0.9999969105044483,
                0.9999869928699973,
                0.9999994956527124,
                0.9999942280772233,
                0.9999978766205269,
                1.2098659719788098e-06
            ],
            [
                1.3709575337078829e-06,
                1.8925157266089433e-05,
                0.0001398220908991855,
                1.4738983729053029e-05,
                2.3823693839154895e-07,
                1.5534975693869924e-06,
                4.2228329411708495e-06,
                2.260323489490968e-06,
                4.785095065132354e-06,
                1.0677031245953668e-06
            ],
            [
                4.450852641737424e-07,
                5.715003107755449e-07,
                2.2603251061849014e-06,
                7.338212429537553e-07,
                1.2098662604291696e-06,
                3.927862002625787e-07,
                1.2098662604291696e-06,
                1.670142383595838e-05,
                1.012999218776902e-05,
                6.475948754012522e-07
            ],
            [
                0.9999892166865044,
                0.9999869928761992,
                3.466327863961242e-07,
                0.9999921107355412,
                4.2228329411708495e-06,
                0.9999892166839346,
                0.999998540623084,
                1.3709572068422585e-06,
                8.315281267834927e-07,
                1.3709572068422585e-06
            ],
            [
                7.338209805224048e-07,
                2.2603253756956754e-06,
                0.9999989969855538,
                0.9999983463110063,
                1.209866260432471e-06,
                0.9999984465024311,
                0.9999972735290809,
                0.9999957771670624,
                0.9999960330155064,
                0.9999981261252875
            ],
            [
                0.9999987121043243,
                1.994730197090463e-06,
                1.0677024881980089e-06,
                3.05902263391829e-07,
                8.315284241650899e-07,
                9.422450432014836e-07,
                5.04347528446051e-07,
                0.9999997300422226,
                0.999985261016291,
                1.2098653950656417e-06
            ],
            [
                0.9999938558261344,
                0.999954602115301,
                0.9999925887227865,
                5.422221555340727e-06,
                3.288749849477628e-06,
                0.9999980052693281,
                2.2603240283888175e-06,
                0.9999898700041988,
                1.5534979397790343e-06,
                0.9999892166826472
            ],
            [
                0.9999945777823265,
                8.315277302788957e-07,
                5.043472879525233e-07,
                0.9999832985781775,
                0.9999877809283678,
                0.9999949062956095,
                3.726638395611981e-06,
                3.2887498494551953e-06,
                0.9999945777784488,
                0.9999972735284305
            ],
            [
                0.9999994284992807,
                4.450848927650143e-07,
                0.9999832985742096,
                9.422450431989127e-07,
                6.475947210012481e-07,
                1.8925157265710765e-05,
                0.9999962733620518,
                0.999996910505554,
                0.9999991148430701,
                0.9999785550516325
            ],
            [
                0.9999832985801889,
                0.9999925887166023,
                0.9999925887201352,
                0.9999934595596636,
                4.222834954778007e-06,
                0.9999756997477506,
                0.9999339478241093,
                0.9999934595627789,
                5.422220909009474e-06,
                0.9999967112513297
            ],
            [
                0.9999910603026367,
                0.8354835411997897,
                0.999992110736483,
                0.9999990577550697,
                0.999996033013142,
                0.9999977396762424,
                0.9999981261243939,
                0.9999989322973853,
                0.9999898700114536,
                0.9999990577554068
            ],
            [
                4.785093353940187e-06,
                8.315283250371857e-07,
                6.475947210012481e-07,
                6.962259569750576e-06,
                5.715003107755449e-07,
                2.5612828213690224e-06,
                1.2098659719757836e-06,
                4.2228339479858295e-06,
                1.5534984953453635e-06,
                3.4663274507713016e-07
            ],
            [
                5.043472879540142e-07,
                9.422449308748773e-07,
                3.726639728348526e-06,
                5.715007195447234e-07,
                1.3709573702822306e-06,
                5.715003107738556e-07,
                0.999975699765101,
                1.2098656835224664e-06,
                1.994730197090463e-06,
                9.422444815792981e-07
            ],
            [
                0.9999995262094421,
                0.9999991148428591,
                0.9999988634362899,
                0.9999993524050476,
                0.9999982396561581,
                0.9999994631249322,
                0.9999994284994169,
                0.9999991684719726,
                0.999999554914789,
                0.9999967112497601
            ],
            [
                8.315280276626197e-07,
                1.3709567165617364e-06,
                1.7603440527286572e-06,
                1.5534984953552536e-06,
                4.450850519403407e-07,
                1.2098653950656417e-06,
                1.7603440527286572e-06,
                7.338208930460318e-07,
                6.475945666051092e-07,
                2.902312677137316e-06
            ],
            [
                1.3709568799760888e-06,
                3.466327863983311e-07,
                4.450848927650143e-07,
                1.370957860576702e-06,
                1.9947292459347367e-06,
                3.0590237279085045e-07,
                2.2603242978871282e-06,
                3.466326211113502e-07,
                9.422448185510695e-07,
                4.450848927658745e-07
            ],
            [
                1.5534975693933505e-06,
                9.422442569208767e-07,
                0.9999724643155444,
                3.7266401726359486e-06,
                3.05902226923399e-07,
                9.4224425692559e-07,
                0.9999952149032298,
                2.561282516042282e-06,
                3.927862470816829e-07,
                8.315280276626197e-07
            ],
            [
                2.699577452775239e-07,
                3.9278615344178325e-07,
                0.9999972735284304,
                1.3709567165617364e-06,
                0.9999952149066489,
                0.9999952149037965,
                9.422448185510695e-07,
                2.90231094723893e-06,
                8.315280276607289e-07,
                0.9999992188517626
            ],
            [
                0.999989870004211,
                1.5534981249574276e-06,
                0.9999724643188266,
                1.3709575336947905e-06,
                0.9999955048200354,
                0.9999869928715577,
                0.9999964991451724,
                1.2098658277451275e-06,
                0.999991601930979,
                3.2887502415767434e-06
            ],
            [
                0.9999957771680678,
                1.994730197090463e-06,
                6.1441746020359e-06,
                1.994729721518893e-06,
                6.144173137126169e-06,
                0.9999599362983397,
                8.315280276546789e-07,
                1.7603436330259153e-06,
                4.53978632394714e-05,
                4.785093924330255e-06
            ],
            [
                2.1444943301674863e-05,
                0.9999546021423301,
                3.2887478892504536e-06,
                9.422448185435711e-07,
                1.0129989772412744e-05,
                6.475951069932288e-07,
                2.2603234895176927e-06,
                8.315281267834927e-07,
                0.99996464376202,
                0.9999910603069007
            ],
            [
                0.9999994956524118,
                0.9999972735297309,
                0.9999994631248043,
                0.999988521231885,
                1.9947299592570416e-06,
                0.9999955048184249,
                0.9999978766212861,
                7.338209805224048e-07,
                0.9999974387174871,
                0.9999832985761833
            ],
            [
                5.715007195447234e-07,
                1.2098659719524008e-06,
                1.2098658277451275e-06,
                2.144495608424996e-05,
                1.5534973842076057e-06,
                1.7603438428660665e-06,
                1.3007133116732079e-05,
                2.2603242978665707e-06,
                2.2603237589779086e-06,
                1.0677029973056687e-06
            ],
            [
                5.715003107738556e-07,
                0.9999861539987621,
                0.9999916019279746,
                0.9999810748450363,
                5.715003107738556e-07,
                0.9999962733616071,
                3.0590237279032884e-07,
                0.9999938558276023,
                1.067703379154416e-06,
                1.7603432133296774e-06
            ],
            [
                0.9999992188519491,
                0.9999989969861512,
                0.9999972735307058,
                0.9999986290421409,
                0.9999981261248407,
                1.3709567165530083e-06,
                0.9999785550516355,
                0.9999970976890542,
                0.9999938558276017,
                2.6995774527718623e-07
            ],
            [
                1.3709575337078829e-06,
                2.5612831267202583e-06,
                7.338212429582604e-07,
                1.3709570433979422e-06,
                0.9999852610180423,
                0.9999852610233111,
                1.7603434231705793e-06,
                0.9999949062931774,
                0.999994906296214,
                4.2228324377740105e-06
            ],
            [
                8.315278294072958e-07,
                0.9999985406234315,
                0.9999916019289735,
                0.999998005269804,
                0.9999910603036986,
                0.9999984465016905,
                1.0129995810463632e-05,
                1.2098655392871682e-06,
                1.5534983101478522e-06,
                0.9999877809269088
            ],
            [
                1.3709578605617394e-06,
                1.5534971990126997e-06,
                0.999996033015506,
                0.9999930377445841,
                1.994729008145876e-06,
                0.9999993106388726,
                8.315283250394546e-07,
                9.422449308748773e-07,
                1.994730197090463e-06,
                0.999996273361607
            ],
            [
                0.999964643749416,
                0.9999989322966214,
                4.539787947559951e-05,
                0.9999977396748949,
                0.9999981261248411,
                6.144176066850984e-06,
                0.9999938558224758,
                4.785096206013061e-06,
                3.927860597945825e-07,
                0.9999977396765122
            ],
            [
                2.2603234895176927e-06,
                1.2098652508424818e-06,
                1.067703124601679e-06,
                5.043476486924565e-07,
                9.422449308748773e-07,
                6.475947210046347e-07,
                2.5612834320563895e-06,
                2.1024326584639497e-07,
                2.699578096403948e-07,
                3.7266410611296085e-06
            ],
            [
                0.999996711249762,
                0.9999974387168747,
                0.9999949062931784,
                0.9999980052695665,
                0.9999974387168755,
                0.9999984465018757,
                0.9999934595635592,
                0.9999989969857928,
                0.9999985406232584,
                0.9999989969862711
            ],
            [
                1.7603440527286572e-06,
                2.90231094723893e-06,
                1.1478769494396542e-05,
                1.5534981249697903e-06,
                4.2228339479858295e-06,
                1.5534975693869924e-06,
                0.9999934595635572,
                3.0590237279032884e-07,
                1.0677027427471959e-06,
                1.0677024882009222e-06
            ],
            [
                1.0677032518785256e-06,
                5.043474081993875e-07,
                2.1024326584582131e-07,
                7.338211554783522e-07,
                6.475947982037486e-07,
                6.475950297971703e-07,
                1.2098655392871682e-06,
                4.785096776468749e-06,
                1.5534979397740895e-06,
                7.338212429537553e-07
            ],
            [
                0.9999934595604383,
                0.9999898700126502,
                0.9999957771650473,
                0.9999989969857926,
                0.999993037742926,
                0.9999972735294055,
                0.999972464295818,
                0.9999952149066474,
                0.9999957771650474,
                1.1478770862735993e-05
            ],
            [
                4.785093353874907e-06,
                0.9999898700126502,
                0.9999646437578114,
                0.9999949062962152,
                0.9999869928731019,
                0.9999910603037021,
                3.288748281329893e-06,
                0.9999898700102351,
                0.9999942280792857,
                0.999915188969151
            ],
            [
                7.338209805224048e-07,
                5.829127250060064e-05,
                5.043475885674441e-07,
                4.785094494811783e-06,
                1.5534981249697903e-06,
                1.3709576971425944e-06,
                1.670141587208191e-05,
                1.3007133116542802e-05,
                7.338209805224048e-07,
                1.994729483705484e-06
            ],
            [
                0.9999957771655524,
                0.9999910603058383,
                0.00010889693530623988,
                4.450850519403407e-07,
                5.043472879540142e-07,
                3.2887482813149375e-06,
                3.288749065406658e-06,
                0.9999977396746261,
                0.999996273358941,
                0.9999962733607184
            ],
            [
                NaN,
                0.9999898700066125,
                8.315284241560147e-07,
                0.999983298578174,
                0.9999599362887829,
                0.9999546021261316,
                7.338209805200689e-07,
                3.05902336324494e-07,
                0.999968798073818,
                3.0590226339061185e-07
            ],
            [
                5.043474683204221e-07,
                3.288749457469787e-06,
                3.7266410611296085e-06,
                7.338208930460318e-07,
                2.902312331170226e-06,
                8.315280276580819e-07,
                5.715005151606823e-07,
                5.4222183235249605e-06,
                0.999997097686632,
                0.9999949062943922
            ],
            [
                0.9999646437535755,
                5.715003107715166e-07,
                6.475945666051092e-07,
                5.422220909009474e-06,
                0.9999962733607168,
                4.2228329411708495e-06,
                2.1024336609843824e-07,
                3.726638839878908e-06,
                6.475949526020042e-07,
                1.2098652508347793e-06
            ],
            [
                0.9999942280813563,
                0.9999832985781708,
                0.9999975938973746,
                0.9999985406230839,
                0.9999981261250644,
                0.9999993106390369,
                0.9999975938970886,
                0.9999885212346296,
                0.999959936293682,
                0.9999942280786017
            ],
            [
                5.144221366623174e-05,
                0.9999982396574173,
                0.9999972735300556,
                0.9999885212277768,
                0.9999993106388727,
                2.9023112932177327e-06,
                0.9999969105051852,
                0.9999960330150336,
                0.9999942280792862,
                0.9999962733598297
            ],
            [
                1.0677033791583005e-06,
                0.9999942280779108,
                0.9999972735287559,
                0.9999955048162821,
                0.9999969105051854,
                0.9999967112505446,
                0.9999930377462495,
                0.9999962733611629,
                4.53978632394714e-05,
                0.9999945777816828
            ],
            [
                2.9023119851899796e-06,
                4.785094494783494e-06,
                2.430025232128576e-05,
                2.4300237838535383e-05,
                1.1478769494250387e-05,
                4.222834954778007e-06,
                2.2603234895372223e-06,
                4.785096776468749e-06,
                6.144176799283803e-06,
                6.144175334418252e-06
            ],
            [
                0.9999984465018759,
                1.3709572068522336e-06,
                5.715007195431641e-07,
                0.9999985406230842,
                0.9999930377420965,
                0.999992588721022,
                2.5612812947508257e-06,
                0.9999942280820413,
                0.9999972735303806,
                1.5534979397740895e-06
            ],
            [
                2.382369383923073e-07,
                3.5356242285703183e-05,
                2.5612812947508257e-06,
                6.9622595696935874e-06,
                2.9023126771227976e-06,
                3.466326624322211e-07,
                2.2603242978871282e-06,
                4.450848927637999e-07,
                1.9947301970813926e-06,
                2.260325375664839e-06
            ],
            [
                0.9999996310115918,
                0.9999964991451695,
                3.288747889284851e-06,
                0.9999990577551818,
                3.726639728348526e-06,
                6.1441731370702875e-06,
                0.9999990577550694,
                0.9999960330150329,
                8.315278294097538e-07,
                0.999999607213753
            ],
            [
                5.043472879540142e-07,
                1.5534971990126997e-06,
                0.999978555054167,
                0.999996499146422,
                0.9999985406236054,
                0.9999921107355381,
                2.9023119851781017e-06,
                0.9999982396565773,
                2.260323758987159e-06,
                0.9999785550490462
            ],
            [
                0.9997040430090205,
                8.315282259089153e-07,
                9.422448185435711e-07,
                6.475950298011458e-07,
                6.144177531767002e-06,
                5.04347348075149e-07,
                2.5612812947508257e-06,
                4.222834451327159e-06,
                1.0677032518785256e-06,
                2.5612831267202583e-06
            ],
            [
                2.561282210740037e-06,
                5.715004470313855e-07,
                3.2887482812506295e-06,
                1.0677024881980089e-06,
                0.9999810748427537,
                4.785096206076165e-06,
                8.939696304311336e-06,
                1.0677032518785256e-06,
                1.2098656835076114e-06,
                4.450851580555361e-07
            ],
            [
                0.9999980052702794,
                0.9999955048168172,
                7.338209805224048e-07,
                0.9999994631249962,
                9.422448185534261e-07,
                0.9999957771680679,
                0.9999962733611613,
                0.9999989969859123,
                1.7603425837855082e-06,
                1.1478765389368729e-05
            ],
            [
                3.726639728348526e-06,
                4.222833444590791e-06,
                0.9999925887174842,
                0.9999989322968763,
                1.994729245917502e-06,
                0.9999885212359899,
                1.5534975693869924e-06,
                0.9999952149043664,
                0.9999955048162803,
                1.2098662604247682e-06
            ],
            [
                1.7603434231705793e-06,
                3.466327037548308e-07,
                1.5534975693933505e-06,
                3.9278629391427843e-07,
                5.043475885674441e-07,
                2.1024336609874897e-07,
                1.2098659719757836e-06,
                9.422444815765128e-07,
                0.9999995818814265,
                2.2603234895289998e-06
            ],
            [
                3.726639728370556e-06,
                0.9999934595643392,
                1.3709573702822306e-06,
                0.9999869928669006,
                1.0677029973192638e-06,
                2.902313023130843e-06,
                0.9999957771675648,
                0.9999975938976626,
                0.9999852610162854,
                0.9999925887183702
            ],
            [
                0.9999916019309811,
                4.785094494783494e-06,
                5.715005832853093e-07,
                5.04347287955046e-07,
                0.9999852610145298,
                3.2887506336235617e-06,
                0.9999957771655524,
                1.5534973842076057e-06,
                3.2887502414436403e-06,
                4.450851049959619e-07
            ],
            [
                0.9999967112509366,
                0.9999960330155087,
                0.9999798543164069,
                0.9999967112501538,
                0.999997593897376,
                0.9999991684722705,
                0.9999994284996213,
                0.9999967112517213,
                0.9999945777816815,
                0.9999955048178907
            ],
            [
                4.450849458200093e-07,
                5.04347348075149e-07,
                5.043475885674441e-07,
                1.2098656835136636e-06,
                2.382369383923073e-07,
                9.422448185534261e-07,
                1.994729483723626e-06,
                1.2098662604192665e-06,
                3.05902226923399e-07,
                1.3709567165579959e-06
            ],
            [
                3.7266379513434106e-06,
                3.2887482812506295e-06,
                2.5612828213690224e-06,
                0.9999957771650474,
                4.4508526417014975e-07,
                9.422449308748773e-07,
                1.5534981249697903e-06,
                5.043474683204221e-07,
                8.315280276580819e-07,
                1.5534975693869924e-06
            ],
            [
                1.2098662604291696e-06,
                3.5356238073889594e-05,
                3.059021539909339e-07,
                1.5534975693933505e-06,
                8.315277302747361e-07,
                8.939694172867777e-06,
                3.0590226339061185e-07,
                1.2098655392871682e-06,
                1.0677026154806063e-06,
                3.9278615344178325e-07
            ],
            [
                0.9999978766205266,
                2.1024341622368903e-07,
                0.9999852610110189,
                8.939697369980456e-06,
                1.7603432133296774e-06,
                0.9999667858131984,
                1.5534971990126997e-06,
                0.999992588717484,
                0.9999930377437577,
                0.999997876621792
            ],
            [
                0.9999984465024313,
                6.475947210012481e-07,
                1.5534981249697903e-06,
                3.466326624322211e-07,
                9.422444815765128e-07,
                4.222831934379152e-06,
                2.5612812947077304e-06,
                1.760344052714248e-06,
                0.9999921107346033,
                0.9999687980961643
            ]
        ]
    },
    {
        "q_id": "9863_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            12,
            13,
            15,
            16,
            17,
            18,
            19,
            20,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            36,
            37,
            38,
            40,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            72,
            73,
            75,
            76,
            78,
            79,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3709576971242028e-06,
                6.9622595696935874e-06,
                1.0677031245783732e-06,
                3.726638839878908e-06,
                1.553497199007048e-06,
                NaN,
                3.726639728348526e-06,
                6.96225873967641e-06,
                7.889264466725156e-06,
                6.962254589914941e-06
            ],
            [
                2.2603245673279107e-06,
                1.5534975693869924e-06,
                1.9947297215125433e-06,
                2.260324028427877e-06,
                4.785096206047877e-06,
                1.3709572068522336e-06,
                1.5534984953510149e-06,
                1.3709575337078829e-06,
                6.144177531811707e-06,
                2.2603240284371276e-06
            ],
            [
                0.9947798733754648,
                0.9999962733602819,
                0.9999964991468571,
                0.9999969105055568,
                1.994730197090463e-06,
                0.9999988634361555,
                1.300712846477255e-05,
                0.9999962733616099,
                0.9999970976880248,
                0.9999972735300598
            ],
            [
                8.315284241650899e-07,
                NaN,
                3.2887506336235617e-06,
                9.422445939054222e-07,
                6.475950298011458e-07,
                1.3709572068522336e-06,
                1.7603440527222532e-06,
                7.88926446679691e-06,
                2.9023130230846496e-06,
                4.2228319344021954e-06
            ],
            [
                1.892514598469098e-05,
                1.1478773599425825e-05,
                4.006370652067535e-05,
                NaN,
                2.144495608378187e-05,
                3.535625914492432e-05,
                6.962255419653012e-06,
                NaN,
                NaN,
                1.1478768125911099e-05
            ],
            [
                1.5534971990169383e-06,
                NaN,
                0.9999952149038025,
                0.9999452402115826,
                1.0677028700422047e-06,
                0.999796573056253,
                0.9999706884686743,
                0.9999861540004492,
                7.88926070489716e-06,
                0.9999910603069385
            ],
            [
                4.222832941193893e-06,
                3.726641061085547e-06,
                3.7266406168827523e-06,
                2.4300232043987867e-05,
                3.1201911373535005e-05,
                4.222835458148261e-06,
                4.78509278348926e-06,
                1.4738980215352592e-05,
                1.0129988564974359e-05,
                1.5534981249574276e-06
            ],
            [
                5.715005832895975e-07,
                6.475947210046347e-07,
                8.315281267882195e-07,
                5.043473480777865e-07,
                7.338208055680009e-07,
                5.043472278322555e-07,
                1.9947297215125433e-06,
                3.927863875616689e-07,
                3.927863875616689e-07,
                2.699576809143613e-07
            ],
            [
                0.9999993916408909,
                0.9999999468421693,
                0.9999964991464232,
                1.0,
                0.9999977396751646,
                2.753568782024347e-05,
                0.9999993106387083,
                0.9999995549150542,
                0.9999993106389549,
                0.999999352405202
            ],
            [
                0.9999822214503229,
                1.5534971990169383e-06,
                1.760343003481596e-06,
                0.9997694932074483,
                5.715004470313855e-07,
                9.422442569315887e-07,
                1.4738981972323349e-05,
                0.999987780921104,
                1.3007131566015624e-05,
                4.450852641737424e-07
            ],
            [
                6.475945666033422e-07,
                9.422449308748773e-07,
                7.338210680021253e-07,
                4.785094494783494e-06,
                6.475946438042047e-07,
                5.715003107738556e-07,
                1.994730434879465e-06,
                8.315283250371857e-07,
                1.0677027427569065e-06,
                8.315280276580819e-07
            ],
            [
                4.785093924362895e-06,
                5.043472879540142e-07,
                1.89251482406672e-05,
                1.0677027427624903e-06,
                1.2098658277451275e-06,
                4.2228329411708495e-06,
                1.5534971990126997e-06,
                5.715005832886879e-07,
                7.3382080556433e-07,
                1.7603436330259153e-06
            ],
            [
                0.9999877809269127,
                3.7266397283908927e-06,
                NaN,
                4.222832437798974e-06,
                0.9999339478321678,
                0.9998204721038729,
                0.9999852610233577,
                NaN,
                1.0677032518814388e-06,
                NaN
            ],
            [
                0.999999554914842,
                0.9999885212291598,
                0.9999995262095551,
                0.9999997761970781,
                0.9999999176675437,
                0.999738809663752,
                0.9999785550541659,
                0.999999814460876,
                1.0129995810463632e-05,
                3.7266379514061143e-06
            ],
            [
                1.0129994602895546e-05,
                6.962256249885085e-06,
                1.0677026154806063e-06,
                6.144176799283803e-06,
                3.466327450756327e-07,
                1.5534977545886537e-06,
                4.450848927650143e-07,
                1.4738989000422955e-05,
                8.315284241650899e-07,
                5.043473480777865e-07
            ],
            [
                5.715007195447234e-07,
                5.043475885674441e-07,
                3.0590237279032884e-07,
                5.71500515159253e-07,
                5.71500515159253e-07,
                3.927862939126708e-07,
                4.450849458218309e-07,
                3.46632497145457e-07,
                6.475951069985296e-07,
                1.7603425837855082e-06
            ],
            [
                8.315283250371857e-07,
                3.7266406168827523e-06,
                6.144172404693786e-06,
                6.962254589914941e-06,
                1.553498124964492e-06,
                1.6701429808632785e-05,
                7.338208930443633e-07,
                2.1444950970626095e-05,
                9.422443692555439e-07,
                1.9947297215125433e-06
            ],
            [
                0.4378234991142019,
                0.9999987901347497,
                0.9999998362623528,
                0.9999993106389549,
                0.9999945777829736,
                6.9622537599680095e-06,
                0.9999955048194955,
                1.1478769494542698e-05,
                0.9999930377420982,
                0.9999942280779099
            ],
            [
                1.994729008145876e-06,
                0.9996200155225029,
                0.9999994956525321,
                0.9999994956525919,
                0.9999996310113279,
                0.9999993106390371,
                0.9999995818813767,
                0.9999992661792824,
                6.1441746020359e-06,
                0.9999996533672137
            ],
            [
                0.9999981261252878,
                NaN,
                0.9999994956524717,
                0.999998239656578,
                2.561281600086738e-06,
                0.9999988634362905,
                0.9999996743686645,
                0.9999998942829224,
                0.9999998257020799,
                0.999992588719253
            ],
            [
                0.9999999006880195,
                0.9999995818814266,
                0.9999998724810027,
                0.9998601778601187,
                0.9991959139708381,
                0.9999999006879958,
                0.9964063977553923,
                0.9999151889387635,
                0.9999999273417749,
                0.9999151889286861
            ],
            [
                8.481108183851022e-05,
                0.9999993106387083,
                NaN,
                0.9999998874649051,
                0.9999339478398399,
                0.9999992661791948,
                0.9999999067051388,
                0.9999992661788447,
                0.9999964991468395,
                0.9999998642567028
            ],
            [
                0.999933947832336,
                8.48110110572346e-05,
                0.9995121427831275,
                0.9999038975401354,
                0.9989677688184727,
                2.9023130231176453e-06,
                0.9996646498717581,
                0.9999741325661557,
                0.9998415638234143,
                0.9999646437578606
            ],
            [
                3.4663262110803996e-07,
                0.999841563751368,
                1.2098653950656417e-06,
                8.315280276580819e-07,
                0.9996200155507589,
                6.475947981975644e-07,
                NaN,
                0.9998204720688617,
                2.69957906184239e-07,
                6.9622587397397306e-06
            ],
            [
                2.699578740032504e-07,
                9.610239212762526e-05,
                1.994729008145876e-06,
                6.475946438055299e-07,
                2.5612828213690224e-06,
                3.9278620026686556e-07,
                1.2098656835252174e-06,
                9.422449308789479e-07,
                3.2887478892683997e-06,
                1.7603432133296774e-06
            ],
            [
                8.31527928532683e-07,
                5.422219616228845e-06,
                2.9023126771227976e-06,
                5.14422075345321e-05,
                8.481103128838341e-05,
                4.78509278348926e-06,
                1.7603434231705793e-06,
                7.889264466725156e-06,
                2.902310947208574e-06,
                6.962257079705671e-06
            ],
            [
                0.9999339478480043,
                0.9997694932648074,
                0.9998204719527318,
                1.6373764720990908e-07,
                0.9998911031307312,
                0.9999646437578849,
                2.1444953527944967e-05,
                0.999996910506293,
                0.009708474914534351,
                2.9023133690980155e-06
            ],
            [
                0.9999957771660549,
                0.9999852610233203,
                0.9999810748472763,
                0.9999417087277601,
                0.9997965730284856,
                1.209865827752005e-06,
                0.9999964991451726,
                0.9999646437409938,
                0.9999756997506362,
                0.9997965731011569
            ],
            [
                0.9999251537915068,
                0.999999761763005,
                0.9999996743686259,
                0.9999984465024313,
                0.9999996310113282,
                0.9999921107393132,
                1.3709576971316842e-06,
                0.9999994956527124,
                0.999999653367462,
                0.9999904837506111
            ],
            [
                0.9999861540004142,
                0.9999852610110174,
                0.9999991148426479,
                0.9999977396748949,
                0.9999994631248043,
                0.9999988634361543,
                0.999998446502617,
                0.9999974387171808,
                NaN,
                0.9999938558268675
            ],
            [
                0.999998712104478,
                0.9999988634364255,
                0.9999992188514834,
                4.450851049991497e-07,
                5.422217030781934e-06,
                0.9999724643156267,
                7.338207180898968e-07,
                8.315277302841894e-07,
                0.9997040428353982,
                0.991422516304903
            ],
            [
                2.3823690999290963e-07,
                1.1253513522447425e-07,
                7.338209805240734e-07,
                9.422448185534261e-07,
                2.699578740032504e-07,
                5.715006514176113e-07,
                3.4663266243308805e-07,
                1.6373766672888118e-07,
                6.47595107001401e-07,
                5.715003107767143e-07
            ],
            [
                0.9999999358794097,
                0.9999987121052454,
                0.9999991684717744,
                1.1478772231232203e-05,
                3.726639284144195e-06,
                0.999999906705072,
                0.999986992865347,
                0.999999943413784,
                0.9998766054261036,
                0.00017952792358181245
            ],
            [
                1.5534984953552536e-06,
                0.9999991148428591,
                0.9999982396569982,
                0.9999996940977003,
                0.9999987121049385,
                0.9999981261239472,
                0.9999916019289748,
                NaN,
                0.9999989322966216,
                0.9999989969862709
            ],
            [
                0.9999993106386261,
                0.9999995262094987,
                0.9999952149072254,
                0.9999998642566543,
                0.0008040858637961603,
                0.9999970976890556,
                0.9999546021207075,
                0.9999996743686645,
                0.9971990726966661,
                0.9999972735290805
            ],
            [
                1.6373774480605869e-07,
                2.102434412875379e-07,
                0.9999599363174471,
                8.315281267882195e-07,
                3.4663278639892215e-07,
                0.9999974387187069,
                1.0677028700422047e-06,
                0.9999986290423037,
                1.5534971990169383e-06,
                2.5612819054028872e-06
            ],
            [
                1.0677024881941248e-06,
                2.2603234895372223e-06,
                1.0677028700363782e-06,
                3.726639728370556e-06,
                1.5534981249574276e-06,
                2.2603234895289998e-06,
                1.553498124964492e-06,
                1.2098662604291696e-06,
                1.9947297215125433e-06,
                3.927860597945825e-07
            ],
            [
                0.9999989969857928,
                0.9999993106387903,
                0.9999984465024311,
                0.9999990577556311,
                0.999998629042794,
                0.9999989969862708,
                0.9999996743687422,
                0.9999991684715761,
                0.9999983463110063,
                0.9999983463106125
            ],
            [
                0.9999977396746257,
                0.9999995818813766,
                5.829126555256903e-05,
                0.9999904837437891,
                0.9999994631248041,
                5.043472278312808e-07,
                0.9999986290421405,
                1.2098652508424818e-06,
                0.9999960330150333,
                0.9999991148429648
            ],
            [
                3.726639284144195e-06,
                0.999999814460854,
                0.999998239656368,
                0.9999982396559483,
                5.043476486915964e-07,
                0.9706877712625633,
                1.2098656835224664e-06,
                2.2603234895372223e-06,
                0.99951214284242,
                NaN
            ],
            [
                2.561281294760143e-06,
                8.315284241650899e-07,
                1.4738985486506781e-05,
                4.450852641737424e-07,
                7.338208930460318e-07,
                4.450849988798682e-07,
                4.450851580566494e-07,
                4.4508505193386385e-07,
                7.338209805224048e-07,
                5.043475885688201e-07
            ],
            [
                1.3709576971463352e-06,
                0.9999969105062917,
                0.9999992188516699,
                0.9999869928746594,
                0.9999988634365613,
                0.9999987901338846,
                1.3709568799919866e-06,
                8.939700567094277e-06,
                0.9999957771670612,
                0.999998790134173
            ],
            [
                3.927863875584984e-07,
                5.422218969858371e-06,
                9.422444815765128e-07,
                1.012999097997104e-05,
                4.785095635624897e-06,
                9.4224425692559e-07,
                3.726639728370556e-06,
                1.3709575337078829e-06,
                1.0677028700363782e-06,
                6.475948754012522e-07
            ],
            [
                2.3823688159237777e-07,
                1.4449798650476187e-07,
                2.3823688159237777e-07,
                3.05902263389638e-07,
                1.7603436330259153e-06,
                5.715006514151423e-07,
                4.450852641717689e-07,
                1.2098661162023305e-06,
                2.6995784182073116e-07,
                2.6995784182073116e-07
            ],
            [
                2.561281600086738e-06,
                0.999998540623954,
                NaN,
                0.9999990577551822,
                0.9999987901340294,
                0.9999994631249324,
                0.9999980052698049,
                0.9999969105051858,
                0.9999988634357481,
                0.2018132150593341
            ],
            [
                0.9999969105055552,
                7.338208930460318e-07,
                1.9947292459347367e-06,
                0.9999646437621135,
                1.994729008145876e-06,
                5.043472278312808e-07,
                1.3007128465151102e-05,
                4.4508510499737865e-07,
                4.785092783519724e-06,
                NaN
            ],
            [
                NaN,
                7.889261645427538e-06,
                1.9947299593078385e-06,
                1.0677028700422047e-06,
                2.2603251062450327e-06,
                6.475945666063607e-07,
                1.5534983101644536e-06,
                NaN,
                NaN,
                6.962258739796719e-06
            ],
            [
                0.9999997463980125,
                3.927860597945825e-07,
                0.9999996743687422,
                0.9999994956527724,
                0.9999993524054336,
                0.9999989969859123,
                0.26894141551050293,
                0.9999990577552942,
                0.9999998555019963,
                0.9999861539888663
            ],
            [
                8.939693107288474e-06,
                9.422444815814404e-07,
                2.2603251062450327e-06,
                2.699577452775239e-07,
                NaN,
                1.8925155009354808e-05,
                1.5534981249736758e-06,
                NaN,
                1.994729483729522e-06,
                8.315281267882195e-07
            ],
            [
                3.466326624336003e-07,
                2.699576809143613e-07,
                1.2751910369310194e-07,
                0.9999993106392012,
                2.6995784182073116e-07,
                0.9999724643057415,
                7.338210680021253e-07,
                4.450848927658745e-07,
                6.475951070002966e-07,
                9.422448185534261e-07
            ],
            [
                1.6701427818034747e-05,
                0.9999967112513307,
                NaN,
                0.9999599363223459,
                0.9999898700126588,
                0.9999869928669357,
                1.1478770862882149e-05,
                9.422447062294175e-07,
                3.5356267573959116e-05,
                7.889261645427538e-06
            ],
            [
                1.1478769494396542e-05,
                2.1024336609843824e-07,
                3.05902263391829e-07,
                2.699576809143613e-07,
                4.0063701745046735e-05,
                1.8553907971813685e-07,
                1.2751908849167202e-07,
                3.2887506336086064e-06,
                1.637377448057981e-07,
                2.102434412871794e-07
            ],
            [
                2.902312677137316e-06,
                3.726639728262097e-06,
                7.889264466545779e-06,
                4.222833947960866e-06,
                1.14787708624228e-05,
                7.88926634755014e-06,
                2.902313023101807e-06,
                6.962254589914941e-06,
                1.300712536350655e-05,
                5.422218323487975e-06
            ],
            [
                6.475945666063607e-07,
                2.5612819054133693e-06,
                8.315282259151545e-07,
                6.475947982037486e-07,
                1.994729721518893e-06,
                3.72663883989755e-06,
                8.481106151541198e-05,
                6.475947210046347e-07,
                2.5612831267202583e-06,
                NaN
            ],
            [
                1.1478768125911099e-05,
                1.209865827740176e-06,
                1.7603425837855082e-06,
                NaN,
                1.760343213335281e-06,
                1.7603438428740716e-06,
                2.561282516042282e-06,
                1.2098659719757836e-06,
                1.5534981249574276e-06,
                1.0677029973192638e-06
            ],
            [
                0.9999904837483277,
                0.999999114843281,
                0.999999495652532,
                0.9999983463110079,
                0.9999962733616128,
                0.9999987901346057,
                0.9999992661791076,
                0.9999986290424677,
                4.785093924362895e-06,
                0.9999986290431209
            ],
            [
                0.9999991684720717,
                0.9999996940977368,
                0.9999998555019274,
                0.9999997126314126,
                0.9999994956526523,
                0.9999995549150544,
                0.9999995262096116,
                0.9999992661787575,
                0.9999991684718735,
                0.9999988634361546
            ],
            [
                1.5534977545886537e-06,
                0.9999904837483258,
                0.9999957771670681,
                0.999994906293182,
                0.9999988634358843,
                0.999998346309824,
                3.05902190458764e-07,
                0.9999964991460075,
                0.9999724643024159,
                4.222832437798974e-06
            ],
            [
                NaN,
                6.9622587397397306e-06,
                6.962257909785973e-06,
                5.043475885688201e-07,
                4.222832437798974e-06,
                2.2603242978871282e-06,
                7.338212429582604e-07,
                4.450848927658745e-07,
                3.9278634073625165e-07,
                NaN
            ],
            [
                8.764242227380856e-08,
                9.931196877517082e-08,
                1.4449798650551755e-07,
                1.4449802095609418e-07,
                1.8553919030708836e-07,
                0.9999967112493715,
                3.9278634073625165e-07,
                1.994729008145876e-06,
                1.637377448057981e-07,
                0.9998911030784431
            ],
            [
                0.999999352405202,
                0.9999996940977003,
                0.9998766053818379,
                0.9997965731005827,
                0.9999646437535655,
                0.9999994956525919,
                0.9999985406243016,
                0.9999997463981636,
                1.0677027427624903e-06,
                0.9999994956524717
            ],
            [
                1.670141786325573e-05,
                0.999996499146842,
                0.9999975938985228,
                0.9999960330131462,
                0.9999599362935956,
                0.9999977396765128,
                0.9999945777823304,
                8.939693107288474e-06,
                0.9999982396574183,
                0.9998911030655169
            ],
            [
                0.9999756997506629,
                0.9999892166852323,
                0.00010889690934918666,
                3.7266397283908927e-06,
                0.9999892166839357,
                0.999738809632069,
                1.209866260432471e-06,
                0.9999706884476419,
                0.9999910603005189,
                0.9999724643155651
            ],
            [
                0.9999992188515767,
                0.9999910603026356,
                0.9999998362622747,
                0.9999038975853564,
                0.9999980052705171,
                0.9999785550413881,
                0.9999969105048166,
                0.9999988634366963,
                0.9999984465028016,
                0.9999996940977732
            ],
            [
                0.9999997897567342,
                0.999995504820032,
                NaN,
                0.999999631011548,
                0.9999785550567303,
                0.9999962733589403,
                0.9999995818811773,
                7.889259764517575e-06,
                NaN,
                0.9999997897566089
            ],
            [
                0.9999986290429574,
                0.9999996940978096,
                0.9999964991460073,
                0.99999854062378,
                0.9999992661787573,
                0.9999989969860319,
                0.9999969105059229,
                8.315279285370317e-07,
                0.999991060300512,
                0.9999989969857926
            ],
            [
                1.0677029973192638e-06,
                2.260324028427877e-06,
                9.422444815765128e-07,
                3.4663266242969896e-07,
                1.892515501014656e-05,
                5.715006514151423e-07,
                7.338213304316717e-07,
                1.0677032518748838e-06,
                4.785094494783494e-06,
                5.715003788993679e-07
            ],
            [
                0.9999995818813271,
                0.9999810748427564,
                0.9999646437578229,
                0.0003799844869822013,
                0.9998204720144431,
                0.9999885212360033,
                0.9999987901344615,
                0.9999996072137998,
                0.9999992188517628,
                0.9999998024946566
            ],
            [
                0.9999996743686645,
                0.999994577781038,
                0.9999996743687034,
                0.9999151889691188,
                0.9999934595651242,
                8.939693107288474e-06,
                0.9999989322967486,
                0.9999970976876718,
                0.9999975938976617,
                4.785093924389007e-06
            ],
            [
                0.9999998942830862,
                0.9999999273418702,
                0.9999997761971049,
                0.9999992661792824,
                0.9999832985761922,
                0.9999964991464224,
                8.315279285370317e-07,
                0.999985261012785,
                0.9999955048173538,
                1.2098661162056318e-06
            ],
            [
                0.999964643749416,
                4.222833444590791e-06,
                3.288747889284851e-06,
                0.9999987121049386,
                0.9999972735294063,
                0.9999977396746261,
                0.9999977396746265,
                0.9999546021152311,
                0.9999984465016907,
                0.999985261023329
            ],
            [
                0.9999960330136168,
                6.144172404693786e-06,
                0.9999972735284316,
                0.9999985406236058,
                0.9999930377404432,
                0.9999978766222987,
                0.999998005270043,
                0.9999938558276068,
                0.9999984465016915,
                1.4738983729535602e-05
            ],
            [
                0.9999993916411811,
                0.999996033015034,
                0.9999992188515766,
                0.9999999067051165,
                0.9999999317439221,
                0.9999485577619656,
                0.9999995549149482,
                0.9999991148431755,
                0.99990389758532,
                0.9999999123574628
            ],
            [
                NaN,
                0.9999989322973853,
                4.450851049991497e-07,
                4.539787406217992e-05,
                1.7603434231833873e-06,
                4.222834451403972e-06,
                1.7603438428800754e-06,
                1.3709568799919866e-06,
                1.0677026154806063e-06,
                8.315281267882195e-07
            ],
            [
                4.4508505193932864e-07,
                1.0677026154806063e-06,
                5.043475885674441e-07,
                1.9947299592933255e-06,
                1.2098659719716573e-06,
                7.338207180864763e-07,
                2.5612816000646084e-06,
                1.5534983101602148e-06,
                1.5534979397740895e-06,
                3.2887494574518405e-06
            ],
            [
                0.9999998724810027,
                0.9999995262096119,
                0.9999999176675534,
                0.9999989322975126,
                0.9999992661791947,
                0.9999999317439465,
                0.9999972735284305,
                0.9999999067050054,
                0.999999931743979,
                0.9999999067050276
            ],
            [
                5.043473480777865e-07,
                1.5534971990169383e-06,
                8.315282259138311e-07,
                1.6373764721072816e-07,
                3.466326211113502e-07,
                1.0677033791612137e-06,
                3.9278634073625165e-07,
                3.059023727894942e-07,
                5.04347348075149e-07,
                9.422445939054222e-07
            ],
            [
                0.999998446502246,
                0.9999984465016905,
                0.9999942280820395,
                0.9999339478244442,
                0.9999930377445911,
                2.3823688159291947e-07,
                4.5397857828200684e-05,
                1.7603438428848787e-06,
                0.9998911030785635,
                0.9999981261239486
            ],
            [
                0.9999993106391191,
                0.9999910603069,
                0.9999952149049381,
                0.9999993106387904,
                0.037326890021390696,
                2.561282210740037e-06,
                8.315283250394546e-07,
                4.0063682641226247e-05,
                5.043475885674441e-07,
                1.147877359957198e-05
            ],
            [
                0.9999993916411086,
                0.9999999067051499,
                0.9999993524050477,
                0.01798621387711511,
                0.999999391640891,
                0.999997273530381,
                0.9999997761970247,
                0.9999978766217917,
                0.9999967112517221,
                0.999999825702163
            ],
            [
                0.9999942280806683,
                0.9999945777797474,
                6.962254589978262e-06,
                0.9999921107374357,
                0.9999974387187086,
                0.9999822214418492,
                0.9999970976880185,
                0.9999546021206901,
                0.999964643736803,
                1.1478772230762415e-05
            ],
            [
                NaN,
                1.1478770861859053e-05,
                8.315278294114555e-07,
                6.962256249885085e-06,
                NaN,
                1.7603430034867993e-06,
                2.5612828213934817e-06,
                1.209865539298447e-06,
                4.785095065232451e-06,
                1.2098652508424818e-06
            ],
            [
                1.8925152753790864e-05,
                0.9999485577803465,
                0.9999998144609424,
                0.9999852610233219,
                0.029312227889470563,
                0.9999996940976638,
                0.9999985406243022,
                0.9999990577552943,
                1.8925152754169532e-05,
                0.9999984465028019
            ],
            [
                0.999998005269806,
                0.9999972735300561,
                0.9999984465020612,
                0.9999978766212879,
                0.9999964991443369,
                0.9999977396746272,
                0.999998005270518,
                0.9999646437578743,
                3.7266406168827523e-06,
                0.999998126124618
            ],
            [
                2.902313023130843e-06,
                6.962254589978262e-06,
                6.475947210031623e-07,
                1.6701423836262173e-05,
                0.9999985406230839,
                9.422449308774482e-07,
                5.715003789046955e-07,
                2.9023116391978967e-06,
                4.785096776499213e-06,
                2.699577774585891e-07
            ],
            [
                0.9999977396746261,
                0.9999982396561585,
                0.9999989322967484,
                0.9998415638234143,
                0.9999977396748954,
                0.9999990577551818,
                0.9999992188513903,
                0.9999984465016907,
                0.9999986290424675,
                0.9999724642958349
            ],
            [
                0.9999991684717745,
                1.3709573702822306e-06,
                0.9999993106389548,
                0.9999985406234317,
                0.9999993524051248,
                0.9999957771680685,
                0.9998911031307502,
                0.9999898700114471,
                NaN,
                2.4300249425247723e-05
            ],
            [
                2.144495097113319e-05,
                1.5534975693933505e-06,
                3.535625914492432e-05,
                0.9999452402245963,
                1.147877359957198e-05,
                4.2228334445658276e-06,
                2.561281600086738e-06,
                NaN,
                5.422219616265831e-06,
                0.9999955048195089
            ],
            [
                1.8553919030858602e-07,
                4.2228339479858295e-06,
                8.315277302841894e-07,
                2.1024339116168358e-07,
                5.715004470326849e-07,
                2.2603234895372223e-06,
                7.338207180898968e-07,
                1.0677028700422047e-06,
                1.760343213335281e-06,
                1.6701417863559525e-05
            ],
            [
                4.222833444590791e-06,
                1.3709576971463352e-06,
                2.2603242978871282e-06,
                2.902313023130843e-06,
                3.2887506336235617e-06,
                4.785094494783494e-06,
                2.902312677137316e-06,
                9.422442569315887e-07,
                2.561281294760143e-06,
                1.6701423836262173e-05
            ],
            [
                1.3709567165579959e-06,
                2.260325106237323e-06,
                9.422444815792981e-07,
                3.05902190458764e-07,
                1.0677026154806063e-06,
                5.043475885674441e-07,
                2.1024336609843824e-07,
                4.450848927650143e-07,
                1.209866260432471e-06,
                3.7266410611296085e-06
            ],
            [
                3.927862939136532e-07,
                3.0590222692437275e-07,
                2.3823688159291947e-07,
                3.466327450765785e-07,
                2.699577774585891e-07,
                6.475946438055299e-07,
                4.450850519403407e-07,
                2.1024326584582131e-07,
                5.043476486915964e-07,
                NaN
            ],
            [
                4.539787947559951e-05,
                0.9998204720573531,
                0.9999955048163067,
                6.962257079832313e-06,
                0.9999417087418132,
                0.9999995818812274,
                0.9999251538001324,
                0.9999983463110077,
                0.9999599362985673,
                8.315279285370317e-07
            ],
            [
                5.715003107755449e-07,
                1.0677027427525368e-06,
                7.338208930315157e-07,
                3.4663249714325014e-07,
                3.9278634073625165e-07,
                2.382369667929001e-07,
                4.450849988798682e-07,
                5.715003789033962e-07,
                4.4508510499737865e-07,
                3.466327037539638e-07
            ],
            [
                2.5612819054133693e-06,
                6.144172404738491e-06,
                6.47595107001401e-07,
                1.0677029973192638e-06,
                1.0677026154730804e-06,
                1.5534973842030142e-06,
                8.315280276580819e-07,
                7.889266347786918e-06,
                1.9947304348703948e-06,
                2.9023130230846496e-06
            ],
            [
                1.8553910183548312e-07,
                0.9999972735303808,
                2.3823702359290413e-07,
                0.9999994284997576,
                1.067703124601679e-06,
                0.9999990577549571,
                2.6995784182073116e-07,
                1.0129988564974359e-05,
                0.9998601778932265,
                0.9999756997621986
            ],
            [
                0.9999724642991231,
                0.9999969105048185,
                0.9999687980924049,
                0.9999910603005092,
                0.9999756997506378,
                0.9999771720110656,
                2.699578096393206e-07,
                0.9999957771665625,
                1.7603427936335396e-06,
                5.422217030747413e-06
            ],
            [
                0.9999994631247403,
                0.9999992188515765,
                0.9999998362622943,
                0.999999310639037,
                0.9999993106389548,
                0.9999996072137062,
                0.9999989969861516,
                0.9999998942830863,
                0.9999987901344615,
                0.9999994631250604
            ],
            [
                4.450849458218309e-07,
                9.422443692555439e-07,
                2.6995774527718623e-07,
                6.475945666063607e-07,
                4.785092783519724e-06,
                2.5612819054133693e-06,
                1.4449803818215767e-07,
                NaN,
                4.450852111135988e-07,
                2.9023119851781017e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                3.9278610661902853e-07,
                1.209865827752005e-06,
                1.067703124601679e-06,
                1.760342793638743e-06,
                4.450850519403407e-07,
                5.04347528446051e-07,
                1.5534973842076057e-06
            ],
            [
                5.043472879540142e-07,
                4.4508505193932864e-07,
                1.0677029973192638e-06,
                9.422448185510695e-07,
                5.04347468323289e-07,
                3.9278615344178325e-07,
                3.927862470899887e-07,
                3.0590226339061185e-07,
                8.315282259138311e-07,
                5.043475885674441e-07
            ],
            [
                1.7603438428800754e-06,
                0.9999978766205257,
                0.9999967112517201,
                0.9999995262095551,
                0.9999957771675652,
                0.999996273362051,
                0.9999969105051852,
                0.9999995262092728,
                0.9999996743688198,
                0.999999495652652
            ],
            [
                0.9999999176675338,
                0.999985261018053,
                0.9999861539971221,
                0.9999991684715762,
                0.9953904283120448,
                0.9999991148427535,
                0.9999983463100208,
                0.9999992188519494,
                0.9999996310116359,
                0.9999996310116359
            ],
            [
                9.422443692555439e-07,
                0.9999984465015056,
                0.9999993916409635,
                3.9278624708775595e-07,
                2.3823690999290963e-07,
                0.9999995549150543,
                6.475947982037486e-07,
                0.9999978766215386,
                0.9999756997506197,
                0.9999995262092728
            ],
            [
                0.9999967112513275,
                6.475947982037486e-07,
                1.3709572068522336e-06,
                0.9999984465016908,
                2.260325375664839e-06,
                2.5612812947508257e-06,
                1.3709572068522336e-06,
                0.9999989969857928,
                7.338208055664991e-07,
                6.9622587397397306e-06
            ],
            [
                4.2228319344021954e-06,
                7.338208055664991e-07,
                5.715005832872586e-07,
                5.043473480766399e-07,
                3.466325384678894e-07,
                1.3709575337159875e-06,
                3.9278605979534166e-07,
                8.315278294097538e-07,
                2.6995790618469934e-07,
                7.338209805224048e-07
            ]
        ]
    },
    {
        "q_id": "9328_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            13,
            16,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            33,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            68,
            73,
            75,
            76,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            96,
            97,
            98,
            101,
            103,
            105,
            107,
            109,
            110,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                3.059022998581767e-07,
                1.8925141473186853e-05,
                9.422442569334097e-07,
                2.382368815932174e-07,
                3.466325797900508e-07,
                3.466326624336003e-07,
                NaN,
                7.338212429594283e-07,
                1.637376862489725e-07,
                5.043476486924565e-07
            ],
            [
                7.734423152941018e-08,
                8.764241182641775e-08,
                3.288748673360027e-06,
                1.2751899728286965e-07,
                2.1024331597262577e-07,
                4.4508510499849186e-07,
                1.6373776432509826e-07,
                2.1024326584639497e-07,
                1.637377448057981e-07,
                6.825597214691097e-08
            ],
            [
                5.422220262599396e-06,
                3.9278605979534166e-07,
                1.760343423160973e-06,
                1.994730434879465e-06,
                2.699576809143613e-07,
                1.3709570434219446e-06,
                1.5534973842076057e-06,
                1.2098662604247682e-06,
                4.222833947960866e-06,
                1.3007134667070165e-05
            ],
            [
                1.5534971990126997e-06,
                3.7266397283908927e-06,
                1.7603434231833873e-06,
                1.7603438428800754e-06,
                5.422218323487975e-06,
                9.422447062270609e-07,
                3.2887478892683997e-06,
                3.7266410611296085e-06,
                5.422219616265831e-06,
                4.222834954778007e-06
            ],
            [
                1.7603434231833873e-06,
                1.0129994602895546e-05,
                6.475950298011458e-07,
                5.715003788993679e-07,
                9.422444815814404e-07,
                2.6995784182140636e-07,
                2.90231094723893e-06,
                5.043474683204221e-07,
                4.222834451382849e-06,
                5.715003789046955e-07
            ],
            [
                NaN,
                4.0063701740091395e-05,
                2.2603237589779086e-06,
                6.962257079705671e-06,
                3.2887482812745586e-06,
                1.9947306726594253e-06,
                4.2228349547223175e-06,
                1.1478766757561534e-05,
                1.3007131566015624e-05,
                1.6701427817730953e-05
            ],
            [
                9.4224425692559e-07,
                5.715003107715166e-07,
                5.715003107755449e-07,
                5.8291293348093234e-05,
                NaN,
                7.338208930391909e-07,
                8.939700567094277e-06,
                1.0677032518700286e-06,
                1.5534979397500702e-06,
                3.0590226339061185e-07
            ],
            [
                7.88926070489716e-06,
                3.288750633569722e-06,
                7.889259764273619e-06,
                9.422443692555439e-07,
                4.785093924251918e-06,
                1.4738989000422955e-05,
                6.144176799283803e-06,
                6.962253759828703e-06,
                1.5534975693869924e-06,
                1.6701421845057263e-05
            ],
            [
                9.422443692489024e-07,
                2.902312677137316e-06,
                7.338210680021253e-07,
                3.059021175247079e-07,
                1.0129989772532511e-05,
                8.315284241650899e-07,
                2.382370235922541e-07,
                8.315281267834927e-07,
                1.7603425837606927e-06,
                1.2098659719757836e-06
            ],
            [
                1.6373764721072816e-07,
                5.043472879540142e-07,
                1.2751899728311609e-07,
                4.4508494582405734e-07,
                5.715005151606823e-07,
                2.6995774527718623e-07,
                3.7266410611296085e-06,
                7.734428685047173e-08,
                5.04347287955046e-07,
                1.3709576971463352e-06
            ],
            [
                8.315281267882195e-07,
                1.2098652508287273e-06,
                5.043476486833397e-07,
                1.3709572068422585e-06,
                1.3709570433979422e-06,
                2.2603237589676295e-06,
                1.5534971990126997e-06,
                5.043472879540142e-07,
                2.5612812947508257e-06,
                1.2098656835136636e-06
            ],
            [
                NaN,
                5.043472278322555e-07,
                3.05902190458764e-07,
                NaN,
                1.3709573702647743e-06,
                1.2098659719788098e-06,
                6.825608606172863e-08,
                8.31528325040778e-07,
                2.5612828213934817e-06,
                9.422445939054222e-07
            ],
            [
                8.939698435560267e-06,
                NaN,
                5.715006514151423e-07,
                0.00013982205735608936,
                1.99472900813862e-06,
                1.4738983729053029e-05,
                1.2098662604247682e-06,
                8.939693107093343e-06,
                4.222834954753043e-06,
                1.3709572068522336e-06
            ],
            [
                1.5534984953552536e-06,
                1.994730197071414e-06,
                1.99472900813862e-06,
                2.5612825160562587e-06,
                5.043473480777865e-07,
                1.5534977545886537e-06,
                7.889259764359722e-06,
                0.0001398220575534256,
                2.9023109471689794e-06,
                4.450850519403407e-07
            ],
            [
                4.4508505193932864e-07,
                1.5534971990126997e-06,
                2.102434412875379e-07,
                1.0677032518785256e-06,
                1.2098652508347793e-06,
                1.2098653950606901e-06,
                1.5534979397740895e-06,
                2.6995771309523475e-07,
                3.726639284125553e-06,
                1.3709576971379186e-06
            ],
            [
                6.475947210012481e-07,
                1.067703251864202e-06,
                6.475951069985296e-07,
                9.422444815765128e-07,
                5.043475885674441e-07,
                8.315282259138311e-07,
                6.144172404693786e-06,
                4.4508510499849186e-07,
                6.475948754012522e-07,
                5.715003107738556e-07
            ],
            [
                1.6373776432509826e-07,
                1.1253513522447425e-07,
                2.3823693839325527e-07,
                1.1253512180925583e-07,
                4.222831934379152e-06,
                0.9999987901338849,
                7.734418542875216e-08,
                3.466327037548308e-07,
                NaN,
                1.1253509497883659e-07
            ],
            [
                0.999997273529084,
                0.9999991148431759,
                0.9999942280806755,
                5.043474081993875e-07,
                1.012998977264307e-05,
                4.785095635624897e-06,
                0.9999962733611651,
                2.902311985079115e-06,
                4.450849988811838e-07,
                2.2603234895372223e-06
            ],
            [
                3.7266397283908927e-06,
                1.760343213335281e-06,
                7.338210679909462e-07,
                2.561282210729555e-06,
                1.5534984953453635e-06,
                2.9023116391675407e-06,
                1.2098659719757836e-06,
                8.315283250371857e-07,
                1.9947299593078385e-06,
                2.9023112932177327e-06
            ],
            [
                NaN,
                2.9023116392097746e-06,
                2.382370235933104e-07,
                0.9999972735300572,
                7.889265407327733e-06,
                0.99999385582248,
                1.5534971990126997e-06,
                7.734425919002834e-08,
                2.1024334103581732e-07,
                2.2603248367949354e-06
            ],
            [
                3.927863407379485e-07,
                6.475950298011458e-07,
                4.450852641717689e-07,
                1.4449805540763184e-07,
                NaN,
                NaN,
                9.422442569315887e-07,
                7.338208055680009e-07,
                5.4222176771176554e-06,
                4.4508510499849186e-07
            ],
            [
                0.9999892166865378,
                0.9999980052705177,
                0.9999975938985227,
                3.05902336324494e-07,
                6.023574911170301e-08,
                0.9999972735303825,
                0.9999984465028023,
                0.9999987121043247,
                0.9999877809240179,
                1.275190276859705e-07
            ],
            [
                1.670141786325573e-05,
                5.422217030747413e-06,
                0.9999938558276132,
                2.9023119851635836e-06,
                0.9999623635396417,
                0.9999934595620072,
                0.9999852610110367,
                5.4222183234485234e-06,
                1.4738987243236881e-05,
                1.0677027427600627e-06
            ],
            [
                2.4300249425247723e-05,
                1.4449802095666915e-07,
                0.9999980052709944,
                3.0590237279032884e-07,
                2.3823682479317953e-07,
                3.05902190458764e-07,
                1.2098659719788098e-06,
                2.1024336609874897e-07,
                1.1253506814842375e-07,
                7.338207180898968e-07
            ],
            [
                2.2603253756874524e-06,
                1.5534981249697903e-06,
                1.5534977545886537e-06,
                4.785092783519724e-06,
                0.9999969105055538,
                2.5612834320563895e-06,
                1.553497384196656e-06,
                6.962257909785973e-06,
                2.260325106237323e-06,
                1.994729483729522e-06
            ],
            [
                1.5534981249574276e-06,
                5.715007195447234e-07,
                7.338207180838067e-07,
                4.450849988811838e-07,
                5.043476486915964e-07,
                1.4738983729294318e-05,
                1.1478770862589836e-05,
                2.5612812947508257e-06,
                6.475947982002148e-07,
                1.5534981249291695e-06
            ],
            [
                2.1024336609843824e-07,
                1.209866260432471e-06,
                NaN,
                1.2098656835136636e-06,
                6.9622537599680095e-06,
                6.144177531767002e-06,
                1.5534977545886537e-06,
                6.962257909785973e-06,
                6.475949525981759e-07,
                4.450851580555361e-07
            ],
            [
                1.9947301970972664e-06,
                9.422447062202052e-07,
                3.7266392836984955e-06,
                1.5534979397500702e-06,
                6.14417753171671e-06,
                7.889266347715168e-06,
                3.2887502414436403e-06,
                3.288748281220719e-06,
                1.9947297214544894e-06,
                1.2098652508287273e-06
            ],
            [
                1.0677026154730804e-06,
                1.55349775456958e-06,
                1.3709567165530083e-06,
                6.475949525981759e-07,
                7.338212429582604e-07,
                4.222831934352267e-06,
                2.9023126771227976e-06,
                NaN,
                5.422219616228845e-06,
                2.2603234895176927e-06
            ],
            [
                1.2098653950656417e-06,
                1.7603425837791042e-06,
                1.0677024881980089e-06,
                1.209865683518615e-06,
                7.338213304316717e-07,
                1.1478765389222573e-05,
                5.715003789017068e-07,
                1.2098659719757836e-06,
                1.0677024881980089e-06,
                3.535624228698939e-05
            ],
            [
                1.4449796928021588e-07,
                1.994729483729522e-06,
                9.422443692574719e-07,
                6.475947210046347e-07,
                1.6373766672973748e-07,
                1.209865827752005e-06,
                9.931189774187203e-08,
                1.6373774480605869e-07,
                3.9278610661902853e-07,
                5.043475885696228e-07
            ],
            [
                3.9278629391427843e-07,
                3.466325797896173e-07,
                7.338212429582604e-07,
                3.7266383956509585e-06,
                2.5612831267202583e-06,
                NaN,
                6.962258739796719e-06,
                NaN,
                1.0677027427624903e-06,
                4.785096206076165e-06
            ],
            [
                1.2098662604247682e-06,
                1.1478768126057254e-05,
                6.962257909785973e-06,
                6.9622595696935874e-06,
                4.222831934379152e-06,
                6.144175334418252e-06,
                4.222834451382849e-06,
                1.5534971990126997e-06,
                8.315278293951957e-07,
                1.3709573702722555e-06
            ],
            [
                3.466327450765785e-07,
                2.6995771309523475e-07,
                2.2603237589779086e-06,
                3.059022998576899e-07,
                3.9278610661902853e-07,
                5.422218969895357e-06,
                NaN,
                2.1444940745839484e-05,
                1.760343003481596e-06,
                NaN
            ],
            [
                2.3823690999323465e-07,
                2.699578096403948e-07,
                9.422444815814404e-07,
                8.315279285370317e-07,
                5.043475284447896e-07,
                3.927861534431675e-07,
                5.043475885674441e-07,
                9.422450432030903e-07,
                6.023569884718319e-08,
                7.338210680021253e-07
            ],
            [
                1.8553910183674878e-07,
                1.8553910183674878e-07,
                4.6911677163762064e-08,
                7.734426841017797e-08,
                NaN,
                5.043475885696228e-07,
                3.05902336324494e-07,
                1.4449803818215767e-07,
                5.043472278322555e-07,
                1.209865539295696e-06
            ],
            [
                0.99999106030052,
                0.9999822214524658,
                1.8553910183674878e-07,
                1.300712536408621e-05,
                0.9999810748540663,
                4.785096776468749e-06,
                1.7603438428800754e-06,
                1.3709575337159875e-06,
                2.382370235933104e-07,
                2.902311985146426e-06
            ],
            [
                8.939697369980456e-06,
                3.927862470899887e-07,
                3.466327037548308e-07,
                6.475950298021765e-07,
                NaN,
                NaN,
                6.144172404738491e-06,
                5.715005832886879e-07,
                3.9278605979534166e-07,
                0.9999945777803892
            ],
            [
                1.4449802095666915e-07,
                1.1253513522447425e-07,
                6.825597214718257e-08,
                1.1253508156363576e-07,
                1.275190732904469e-07,
                6.023568448589658e-08,
                8.764242227418718e-08,
                1.1253506814842375e-07,
                7.734428685047173e-08,
                4.450852111155216e-07
            ],
            [
                2.1024341622426268e-07,
                8.315281267834927e-07,
                5.043472879540142e-07,
                8.315277302841894e-07,
                2.1024341622368903e-07,
                3.927862470899887e-07,
                3.288749849529972e-06,
                5.043472278322555e-07,
                1.0677033791612137e-06,
                3.9278610661902853e-07
            ],
            [
                3.9278629391427843e-07,
                1.275190732904469e-07,
                4.450852111148132e-07,
                6.475947210046347e-07,
                1.444980381819277e-07,
                6.1441767993788005e-06,
                5.043476486924565e-07,
                2.6995784182183607e-07,
                1.0677033791583005e-06,
                3.2887478892683997e-06
            ],
            [
                2.6995784182183607e-07,
                7.33821330437595e-07,
                1.2098656835224664e-06,
                1.994730434879465e-06,
                3.05902336324494e-07,
                3.726639284103523e-06,
                5.043475885696228e-07,
                1.9947297214182054e-06,
                2.6995771309523475e-07,
                7.338209805240734e-07
            ],
            [
                1.99472900813862e-06,
                1.0677032518785256e-06,
                9.422444815765128e-07,
                1.9947297215043796e-06,
                1.0677031245905116e-06,
                1.3709575337078829e-06,
                7.889261645355786e-06,
                5.144220140264605e-05,
                9.422449308748773e-07,
                3.726638395611981e-06
            ],
            [
                9.422448185478557e-07,
                2.5612828213818346e-06,
                6.475945666051092e-07,
                8.315283250371857e-07,
                3.7266383955882547e-06,
                9.422444815765128e-07,
                7.338211554783522e-07,
                1.5534979397740895e-06,
                1.7603427936263351e-06,
                1.2098658277451275e-06
            ],
            [
                6.475949525981759e-07,
                4.450852111135988e-07,
                8.315283250371857e-07,
                1.5534971990126997e-06,
                1.7603438428740716e-06,
                7.889261645355786e-06,
                9.422444815628016e-07,
                1.0677026154730804e-06,
                5.715003789017068e-07,
                4.222832437747125e-06
            ],
            [
                1.1478770862589836e-05,
                9.4224425692559e-07,
                1.6701419853852583e-05,
                7.484624512366966e-05,
                1.5534971990126997e-06,
                4.78509278348926e-06,
                2.2603242978665707e-06,
                1.760343213335281e-06,
                1.5534971990126997e-06,
                7.889261645269683e-06
            ],
            [
                7.338208055664991e-07,
                2.699578740032504e-07,
                1.855390576008354e-07,
                2.102434162245973e-07,
                2.1024336609874897e-07,
                2.3823688159291947e-07,
                NaN,
                5.043475885696228e-07,
                2.6995784182140636e-07,
                5.04347287955046e-07
            ],
            [
                3.2887502413389517e-06,
                2.5612828213934817e-06,
                2.2603242978007868e-06,
                1.3709573702778664e-06,
                1.994729721469003e-06,
                3.2887478892683997e-06,
                2.5612816000145246e-06,
                6.475945666033422e-07,
                8.31527928532683e-07,
                9.422443692527585e-07
            ],
            [
                3.0590237279085045e-07,
                3.059022269250683e-07,
                1.6373766672973748e-07,
                1.5534975693979422e-06,
                1.3709576971463352e-06,
                2.3823690999236795e-07,
                3.9278605979534166e-07,
                1.8553919030858602e-07,
                6.475947210031623e-07,
                5.04347287955046e-07
            ],
            [
                NaN,
                5.715003107755449e-07,
                1.6701423834226767e-05,
                NaN,
                3.120192625482384e-05,
                4.4508515805735777e-07,
                2.699576809143613e-07,
                3.0590237279085045e-07,
                8.315284241650899e-07,
                2.561281294760143e-06
            ],
            [
                4.4508515805735777e-07,
                1.3709573702822306e-06,
                8.939694172957213e-06,
                1.5534984953453635e-06,
                NaN,
                1.2098659719757836e-06,
                5.043473480777865e-07,
                8.315280276626197e-07,
                5.715003107767143e-07,
                6.144173869603344e-06
            ],
            [
                4.450851580555361e-07,
                1.4449795205457127e-07,
                2.5612819054028872e-06,
                3.05902190458764e-07,
                1.8553919030858602e-07,
                5.715003107755449e-07,
                2.1024331597262577e-07,
                2.1024336609843824e-07,
                3.927860597935108e-07,
                1.0129995810463632e-05
            ],
            [
                1.8553905760062447e-07,
                1.2098656835224664e-06,
                6.475947210046347e-07,
                1.4449796927932878e-07,
                1.0677032518785256e-06,
                4.450852111148132e-07,
                5.043472879540142e-07,
                1.8553907971855875e-07,
                4.450849988811838e-07,
                1.0677029973192638e-06
            ],
            [
                1.0677028700422047e-06,
                1.2098659719788098e-06,
                1.994730434879465e-06,
                NaN,
                6.47595107001401e-07,
                6.144176066901277e-06,
                4.450852111148132e-07,
                2.430024073461624e-05,
                1.9947292459347367e-06,
                1.7603434231833873e-06
            ],
            [
                8.315281267834927e-07,
                6.47595107001401e-07,
                NaN,
                1.8553914607267268e-07,
                1.3709576971463352e-06,
                2.382368815932174e-07,
                4.006370652067535e-05,
                0.9999573525426652,
                6.475946438055299e-07,
                1.4449796928021588e-07
            ],
            [
                3.466325797888292e-07,
                1.2098659719788098e-06,
                7.338209805224048e-07,
                8.315280276626197e-07,
                9.422443692574719e-07,
                3.726637951387472e-06,
                1.8553907971879076e-07,
                5.043473480766399e-07,
                1.8553919030858602e-07,
                1.9947292459265734e-06
            ],
            [
                1.3709573702822306e-06,
                9.422445939054222e-07,
                1.0677026154806063e-06,
                6.962257909785973e-06,
                9.422442569315887e-07,
                7.88926446679691e-06,
                1.9947304348595095e-06,
                1.2098658277451275e-06,
                1.2098662604247682e-06,
                5.04347468318358e-07
            ],
            [
                2.5612834320563895e-06,
                2.9023116392097746e-06,
                1.2751904288739315e-07,
                3.059021175261338e-07,
                6.475947210046347e-07,
                3.466325797896173e-07,
                3.927860597935108e-07,
                8.315281267882195e-07,
                2.5612834320563895e-06,
                5.715006514176113e-07
            ],
            [
                3.927862002663297e-07,
                2.753568782024347e-05,
                3.466326211113502e-07,
                2.56128282131428e-06,
                8.315280276607289e-07,
                3.7266401726359486e-06,
                5.043474081993875e-07,
                2.430024942462891e-05,
                2.9023133690980155e-06,
                0.9999885212319407
            ],
            [
                3.288750241561788e-06,
                2.699576809143613e-07,
                9.931202796993203e-08,
                8.315284241650899e-07,
                2.2603253756956754e-06,
                5.422220262636381e-06,
                9.422447062294175e-07,
                NaN,
                7.88926634755014e-06,
                6.475950298011458e-07
            ],
            [
                1.2751902768612997e-07,
                1.4738983729294318e-05,
                1.760343003481596e-06,
                5.71500719545698e-07,
                9.931186222523604e-08,
                0.9999955048184339,
                4.4508515805735777e-07,
                0.9999983463108099,
                0.9999980052709949,
                3.927863407379485e-07
            ],
            [
                7.338209805240734e-07,
                1.5534983101301911e-06,
                5.043472278322555e-07,
                2.2603253756956754e-06,
                3.466327037548308e-07,
                5.422220262636381e-06,
                NaN,
                1.9947301970972664e-06,
                2.9023119851781017e-06,
                5.829128639666634e-05
            ],
            [
                1.0677032518814388e-06,
                6.475945666063607e-07,
                2.5612828213934817e-06,
                1.0677032518814388e-06,
                1.0677026154806063e-06,
                1.2098656835224664e-06,
                4.450852641737424e-07,
                4.785093924362895e-06,
                4.450852641737424e-07,
                9.422448185534261e-07
            ],
            [
                7.338213304363436e-07,
                0.9999957771680741,
                8.315277302841894e-07,
                2.10243290909724e-07,
                0.9999972735307101,
                2.5612819054133693e-06,
                5.04347528446051e-07,
                3.466326211113502e-07,
                3.4663266243308805e-07,
                6.475945666051092e-07
            ],
            [
                9.422442569315887e-07,
                1.3007130015488633e-05,
                2.7535700949523498e-05,
                2.1024339116168358e-07,
                3.4663278639892215e-07,
                1.2098652508424818e-06,
                1.7603438428800754e-06,
                3.466326624336003e-07,
                4.450848927658745e-07,
                7.338208930460318e-07
            ],
            [
                1.4738976701411704e-05,
                1.637376862489725e-07,
                1.8553910183674878e-07,
                2.3823688159291947e-07,
                NaN,
                5.144222593244026e-05,
                1.2098661162056318e-06,
                2.699576809143613e-07,
                2.3823690999323465e-07,
                8.315279285370317e-07
            ],
            [
                NaN,
                8.939693107093343e-06,
                3.726639728370556e-06,
                6.962257909785973e-06,
                2.2603234895289998e-06,
                1.5534984953552536e-06,
                1.5534975693979422e-06,
                8.315282259138311e-07,
                5.422220262636381e-06,
                4.7850950649408664e-06
            ],
            [
                5.04347287955046e-07,
                1.0129992187658463e-05,
                5.043472879540142e-07,
                4.0063682639477306e-05,
                1.4738976701411704e-05,
                1.1478768126057254e-05,
                5.422218969858371e-06,
                6.9622595696935874e-06,
                2.753568453712307e-05,
                1.0677026154806063e-06
            ],
            [
                1.0677029972920738e-06,
                2.2603234895372223e-06,
                3.466327863961242e-07,
                8.315278294072958e-07,
                NaN,
                3.2887482812745586e-06,
                9.422447062202052e-07,
                1.9947306726594253e-06,
                5.043472879540142e-07,
                9.422445938728576e-07
            ],
            [
                9.422448185510695e-07,
                1.300712536350655e-05,
                8.315283250394546e-07,
                7.338208930391909e-07,
                1.994729483666479e-06,
                9.42244930862237e-07,
                4.222832941142044e-06,
                5.043472879540142e-07,
                1.0129989772532511e-05,
                9.422444815679433e-07
            ],
            [
                4.2228329411708495e-06,
                NaN,
                6.144172404693786e-06,
                5.04347468323289e-07,
                2.2603242978871282e-06,
                1.760343003481596e-06,
                1.3709572068478697e-06,
                8.315278294114555e-07,
                1.209866260432471e-06,
                1.0677029973192638e-06
            ],
            [
                2.382368531929327e-07,
                3.927862002663297e-07,
                3.466327037548308e-07,
                2.10243290909724e-07,
                2.3823693839290317e-07,
                1.6373762769138607e-07,
                2.699577774585891e-07,
                3.059021175261338e-07,
                3.05902190458764e-07,
                3.288748673376478e-06
            ],
            [
                NaN,
                5.422217677152175e-06,
                6.962255419728997e-06,
                7.889261645090304e-06,
                1.9947297214944016e-06,
                6.1441724044534996e-06,
                1.473897670007122e-05,
                3.72664061681327e-06,
                3.7266392839832006e-06,
                2.753568782024347e-05
            ],
            [
                1.994729008145876e-06,
                9.422445939054222e-07,
                8.315278294072958e-07,
                8.315280276546789e-07,
                5.043475885674441e-07,
                1.994729245917502e-06,
                2.5612812947077304e-06,
                1.5534977545886537e-06,
                1.994729959224386e-06,
                3.2887502415438413e-06
            ],
            [
                2.260324836787226e-06,
                NaN,
                4.222832941193893e-06,
                1.067703124601679e-06,
                1.1478765389368729e-05,
                1.8553905760062447e-07,
                2.1024341622426268e-07,
                9.422445939054222e-07,
                7.338208930460318e-07,
                1.2098662604291696e-06
            ],
            [
                1.2098662604291696e-06,
                3.927862002654366e-07,
                6.962257909785973e-06,
                NaN,
                1.994730434879465e-06,
                1.0677029973158649e-06,
                2.7535704231844484e-05,
                6.475947210012481e-07,
                7.338212429504183e-07,
                1.1478773599425825e-05
            ],
            [
                1.760343633031919e-06,
                3.9278638755992735e-07,
                4.450849988798682e-07,
                1.0677029973192638e-06,
                2.5612812947380135e-06,
                9.422450432014836e-07,
                2.2603234895176927e-06,
                4.450851580555361e-07,
                9.422442569208767e-07,
                2.5612831267202583e-06
            ],
            [
                1.5534979397790343e-06,
                4.222831934379152e-06,
                2.1444950971601277e-05,
                1.5534981249697903e-06,
                1.2098662604291696e-06,
                0.00012339463384858465,
                1.8553910183607374e-07,
                1.6373766672973748e-07,
                1.5534981249697903e-06,
                8.315281267861397e-07
            ],
            [
                1.760342793583908e-06,
                2.5612834320470717e-06,
                1.0677028700363782e-06,
                5.715005151550947e-07,
                7.338212429537553e-07,
                4.785092783519724e-06,
                1.5534984953453635e-06,
                1.5534971990126997e-06,
                1.760344052714248e-06,
                1.3709572068422585e-06
            ],
            [
                1.1478770862882149e-05,
                2.2603253756956754e-06,
                7.33821330437595e-07,
                5.043475885696228e-07,
                NaN,
                9.422445939002803e-07,
                NaN,
                2.699578096393206e-07,
                9.4224425692559e-07,
                2.902312677137316e-06
            ],
            [
                1.5534984953453635e-06,
                1.7603427936335396e-06,
                1.553497754577351e-06,
                2.902313369111213e-06,
                1.7603427936335396e-06,
                1.3709570434122812e-06,
                1.994729483705484e-06,
                9.422450432014836e-07,
                NaN,
                6.475945666051092e-07
            ],
            [
                3.4663262110945863e-07,
                6.475947210046347e-07,
                5.715004470313855e-07,
                1.8553903548231313e-07,
                8.315284241597959e-07,
                2.102434412875379e-07,
                1.2098655392811161e-06,
                4.450851580555361e-07,
                5.043474683204221e-07,
                2.69957906184239e-07
            ],
            [
                6.475946437996402e-07,
                1.5534983101602148e-06,
                2.260324297853209e-06,
                6.475945666051092e-07,
                3.7266406168827523e-06,
                2.5612819054133693e-06,
                0.0001233945892201689,
                2.382368815916736e-07,
                1.0129987357287368e-05,
                2.1444943301674863e-05
            ],
            [
                1.9947292459347367e-06,
                1.2098662604291696e-06,
                5.71500515159253e-07,
                1.7603438428800754e-06,
                1.994729483723626e-06,
                2.9023119851635836e-06,
                9.422450431989127e-07,
                1.3709573702822306e-06,
                4.4508494582405734e-07,
                1.7603427936335396e-06
            ],
            [
                5.04347468323289e-07,
                1.0129988564974359e-05,
                3.059022269250683e-07,
                5.715003789017068e-07,
                6.47594952595231e-07,
                6.144172404587612e-06,
                3.466326624336003e-07,
                NaN,
                8.939696304311336e-06,
                8.315279285351409e-07
            ],
            [
                6.962253759752719e-06,
                2.699578096403948e-07,
                2.382370235933104e-07,
                1.9947301970972664e-06,
                NaN,
                2.1024336609843824e-07,
                3.05902336324494e-07,
                1.4449802095666915e-07,
                3.05902336324494e-07,
                2.1024339116168358e-07
            ],
            [
                1.5534981249697903e-06,
                1.0677032518785256e-06,
                0.0,
                NaN,
                7.338208055664991e-07,
                9.422445939002803e-07,
                1.1478773599102191e-05,
                7.889266347715168e-06,
                2.430024073461624e-05,
                3.0590233632400716e-07
            ],
            [
                1.6701419854156377e-05,
                8.939697369980456e-06,
                6.475950298011458e-07,
                3.2887502415438413e-06,
                1.3709570434219446e-06,
                3.2887478892504536e-06,
                1.3007134667259441e-05,
                4.222834954778007e-06,
                1.5534981249697903e-06,
                2.2603253756874524e-06
            ],
            [
                6.9622587396067566e-06,
                9.422444815765128e-07,
                1.0129994602656007e-05,
                6.962256249821764e-06,
                1.209865683518615e-06,
                1.7603425837606927e-06,
                1.99472900813862e-06,
                6.475945666033422e-07,
                3.927863875584984e-07,
                1.7603427935518875e-06
            ],
            [
                7.338213304363436e-07,
                1.012998735687278e-05,
                8.315279285351409e-07,
                4.222834954778007e-06,
                8.939693107190907e-06,
                5.043472879540142e-07,
                1.3007134667259441e-05,
                2.902312677137316e-06,
                5.422217676925328e-06,
                3.1201907657271834e-05
            ],
            [
                8.939700567004841e-06,
                1.3709567165617364e-06,
                7.889265407255982e-06,
                2.561281905376098e-06,
                4.785092783519724e-06,
                1.7603427936263351e-06,
                1.5534975693933505e-06,
                4.222832437639588e-06,
                6.1441760667392215e-06,
                2.2603242978871282e-06
            ],
            [
                NaN,
                1.994730434879465e-06,
                NaN,
                1.553497384196656e-06,
                2.6995790618350237e-07,
                1.3709575337078829e-06,
                9.422444815765128e-07,
                2.2603251062450327e-06,
                1.2751904288710323e-07,
                1.7603434231777837e-06
            ]
        ]
    },
    {
        "q_id": "9503_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998555019274,
                0.9999998144608541,
                0.9999999226557224,
                0.9999999397642868,
                0.9999998874648515,
                0.9999997617630901,
                0.9999998942830485,
                0.9999998362623529,
                0.9999999123574838,
                0.9999999123574629
            ],
            [
                0.9999998802069017,
                0.9999999317439058,
                0.9999998024947273,
                0.9999999226557778,
                0.9999997897565588,
                0.9999999176675436,
                0.9999998461826956,
                0.999999872480942,
                0.9999998802069444,
                0.999999906705061
            ],
            [
                0.9999999006879957,
                0.9999998555019963,
                0.999999653367255,
                0.9999999500628453,
                0.9999999397643154,
                0.9999999226557408,
                0.9999998802069017,
                0.9999996743688199,
                0.9999999434137367,
                0.9999997617629766
            ],
            [
                0.9999997761971849,
                0.9999998024947037,
                0.9999998144609645,
                0.9999999358793639,
                0.9999999317439058,
                0.9999998874648112,
                0.9999999067050609,
                0.9999999226557778,
                0.9999999500627739,
                0.9999999123575255
            ],
            [
                0.999999906705072,
                0.9999999123574523,
                0.9999998024946095,
                1.0,
                0.9999998874649051,
                0.9999999358794021,
                0.9999999317440198,
                0.9999998874648648,
                0.9999999226558515,
                0.9999998144608319
            ],
            [
                0.9999997463980729,
                0.9999998874647978,
                0.9999998942829098,
                0.9999994284994853,
                0.999999802494633,
                0.9999997463980125,
                0.9999998555019274,
                0.999999894283061,
                0.9999998724809875,
                0.9999998362623723
            ],
            [
                0.9999994284993489,
                0.9999999397642078,
                1.0,
                0.9999999273418702,
                0.9999998024946566,
                0.999999946842163,
                0.9999999176675535,
                0.9999998144608762,
                0.9999999273418703,
                0.999999802494586
            ],
            [
                0.9999999176674357,
                0.9999998362623529,
                0.9999998724808964,
                0.9999999006880786,
                0.9999997761970248,
                0.9999999006880668,
                0.9999998942829477,
                0.9999999358793714,
                0.9999998555020135,
                0.9999997897567092
            ],
            [
                0.9999999176675338,
                0.9999998802069874,
                0.999999931743914,
                0.9999999317439221,
                0.9999999468420996,
                0.9999998555019619,
                0.999999825702059,
                0.9999998144608541,
                0.9999998642566866,
                0.9999999123575674
            ],
            [
                0.9999998461826406,
                0.9999996940978462,
                0.9999998642567351,
                0.9999998024947272,
                0.9999999317440035,
                0.9999998257021837,
                0.9999998362623529,
                0.9999998555019274,
                0.9999998874647977,
                0.9999998802069731
            ],
            [
                0.9999999067050609,
                1.0,
                0.9999999123574732,
                0.9999999358794402,
                0.9999999226557225,
                0.9999999067051387,
                0.999999943413811,
                0.9999996940978098,
                1.0,
                0.9999999273417923
            ],
            [
                0.9999997617631753,
                0.9999999123575778,
                0.9999999434137841,
                0.999999900688055,
                0.999999554914789,
                0.9999998942830233,
                0.9999999123574523,
                0.9999998942829602,
                0.9999998942830106,
                0.9999999358793944
            ],
            [
                0.9999998144609424,
                0.9999996940977004,
                0.9999999226557685,
                0.9999994284994853,
                0.999999526209273,
                0.9999996533672965,
                0.9999998362622748,
                0.9999993524051249,
                0.9999997617631754,
                0.9999998802069731
            ],
            [
                0.9999998642566381,
                0.9999998802069587,
                0.9999997897565589,
                0.999999917667475,
                0.9999998874647978,
                0.9999999317439546,
                0.9999999397643156,
                0.9999993106389553,
                0.9999996072137063,
                0.9999998724809267
            ],
            [
                0.9999997126313098,
                0.9999996533674205,
                0.9999998874647977,
                0.9999997897567342,
                0.9999998024945624,
                0.9999997897566592,
                0.9999998362623724,
                0.999999802494586,
                0.9999998802069731,
                0.9999998144609646
            ],
            [
                0.9999998144608983,
                0.9999999559306312,
                0.9999999468421567,
                0.9999999067051277,
                0.9999996940978462,
                0.9999999273418876,
                0.999999825702059,
                0.9999998724809115,
                0.9999999317439953,
                0.9999998942829476
            ],
            [
                0.9999999226558238,
                0.9999999176675437,
                0.9999999123575464,
                0.9999999123574732,
                0.9999999006880668,
                0.9999999656787284,
                0.9999998802069302,
                0.9999999317439221,
                0.9999999123575778,
                0.9999999434137907
            ],
            [
                0.9999998802069017,
                0.999999730042094,
                0.9999999530883452,
                0.9999999123575778,
                0.9999999226557224,
                0.999999917667524,
                0.9999996533673378,
                0.9999998942829477,
                0.9999998555020136,
                0.9999995818814266
            ],
            [
                0.9999999273417663,
                0.9999999176675239,
                1.0,
                0.9999999273418009,
                0.9999999176675632,
                0.99999992265575,
                0.9999998802069017,
                1.0,
                1.0,
                0.9999999176674946
            ],
            [
                0.9999999397642437,
                0.999999931743979,
                1.0,
                0.9999999123574733,
                0.999999922655787,
                0.9999999123574838,
                0.999999887464744,
                0.999999730042094,
                0.9999999123574419,
                0.9999999273418703
            ],
            [
                0.9999997300423192,
                0.9999998144608541,
                0.9999998257021631,
                0.9999996533672963,
                0.9999998144609424,
                0.9999997300422226,
                0.9999999176674357,
                0.9999998257021422,
                0.9999997463980125,
                0.9999999226558423
            ],
            [
                0.9999998024947037,
                0.9999999358793867,
                0.9999999226558423,
                0.9999998724809723,
                0.9999999067050276,
                0.9999999123574523,
                0.9999999530883396,
                0.9999998144609203,
                0.9999998555020481,
                0.9999996743688199
            ],
            [
                0.9999999123575882,
                0.9999999468421693,
                0.9999999176674357,
                0.9999999317440197,
                0.9999999611088811,
                0.999999946842106,
                0.9999999358793715,
                0.9999999559306259,
                0.9999998362623723,
                0.9999999358793638
            ],
            [
                0.9999998642566219,
                0.9999997463982241,
                0.9999998461826588,
                0.999999887464744,
                1.0,
                0.9999998642566219,
                0.9999997463981334,
                0.9999998461827139,
                0.9999998724809268,
                0.9999998942829225
            ],
            [
                0.9999998802068873,
                0.9999997126313099,
                0.9999999273418528,
                0.9999998257022045,
                0.9999999006880786,
                0.9999998802069017,
                0.9999998555019274,
                0.999999730042255,
                0.9999998362622358,
                0.9999998874648782
            ],
            [
                0.9999999273417923,
                0.9999999273417663,
                0.9999998461827139,
                0.9999998555019447,
                0.999999802494633,
                0.9999998724809724,
                0.9999999006879957,
                0.9999999176675829,
                0.9999998555019963,
                0.9999999123574733
            ],
            [
                0.9999999123575359,
                0.9999999358793638,
                1.0,
                1.0,
                0.9999999500628274,
                0.9999999226558054,
                0.9999999434137571,
                0.9999999317439546,
                0.9999999006881378,
                1.0
            ],
            [
                0.9999998802069587,
                0.9999997300421906,
                0.9999996743688975,
                0.9999998024946567,
                0.9999997897567092,
                0.9999996940977733,
                0.9999996072137063,
                0.9999998642566543,
                0.999998790134173,
                0.9999994284994853
            ],
            [
                0.9999997897567342,
                0.999999961108909,
                0.9999998024945624,
                0.9999999123575881,
                0.9999999500628274,
                0.999999900687972,
                0.9999999634651487,
                0.999999943413811,
                0.9999998144608981,
                0.9999999226557224
            ],
            [
                0.9999999468421756,
                0.9999999358794097,
                0.9999998874648246,
                0.99999992265575,
                0.9999999611088951,
                0.9999997126315153,
                1.0,
                0.9999999317440034,
                0.9999999586005999,
                0.9999997897566341
            ],
            [
                1.0,
                0.9999999067050387,
                0.9999998555019447,
                1.0,
                1.0,
                0.9999999067051499,
                0.9999998555020309,
                1.0,
                1.0,
                0.9999998642567353
            ],
            [
                0.9999999067050943,
                0.9999999468421567,
                0.999999900687984,
                0.9999999434138043,
                0.9999999273417923,
                1.0,
                0.9999998642567353,
                0.9999999434137098,
                1.0,
                1.0
            ],
            [
                0.9999998802069444,
                0.9999997126313783,
                0.999999887464838,
                0.9999992188512975,
                1.0,
                0.9999999530883508,
                0.9999997126313441,
                0.9999998874648782,
                1.0,
                0.9999999317439139
            ],
            [
                0.9999999176675239,
                0.9999998874647441,
                0.9999999226557593,
                0.9999996533675031,
                0.9999999273418009,
                0.9999999006881259,
                0.9999999468421249,
                0.999999917667524,
                0.9999998024946095,
                0.9999999123575464
            ],
            [
                0.9999999067050721,
                0.9999997126315153,
                0.9999999123575359,
                0.999999946842144,
                0.9999999123574838,
                0.9999999067050498,
                0.9999998874648112,
                0.9999999226557408,
                0.9999999006880195,
                0.9999999358793333
            ],
            [
                0.9999997463981939,
                0.9999997761971849,
                0.9999997300421583,
                0.999999526209612,
                0.9999998555019791,
                0.999999789756609,
                0.9999998144608541,
                0.999999825702163,
                0.9999998724809723,
                0.9999995818812772
            ],
            [
                0.9999997761972116,
                0.9999992661791947,
                0.9999998642566219,
                0.9999998257020591,
                0.9999998942830863,
                0.9999999317439221,
                0.9999998642567028,
                0.999999730042094,
                0.9999998942830485,
                0.9999998724809115
            ],
            [
                0.9999998874647307,
                0.9999998555020309,
                0.9999999226557225,
                0.9999998874648648,
                1.0,
                1.0,
                0.9999998555019619,
                0.9999998362623529,
                1.0,
                0.9999998642566866
            ],
            [
                0.9999999559306101,
                0.9999998362623528,
                0.9999999530883898,
                0.9999999434137907,
                0.9999999273418355,
                0.9999998874649318,
                0.9999997126313098,
                1.0,
                0.9999999273417922,
                0.9999998144608098
            ],
            [
                0.9999998144609424,
                0.9999999006881259,
                0.9999998257020799,
                0.9999997463980428,
                0.9999998555019619,
                0.9999999273418616,
                0.9999997761971849,
                0.9999998555019963,
                0.9999996940978098,
                0.9999997761970516
            ],
            [
                1.0,
                0.9999999397642365,
                0.9999999586006393,
                0.9999999317439546,
                0.9999999226557501,
                0.9999999397642365,
                0.9999999358793332,
                0.9999999123575672,
                0.9999999226557224,
                0.9999999397642365
            ],
            [
                0.999999825702059,
                0.9999999434137434,
                0.9999998802069445,
                0.9999998942829225,
                0.9999998642567351,
                0.9999998555019963,
                0.9999999176674749,
                0.9999997897565839,
                0.999999939764258,
                0.9999998724808963
            ],
            [
                0.9999997761972116,
                0.9999999358793332,
                0.9999998874649185,
                0.9999998024946095,
                0.9999999067051166,
                0.9999998942829854,
                1.0,
                0.9999999123575569,
                0.9999998874647574,
                1.0
            ],
            [
                0.9999999006881497,
                0.9999998144609645,
                0.9999997761971583,
                0.999999917667475,
                0.9999998257021214,
                0.9999996940978826,
                0.9999999067051055,
                0.9999999397642437,
                0.999999927341827,
                0.9999999317439465
            ],
            [
                0.999999927341801,
                0.9999998942829981,
                0.9999999468421567,
                0.999999900687972,
                0.9999999586005949,
                1.0,
                1.0,
                0.999999927341775,
                0.9999999500628453,
                1.0
            ],
            [
                0.999999927341853,
                0.9999998724809268,
                0.9999995549147361,
                0.9999997761971317,
                0.9999999468421187,
                0.9999999358793409,
                0.9999998942828973,
                0.9999999123574733,
                0.9999997761970515,
                0.9999998874648782
            ],
            [
                0.9999996743687035,
                0.9999995549150545,
                0.9999998555019791,
                0.9999999067051055,
                0.9999998024945624,
                0.9999998874648917,
                0.9999997300422548,
                0.9999998942829855,
                0.9999998024947038,
                0.9999996940978463
            ],
            [
                0.9999998144608098,
                0.9999998874647844,
                0.9999998802069445,
                0.9999998802069302,
                0.9999998024946096,
                0.9999998461826588,
                0.9999997463981938,
                0.9999989322972591,
                0.9999998144609645,
                0.9999998257021214
            ],
            [
                0.9999998024945624,
                0.9999998555020135,
                0.9999999123575465,
                0.999999825702059,
                1.0,
                0.9999999397642508,
                0.9999999358794173,
                0.9999999559306206,
                0.9999999123575777,
                0.9999999317439546
            ],
            [
                0.9999999500627916,
                0.9999999468421187,
                0.9999999123575672,
                0.999999900687984,
                0.9999997300422869,
                0.9999999067050165,
                0.9999999226558238,
                0.9999998942829602,
                0.9999999067050054,
                0.9999999226558053
            ],
            [
                0.9999998802069445,
                0.999999352404971,
                0.9999997897567092,
                0.9999996743686257,
                0.9999999317439953,
                0.9999999006879957,
                0.9999996940978462,
                0.999999631011328,
                0.999999825702163,
                0.9999997761970515
            ],
            [
                0.9999999530884012,
                1.0,
                1.0,
                0.999999864256719,
                0.9999999586006195,
                0.9999999176675143,
                0.9999998724809572,
                0.9999999273418616,
                0.9999997617630334,
                1.0
            ],
            [
                0.9999999176675436,
                0.9999999123575986,
                0.999998126123948,
                0.9999999067050498,
                0.999999917667573,
                0.999999894282935,
                0.9999998144608541,
                0.9999997463981939,
                0.9999999123575987,
                0.9999998257021422
            ],
            [
                0.9999998362622552,
                0.9999999397642797,
                0.999999391640746,
                0.9999999434138109,
                0.9999998642566381,
                0.999999674368781,
                0.999999922655833,
                0.9999998874648917,
                0.9999998942830862,
                0.9999998257021837
            ],
            [
                0.9999998642567028,
                0.9999998942830359,
                0.9999998257021838,
                1.0,
                0.9999998144608319,
                0.9999998802068873,
                0.9999998942830737,
                0.9999998362622553,
                1.0,
                0.9999997897566841
            ],
            [
                0.9999999176674945,
                0.9999998724808963,
                0.9999998362623724,
                0.9999993106387912,
                0.9999998257021422,
                0.9999998024946566,
                0.9999999358793562,
                0.9999998024945624,
                0.999999789756634,
                0.9999999123574629
            ],
            [
                0.9999998642566866,
                0.9999997897565588,
                0.9999998257021214,
                0.9999999006880904,
                0.999999922655833,
                0.9999999397642725,
                0.999999939764215,
                0.9999998362623724,
                0.9999999226558515,
                0.9999999006880076
            ],
            [
                0.9999998461826589,
                0.9999999123575046,
                0.9999999067050053,
                0.9999998802069445,
                0.9999998724809571,
                0.9999997126313442,
                0.9999999226558423,
                0.9999998024947037,
                0.9999998362622943,
                0.9999998802069017
            ],
            [
                0.9999999358793791,
                0.9999999611088951,
                0.9999993524052794,
                0.999999927341853,
                0.9999999500628036,
                0.9999999611088811,
                0.9999997126313098,
                0.9999998724809723,
                0.9999998874648514,
                0.999999943413757
            ],
            [
                0.9999999317439708,
                0.9999999226557409,
                0.9999998362622358,
                0.9999998461826406,
                0.9999998942830862,
                0.9999998024945624,
                0.9999999434137233,
                0.9999998024946566,
                0.9999999176675632,
                0.9999998555019619
            ],
            [
                0.9999999176674945,
                0.9999999397642725,
                0.9999999176675044,
                0.9999999273418009,
                0.9999998802069159,
                0.9999997761971317,
                0.9999998555019275,
                0.9999998024946095,
                0.9999997897567342,
                0.999999961108909
            ],
            [
                0.9999998642567028,
                0.9999999530883731,
                0.999999906705072,
                0.999999946842106,
                0.9999999500628215,
                0.9999998724809723,
                0.9999999358793562,
                1.0,
                0.999999931743914,
                0.9999999468420996
            ],
            [
                1.0,
                0.9999999123575568,
                0.9999998802069731,
                0.9999999317440034,
                0.999999887464838,
                0.9999998461826038,
                0.9999996940976638,
                0.9999999317439302,
                0.9999999067050276,
                0.9999999434138109
            ],
            [
                0.9999999006880312,
                0.9999999176675043,
                0.9999999273418009,
                0.9999998802069731,
                0.9999998555019963,
                1.0,
                0.9999999176675338,
                1.0,
                0.9999998642566381,
                0.9999996940977004
            ],
            [
                0.9999998642566381,
                0.9999996533675031,
                0.999999761763147,
                0.9999996533674204,
                0.9999998724809875,
                0.9999997761970248,
                0.999999825702059,
                0.999999746398194,
                0.9999996533675031,
                0.9999996940976273
            ],
            [
                0.9999998461826954,
                0.9999998461827139,
                0.9999999226558146,
                0.9999998555019618,
                0.9999999006880195,
                0.9999997126314126,
                0.9999997761972116,
                0.9999998642566381,
                0.9999998802068873,
                0.9999998144609645
            ],
            [
                0.9999999468421883,
                0.9999992188515767,
                0.9999999397642293,
                0.9999997126315496,
                0.9999999176675338,
                0.9999999226558238,
                0.9999998461826588,
                0.9999998461827139,
                0.9999999176675142,
                0.9999997897567091
            ],
            [
                0.9999998257021837,
                1.0,
                0.9999998144608098,
                0.9999996743688586,
                0.9999999434137098,
                0.9999996533674617,
                0.9999999317440034,
                0.9999997617630617,
                0.999999631011416,
                0.9999999397642151
            ],
            [
                0.9999999273418009,
                0.9999997300423192,
                0.9999998802068873,
                0.9999998555020309,
                0.999999872480942,
                0.9999998257021837,
                0.9999997761970248,
                0.9999998942830737,
                0.999999057755407,
                0.9999998024945624
            ],
            [
                0.999999631011372,
                0.9999998874647306,
                0.9999996310115479,
                0.9999999123574629,
                0.9999996940976638,
                0.9999997463980125,
                0.9999998461826588,
                0.999999789756634,
                1.0,
                0.999999906705072
            ],
            [
                1.0,
                1.0,
                0.9999997617631754,
                0.9999998257022045,
                0.9999997897565588,
                0.9999999273418095,
                1.0,
                0.9999997617630334,
                1.0,
                1.0
            ],
            [
                0.9999998555019618,
                0.9999999273418876,
                0.999999946842163,
                0.9999997897565589,
                0.9999999123574523,
                0.9999999317440279,
                0.9999999067051055,
                0.9999998555019447,
                0.9999998461827139,
                0.999999917667524
            ],
            [
                0.9999998724809571,
                0.9999999176674454,
                0.999999495652472,
                0.9999999006881378,
                0.999999730042094,
                0.999999776197025,
                0.9999998024947272,
                0.9999998874649318,
                0.9999987121046331,
                0.9999999176675043
            ],
            [
                0.9999999317439058,
                0.9999999067050165,
                0.9999999226557316,
                0.9999997897565839,
                0.9999999358794479,
                0.9999999434137637,
                0.9999999434138109,
                0.9999999317440278,
                0.9999999397642796,
                1.0
            ],
            [
                0.9999999176674456,
                0.999999825702059,
                0.9999997617631753,
                0.9999998024945624,
                0.9999998942830233,
                0.9999999067049831,
                0.999999746398073,
                0.999999922655787,
                0.9999998257022046,
                0.999999931743914
            ],
            [
                1.0,
                0.9999998024945624,
                0.9999998802069873,
                0.9999999317439302,
                0.9999999434137503,
                0.9999998555019963,
                0.9999998874648648,
                0.9999999123575359,
                1.0,
                1.0
            ],
            [
                0.9999997617631753,
                0.9999998802068873,
                0.9999997761971583,
                0.9999997617630049,
                0.9999997463981335,
                0.999999789756634,
                0.9999999226557131,
                0.999999730042287,
                0.9999999006881496,
                0.999999789756659
            ],
            [
                0.9999999067049942,
                0.9999999397642078,
                0.9999999434137367,
                0.9999998362622747,
                0.9999999273418703,
                0.9999999006881023,
                0.9999998555020481,
                0.999999789756609,
                0.9999998802069444,
                0.9999998724809268
            ],
            [
                0.9999999530884011,
                0.9999999226557409,
                0.9999999500627976,
                0.9999997897566589,
                0.9999999634651966,
                0.9999999176675437,
                0.9999999586006542,
                0.9999999434137368,
                0.9999999468421059,
                0.9999999226557501
            ],
            [
                0.9999998362623138,
                0.9999998942829729,
                0.9999999176675239,
                0.9999997126313099,
                0.9999998942830611,
                0.9999997617630901,
                0.9999998257020799,
                0.9999998024946802,
                0.9999996743687034,
                0.9999998362622748
            ],
            [
                1.0,
                0.9999999586006344,
                1.0,
                1.0,
                0.9999999273417836,
                0.9999998461826405,
                0.9999999397643012,
                0.9999999500627917,
                0.9999999123575046,
                1.0
            ],
            [
                0.9999999677581183,
                0.9999998874648112,
                0.9999999358793792,
                0.999999746398073,
                0.9999999530883563,
                0.9999996743687034,
                0.9999999500627857,
                0.9999998874648649,
                0.9999998461826405,
                0.9999998642567351
            ],
            [
                0.9999999317439465,
                0.9999998802069874,
                0.9999998461826223,
                0.9999998024946801,
                0.999999802494586,
                0.9999998555020135,
                0.9999998642567351,
                0.9999998555019791,
                0.9999999006880668,
                0.9999998555019447
            ],
            [
                0.999999900687984,
                0.9999998024947273,
                0.9999999067051499,
                0.9999998802068873,
                0.9999998874648782,
                0.999999931743914,
                0.9999999176674848,
                1.0,
                0.9999998461826589,
                0.9999998461826956
            ],
            [
                0.9999998802069302,
                0.9999998874648514,
                0.999999887464838,
                0.9999999397642724,
                0.9999999226558515,
                0.9999998642567028,
                0.999999900687984,
                0.9999999006881259,
                0.9999998362623334,
                1.0
            ],
            [
                0.9999999176675829,
                0.9999997463980731,
                0.999999814460832,
                0.9999997761972116,
                0.9999991684721715,
                0.9999997761971315,
                0.9999997126314468,
                0.9999997761971317,
                0.9999992661787579,
                0.9999998642567028
            ],
            [
                0.9999998024945626,
                0.9999998942829477,
                1.0,
                0.9999999500627917,
                0.9999999226557593,
                0.9999998257021213,
                1.0,
                0.9999999176674357,
                1.0,
                1.0
            ],
            [
                0.9999999358793639,
                1.0,
                0.9999999586006048,
                1.0,
                0.9999998724809419,
                1.0,
                1.0,
                0.9999999123575151,
                0.9999999006881259,
                0.9999997761971583
            ],
            [
                1.0,
                0.9999999123575359,
                0.9999998555019275,
                0.9999998874649051,
                0.999999939764294,
                1.0,
                0.9999998362623138,
                0.9999999586006344,
                1.0,
                0.9999998802068873
            ],
            [
                0.9999998461826222,
                0.9999996533673791,
                0.9999995262093858,
                0.9999997126313784,
                0.9999999530883172,
                1.0,
                0.9999999468420996,
                0.999999846182714,
                0.9999999434137975,
                0.9999999317440035
            ],
            [
                0.9999999176674552,
                0.9999998362622747,
                0.9999999317439139,
                0.9999998874647307,
                0.9999998144609424,
                0.9999998024947038,
                0.9999999123575359,
                0.9999997761972116,
                0.9999999176674946,
                0.9999998024946566
            ],
            [
                0.9999998555020481,
                0.9999998724810027,
                0.999999946842144,
                0.9999999397642222,
                0.9999998642567351,
                0.9999998362623724,
                0.9999998461827322,
                0.9999999434137233,
                0.9999998362623138,
                0.9999998874647843
            ],
            [
                1.0,
                0.9999995262093858,
                0.9999999611088951,
                1.0,
                0.9999999226558146,
                0.9999999530884011,
                0.9999999468421821,
                0.9999998024946095,
                0.9999998724808963,
                0.9999999067050609
            ],
            [
                0.9999996072137532,
                0.9999999123575464,
                0.9999997300421584,
                0.9999997617629766,
                0.999999802494586,
                0.9999998362622358,
                0.9999999067050276,
                0.9999998802069017,
                1.0,
                0.9999996940977003
            ],
            [
                0.9999998874647307,
                1.0,
                0.999999814460854,
                0.9999998724809877,
                0.9999998942828973,
                0.9999999067050276,
                1.0,
                1.0,
                0.9999998802068873,
                0.9999998802069731
            ],
            [
                0.9999998362623334,
                0.9999998874647307,
                0.9999999006879957,
                0.9999999273417923,
                0.9999997761972116,
                0.9999998362622552,
                0.9999998942830106,
                0.9999999273418875,
                0.9999998642567189,
                0.9999999273418702
            ],
            [
                0.9999998642566705,
                0.9999999006880312,
                0.9999999397642797,
                0.9999999067050276,
                0.9999998362623139,
                1.0,
                0.9999999006881259,
                0.9999999500628572,
                0.9999994956524118,
                0.9999999123575987
            ],
            [
                0.9999999397642078,
                0.9999999176675829,
                0.9999999358793867,
                0.9999999226557132,
                0.9999999067050721,
                0.9999999123574838,
                0.9999998642566704,
                0.9999999468421313,
                0.9999998024947037,
                0.9999999006881142
            ],
            [
                0.9999999317439708,
                0.9999997897567092,
                0.9999999586006443,
                0.9999998362622748,
                0.9999999434137974,
                0.9999995549150544,
                0.9999998802069444,
                0.9999999226557409,
                0.999999917667475,
                0.9999999317439058
            ],
            [
                0.9999999468421756,
                1.0,
                0.9999997897566089,
                0.999999906705061,
                0.9999997617630333,
                0.9999999397642724,
                1.0,
                0.9999999434137704,
                0.9999998257020799,
                0.999999953088362
            ],
            [
                0.9999989969859124,
                0.9999995818811775,
                0.9999995818812772,
                0.9999995549151076,
                0.9999994284996215,
                0.9999997126313441,
                0.9999995818812774,
                0.9999999468420996,
                0.9999997463980428,
                0.9999996533672552
            ],
            [
                0.9999998802069874,
                0.999999946842182,
                0.9999999317439627,
                0.999999927341853,
                0.9999997126314127,
                0.9999998362622357,
                0.999999931743979,
                0.9999997617630617,
                0.9999997761971049,
                0.9999999358794096
            ],
            [
                0.9999998362623723,
                0.9999998257020798,
                0.9999998724809116,
                0.9999999006880195,
                0.9999997761970516,
                0.9999998024946095,
                0.9999999273417836,
                0.999999825702163,
                0.999999887464771,
                0.9999997761971315
            ],
            [
                0.9999997897567343,
                0.9999998144609203,
                0.9999997617631753,
                0.9999998257021007,
                0.9999998461826405,
                0.9999998942829728,
                0.9999999006880786,
                0.9999998144608541,
                0.9999997126315154,
                0.9999997300422226
            ],
            [
                0.9999999559305787,
                0.9999999226557408,
                0.9999998257021838,
                0.9999999586006443,
                0.9999998555019446,
                0.9999999397642221,
                0.9999999317440035,
                0.999999887464838,
                0.9999999500628095,
                0.9999999176675632
            ],
            [
                0.9999998942829351,
                0.9999999434137773,
                0.999999730042287,
                0.999999927341801,
                0.9999999226558515,
                0.9999999226558146,
                0.9999996072136594,
                0.9999998257021214,
                0.9999999006880668,
                0.9999997463981638
            ],
            [
                0.9999999273418096,
                0.9999998942830107,
                0.9999998874649318,
                0.9999996533672139,
                0.9999997897567343,
                0.9999997463981939,
                0.999999935879425,
                0.9999998024945624,
                0.9999998024946567,
                0.9999998461827139
            ],
            [
                0.9999999586006344,
                0.9999999176675142,
                0.9999997897565588,
                0.9999999634651531,
                0.9999999123575464,
                0.9999998362623138,
                0.9999998874648648,
                0.9999999123575255,
                1.0,
                0.9999994631248684
            ],
            [
                0.9999998461826222,
                0.9999999123575464,
                0.9999998642567353,
                0.9999999006879721,
                0.9999997897565839,
                0.9999999176674848,
                0.9999999006880076,
                0.9999999611089043,
                0.9999999006880195,
                0.9999994631251244
            ],
            [
                0.9999999226557409,
                0.9999998724810027,
                0.9999996743688586,
                0.9999999067051165,
                0.9999999317440035,
                0.9999999273418009,
                0.9999999123574628,
                0.9999998724809875,
                0.9999998724809875,
                0.9999998257022045
            ],
            [
                0.9999999067051165,
                0.9999999067050832,
                0.9999999006881142,
                0.999999674368781,
                0.9999998555020135,
                0.9999999176674749,
                0.9999999176675143,
                0.9999999397642796,
                0.9999999067049943,
                0.9999999226557962
            ],
            [
                0.999999935879425,
                0.9999998555019274,
                0.999999789756634,
                0.9999997617631469,
                0.9999998802069017,
                0.9999999176675731,
                0.9999999176675437,
                0.9999999006881377,
                0.9999999123575464,
                0.9999999123575255
            ],
            [
                0.9999999397642653,
                0.9999997897565589,
                1.0,
                0.9999997617630901,
                0.9999998024946095,
                0.9999999468421756,
                0.9999999468421249,
                1.0,
                0.9999999123575046,
                0.9999999358794402
            ],
            [
                0.9999998724809267,
                0.9999998555020135,
                0.9999997761970515,
                0.9999997761972116,
                0.9999999226558515,
                0.9999999006879838,
                0.9999998874648648,
                0.9999999176675239,
                0.9999999611088534,
                0.9999999530883843
            ],
            [
                1.3709570434178922e-06,
                6.144176066795103e-06,
                1.3709567165386693e-06,
                2.699578418198104e-07,
                7.338211554725124e-07,
                8.315283250305684e-07,
                1.0677026154730804e-06,
                9.422445938917108e-07,
                4.450852111100568e-07,
                1.0677029973158649e-06
            ],
            [
                0.9999999358794479,
                0.9999998802069444,
                0.9999999397642222,
                0.9999999434137975,
                0.9999998874649184,
                0.9999998942829729,
                0.9999999067050388,
                0.9999999434137974,
                0.9999997463980125,
                0.9999999397642365
            ],
            [
                0.9999999500627857,
                0.9999998024946095,
                0.999999746398073,
                0.9999999067051054,
                0.9999999500628215,
                0.9999999006881259,
                0.9999998942829098,
                1.0,
                0.9999999397642653,
                1.0
            ],
            [
                0.9999999067049942,
                0.9999999123575151,
                0.9999997761971583,
                0.9999998802069302,
                0.9999993524048936,
                0.9999999273418182,
                0.9999998802069445,
                0.9999998144609205,
                0.9999999226557778,
                0.9999999123574941
            ],
            [
                0.9999998024947038,
                0.999999802494633,
                0.9999997617630049,
                0.9999997300422226,
                0.9999998144609646,
                0.9999998874647843,
                0.9999998802068873,
                0.999999802494586,
                0.9999997897566089,
                0.9999998642566543
            ],
            [
                0.9999997897567092,
                0.9999998802068873,
                0.9999993524054342,
                0.9999998802069159,
                0.9999998874648514,
                0.9999998461826956,
                0.999999887464932,
                0.9999999226557962,
                0.9999994956524721,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999999358793944,
                0.9999999559305786,
                0.9999998874649185,
                0.9999998942830233,
                0.9999999317440035,
                0.9999999468421567,
                0.9999999226558423,
                0.9999999226557592
            ],
            [
                0.9999997126314469,
                0.9999999226557778,
                0.9999998461826589,
                0.9999998642566381,
                0.9999998461826406,
                0.9999998024946095,
                0.9999997126313784,
                0.9999997300422548,
                0.9999997761972116,
                0.999999581881327
            ],
            [
                0.9999999317439384,
                0.9999999634651487,
                1.0,
                0.9999998942829098,
                0.9999997300421261,
                0.9999999500628631,
                0.9999998942830233,
                0.9999998874647307,
                0.999999931743971,
                0.9999999434137704
            ],
            [
                0.9999996940977003,
                0.9999997761972116,
                0.9999999500628394,
                0.9999997897565588,
                0.9999999500628215,
                0.9999999226557224,
                0.9999999530883787,
                0.9999998144608098,
                1.0,
                0.999999789756609
            ],
            [
                0.9999995818814266,
                0.9999995818813269,
                0.9999999468421376,
                0.9999999176675534,
                0.999999855502048,
                0.999999730042094,
                0.9999998642566381,
                0.9999996940978096,
                0.9999997300423192,
                0.9999999317440278
            ],
            [
                0.9999998724809268,
                1.0,
                0.9999998144609425,
                0.9999995262094425,
                0.9999999006880904,
                0.9999998461826038,
                0.9999998362622358,
                0.9999998942830863,
                0.9999998874648917,
                0.9999993916408914
            ],
            [
                0.9999998144609203,
                0.9999999358794173,
                0.9999996940978462,
                0.9999998874647977,
                0.9999998642566381,
                0.9999999123574838,
                1.0,
                0.9999999123574733,
                0.9999998024946567,
                0.9999998555019963
            ],
            [
                0.9999998144608983,
                0.999999631011416,
                0.9999998362622358,
                0.9999998144609203,
                0.999999789756634,
                0.9999996940977732,
                0.9999998802069017,
                0.9999998144608098,
                0.9999998942828973,
                0.9999998802069017
            ]
        ]
    },
    {
        "q_id": "9086_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            109,
            110,
            111,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127,
            102,
            108,
            112
        ],
        "rewards": [
            [
                1.760342793638743e-06,
                7.338210680021253e-07,
                1.8553919030858602e-07,
                5.715005832886879e-07,
                6.475947982022763e-07,
                6.475948754012522e-07,
                3.9278610661902853e-07,
                2.1024331597262577e-07,
                9.422448185534261e-07,
                5.715003107755449e-07
            ],
            [
                1.209865539295696e-06,
                8.315278294097538e-07,
                5.71500719545698e-07,
                8.315279285370317e-07,
                1.067702870039777e-06,
                2.6995790618469934e-07,
                6.475950298011458e-07,
                5.715005151606823e-07,
                5.04347468323289e-07,
                3.927862002663297e-07
            ],
            [
                1.5534975693979422e-06,
                5.715005151606823e-07,
                3.059022269250683e-07,
                4.450852111135988e-07,
                7.338209805240734e-07,
                2.90231094723893e-06,
                5.043475885696228e-07,
                5.715006514167015e-07,
                2.90231094723893e-06,
                NaN
            ],
            [
                1.2098656835224664e-06,
                6.962254589978262e-06,
                1.0677032518814388e-06,
                2.382369951932796e-07,
                1.0677027427624903e-06,
                5.043473480777865e-07,
                2.699576809143613e-07,
                1.0677029973219343e-06,
                3.726639284125553e-06,
                6.475949526020042e-07
            ],
            [
                1.637377057680051e-07,
                3.059021175261338e-07,
                4.450852641737424e-07,
                3.4663274507713016e-07,
                2.1024339116168358e-07,
                5.043476486924565e-07,
                3.4663274507713016e-07,
                2.102434162245973e-07,
                9.422444815814404e-07,
                1.6373776432509826e-07
            ],
            [
                1.5534977545886537e-06,
                2.3823688159291947e-07,
                3.0590237279085045e-07,
                5.043476486915964e-07,
                3.05902190458764e-07,
                3.9278610661902853e-07,
                1.8553919030858602e-07,
                6.47595107001401e-07,
                5.715003789046955e-07,
                3.059022269250683e-07
            ],
            [
                3.7266397283908927e-06,
                2.260324028427877e-06,
                6.475946438055299e-07,
                1.067703124601679e-06,
                2.5612819054133693e-06,
                4.450852111155216e-07,
                7.338208055680009e-07,
                7.338208055664991e-07,
                5.422217030781934e-06,
                5.715005832886879e-07
            ],
            [
                1.0677024882009222e-06,
                8.315281267861397e-07,
                5.715007195447234e-07,
                6.475949525981759e-07,
                7.338208055664991e-07,
                2.5612831267202583e-06,
                5.043472879540142e-07,
                3.0590215399183813e-07,
                4.450851580555361e-07,
                9.422445939032799e-07
            ],
            [
                1.2098658277451275e-06,
                5.043472879540142e-07,
                2.260324567337161e-06,
                8.315280276546789e-07,
                5.715004470313855e-07,
                1.2098653950656417e-06,
                5.71500515159253e-07,
                3.288748673295719e-06,
                1.2098655392871682e-06,
                1.2098662604291696e-06
            ],
            [
                2.5612831267202583e-06,
                5.715005151606823e-07,
                2.260324567337161e-06,
                8.315281267882195e-07,
                9.422450431989127e-07,
                2.3823688159291947e-07,
                9.422442569315887e-07,
                2.382369951932796e-07,
                4.450850519403407e-07,
                1.5534975693979422e-06
            ],
            [
                9.422443692574719e-07,
                1.5534971990169383e-06,
                1.6373772528704005e-07,
                5.715006514176113e-07,
                1.6373766672973748e-07,
                1.209865827752005e-06,
                2.382370235933104e-07,
                1.6373764721072816e-07,
                1.6373772528704005e-07,
                6.475950298021765e-07
            ],
            [
                8.315281267882195e-07,
                9.422445939032799e-07,
                4.785093924362895e-06,
                4.785094494783494e-06,
                8.315281267861397e-07,
                1.3709575337125585e-06,
                3.927863875616689e-07,
                5.04347287955046e-07,
                1.6701419854156377e-05,
                2.6995790618350237e-07
            ],
            [
                9.422448185510695e-07,
                2.5612828213934817e-06,
                1.067702870039777e-06,
                1.0677024881980089e-06,
                1.5534973842076057e-06,
                4.450852111148132e-07,
                8.315282259117513e-07,
                5.043475284447896e-07,
                1.7603436330259153e-06,
                9.422442569315887e-07
            ],
            [
                5.71500651413193e-07,
                1.3709576971463352e-06,
                7.338211554783522e-07,
                5.422221555414699e-06,
                6.475950298021765e-07,
                1.3709572068478697e-06,
                2.2603253756956754e-06,
                1.0677029973219343e-06,
                1.2098653950716937e-06,
                1.209865827752005e-06
            ],
            [
                0.9999992188518566,
                0.9999984465022483,
                0.9999996072136127,
                0.999999607213847,
                0.9999984465022472,
                0.9999984465022475,
                0.9999997463981335,
                0.9999955048178892,
                0.9999996940977732,
                0.9999986290432846
            ],
            [
                0.9999995549147365,
                0.9999994631251248,
                0.999999761763147,
                0.9999998724810027,
                0.9999996743686648,
                0.9999996743686259,
                0.999999310638791,
                0.9999996940978461,
                0.9999997463980729,
                0.9999989969862716
            ],
            [
                9.422450432014836e-07,
                6.475950298011458e-07,
                1.7603440527286572e-06,
                2.902313023130843e-06,
                1.7603440527286572e-06,
                2.260323758987159e-06,
                5.043472879540142e-07,
                1.5534984953510149e-06,
                1.5534973842030142e-06,
                1.2098658277489788e-06
            ],
            [
                6.475950298011458e-07,
                5.715003789046955e-07,
                9.422448185534261e-07,
                5.715005832886879e-07,
                6.475949526020042e-07,
                5.04347528446051e-07,
                3.927862470899887e-07,
                1.0677027427600627e-06,
                1.3709576971425944e-06,
                5.043472278322555e-07
            ],
            [
                8.315284241650899e-07,
                4.4508494582405734e-07,
                3.466325797896173e-07,
                7.338213304363436e-07,
                3.4663249714612693e-07,
                8.315279285351409e-07,
                6.475947982037486e-07,
                9.422450431989127e-07,
                1.760343213335281e-06,
                5.04347287955046e-07
            ],
            [
                3.466327037548308e-07,
                5.715002426475718e-07,
                3.9278605979534166e-07,
                8.315279285370317e-07,
                2.260323758987159e-06,
                4.4508526417298334e-07,
                1.0677033791583005e-06,
                4.450852111148132e-07,
                8.315279285351409e-07,
                4.450848927658745e-07
            ],
            [
                3.726638839878908e-06,
                6.962255419931625e-06,
                1.0677027427600627e-06,
                2.260324836787226e-06,
                3.535624650279074e-05,
                9.422450431989127e-07,
                2.260324567337161e-06,
                NaN,
                1.209865539295696e-06,
                1.30071315662049e-05
            ],
            [
                2.102434412875379e-07,
                3.927863875616689e-07,
                3.0590237279085045e-07,
                3.059021175261338e-07,
                1.0677027427624903e-06,
                3.059022998581767e-07,
                1.370957860576702e-06,
                1.2098652508424818e-06,
                1.3709576971463352e-06,
                3.05902336324494e-07
            ],
            [
                6.144177531811707e-06,
                3.288749065436569e-06,
                1.7603430034867993e-06,
                1.994729721518893e-06,
                3.05902263391829e-07,
                2.9023116392097746e-06,
                6.144176066901277e-06,
                4.2228319344021954e-06,
                3.2887494574832472e-06,
                4.450851049991497e-07
            ],
            [
                8.315284241650899e-07,
                9.422450432014836e-07,
                2.3823699519290042e-07,
                3.0590237279032884e-07,
                1.7603436330259153e-06,
                6.475947982037486e-07,
                4.450852111148132e-07,
                3.9278634073732336e-07,
                1.994729008145876e-06,
                3.0590237279032884e-07
            ],
            [
                5.71500515159253e-07,
                6.475945666051092e-07,
                1.0677029973192638e-06,
                4.4508526417298334e-07,
                1.8553907971855875e-07,
                4.4508510499849186e-07,
                1.444979692800516e-07,
                3.927860597945825e-07,
                5.043476486924565e-07,
                5.715003789046955e-07
            ],
            [
                1.067703124601679e-06,
                1.444980209564556e-07,
                4.4508494582405734e-07,
                1.760343213335281e-06,
                2.2603234895372223e-06,
                3.46632497145457e-07,
                4.4508510499849186e-07,
                9.422448185534261e-07,
                8.315278294114555e-07,
                8.93969950132721e-06
            ],
            [
                3.05902336324494e-07,
                1.0677033791612137e-06,
                9.422450432014836e-07,
                4.450848927658745e-07,
                2.2603253756956754e-06,
                1.1253525596174225e-07,
                6.475947210046347e-07,
                1.6373764721072816e-07,
                1.6373776432509826e-07,
                3.7266410611296085e-06
            ],
            [
                9.422445939054222e-07,
                5.043472278322555e-07,
                1.2098659719788098e-06,
                5.715006514176113e-07,
                1.067703124601679e-06,
                1.8553905760062447e-07,
                2.561281600086738e-06,
                3.927862470899887e-07,
                9.422444815814404e-07,
                2.6995774527718623e-07
            ],
            [
                5.043472278322555e-07,
                NaN,
                2.561282821402217e-06,
                2.699578096403948e-07,
                NaN,
                6.47595107001401e-07,
                3.9278620026686556e-07,
                2.3823696679327928e-07,
                3.466325797900508e-07,
                5.71500515161527e-07
            ],
            [
                0.9999985406239548,
                0.9999952149049474,
                0.9999970976883669,
                0.999998629042468,
                0.9999952149032372,
                0.9999974387168779,
                0.9999970976869944,
                0.9999985406234326,
                0.9999916019279812,
                0.9999974387165749
            ],
            [
                5.043476486915964e-07,
                3.05902190458764e-07,
                7.338213304363436e-07,
                9.422449308774482e-07,
                7.338208930460318e-07,
                9.422442569315887e-07,
                1.2098652508424818e-06,
                5.04347528446051e-07,
                9.422443692555439e-07,
                3.9278610661902853e-07
            ],
            [
                2.1444943302181958e-05,
                5.422220262636381e-06,
                1.0129993395336818e-05,
                1.3709567165579959e-06,
                2.561282210729555e-06,
                2.5612828213690224e-06,
                2.5612812947508257e-06,
                6.144177531767002e-06,
                1.3007128465151102e-05,
                4.006367786720367e-05
            ],
            [
                4.4508510499849186e-07,
                9.422443692574719e-07,
                4.4508494582405734e-07,
                3.05902336324494e-07,
                2.3823696679327928e-07,
                1.444979692800516e-07,
                1.8553919030858602e-07,
                3.466327037553825e-07,
                8.315282259138311e-07,
                4.222834954801051e-06
            ],
            [
                2.3823690999290963e-07,
                2.561281600086738e-06,
                2.1024339116168358e-07,
                7.338208055680009e-07,
                4.4508526417298334e-07,
                5.04347468323289e-07,
                7.338208055664991e-07,
                6.475945666051092e-07,
                2.102434412875379e-07,
                3.05902190458764e-07
            ],
            [
                1.0677029973192638e-06,
                3.927862002663297e-07,
                8.315277302841894e-07,
                1.994729483723626e-06,
                1.994730197090463e-06,
                1.5534979397790343e-06,
                9.422447062270609e-07,
                6.475949526020042e-07,
                8.315283250394546e-07,
                1.067702870039777e-06
            ],
            [
                3.2887506336235617e-06,
                3.4663249714612693e-07,
                4.4508494582405734e-07,
                5.715003789046955e-07,
                2.2603245673443566e-06,
                4.450850519403407e-07,
                4.450852111148132e-07,
                1.0677026154806063e-06,
                3.059022269250683e-07,
                5.71500719545698e-07
            ],
            [
                2.902312677150514e-06,
                3.927862470899887e-07,
                5.715003107767143e-07,
                2.699577774585891e-07,
                5.71500719545698e-07,
                1.9947304348862686e-06,
                7.338212429582604e-07,
                5.04347528446051e-07,
                5.04347468323289e-07,
                2.902312677137316e-06
            ],
            [
                4.222832941193893e-06,
                1.5534973842076057e-06,
                4.450848927658745e-07,
                5.043474683240344e-07,
                4.450848927658745e-07,
                4.4508494582405734e-07,
                1.3709573702822306e-06,
                3.9278610661902853e-07,
                1.2098661162056318e-06,
                1.209865539295696e-06
            ],
            [
                3.4663278639892215e-07,
                5.422217030781934e-06,
                7.338210680021253e-07,
                5.715003107767143e-07,
                4.450852111148132e-07,
                5.04347287955046e-07,
                9.422442569315887e-07,
                7.338207180898968e-07,
                7.338208930460318e-07,
                5.715002426475718e-07
            ],
            [
                5.715003789046955e-07,
                1.2098661162056318e-06,
                2.5612819054133693e-06,
                8.315282259138311e-07,
                1.5534977545886537e-06,
                7.338208055680009e-07,
                8.315277302841894e-07,
                4.22283545819819e-06,
                3.466325797896173e-07,
                7.338212429582604e-07
            ],
            [
                8.315279285370317e-07,
                7.338207180898968e-07,
                8.315281267882195e-07,
                1.760343213335281e-06,
                5.715003107767143e-07,
                4.450852641737424e-07,
                1.370957860576702e-06,
                1.5534975693979422e-06,
                6.475947982037486e-07,
                8.315280276626197e-07
            ],
            [
                3.4663278639892215e-07,
                1.3709567165617364e-06,
                1.5534979397740895e-06,
                1.2098659719788098e-06,
                1.2098661162056318e-06,
                1.994730434879465e-06,
                3.288747889284851e-06,
                1.2098652508424818e-06,
                1.5534981249697903e-06,
                1.0677029973192638e-06
            ],
            [
                8.315280276626197e-07,
                3.4663278639892215e-07,
                1.0677028700422047e-06,
                3.927862470899887e-07,
                2.6995784182183607e-07,
                3.4663249714612693e-07,
                1.4449803818215767e-07,
                1.209865827752005e-06,
                4.450852111155216e-07,
                5.715003789046955e-07
            ],
            [
                1.5534971990169383e-06,
                3.927863875616689e-07,
                5.715005151606823e-07,
                3.7266410611296085e-06,
                5.043475885696228e-07,
                3.927863875616689e-07,
                9.422448185534261e-07,
                7.338208055680009e-07,
                8.315284241650899e-07,
                NaN
            ],
            [
                1.7603425837855082e-06,
                1.9947292459347367e-06,
                8.315284241650899e-07,
                1.5534973842076057e-06,
                1.7603440527286572e-06,
                5.715003789033962e-07,
                3.2887506336235617e-06,
                1.7603440527286572e-06,
                5.043476486915964e-07,
                1.7603438428800754e-06
            ],
            [
                1.209865827752005e-06,
                3.9278634073732336e-07,
                1.300712536408621e-05,
                5.04347528446051e-07,
                2.102434162245973e-07,
                9.422450432014836e-07,
                1.3709576971463352e-06,
                3.9278605979534166e-07,
                9.422445939032799e-07,
                6.47595107001401e-07
            ],
            [
                3.4663266243308805e-07,
                7.338213304363436e-07,
                1.4449798650551755e-07,
                4.4508526417298334e-07,
                8.315282259138311e-07,
                2.6995774527718623e-07,
                3.059022269250683e-07,
                5.4222183235249605e-06,
                6.475947210046347e-07,
                4.450852111155216e-07
            ],
            [
                4.785096776499213e-06,
                9.422447062294175e-07,
                1.2098658277451275e-06,
                3.2887502415767434e-06,
                1.7603438428800754e-06,
                1.0677029973192638e-06,
                4.785092783519724e-06,
                1.2098659719757836e-06,
                7.338209805224048e-07,
                2.561282210740037e-06
            ],
            [
                4.4508494582405734e-07,
                5.715005151606823e-07,
                2.1024331597262577e-07,
                3.927862002663297e-07,
                6.475949526020042e-07,
                8.315282259138311e-07,
                5.715005832886879e-07,
                3.4663278639892215e-07,
                3.927862002663297e-07,
                3.927863875616689e-07
            ],
            [
                4.450850519403407e-07,
                7.889264466868659e-06,
                6.475949526020042e-07,
                4.450852111148132e-07,
                5.422220262636381e-06,
                2.6995774527718623e-07,
                7.338212429582604e-07,
                9.422448185534261e-07,
                3.9278605979534166e-07,
                7.338212429582604e-07
            ],
            [
                4.2228329411708495e-06,
                2.902312677137316e-06,
                2.4300234941880266e-05,
                8.31527928532683e-07,
                1.30071315662049e-05,
                4.785093353940187e-06,
                1.2098662604291696e-06,
                1.209865539295696e-06,
                5.422217030781934e-06,
                6.475945666051092e-07
            ],
            [
                0.9999981261239497,
                0.9999987901341756,
                0.9999984465026185,
                0.999998446501508,
                0.9999960330122005,
                0.9999987901346079,
                0.9999995262095555,
                0.999999631011636,
                0.9999986290429584,
                0.9999987901344627
            ],
            [
                5.04347287955046e-07,
                1.2098653950692178e-06,
                5.04347468323289e-07,
                5.715007195447234e-07,
                8.315284241650899e-07,
                3.927862470899887e-07,
                3.9278605979534166e-07,
                1.0677024882029858e-06,
                9.422444815814404e-07,
                7.338209805240734e-07
            ],
            [
                0.9999988634364259,
                0.9999989969854347,
                0.9999993106387907,
                0.9999983463106142,
                0.9999974387174876,
                0.9999992188517635,
                0.9999984465026176,
                0.9999994284994173,
                0.9999991148430706,
                0.9999991148431758
            ],
            [
                2.9023116391978967e-06,
                3.2887506336086064e-06,
                2.260324567337161e-06,
                1.5534983101602148e-06,
                1.7603434231777837e-06,
                2.260325106237323e-06,
                2.2603234895289998e-06,
                3.2887506336086064e-06,
                8.939694172957213e-06,
                1.3709570434178922e-06
            ],
            [
                5.043476486915964e-07,
                4.4508515805735777e-07,
                2.2603248367949354e-06,
                1.5534975693979422e-06,
                5.715002426486762e-07,
                4.450852641737424e-07,
                8.315284241650899e-07,
                1.5534981249697903e-06,
                9.422443692555439e-07,
                5.715003789046955e-07
            ],
            [
                3.288749065423109e-06,
                3.7266397283908927e-06,
                1.9947301970972664e-06,
                6.962257079832313e-06,
                5.422219616265831e-06,
                1.5534977545886537e-06,
                2.2603253756956754e-06,
                7.889261645427538e-06,
                7.889265407255982e-06,
                1.209866260432471e-06
            ],
            [
                1.9947292459347367e-06,
                1.7603430034867993e-06,
                7.338213304363436e-07,
                8.315284241650899e-07,
                5.04347287955046e-07,
                1.209866260432471e-06,
                1.5534973842076057e-06,
                4.450852641737424e-07,
                7.338210680021253e-07,
                6.475945666051092e-07
            ],
            [
                3.059022269250683e-07,
                4.4508510499849186e-07,
                3.059022269250683e-07,
                2.699578740032504e-07,
                1.370957860576702e-06,
                4.4508526417298334e-07,
                1.855391239544352e-07,
                8.315282259138311e-07,
                9.931199245292204e-08,
                5.04347287955046e-07
            ],
            [
                3.927863875616689e-07,
                7.338213304363436e-07,
                2.382368531929327e-07,
                5.04347287955046e-07,
                3.466326211113502e-07,
                7.338208930460318e-07,
                3.466325384678894e-07,
                4.450850519403407e-07,
                5.043476486924565e-07,
                6.475946438055299e-07
            ],
            [
                5.715005151606823e-07,
                4.4508494582405734e-07,
                1.3709567165617364e-06,
                2.6995774527718623e-07,
                5.715003789046955e-07,
                1.9947301970972664e-06,
                8.315284241650899e-07,
                1.7603440527286572e-06,
                2.6995790618469934e-07,
                3.927862002663297e-07
            ],
            [
                2.699577774585891e-07,
                5.71500515159253e-07,
                1.637377448057981e-07,
                2.1024336609843824e-07,
                2.699577774585891e-07,
                5.04347528446051e-07,
                3.05902190458764e-07,
                3.466327450765785e-07,
                7.889265407255982e-06,
                5.043473480777865e-07
            ],
            [
                1.3709572068522336e-06,
                5.04347528446051e-07,
                2.9023119851899796e-06,
                1.3709573702822306e-06,
                1.3709573702822306e-06,
                5.715007195447234e-07,
                3.726638839878908e-06,
                6.475945666051092e-07,
                1.3709578605729614e-06,
                1.9947299593078385e-06
            ],
            [
                4.4508515805735777e-07,
                1.855391681906175e-07,
                4.4508494582405734e-07,
                3.9278605979534166e-07,
                5.715005832895975e-07,
                2.3823693839325527e-07,
                6.475947210046347e-07,
                2.102434412875379e-07,
                3.927863875616689e-07,
                1.2098659719788098e-06
            ],
            [
                9.422449308774482e-07,
                9.422443692555439e-07,
                5.043476486915964e-07,
                3.7266410611296085e-06,
                3.466325797896173e-07,
                6.475950298011458e-07,
                6.475950298011458e-07,
                7.338210680021253e-07,
                1.0677028700422047e-06,
                1.7603430034867993e-06
            ],
            [
                3.927862002663297e-07,
                9.422445939054222e-07,
                1.0677027427600627e-06,
                3.927862470899887e-07,
                3.4663266243308805e-07,
                2.6995784182140636e-07,
                6.475949526020042e-07,
                2.6995784182140636e-07,
                4.4508499888219586e-07,
                2.10243290909724e-07
            ],
            [
                5.715005832886879e-07,
                4.4508515805735777e-07,
                5.715002426486762e-07,
                3.288748281329893e-06,
                1.5534971990126997e-06,
                3.927863875616689e-07,
                5.04347287955046e-07,
                6.962258739796719e-06,
                1.994729483729522e-06,
                1.3709572068522336e-06
            ],
            [
                0.9999986290421407,
                0.9999994631250605,
                0.999998712104632,
                0.9999989969860325,
                0.9999972735287606,
                0.9999994284992808,
                0.999998346310219,
                0.9999980052707564,
                0.9999987901347502,
                0.9999989322967492
            ],
            [
                0.9999990577549576,
                0.9999995818812276,
                0.9999995262092728,
                0.9999997463980731,
                0.9999990577549573,
                0.9999994631247405,
                0.9999898700079086,
                0.9999990577551822,
                0.9999996743687422,
                0.9999993524051253
            ],
            [
                0.9999981261241715,
                1.99473067264854e-06,
                0.999999352405048,
                0.9999980052702833,
                0.9999993106392017,
                6.144176799227922e-06,
                1.300712691403299e-05,
                0.999999428499758,
                0.9999969105055561,
                0.9999985406237809
            ],
            [
                1.9947299593078385e-06,
                3.288747889284851e-06,
                2.6995784182140636e-07,
                2.902312331170226e-06,
                3.288749849529972e-06,
                1.3709567165617364e-06,
                5.715005832886879e-07,
                3.288749849529972e-06,
                8.315283250394546e-07,
                8.315280276626197e-07
            ],
            [
                2.6995774527657245e-07,
                2.6995784182140636e-07,
                2.6995784182140636e-07,
                2.699577774585891e-07,
                2.1024336609843824e-07,
                3.927862002663297e-07,
                5.715006514167015e-07,
                5.715006514167015e-07,
                9.422449308774482e-07,
                3.466325797888292e-07
            ],
            [
                2.382370235933104e-07,
                7.338207180898968e-07,
                1.6373772528704005e-07,
                8.764242227418718e-08,
                4.4508494582405734e-07,
                2.1024331597262577e-07,
                4.450850519403407e-07,
                3.927862002663297e-07,
                9.931186222523604e-08,
                3.05902336324494e-07
            ],
            [
                1.2098659719757836e-06,
                5.715004470326849e-07,
                9.422449308774482e-07,
                6.475950298011458e-07,
                3.4663278639892215e-07,
                5.043476486915964e-07,
                1.9947304348862686e-06,
                5.04347528446051e-07,
                6.475945666051092e-07,
                1.5534975693979422e-06
            ],
            [
                3.059022269254856e-07,
                1.5534971990169383e-06,
                3.0590237279085045e-07,
                1.0677027427624903e-06,
                7.33821330437595e-07,
                4.222834451403972e-06,
                6.47595107001401e-07,
                4.222833444590791e-06,
                1.3709567165617364e-06,
                0.9999985406234329
            ],
            [
                2.2603253756874524e-06,
                8.315281267882195e-07,
                5.043473480777865e-07,
                3.466325797896173e-07,
                8.315280276626197e-07,
                5.422218969895357e-06,
                7.338213304363436e-07,
                2.3823688159291947e-07,
                9.422442569315887e-07,
                2.699576809143613e-07
            ],
            [
                0.9999989322975128,
                0.9999964991460114,
                0.9999996940978461,
                0.9999996310115479,
                0.9999995262094423,
                0.9999991684718736,
                0.999999581881277,
                0.9999992188519491,
                0.9999994631251882,
                0.9999993524053565
            ],
            [
                8.315280276626197e-07,
                6.475947982037486e-07,
                3.288749065423109e-06,
                2.5612828213934817e-06,
                1.0677033791612137e-06,
                1.5534973842076057e-06,
                4.450852641737424e-07,
                9.422447062294175e-07,
                1.0677026154806063e-06,
                7.338208930460318e-07
            ],
            [
                6.475947982037486e-07,
                2.3823693839325527e-07,
                5.043476486924565e-07,
                6.475947210046347e-07,
                7.338207180898968e-07,
                4.450848927658745e-07,
                2.382370235933104e-07,
                5.043476486924565e-07,
                1.1253509497883659e-07,
                1.6373772528704005e-07
            ],
            [
                3.059021904580685e-07,
                5.043473480777865e-07,
                5.043472278312808e-07,
                3.288748281329893e-06,
                8.315277302857965e-07,
                5.043473480777865e-07,
                1.444979692800516e-07,
                5.715003107755449e-07,
                6.475947210046347e-07,
                6.475947982037486e-07
            ],
            [
                6.144177531811707e-06,
                1.0129987357517693e-05,
                3.726639284144195e-06,
                2.561281600086738e-06,
                4.539786324145319e-05,
                0.9820137936239376,
                7.889264466868659e-06,
                1.3007128465151102e-05,
                3.2887494574832472e-06,
                1.0677027427624903e-06
            ],
            [
                3.4663249714612693e-07,
                5.04347287955046e-07,
                2.10243290909724e-07,
                7.338208930460318e-07,
                7.338209805240734e-07,
                1.6373770576776313e-07,
                1.209866260432471e-06,
                2.3823682479292225e-07,
                3.466327450765785e-07,
                1.370957860576702e-06
            ],
            [
                5.422219616228845e-06,
                5.422217030747413e-06,
                2.561282210729555e-06,
                2.5612831267202583e-06,
                1.5534975693869924e-06,
                7.889264466725156e-06,
                4.2228334445370225e-06,
                3.726639728370556e-06,
                4.222834451382849e-06,
                4.785095635624897e-06
            ],
            [
                7.338212429582604e-07,
                5.043476486915964e-07,
                9.422442569315887e-07,
                1.3709572068522336e-06,
                7.338209805224048e-07,
                2.4300234941880266e-05,
                5.715005151606823e-07,
                6.475945666051092e-07,
                1.0677027427624903e-06,
                3.059022269250683e-07
            ],
            [
                3.466327037553825e-07,
                3.05902263391829e-07,
                1.3709576971463352e-06,
                5.715005832895975e-07,
                NaN,
                9.422442569334097e-07,
                NaN,
                9.422450432030903e-07,
                NaN,
                1.5534983101644536e-06
            ],
            [
                1.0677029973219343e-06,
                2.2603251062450327e-06,
                3.288749457469787e-06,
                1.7603438428800754e-06,
                8.315281267861397e-07,
                1.5534981249697903e-06,
                1.9947301970972664e-06,
                6.475950298011458e-07,
                3.288747889284851e-06,
                8.315280276626197e-07
            ],
            [
                0.9999998642567351,
                0.9999994284993488,
                0.9999996072138937,
                0.9999994956527725,
                0.9999996940978826,
                0.9999993916411087,
                0.9999981261243946,
                0.999999114843281,
                0.999997273529406,
                0.9999994284992809
            ],
            [
                1.3709576971379186e-06,
                4.4508494582314646e-07,
                4.450852641737424e-07,
                1.6373764721072816e-07,
                1.9947299593014888e-06,
                3.9278605979534166e-07,
                1.3709572068522336e-06,
                8.315283250371857e-07,
                7.338208930443633e-07,
                8.315284241650899e-07
            ],
            [
                8.315279285351409e-07,
                5.04347468323289e-07,
                8.315277302841894e-07,
                5.715002426475718e-07,
                9.422448185534261e-07,
                8.315279285351409e-07,
                2.260325106237323e-06,
                1.0677026154806063e-06,
                9.422450431989127e-07,
                5.715007195431641e-07
            ],
            [
                1.067702870039777e-06,
                3.0590226339061185e-07,
                1.5534983101602148e-06,
                1.9947299593078385e-06,
                8.315284241650899e-07,
                1.994729483729522e-06,
                2.5612831267202583e-06,
                5.715005832886879e-07,
                3.466327450765785e-07,
                4.785093353940187e-06
            ],
            [
                5.043476486915964e-07,
                3.9278615344178325e-07,
                7.338212429582604e-07,
                1.3709570434122812e-06,
                8.315281267861397e-07,
                NaN,
                2.5612819054133693e-06,
                9.422448185478557e-07,
                7.338209805224048e-07,
                2.6995771309523475e-07
            ],
            [
                4.539787406217992e-05,
                5.422220262555012e-06,
                5.715003789033962e-07,
                2.2603234895289998e-06,
                2.5612831267202583e-06,
                1.0677024881980089e-06,
                4.450848927650143e-07,
                4.222834954753043e-06,
                2.9023119851635836e-06,
                6.475950298011458e-07
            ],
            [
                6.475947210046347e-07,
                9.422449308774482e-07,
                3.4663249714612693e-07,
                3.9278634073732336e-07,
                3.059022998576899e-07,
                3.4663274507713016e-07,
                8.315284241650899e-07,
                3.9278629391427843e-07,
                5.715002426475718e-07,
                2.6995774527718623e-07
            ],
            [
                3.9278605979208185e-07,
                3.0590226339061185e-07,
                2.3823702359290413e-07,
                1.2098661162056318e-06,
                4.785094494811783e-06,
                9.422448185510695e-07,
                3.927863407379485e-07,
                6.475946438055299e-07,
                8.315284241650899e-07,
                5.043475885674441e-07
            ],
            [
                6.47595107001401e-07,
                2.2603251062450327e-06,
                2.2603248367949354e-06,
                5.043475885696228e-07,
                3.726639284144195e-06,
                1.9947304348862686e-06,
                3.2887494574832472e-06,
                NaN,
                6.144177531811707e-06,
                NaN
            ],
            [
                3.2887502415767434e-06,
                0.9999967112505479,
                0.9999983463100216,
                0.9999992188512978,
                6.144175334468545e-06,
                5.4222183235249605e-06,
                4.785094494811783e-06,
                9.422442569315887e-07,
                1.0677033791583005e-06,
                1.1478766757718129e-05
            ],
            [
                1.760343213335281e-06,
                1.6373766672973748e-07,
                1.3709576971425944e-06,
                1.067702870039777e-06,
                9.422448185534261e-07,
                3.466326211113502e-07,
                6.475947210046347e-07,
                3.927863875616689e-07,
                6.475945666051092e-07,
                5.04347528446051e-07
            ],
            [
                2.382369667929001e-07,
                4.4508494582405734e-07,
                3.9278629391427843e-07,
                1.209865827752005e-06,
                8.315283250394546e-07,
                1.2098656835224664e-06,
                1.0677032518814388e-06,
                3.927862002663297e-07,
                1.6373764721072816e-07,
                2.3823696679327928e-07
            ],
            [
                1.5534984953552536e-06,
                1.9947292459347367e-06,
                8.315281267882195e-07,
                1.3709572068553509e-06,
                1.2098658277489788e-06,
                1.2098656835224664e-06,
                9.422443692555439e-07,
                8.315281267882195e-07,
                1.760343213335281e-06,
                1.0677029973219343e-06
            ],
            [
                3.05902190458764e-07,
                5.043473480777865e-07,
                3.9278634073732336e-07,
                3.927862470899887e-07,
                1.3709573702822306e-06,
                2.382369667929001e-07,
                2.902313023130843e-06,
                3.059021175261338e-07,
                2.561282516066741e-06,
                1.067703124601679e-06
            ],
            [
                9.422448185534261e-07,
                9.422442569315887e-07,
                1.5534971990169383e-06,
                5.043476486915964e-07,
                2.5612819054133693e-06,
                6.475947982037486e-07,
                2.260324567337161e-06,
                7.338213304363436e-07,
                5.043473480777865e-07,
                7.338211554783522e-07
            ],
            [
                5.715003789046955e-07,
                3.288749065423109e-06,
                5.043476486915964e-07,
                4.450848927658745e-07,
                1.209865539295696e-06,
                8.315279285351409e-07,
                7.338208055680009e-07,
                3.288748281329893e-06,
                2.699576809143613e-07,
                2.1024331597262577e-07
            ],
            [
                9.931187406410953e-08,
                7.734418542875216e-08,
                1.637376862489725e-07,
                1.1253525596174225e-07,
                1.2751902768612997e-07,
                1.27519088491875e-07,
                1.6373774480605869e-07,
                1.4449803818215767e-07,
                7.73442776303243e-08,
                1.1253513522447425e-07
            ],
            [
                3.4663249714612693e-07,
                4.450848927650143e-07,
                5.715005151606823e-07,
                5.715003789046955e-07,
                2.1444943302181958e-05,
                5.422221555380179e-06,
                1.5534971990126997e-06,
                3.466325384678894e-07,
                2.3823690999290963e-07,
                2.260323758987159e-06
            ],
            [
                2.5612834320470717e-06,
                3.4663266243308805e-07,
                7.338212429582604e-07,
                1.994730672675753e-06,
                2.2603234895372223e-06,
                2.699576809143613e-07,
                3.927862470899887e-07,
                1.0677033791612137e-06,
                7.338212429582604e-07,
                2.699576809143613e-07
            ],
            [
                6.475950298011458e-07,
                0.9997965730352277,
                1.0677033791612137e-06,
                6.475947982037486e-07,
                3.466327450765785e-07,
                2.6995784182140636e-07,
                3.9278610661902853e-07,
                3.466327037548308e-07,
                4.450852111155216e-07,
                5.715002426486762e-07
            ],
            [
                5.04347287955046e-07,
                3.927863875616689e-07,
                9.422448185534261e-07,
                2.3823682479292225e-07,
                3.059021175261338e-07,
                2.3823696679327928e-07,
                4.4508515805735777e-07,
                4.450851580566494e-07,
                1.9947299593078385e-06,
                5.04347287955046e-07
            ],
            [
                0.9999984465018774,
                0.9999967112501634,
                0.9999978766220523,
                0.9999970976880218,
                0.9999934595620057,
                0.999997593897378,
                0.9999938558232233,
                0.9999991148431759,
                0.9999983463102202,
                0.9999960330136288
            ],
            [
                6.475945666063607e-07,
                2.1024331597262577e-07,
                4.4508510499849186e-07,
                9.422447062270609e-07,
                1.994729008145876e-06,
                3.466326211113502e-07,
                3.05902190458764e-07,
                9.422449308774482e-07,
                2.3823696679327928e-07,
                5.715005832886879e-07
            ],
            [
                5.043475885696228e-07,
                8.315284241650899e-07,
                7.338207180898968e-07,
                6.475950298021765e-07,
                1.2751902768612997e-07,
                1.5534971990169383e-06,
                1.9947292459406333e-06,
                6.47595107001401e-07,
                1.067703124601679e-06,
                5.71500719545698e-07
            ],
            [
                7.338208930460318e-07,
                1.0677032518814388e-06,
                8.315279285370317e-07,
                4.4508494582405734e-07,
                3.4663278639892215e-07,
                2.699577774585891e-07,
                1.0677026154827912e-06,
                7.338208930460318e-07,
                3.288748281329893e-06,
                1.3709576971463352e-06
            ],
            [
                NaN,
                1.4449798650569826e-07,
                1.6373764721072816e-07,
                1.8553907971855875e-07,
                1.6373772528704005e-07,
                2.102434162245973e-07,
                2.699578740032504e-07,
                1.8553905760062447e-07,
                2.3823702359138736e-07,
                3.05902190458764e-07
            ],
            [
                2.5612828213934817e-06,
                2.6995784182183607e-07,
                3.4663249714612693e-07,
                4.450852111155216e-07,
                8.315279285370317e-07,
                2.6995784182183607e-07,
                8.315277302857965e-07,
                5.422217030781934e-06,
                1.3709576971463352e-06,
                2.9023116392097746e-06
            ],
            [
                5.715004470295662e-07,
                3.7266379514061143e-06,
                1.7603438428848787e-06,
                7.338208055680009e-07,
                1.0677027427471959e-06,
                8.31528325040778e-07,
                4.4508515805735777e-07,
                7.338212429594283e-07,
                1.3709573702856596e-06,
                6.47595107001401e-07
            ],
            [
                4.450850519403407e-07,
                2.9023119851899796e-06,
                5.04347528446051e-07,
                4.4508494582405734e-07,
                1.855391681906175e-07,
                5.04347287955046e-07,
                3.4663249714612693e-07,
                7.338212429582604e-07,
                5.715007195447234e-07,
                1.5534975693979422e-06
            ],
            [
                8.315281267861397e-07,
                5.4222183235249605e-06,
                1.3709568799919866e-06,
                8.315278294114555e-07,
                9.422442569315887e-07,
                3.466325797888292e-07,
                5.715006514167015e-07,
                1.2098661162056318e-06,
                6.475946438042047e-07,
                5.715005151606823e-07
            ],
            [
                0.999999855501979,
                0.9999997300421262,
                0.9999998942829477,
                0.9999997463980427,
                0.9999998144609203,
                0.9999997897567092,
                0.9999991148426484,
                0.9999995818812273,
                0.9999997897566089,
                0.9999986290421412
            ]
        ]
    },
    {
        "q_id": "10338_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            5,
            6,
            8,
            9,
            10,
            12,
            13,
            18,
            20,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            33,
            35,
            37,
            38,
            40,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            57,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            68,
            69,
            70,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            83,
            84,
            85,
            86,
            88,
            89,
            91,
            92,
            93,
            95,
            98,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            117,
            119,
            122,
            123,
            126
        ],
        "rewards": [
            [
                4.785095635592258e-06,
                2.5612819054028872e-06,
                NaN,
                5.715004470313855e-07,
                NaN,
                8.939696304002375e-06,
                2.9023126771227976e-06,
                4.450848927650143e-07,
                2.561281905390075e-06,
                4.785093353940187e-06
            ],
            [
                3.726637951387472e-06,
                2.5612819054028872e-06,
                3.726638395634011e-06,
                3.726638839878908e-06,
                NaN,
                5.422220262636381e-06,
                NaN,
                1.9947292459347367e-06,
                1.3709568799919866e-06,
                2.5612819054133693e-06
            ],
            [
                3.0590237279032884e-07,
                3.466327037553825e-07,
                6.475950298011458e-07,
                3.726637951387472e-06,
                5.043472278322555e-07,
                6.144172404738491e-06,
                1.3709567165617364e-06,
                8.315278294114555e-07,
                3.4663274507713016e-07,
                3.9278605979534166e-07
            ],
            [
                NaN,
                6.144174601991196e-06,
                7.889262585886274e-06,
                1.553498124964492e-06,
                1.9947292459265734e-06,
                2.561283432035425e-06,
                2.5612812947508257e-06,
                1.9947299593014888e-06,
                3.7266410611296085e-06,
                8.315279285351409e-07
            ],
            [
                6.144176066795103e-06,
                3.726638395611981e-06,
                NaN,
                7.889266347356409e-06,
                3.726638395611981e-06,
                2.4300246526646385e-05,
                1.1478770862255766e-05,
                2.144495608327478e-05,
                3.2887506336086064e-06,
                1.4738983729535602e-05
            ],
            [
                2.902313023130843e-06,
                3.05902263391829e-07,
                2.902313369111213e-06,
                9.422450431989127e-07,
                1.7603425837903113e-06,
                5.715005832872586e-07,
                1.8553907971879076e-07,
                3.466327037553825e-07,
                1.994730434879465e-06,
                5.715003107767143e-07
            ],
            [
                3.059022269254856e-07,
                4.006368741510365e-05,
                2.699577452775239e-07,
                9.422444815814404e-07,
                3.0590237279085045e-07,
                4.222831934352267e-06,
                2.382369667929001e-07,
                6.47595107001401e-07,
                8.939696304311336e-06,
                7.338209805240734e-07
            ],
            [
                3.059022998576899e-07,
                4.4508510499849186e-07,
                3.9278634073625165e-07,
                1.2098662604247682e-06,
                2.382368531929327e-07,
                3.059022998576899e-07,
                6.475947210031623e-07,
                9.422447062240614e-07,
                1.2098658277489788e-06,
                2.382370235933104e-07
            ],
            [
                1.6701423835624208e-05,
                1.760343213335281e-06,
                4.785093353909723e-06,
                NaN,
                5.422220262636381e-06,
                3.535625071602016e-05,
                NaN,
                6.144176799334096e-06,
                1.1478772230929451e-05,
                2.7535700949523498e-05
            ],
            [
                3.927862470905692e-07,
                NaN,
                8.315278294114555e-07,
                NaN,
                1.0677028700422047e-06,
                NaN,
                NaN,
                3.059022998581767e-07,
                3.288747889284851e-06,
                NaN
            ],
            [
                5.04347468323289e-07,
                3.466325797896173e-07,
                8.315281267861397e-07,
                4.785093353909723e-06,
                2.5612816000646084e-06,
                3.726639728370556e-06,
                8.31528424162821e-07,
                4.785095065204162e-06,
                6.9622587397397306e-06,
                2.260324567337161e-06
            ],
            [
                5.144223205871514e-05,
                1.0677032518785256e-06,
                0.9997388097907725,
                0.9999810748450797,
                3.46632497145457e-07,
                1.3709567165530083e-06,
                0.9999417087211061,
                8.939693107190907e-06,
                1.5534975693933505e-06,
                0.9999251537465672
            ],
            [
                4.006367785875045e-05,
                1.4738976699749503e-05,
                0.9998977001597306,
                1.2098662604291696e-06,
                1.8925152752586028e-05,
                0.9998977001540326,
                0.9999296881271105,
                1.6701417862648148e-05,
                6.9622579095833456e-06,
                1.4738985485997396e-05
            ],
            [
                7.338209805200689e-07,
                1.3709573702822306e-06,
                1.553498124964492e-06,
                1.2098662604291696e-06,
                1.2098662604247682e-06,
                1.3709575337125585e-06,
                6.475948754012522e-07,
                1.0677033791612137e-06,
                1.209865539295696e-06,
                1.2098659719788098e-06
            ],
            [
                6.962257079832313e-06,
                NaN,
                1.209866260432471e-06,
                5.043474082005342e-07,
                5.71500651413193e-07,
                NaN,
                1.9947292459347367e-06,
                1.0677024882009222e-06,
                2.2603242978871282e-06,
                3.466325797896173e-07
            ],
            [
                5.4222209089700225e-06,
                1.3007123813382511e-05,
                NaN,
                2.2603242978871282e-06,
                5.043476486915964e-07,
                7.889261645427538e-06,
                1.9947297215043796e-06,
                1.3007125363908762e-05,
                2.699578096403948e-07,
                5.1442225927013303e-05
            ],
            [
                NaN,
                1.5534971990169383e-06,
                2.260325106237323e-06,
                NaN,
                3.7266410611296085e-06,
                1.9947299593078385e-06,
                NaN,
                1.553498124964492e-06,
                NaN,
                1.147877359926923e-05
            ],
            [
                9.422444815814404e-07,
                8.315277302857965e-07,
                2.5612834320470717e-06,
                1.5534971990169383e-06,
                1.2751899728311609e-07,
                3.0590215399183813e-07,
                NaN,
                3.059022998581767e-07,
                6.475947210046347e-07,
                6.475949526020042e-07
            ],
            [
                1.275190124846946e-07,
                9.422450432014836e-07,
                NaN,
                NaN,
                NaN,
                3.466326624336003e-07,
                3.7266410611296085e-06,
                3.7266397283908927e-06,
                NaN,
                1.3709576971463352e-06
            ],
            [
                9.422442569334097e-07,
                8.315278294114555e-07,
                1.6373774480605869e-07,
                NaN,
                2.902313023130843e-06,
                1.209866260432471e-06,
                3.059022998581767e-07,
                9.422450432014836e-07,
                1.7603438428800754e-06,
                9.422444815814404e-07
            ],
            [
                8.315277302857965e-07,
                2.1024326584639497e-07,
                1.5534983101602148e-06,
                1.3709575337078829e-06,
                3.466325797888292e-07,
                7.338208930460318e-07,
                3.9278629391427843e-07,
                4.450851049991497e-07,
                1.5534973842076057e-06,
                2.3823693839325527e-07
            ],
            [
                4.785095635655362e-06,
                2.4300243631890864e-05,
                NaN,
                NaN,
                3.1201907657271834e-05,
                NaN,
                8.315283250371857e-07,
                2.9023116392097746e-06,
                5.8291265555961825e-05,
                6.475947982037486e-07
            ],
            [
                0.9999097196454807,
                2.1444943301674863e-05,
                0.9999599363032848,
                0.9999798543166438,
                0.9999898700054374,
                0.999968798085198,
                0.9996646498951547,
                0.9999898700127002,
                0.9999599362891254,
                0.9999869928731383
            ],
            [
                0.9999379495123486,
                1.0677032518785256e-06,
                2.2603248367949354e-06,
                5.71500719545698e-07,
                3.05902263391829e-07,
                1.0677033791612137e-06,
                6.475945666051092e-07,
                1.0677033791612137e-06,
                6.47594952603035e-07,
                5.4222176771176554e-06
            ],
            [
                1.994730434879465e-06,
                1.5534984953510149e-06,
                1.2098662604291696e-06,
                8.315279285370317e-07,
                4.4508494582405734e-07,
                1.5534981249697903e-06,
                7.338213304363436e-07,
                NaN,
                1.2098659719757836e-06,
                5.043472879540142e-07
            ],
            [
                8.315282259009745e-07,
                3.059021175261338e-07,
                1.5534979397740895e-06,
                1.5534973842076057e-06,
                3.7266383955882547e-06,
                9.422447062202052e-07,
                1.5534977545886537e-06,
                3.466325797888292e-07,
                9.422444815765128e-07,
                1.0677027427600627e-06
            ],
            [
                1.5534971990126997e-06,
                NaN,
                2.5612819054133693e-06,
                2.260324836787226e-06,
                2.260324836776948e-06,
                NaN,
                8.315284241650899e-07,
                4.785095065232451e-06,
                3.288749457469787e-06,
                NaN
            ],
            [
                8.315283250371857e-07,
                1.9947304348862686e-06,
                3.2887498495150166e-06,
                1.994730434879465e-06,
                5.715004470313855e-07,
                9.422447062270609e-07,
                6.475947210031623e-07,
                7.338211554783522e-07,
                9.422444815765128e-07,
                2.561282516066741e-06
            ],
            [
                4.2228319344021954e-06,
                NaN,
                3.7266410611296085e-06,
                1.4738978458382043e-05,
                NaN,
                1.670142980893658e-05,
                NaN,
                2.260325106237323e-06,
                4.222834954778007e-06,
                7.889262585814522e-06
            ],
            [
                3.05902336324494e-07,
                1.8553919030858602e-07,
                3.0590237279085045e-07,
                1.209866260432471e-06,
                2.260324836776948e-06,
                NaN,
                2.260324028427877e-06,
                NaN,
                3.0590237279085045e-07,
                2.5612831267202583e-06
            ],
            [
                2.902311639183378e-06,
                7.88926446679691e-06,
                NaN,
                3.288749065423109e-06,
                1.8925145985895816e-05,
                7.889266347715168e-06,
                9.422449308774482e-07,
                1.4738981972323349e-05,
                2.2603245673443566e-06,
                5.144223206414209e-05
            ],
            [
                3.059023727894942e-07,
                3.466327037548308e-07,
                7.338208930460318e-07,
                3.0590237279085045e-07,
                1.6373762769138607e-07,
                3.059021175247079e-07,
                3.0590215399183813e-07,
                3.927862939126708e-07,
                1.6373762769138607e-07,
                3.0590226339061185e-07
            ],
            [
                1.1478766757404937e-05,
                1.1478768125911099e-05,
                1.994730434879465e-06,
                5.715003107767143e-07,
                5.422220909009474e-06,
                2.260323758987159e-06,
                1.994729721518893e-06,
                NaN,
                5.04347287955046e-07,
                2.2603234895372223e-06
            ],
            [
                4.222831934379152e-06,
                7.338209805240734e-07,
                2.5612812947380135e-06,
                1.5534983101602148e-06,
                2.260325106237323e-06,
                3.7266410611296085e-06,
                0.9991959139027463,
                6.475947982037486e-07,
                2.9023112932177327e-06,
                9.422443692574719e-07
            ],
            [
                8.315277302841894e-07,
                5.043472879540142e-07,
                4.4508494582405734e-07,
                6.475948754012522e-07,
                4.785096776499213e-06,
                NaN,
                6.475948754028718e-07,
                8.315284241650899e-07,
                4.4508494582405734e-07,
                6.475947982002148e-07
            ],
            [
                1.0677026154806063e-06,
                6.475947982002148e-07,
                6.475947210012481e-07,
                5.043472879540142e-07,
                2.260325106237323e-06,
                NaN,
                NaN,
                2.5612834320470717e-06,
                NaN,
                1.7603440527286572e-06
            ],
            [
                4.222834451382849e-06,
                8.939693107093343e-06,
                5.422218969769604e-06,
                8.315277302788957e-07,
                1.89251482406672e-05,
                7.889265407090955e-06,
                3.2887506335906595e-06,
                1.7603425837606927e-06,
                6.962257909722651e-06,
                2.902313023101807e-06
            ],
            [
                NaN,
                8.939693107093343e-06,
                2.260324567337161e-06,
                6.605213682159303e-05,
                2.7535700948722127e-05,
                4.222834954778007e-06,
                3.288749849498565e-06,
                1.3007123813193233e-05,
                8.939694172770212e-06,
                1.1478766757718129e-05
            ],
            [
                3.7266406168827523e-06,
                3.288749849498565e-06,
                5.4222176771176554e-06,
                3.7266406168827523e-06,
                2.5612831267202583e-06,
                3.288747889229516e-06,
                7.88926446679691e-06,
                NaN,
                1.3709576971379186e-06,
                4.785093353909723e-06
            ],
            [
                0.9996646499073311,
                0.9999417087570689,
                0.9999417087491798,
                0.9999646437494898,
                0.9997694932885369,
                0.9998766053682664,
                0.9999203269828899,
                3.726641061085547e-06,
                0.999876605385901,
                0.9998204719837572
            ],
            [
                4.450852111148132e-07,
                2.382368815932174e-07,
                9.422448185534261e-07,
                3.927863875616689e-07,
                NaN,
                1.4449795205472734e-07,
                NaN,
                NaN,
                NaN,
                4.4508494582405734e-07
            ],
            [
                9.422443692555439e-07,
                2.2603253756956754e-06,
                1.2098652508424818e-06,
                1.7603432133296774e-06,
                9.422442569315887e-07,
                1.0677027427600627e-06,
                7.338208930460318e-07,
                2.9023119851899796e-06,
                9.422445939032799e-07,
                5.715006514176113e-07
            ],
            [
                0.9999599362892547,
                0.9999485577745866,
                4.2228324377740105e-06,
                4.78509392429544e-06,
                2.1444945856418342e-05,
                2.9023126771227976e-06,
                2.9023119851781017e-06,
                5.422219616228845e-06,
                2.561281905390075e-06,
                5.422219616228845e-06
            ],
            [
                5.422219616026655e-06,
                1.9947304348595095e-06,
                4.7850950649408664e-06,
                3.726639284017094e-06,
                3.288747889178668e-06,
                NaN,
                6.962253759904688e-06,
                1.5534981249697903e-06,
                5.715003789017068e-07,
                3.7266392838544054e-06
            ],
            [
                8.315282259089153e-07,
                6.475947210031623e-07,
                1.7603434231705793e-06,
                3.466325797888292e-07,
                1.5534979397740895e-06,
                1.3709575337078829e-06,
                9.422450431989127e-07,
                1.5534981249574276e-06,
                2.561283432035425e-06,
                1.2098662604247682e-06
            ],
            [
                4.2228334445658276e-06,
                1.7603425837855082e-06,
                NaN,
                NaN,
                3.120191137659974e-05,
                6.962254589914941e-06,
                NaN,
                NaN,
                3.726639728370556e-06,
                2.260324836787226e-06
            ],
            [
                2.5612831267202583e-06,
                NaN,
                NaN,
                3.726641061058432e-06,
                4.222834954778007e-06,
                1.5534983101478522e-06,
                5.422218323231539e-06,
                9.422448185510695e-07,
                1.7603436330259153e-06,
                4.78509392429544e-06
            ],
            [
                0.9998204720179328,
                1.3007130015488633e-05,
                1.0677029973192638e-06,
                0.9994472214137256,
                0.999972464318963,
                1.4738981972564636e-05,
                1.5534975693933505e-06,
                2.9023119851781017e-06,
                NaN,
                8.315283250394546e-07
            ],
            [
                1.7603434231705793e-06,
                2.90231094723893e-06,
                2.2603234895289998e-06,
                9.422448185510695e-07,
                1.3007133116542802e-05,
                8.939699501229642e-06,
                3.726638839833152e-06,
                2.260324836787226e-06,
                4.2228334445370225e-06,
                2.902311985146426e-06
            ],
            [
                2.6995774527657245e-07,
                1.4449798650551755e-07,
                1.2751905808881762e-07,
                2.1024334103581732e-07,
                1.6373766672973748e-07,
                4.450850519403407e-07,
                1.6373766672973748e-07,
                1.637377448057981e-07,
                1.1253514863968147e-07,
                NaN
            ],
            [
                8.939700566801578e-06,
                3.288749457409966e-06,
                1.0129990979694647e-05,
                1.7603427936183298e-06,
                1.0677031245905116e-06,
                3.120192253242944e-05,
                2.260323489490968e-06,
                1.0129987357287368e-05,
                2.5612819053586272e-06,
                NaN
            ],
            [
                1.553497384196656e-06,
                0.00015843627361555366,
                2.2603253756956754e-06,
                9.422442569315887e-07,
                NaN,
                1.5534977545886537e-06,
                NaN,
                7.338211554801876e-07,
                NaN,
                1.0677024882009222e-06
            ],
            [
                7.338212429582604e-07,
                9.422442569315887e-07,
                5.715005832886879e-07,
                4.4508494582405734e-07,
                2.561282210740037e-06,
                2.699577774585891e-07,
                3.288748281329893e-06,
                2.430023493865361e-05,
                3.7266401726173067e-06,
                1.760343213335281e-06
            ],
            [
                9.93120161306789e-08,
                2.699578740032504e-07,
                2.1024336609843824e-07,
                1.275190276859705e-07,
                2.1024341622426268e-07,
                3.927860597945825e-07,
                2.1024344128584085e-07,
                1.275190276859705e-07,
                8.315284241650899e-07,
                2.6995771309523475e-07
            ],
            [
                2.699576809143613e-07,
                2.6995771309523475e-07,
                3.466326211113502e-07,
                2.382370235933104e-07,
                5.04347468323289e-07,
                3.05902190458764e-07,
                3.05902190458764e-07,
                4.4508505193932864e-07,
                3.05902190458764e-07,
                2.6995774527718623e-07
            ],
            [
                1.9947299593078385e-06,
                3.7266379513162962e-06,
                7.889263526093993e-06,
                2.5612819054028872e-06,
                1.2098661161861e-06,
                1.0129992186939844e-05,
                1.994730434879465e-06,
                3.7266410609940346e-06,
                2.5612834320214477e-06,
                4.222834451327159e-06
            ],
            [
                NaN,
                3.0590226339061185e-07,
                6.962255419804982e-06,
                2.5612831267202583e-06,
                3.288749065423109e-06,
                1.760343633031919e-06,
                3.05902190458764e-07,
                2.699578096393206e-07,
                1.855391239544352e-07,
                2.1024331597262577e-07
            ],
            [
                1.2098659719757836e-06,
                1.0677026154806063e-06,
                2.9023130231176453e-06,
                1.760343003481596e-06,
                2.5612831267202583e-06,
                1.4738981972082061e-05,
                1.6701421842961097e-05,
                1.0677026154806063e-06,
                NaN,
                1.3709572068422585e-06
            ],
            [
                1.5534984953552536e-06,
                NaN,
                NaN,
                8.315279285370317e-07,
                1.994729483729522e-06,
                0.9999599363175223,
                NaN,
                NaN,
                2.2603248367949354e-06,
                1.0677028700422047e-06
            ],
            [
                1.3709573702778664e-06,
                2.2603251062450327e-06,
                4.539787406217992e-05,
                7.889262585886274e-06,
                2.430023204460668e-05,
                5.422218323487975e-06,
                1.8925143729575624e-05,
                8.939698435657833e-06,
                6.962254589914941e-06,
                1.3709576971425944e-06
            ],
            [
                5.715003107767143e-07,
                1.370957860576702e-06,
                3.7266410611296085e-06,
                1.0677027427624903e-06,
                3.927862002663297e-07,
                1.067703124601679e-06,
                2.3823696679230424e-07,
                3.466325797900508e-07,
                1.0677027427624903e-06,
                2.699577452775239e-07
            ],
            [
                1.209865539295696e-06,
                NaN,
                3.2887502415767434e-06,
                NaN,
                8.315279285370317e-07,
                1.0677028700422047e-06,
                2.5612819054133693e-06,
                NaN,
                1.0677028700422047e-06,
                NaN
            ],
            [
                2.9023112931213857e-06,
                NaN,
                4.222833444506298e-06,
                4.222831934379152e-06,
                3.4663278639738526e-07,
                2.2603253756956754e-06,
                1.7603434231777837e-06,
                1.2098658277451275e-06,
                4.539787946932385e-05,
                7.338212429504183e-07
            ],
            [
                4.222835458175145e-06,
                3.7266401726173067e-06,
                9.422445939032799e-07,
                8.315284241650899e-07,
                NaN,
                2.902312677104321e-06,
                6.962256249821764e-06,
                2.2603253756874524e-06,
                9.422444815765128e-07,
                7.338208055680009e-07
            ],
            [
                8.93969950132721e-06,
                2.561283432035425e-06,
                NaN,
                1.0677029973192638e-06,
                8.315278294072958e-07,
                1.4449805540763184e-07,
                1.8553905760062447e-07,
                NaN,
                NaN,
                2.2603234895289998e-06
            ],
            [
                1.3709567165461505e-06,
                1.5534977545886537e-06,
                6.475947210012481e-07,
                1.5534975693869924e-06,
                1.2098655392871682e-06,
                7.338211554783522e-07,
                2.382369667929001e-07,
                8.315283250371857e-07,
                1.0677028700363782e-06,
                2.260324836696773e-06
            ],
            [
                2.561282821352716e-06,
                1.370957860567974e-06,
                1.2098653950656417e-06,
                1.2098661161927025e-06,
                1.2098659719716573e-06,
                3.2887502415243994e-06,
                3.288747889178668e-06,
                1.0677032518748838e-06,
                8.315284241597959e-07,
                1.0677027427525368e-06
            ],
            [
                3.7266406168624155e-06,
                NaN,
                7.338209805240734e-07,
                1.147877359957198e-05,
                2.561281600086738e-06,
                1.3709567165617364e-06,
                NaN,
                NaN,
                2.2603242978007868e-06,
                NaN
            ],
            [
                NaN,
                NaN,
                6.475947210046347e-07,
                4.450852111148132e-07,
                2.5612828213934817e-06,
                NaN,
                7.889266347715168e-06,
                9.422448185534261e-07,
                1.9947304348862686e-06,
                7.338209805240734e-07
            ],
            [
                4.222832437798974e-06,
                6.962259569750576e-06,
                3.726639284144195e-06,
                1.1478765389368729e-05,
                3.7266410611296085e-06,
                2.2603251062450327e-06,
                4.5397857828200684e-05,
                4.785095635655362e-06,
                2.430024073523505e-05,
                1.670141786325573e-05
            ],
            [
                8.315283250394546e-07,
                2.6995790618469934e-07,
                2.1444953526969788e-05,
                2.382369951932796e-07,
                1.637377448057981e-07,
                2.1024331597262577e-07,
                1.6373770576776313e-07,
                2.1024336609843824e-07,
                6.825601283086733e-08,
                2.1024341622426268e-07
            ],
            [
                2.2603240284371276e-06,
                NaN,
                1.209866260432471e-06,
                1.99472900813862e-06,
                NaN,
                5.4222209089700225e-06,
                NaN,
                5.422218969818919e-06,
                1.5534975693979422e-06,
                NaN
            ],
            [
                5.715005151606823e-07,
                2.6995790618350237e-07,
                8.315280276546789e-07,
                2.260324836787226e-06,
                2.9023112931688987e-06,
                1.2098662604247682e-06,
                3.288750241561788e-06,
                3.059023727894942e-07,
                8.315281267861397e-07,
                1.3709567165617364e-06
            ],
            [
                9.422445939032799e-07,
                9.422444815814404e-07,
                NaN,
                1.0677029973192638e-06,
                5.422219616228845e-06,
                1.9947292459347367e-06,
                1.5534981249697903e-06,
                2.90231094723893e-06,
                NaN,
                1.0677028700363782e-06
            ],
            [
                9.931196877517082e-08,
                6.825601283086733e-08,
                6.825600469412533e-08,
                3.653479902594117e-08,
                6.023569166654288e-08,
                5.3157837044597743e-08,
                8.764244316973974e-08,
                4.691159887151251e-08,
                6.825598842065202e-08,
                1.2751905808881762e-07
            ],
            [
                1.760343003481596e-06,
                NaN,
                NaN,
                6.962259569630266e-06,
                5.829126554917624e-05,
                1.670141786231398e-05,
                1.0129990979547237e-05,
                0.00015843616030417933,
                7.889260704732132e-06,
                8.481103126678738e-05
            ],
            [
                4.4508510499849186e-07,
                3.927862470899887e-07,
                3.927863875616689e-07,
                6.475946438055299e-07,
                5.715005832853093e-07,
                1.8553910183607374e-07,
                1.9947301970972664e-06,
                1.5534981249496567e-06,
                NaN,
                5.04347468323289e-07
            ],
            [
                NaN,
                1.5534979397740895e-06,
                2.5612828213352452e-06,
                1.5534977545603963e-06,
                8.939693107190907e-06,
                2.902312677060767e-06,
                6.144174601879434e-06,
                1.5534971989992774e-06,
                3.726638839833152e-06,
                1.2098653950551882e-06
            ],
            [
                2.1024336609843824e-07,
                2.6995774527718623e-07,
                7.73441946488886e-08,
                1.8553919030858602e-07,
                7.734421308914719e-08,
                1.275191036933194e-07,
                1.855391681906175e-07,
                5.043476486915964e-07,
                1.2751901248454963e-07,
                3.4663266243308805e-07
            ],
            [
                9.422447062270609e-07,
                5.043473480777865e-07,
                3.0590237279085045e-07,
                5.715007195431641e-07,
                4.222832437798974e-06,
                NaN,
                8.315277302841894e-07,
                1.9947299593014888e-06,
                8.315282259138311e-07,
                NaN
            ],
            [
                1.994729483723626e-06,
                1.3709567165617364e-06,
                2.5612825160562587e-06,
                1.5534984953510149e-06,
                2.561282210729555e-06,
                4.450852111155216e-07,
                3.2887506336235617e-06,
                2.2603234895372223e-06,
                2.2603253756956754e-06,
                3.288748281329893e-06
            ],
            [
                6.475950298011458e-07,
                3.2887502415438413e-06,
                5.422218323399208e-06,
                4.78509278348926e-06,
                5.144223201941656e-05,
                2.902311639183378e-06,
                3.9278605979534166e-07,
                1.1478769494396542e-05,
                2.9023109471689794e-06,
                2.902312677137316e-06
            ],
            [
                7.88926446679691e-06,
                NaN,
                3.2887506336086064e-06,
                2.90231094723893e-06,
                7.889262585814522e-06,
                2.2603242978871282e-06,
                1.0677031245905116e-06,
                3.288747889229516e-06,
                1.0129987357407137e-05,
                2.5612819054028872e-06
            ],
            [
                1.370957860576702e-06,
                1.3709576971425944e-06,
                1.2098655392871682e-06,
                1.7603427936263351e-06,
                1.7603440527222532e-06,
                1.4738987242968784e-05,
                2.260325106237323e-06,
                1.2098656835224664e-06,
                1.7603427936335396e-06,
                5.043474081993875e-07
            ],
            [
                1.5534971990169383e-06,
                2.1444940745839484e-05,
                9.422447062294175e-07,
                1.2751902768612997e-07,
                NaN,
                5.043474082005342e-07,
                NaN,
                2.2603251062450327e-06,
                0.9975273769731523,
                1.5534971990169383e-06
            ],
            [
                5.4222202624563834e-06,
                2.9023126771227976e-06,
                4.2228324377164004e-06,
                6.1441731370702875e-06,
                4.006370174184034e-05,
                7.338211554783522e-07,
                3.726638395611981e-06,
                5.422218969818919e-06,
                NaN,
                1.0129988564716393e-05
            ],
            [
                3.927862470899887e-07,
                2.5612831266165976e-06,
                5.043474683204221e-07,
                NaN,
                3.927860597935108e-07,
                3.05902190458764e-07,
                3.059022998576899e-07,
                2.1024334103505245e-07,
                1.3709572068522336e-06,
                3.0590237279085045e-07
            ],
            [
                1.994729483729522e-06,
                8.315280276626197e-07,
                3.927862470905692e-07,
                3.72663883989755e-06,
                8.315277302857965e-07,
                2.6995784182183607e-07,
                9.422443692574719e-07,
                1.0,
                9.422443692574719e-07,
                NaN
            ],
            [
                NaN,
                1.5534973842076057e-06,
                3.288749065423109e-06,
                1.209865539295696e-06,
                6.475946438055299e-07,
                NaN,
                NaN,
                1.5534981249697903e-06,
                NaN,
                9.422450431989127e-07
            ]
        ]
    },
    {
        "q_id": "9805_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            48,
            51,
            52,
            54,
            55,
            56,
            57,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            82,
            83,
            84,
            85,
            87,
            88,
            89,
            90,
            91,
            92,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.222834451355964e-06,
                1.0129989772532511e-05,
                2.9023130230846496e-06,
                3.7266379513434106e-06,
                6.962257909722651e-06,
                0.00010889688336837233,
                2.2603234895176927e-06,
                1.6701429808632785e-05,
                3.2887502415438413e-06,
                1.99472900813862e-06
            ],
            [
                1.3709572068522336e-06,
                5.422217030747413e-06,
                7.338209805240734e-07,
                0.9999994956527727,
                7.338209805240734e-07,
                4.222833444590791e-06,
                1.994729483729522e-06,
                3.72663883989755e-06,
                NaN,
                1.209866260432471e-06
            ],
            [
                1.4738978458382043e-05,
                3.726638839878908e-06,
                1.3709573702822306e-06,
                2.5612819054133693e-06,
                1.4738981972564636e-05,
                2.260324567337161e-06,
                0.9998911030795697,
                2.561282210740037e-06,
                2.9023119851781017e-06,
                9.422445939032799e-07
            ],
            [
                1.0677029973192638e-06,
                8.315279285370317e-07,
                2.5612812947508257e-06,
                6.962253760024999e-06,
                7.88926446679691e-06,
                1.5534977545886537e-06,
                2.902312677150514e-06,
                4.222834451382849e-06,
                2.7535700948722127e-05,
                5.715005151606823e-07
            ],
            [
                5.043472879525233e-07,
                4.4508505193791187e-07,
                2.699577130944368e-07,
                8.315281267861397e-07,
                4.450849988811838e-07,
                4.450852111148132e-07,
                2.699576809121209e-07,
                1.0677029973192638e-06,
                7.338213304363436e-07,
                1.8925143728749452e-05
            ],
            [
                1.3709572068422585e-06,
                1.067703379154416e-06,
                3.7266406168624155e-06,
                4.450849988811838e-07,
                1.5534981249697903e-06,
                6.962254589914941e-06,
                4.222833947960866e-06,
                7.889265407255982e-06,
                5.422220262599396e-06,
                2.75356878194421e-05
            ],
            [
                1.2098656835224664e-06,
                2.2603242978871282e-06,
                5.422220909009474e-06,
                3.726639728370556e-06,
                6.962257909785973e-06,
                6.144173869603344e-06,
                0.9999945777823328,
                0.00017952794488272354,
                4.785093353940187e-06,
                2.5612819054133693e-06
            ],
            [
                7.338210680002898e-07,
                2.5612819054133693e-06,
                7.889265407327733e-06,
                1.0129990980100021e-05,
                6.962257909842961e-06,
                3.2887506336235617e-06,
                1.6701427818034747e-05,
                4.785096206076165e-06,
                1.2098659719788098e-06,
                1.7603438428800754e-06
            ],
            [
                1.855391681906175e-07,
                1.4449798650551755e-07,
                2.6995790618469934e-07,
                2.699576809143613e-07,
                1.1253509497883659e-07,
                7.734415776836702e-08,
                1.1253509497883659e-07,
                1.4449805540763184e-07,
                1.1253512180925583e-07,
                7.338207180898968e-07
            ],
            [
                3.7266401726359486e-06,
                1.209866260432471e-06,
                5.04347528446051e-07,
                4.785095065232451e-06,
                1.0677026154806063e-06,
                4.2228319344021954e-06,
                1.209866260432471e-06,
                1.012998977264307e-05,
                1.1478765389368729e-05,
                6.475949526003845e-07
            ],
            [
                6.144176799283803e-06,
                3.0590215399183813e-07,
                6.144173869558639e-06,
                1.4738983729294318e-05,
                7.338211554758494e-07,
                5.043472879540142e-07,
                9.422445939002803e-07,
                7.338213304316717e-07,
                9.422443692555439e-07,
                1.3709576971425944e-06
            ],
            [
                6.47595107001401e-07,
                3.05902263391829e-07,
                4.450848927658745e-07,
                5.715006514176113e-07,
                5.043472278322555e-07,
                2.1024339116168358e-07,
                6.475947982037486e-07,
                6.475945666063607e-07,
                3.466327037553825e-07,
                1.275190732904469e-07
            ],
            [
                4.539785241676547e-05,
                4.2228319344021954e-06,
                2.7535694384882703e-05,
                7.889262585886274e-06,
                1.4738978458382043e-05,
                1.2098658277489788e-06,
                2.1444953527944967e-05,
                2.1444940746307572e-05,
                0.9999251537910461,
                1.8925143729575624e-05
            ],
            [
                4.785096776468749e-06,
                5.422219616228845e-06,
                5.422218323487975e-06,
                7.889261645427538e-06,
                1.3007134667070165e-05,
                3.288750241561788e-06,
                6.962256249885085e-06,
                1.1478773599425825e-05,
                5.422220909009474e-06,
                6.962257909785973e-06
            ],
            [
                9.422444815814404e-07,
                5.422218323487975e-06,
                7.338208930460318e-07,
                2.5612828213934817e-06,
                5.715005832895975e-07,
                2.430024942462891e-05,
                5.422217030747413e-06,
                9.610238067382736e-05,
                1.3709568799919866e-06,
                4.006368741670684e-05
            ],
            [
                0.9999970976869818,
                0.9999960330131487,
                0.9999992188516703,
                0.9999974387165708,
                2.561281600086738e-06,
                2.430024073461624e-05,
                5.8291293348093234e-05,
                5.422217030747413e-06,
                2.2603234895289998e-06,
                4.539787406217992e-05
            ],
            [
                2.102434412871794e-07,
                0.9999995818813769,
                0.9999996533672137,
                0.9999994956524717,
                0.9999996072136128,
                0.9999997126313784,
                0.9999996743688975,
                0.9999997761971317,
                0.9999417087416494,
                0.9999995549150543
            ],
            [
                0.9999987121052456,
                5.715006514167015e-07,
                0.9999994284996895,
                6.475947210031623e-07,
                0.9999981261237245,
                0.9999981261246182,
                0.9999996743687422,
                1.7603434231833873e-06,
                0.9999993524051248,
                0.9999997761971849
            ],
            [
                2.5612831267202583e-06,
                1.994729721518893e-06,
                5.1442207537151994e-05,
                5.144219527356777e-05,
                7.484624513510494e-05,
                0.0001584361792827627,
                1.4738983729535602e-05,
                1.670142980893658e-05,
                1.4738989000422955e-05,
                1.7603430034867993e-06
            ],
            [
                NaN,
                4.539789029401802e-05,
                0.00015843621702094375,
                5.8291244705086375e-05,
                4.785093924362895e-06,
                3.535625914492432e-05,
                1.6701415872385704e-05,
                1.0129987357407137e-05,
                2.7535694384882703e-05,
                2.9023130231176453e-06
            ],
            [
                3.726639284144195e-06,
                9.42244818532859e-07,
                1.994729721518893e-06,
                3.7266379514061143e-06,
                1.0677024882029858e-06,
                7.338208930460318e-07,
                8.315281267882195e-07,
                9.422450432030903e-07,
                1.994729721518893e-06,
                1.7603425837903113e-06
            ],
            [
                1.9947299593078385e-06,
                1.8553919030858602e-07,
                3.288748281329893e-06,
                4.222834954801051e-06,
                2.902312331170226e-06,
                2.9023119851899796e-06,
                6.475947210046347e-07,
                8.764247451307293e-08,
                9.610244940712274e-05,
                1.0677029973219343e-06
            ],
            [
                7.889266347715168e-06,
                1.3007133116353526e-05,
                3.2887478892683997e-06,
                4.222834954778007e-06,
                8.939696304311336e-06,
                1.89251527534122e-05,
                1.1478768126057254e-05,
                6.9622537599680095e-06,
                1.4738987243236881e-05,
                4.785096776468749e-06
            ],
            [
                0.9999988634366965,
                0.9999995262093294,
                0.9999988634365612,
                0.9999994284996896,
                0.9999994631248044,
                0.9999992188512974,
                0.9999992188518558,
                0.9999996940978096,
                0.9999997463981637,
                0.9999989969859124
            ],
            [
                1.209866260432471e-06,
                5.043472278322555e-07,
                4.4508510499849186e-07,
                1.2098661162056318e-06,
                1.0677032518814388e-06,
                1.5534975693979422e-06,
                1.0677033791612137e-06,
                3.05902190458764e-07,
                2.699577774585891e-07,
                8.315277302857965e-07
            ],
            [
                5.04347287955046e-07,
                1.6373766672994222e-07,
                4.785093924330255e-06,
                6.962256249885085e-06,
                1.760342793638743e-06,
                3.726637951387472e-06,
                3.288749065406658e-06,
                2.1444943301674863e-05,
                3.7266410611296085e-06,
                6.962254589851619e-06
            ],
            [
                1.1478768126057254e-05,
                2.4300243631890864e-05,
                1.4738985486506781e-05,
                5.422218969895357e-06,
                0.9999991148432833,
                7.889261645427538e-06,
                5.422217677152175e-06,
                1.760343213335281e-06,
                3.2887498495150166e-06,
                1.5534975693979422e-06
            ],
            [
                5.422221555414699e-06,
                8.939694172957213e-06,
                2.9023119851899796e-06,
                1.2098659719788098e-06,
                6.144176066943187e-06,
                2.2603234895372223e-06,
                2.144495608424996e-05,
                6.475947210046347e-07,
                1.3709576971463352e-06,
                2.9023119851899796e-06
            ],
            [
                4.450852111135988e-07,
                8.939696304311336e-06,
                1.1478765389368729e-05,
                2.9023112931873767e-06,
                4.785092783519724e-06,
                1.0677027427600627e-06,
                1.4738983729535602e-05,
                6.962257909722651e-06,
                8.93969950132721e-06,
                8.315277302841894e-07
            ],
            [
                1.0677027427624903e-06,
                1.1478766757718129e-05,
                7.338208055680009e-07,
                2.561282210740037e-06,
                1.892514598551715e-05,
                2.902313369111213e-06,
                0.9999706884476152,
                1.8925148241872038e-05,
                6.605216044933028e-05,
                7.88926446679691e-06
            ],
            [
                2.5612812947508257e-06,
                1.0129995810343862e-05,
                1.5534971990126997e-06,
                7.889264466725156e-06,
                2.9023126771227976e-06,
                1.9947297215125433e-06,
                1.6701429808632785e-05,
                4.450850519403407e-07,
                6.144172404693786e-06,
                2.5612812947380135e-06
            ],
            [
                2.2603253756956754e-06,
                4.785095065232451e-06,
                1.5534971990169383e-06,
                0.00023050668823639762,
                6.962259569750576e-06,
                2.5612819054133693e-06,
                6.962253760024999e-06,
                5.4222183235249605e-06,
                8.939694172957213e-06,
                6.962259569750576e-06
            ],
            [
                1.2098653950692178e-06,
                4.222833444590791e-06,
                4.222834954778007e-06,
                5.715003789046955e-07,
                1.7603440527286572e-06,
                7.484624511822428e-05,
                1.5534973842076057e-06,
                4.4508526417298334e-07,
                1.4738980215352592e-05,
                4.4508526417298334e-07
            ],
            [
                6.1441746020359e-06,
                7.889265407327733e-06,
                2.902312677150514e-06,
                0.9999599362889149,
                1.3007133116732079e-05,
                4.006368741831004e-05,
                1.6701425827133152e-05,
                NaN,
                6.144176066901277e-06,
                2.753569110256289e-05
            ],
            [
                0.9999994631250603,
                0.9999997300421585,
                0.9999999397643011,
                2.1024334103581732e-07,
                0.9999996072139404,
                0.9999998024947273,
                0.9999998257020798,
                0.9999998555019962,
                0.9999999006880195,
                0.9999998257021214
            ],
            [
                1.5534973842076057e-06,
                0.9999930377462499,
                7.338208055664991e-07,
                8.939693107288474e-06,
                0.999996273362052,
                0.9999992188514835,
                3.9278634073732336e-07,
                0.999999266178845,
                0.9999724643089656,
                0.9999986290423036
            ],
            [
                1.7603425837903113e-06,
                4.2228319344021954e-06,
                6.144177531811707e-06,
                2.1444950971601277e-05,
                3.7266383956509585e-06,
                3.1201922535494165e-05,
                1.3007123813382511e-05,
                2.753568782024347e-05,
                1.0677028700422047e-06,
                1.5534984953552536e-06
            ],
            [
                7.338208930460318e-07,
                1.209865827752005e-06,
                6.962259569750576e-06,
                1.2098652508424818e-06,
                1.3709568799919866e-06,
                4.450849988811838e-07,
                2.753569110256289e-05,
                0.9999599363226042,
                2.2603242978871282e-06,
                1.0129994602895546e-05
            ],
            [
                NaN,
                4.0063701745046735e-05,
                2.4300252321904572e-05,
                3.535625493182252e-05,
                1.8925157266089433e-05,
                8.481106162154104e-05,
                4.785094494783494e-06,
                NaN,
                3.2887506336235617e-06,
                0.0005527785512542539
            ],
            [
                4.539785781961294e-05,
                2.9023126771227976e-06,
                7.889259764273619e-06,
                0.0001584362924696706,
                6.144172404587612e-06,
                3.726639728370556e-06,
                2.4300232043987867e-05,
                0.0010322308458857235,
                6.962253759670401e-06,
                0.00017952796627505744
            ],
            [
                4.785093924389007e-06,
                1.8925157266089433e-05,
                1.3709576971463352e-06,
                1.3709575337159875e-06,
                2.9023119851899796e-06,
                2.260325106237323e-06,
                1.9947292459347367e-06,
                1.6373764721072816e-07,
                6.962257079889302e-06,
                6.962257909842961e-06
            ],
            [
                2.9023112932045342e-06,
                5.4222176771176554e-06,
                2.4300237837960777e-05,
                5.422221555380179e-06,
                6.962254589914941e-06,
                4.785096776468749e-06,
                2.5612819054028872e-06,
                1.6701421845361053e-05,
                3.466327863983311e-07,
                6.475950298011458e-07
            ],
            [
                3.1201926253802263e-05,
                4.785094494783494e-06,
                1.553497199007048e-06,
                7.889259764273619e-06,
                1.4738987243236881e-05,
                3.2887478892504536e-06,
                6.144174601991196e-06,
                2.902312331125353e-06,
                1.012999218752948e-05,
                6.962254589851619e-06
            ],
            [
                2.3823693839290317e-07,
                1.9947301970972664e-06,
                9.422444815814404e-07,
                5.71500515161527e-07,
                1.4449802095666915e-07,
                4.450850519409479e-07,
                3.05902263391829e-07,
                2.699577774589574e-07,
                2.561281600086738e-06,
                1.8553910183674878e-07
            ],
            [
                7.338208055680009e-07,
                NaN,
                1.994729721518893e-06,
                1.9947299593078385e-06,
                4.450850519403407e-07,
                NaN,
                5.715005832886879e-07,
                2.9023119851899796e-06,
                5.043474081993875e-07,
                NaN
            ],
            [
                2.5612834320563895e-06,
                1.9947292459347367e-06,
                2.561281294760143e-06,
                1.9947292459347367e-06,
                3.05902263391829e-07,
                0.9999960330155133,
                8.315281267882195e-07,
                3.927862470899887e-07,
                2.75356812556058e-05,
                6.475949526020042e-07
            ],
            [
                0.9999996533673378,
                0.9999982396563687,
                0.999999927341853,
                0.9999998555020135,
                0.9999999273418615,
                0.9999981261252882,
                0.9999998874647575,
                0.9999998724809116,
                0.999999168472171,
                0.9999987901337402
            ],
            [
                1.4449807263312446e-07,
                3.2887502415767434e-06,
                7.338207180898968e-07,
                5.422217030781934e-06,
                1.1253526937697666e-07,
                2.6995790618469934e-07,
                7.734415776836702e-08,
                1.994730672675753e-06,
                9.422443692574719e-07,
                7.889261645427538e-06
            ],
            [
                3.466327450765785e-07,
                0.9999997300421262,
                0.9999995818814267,
                0.9999994284995533,
                0.9999995262092729,
                0.9999997463980428,
                0.9999990577556315,
                0.9999994284996897,
                0.999999554914789,
                0.9999997761971583
            ],
            [
                1.0677026154774503e-06,
                3.9278615344178325e-07,
                5.043476486915964e-07,
                5.043472879540142e-07,
                5.422217677152175e-06,
                1.2098662604291696e-06,
                2.2603245673155757e-06,
                7.338210680021253e-07,
                7.338208055664991e-07,
                7.338208055664991e-07
            ],
            [
                2.561281294760143e-06,
                3.288750241561788e-06,
                3.2887506336235617e-06,
                1.0129987357517693e-05,
                1.012999218776902e-05,
                2.902312677150514e-06,
                3.1201900218617364e-05,
                7.889262585886274e-06,
                1.9947304348862686e-06,
                6.475946438055299e-07
            ],
            [
                6.475950298021765e-07,
                9.422447062270609e-07,
                1.994730672668496e-06,
                2.561282516066741e-06,
                8.315277302841894e-07,
                6.144177531811707e-06,
                1.1478772231232203e-05,
                NaN,
                2.902313023130843e-06,
                1.9947299593078385e-06
            ],
            [
                1.3007128464346676e-05,
                7.4846254021955e-05,
                2.4300243628620005e-05,
                1.3007131565376817e-05,
                1.4738988999672284e-05,
                7.484626294855732e-05,
                8.93969630388855e-06,
                7.484620050755993e-05,
                2.9023109471689794e-06,
                8.481104138298063e-05
            ],
            [
                6.475949526020042e-07,
                5.04347528446051e-07,
                0.999993855826873,
                3.927862470899887e-07,
                1.209866260432471e-06,
                4.450852641737424e-07,
                0.9999988634366971,
                6.475946438055299e-07,
                5.715005151606823e-07,
                2.6995784182140636e-07
            ],
            [
                3.7266410611296085e-06,
                5.715003789046955e-07,
                4.785096776499213e-06,
                8.315277302857965e-07,
                2.2603242978871282e-06,
                1.0677024882009222e-06,
                6.962257909785973e-06,
                1.9947299593014888e-06,
                8.939693107288474e-06,
                5.715005151606823e-07
            ],
            [
                1.5534979397790343e-06,
                2.9023119851899796e-06,
                1.3709568799919866e-06,
                8.315282259138311e-07,
                1.5534975693979422e-06,
                8.315283250371857e-07,
                5.422217030781934e-06,
                1.3007123813559956e-05,
                3.7266379514061143e-06,
                1.0677028700422047e-06
            ],
            [
                0.9999996310114602,
                0.999999694097664,
                0.9999995818813768,
                0.9999995818811777,
                0.9999996072137531,
                0.9999998024946567,
                0.9999996940978827,
                0.9997694933702762,
                2.699576809143613e-07,
                0.9999977396746268
            ],
            [
                8.939697369980456e-06,
                0.9999991684715765,
                7.889263526345123e-06,
                0.9999997897567342,
                0.9999996743688975,
                0.9999994284993491,
                0.9999967112501551,
                0.9999991684718739,
                0.999999631011592,
                0.9999952149055152
            ],
            [
                2.699577774585891e-07,
                1.994730197090463e-06,
                4.22283545819819e-06,
                NaN,
                1.1478773599425825e-05,
                6.144175334468545e-06,
                4.785092783519724e-06,
                2.10243290909724e-07,
                1.5534981249697903e-06,
                1.2098661162056318e-06
            ],
            [
                4.785095635592258e-06,
                2.2603234895372223e-06,
                1.0677028700363782e-06,
                3.466327450756327e-07,
                0.9999892166839464,
                3.7266401726359486e-06,
                1.4738976701411704e-05,
                2.260324028427877e-06,
                2.6995787400282076e-07,
                7.338213304363436e-07
            ],
            [
                6.144173137170873e-06,
                2.1024334103581732e-07,
                3.2887502415767434e-06,
                1.444979692800516e-07,
                0.9999991148427542,
                4.4508515805735777e-07,
                3.927862002663297e-07,
                1.892515501014656e-05,
                3.4663278639892215e-07,
                1.7603430034867993e-06
            ],
            [
                2.561281600086738e-06,
                NaN,
                2.102434412871794e-07,
                2.90231094723893e-06,
                2.2603242978871282e-06,
                NaN,
                2.4300252317086683e-05,
                2.9023116391978967e-06,
                1.0677029973219343e-06,
                6.962255419931625e-06
            ],
            [
                4.222834954801051e-06,
                5.422220909009474e-06,
                NaN,
                1.994730197090463e-06,
                5.4222183235249605e-06,
                4.2228319344021954e-06,
                1.7603438428800754e-06,
                0.9996200154280837,
                4.785092783519724e-06,
                7.88926446679691e-06
            ],
            [
                NaN,
                1.7603438428740716e-06,
                4.222834954801051e-06,
                NaN,
                3.2887506336235617e-06,
                2.2603240284371276e-06,
                1.9947304348703948e-06,
                1.553497754577351e-06,
                4.22283545819819e-06,
                3.726637951387472e-06
            ],
            [
                0.9999967112517247,
                1.5534975693979422e-06,
                7.338207180898968e-07,
                3.288749065423109e-06,
                NaN,
                5.715006514176113e-07,
                1.2098661162056318e-06,
                1.8925141473599938e-05,
                1.7603434231833873e-06,
                1.994729721518893e-06
            ],
            [
                1.9947292459406333e-06,
                5.043472278322555e-07,
                3.288748281329893e-06,
                1.3007133116732079e-05,
                2.5612819054028872e-06,
                0.0006263340334301912,
                0.9999151889492961,
                1.067703124601679e-06,
                0.9820137914196813,
                5.043476486924565e-07
            ],
            [
                2.7535700949523498e-05,
                1.8925152753790864e-05,
                7.889262585886274e-06,
                5.4222183235249605e-06,
                5.715005832886879e-07,
                5.71500719545698e-07,
                4.006368741670684e-05,
                5.715006514176113e-07,
                2.902312677150514e-06,
                1.3709572068522336e-06
            ],
            [
                2.2603251062450327e-06,
                0.9740426398352605,
                3.927863407379485e-07,
                1.994729008151319e-06,
                8.93969950132721e-06,
                2.1444958640087166e-05,
                NaN,
                3.05902190458764e-07,
                3.9278629391427843e-07,
                5.422217030781934e-06
            ],
            [
                0.9999741325721629,
                0.9999756997565358,
                0.0019267349592826685,
                0.9999573525120565,
                6.144172404738491e-06,
                5.144221366885164e-05,
                1.0129989772532511e-05,
                1.670141786325573e-05,
                4.222832437798974e-06,
                0.014063623956902305
            ],
            [
                6.475947982037486e-07,
                3.726639284125553e-06,
                8.939694172957213e-06,
                5.04347287955046e-07,
                9.422448185534261e-07,
                4.4508515805735777e-07,
                2.2603242978871282e-06,
                8.481106162154104e-05,
                2.902313369111213e-06,
                3.726638395634011e-06
            ],
            [
                8.93969843573914e-06,
                2.902312677150514e-06,
                6.475947982037486e-07,
                4.785095635655362e-06,
                2.3823696679327928e-07,
                2.69957906184239e-07,
                1.855391239544352e-07,
                7.338208930460318e-07,
                1.0677029973219343e-06,
                4.4508510499849186e-07
            ],
            [
                0.9999986290421411,
                0.9999994631251248,
                0.999999114842648,
                0.9999997761970516,
                0.9999991148429648,
                0.9999993916409637,
                1.855391239539711e-07,
                0.999998629042141,
                0.999999746398194,
                0.9999992188512975
            ],
            [
                3.7266406168624155e-06,
                6.144174601991196e-06,
                1.4738983729294318e-05,
                2.26032402841657e-06,
                1.553498124964492e-06,
                1.0129987357287368e-05,
                1.3007130015488633e-05,
                4.222832437747125e-06,
                1.3709576971316842e-06,
                2.5612831267086116e-06
            ],
            [
                2.1444945858485726e-05,
                2.260325106237323e-06,
                1.2098652508347793e-06,
                1.3007123813382511e-05,
                1.9947292459265734e-06,
                1.9947297215125433e-06,
                1.9947292459347367e-06,
                1.3709567165617364e-06,
                1.067703124601679e-06,
                3.726638395611981e-06
            ],
            [
                0.9999997300423193,
                0.9999982396561592,
                0.999999114843176,
                0.9999981261248411,
                0.9999998362623723,
                7.338208055680009e-07,
                0.9999987121041714,
                0.9999987901341731,
                0.9999990577550698,
                0.9999996072136595
            ],
            [
                2.561283126728994e-06,
                4.785094494783494e-06,
                3.2887494574832472e-06,
                2.2603248367949354e-06,
                6.962257079889302e-06,
                8.315283250371857e-07,
                8.939698435657833e-06,
                3.059022269250683e-07,
                7.889265407327733e-06,
                4.785095635655362e-06
            ],
            [
                9.422444815814404e-07,
                2.902312331170226e-06,
                1.7603425837903113e-06,
                3.72663883989755e-06,
                4.0063677865600476e-05,
                1.4738981972564636e-05,
                2.9023116392097746e-06,
                1.2098659719788098e-06,
                2.2603234895372223e-06,
                1.7603430034867993e-06
            ],
            [
                9.422447062240614e-07,
                5.043476486915964e-07,
                8.315277302819205e-07,
                6.475945666051092e-07,
                2.1024341622426268e-07,
                1.7603425837903113e-06,
                3.466327037539638e-07,
                1.994729721518893e-06,
                6.475945666051092e-07,
                3.46632497145457e-07
            ],
            [
                0.00010889696127518294,
                1.9947299593078385e-06,
                4.2228319344021954e-06,
                4.785092783519724e-06,
                5.715002426486762e-07,
                2.1444940745371397e-05,
                NaN,
                5.144221980055201e-05,
                1.9947292459347367e-06,
                1.4738983729535602e-05
            ],
            [
                5.043474081993875e-07,
                1.9947292459265734e-06,
                6.475945666033422e-07,
                8.315279285351409e-07,
                1.2098662604291696e-06,
                2.561281294760143e-06,
                7.338208930443633e-07,
                1.0677032518785256e-06,
                5.71500515159253e-07,
                3.7266401726359486e-06
            ],
            [
                0.9999983463104172,
                0.9999991684719731,
                0.9999997300422547,
                0.9999985406230846,
                1.8553905760062447e-07,
                0.9999989969854343,
                0.999997739674897,
                0.9999995262095556,
                0.9999995549151076,
                0.9999995549147362
            ],
            [
                1.670142383595838e-05,
                3.12019150949065e-05,
                5.144223819322476e-05,
                1.6701429808632785e-05,
                7.889259764445822e-06,
                6.144176066850984e-06,
                2.5612819054028872e-06,
                1.0129987357287368e-05,
                7.88926070489716e-06,
                1.3007131566015624e-05
            ],
            [
                0.9999998362622748,
                0.9999996743686648,
                0.9999991684716756,
                1.275190276859705e-07,
                0.9999996940977004,
                0.9999997617630617,
                0.9999997300421904,
                0.9999998144609205,
                0.9999996533672965,
                0.9999998024945861
            ],
            [
                6.1441746020359e-06,
                4.785092783519724e-06,
                7.889261645427538e-06,
                7.484621836619826e-05,
                1.6701423836262173e-05,
                2.5612828213934817e-06,
                3.535626757524533e-05,
                4.2228319344021954e-06,
                5.144221366623174e-05,
                1.6701415872385704e-05
            ],
            [
                9.422445939002803e-07,
                2.561281905390075e-06,
                2.561281600049467e-06,
                5.422221555296344e-06,
                3.288749849498565e-06,
                2.2603242978665707e-06,
                2.2603245672497918e-06,
                1.7603440527046419e-06,
                2.5612828213690224e-06,
                7.889259764359722e-06
            ],
            [
                4.4508505193791187e-07,
                6.9622587397397306e-06,
                6.962257909785973e-06,
                1.760343003481596e-06,
                1.300712536350655e-05,
                1.6701419854156377e-05,
                5.4222183234485234e-06,
                1.0129995810343862e-05,
                4.539785782605375e-05,
                4.539786865090791e-05
            ],
            [
                2.5612828213818346e-06,
                2.2603234895176927e-06,
                6.144176799334096e-06,
                2.144494585747154e-05,
                6.144175334418252e-06,
                2.2603253756874524e-06,
                4.0063696967815485e-05,
                1.0129992187658463e-05,
                6.962257909785973e-06,
                5.422220262599396e-06
            ],
            [
                0.9999546021099659,
                7.484621836619826e-05,
                NaN,
                0.9998204720140409,
                0.9997694933451851,
                0.9999546021423972,
                6.9622595696935874e-06,
                4.785095635624897e-06,
                9.610239210035764e-05,
                4.2228329411708495e-06
            ],
            [
                1.855391239544352e-07,
                9.422443692574719e-07,
                5.715002426486762e-07,
                3.9278629391427843e-07,
                1.0677029973192638e-06,
                4.450852641737424e-07,
                3.4663249714612693e-07,
                4.450850519403407e-07,
                3.7266397283908927e-06,
                1.8553919030858602e-07
            ],
            [
                0.9999996533675032,
                0.9999996310115481,
                0.999998932296749,
                0.9999997617631753,
                0.9999989322972583,
                3.2887502415767434e-06,
                3.72663883989755e-06,
                0.9999997463981636,
                0.9999998642566542,
                0.999999776197185
            ],
            [
                5.14422075345321e-05,
                5.422218323487975e-06,
                1.0677029973192638e-06,
                1.994730434879465e-06,
                1.9947292459265734e-06,
                1.7603427936263351e-06,
                6.144177531767002e-06,
                1.300712846477255e-05,
                1.9947304348703948e-06,
                4.222833947932061e-06
            ],
            [
                0.0003353501112555357,
                5.422220262636381e-06,
                2.3823696679327928e-07,
                1.8925145985895816e-05,
                1.6701419854156377e-05,
                NaN,
                2.4300237837960777e-05,
                2.7535697667202906e-05,
                1.0129987357407137e-05,
                8.939696304311336e-06
            ],
            [
                4.450849988811838e-07,
                2.1024339116134898e-07,
                3.0590215399183813e-07,
                3.0590237279032884e-07,
                9.422447062202052e-07,
                3.059022998558814e-07,
                1.8553916819032217e-07,
                3.466327037548308e-07,
                1.5534983101602148e-06,
                9.422448185510695e-07
            ],
            [
                1.0677024882009222e-06,
                6.144173137126169e-06,
                NaN,
                4.450852641737424e-07,
                4.222835458148261e-06,
                3.7266406168403854e-06,
                0.001032230972771653,
                6.605212894856585e-05,
                1.6701429808632785e-05,
                1.994729483729522e-06
            ],
            [
                0.999999761763005,
                0.9999987901343174,
                0.9999988634366964,
                0.9999991684715764,
                0.9999986290429576,
                0.9999983463106126,
                0.999999814460876,
                0.9999983463108092,
                0.9999996940976639,
                0.9999988634361543
            ],
            [
                3.9278634073732336e-07,
                7.338210680021253e-07,
                6.1441746020359e-06,
                1.760342793638743e-06,
                3.4663278639892215e-07,
                2.561282210740037e-06,
                3.7266397283908927e-06,
                1.0677032518814388e-06,
                1.2098659719788098e-06,
                4.450848927658745e-07
            ],
            [
                5.8291244705086375e-05,
                2.7535700949523498e-05,
                3.1201926253802263e-05,
                1.8925141473599938e-05,
                1.3007133116732079e-05,
                1.4738985486506781e-05,
                0.010986941659076578,
                2.90231094723893e-06,
                1.1478768126057254e-05,
                1.2098661162056318e-06
            ],
            [
                0.9999646437325065,
                8.939699501416646e-06,
                4.539787947559951e-05,
                1.209865539295696e-06,
                6.1441767993788005e-06,
                1.6701425827133152e-05,
                1.3709572068522336e-06,
                2.2603251062450327e-06,
                1.760343213335281e-06,
                1.370957860576702e-06
            ],
            [
                5.829128639666634e-05,
                2.2603248367949354e-06,
                9.422448185510695e-07,
                2.5612819054028872e-06,
                3.9278615344178325e-07,
                3.0590226339061185e-07,
                4.450852641737424e-07,
                2.2603234895289998e-06,
                0.9999964991439233,
                1.0677032518814388e-06
            ],
            [
                2.2603242978778778e-06,
                4.785094494783494e-06,
                1.670141786325573e-05,
                1.4738983729294318e-05,
                0.000261190372224901,
                0.0001584362736893196,
                4.785093924330255e-06,
                6.605216044933028e-05,
                1.3007130015488633e-05,
                2.4300234941261454e-05
            ],
            [
                1.0129987357158383e-05,
                0.9997388095917755,
                2.2603248367358324e-06,
                6.962256249517824e-06,
                9.422450431860582e-07,
                0.0008040857687202314,
                0.9999904837438985,
                1.4738981972082061e-05,
                2.902311985146426e-06,
                2.9023116391675407e-06
            ],
            [
                1.1478766757561534e-05,
                2.9023133690980155e-06,
                1.2098661161927025e-06,
                0.9999771720111373,
                3.120191881423529e-05,
                4.785093924330255e-06,
                1.3709567165579959e-06,
                3.2887482813149375e-06,
                0.0009110510268190825,
                2.260324836787226e-06
            ],
            [
                4.222833444590791e-06,
                2.2603242978871282e-06,
                2.902313369111213e-06,
                2.561281600086738e-06,
                6.475947210046347e-07,
                1.994729008145876e-06,
                1.3709572068522336e-06,
                9.422443692555439e-07,
                1.0677029973219343e-06,
                3.466325797896173e-07
            ],
            [
                1.6373764721072816e-07,
                0.9999379494974752,
                1.855391681906175e-07,
                1.5534971990126997e-06,
                2.5612834320563895e-06,
                2.9023116392097746e-06,
                8.315277302857965e-07,
                1.209865827752005e-06,
                1.5534983101644536e-06,
                6.475950298011458e-07
            ],
            [
                1.8925157265710765e-05,
                6.962259569560613e-06,
                1.4738978458382043e-05,
                1.47389854857293e-05,
                1.760344052714248e-06,
                0.00012339461912625076,
                6.605215256765022e-05,
                1.47389854857293e-05,
                2.1444948414321717e-05,
                9.61024493609775e-05
            ],
            [
                2.6995784182073116e-07,
                5.043474081993875e-07,
                3.059022998576899e-07,
                2.3823702359290413e-07,
                4.450850519403407e-07,
                7.338212429537553e-07,
                3.9278638755992735e-07,
                7.338208055664991e-07,
                5.043472879540142e-07,
                1.4449805540740185e-07
            ],
            [
                0.00012339454552178923,
                4.785095635624897e-06,
                0.9999706884549602,
                3.535625070778844e-05,
                0.9999952149072393,
                0.9999930377430493,
                5.829127944184748e-05,
                0.999996273360762,
                0.999997438718415,
                7.484624512911504e-05
            ],
            [
                8.93969950132721e-06,
                3.1201922535494165e-05,
                NaN,
                1.4738985486506781e-05,
                6.962256249885085e-06,
                2.753569110256289e-05,
                5.4222176771176554e-06,
                6.9622587397397306e-06,
                2.5612828213934817e-06,
                2.144495608378187e-05
            ],
            [
                7.889261645427538e-06,
                8.939696304311336e-06,
                0.9999546021369816,
                1.5534977545886537e-06,
                0.9995694428162171,
                1.7603430034867993e-06,
                5.043474081993875e-07,
                3.7266410611296085e-06,
                5.422217030747413e-06,
                3.72663883989755e-06
            ]
        ]
    },
    {
        "q_id": "9411_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            20,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.2751905808881762e-07,
                2.1024336609874897e-07,
                4.1399410020127234e-08,
                9.931189774187203e-08,
                5.3157837044597743e-08,
                1.8553907971855875e-07,
                1.275191036933194e-07,
                1.444980209564556e-07,
                7.734424996967756e-08,
                8.764242227418718e-08
            ],
            [
                2.6995790618469934e-07,
                3.0590237279085045e-07,
                1.2751899728311609e-07,
                8.315277302857965e-07,
                2.1024336609874897e-07,
                5.715003107767143e-07,
                2.699578096403948e-07,
                2.382368815932174e-07,
                3.05902190458764e-07,
                3.4663249714612693e-07
            ],
            [
                2.6995784182183607e-07,
                1.855391239547094e-07,
                5.043476486924565e-07,
                1.6373772528704005e-07,
                2.699578740032504e-07,
                2.3823690999323465e-07,
                3.9278605979534166e-07,
                2.3823696679327928e-07,
                5.043475885696228e-07,
                9.422450432030903e-07
            ],
            [
                1.1253509497883659e-07,
                1.4449798650551755e-07,
                1.1253509497883659e-07,
                1.444979692797559e-07,
                8.764247451307293e-08,
                8.764244316973974e-08,
                1.2751901248454963e-07,
                1.444979692800516e-07,
                0.9999999006879957,
                9.931189774187203e-08
            ],
            [
                0.9999999586006195,
                0.9999999358793868,
                0.9999999123574732,
                0.9999999317440197,
                0.9999999500628095,
                0.9999999559305629,
                0.9999999123575882,
                0.9999999559305522,
                0.9999999176674651,
                1.0
            ],
            [
                0.9999999123575255,
                0.9999999358793867,
                0.9999997300421262,
                0.999999825702059,
                0.9999999358794402,
                0.999999712631481,
                0.999999631011592,
                0.9999998874647709,
                0.9999999006880076,
                0.9999999006880668
            ],
            [
                0.9999998461826038,
                0.9999998024946801,
                0.999999631011548,
                0.9999996310115039,
                0.9999995549148952,
                0.9999993106390371,
                0.9999987901347499,
                0.9999997126315496,
                0.9999991684722704,
                0.9999998024946566
            ],
            [
                1.8553916819032217e-07,
                1.444980209564556e-07,
                1.4449802095666915e-07,
                1.1253512180925583e-07,
                3.05902336324494e-07,
                1.6373774480605869e-07,
                6.475945666063607e-07,
                2.699577774585891e-07,
                2.10243290909724e-07,
                2.6995784182183607e-07
            ],
            [
                0.9999998555020135,
                0.999999917667524,
                0.9999998942829854,
                0.9999999067050943,
                0.9999999006880786,
                1.0,
                0.9999998874647709,
                0.9999999273418269,
                0.9999999067050388,
                0.9999997761970248
            ],
            [
                0.9999998802068873,
                0.9999998942830863,
                0.9999998024946566,
                0.9999998642566219,
                0.9999997126314468,
                0.9999998362623723,
                0.9999998362623529,
                0.9999998555019963,
                0.9999998362622358,
                0.9999998802069873
            ],
            [
                7.338213304363436e-07,
                3.059022269250683e-07,
                1.7603434231833873e-06,
                2.3823690999290963e-07,
                3.4663274507713016e-07,
                5.04347287955046e-07,
                3.0590237279085045e-07,
                5.04347287955046e-07,
                3.059021175261338e-07,
                5.043473480777865e-07
            ],
            [
                1.27519088491875e-07,
                9.93120161310289e-08,
                8.764241182641775e-08,
                2.382369951932796e-07,
                1.4449802095666915e-07,
                1.4449802095666915e-07,
                1.4449805540763184e-07,
                5.04347287955046e-07,
                3.4663249714612693e-07,
                1.855391239544352e-07
            ],
            [
                1.6373764721072816e-07,
                2.1024331597262577e-07,
                2.1024341622426268e-07,
                2.6995774527718623e-07,
                3.059022269250683e-07,
                1.444979692800516e-07,
                2.1024341622426268e-07,
                2.10243290909724e-07,
                8.764255809528314e-08,
                9.931189774187203e-08
            ],
            [
                1.855391239544352e-07,
                1.4449805540740185e-07,
                2.699576809143613e-07,
                2.102434412871794e-07,
                2.102434412875379e-07,
                9.931198061405701e-08,
                2.1024329090929374e-07,
                1.444980726324838e-07,
                3.9278605979534166e-07,
                2.6995784182140636e-07
            ],
            [
                1.444980209564556e-07,
                1.1253508156363576e-07,
                3.0590237279085045e-07,
                5.043472278322555e-07,
                2.382369951932796e-07,
                2.6995774527718623e-07,
                2.102434412875379e-07,
                2.3823688159291947e-07,
                2.6995774527718623e-07,
                3.05902336324494e-07
            ],
            [
                0.9999990577556309,
                0.9999995818812769,
                0.999999266179282,
                0.9999996533672549,
                0.9999995262093292,
                0.9999996533672137,
                0.9999996310116358,
                0.999999428499485,
                0.9999997300420939,
                0.999999495652652
            ],
            [
                0.9999996743687034,
                0.9999992661790199,
                0.9999996072139403,
                0.9999991684717746,
                0.9999993524049706,
                0.9999993524052794,
                0.9999997617631754,
                0.9999993916407461,
                0.9999997897565587,
                0.9999991148431756
            ],
            [
                2.6995774527718623e-07,
                6.962254589914941e-06,
                2.382370235933104e-07,
                1.2751905808881762e-07,
                1.6373762769138607e-07,
                8.31527928532683e-07,
                1.0677029973192638e-06,
                1.6373776432509826e-07,
                1.637377448057981e-07,
                8.315284241650899e-07
            ],
            [
                0.9999997617629766,
                0.9999994956527124,
                0.999999631011592,
                0.9999995549147892,
                0.9999994631250604,
                0.9999998144608319,
                0.99999976176309,
                0.9999996310115918,
                0.9999997126315496,
                0.999999802494633
            ],
            [
                2.10243290909724e-07,
                1.6373764721072816e-07,
                1.6373770576776313e-07,
                1.444980209564556e-07,
                1.1253513522447425e-07,
                9.931187406410953e-08,
                3.927862002663297e-07,
                1.4449807263312446e-07,
                1.2751904288739315e-07,
                7.734421308914719e-08
            ],
            [
                0.9999998144608319,
                0.9999998362622552,
                0.9999998257021006,
                0.9999998555019447,
                0.999999802494633,
                0.9999999273418269,
                0.9999999123574628,
                0.9999994956524718,
                0.9999998024947273,
                0.9999998942830233
            ],
            [
                0.9999997126314126,
                0.999999802494586,
                0.999999730042287,
                0.999999814460854,
                0.9999996940976638,
                0.9999995818814265,
                0.999998996985434,
                0.9999996940977368,
                0.9999997300422869,
                0.9999990577551819
            ],
            [
                8.315281267882195e-07,
                2.1024331597262577e-07,
                4.4508494582405734e-07,
                1.1253509497883659e-07,
                3.05902336324494e-07,
                6.475945666063607e-07,
                3.927863875616689e-07,
                1.275191036933194e-07,
                8.315278294114555e-07,
                1.6373772528704005e-07
            ],
            [
                0.9999997897567091,
                0.9999997897567342,
                0.9999997897567342,
                0.9999997761971315,
                0.999999943413757,
                0.9999998024947037,
                0.9999998724809723,
                0.9999999123574419,
                0.9999998942830233,
                0.9999998942828973
            ],
            [
                1.8553905760062447e-07,
                2.699578096403948e-07,
                2.3823682479292225e-07,
                2.102434412875379e-07,
                3.466326211113502e-07,
                3.4663274507713016e-07,
                6.825606165129312e-08,
                5.043473480777865e-07,
                2.3823685319244518e-07,
                9.931190958076104e-08
            ],
            [
                2.69957906184239e-07,
                2.69957906184239e-07,
                2.382370235933104e-07,
                5.715003789046955e-07,
                1.8553914607267268e-07,
                1.637377448057981e-07,
                5.715006514176113e-07,
                2.3823682479292225e-07,
                3.0590237279085045e-07,
                1.6373776432509826e-07
            ],
            [
                1.444980209564556e-07,
                8.764247451307293e-08,
                6.825600469412533e-08,
                1.4449807263312446e-07,
                1.2751905808881762e-07,
                2.102434162245973e-07,
                8.764247451307293e-08,
                1.4449798650551755e-07,
                6.825598842065202e-08,
                1.4449805540763184e-07
            ],
            [
                8.764242227418718e-08,
                2.1024341622426268e-07,
                1.6373776432509826e-07,
                2.6995790618469934e-07,
                1.6373764721072816e-07,
                1.4449807263312446e-07,
                4.450852111155216e-07,
                7.734418542875216e-08,
                3.466327037548308e-07,
                2.1024339116168358e-07
            ],
            [
                1.4449802095666915e-07,
                1.1253509497883659e-07,
                1.637376862489725e-07,
                6.825598842065202e-08,
                9.931187406410953e-08,
                1.2751901248454963e-07,
                1.275190732904469e-07,
                7.734418542875216e-08,
                1.275190428875671e-07,
                8.764245361752286e-08
            ],
            [
                2.10243290909724e-07,
                1.4449805540763184e-07,
                8.764244316973974e-08,
                2.1024339116168358e-07,
                1.2751899728311609e-07,
                5.715003107767143e-07,
                2.699578740032504e-07,
                2.1024341622426268e-07,
                8.7642516304188e-08,
                3.927863407379485e-07
            ],
            [
                0.9999999067049831,
                0.9999998144609646,
                0.999999887464932,
                0.9999998874648917,
                0.9999998642566542,
                1.0,
                0.9999998257020591,
                1.0,
                0.9999998802069017,
                0.9999998461827322
            ],
            [
                2.5612828213934817e-06,
                9.422447062270609e-07,
                8.315277302841894e-07,
                5.422217030747413e-06,
                1.994729483723626e-06,
                2.5612831267202583e-06,
                5.043472879540142e-07,
                6.144177531767002e-06,
                9.422443692574719e-07,
                8.315283250394546e-07
            ],
            [
                0.9999995818810776,
                0.9999997761970781,
                0.9999994631247404,
                0.999999789756659,
                0.9999996940978096,
                0.9999997463981334,
                0.999999554914842,
                0.9999997761971848,
                0.9999997897565588,
                0.9999997761971315
            ],
            [
                2.382368531929327e-07,
                1.637377057680051e-07,
                1.6373764721072816e-07,
                2.6995784182140636e-07,
                3.9278610661902853e-07,
                1.1253509497883659e-07,
                1.6373772528704005e-07,
                1.444980209564556e-07,
                3.059021175261338e-07,
                1.1253514863968147e-07
            ],
            [
                2.2603234895372223e-06,
                2.3823693839290317e-07,
                5.043473480777865e-07,
                1.5534977545886537e-06,
                2.3823688159237777e-07,
                1.994729483729522e-06,
                4.450850519403407e-07,
                1.125352291309328e-07,
                3.059022998576899e-07,
                9.422445939054222e-07
            ],
            [
                1.0,
                0.9999998874648782,
                0.9999999123575881,
                1.0,
                0.9999999006881497,
                0.9999999176675632,
                0.9999999358793562,
                0.9999999226557408,
                0.9999999273418615,
                0.9999999468421313
            ],
            [
                0.9999997300421583,
                0.999999631011328,
                0.9999998362623528,
                0.9999998461826405,
                0.9999999123574942,
                0.9999997761972116,
                0.999999887464932,
                0.9999998642567189,
                0.9999997761971049,
                0.9999995818814267
            ],
            [
                1.1253512180925583e-07,
                1.1253512180925583e-07,
                2.382370235933104e-07,
                1.27519088491875e-07,
                1.444979692800516e-07,
                1.1253508156363576e-07,
                5.04347287955046e-07,
                1.8553905760062447e-07,
                2.382370235933104e-07,
                1.2751908849167202e-07
            ],
            [
                1.855391681906175e-07,
                2.1024334103581732e-07,
                2.699578096403948e-07,
                2.6995790618469934e-07,
                1.275190428875671e-07,
                3.059022998581767e-07,
                1.1253513522447425e-07,
                1.1253506814842375e-07,
                3.059022998581767e-07,
                2.382369951932796e-07
            ],
            [
                0.9999998724809116,
                0.999999855502048,
                0.9999999123575672,
                0.9999988634365611,
                0.9999997463980125,
                0.9999998642566543,
                0.999999581881277,
                0.9999997617629764,
                0.9999998942829099,
                0.9999998874647574
            ],
            [
                9.931189774187203e-08,
                1.1253524254615121e-07,
                1.1253510839355284e-07,
                5.3157837044597743e-08,
                1.275190732904469e-07,
                1.444979692800516e-07,
                1.275190580890061e-07,
                1.4449805540740185e-07,
                2.1024331597262577e-07,
                9.93120161306789e-08
            ],
            [
                0.9999998362622358,
                0.9999997126314812,
                0.9999998362623332,
                0.9999999176674552,
                0.9999999067050609,
                0.9999998257021007,
                0.999999631011636,
                0.9999998642566381,
                0.999999825702163,
                0.9999993106387084
            ],
            [
                0.9999998874648246,
                0.9999997300421583,
                0.9999994284995533,
                0.9999997761970515,
                0.999999674368781,
                0.9999997761971849,
                0.9999997463981636,
                0.9999992188518559,
                0.999999825702163,
                0.9999992188512971
            ],
            [
                0.9999997761971583,
                0.999999730042255,
                0.9999994631249323,
                0.9999998024946095,
                0.9999995549150013,
                0.9999998874648915,
                0.9999989322967487,
                0.9999998461826405,
                0.999999789756634,
                0.9999996940977367
            ],
            [
                2.2603234895176927e-06,
                1.7603427936263351e-06,
                6.475945666051092e-07,
                1.0677032518785256e-06,
                3.7266406168624155e-06,
                6.475945666051092e-07,
                1.067702870039777e-06,
                2.902312677137316e-06,
                2.144495608424996e-05,
                1.7603436330259153e-06
            ],
            [
                0.9999999123574419,
                0.9999998942829729,
                0.9999999468420996,
                0.9999999434137165,
                0.9999998802069017,
                0.9999999397642508,
                0.9999999317439139,
                0.9999998555019791,
                0.9999996940978462,
                0.9999999500627916
            ],
            [
                7.734421308914719e-08,
                8.764245361752286e-08,
                1.1253509497883659e-07,
                1.27519088491875e-07,
                1.8553919030858602e-07,
                9.931190958076104e-08,
                1.4449798650569826e-07,
                1.1253518888531272e-07,
                6.023571320847322e-08,
                2.3823685319244518e-07
            ],
            [
                0.9999998942829477,
                0.9999999176675437,
                0.9999999273418702,
                0.9999998874648246,
                0.9999999067050387,
                0.9999998724809572,
                0.999999927341853,
                1.0,
                0.9999999273418962,
                0.9999999067051054
            ],
            [
                0.9999998724809875,
                0.9999998802069587,
                0.9999999434137233,
                0.9999998257021422,
                0.9999998642566381,
                0.9999998942830233,
                0.9999999358793332,
                0.9999998642566542,
                0.9999998724809723,
                0.9999999434137165
            ],
            [
                9.422444815726566e-07,
                5.71500719545698e-07,
                9.422447062150634e-07,
                3.059021175261338e-07,
                5.043475885696228e-07,
                1.0677033791583005e-06,
                2.5612812947380135e-06,
                3.466325797896173e-07,
                1.2751904288739315e-07,
                2.3823688159291947e-07
            ],
            [
                3.466326624336003e-07,
                1.2098652508424818e-06,
                3.05902336324494e-07,
                3.059022998581767e-07,
                2.3823702359290413e-07,
                3.4663274507713016e-07,
                1.3709567165617364e-06,
                1.8553919030858602e-07,
                1.2098659719788098e-06,
                4.785095065232451e-06
            ],
            [
                0.9999999586006443,
                0.9999999176675437,
                0.9999999273417922,
                0.9999999226557962,
                0.9999999500627738,
                0.9999999500627857,
                0.9999998555019791,
                0.9999999500628513,
                0.9999998942830485,
                1.0
            ],
            [
                0.9999998642566381,
                0.9999997463980426,
                0.9999998257022045,
                0.9999997761971582,
                0.9999997617630617,
                0.9999998874649318,
                0.9999993106387903,
                0.9999998257021837,
                0.999999631011416,
                0.9999998802068873
            ],
            [
                0.9999996743688199,
                0.9999990577556315,
                0.9999994956527123,
                0.9999997761971315,
                0.9999997463982241,
                0.9999998362622747,
                0.9999995549151075,
                0.9999995818813767,
                0.9999991148432813,
                0.9999996072138466
            ],
            [
                0.9999999226558515,
                0.9999997761971315,
                0.9999999434137098,
                0.9999999317439872,
                0.9999999611088766,
                0.999999939764294,
                0.999999939764251,
                0.9999999317439384,
                0.9999999358793639,
                1.0
            ],
            [
                0.9999998257021838,
                0.9999998144609645,
                0.9999998555020309,
                0.9999997126313441,
                0.9999996940976638,
                0.9999996940978096,
                0.9999997126315154,
                0.9999994956524118,
                0.9999995818812272,
                0.9999997463981334
            ],
            [
                0.9999998724809419,
                0.9999998144608981,
                0.9999997463982241,
                0.9999998144609425,
                0.999999631011372,
                0.9999994631251243,
                0.9999997463980729,
                0.9999993916407461,
                0.9999996072139403,
                0.9999997617630617
            ],
            [
                0.9999998724809267,
                0.9999998942829854,
                0.9999999006880195,
                0.9999999006880076,
                0.9999998874647843,
                0.9999998461826772,
                0.9999999067051499,
                0.9999997897567343,
                0.9999996940978827,
                0.9999999317440197
            ],
            [
                1.855391239544352e-07,
                1.6373764721072816e-07,
                2.69957906184239e-07,
                4.450852111135988e-07,
                2.699578096393206e-07,
                2.1024336609843824e-07,
                5.043474081993875e-07,
                1.4449800373065699e-07,
                2.699578096393206e-07,
                1.4449795205429202e-07
            ],
            [
                2.1024331597262577e-07,
                9.931187406410953e-08,
                2.102434162245973e-07,
                1.1253524254650944e-07,
                3.059021175261338e-07,
                2.699578740032504e-07,
                9.931193325852072e-08,
                2.1024331597262577e-07,
                7.734418542875216e-08,
                9.931189774187203e-08
            ],
            [
                7.734415776836702e-08,
                1.4449807263312446e-07,
                6.82560779249779e-08,
                1.4449802095666915e-07,
                7.734418542875216e-08,
                7.73441946488886e-08,
                8.764241182641775e-08,
                9.931199245292204e-08,
                1.1253508156363576e-07,
                8.764253720001207e-08
            ],
            [
                3.927862470899887e-07,
                1.1253518888531272e-07,
                7.734421308914719e-08,
                1.6373764721072816e-07,
                4.450852641737424e-07,
                2.1024339116168358e-07,
                1.8553914607267268e-07,
                2.3823688159291947e-07,
                3.9278605979534166e-07,
                1.444979692800516e-07
            ],
            [
                0.9999994284994852,
                0.9999997126314811,
                0.9999995549148951,
                0.999999802494633,
                0.9999997126313098,
                0.9999995549148951,
                0.9999994631249963,
                0.9999998024945861,
                0.9999996743687034,
                0.9999995262092728
            ],
            [
                0.9999996072136126,
                0.9999993916408185,
                0.9999997897565588,
                0.9999998362623723,
                0.9999997300421904,
                0.9999997761970515,
                0.9999997463980125,
                0.9999993106389549,
                0.9999996533672137,
                0.9999994956525919
            ],
            [
                3.4663249714612693e-07,
                4.4508515805735777e-07,
                5.715003789046955e-07,
                1.2098652508424818e-06,
                1.637377448057981e-07,
                3.059022998576899e-07,
                5.043476486915964e-07,
                1.7603434231833873e-06,
                1.760343213335281e-06,
                5.715003107767143e-07
            ],
            [
                0.999999922655833,
                0.9999999067051054,
                0.9999999123575569,
                0.9999998802069873,
                0.999999887464932,
                0.9999998555019446,
                0.9999998257021213,
                0.9999999500628036,
                0.9999998802069587,
                0.9999999397642079
            ],
            [
                1.27519088491875e-07,
                1.1253517547010071e-07,
                6.825600469412533e-08,
                1.27519088491875e-07,
                1.1253510839355284e-07,
                5.315787506598473e-08,
                3.05902336324494e-07,
                9.931190958076104e-08,
                1.275190276859705e-07,
                1.855391239544352e-07
            ],
            [
                1.0,
                0.9999999123575359,
                1.0,
                0.9999999317440035,
                1.0,
                0.9999998802068873,
                0.9999998461826222,
                0.9999998874647977,
                1.0,
                0.9999999317439954
            ],
            [
                0.9999997300423192,
                0.9999995549148422,
                0.999998863436561,
                0.9999996072136595,
                0.9999996743687422,
                0.9999997897567343,
                0.9999994631251884,
                0.9999994284996213,
                0.9999997617631753,
                0.9999962733593855
            ],
            [
                2.699577130960941e-07,
                2.382370235933104e-07,
                1.855391681906175e-07,
                3.9278629391427843e-07,
                2.3823690999323465e-07,
                1.8553919030858602e-07,
                3.4663249714612693e-07,
                3.927863407379485e-07,
                1.275190732904469e-07,
                2.382370235933104e-07
            ],
            [
                1.275190732904469e-07,
                3.9278610661902853e-07,
                4.4508526417298334e-07,
                8.764242227418718e-08,
                3.05902190458764e-07,
                1.6373764721072816e-07,
                1.855391681906175e-07,
                3.05902336324494e-07,
                2.382370235933104e-07,
                2.699576809143613e-07
            ],
            [
                1.1253509497883659e-07,
                1.4449803818215767e-07,
                1.8553919030858602e-07,
                1.8553907971855875e-07,
                2.699578740032504e-07,
                4.4508515805735777e-07,
                1.1253525596174225e-07,
                2.1024334103581732e-07,
                3.059021175261338e-07,
                8.7642558095602e-08
            ],
            [
                1.275190732904469e-07,
                2.6995790618469934e-07,
                2.1024339116168358e-07,
                9.931189774187203e-08,
                3.927862002663297e-07,
                9.931189774187203e-08,
                9.931185038635267e-08,
                2.699578096403948e-07,
                5.715006514176113e-07,
                2.382369951932796e-07
            ],
            [
                0.9999999434137907,
                0.9999999317439546,
                1.0,
                0.9999999397643156,
                0.999999943413784,
                1.0,
                1.0,
                0.9999999468421439,
                0.9999999468421567,
                1.0
            ],
            [
                0.9999998461826405,
                0.9999996310115479,
                0.9999999397642222,
                0.9999998461826038,
                0.9999998802069587,
                0.9999996743688586,
                0.999999917667573,
                0.9999999067050943,
                0.9999999358794479,
                0.9999999176675535
            ],
            [
                0.9999998461827322,
                0.9999997617630049,
                0.9999996072139404,
                0.999999653367255,
                0.9999997126314468,
                0.9999998461826405,
                0.9999998144609424,
                0.9999992661790199,
                0.9999998144608319,
                0.9999998257021007
            ],
            [
                8.764247451307293e-08,
                1.8553903548231313e-07,
                2.1024334103581732e-07,
                1.4449807263312446e-07,
                1.4449803818215767e-07,
                2.699576809143613e-07,
                2.102434412875379e-07,
                3.0590237279085045e-07,
                1.1253512180925583e-07,
                1.444979692800516e-07
            ],
            [
                5.043476486924565e-07,
                3.4663249714612693e-07,
                3.059023363221292e-07,
                2.3823690999323465e-07,
                5.043476486915964e-07,
                2.3823688159291947e-07,
                4.450849988811838e-07,
                2.382369383923073e-07,
                2.382369383923073e-07,
                3.059022998576899e-07
            ],
            [
                1.0,
                0.9999998874648112,
                0.9999999123575987,
                0.9999999226558423,
                0.9999999006881142,
                0.9999998555020135,
                0.9999994631249963,
                0.9999998942829981,
                0.9999996072138,
                0.9999996072136126
            ],
            [
                2.1024336609874897e-07,
                1.6373774480605869e-07,
                1.2751902768612997e-07,
                5.315781803390236e-08,
                1.4449796928021588e-07,
                6.023569166654288e-08,
                1.6373772528704005e-07,
                6.825608606172863e-08,
                5.3157830707696514e-08,
                7.734416698849138e-08
            ],
            [
                0.9999995262094987,
                0.9999996072136126,
                0.9999998257020798,
                0.999999789756634,
                0.999999864256719,
                0.9999998802069587,
                0.9999998874647843,
                0.9999998874647843,
                0.9999998461827139,
                0.9999998802069159
            ],
            [
                0.999999825702059,
                0.9999998144609646,
                0.9999998362623528,
                0.999999789756659,
                0.9999998555020307,
                1.0,
                0.9999998555020307,
                0.9999998257021422,
                0.9999999067050276,
                0.999999855502048
            ],
            [
                3.05902190458764e-07,
                7.734424996967756e-08,
                1.2751908849167202e-07,
                6.825598842065202e-08,
                2.699578740032504e-07,
                1.1253508156363576e-07,
                8.764245361752286e-08,
                2.699576809143613e-07,
                3.4663266243308805e-07,
                1.6373774480605869e-07
            ],
            [
                3.059022998576899e-07,
                1.1253516205489029e-07,
                2.382370235933104e-07,
                1.855391681906175e-07,
                4.4508494582405734e-07,
                3.0590237279085045e-07,
                1.6373774480605869e-07,
                1.275190276859705e-07,
                3.466326211113502e-07,
                3.059022269250683e-07
            ],
            [
                0.9999982396563685,
                0.9999981261252888,
                0.9999994284996215,
                0.9999989969860319,
                0.9999998257021006,
                0.9999997761970515,
                0.9999998461826771,
                0.9999998461827139,
                0.999998540623606,
                0.9999991684717745
            ],
            [
                1.6373766672888118e-07,
                2.382368247924618e-07,
                1.6373766672888118e-07,
                2.1024334103505245e-07,
                2.3823693839057394e-07,
                2.6995774527657245e-07,
                3.059021904543821e-07,
                3.927862939113312e-07,
                1.8553919030708836e-07,
                1.4449798650476187e-07
            ],
            [
                0.9999999358793333,
                0.9999999006880786,
                0.9999998555020307,
                1.0,
                0.9999998802069302,
                0.9999998555019446,
                0.9999998724809419,
                0.9999997761971315,
                1.0,
                0.9999998802068873
            ],
            [
                0.9999994631250604,
                0.9999997126315496,
                0.999999653367379,
                0.9999993524054338,
                0.9999998257020798,
                0.9999996072138936,
                0.9999994284992808,
                0.999999730042287,
                0.9999996743686257,
                0.9999998144609424
            ],
            [
                0.9999998257021214,
                0.99999926617867,
                0.9999998144609203,
                0.9999999397642437,
                0.9999997126314811,
                0.9999998942828973,
                0.9999997126313441,
                0.9999998144608098,
                0.9999998461826222,
                0.9999996940977003
            ],
            [
                6.475947982037486e-07,
                1.0677027427600627e-06,
                3.466325797896173e-07,
                1.994730434879465e-06,
                1.2098656835224664e-06,
                1.7603425837855082e-06,
                9.422448185534261e-07,
                3.05902190458764e-07,
                1.5534975693933505e-06,
                5.715005832886879e-07
            ],
            [
                0.999999855502048,
                0.999999631011372,
                0.999999776197025,
                0.9999997463982241,
                0.9999995549150015,
                0.9999993524052794,
                0.9999998461826405,
                0.9999996940976639,
                0.9999994284996214,
                0.9999994631251243
            ],
            [
                1.0,
                1.0,
                0.9999999006881259,
                1.0,
                0.9999999226557408,
                1.0,
                1.0,
                0.9999999273417837,
                0.9999999067050943,
                1.0
            ],
            [
                1.4449800373118268e-07,
                2.3823696679327928e-07,
                5.043475284468537e-07,
                1.8553907971855875e-07,
                2.102434162245973e-07,
                3.059022998581767e-07,
                1.6373772528704005e-07,
                3.4663278639892215e-07,
                2.382368531929327e-07,
                1.4449802095666915e-07
            ],
            [
                7.734416698849138e-08,
                3.4663266243308805e-07,
                1.855391681906175e-07,
                1.275190732904469e-07,
                1.4449805540740185e-07,
                2.382369951932796e-07,
                1.6373772528704005e-07,
                1.8553919030858602e-07,
                1.27519088491875e-07,
                9.931189774187203e-08
            ],
            [
                3.466327863983311e-07,
                3.927862939126708e-07,
                7.338208055664991e-07,
                4.450848927658745e-07,
                5.715003107755449e-07,
                3.4663249714451116e-07,
                4.450848927650143e-07,
                2.1024331597262577e-07,
                9.422442569315887e-07,
                3.0590226339061185e-07
            ],
            [
                0.9999995262093292,
                0.9999997761970248,
                0.9999995818812272,
                0.9999998024947273,
                0.9999997300422547,
                0.9999996743688198,
                0.9999998024946566,
                0.999999631011416,
                0.9999993106387083,
                0.999999712631344
            ],
            [
                2.1024339116168358e-07,
                2.1024334103581732e-07,
                1.6373766672973748e-07,
                2.382369951932796e-07,
                1.444979692800516e-07,
                2.3823685319320354e-07,
                4.4508494582405734e-07,
                2.382369951932796e-07,
                1.444980209564556e-07,
                1.4449803818215767e-07
            ],
            [
                2.1024326584582131e-07,
                3.4663278639892215e-07,
                1.1253513522447425e-07,
                2.10243290909724e-07,
                8.764245361752286e-08,
                7.734418542875216e-08,
                4.691164920214251e-08,
                8.764245361752286e-08,
                9.931187406410953e-08,
                9.931193325852072e-08
            ],
            [
                0.9999995818811276,
                0.9999996072136127,
                0.9999996072138467,
                0.9999998257021006,
                0.999999814460876,
                0.999999631011416,
                0.9999995818813269,
                0.9999997463980125,
                0.9999997463981637,
                0.9999997761971849
            ],
            [
                8.764249540862797e-08,
                6.023573475041126e-08,
                6.825601283086733e-08,
                8.764245361752286e-08,
                9.931193325852072e-08,
                1.2751904288739315e-07,
                1.275190428875671e-07,
                5.315784971839039e-08,
                6.825598842065202e-08,
                1.4449807263312446e-07
            ],
            [
                0.9999998461826588,
                0.9999998642566381,
                0.9999997897565839,
                1.0,
                0.9999998362623334,
                0.9999999123575255,
                0.9999999226558238,
                0.9999999273418788,
                0.9999999123574838,
                0.9999997463980729
            ],
            [
                2.3823696679327928e-07,
                1.444979692800516e-07,
                1.8553905760062447e-07,
                9.931196877517082e-08,
                1.8553914607267268e-07,
                1.275190732904469e-07,
                1.2751901248454963e-07,
                9.931190958076104e-08,
                1.6373776432509826e-07,
                1.444979692800516e-07
            ],
            [
                6.825598842065202e-08,
                6.825598842065202e-08,
                1.8553907971879076e-07,
                1.4449796928021588e-07,
                5.3157887739943563e-08,
                1.4449800373118268e-07,
                8.764253720001207e-08,
                3.466325797896173e-07,
                2.382368815932174e-07,
                3.05902336324494e-07
            ],
            [
                0.9999997897565588,
                0.9999997761971315,
                0.9999998362622357,
                0.9999995549149482,
                0.9999995549150543,
                0.9999992188515765,
                0.9999991148430699,
                0.999999631011592,
                0.9999997761971315,
                0.9999995549150543
            ],
            [
                5.043476486915964e-07,
                1.2098661162056318e-06,
                6.144175334468545e-06,
                2.5612828213934817e-06,
                2.382369667929001e-07,
                5.043472278322555e-07,
                3.4663278639892215e-07,
                7.889259764517575e-06,
                3.466325384678894e-07,
                4.785092783519724e-06
            ],
            [
                6.144173869558639e-06,
                0.9999998874648782,
                4.4508510499849186e-07,
                0.9999998724809875,
                9.422444815814404e-07,
                0.9999993524052792,
                6.47595107001401e-07,
                2.3823690999290963e-07,
                2.5612812947508257e-06,
                0.9999997761970515
            ],
            [
                3.05902190458764e-07,
                2.1024339116168358e-07,
                3.0590237279085045e-07,
                2.3823682479292225e-07,
                5.715007195447234e-07,
                2.6995790618469934e-07,
                2.102434162245973e-07,
                4.450848927658745e-07,
                2.382369667929001e-07,
                3.0590237279085045e-07
            ],
            [
                0.999999554914736,
                0.9999998461827322,
                0.9999989969859125,
                0.9999998024946566,
                0.999999581881277,
                0.9999996743688586,
                0.9999997126313098,
                0.9999998024946567,
                0.999999802494586,
                0.9999995549151075
            ],
            [
                4.4508515805735777e-07,
                1.6373774480605869e-07,
                9.931195693628605e-08,
                7.734418542875216e-08,
                3.466327037553825e-07,
                9.93120161310289e-08,
                2.1024331597262577e-07,
                1.444980209564556e-07,
                1.444980209564556e-07,
                2.699577774585891e-07
            ],
            [
                0.9999998024945624,
                0.999999864256719,
                0.9999998874648648,
                0.9999997617630617,
                0.9999998362622358,
                0.9999998461826405,
                0.9999996940976275,
                0.9999996743688199,
                0.9999995818811773,
                0.9999998144608541
            ],
            [
                2.3823693839325527e-07,
                9.931190958076104e-08,
                1.275190276859705e-07,
                2.3823693839290317e-07,
                1.275190732904469e-07,
                9.931185038635267e-08,
                9.931185038635267e-08,
                1.6373776432509826e-07,
                1.6373772528704005e-07,
                1.6373762769138607e-07
            ],
            [
                1.3007130015488633e-05,
                0.9999989969855536,
                0.9999994956524116,
                0.9999997897565588,
                0.9999986290429576,
                0.9999990577557435,
                0.9999994956525319,
                0.9999997300421583,
                0.9999987901347496,
                9.610239210944684e-05
            ],
            [
                1.8553907971855875e-07,
                2.1024331597262577e-07,
                1.444979692797559e-07,
                9.931193325852072e-08,
                3.05902190458764e-07,
                1.1253512180925583e-07,
                3.059022269250683e-07,
                1.2751910369275402e-07,
                2.1024341622426268e-07,
                1.637377448057981e-07
            ],
            [
                4.222834451382849e-06,
                6.9622587397397306e-06,
                6.144173137126169e-06,
                4.4508510499849186e-07,
                5.04347528446051e-07,
                3.726637951387472e-06,
                3.2887506336086064e-06,
                1.8925150497848527e-05,
                1.067702870039777e-06,
                1.209866260432471e-06
            ],
            [
                0.9999997761972116,
                0.9999997617631752,
                0.9999998642566381,
                0.9999996533673376,
                0.9999997617630333,
                0.9999996743688975,
                0.9999998024946801,
                0.9999998461826771,
                0.999999218851856,
                0.999999789756634
            ],
            [
                2.382370235933104e-07,
                1.6373776432509826e-07,
                1.27519088491875e-07,
                2.3823688159237777e-07,
                1.6373764721072816e-07,
                1.444979692800516e-07,
                1.275190276859705e-07,
                9.931189774187203e-08,
                9.931186222523604e-08,
                1.6373762769138607e-07
            ],
            [
                1.637377448057981e-07,
                1.6373772528704005e-07,
                1.1253512180925583e-07,
                1.275190276859705e-07,
                1.1253506814797596e-07,
                2.3823688159291947e-07,
                2.3823690999323465e-07,
                2.382369667929001e-07,
                1.275190428875671e-07,
                1.1253508156363576e-07
            ],
            [
                0.9999993524050478,
                0.9999986290429583,
                0.9999998362623334,
                0.9999993106387911,
                0.9999993106391194,
                0.9999992188514838,
                0.9999993524054338,
                0.9999998461826589,
                0.9999999273418182,
                0.9999999273418095
            ],
            [
                0.9999997126315153,
                0.9999996072139403,
                0.999999554914736,
                0.9999999123575464,
                0.9999998802069873,
                0.9999998724809875,
                0.9999998555019618,
                0.9999995262095552,
                0.9999997463981939,
                2.10243290909724e-07
            ],
            [
                0.9999996310114161,
                0.9999997617631469,
                0.9999997761972116,
                0.9999981261252899,
                0.9999997761971583,
                0.999999057755182,
                0.9999996072136126,
                0.9999997617631469,
                0.9999995549150013,
                0.9999989322970038
            ],
            [
                1.8553919030858602e-07,
                1.855391681906175e-07,
                1.1253516205489029e-07,
                8.764249540862797e-08,
                2.1024331597262577e-07,
                2.102434162245973e-07,
                2.1024326584639497e-07,
                2.6995784182183607e-07,
                5.043476486924565e-07,
                2.382369667929001e-07
            ],
            [
                0.9999997126314811,
                0.9999997761970782,
                0.9999997897566841,
                0.9999995549148952,
                0.9999996072138938,
                0.9999996743687034,
                0.9999995549147891,
                0.9999998024947037,
                0.9999995262096117,
                0.999999631011372
            ],
            [
                1.855391239544352e-07,
                1.6373772528704005e-07,
                5.715002426475718e-07,
                1.8553903548231313e-07,
                1.8553905760062447e-07,
                1.2751904288710323e-07,
                3.288748281329893e-06,
                6.475947982022763e-07,
                3.059022998576899e-07,
                1.8553910183607374e-07
            ],
            [
                2.10243290909724e-07,
                2.10243290909724e-07,
                1.1253508156363576e-07,
                1.6373766672973748e-07,
                1.1253512180925583e-07,
                1.1253512180925583e-07,
                2.1024336609843824e-07,
                9.931186222523604e-08,
                1.1253512180925583e-07,
                1.2751899728311609e-07
            ]
        ]
    },
    {
        "q_id": "9443_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            88,
            92,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.222833444590791e-06,
                2.699577774585891e-07,
                4.2228339479858295e-06,
                4.450849988798682e-07,
                1.5534975693979422e-06,
                3.7266397283908927e-06,
                1.3709573702822306e-06,
                7.338208055664991e-07,
                7.338207180864763e-07,
                1.5534971990126997e-06
            ],
            [
                5.043475885696228e-07,
                6.475947210046347e-07,
                1.8553919030858602e-07,
                9.422447062294175e-07,
                6.475947982037486e-07,
                1.994729721518893e-06,
                5.715005832886879e-07,
                1.0677028700422047e-06,
                1.370957860576702e-06,
                6.47595107001401e-07
            ],
            [
                0.9999994284995533,
                0.9999995262092164,
                0.9999982396567881,
                0.9999982396563691,
                0.9999991148429648,
                2.7535704232595768e-05,
                1.5534983101602148e-06,
                5.422218969895357e-06,
                0.9999962733611661,
                0.9999985406230842
            ],
            [
                0.9999990577551817,
                0.9999942280813566,
                0.999999631011548,
                0.999998126124171,
                0.9999980052705191,
                0.9999981261241718,
                0.9999969105066624,
                0.9999992188516701,
                0.9999989322968765,
                0.9999977396748959
            ],
            [
                4.0063696967815485e-05,
                5.422217030663578e-06,
                1.760343423160973e-06,
                7.889265407004852e-06,
                4.222835458117536e-06,
                4.222831934202483e-06,
                1.012999460278499e-05,
                NaN,
                6.962258739530771e-06,
                4.78509392429544e-06
            ],
            [
                0.9999832985801937,
                0.9999989322971311,
                0.999978555059345,
                0.9999969105040856,
                0.9999975938976648,
                0.999978555051695,
                0.9999992188518566,
                0.9999885212346795,
                0.9999981261252892,
                5.829127945202588e-05
            ],
            [
                0.9999972735284335,
                0.999993037744612,
                0.999986992871595,
                0.9999985406236074,
                0.9999952149038075,
                0.9999980052698074,
                0.9999970976869842,
                0.9999964991468439,
                0.9999985406234331,
                0.9999977396751688
            ],
            [
                0.9999945777797493,
                4.2228319344021954e-06,
                4.785095065232451e-06,
                1.892515501014656e-05,
                2.3823702359290413e-07,
                1.3709575337125585e-06,
                1.0677032518814388e-06,
                NaN,
                0.9999986290429588,
                1.8553907971855875e-07
            ],
            [
                0.9999977396765147,
                0.9999987901344616,
                0.9999990577550701,
                0.9999988634358841,
                0.9999989322968762,
                0.9999989322973858,
                0.9999980052700433,
                2.260324028443809e-06,
                0.9999989969862714,
                3.7266383956509585e-06
            ],
            [
                0.9999843104447614,
                0.9999998555020136,
                0.9999989322973852,
                0.00023050677068656142,
                0.9999957771680713,
                0.9999989322970038,
                0.9999978766222997,
                0.9999910603047801,
                0.9999987121041711,
                0.9999970976873268
            ],
            [
                0.9999988634358841,
                1.4738978458382043e-05,
                0.9999982396565795,
                0.999997876621287,
                0.9999975938976646,
                0.9999983463108101,
                0.9999983463098248,
                0.9999969105040833,
                0.9999996310114602,
                0.9999982396574186
            ],
            [
                0.9999964991468493,
                0.9999785550441275,
                0.9999949062937947,
                0.9999982396567919,
                0.9999898700114643,
                0.9999930377421306,
                5.422217030781934e-06,
                1.4738976701652988e-05,
                1.4738985486506781e-05,
                0.9999930377437727
            ],
            [
                1.0677024882029858e-06,
                1.2751902768612997e-07,
                3.927863407379485e-07,
                7.338212429594283e-07,
                2.1024334103581732e-07,
                2.699577774589574e-07,
                4.4508499888275247e-07,
                6.47594952603035e-07,
                3.535625914749675e-05,
                1.444979692800516e-07
            ],
            [
                0.9999993106387907,
                0.9999995262095552,
                0.9999960330126699,
                0.9999921107346145,
                0.9999978766210332,
                0.9999962733602772,
                0.999999802494586,
                0.9999967112517226,
                0.9999988634360194,
                0.9999945777797402
            ],
            [
                0.999999825702163,
                0.9999994631247403,
                0.9999991148428591,
                0.9999999226557684,
                0.9999977396754344,
                0.9999964991460065,
                2.2603251062450327e-06,
                0.9999991148428591,
                0.9999982396563681,
                0.9999995262094422
            ],
            [
                0.9999916019240032,
                1.8925155009767892e-05,
                0.9999960330140947,
                1.5534975693979422e-06,
                0.9999972735307134,
                0.999998346310023,
                2.7535681254804434e-05,
                0.9999993524050482,
                0.9999967112521168,
                0.9999892166865287
            ],
            [
                1.994729483729522e-06,
                1.9947299593014888e-06,
                0.9999975938968013,
                0.999992588718379,
                0.9999904837449178,
                0.9999904837471986,
                0.9999972735297332,
                0.9999974387177925,
                1.012998977264307e-05,
                0.9999485577987985
            ],
            [
                1.99472900813862e-06,
                2.9023109472244114e-06,
                2.260324028427877e-06,
                1.3709570434178922e-06,
                1.8925143729954285e-05,
                2.561282210729555e-06,
                7.338211554783522e-07,
                3.2887506335906595e-06,
                9.422444815765128e-07,
                1.9947292459265734e-06
            ],
            [
                1.067703124601679e-06,
                1.0677032518814388e-06,
                2.2603245673443566e-06,
                3.4663266243308805e-07,
                2.4300243630653244e-05,
                5.71500515161527e-07,
                6.475950298011458e-07,
                2.2603248367949354e-06,
                6.144173137170873e-06,
                5.715003788993679e-07
            ],
            [
                1.3709572068553509e-06,
                4.22283545819819e-06,
                7.338212429594283e-07,
                1.7603438428848787e-06,
                1.3709572068553509e-06,
                3.2887502415767434e-06,
                8.315278294114555e-07,
                5.422217030781934e-06,
                3.927863407379485e-07,
                1.3709575337159875e-06
            ],
            [
                7.889259764517575e-06,
                6.962255419931625e-06,
                4.785093353940187e-06,
                1.1478772231232203e-05,
                6.605216044933028e-05,
                8.939696304311336e-06,
                3.7266401726359486e-06,
                0.9999756997680224,
                0.9999989969859128,
                5.1442238195844654e-05
            ],
            [
                2.9023116392097746e-06,
                7.338208055680009e-07,
                5.715006514176113e-07,
                1.7603440527334603e-06,
                5.715006514176113e-07,
                5.715005151606823e-07,
                9.422443692574719e-07,
                1.7603440527334603e-06,
                3.0590237279085045e-07,
                1.994729008151319e-06
            ],
            [
                1.994729008145876e-06,
                6.144177531811707e-06,
                2.144495097113319e-05,
                2.2603253756956754e-06,
                1.1478772231232203e-05,
                4.2228319344021954e-06,
                1.8925157266089433e-05,
                4.785092783519724e-06,
                1.012999098021058e-05,
                1.4738983729535602e-05
            ],
            [
                0.9999995549149486,
                0.9999993524052795,
                0.9999996310113722,
                0.9999998555019791,
                0.9999969105048259,
                0.9999997897565588,
                0.999999789756609,
                0.9999990577551824,
                0.9999993524048936,
                0.9999996533674618
            ],
            [
                2.753569766795419e-05,
                7.338207180898968e-07,
                0.9999822214503609,
                0.9999991684720723,
                0.9999974387187085,
                0.9999977396762425,
                9.422445939054222e-07,
                6.475945666063607e-07,
                1.9947301970972664e-06,
                1.7603425837855082e-06
            ],
            [
                1.1478765389222573e-05,
                5.422218969895357e-06,
                1.4738983729294318e-05,
                6.144173137126169e-06,
                2.430024073461624e-05,
                1.0129988564974359e-05,
                6.605212107986466e-05,
                8.939698435657833e-06,
                3.2887506336086064e-06,
                6.962255419804982e-06
            ],
            [
                0.9999910603016208,
                0.9999921107374391,
                0.9999983463102204,
                8.939693107093343e-06,
                0.9999869928685537,
                4.222834451355964e-06,
                0.9999877809240142,
                0.9999980052709968,
                2.144494841482881e-05,
                0.9999949062968437
            ],
            [
                1.4738985486506781e-05,
                7.889265407327733e-06,
                9.422443692574719e-07,
                1.8925145985895816e-05,
                9.422447062294175e-07,
                4.222834451403972e-06,
                1.5534973842076057e-06,
                7.889262585958025e-06,
                1.5534973841895917e-06,
                2.2603251062450327e-06
            ],
            [
                0.9999938558239528,
                0.9998204719503079,
                0.9999985406230849,
                6.475950298021765e-07,
                9.422442569334097e-07,
                2.2603248367949354e-06,
                2.3823690999323465e-07,
                2.260324028443809e-06,
                1.5534983101644536e-06,
                3.72663883989755e-06
            ],
            [
                0.9999989969854349,
                0.9999970976890593,
                0.9999964991455904,
                0.9999949062950274,
                0.999998346310614,
                1.8925148242250705e-05,
                8.939700567094277e-06,
                1.012999218776902e-05,
                0.9999978766205299,
                NaN
            ],
            [
                0.9999930377404596,
                0.9999988634361557,
                1.670142980893658e-05,
                0.9999993916408912,
                0.9999985406237822,
                0.9999916019280032,
                0.9999986290427954,
                0.9999975938968039,
                0.9999987121044791,
                0.9999986290424702
            ],
            [
                1.1478768126057254e-05,
                7.889264466868659e-06,
                1.994730434879465e-06,
                6.962258739796719e-06,
                1.2098656835224664e-06,
                4.2228319344021954e-06,
                3.72663883989755e-06,
                1.209865539295696e-06,
                4.22283545819819e-06,
                1.2098656835224664e-06
            ],
            [
                2.260324028404236e-06,
                9.422443692446175e-07,
                1.7603430034655858e-06,
                1.3709572068272963e-06,
                2.2603242978377903e-06,
                2.260324028404236e-06,
                0.9999988634360206,
                1.9947306726594253e-06,
                0.9999822214503647,
                0.9999925887219561
            ],
            [
                3.288748673376478e-06,
                NaN,
                1.9947292459406333e-06,
                7.338208930460318e-07,
                1.5534981249736758e-06,
                3.2887506336235617e-06,
                1.3709572068553509e-06,
                6.962258739796719e-06,
                1.3709573702822306e-06,
                1.994729008145876e-06
            ],
            [
                7.338207180898968e-07,
                2.5612819054133693e-06,
                NaN,
                0.999995777167574,
                1.5534973842076057e-06,
                1.994729721518893e-06,
                8.315278294114555e-07,
                3.7266397283908927e-06,
                7.889264466868659e-06,
                1.5534984953552536e-06
            ],
            [
                0.9999934595643669,
                0.9999785550415096,
                0.9999967112505526,
                0.9999984465018786,
                0.9998204720588628,
                0.9999982396565811,
                0.9999986290427968,
                0.9999877809182611,
                0.9999892166839782,
                0.999996499145183
            ],
            [
                0.9999992188516699,
                0.9999975938968011,
                0.999999554914842,
                0.9999997300422548,
                0.9999995818811773,
                0.9999999176675142,
                0.9999975938965148,
                0.9999997617629766,
                0.9999987901344615,
                0.9999996743686257
            ],
            [
                3.466325797888292e-07,
                1.4449807263287805e-07,
                1.1253518888531272e-07,
                1.4449807263287805e-07,
                1.1253508156363576e-07,
                1.1253520230052635e-07,
                1.2751899728286965e-07,
                6.825601283086733e-08,
                1.2751904288710323e-07,
                2.3823688159291947e-07
            ],
            [
                1.0677026154827912e-06,
                3.7266379514061143e-06,
                0.999999495652592,
                3.7266383956509585e-06,
                0.9999999006879721,
                5.422217030781934e-06,
                0.9999991148427539,
                0.9999977396746279,
                1.5534981249736758e-06,
                1.0677027427624903e-06
            ],
            [
                9.422443692527585e-07,
                2.260324567337161e-06,
                8.315279285351409e-07,
                2.6995774527718623e-07,
                3.059022269250683e-07,
                9.422448185510695e-07,
                7.338212429582604e-07,
                8.315282259089153e-07,
                1.4449800373065699e-07,
                5.043472879540142e-07
            ],
            [
                7.889262585814522e-06,
                4.222835458148261e-06,
                7.889259764445822e-06,
                3.288747889229516e-06,
                5.144220140002614e-05,
                4.785096776433933e-06,
                2.5612825160271407e-06,
                5.422220262555012e-06,
                4.0063696966212295e-05,
                4.222834954753043e-06
            ],
            [
                0.00048785706340468153,
                0.9999983463106161,
                5.144221980055201e-05,
                0.9999994284995538,
                0.9999546021371127,
                0.9999996533672552,
                0.9999904837506152,
                0.9999969105051928,
                0.9999975938970911,
                0.9999977396765148
            ],
            [
                3.2887502415767434e-06,
                0.9999667858173195,
                8.31528325040778e-07,
                0.9999706884546748,
                2.2603251062450327e-06,
                1.3709575337159875e-06,
                6.962258739796719e-06,
                6.144176066901277e-06,
                0.999997593898237,
                0.9999970976869813
            ],
            [
                0.9999981261239481,
                2.561283126728994e-06,
                1.3007130015677909e-05,
                0.9999986290431214,
                0.9999952149043745,
                2.753568453792444e-05,
                0.9999996743687811,
                0.9999970976876716,
                0.999999114843176,
                0.9999942280779202
            ],
            [
                0.9999877809270604,
                6.144176799283803e-06,
                0.9999960330136461,
                0.9999546021273802,
                0.9999974387178133,
                0.999997097689074,
                0.9994472214583289,
                0.9999785550418943,
                0.9993736659469316,
                0.9999942280793236
            ],
            [
                0.999999114843282,
                0.9999985406243027,
                0.9999981261243969,
                0.9999993524050483,
                0.9999974387177963,
                0.999996273360281,
                0.9999974387168798,
                0.9999955048184356,
                0.9999962733616171,
                0.9999934595635867
            ],
            [
                2.26032402841657e-06,
                2.260324567337161e-06,
                4.5397857828200684e-05,
                2.2603253756956754e-06,
                4.785095635624897e-06,
                5.715002426475718e-07,
                3.288749065423109e-06,
                1.1478770862882149e-05,
                NaN,
                3.726638395611981e-06
            ],
            [
                5.422221555069497e-06,
                8.939698435560267e-06,
                3.4663278639265633e-07,
                1.0677028700130727e-06,
                2.2603251062270446e-06,
                6.144172404693786e-06,
                4.78509563546605e-06,
                9.42244930862237e-07,
                6.475945666051092e-07,
                4.222833444467892e-06
            ],
            [
                9.422443692489024e-07,
                0.9999756997535397,
                1.0129989772412744e-05,
                7.338209805224048e-07,
                5.715004470295662e-07,
                9.422443692446175e-07,
                1.9947306726358406e-06,
                1.55349775456958e-06,
                4.222833947960866e-06,
                1.2098661161927025e-06
            ],
            [
                3.288748673376478e-06,
                3.927862002663297e-07,
                7.338212429582604e-07,
                1.2098659719788098e-06,
                3.726637951387472e-06,
                3.927862470899887e-07,
                8.315284241650899e-07,
                7.338207180898968e-07,
                3.466326211113502e-07,
                5.715003107755449e-07
            ],
            [
                9.422447062270609e-07,
                1.3709573702822306e-06,
                1.0677027427569065e-06,
                1.2098659719716573e-06,
                1.3709570434178922e-06,
                5.04347468318358e-07,
                1.2098653950656417e-06,
                8.31528424162821e-07,
                2.260324028427877e-06,
                1.3709578605729614e-06
            ],
            [
                4.222832437798974e-06,
                3.726639284144195e-06,
                1.209866260432471e-06,
                3.7266397283908927e-06,
                1.994729483729522e-06,
                3.7266410611296085e-06,
                6.144177531811707e-06,
                8.939696304213768e-06,
                1.760342793638743e-06,
                3.7266383956509585e-06
            ],
            [
                0.9999978766207803,
                0.9999945777784541,
                0.9999810748473318,
                4.450851580540182e-07,
                5.422217030781934e-06,
                2.430025232247918e-05,
                0.9999975938968017,
                8.93969630439264e-06,
                0.9999974387187074,
                0.9999983463110067
            ],
            [
                2.9023126771227976e-06,
                1.99472900813862e-06,
                3.927862002654366e-07,
                8.939695238439078e-06,
                1.1478772230762415e-05,
                2.2603245673279107e-06,
                2.561282210729555e-06,
                1.0677032518413822e-06,
                7.889262585886274e-06,
                6.9622579096593295e-06
            ],
            [
                0.999991060304778,
                0.9999995818812774,
                0.99999916847227,
                0.9999991148433868,
                0.9999930377445976,
                0.9999984465016912,
                0.9999991148428589,
                0.9999998362622747,
                0.9999964991443409,
                0.999999495652652
            ],
            [
                6.962257909842961e-06,
                1.3709575337159875e-06,
                8.315279285370317e-07,
                6.1441767993788005e-06,
                1.994730672675753e-06,
                5.043475885696228e-07,
                6.144173137170873e-06,
                9.422450432014836e-07,
                1.994729721518893e-06,
                6.47595107001401e-07
            ],
            [
                0.9999983463110065,
                0.9999993106391191,
                0.999999266179195,
                0.9999980052693296,
                0.9999987121044782,
                0.9999993106392016,
                0.9999991148426479,
                0.9999981261250656,
                0.9999995262095552,
                0.9999991148433867
            ],
            [
                0.9999989322966217,
                6.962257909785973e-06,
                8.939693107288474e-06,
                0.9999989969857934,
                0.999999495652532,
                0.9999981261243948,
                1.0129989772532511e-05,
                1.012999581057419e-05,
                0.9999983463104156,
                2.902312331170226e-06
            ],
            [
                6.47594952603035e-07,
                2.3823693839325527e-07,
                1.0677027427624903e-06,
                0.9999998144609646,
                5.043476486924565e-07,
                2.2603237589938405e-06,
                2.2603251062450327e-06,
                0.9999984465026172,
                7.338207180898968e-07,
                2.3823690999323465e-07
            ],
            [
                6.475950298021765e-07,
                1.994729721518893e-06,
                3.4663274507713016e-07,
                5.043475885696228e-07,
                0.9999991684718736,
                3.0590237279085045e-07,
                8.315278294114555e-07,
                1.3709575337159875e-06,
                4.450848927658745e-07,
                1.209866260432471e-06
            ],
            [
                6.962255419868303e-06,
                6.475951069985296e-07,
                4.2228349547223175e-06,
                4.4508505193791187e-07,
                5.715004470313855e-07,
                6.475945666051092e-07,
                5.043476486902204e-07,
                2.260324567337161e-06,
                1.760343213322473e-06,
                1.3709570434178922e-06
            ],
            [
                8.939699501416646e-06,
                2.902313369111213e-06,
                8.939695238634211e-06,
                2.9023116392097746e-06,
                3.120190393896595e-05,
                2.5612819054133693e-06,
                4.222832941193893e-06,
                1.5534983101602148e-06,
                2.561283126728994e-06,
                NaN
            ],
            [
                1.994729483729522e-06,
                8.939698435657833e-06,
                7.889262585886274e-06,
                3.726638395634011e-06,
                0.9998601779778796,
                3.1201900218617364e-05,
                3.288749849529972e-06,
                1.4738978458623327e-05,
                2.5612819054133693e-06,
                1.7603427936335396e-06
            ],
            [
                1.3709573702822306e-06,
                1.7603440527334603e-06,
                4.4508494582405734e-07,
                2.9023116392097746e-06,
                3.0590222692437275e-07,
                3.4663253846718004e-07,
                1.0677026154827912e-06,
                4.450848927658745e-07,
                5.04347468323289e-07,
                4.4508515805735777e-07
            ],
            [
                0.9999203270201915,
                2.3823702359290413e-07,
                0.9999599362984288,
                1.9947299593078385e-06,
                0.9999877809240132,
                0.9999485577806115,
                6.475949526020042e-07,
                1.855391239544352e-07,
                7.338210680021253e-07,
                3.9278634073732336e-07
            ],
            [
                2.90231094723893e-06,
                2.2603253756956754e-06,
                6.962255419931625e-06,
                2.902313023130843e-06,
                2.2603253756956754e-06,
                3.288748281329893e-06,
                3.726639284144195e-06,
                7.338212429582604e-07,
                1.7603434231833873e-06,
                3.288749065423109e-06
            ],
            [
                0.9999990577551825,
                0.9999992661791075,
                0.9999986290431212,
                0.9999987121043258,
                0.9999949062925904,
                0.9999982396574186,
                3.726641061085547e-06,
                0.999999057755632,
                0.9999994956525922,
                0.999998712104325
            ],
            [
                3.2887478892683997e-06,
                1.7603438428800754e-06,
                5.715003789046955e-07,
                2.5612828213934817e-06,
                4.785095635624897e-06,
                2.9023119851781017e-06,
                6.475947210046347e-07,
                1.5534981249697903e-06,
                7.889262585814522e-06,
                1.3709567165579959e-06
            ],
            [
                5.4222202626709005e-06,
                2.1444940746307572e-05,
                1.3007123813559956e-05,
                1.012998977264307e-05,
                3.7266397283908927e-06,
                3.726639284144195e-06,
                2.5612831267202583e-06,
                1.892514598627448e-05,
                2.430024073523505e-05,
                1.209865827752005e-06
            ],
            [
                0.9999987121043244,
                0.9999992661789324,
                1.0129995810343862e-05,
                4.450852111148132e-07,
                0.99999691050445,
                9.422448185510695e-07,
                0.9999960330126695,
                0.9999995818811276,
                2.260325106237323e-06,
                0.9999983463098234
            ],
            [
                0.999997739675167,
                0.999991060299515,
                1.3709567165617364e-06,
                0.9999969105048265,
                1.5534983101602148e-06,
                0.9999955048195089,
                0.9999981261237267,
                4.006371129776199e-05,
                1.994730197090463e-06,
                0.9998415637666652
            ],
            [
                6.962254589914941e-06,
                5.422220262636381e-06,
                0.9999930377421015,
                2.2603253756956754e-06,
                8.939698435657833e-06,
                4.785095065232451e-06,
                3.4663249714612693e-07,
                3.9278610661902853e-07,
                5.422218969895357e-06,
                8.93969950132721e-06
            ],
            [
                0.999998629042306,
                0.9999991148429649,
                0.9999988634360206,
                0.999999310638955,
                0.9999992661788452,
                0.9999987901346059,
                0.9999991148428595,
                0.9999993916408186,
                0.9999993916410362,
                0.9999984465015063
            ],
            [
                0.9999970976887099,
                0.9999997761971315,
                1.6701415872659116e-05,
                0.9999798543045043,
                1.7603434231833873e-06,
                0.9999741325751982,
                0.9999972735294073,
                0.9999970976876738,
                0.9999952149043735,
                0.9999417087069173
            ],
            [
                1.7603436330179102e-06,
                1.4738978458140753e-05,
                6.144175334367959e-06,
                2.2603242978665707e-06,
                4.785094494750855e-06,
                3.288749849498565e-06,
                1.9947301970972664e-06,
                1.760343213322473e-06,
                2.5612825160271407e-06,
                1.3709572068422585e-06
            ],
            [
                0.9999904837449445,
                0.9999916019290166,
                0.999994577782993,
                0.9999942280800005,
                8.315283250305684e-07,
                0.9999967112509441,
                0.9999978766210369,
                0.9999930377446223,
                0.9999942280813725,
                0.9999925887201547
            ],
            [
                0.9999810748450416,
                0.9999975938965152,
                0.9999981261237241,
                9.422449308748773e-07,
                0.9999952149055091,
                0.9999996940978826,
                0.999998005269567,
                0.9999964991464236,
                0.9999852610110377,
                0.9989677692048926
            ],
            [
                2.1444940745371397e-05,
                3.288749065423109e-06,
                4.006368264282944e-05,
                8.939693107288474e-06,
                0.9999990577551827,
                4.2228339479858295e-06,
                1.6701421844753466e-05,
                0.999998863435749,
                2.430024073461624e-05,
                0.9999984465028026
            ],
            [
                1.1478772231086046e-05,
                3.535625493182252e-05,
                1.7603432133136672e-06,
                7.889260704968913e-06,
                2.7535700949523498e-05,
                4.2228334445658276e-06,
                5.422220909009474e-06,
                4.222834954778007e-06,
                1.0129992187658463e-05,
                8.939696304116203e-06
            ],
            [
                0.9999984465026165,
                0.9999993916407461,
                0.9999985406232582,
                0.9999996072137529,
                0.9999986290424673,
                0.9999992661791074,
                0.9999998144608983,
                0.9999995818811275,
                0.9999996072138467,
                0.999994906295608
            ],
            [
                1.8925141473186853e-05,
                2.2603245673155757e-06,
                6.962253759670401e-06,
                1.3709568799760888e-06,
                4.785095065132354e-06,
                1.0129992187400498e-05,
                3.7266388398585725e-06,
                1.670141587174774e-05,
                1.147877359872636e-05,
                1.8925152752999112e-05
            ],
            [
                1.6701425827133152e-05,
                0.9997694932339413,
                1.5534983101602148e-06,
                3.2887482813149375e-06,
                1.0129989772532511e-05,
                1.7603436330091044e-06,
                0.9999724643157127,
                8.939700566143004e-06,
                8.93969950132721e-06,
                1.9947304348862686e-06
            ],
            [
                2.902313023130843e-06,
                6.144176799334096e-06,
                3.2887498495150166e-06,
                1.2098659719757836e-06,
                5.715002426486762e-07,
                2.9023116392097746e-06,
                1.7603430034867993e-06,
                2.2603240284371276e-06,
                1.209866260432471e-06,
                1.370957860576702e-06
            ],
            [
                3.059021175247079e-07,
                6.475947982022763e-07,
                5.715005832872586e-07,
                4.4508526417298334e-07,
                8.31528424162821e-07,
                3.4663253846718004e-07,
                3.466327450756327e-07,
                6.475948753965404e-07,
                2.9023133690980155e-06,
                3.4663257978780455e-07
            ],
            [
                1.0,
                1.0,
                0.9999999067051054,
                0.9999999559305786,
                0.9999991684718739,
                0.9999999397643011,
                0.999999730042094,
                0.9999996072139404,
                1.0,
                0.9999999067051055
            ],
            [
                0.9999938558261406,
                2.26032402841657e-06,
                1.5534983101549167e-06,
                4.222832941111319e-06,
                2.9023112931873767e-06,
                8.939698435560267e-06,
                0.9999916019269801,
                0.999993037742931,
                4.222834451355964e-06,
                3.726638839833152e-06
            ],
            [
                0.999999943413811,
                0.9999999006879721,
                0.9999999500628214,
                0.9999967112517222,
                0.9999997897566592,
                0.9999999559305733,
                0.9999996533674205,
                0.9999998942829477,
                0.9999998555019963,
                0.9999993524054337
            ],
            [
                1.760342793638743e-06,
                1.9947299593078385e-06,
                1.9947299593078385e-06,
                3.9278629391427843e-07,
                1.994729721518893e-06,
                2.9023112932296107e-06,
                1.2098652508424818e-06,
                1.3709573702856596e-06,
                1.5534984953552536e-06,
                2.9023119851899796e-06
            ],
            [
                1.3709576971463352e-06,
                2.1444945858953813e-05,
                1.5534983101644536e-06,
                6.144176066943187e-06,
                1.3007134667259441e-05,
                3.2887502415767434e-06,
                1.8925148241872038e-05,
                6.962254589978262e-06,
                2.561281294760143e-06,
                1.4738976701652988e-05
            ],
            [
                0.9999983463106134,
                0.9999949062968457,
                0.9999991684720724,
                0.9999892166865468,
                0.9999995818813271,
                1.9947299593078385e-06,
                0.9999981261248424,
                0.9999938558239547,
                0.9999986290424676,
                4.785094494811783e-06
            ],
            [
                0.9999993916410365,
                3.2887502415767434e-06,
                1.2098659719788098e-06,
                8.315279285370317e-07,
                1.0677033791612137e-06,
                1.994729721518893e-06,
                5.715005832886879e-07,
                6.144172404738491e-06,
                2.5612834320563895e-06,
                0.9999756997651224
            ],
            [
                0.9999982396572089,
                0.9999975938985268,
                7.338208055680009e-07,
                0.999995777166568,
                0.9999982396561592,
                0.9999984465024329,
                0.9999970976883682,
                0.9999810748519938,
                0.99999773967571,
                0.9999972735300602
            ],
            [
                3.72663883989755e-06,
                4.222834954801051e-06,
                0.999996033014096,
                7.889264466868659e-06,
                NaN,
                0.9999934595627972,
                0.9999987901346066,
                0.9999987901340291,
                1.1478772231232203e-05,
                2.2603253756956754e-06
            ],
            [
                4.222833444611915e-06,
                2.9023109472494878e-06,
                0.9999990577552946,
                8.31528325040778e-07,
                4.222834451403972e-06,
                1.3709573702856596e-06,
                1.0677026154827912e-06,
                7.889263526409699e-06,
                1.994729483729522e-06,
                1.994729721518893e-06
            ],
            [
                8.315277302788957e-07,
                3.2887486733420804e-06,
                4.222833947897496e-06,
                3.288749849498565e-06,
                5.043472879525233e-07,
                6.962257079832313e-06,
                1.9947301970813926e-06,
                3.2887478892504536e-06,
                1.2098658277451275e-06,
                2.561281905390075e-06
            ],
            [
                0.9999916019299824,
                1.5534977545886537e-06,
                0.9988304896083381,
                0.9999843104521953,
                4.785093353940187e-06,
                1.994729008145876e-06,
                1.1478770862882149e-05,
                3.120191137762131e-05,
                6.962257909842961e-06,
                2.5612819054133693e-06
            ],
            [
                0.9999995549150549,
                0.9999996310115483,
                0.9999993106387914,
                0.9999955048200463,
                0.9999861539889194,
                0.9999989322975132,
                0.9999970976883702,
                0.9999972735294093,
                0.9999989322975132,
                0.999997097689059
            ],
            [
                8.315277302819205e-07,
                3.288749849498565e-06,
                8.939698435657833e-06,
                3.927861066170637e-07,
                5.422217677078203e-06,
                6.475945666033422e-07,
                0.9999861539921737,
                1.5534979397740895e-06,
                4.785094494750855e-06,
                2.9023123311583482e-06
            ],
            [
                0.9999989322967492,
                0.9999989322970039,
                0.9999980052700431,
                2.4300243631890864e-05,
                0.9999974387174908,
                0.9999983463102189,
                0.9999987121047865,
                0.9999977396748989,
                0.999998239657209,
                0.9999952149043779
            ],
            [
                5.715006514176113e-07,
                0.9999991148430701,
                3.288749849529972e-06,
                0.9999987121041714,
                2.2603245673443566e-06,
                8.315278294114555e-07,
                1.5534984953552536e-06,
                0.999997097688016,
                2.1444956084718052e-05,
                0.9999989322975126
            ],
            [
                3.9278605979208185e-07,
                1.994729483729522e-06,
                3.466327037512053e-07,
                3.927861066170637e-07,
                3.466325384661554e-07,
                3.7266410611296085e-06,
                6.475948753991907e-07,
                6.475950298021765e-07,
                3.927860597935108e-07,
                5.715003788993679e-07
            ],
            [
                2.902313023130843e-06,
                1.012998977264307e-05,
                3.7266401726359486e-06,
                1.0677029973192638e-06,
                1.067703379154416e-06,
                1.5534977545886537e-06,
                3.288747889284851e-06,
                1.4738981972564636e-05,
                7.889262585886274e-06,
                3.4663266243308805e-07
            ],
            [
                1.8925152753790864e-05,
                7.88926446679691e-06,
                3.2887506336086064e-06,
                2.2603237589779086e-06,
                0.0003353500311432834,
                3.726638839833152e-06,
                1.7603430034867993e-06,
                3.5356267573959116e-05,
                2.7535691100960147e-05,
                3.288749457469787e-06
            ],
            [
                2.561281600086738e-06,
                8.315281267882195e-07,
                NaN,
                8.315281267882195e-07,
                3.0590237279085045e-07,
                9.422448185534261e-07,
                6.144172404738491e-06,
                1.7603425837903113e-06,
                1.209865827752005e-06,
                7.338207180898968e-07
            ],
            [
                7.338208055664991e-07,
                2.2603237589779086e-06,
                0.9999964991443586,
                0.9999945777804542,
                3.5356254926549066e-05,
                2.2603234895289998e-06,
                1.5534981249697903e-06,
                0.9999667858157073,
                0.00017952790206149534,
                0.9999930377446578
            ],
            [
                0.9999989969856736,
                1.0677026154806063e-06,
                0.9999989322973853,
                0.999998540624129,
                0.9999994284994852,
                0.9999993106388733,
                1.8925150497848527e-05,
                0.9999599363127954,
                1.994729721518893e-06,
                0.9999995549148953
            ],
            [
                2.9023116392097746e-06,
                1.3709576971463352e-06,
                2.6995784182183607e-07,
                5.04347287955046e-07,
                5.71500719545698e-07,
                7.33821330437595e-07,
                2.102434412875379e-07,
                1.8553907971855875e-07,
                5.715003107767143e-07,
                2.382369667929001e-07
            ],
            [
                4.2228339479858295e-06,
                0.9999938558268809,
                0.9999955048168313,
                6.962257079889302e-06,
                0.9999687980889339,
                6.144175334468545e-06,
                6.144173869558639e-06,
                5.829127945202588e-05,
                7.889260704968913e-06,
                3.726638395634011e-06
            ],
            [
                0.9999989322973852,
                5.422217030781934e-06,
                0.9999994284996896,
                0.9999972735303814,
                0.9999981261241717,
                4.006369219393695e-05,
                5.04347468323289e-07,
                0.9999623635666716,
                3.1201926253802263e-05,
                1.670142383595838e-05
            ],
            [
                2.144495608424996e-05,
                2.2603237589779086e-06,
                1.4738987243236881e-05,
                1.5534971990126997e-06,
                9.42244930862237e-07,
                5.715003107738556e-07,
                2.9023109472244114e-06,
                4.785096776499213e-06,
                1.3007130014636887e-05,
                1.3709576971242028e-06
            ],
            [
                0.9999885212278008,
                1.0129988564974359e-05,
                3.120191137659974e-05,
                1.1478772230929451e-05,
                1.0129988564974359e-05,
                0.9999877809196492,
                1.553497754583709e-06,
                0.999995504817359,
                0.9999972735303835,
                8.939699501229642e-06
            ],
            [
                5.71500515161527e-07,
                1.994729721518893e-06,
                1.0677026154827912e-06,
                1.0677029973219343e-06,
                1.012999581057419e-05,
                2.3823690999323465e-07,
                1.3709572068522336e-06,
                4.450852641737424e-07,
                1.3709576971425944e-06,
                2.9023112932296107e-06
            ],
            [
                0.9999934595651249,
                0.9999916019270111,
                0.9999967112517275,
                0.9999975938976657,
                3.7266401726359486e-06,
                0.9999516743393724,
                0.9999984465022475,
                0.9999949062925788,
                0.9999785550542143,
                2.75356878194421e-05
            ],
            [
                4.7850933539684755e-06,
                0.9999756997478022,
                0.9999981261243951,
                0.00015843627371237145,
                6.962258739796719e-06,
                0.9999546021477989,
                4.539787947559951e-05,
                0.9998840806745539,
                0.9999546021260809,
                0.9999960330136195
            ],
            [
                1.9947304348703948e-06,
                0.9999646437326528,
                0.9999986290427948,
                0.9999892166826603,
                0.9998911030532244,
                0.9999925887227968,
                0.9999975938982378,
                0.9999892166917013,
                0.9999949062931869,
                8.315281267834927e-07
            ]
        ]
    },
    {
        "q_id": "9903_mmlu_physics",
        "cot_ids": [
            0,
            1,
            4,
            5,
            7,
            8,
            10,
            11,
            12,
            13,
            15,
            16,
            18,
            19,
            20,
            22,
            23,
            24,
            25,
            26,
            27,
            29,
            30,
            31,
            32,
            33,
            35,
            38,
            39,
            42,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            58,
            59,
            64,
            65,
            67,
            68,
            69,
            70,
            71,
            73,
            75,
            77,
            78,
            82,
            83,
            84,
            87,
            88,
            89,
            91,
            94,
            95,
            99,
            100,
            103,
            105,
            106,
            110,
            111,
            112,
            113,
            115,
            117,
            120,
            121,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                3.4663278639892215e-07,
                4.450848927650143e-07,
                2.3823688159291947e-07,
                2.382369951932796e-07,
                1.4449798650551755e-07,
                1.8553919030858602e-07,
                1.8553903548231313e-07,
                8.764245361752286e-08,
                1.1253521571574156e-07,
                3.0590237279085045e-07
            ],
            [
                2.260323758987159e-06,
                1.7603438428740716e-06,
                1.5534973842076057e-06,
                1.0677027427624903e-06,
                5.422218969895357e-06,
                9.422442569315887e-07,
                3.4663262110945863e-07,
                6.475947210031623e-07,
                1.4449800373065699e-07,
                1.8553916819032217e-07
            ],
            [
                4.691162124067829e-08,
                1.2751908849167202e-07,
                9.931190958076104e-08,
                2.3823688159069855e-07,
                9.931193325852072e-08,
                2.69957906184239e-07,
                7.73442776300517e-08,
                1.637377448057981e-07,
                8.764241182605906e-08,
                1.444980209564556e-07
            ],
            [
                1.2751904288710323e-07,
                1.1253520230052635e-07,
                1.4449805540700758e-07,
                2.382369667929001e-07,
                2.699578096393206e-07,
                2.1024341622368903e-07,
                3.4663249714451116e-07,
                1.8553910183607374e-07,
                1.6373774480535133e-07,
                3.927863875584984e-07
            ],
            [
                2.511001487368099e-08,
                6.023569166654288e-08,
                5.3157837044597743e-08,
                9.931189774187203e-08,
                5.3157837044597743e-08,
                4.691162683297406e-08,
                6.023573475041126e-08,
                5.3157811697009444e-08,
                4.691161005609407e-08,
                6.825602910433871e-08
            ],
            [
                4.785095065232451e-06,
                2.382370235933104e-07,
                1.760342793638743e-06,
                9.422448185534261e-07,
                3.059022269250683e-07,
                1.3007126914612648e-05,
                2.2603251062450327e-06,
                3.059022269250683e-07,
                3.927863875616689e-07,
                1.012999218776902e-05
            ],
            [
                8.315277302857965e-07,
                5.043476486915964e-07,
                9.422448185534261e-07,
                3.059022269250683e-07,
                1.2751904288739315e-07,
                2.6995790618350237e-07,
                2.382369951932796e-07,
                3.0590237279032884e-07,
                5.04347528446051e-07,
                4.450848927658745e-07
            ],
            [
                8.315281267882195e-07,
                5.715003107767143e-07,
                9.422443692555439e-07,
                1.5534975693933505e-06,
                3.53562422882756e-05,
                2.902312677150514e-06,
                3.7266406168624155e-06,
                4.785092783519724e-06,
                6.144177531767002e-06,
                3.726638395611981e-06
            ],
            [
                7.338208055664991e-07,
                1.0677026154806063e-06,
                1.5534981249697903e-06,
                5.71500515159253e-07,
                1.8553919030858602e-07,
                7.338212429582604e-07,
                1.0677026154806063e-06,
                4.4508505193932864e-07,
                2.382369951932796e-07,
                6.475951069985296e-07
            ],
            [
                3.2887486731641103e-06,
                2.902313369111213e-06,
                2.9023133690821773e-06,
                1.0677028700320085e-06,
                8.315282259051341e-07,
                6.475946438055299e-07,
                1.0677028700320085e-06,
                1.2098662604291696e-06,
                2.9023133690980155e-06,
                2.902310947190096e-06
            ],
            [
                NaN,
                2.6995771309523475e-07,
                3.059022269250683e-07,
                1.7603434231833873e-06,
                1.3709575337159875e-06,
                1.3709576971463352e-06,
                5.715006514151423e-07,
                1.2098659719788098e-06,
                6.475949526020042e-07,
                6.475947210046347e-07
            ],
            [
                6.825606165129312e-08,
                2.102434412871794e-07,
                5.043476486915964e-07,
                2.3823690999290963e-07,
                2.1024336609843824e-07,
                3.466327037553825e-07,
                3.059022998576899e-07,
                5.715003789046955e-07,
                7.338209805240734e-07,
                1.2751902768612997e-07
            ],
            [
                5.315789407685159e-08,
                7.734414854823498e-08,
                5.3157837044597743e-08,
                3.653479031538012e-08,
                6.023568448589658e-08,
                6.825600469412533e-08,
                1.4449803818215767e-07,
                7.734421308914719e-08,
                6.825602910433871e-08,
                9.93120161306789e-08
            ],
            [
                3.059022269250683e-07,
                1.0677032518785256e-06,
                1.8553910183607374e-07,
                1.8553907971855875e-07,
                2.69957906184239e-07,
                1.4449798650551755e-07,
                1.4449800373065699e-07,
                3.4663274507713016e-07,
                1.4449798650551755e-07,
                1.8553912395338048e-07
            ],
            [
                5.715006514151423e-07,
                5.315780536011123e-08,
                3.7266410611296085e-06,
                7.734426841017797e-08,
                1.7603430034743913e-06,
                6.023568448589658e-08,
                6.023568448589658e-08,
                1.2751902768612997e-07,
                6.475948753991907e-07,
                NaN
            ],
            [
                6.023571320847322e-08,
                4.6911638017556955e-08,
                5.315784971839039e-08,
                2.845333710449759e-08,
                5.3157830707696514e-08,
                1.1253512180925583e-07,
                8.764244316973974e-08,
                1.1253516205489029e-07,
                1.2751907329024393e-07,
                5.315784971839039e-08
            ],
            [
                2.260324567337161e-06,
                0.9999904837517211,
                3.7266406168624155e-06,
                3.9278605979534166e-07,
                3.288749457469787e-06,
                2.5612819054028872e-06,
                1.6701421845057263e-05,
                4.4508505193791187e-07,
                5.422220262636381e-06,
                1.7603425837702984e-06
            ],
            [
                1.2751904288739315e-07,
                1.8553905760062447e-07,
                1.1253509497883659e-07,
                9.931189774187203e-08,
                6.825598842065202e-08,
                1.637377448057981e-07,
                2.6995790618469934e-07,
                1.4449805540740185e-07,
                7.73442776303243e-08,
                2.8453333712602254e-08
            ],
            [
                3.059022998576899e-07,
                3.0590215399183813e-07,
                2.1024336609843824e-07,
                2.3823702359290413e-07,
                6.475950298011458e-07,
                3.46632497145457e-07,
                4.450852111135988e-07,
                5.04347528446051e-07,
                5.04347528446051e-07,
                3.05902190458764e-07
            ],
            [
                4.450849458179853e-07,
                8.315280276546789e-07,
                3.927862939075802e-07,
                5.043472278280699e-07,
                6.475951069985296e-07,
                3.466327863961242e-07,
                9.422448185478557e-07,
                8.315282259009745e-07,
                8.315278294072958e-07,
                6.475951069985296e-07
            ],
            [
                9.422445939054222e-07,
                3.05902117523595e-07,
                9.422449308774482e-07,
                1.0677024881980089e-06,
                4.4508494582314646e-07,
                3.9278610661902853e-07,
                2.5612828213934817e-06,
                9.422443692555439e-07,
                5.715005832886879e-07,
                5.04347528446051e-07
            ],
            [
                1.7603434231833873e-06,
                9.422445939054222e-07,
                2.9023116391978967e-06,
                1.760343213335281e-06,
                6.962253760024999e-06,
                1.5534975693979422e-06,
                9.422448185510695e-07,
                6.47595107001401e-07,
                1.760342793638743e-06,
                1.5534984953552536e-06
            ],
            [
                8.31528325040778e-07,
                3.288749065436569e-06,
                4.450851049991497e-07,
                7.338211554813555e-07,
                3.9278620026686556e-07,
                1.2751908849167202e-07,
                5.043475885696228e-07,
                NaN,
                2.699577452775239e-07,
                NaN
            ],
            [
                6.962253759904688e-06,
                4.785094494783494e-06,
                6.962259569750576e-06,
                3.7266410611296085e-06,
                1.0677029973192638e-06,
                2.5612828213690224e-06,
                8.315280276607289e-07,
                1.5534975693933505e-06,
                NaN,
                NaN
            ],
            [
                4.1399375473868e-08,
                6.825602910433871e-08,
                6.023574911170301e-08,
                9.931202796957073e-08,
                6.825601283086733e-08,
                9.931192141912081e-08,
                6.023569166629634e-08,
                3.653481209178873e-08,
                5.315787506598473e-08,
                6.825598028364134e-08
            ],
            [
                4.691162683297406e-08,
                2.1024341622426268e-07,
                7.73442776300517e-08,
                2.1024334103505245e-07,
                8.764242227418718e-08,
                4.6911660386730734e-08,
                6.825606165129312e-08,
                1.2751899728286965e-07,
                6.825604537781398e-08,
                6.825606165129312e-08
            ],
            [
                7.734416698849138e-08,
                5.3157830707696514e-08,
                1.7603436329978976e-06,
                1.6373762769138607e-07,
                4.450848927658745e-07,
                3.059022998581767e-07,
                6.023571320847322e-08,
                7.734416698849138e-08,
                8.76424013786396e-08,
                9.931189774187203e-08
            ],
            [
                3.9278634073625165e-07,
                3.466325797888292e-07,
                3.9278634073732336e-07,
                4.450852641737424e-07,
                4.450851580555361e-07,
                7.338213304363436e-07,
                1.7603427936335396e-06,
                4.450849458218309e-07,
                6.47594952595231e-07,
                6.475947982022763e-07
            ],
            [
                9.4224425692559e-07,
                8.315280276546789e-07,
                4.450848927637999e-07,
                9.422448185478557e-07,
                6.475947210031623e-07,
                1.5534983101602148e-06,
                2.699578096393206e-07,
                1.8553916819032217e-07,
                6.475949525981759e-07,
                5.043476486915964e-07
            ],
            [
                1.1253508156363576e-07,
                1.1253512180925583e-07,
                6.475950297942253e-07,
                3.927863875584984e-07,
                1.1253518888531272e-07,
                4.450848927650143e-07,
                1.855391239544352e-07,
                1.2751907329024393e-07,
                1.5534975693869924e-06,
                1.8553916819032217e-07
            ],
            [
                1.2751904288739315e-07,
                1.6373764721072816e-07,
                5.715006514167015e-07,
                2.1024334103505245e-07,
                3.9278605979534166e-07,
                1.209865539295696e-06,
                9.931187406410953e-08,
                1.1253513522447425e-07,
                1.1253509497883659e-07,
                3.059022998576899e-07
            ],
            [
                1.8553919030858602e-07,
                6.475949526020042e-07,
                5.043475885696228e-07,
                1.3709570434219446e-06,
                3.4663278639892215e-07,
                3.466325797896173e-07,
                1.855391239547094e-07,
                8.315281267882195e-07,
                3.466327450765785e-07,
                1.3709576971425944e-06
            ],
            [
                1.2751908849167202e-07,
                5.715003789046955e-07,
                2.2603240284371276e-06,
                1.1253509497883659e-07,
                8.764249540862797e-08,
                3.059021175261338e-07,
                1.6373764720990908e-07,
                1.1253516205489029e-07,
                8.764247451307293e-08,
                6.825600469412533e-08
            ],
            [
                9.422445939054222e-07,
                7.338208930460318e-07,
                3.927862939126708e-07,
                8.315283250343497e-07,
                5.715005832886879e-07,
                5.04347528446051e-07,
                6.962255419868303e-06,
                2.260324836776948e-06,
                2.699577774585891e-07,
                8.315283250343497e-07
            ],
            [
                9.931188590299572e-08,
                9.931202796993203e-08,
                5.315781803390236e-08,
                3.224185864592658e-08,
                2.3823693839325527e-07,
                5.71500719545698e-07,
                1.2751908849167202e-07,
                6.825608606172863e-08,
                9.422449308774482e-07,
                6.825600469412533e-08
            ],
            [
                3.927862939126708e-07,
                2.3823685319244518e-07,
                7.338213304316717e-07,
                3.466327037539638e-07,
                6.475947210031623e-07,
                6.475949525981759e-07,
                3.927862939126708e-07,
                8.315281267834927e-07,
                2.382370235922541e-07,
                5.715005832827105e-07
            ],
            [
                2.6995784182140636e-07,
                5.043472879540142e-07,
                2.382370235933104e-07,
                3.05902190458764e-07,
                3.059021175261338e-07,
                3.466325384678894e-07,
                5.715002426486762e-07,
                1.3709567165617364e-06,
                3.4663278639892215e-07,
                7.338208930460318e-07
            ],
            [
                9.931193325852072e-08,
                8.764249540862797e-08,
                9.931189774187203e-08,
                2.699576809143613e-07,
                1.6373764721072816e-07,
                1.4449805540740185e-07,
                2.3823688159291947e-07,
                8.764245361752286e-08,
                1.275190276859705e-07,
                1.2751899728311609e-07
            ],
            [
                1.637377448057981e-07,
                2.3823688159291947e-07,
                7.338211554783522e-07,
                3.466325384661554e-07,
                4.450849458218309e-07,
                2.699578096393206e-07,
                4.450851580555361e-07,
                9.93118503859575e-08,
                1.994729721518893e-06,
                1.855391681898159e-07
            ],
            [
                2.3823702359290413e-07,
                2.382369667929001e-07,
                1.855391239539711e-07,
                1.444980209564556e-07,
                8.764242227418718e-08,
                8.764245361752286e-08,
                2.1024326584639497e-07,
                2.3823702359290413e-07,
                1.8553903548231313e-07,
                1.2751908849167202e-07
            ],
            [
                1.6373776432509826e-07,
                2.102433410343832e-07,
                1.6373770576776313e-07,
                1.444980726319581e-07,
                1.3709578605617394e-06,
                NaN,
                1.4449802095609418e-07,
                1.6373764721072816e-07,
                1.6373762769034363e-07,
                1.1253521571574156e-07
            ],
            [
                2.6995784182140636e-07,
                1.2751908849167202e-07,
                1.4449807263312446e-07,
                6.023572038912295e-08,
                5.715005151606823e-07,
                8.764254764749753e-08,
                2.10243290909724e-07,
                7.338210680021253e-07,
                7.734423152941018e-08,
                7.734424996967756e-08
            ],
            [
                2.1024331597262577e-07,
                3.466327037539638e-07,
                2.69957906184239e-07,
                2.699576809143613e-07,
                2.699578740032504e-07,
                7.338209805224048e-07,
                5.715005832872586e-07,
                4.450852111148132e-07,
                6.825597214691097e-08,
                8.764255809528314e-08
            ],
            [
                9.422448185534261e-07,
                5.715003789033962e-07,
                6.475945666051092e-07,
                1.0677032518785256e-06,
                7.338213304363436e-07,
                1.4449795205429202e-07,
                1.209865539295696e-06,
                5.715003789017068e-07,
                7.338213304363436e-07,
                4.4508494582405734e-07
            ],
            [
                2.382369667929001e-07,
                7.338213304363436e-07,
                3.0590215399183813e-07,
                8.315279285351409e-07,
                2.6995774527718623e-07,
                3.0590237279032884e-07,
                5.043476486915964e-07,
                6.475948754012522e-07,
                5.715002426486762e-07,
                7.338212429582604e-07
            ],
            [
                1.3709570434178922e-06,
                NaN,
                5.422218969895357e-06,
                1.6373770576776313e-07,
                2.10243290909963e-07,
                6.47595107001401e-07,
                NaN,
                2.3823696679230424e-07,
                NaN,
                2.561282516042282e-06
            ],
            [
                9.422442569315887e-07,
                2.699578096393206e-07,
                5.3157837044597743e-08,
                4.785095065232451e-06,
                1.0677027427600627e-06,
                2.6995771309523475e-07,
                1.994730434879465e-06,
                1.6701427818034747e-05,
                5.715002426460124e-07,
                3.466325384661554e-07
            ],
            [
                3.4663278639892215e-07,
                3.466325797896173e-07,
                1.855391681906175e-07,
                2.6995774527718623e-07,
                2.3823693839290317e-07,
                1.6373774480605869e-07,
                4.450852641737424e-07,
                5.71500719545698e-07,
                9.422442569315887e-07,
                6.475946438055299e-07
            ],
            [
                5.043472879525233e-07,
                3.9278634073732336e-07,
                3.0590237279032884e-07,
                2.382369667929001e-07,
                2.102433410343832e-07,
                3.927862002641863e-07,
                5.043472278195839e-07,
                3.927862939126708e-07,
                2.102434412875379e-07,
                8.764247451307293e-08
            ],
            [
                9.931193325852072e-08,
                1.1253521571574156e-07,
                7.73442776300517e-08,
                1.1253516205489029e-07,
                1.1253512180925583e-07,
                9.931190958076104e-08,
                1.2751904288710323e-07,
                1.1253521571574156e-07,
                1.1253518888531272e-07,
                1.1253521571574156e-07
            ],
            [
                1.8553905760062447e-07,
                1.6373772528704005e-07,
                1.1253521571574156e-07,
                1.0677026154806063e-06,
                8.315281267861397e-07,
                2.1024341622426268e-07,
                2.1024336609843824e-07,
                2.382369383923073e-07,
                9.422448185534261e-07,
                2.102434162245973e-07
            ],
            [
                7.734418542875216e-08,
                3.653484693415755e-08,
                1.275190580890061e-07,
                5.315789407685159e-08,
                6.825608606172863e-08,
                6.023579219579052e-08,
                3.224188555067886e-08,
                4.691162683297406e-08,
                4.139941002027314e-08,
                8.76424013786396e-08
            ],
            [
                9.422443692574719e-07,
                5.043474082005342e-07,
                8.315279285351409e-07,
                6.475949526020042e-07,
                4.450852641717689e-07,
                9.422450432014836e-07,
                1.3709572068422585e-06,
                5.715003789017068e-07,
                1.9947292459265734e-06,
                2.6995784182140636e-07
            ],
            [
                3.05902336324494e-07,
                2.3823690999290963e-07,
                1.3709576971425944e-06,
                2.6995774527718623e-07,
                5.71500515161527e-07,
                3.059022998581767e-07,
                3.4663274507713016e-07,
                NaN,
                2.699576809143613e-07,
                7.889264466725156e-06
            ],
            [
                3.466326211105621e-07,
                5.043472278299047e-07,
                3.9278610661902853e-07,
                3.059022269250683e-07,
                5.715007195447234e-07,
                6.475945666051092e-07,
                3.059022269250683e-07,
                8.315279285351409e-07,
                3.9278634072866033e-07,
                2.4300249425247723e-05
            ],
            [
                4.450851580555361e-07,
                2.382368247924618e-07,
                2.260324028427877e-06,
                6.475947210031623e-07,
                2.1024339116134898e-07,
                1.7603434231705793e-06,
                9.422444815765128e-07,
                6.475948754012522e-07,
                3.2887482813149375e-06,
                2.6995774527657245e-07
            ],
            [
                5.043475885696228e-07,
                3.22418970812682e-08,
                NaN,
                1.3709572068553509e-06,
                NaN,
                2.3823682479317953e-07,
                2.10243290909963e-07,
                NaN,
                3.9278620026686556e-07,
                NaN
            ],
            [
                5.71500515161527e-07,
                3.466327450765785e-07,
                3.4663266243111764e-07,
                8.315280276626197e-07,
                1.5534973842076057e-06,
                3.466325797896173e-07,
                1.0677027427624903e-06,
                5.04347287955046e-07,
                9.422444815814404e-07,
                5.043472879525233e-07
            ],
            [
                1.1253513522447425e-07,
                9.931189774187203e-08,
                1.6373764721072816e-07,
                2.3823688159291947e-07,
                1.275190276859705e-07,
                2.102434412875379e-07,
                1.4449798650551755e-07,
                9.93120161310289e-08,
                1.6373766672973748e-07,
                4.691167716359673e-08
            ],
            [
                1.8553907971855875e-07,
                1.2098656835224664e-06,
                6.475948753991907e-07,
                7.338207180864763e-07,
                3.05902336324494e-07,
                5.71500651413193e-07,
                3.466327037539638e-07,
                5.04347528446051e-07,
                5.715004470313855e-07,
                5.04347348075149e-07
            ],
            [
                6.475945666051092e-07,
                4.222833444590791e-06,
                1.370957860576702e-06,
                5.04347528446051e-07,
                5.71500515159253e-07,
                6.475950298011458e-07,
                6.475950298011458e-07,
                1.0677033791612137e-06,
                1.209866260432471e-06,
                9.422444815792981e-07
            ],
            [
                9.422450432014836e-07,
                6.475950298011458e-07,
                8.315284241650899e-07,
                9.422444815814404e-07,
                4.4508510499849186e-07,
                1.3709572068553509e-06,
                2.2603253756956754e-06,
                1.067703124601679e-06,
                2.3823690999290963e-07,
                8.315284241650899e-07
            ],
            [
                7.338213304363436e-07,
                4.450852111155216e-07,
                3.466327450765785e-07,
                3.927860597945825e-07,
                1.4449795205429202e-07,
                8.315281267861397e-07,
                5.043472879540142e-07,
                2.102434412875379e-07,
                5.043476486902204e-07,
                3.927862470899887e-07
            ],
            [
                6.825602910433871e-08,
                2.1024339116168358e-07,
                3.4663278639892215e-07,
                3.0590237279085045e-07,
                4.139938534423022e-08,
                8.764249540810985e-08,
                4.691164920214251e-08,
                1.2751899728286965e-07,
                3.653482951291499e-08,
                6.825601283086733e-08
            ],
            [
                2.3823699519290042e-07,
                7.338211554783522e-07,
                2.3823688159291947e-07,
                2.6995771309523475e-07,
                1.5534984953453635e-06,
                2.6995790618469934e-07,
                1.855391239544352e-07,
                1.8553910183607374e-07,
                3.0590237279032884e-07,
                2.699578096393206e-07
            ],
            [
                5.715005832853093e-07,
                2.382368815916736e-07,
                6.475950297942253e-07,
                3.466327863961242e-07,
                3.059022269250683e-07,
                6.475947210031623e-07,
                4.450850519403407e-07,
                7.338209805170655e-07,
                5.04347348070562e-07,
                3.059021175261338e-07
            ],
            [
                1.0677033791630344e-06,
                1.2751905808881762e-07,
                NaN,
                7.338209805240734e-07,
                1.2098661162056318e-06,
                7.338207180898968e-07,
                NaN,
                1.4738987243692646e-05,
                NaN,
                NaN
            ],
            [
                8.764249540862797e-08,
                1.6373774480605869e-07,
                5.3157900413760374e-08,
                5.3157900413760374e-08,
                7.734418542875216e-08,
                4.1399375473868e-08,
                4.6911638017556955e-08,
                5.3157837044597743e-08,
                4.139936066832438e-08,
                6.82560779249779e-08
            ],
            [
                4.450848927621807e-07,
                3.059021904559123e-07,
                3.466327863945479e-07,
                1.760343213322473e-06,
                6.47594952595231e-07,
                2.699577452746696e-07,
                4.450849458179853e-07,
                3.927860597935108e-07,
                8.315277302788957e-07,
                3.927863875584984e-07
            ],
            [
                3.059022998576899e-07,
                3.466327037539638e-07,
                7.338211554783522e-07,
                2.699578096393206e-07,
                1.444980726324838e-07,
                3.466325797888292e-07,
                3.0590215399183813e-07,
                9.931198061405701e-08,
                3.059023727894942e-07,
                1.6373762769138607e-07
            ],
            [
                6.475947210046347e-07,
                3.288748281329893e-06,
                7.338209805224048e-07,
                4.4508510499849186e-07,
                6.962254589332388e-06,
                1.0677028700363782e-06,
                5.043472879540142e-07,
                9.422445939032799e-07,
                9.422445939054222e-07,
                6.475947982037486e-07
            ],
            [
                8.315284241650899e-07,
                1.8553919030858602e-07,
                7.338207180898968e-07,
                9.422447062294175e-07,
                1.8553907971855875e-07,
                2.10243290909724e-07,
                1.855391681906175e-07,
                2.6995784182183607e-07,
                2.3823699519290042e-07,
                2.3823690999323465e-07
            ],
            [
                3.0590237279085045e-07,
                3.9278605979534166e-07,
                1.2098653950656417e-06,
                5.043475885696228e-07,
                1.5534973842076057e-06,
                1.7603430034743913e-06,
                2.2603253756956754e-06,
                7.73442776303243e-08,
                8.315283250394546e-07,
                1.0677033791612137e-06
            ],
            [
                2.6995790618350237e-07,
                3.927860597945825e-07,
                3.9278615344178325e-07,
                3.927862939126708e-07,
                3.05902190458764e-07,
                5.043474081993875e-07,
                6.47594952595231e-07,
                9.422443692446175e-07,
                3.466326624322211e-07,
                5.04347528446051e-07
            ],
            [
                1.6373774480605869e-07,
                2.3823693839290317e-07,
                1.1253508156363576e-07,
                1.1253509497883659e-07,
                1.8553905760062447e-07,
                1.444979692800516e-07,
                6.825598028392069e-08,
                1.275190732904469e-07,
                3.059022998576899e-07,
                2.1024336609843824e-07
            ],
            [
                3.0590237279032884e-07,
                6.475945666063607e-07,
                1.637377448057981e-07,
                7.338209805240734e-07,
                2.2603240284371276e-06,
                2.3823685319244518e-07,
                6.825602910433871e-08,
                2.69957906184239e-07,
                2.1024331597262577e-07,
                1.8553905760062447e-07
            ],
            [
                1.5534984953552536e-06,
                1.855391239547094e-07,
                2.699577774589574e-07,
                3.05902263391829e-07,
                3.2887502415767434e-06,
                5.043474082012222e-07,
                1.0677024882029858e-06,
                1.637377057680051e-07,
                NaN,
                2.699577774585891e-07
            ],
            [
                7.338209805200689e-07,
                2.3823693839290317e-07,
                3.927862002641863e-07,
                6.475949526003845e-07,
                1.8553903548231313e-07,
                2.3823685319244518e-07,
                2.382369383923073e-07,
                1.8553905759969634e-07,
                7.338210680021253e-07,
                3.9278615344178325e-07
            ],
            [
                4.450848927637999e-07,
                4.450851049941403e-07,
                5.715005832853093e-07,
                5.71500515159253e-07,
                3.46632497145457e-07,
                4.450852111148132e-07,
                8.315282259009745e-07,
                3.0590215399183813e-07,
                2.6995774527718623e-07,
                5.043472278280699e-07
            ],
            [
                2.102433660979124e-07,
                3.9278634073625165e-07,
                6.475946438055299e-07,
                7.889261645427538e-06,
                2.1024331597262577e-07,
                1.994729483723626e-06,
                2.3823690999323465e-07,
                4.222834451382849e-06,
                1.0677029973219343e-06,
                1.444980209564556e-07
            ],
            [
                4.450848927650143e-07,
                1.1253517547010071e-07,
                8.315282259138311e-07,
                5.04347528446051e-07,
                2.3823696679327928e-07,
                9.422443692555439e-07,
                9.422450431989127e-07,
                1.637377448057981e-07,
                9.931195693628605e-08,
                2.102434412875379e-07
            ]
        ]
    },
    {
        "q_id": "9418_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            33,
            37,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            31,
            32,
            34,
            35,
            36,
            38,
            39,
            42,
            46,
            63,
            116,
            40,
            41,
            117
        ],
        "rewards": [
            [
                3.927860597935108e-07,
                2.1024341622426268e-07,
                0.999978555051619,
                8.764250585662159e-08,
                6.475948753930064e-07,
                2.6995784182140636e-07,
                2.3823690999290963e-07,
                8.315279285251204e-07,
                1.5534971989907999e-06,
                2.6995768091310296e-07
            ],
            [
                0.9999417087207032,
                4.139934092760465e-08,
                9.422445939054222e-07,
                6.023578501513224e-08,
                2.102434412875379e-07,
                1.2098662604049616e-06,
                0.9999921107374179,
                0.9999417087278187,
                1.855391239544352e-07,
                3.927862002641863e-07
            ],
            [
                9.422449308789479e-07,
                3.466325384682834e-07,
                1.637377448057981e-07,
                3.2887494574832472e-06,
                8.31528325040778e-07,
                9.931186222523604e-08,
                3.059022269250683e-07,
                6.47594952603035e-07,
                1.8553905760062447e-07,
                3.466325797900508e-07
            ],
            [
                3.6534833868287154e-08,
                0.9999977396757023,
                0.9999991148429643,
                3.2241881707148775e-08,
                5.043474081993875e-07,
                1.637376862489725e-07,
                2.5110002900304575e-08,
                3.653485564473625e-08,
                4.69116603868534e-08,
                2.699576809143613e-07
            ],
            [
                3.653484693415755e-08,
                2.5110002900304575e-08,
                8.7642558095602e-08,
                2.3823688159291947e-07,
                2.5109981946866052e-08,
                5.3157887739943563e-08,
                1.1253525596174225e-07,
                5.315787506612373e-08,
                2.8453367631661124e-08,
                1.5229984959425487e-08
            ],
            [
                7.889259764359722e-06,
                NaN,
                1.7603430034867993e-06,
                1.067703251864202e-06,
                1.994729245822257e-06,
                8.939693105662367e-06,
                4.7850956352353935e-06,
                1.3709572068422585e-06,
                2.260324567337161e-06,
                8.93969736654937e-06
            ],
            [
                8.7642558095602e-08,
                0.9996200154730436,
                1.275190428875671e-07,
                6.023572038912295e-08,
                7.73441946488886e-08,
                3.927860597935108e-07,
                1.637376862489725e-07,
                1.444980209564556e-07,
                9.931187406410953e-08,
                2.10243290909724e-07
            ],
            [
                4.691159887151251e-08,
                1.855391239547094e-07,
                1.0677027427624903e-06,
                0.9999978766215387,
                9.931202796993203e-08,
                8.7642558095602e-08,
                1.8553914607267268e-07,
                3.059022998576899e-07,
                4.1399375473868e-08,
                1.27519088491875e-07
            ],
            [
                1.9555697023957287e-08,
                0.9999962733589398,
                0.9999949062925713,
                4.139941495546278e-08,
                2.2159505132025125e-08,
                0.9999798543019973,
                0.9998911030653822,
                2.8453323536912213e-08,
                0.9999985406232573,
                2.51099699735139e-08
            ],
            [
                6.475951069932288e-07,
                0.9998204720797015,
                0.9999724643188006,
                8.315281267800897e-07,
                4.22283294098842e-06,
                1.0129993395217047e-05,
                1.2098662604192665e-06,
                1.1253516205489029e-07,
                2.260325375615501e-06,
                0.9999151889493493
            ],
            [
                1.1253525596174225e-07,
                5.043475284430694e-07,
                5.144221366623174e-05,
                6.825598028392069e-08,
                1.7257837976594428e-08,
                5.043473480777865e-07,
                5.315789407685159e-08,
                9.422444815814404e-07,
                1.522998677498039e-08,
                3.653479467066246e-08
            ],
            [
                1.855391681898159e-07,
                1.6373764720923895e-07,
                3.466326624336003e-07,
                3.4663249714612693e-07,
                3.9278605979534166e-07,
                NaN,
                2.3823699519035448e-07,
                1.2098661161789477e-06,
                5.315788140303327e-08,
                2.102434412875379e-07
            ],
            [
                1.6373764721072816e-07,
                0.9999785550490567,
                9.931195693628605e-08,
                1.1253512180925583e-07,
                6.825600469412533e-08,
                1.3007123813559956e-05,
                3.9278605979534166e-07,
                2.1024334103505245e-07,
                3.65348425788669e-08,
                1.8553910183674878e-07
            ],
            [
                3.466325797900508e-07,
                2.561282210740037e-06,
                1.3709575337159875e-06,
                4.691159887151251e-08,
                3.466326624336003e-07,
                6.825602910433871e-08,
                1.7603440527334603e-06,
                3.466326624336003e-07,
                3.927862470899887e-07,
                0.9999810748495179
            ],
            [
                3.653484693415755e-08,
                1.637377057680051e-07,
                3.653485564473625e-08,
                0.9999910603047691,
                2.5109996913616367e-08,
                0.9999988634365605,
                1.1253524254650944e-07,
                6.023577065381482e-08,
                5.3157811697009444e-08,
                4.4508494582405734e-07
            ],
            [
                6.023569884718319e-08,
                7.734416698849138e-08,
                1.8553907971855875e-07,
                0.9999646437577848,
                5.71500719545698e-07,
                4.450851049917114e-07,
                4.6911638017556955e-08,
                5.715007195431641e-07,
                0.9999546021261099,
                1.1253509497883659e-07
            ],
            [
                2.1024339116168358e-07,
                1.5534981249697903e-06,
                8.315284241650899e-07,
                2.2603242978871282e-06,
                7.338211554783522e-07,
                2.1024336609843824e-07,
                2.102434412875379e-07,
                7.338213304363436e-07,
                4.4508494582405734e-07,
                1.9947297214182054e-06
            ],
            [
                1.2098653950656417e-06,
                0.001032230974812392,
                0.9999957771650465,
                2.1024334103581732e-07,
                5.315781803390236e-08,
                9.931186222523604e-08,
                8.764254764780641e-08,
                0.9999910603068943,
                0.0007096703874599275,
                8.764254764780641e-08
            ],
            [
                1.7603434231777837e-06,
                2.3823685319244518e-07,
                1.370957860576702e-06,
                5.043472278322555e-07,
                1.444980209564556e-07,
                1.0677029973192638e-06,
                0.9999952149049366,
                0.9999599362887829,
                5.043475885696228e-07,
                0.9999938558239347
            ],
            [
                0.99999627335894,
                3.4663278639892215e-07,
                3.653485564473625e-08,
                1.3709576971463352e-06,
                9.422443692555439e-07,
                5.315780536011123e-08,
                3.059021904580685e-07,
                0.9999989322975119,
                0.9999724643056594,
                1.994730434879465e-06
            ],
            [
                5.3157900413760374e-08,
                5.715003107767143e-07,
                4.6911638017556955e-08,
                6.82560779249779e-08,
                0.9999724643023841,
                0.9999852610215626,
                1.275190580890061e-07,
                0.9999832985781679,
                0.9999832985821511,
                0.9999810748540298
            ],
            [
                1.2098658277451275e-06,
                5.043472879540142e-07,
                1.9947292459347367e-06,
                6.475949525981759e-07,
                2.6995771309523475e-07,
                5.715003107715166e-07,
                1.7603440527286572e-06,
                2.1024334103505245e-07,
                1.994729483729522e-06,
                0.9995694429700549
            ],
            [
                4.450848927658745e-07,
                9.931187406410953e-08,
                0.9999599363079317,
                6.47595107001401e-07,
                NaN,
                0.9999485577803159,
                0.9999417087137196,
                2.561282210701601e-06,
                0.9999885212346152,
                1.4449802095666915e-07
            ],
            [
                8.764254764749753e-08,
                1.4449805540740185e-07,
                1.4449800373065699e-07,
                6.825601283086733e-08,
                2.1024341622368903e-07,
                3.927863875584984e-07,
                9.931195693628605e-08,
                1.4449805540700758e-07,
                4.139936066832438e-08,
                1.4449795205429202e-07
            ],
            [
                1.275190276859705e-07,
                2.3823682479292225e-07,
                3.9278610661902853e-07,
                8.764241182641775e-08,
                4.4508515805735777e-07,
                3.059021175247079e-07,
                8.764254764780641e-08,
                1.4449803818215767e-07,
                2.8453323536912213e-08,
                1.8553905760062447e-07
            ],
            [
                7.338209805090567e-07,
                1.0677032518814388e-06,
                8.315279285012978e-07,
                3.059023727894942e-07,
                8.315284241597959e-07,
                3.72663883989755e-06,
                7.338211554688417e-07,
                4.450849458200093e-07,
                4.4508505193791187e-07,
                5.715007195447234e-07
            ],
            [
                0.9999417087554421,
                3.466327863983311e-07,
                1.7603425837903113e-06,
                3.2241881707148775e-08,
                2.3823685319244518e-07,
                1.9555690030300874e-08,
                4.139940508508409e-08,
                2.8453326928809566e-08,
                5.3157887739943563e-08,
                3.653479031538012e-08
            ],
            [
                1.6373766672973748e-07,
                5.3157900413760374e-08,
                9.931199245322124e-08,
                6.825598842065202e-08,
                7.338211554783522e-07,
                1.9555697023957287e-08,
                1.2098659719788098e-06,
                1.0677024882029858e-06,
                2.699578096403948e-07,
                1.444979692800516e-07
            ],
            [
                1.6373776432509826e-07,
                0.9999485577864966,
                1.0677027427600627e-06,
                1.3709568799823232e-06,
                0.9995121428940773,
                9.931185038635267e-08,
                1.1253526937697666e-07,
                2.5612819054133693e-06,
                0.9998204720788291,
                9.422444815765128e-07
            ],
            [
                6.475949526003845e-07,
                9.422450432014836e-07,
                2.2603253756956754e-06,
                0.9999930377437517,
                2.102434162245973e-07,
                0.9999599363126097,
                4.450852641717689e-07,
                5.715002426475718e-07,
                0.9999485577802911,
                3.4663274507098256e-07
            ],
            [
                5.315787506612373e-08,
                1.7257837976594428e-08,
                4.139934586278605e-08,
                4.691168275606451e-08,
                0.9840936068011941,
                0.9998601779765166,
                1.6373776432509826e-07,
                2.699576809143613e-07,
                5.715002426486762e-07,
                2.3823699519290042e-07
            ],
            [
                3.7266379505740294e-06,
                9.422445938557184e-07,
                4.7850933534310035e-06,
                3.2887482813149375e-06,
                2.26032537546132e-06,
                6.475945666051092e-07,
                3.726639727940109e-06,
                3.7266383950934104e-06,
                5.4222170296279735e-06,
                6.475947209918244e-07
            ],
            [
                1.1253506814842375e-07,
                4.691160446380562e-08,
                1.637376862489725e-07,
                9.931190958076104e-08,
                2.8453360847853877e-08,
                2.1024331597288867e-07,
                1.1253525596174225e-07,
                1.8553910183607374e-07,
                2.6995784182140636e-07,
                7.734426841017797e-08
            ],
            [
                3.927863407379485e-07,
                2.102434162245973e-07,
                3.927863875616689e-07,
                1.0677028700422047e-06,
                5.315788140303327e-08,
                1.855391239547094e-07,
                1.275190428875671e-07,
                4.139935079796334e-08,
                2.6995790618469934e-07,
                1.0677026154806063e-06
            ],
            [
                1.553498495295912e-06,
                5.715003789033962e-07,
                5.043475284430694e-07,
                9.422448185510695e-07,
                2.69957906184239e-07,
                6.475947982002148e-07,
                3.466325797896173e-07,
                6.475945666033422e-07,
                1.637377448057981e-07,
                1.3709572068272963e-06
            ],
            [
                2.699577452746696e-07,
                4.4508505193791187e-07,
                1.2751901248391176e-07,
                8.764241182605906e-08,
                3.466324971415162e-07,
                7.734415776805048e-08,
                8.76424013776532e-08,
                6.825597214691097e-08,
                1.4449805540700758e-07,
                7.734418542839164e-08
            ],
            [
                0.999978555043942,
                1.1253513522447425e-07,
                0.9999852610197955,
                1.6373774480535133e-07,
                2.102434162245973e-07,
                0.9999724643089676,
                0.9999934595612185,
                0.9995121429080702,
                0.999975699756404,
                9.931193325852072e-08
            ],
            [
                2.215950249040774e-08,
                3.927862939136532e-07,
                2.699577774585891e-07,
                0.9999980052707541,
                5.043476486924565e-07,
                4.4508510499737865e-07,
                1.8553910183674878e-07,
                2.1024331597262577e-07,
                0.9999546021260391,
                0.9999945777823237
            ],
            [
                1.8553907971855875e-07,
                8.315281267882195e-07,
                3.927862470905692e-07,
                1.9947304348862686e-06,
                4.450852111148132e-07,
                5.04347468323289e-07,
                1.6373770576776313e-07,
                8.315280276626197e-07,
                1.637376862489725e-07,
                2.2603242978871282e-06
            ],
            [
                7.734428685047173e-08,
                3.9278634073732336e-07,
                0.9998601779435066,
                1.8553905760062447e-07,
                1.046740792423576e-08,
                2.5110005893648856e-08,
                0.9999785550541535,
                1.1253526937697666e-07,
                6.475946438055299e-07,
                2.511001487368099e-08
            ],
            [
                0.9998415638034883,
                1.7603425837903113e-06,
                1.725784003388814e-08,
                4.691167157146029e-08,
                3.927862939136532e-07,
                0.9999957771670598,
                1.8553905760062447e-07,
                1.275190124842887e-07,
                6.825606978822427e-08,
                4.139934586278605e-08
            ],
            [
                2.5612819053166966e-06,
                5.043475885674441e-07,
                4.450851049959619e-07,
                4.450851580555361e-07,
                1.8553910183607374e-07,
                2.3823685319244518e-07,
                6.475949525981759e-07,
                6.47594798194325e-07,
                5.715003107738556e-07,
                4.450848927650143e-07
            ],
            [
                1.3709567165530083e-06,
                1.6373762769138607e-07,
                3.059022269250683e-07,
                2.699578740011634e-07,
                5.043474683204221e-07,
                0.9999952149066468,
                1.8553910183674878e-07,
                1.8553910183674878e-07,
                6.475947210012481e-07,
                0.9999832985761876
            ],
            [
                8.315282259009745e-07,
                0.9999756997680022,
                0.99991518898974,
                0.9999546021477018,
                6.825608606172863e-08,
                0.9999970976876695,
                0.9999952149060766,
                NaN,
                3.9278634072580244e-07,
                2.1024326584639497e-07
            ],
            [
                0.9999930377437549,
                1.4449803818215767e-07,
                5.3157837044597743e-08,
                8.764242227418718e-08,
                3.7266383955882547e-06,
                3.927862002641863e-07,
                3.05902336324494e-07,
                1.2098662604192665e-06,
                1.8553907971879076e-07,
                0.999989870010236
            ],
            [
                6.825608606172863e-08,
                3.4663249714612693e-07,
                3.653484693415755e-08,
                5.3157811697009444e-08,
                1.2751902768612997e-07,
                3.224189323773857e-08,
                2.5612819054028872e-06,
                3.059021175261338e-07,
                1.4449796928021588e-07,
                3.653485564473625e-08
            ],
            [
                6.023571320847322e-08,
                9.422442569315887e-07,
                9.931187406410953e-08,
                1.1253509497883659e-07,
                4.450852641737424e-07,
                5.043475284468537e-07,
                7.889264466868659e-06,
                0.9999546021477292,
                1.1253516205489029e-07,
                7.889266347715168e-06
            ],
            [
                0.9999952149066489,
                0.9999687980998273,
                0.9999921107355375,
                0.9999952149043662,
                0.9999910603015718,
                0.9999985406236053,
                0.9999974387184007,
                5.715003107767143e-07,
                1.4449800373118268e-07,
                8.764254764780641e-08
            ],
            [
                0.9999910603015673,
                0.9999832985781686,
                0.9999485577618699,
                0.9999546021314538,
                2.511001487368099e-08,
                4.691167157146029e-08,
                0.999983298574185,
                0.9999785550541648,
                0.9999898700114412,
                0.9999038976198842
            ],
            [
                1.2751901248454963e-07,
                0.9999810748518133,
                5.315781803390236e-08,
                5.315789407685159e-08,
                1.0677026154827912e-06,
                3.466325797896173e-07,
                8.764241182641775e-08,
                1.855391239544352e-07,
                0.9999339478399807,
                1.8553910183674878e-07
            ],
            [
                5.315787506612373e-08,
                0.9999892166903606,
                7.734416698849138e-08,
                1.5534981249697903e-06,
                0.9999967112509355,
                1.855391239547094e-07,
                0.999941708706721,
                2.8453357455950862e-08,
                9.422443692574719e-07,
                7.338208055680009e-07
            ],
            [
                1.0677028700422047e-06,
                0.999983298574185,
                1.6373766672973748e-07,
                0.9999546021422797,
                2.102433660979124e-07,
                4.539785241676547e-05,
                1.1253521571603583e-07,
                0.9998415637277122,
                2.3823690999236795e-07,
                0.9999916019289705
            ],
            [
                0.9999646437409275,
                0.9999151889185262,
                2.382370235933104e-07,
                9.931187406410953e-08,
                4.4508515805735777e-07,
                0.9999339478713157,
                5.715005832886879e-07,
                9.931202796993203e-08,
                3.0590226339061185e-07,
                1.8553910183607374e-07
            ],
            [
                0.9999869928653669,
                0.999997739676511,
                1.553498495338299e-06,
                1.473897845457507e-05,
                5.04347648686092e-07,
                3.466325384661554e-07,
                1.0677029972920738e-06,
                2.10243290909724e-07,
                0.9999970976880169,
                1.0677027427471959e-06
            ],
            [
                0.99987660539665,
                0.9998911030520646,
                2.3823693839290317e-07,
                0.9999339478791537,
                6.825600469412533e-08,
                4.1399400149893274e-08,
                2.699578096403948e-07,
                0.9999724643056498,
                9.422444815495185e-07,
                1.4449798650569826e-07
            ],
            [
                6.82560779249779e-08,
                2.8453360847853877e-08,
                2.8453371023563735e-08,
                8.7642526752214e-08,
                2.9023119851781017e-06,
                2.561282210740037e-06,
                4.139941495546278e-08,
                1.7257837976594428e-08,
                1.955569236151977e-08,
                4.139941495546278e-08
            ],
            [
                3.4663253846718004e-07,
                9.93120161310289e-08,
                6.825600469412533e-08,
                3.224185480240153e-08,
                2.1024339116168358e-07,
                0.9997965731006301,
                8.764245361752286e-08,
                1.8553914607237736e-07,
                6.825606978822427e-08,
                1.1253513522447425e-07
            ],
            [
                2.10243290909724e-07,
                2.2603245673443566e-06,
                3.4663278639892215e-07,
                2.699577130960941e-07,
                7.338209805240734e-07,
                1.760343003481596e-06,
                1.7603425837903113e-06,
                4.4508510499849186e-07,
                3.059022269250683e-07,
                1.0677027427624903e-06
            ],
            [
                4.450848927650143e-07,
                1.4449805540763184e-07,
                1.444979692800516e-07,
                9.422442569315887e-07,
                9.931189774187203e-08,
                1.0677032518578904e-06,
                7.338210680021253e-07,
                1.2098661162056318e-06,
                8.764244316973974e-08,
                1.6373766672973748e-07
            ],
            [
                7.338208930265102e-07,
                4.691168275606451e-08,
                5.3157887739943563e-08,
                1.6373766672973748e-07,
                1.4738987243692646e-05,
                3.927861066170637e-07,
                9.931187406410953e-08,
                1.6373772528704005e-07,
                4.450852641737424e-07,
                1.2751908849167202e-07
            ],
            [
                1.4449796928021588e-07,
                1.994729721518893e-06,
                9.610238067382736e-05,
                8.764242227418718e-08,
                1.1253509497883659e-07,
                2.10243290909963e-07,
                7.338207180898968e-07,
                1.3709575336654889e-06,
                6.475947982037486e-07,
                4.450849988811838e-07
            ],
            [
                4.222834954801051e-06,
                1.5534971990169383e-06,
                1.4449805540763184e-07,
                7.734423152941018e-08,
                2.699578096403948e-07,
                7.338212429582604e-07,
                2.1024341622426268e-07,
                2.6995774527718623e-07,
                6.825608606172863e-08,
                4.691162124067829e-08
            ],
            [
                1.6373770576776313e-07,
                1.1253525596174225e-07,
                2.6995774527718623e-07,
                2.382370235933104e-07,
                9.931202796993203e-08,
                5.3157830707696514e-08,
                4.139934586278605e-08,
                1.6373772528704005e-07,
                6.023578501513224e-08,
                4.139940508508409e-08
            ],
            [
                1.3709573702856596e-06,
                6.475947209918244e-07,
                1.7603430034867993e-06,
                4.450848927658745e-07,
                1.855391239547094e-07,
                7.734424996987981e-08,
                4.691160446380562e-08,
                1.855390576008354e-07,
                1.3709567165579959e-06,
                3.466325797900508e-07
            ],
            [
                1.2098659719757836e-06,
                1.2751901248454963e-07,
                6.605212107553962e-05,
                1.209865827752005e-06,
                1.994729008151319e-06,
                9.931185038635267e-08,
                3.059022269250683e-07,
                2.902312331170226e-06,
                3.7266379514061143e-06,
                0.9999151889794307
            ],
            [
                9.422443692555439e-07,
                0.999985261011009,
                1.8925143729954285e-05,
                1.855391239544352e-07,
                9.422448185478557e-07,
                1.994729483729522e-06,
                1.637377057680051e-07,
                3.4663278639892215e-07,
                3.059022269250683e-07,
                9.422442569334097e-07
            ],
            [
                2.5612828213934817e-06,
                1.5534973842030142e-06,
                1.6373776432509826e-07,
                2.6995768091310296e-07,
                2.102434412875379e-07,
                1.0677032518814388e-06,
                5.043472879525233e-07,
                2.5612825160562587e-06,
                1.2751899728311609e-07,
                1.1253516205489029e-07
            ],
            [
                0.9998601778763104,
                0.9999885212359866,
                0.999290329714045,
                0.9999832985801618,
                3.7266383956509585e-06,
                0.9999852610110108,
                4.139935079796334e-08,
                7.73442776303243e-08,
                0.9999724642990885,
                4.4508515805735777e-07
            ],
            [
                5.315787506612373e-08,
                6.825606165129312e-08,
                1.4449798650551755e-07,
                2.382370235933104e-07,
                6.825598028392069e-08,
                8.764241182641775e-08,
                0.9998766053673042,
                3.726638839878908e-06,
                0.9999756997651071,
                7.734428685047173e-08
            ],
            [
                7.734428685047173e-08,
                0.9999546021265188,
                2.1024334103581732e-07,
                4.691161005609407e-08,
                0.9999339478241472,
                2.215950249040774e-08,
                2.5110002900304575e-08,
                2.2159505132025125e-08,
                3.224189323773857e-08,
                0.9999852610110133
            ],
            [
                3.927862470899887e-07,
                2.5612822106654943e-06,
                2.1024344128660572e-07,
                6.023573475041126e-08,
                1.5534983101478522e-06,
                8.315282259009745e-07,
                2.5612834320214477e-06,
                4.691162683297406e-08,
                1.444979692787374e-07,
                9.422443692489024e-07
            ],
            [
                0.9999151889590318,
                1.3007123813559956e-05,
                9.422448185435711e-07,
                6.475950297971703e-07,
                3.7266410611465547e-06,
                4.450849988798682e-07,
                1.3709572068522336e-06,
                3.927862002663297e-07,
                6.023569166654288e-08,
                5.315780536011123e-08
            ],
            [
                2.1024334103505245e-07,
                4.222834451403972e-06,
                7.338213304283347e-07,
                2.5612828213934817e-06,
                2.561282210701601e-06,
                3.0590226339061185e-07,
                2.6995774527577444e-07,
                5.043474683220276e-07,
                1.1253524254650944e-07,
                6.825601283086733e-08
            ],
            [
                1.6373772528704005e-07,
                9.931193325852072e-08,
                0.9999599363222613,
                4.450848927650143e-07,
                3.0590237279085045e-07,
                0.9999994631248041,
                5.315780536011123e-08,
                5.315786239218605e-08,
                7.734423152941018e-08,
                1.6373776432509826e-07
            ],
            [
                8.315277302788957e-07,
                1.0677028700266676e-06,
                3.9278629391427843e-07,
                1.1253516205489029e-07,
                1.5534975693979422e-06,
                1.7603425837903113e-06,
                5.043472278322555e-07,
                2.753570421361326e-05,
                1.0677032518748838e-06,
                1.209865539298447e-06
            ],
            [
                1.1253506814842375e-07,
                1.5229990406090843e-08,
                0.9999967112505435,
                3.653479467066246e-08,
                0.9999910603036973,
                2.382369951932796e-07,
                0.9999982396561573,
                9.422445939002803e-07,
                0.9999599362984612,
                3.2241847115356483e-08
            ],
            [
                1.6373762769187936e-07,
                9.931202796993203e-08,
                0.9999785550567114,
                2.2159473432612064e-08,
                1.855391681906175e-07,
                3.2241889394209404e-08,
                3.0590215399183813e-07,
                6.023569884718319e-08,
                2.1024344128660572e-07,
                0.9999885212318786
            ],
            [
                0.9999339478714055,
                5.043473480777865e-07,
                1.9947292459406333e-06,
                7.734421308914719e-08,
                7.338210680021253e-07,
                0.9999885212318821,
                4.139935079796334e-08,
                1.5534979397790343e-06,
                5.043473480777865e-07,
                2.1024336609843824e-07
            ],
            [
                0.9999869928684486,
                0.9999687980924351,
                0.9999869928700097,
                0.9999983463102173,
                0.9999970976883616,
                0.9999724643187743,
                8.764253720001207e-08,
                0.9999646437452351,
                0.9999982396563671,
                2.5110011880337063e-08
            ],
            [
                1.6373766672973748e-07,
                8.764241182641775e-08,
                0.99998987000541,
                4.785094494811783e-06,
                1.1253508156363576e-07,
                5.315780536011123e-08,
                4.691162124067829e-08,
                NaN,
                2.699577452775239e-07,
                3.2241839428313264e-08
            ],
            [
                9.931185038635267e-08,
                2.561283126728994e-06,
                6.023568448589658e-08,
                1.0677033791630344e-06,
                5.422220909041528e-06,
                1.1253513522447425e-07,
                1.760343633036322e-06,
                4.1399375473868e-08,
                3.927861066194751e-07,
                1.9947304348862686e-06
            ],
            [
                2.144494074201677e-05,
                2.5612815999423112e-06,
                0.9998415638425935,
                0.9998766054712779,
                9.4224425692559e-07,
                0.9999843104446833,
                2.9023123310290063e-06,
                0.999447221287987,
                0.9999667857934675,
                0.9998601778607799
            ],
            [
                1.2098658277451275e-06,
                3.9278605979534166e-07,
                1.444980209564556e-07,
                9.422444815814404e-07,
                5.422219616228845e-06,
                2.6995774527577444e-07,
                1.2751899728311609e-07,
                3.466325797896173e-07,
                1.6373764721072816e-07,
                0.9998415637275554
            ],
            [
                3.05902190458764e-07,
                4.450852641737424e-07,
                1.8553905760062447e-07,
                1.4449803818215767e-07,
                1.8553903548231313e-07,
                1.760343003481596e-06,
                5.043476486915964e-07,
                2.215950249040774e-08,
                2.6995774527657245e-07,
                3.059021175261338e-07
            ],
            [
                9.422444815814404e-07,
                1.5534973842076057e-06,
                5.043475284430694e-07,
                3.059022998576899e-07,
                6.475948754012522e-07,
                3.4663266243308805e-07,
                1.855391239544352e-07,
                8.764242227418718e-08,
                0.9999810748427528,
                3.2887506336235617e-06
            ],
            [
                4.139941002027314e-08,
                2.1024339116082313e-07,
                9.422448185435711e-07,
                1.3709568799919866e-06,
                2.3823702359290413e-07,
                7.734418542875216e-08,
                7.734416698849138e-08,
                5.715004470313855e-07,
                1.6373764721091427e-07,
                2.8453371023563735e-08
            ],
            [
                6.825598842065202e-08,
                1.6373770576776313e-07,
                5.043474081993875e-07,
                1.3709575336947905e-06,
                3.9278634072866033e-07,
                4.222832940646604e-06,
                1.5534975693792215e-06,
                1.0677028699955933e-06,
                3.7266401726359486e-06,
                2.699578418172324e-07
            ],
            [
                1.275191036933194e-07,
                7.338207180801359e-07,
                0.9999898700054036,
                2.1024334103581732e-07,
                1.1253525596174225e-07,
                1.7603432133032607e-06,
                5.715002426460124e-07,
                3.9278634073732336e-07,
                0.9999921107374171,
                7.734418542875216e-08
            ],
            [
                6.962256249821764e-06,
                1.2098656835224664e-06,
                1.2098656835224664e-06,
                7.338208930391909e-07,
                5.422217030747413e-06,
                2.6995790618469934e-07,
                6.475949525919915e-07,
                5.043476486902204e-07,
                1.2098653950656417e-06,
                1.5534983101393749e-06
            ],
            [
                5.04347287955046e-07,
                5.043476486915964e-07,
                3.059022998581767e-07,
                1.444979692800516e-07,
                5.04347287955046e-07,
                1.4449807263312446e-07,
                4.691159887151251e-08,
                1.2751904288739315e-07,
                2.3823696679327928e-07,
                9.931200429212718e-08
            ],
            [
                5.715003107767143e-07,
                0.9997965731025479,
                0.9999687980775263,
                3.05902190458764e-07,
                1.1253512180925583e-07,
                4.450850519403407e-07,
                1.275190428875671e-07,
                1.0677033791437343e-06,
                2.3823690999323465e-07,
                2.3823693839325527e-07
            ],
            [
                5.043474081993875e-07,
                0.9999485577618527,
                0.9999724642958001,
                2.260325106237323e-06,
                3.927862002663297e-07,
                4.691160446380562e-08,
                2.6995774527718623e-07,
                0.9999339478476429,
                2.9023112932177327e-06,
                2.6995784182140636e-07
            ],
            [
                8.315279285251204e-07,
                2.2603251061458426e-06,
                7.338207180801359e-07,
                3.466327037539638e-07,
                1.209866116170145e-06,
                6.475947981975644e-07,
                6.475948753930064e-07,
                7.338210679816025e-07,
                1.2098652508287273e-06,
                3.7266401724291984e-06
            ],
            [
                9.93120161310289e-08,
                0.9999756997505957,
                4.222833948008874e-06,
                5.315789407685159e-08,
                0.9998766054257715,
                0.9997694932595356,
                5.715006514176113e-07,
                1.0677033791630344e-06,
                3.466327037553825e-07,
                1.855390576008354e-07
            ],
            [
                6.023572038912295e-08,
                8.764245361752286e-08,
                1.2751908849167202e-07,
                2.1024336609843824e-07,
                2.6995768091383957e-07,
                1.1253506814842375e-07,
                3.466327037539638e-07,
                1.1253506814842375e-07,
                7.734415776836702e-08,
                3.653482080235082e-08
            ],
            [
                2.1024339116082313e-07,
                1.855390576008354e-07,
                1.5534979397740895e-06,
                3.059021175261338e-07,
                1.5229988590535506e-08,
                2.8453371023563735e-08,
                1.8553907971855875e-07,
                6.023578501513224e-08,
                8.764254764780641e-08,
                2.5110002900304575e-08
            ],
            [
                2.845337441546675e-08,
                0.9999982396561572,
                0.9998601779771695,
                1.7257844148474332e-08,
                6.825598028392069e-08,
                0.9999984465020604,
                1.2098656835252174e-06,
                3.224185480240153e-08,
                6.023569884718319e-08,
                1.5534981249697903e-06
            ],
            [
                0.9999945777797387,
                6.023579219579052e-08,
                3.0590237279032884e-07,
                0.999999057755294,
                8.764242227418718e-08,
                0.9999646437535655,
                6.825597214718257e-08,
                5.3157900413760374e-08,
                5.315788140303327e-08,
                8.7642516304188e-08
            ],
            [
                0.9999756997650937,
                3.224189323773857e-08,
                7.73442776303243e-08,
                1.6373774480605869e-07,
                8.764254764780641e-08,
                0.9999785550541627,
                0.9999925887183683,
                0.9999832985761973,
                6.825598842065202e-08,
                6.023578501513224e-08
            ],
            [
                1.9555664386890228e-08,
                4.139941495546278e-08,
                0.9999546021477371,
                0.999925153737218,
                0.9999916019249682,
                6.023579219579052e-08,
                0.99999844650169,
                1.9555687699082254e-08,
                0.9999962733611613,
                8.764245361752286e-08
            ],
            [
                1.0677033791630344e-06,
                3.927863407379485e-07,
                2.6995790618469934e-07,
                1.7603440527334603e-06,
                6.023574911170301e-08,
                3.653479467066246e-08,
                6.023578501513224e-08,
                5.315789407685159e-08,
                8.764245361752286e-08,
                4.691162124067829e-08
            ],
            [
                5.315781803390236e-08,
                5.04347287955046e-07,
                3.9278634073732336e-07,
                1.2751902768612997e-07,
                4.139936066832438e-08,
                0.9999960330126674,
                7.338209805200689e-07,
                1.8553919030858602e-07,
                8.764242227418718e-08,
                0.9999986290426298
            ],
            [
                3.059022998576899e-07,
                0.00020342704642313173,
                1.7603436330179102e-06,
                0.9996646500196891,
                8.315277302788957e-07,
                0.9999724643154996,
                1.4449803818215767e-07,
                2.102434162245973e-07,
                1.275190580890061e-07,
                2.699576809143613e-07
            ],
            [
                5.715005832853093e-07,
                5.715005832853093e-07,
                1.3709576971425944e-06,
                1.0677024881980089e-06,
                1.760344052714248e-06,
                7.338209805224048e-07,
                1.3709573702647743e-06,
                1.5534971990126997e-06,
                1.5534977545886537e-06,
                5.043476486915964e-07
            ],
            [
                0.9999957771680668,
                4.691160446380562e-08,
                3.224185480240153e-08,
                2.5110011880337063e-08,
                3.653485564473625e-08,
                3.653485128944664e-08,
                3.0590237279032884e-07,
                1.1253521571603583e-07,
                4.691167157146029e-08,
                1.522998677498039e-08
            ],
            [
                5.043472278280699e-07,
                2.2603248367358324e-06,
                4.450851580555361e-07,
                9.422444815726566e-07,
                4.450851580555361e-07,
                8.315280276580819e-07,
                4.450849988811838e-07,
                5.715003107755449e-07,
                5.715002426439334e-07,
                1.0129993395336818e-05
            ],
            [
                1.2751908849167202e-07,
                1.1253506814842375e-07,
                0.9995121427698441,
                3.0590237279032884e-07,
                1.3709570434178922e-06,
                1.637376862489725e-07,
                7.338212429582604e-07,
                1.1253513522447425e-07,
                3.9278615344178325e-07,
                4.222834451403972e-06
            ],
            [
                2.10243290909724e-07,
                9.93120161310289e-08,
                0.9999724643056397,
                5.715003789033962e-07,
                3.466327037548308e-07,
                0.9999546021151863,
                1.8553905760062447e-07,
                0.99992515375513,
                5.715005151606823e-07,
                0.9999151889589996
            ],
            [
                6.144173869502757e-06,
                6.475949525981759e-07,
                2.382368531929327e-07,
                1.4449798650551755e-07,
                0.9999898700078214,
                0.9999916019239675,
                1.4449803818215767e-07,
                0.9999904837483131,
                0.999986153992153,
                1.8553919030858602e-07
            ],
            [
                3.927863407379485e-07,
                2.1024339116168358e-07,
                1.370956716529941e-06,
                2.699578740032504e-07,
                7.734424996967756e-08,
                0.9999934595596576,
                1.4449800373118268e-07,
                1.2098659719441482e-06,
                6.023572038912295e-08,
                1.8553905760062447e-07
            ],
            [
                2.1024336609843824e-07,
                2.10243290909724e-07,
                0.9999687980812412,
                3.927863875616689e-07,
                4.450852111155216e-07,
                3.05902263391829e-07,
                8.315278294114555e-07,
                3.9278629391427843e-07,
                2.699578096393206e-07,
                9.931186222523604e-08
            ],
            [
                5.4222183235249605e-06,
                5.715006514176113e-07,
                2.2159497207173906e-08,
                NaN,
                6.825598842065202e-08,
                1.9555687699082254e-08,
                0.9997040429012288,
                4.691167157146029e-08,
                0.9770226315535094,
                1.1253508156363576e-07
            ],
            [
                1.994729483705484e-06,
                6.47595107001401e-07,
                3.0590226339061185e-07,
                1.8553916819032217e-07,
                7.734416698849138e-08,
                8.764249540862797e-08,
                2.3823699519225038e-07,
                1.8553903548231313e-07,
                1.2751901248391176e-07,
                3.9278615344178325e-07
            ],
            [
                0.9999852610127715,
                0.9999687980923908,
                8.764242227418718e-08,
                7.734428685047173e-08,
                0.9999756997622059,
                0.9999546021152134,
                1.5534981249736758e-06,
                9.422450432030903e-07,
                7.734426841017797e-08,
                4.2228339479858295e-06
            ],
            [
                2.1024341622426268e-07,
                2.3823688159291947e-07,
                7.734415776836702e-08,
                1.1253525596174225e-07,
                7.3382080556433e-07,
                4.4508494582314646e-07,
                8.315282259051341e-07,
                4.691162124067829e-08,
                0.9999810748472581,
                6.023568448589658e-08
            ],
            [
                5.043473480777865e-07,
                5.715002426475718e-07,
                0.9997040428736222,
                1.2098653950692178e-06,
                6.475949526020042e-07,
                1.1253526937697666e-07,
                1.99473067264854e-06,
                5.715005151606823e-07,
                1.3709567165579959e-06,
                3.653485128944664e-08
            ],
            [
                1.4449805540740185e-07,
                3.466325797888292e-07,
                1.855391239544352e-07,
                1.0677033791437343e-06,
                0.9999646437535583,
                2.6995774527577444e-07,
                1.6373764721072816e-07,
                2.561283432005142e-06,
                1.6373774480535133e-07,
                4.4508494582405734e-07
            ],
            [
                9.931189774187203e-08,
                2.69957906184239e-07,
                1.855391239544352e-07,
                8.315282259138311e-07,
                6.825608606172863e-08,
                0.9999485577742782,
                2.3823685319244518e-07,
                3.9278615344178325e-07,
                1.27519088491875e-07,
                0.9999485577864431
            ],
            [
                1.855391239544352e-07,
                1.0677028700130727e-06,
                1.1253508156363576e-07,
                NaN,
                3.05902336324494e-07,
                3.466326624336003e-07,
                1.0677028700363782e-06,
                8.315284241560147e-07,
                1.3709575337159875e-06,
                1.6373776432509826e-07
            ],
            [
                8.764253720001207e-08,
                2.7535704229340197e-05,
                2.1024326584702836e-07,
                0.9999987121049382,
                0.9999949062937851,
                0.9999724643056775,
                6.825609419848033e-08,
                6.023569884718319e-08,
                0.999986992866902,
                0.9999978766205255
            ],
            [
                0.9999967112509354,
                2.699578740032504e-07,
                8.315277302747361e-07,
                8.764245361752286e-08,
                1.2098662604049616e-06,
                1.4449805540763184e-07,
                1.067703124601679e-06,
                5.04347468323289e-07,
                2.1024336609843824e-07,
                3.6534807736504303e-08
            ],
            [
                7.734416698849138e-08,
                2.2159499848790667e-08,
                1.9947299592933255e-06,
                6.023578501513224e-08,
                0.9999687980923566,
                0.9999885212359819,
                1.9555685367863357e-08,
                5.3157811697009444e-08,
                4.691160446380562e-08,
                3.927863407379485e-07
            ],
            [
                1.3709572068553509e-06,
                NaN,
                6.825597214718257e-08,
                4.450852641737424e-07,
                1.3709573702856596e-06,
                2.699577774589574e-07,
                2.3823685319244518e-07,
                1.760343633036322e-06,
                1.0677033791630344e-06,
                1.855391681906175e-07
            ],
            [
                0.9999546021098811,
                3.466325797888292e-07,
                4.691159887151251e-08,
                0.9999852610197949,
                1.5534981249736758e-06,
                4.4508515805735777e-07,
                3.9278605979534166e-07,
                2.2603242978943238e-06,
                9.610239212762526e-05,
                0.9997965729312374
            ],
            [
                1.444979692800516e-07,
                1.0677024881980089e-06,
                0.9999339478240948,
                9.931193325852072e-08,
                3.0590226339137693e-07,
                0.9999251537463113,
                2.5612822106654943e-06,
                8.315279284937352e-07,
                9.42244930862237e-07,
                0.9999038975968478
            ],
            [
                0.99999709768767,
                0.9999970976890531,
                3.22418970812682e-08,
                0.9999910603036999,
                4.139941495546278e-08,
                8.315281267882195e-07,
                2.5110011880337063e-08,
                0.999996711251327,
                0.9999756997477157,
                3.927861066170637e-07
            ],
            [
                8.939693105662367e-06,
                2.382370235922541e-07,
                0.9999687980849624,
                0.9999038975398333,
                4.4508505193791187e-07,
                9.931195693628605e-08,
                8.31527730252048e-07,
                1.1478770858372173e-05,
                1.9947306726213275e-06,
                1.9947306726213275e-06
            ],
            [
                2.561282210562998e-06,
                2.3823693839290317e-07,
                6.962259569117366e-06,
                9.931193325852072e-08,
                3.4663266243308805e-07,
                4.7850933534310035e-06,
                8.315280276626197e-07,
                8.315279285251204e-07,
                7.734415776836702e-08,
                1.7603432133296774e-06
            ]
        ]
    },
    {
        "q_id": "9631_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                5.715005832886879e-07,
                2.6995784182140636e-07,
                3.7266406168827523e-06,
                8.315281267882195e-07,
                5.043476486915964e-07,
                1.760343633031919e-06,
                3.726637951387472e-06,
                1.2098656835224664e-06,
                5.715005832886879e-07,
                8.315279285351409e-07
            ],
            [
                9.422448185534261e-07,
                4.4508494582405734e-07,
                1.9947297215125433e-06,
                2.1024331597262577e-07,
                5.715004470313855e-07,
                0.999999168471973,
                2.5612819054133693e-06,
                6.475949526020042e-07,
                1.3709572068522336e-06,
                3.726638395634011e-06
            ],
            [
                0.999998863436426,
                0.999998932297513,
                0.9999988634358838,
                0.9999991148433872,
                0.9999970976869823,
                0.9999942280772338,
                0.9999991148431762,
                0.9999985406236068,
                0.9999991684719732,
                0.9999991684717751
            ],
            [
                0.9999989969862721,
                0.999999266178933,
                0.9999987901341744,
                0.9999989322975144,
                0.9999985406243018,
                0.9999989322966232,
                0.999999114843282,
                0.9999988634360208,
                0.9999992661791952,
                0.9999987121047863
            ],
            [
                0.999998932296623,
                0.9999983463096305,
                0.999994906295621,
                0.9999983463104188,
                0.9999984465016934,
                0.9999986290421433,
                0.9999983463100244,
                0.9999987121041737,
                0.9999988634366982,
                0.9999975938982412
            ],
            [
                9.422448185534261e-07,
                1.6373766672973748e-07,
                1.9947304348862686e-06,
                1.444979692800516e-07,
                1.8553905760062447e-07,
                4.2228319344021954e-06,
                5.04347287955046e-07,
                4.450850519403407e-07,
                9.931202796993203e-08,
                1.8553905760062447e-07
            ],
            [
                5.71500515159253e-07,
                1.855391239544352e-07,
                3.0590215399183813e-07,
                2.382370235933104e-07,
                2.3823690999290963e-07,
                5.04347528446051e-07,
                2.10243290909724e-07,
                2.382369667929001e-07,
                3.0590237279032884e-07,
                2.3823685319244518e-07
            ],
            [
                0.9999991148428603,
                0.9999992661788455,
                0.9999991148426486,
                0.9999952149032375,
                0.9999986290426328,
                0.9999989322971311,
                0.9999987901340294,
                0.9999975938965169,
                0.999999114842966,
                0.9999989322973857
            ],
            [
                0.9999992188516702,
                0.9999994284993493,
                0.9999993524048937,
                0.9999992188513908,
                0.999999310638791,
                0.9999972735307071,
                0.9999993106387086,
                0.9999993524052023,
                0.9999975938985237,
                0.9999991148428601
            ],
            [
                1.8553905760024476e-07,
                1.637377643243723e-07,
                1.3709578605729614e-06,
                5.043473480766399e-07,
                1.637377057673536e-07,
                1.067703124601679e-06,
                3.059021904571643e-07,
                6.475945666033422e-07,
                1.8553907971813685e-07,
                1.8553907971813685e-07
            ],
            [
                5.043476486915964e-07,
                7.338212429582604e-07,
                8.315279285351409e-07,
                5.043472879540142e-07,
                1.209865539295696e-06,
                4.450848927650143e-07,
                2.5612819054133693e-06,
                3.0590215399183813e-07,
                2.6995774527718623e-07,
                1.444980209564556e-07
            ],
            [
                0.9999995549151075,
                0.9999996072138,
                0.9999994284997579,
                0.9999981261250649,
                0.9999982396559487,
                0.9999995818814267,
                0.9999993524050479,
                0.9999996072136595,
                0.9999991684717747,
                0.9999994284994853
            ],
            [
                0.9999930377404432,
                0.9999974387165725,
                0.9999989969857934,
                0.9999974387177912,
                0.9999990577557444,
                0.999993459560447,
                0.9999986290426311,
                0.9999974387171822,
                0.9999969105062928,
                0.9999987901344625
            ],
            [
                0.9999996072139404,
                0.9999998024945861,
                0.9999994631247403,
                0.9999992188512975,
                0.9999992661786699,
                0.9999995549147891,
                0.9999994956526521,
                0.9999987121043248,
                0.9999997761970782,
                0.9999998362623529
            ],
            [
                0.9999991148429652,
                0.9999975938970888,
                0.9999991684718745,
                0.999999310639202,
                0.999998446501692,
                0.9999930377421065,
                0.9999992661791955,
                0.9999991148426486,
                0.9999955048168206,
                0.9999989969855541
            ],
            [
                6.962255419868303e-06,
                3.288749457469787e-06,
                5.422217030707961e-06,
                3.2887502415438413e-06,
                0.9999921107346244,
                8.481103128838341e-05,
                2.1444958640087166e-05,
                5.4222183234485234e-06,
                3.5356267573959116e-05,
                1.3007131566015624e-05
            ],
            [
                1.2098652508424818e-06,
                1.6373776432509826e-07,
                1.5534983101602148e-06,
                9.422447062294175e-07,
                2.382369667929001e-07,
                4.4508494582314646e-07,
                6.962256249885085e-06,
                7.889260704968913e-06,
                6.144176066901277e-06,
                7.889265407327733e-06
            ],
            [
                2.7535704232595768e-05,
                2.699577774585891e-07,
                2.430024652792821e-05,
                0.0004878571799743534,
                5.422220909009474e-06,
                0.9999972735294055,
                5.043476486915964e-07,
                1.3709567165579959e-06,
                7.338210680021253e-07,
                4.785094494783494e-06
            ],
            [
                0.9999988634357481,
                0.9999987121050925,
                0.9999969105044534,
                0.9999996310116359,
                0.9999987121041715,
                0.9999990577551824,
                0.9999980052707557,
                0.9999992188514839,
                0.999998932296876,
                0.9999989969855544
            ],
            [
                0.9999296881251298,
                0.999195913928842,
                0.9999985406230838,
                1.670142980893658e-05,
                2.3823690999063455e-07,
                0.9999964991468401,
                2.6995771309523475e-07,
                0.9999995549150015,
                0.9999984465026174,
                0.999999114842965
            ],
            [
                1.3709578605729614e-06,
                5.715005151574337e-07,
                0.9999852610180913,
                0.9999942280813576,
                1.0677026154774503e-06,
                1.209865683518615e-06,
                2.2603251062270446e-06,
                0.9999934595612505,
                0.00020342692517810748,
                9.422450431989127e-07
            ],
            [
                0.9999938558232113,
                0.9999989322968771,
                0.9999964991447562,
                0.9999987901338857,
                0.9999957771655632,
                0.9999981261237254,
                0.9999985406232598,
                0.9999989322967495,
                0.9999955048168292,
                0.9999972735284329
            ],
            [
                1.0677033791495609e-06,
                0.999995214904941,
                6.144174601991196e-06,
                1.3709570434178922e-06,
                0.9999986290427952,
                4.222833947960866e-06,
                0.999998790134462,
                7.48462005189952e-05,
                0.9999938558254148,
                5.829124470847917e-05
            ],
            [
                0.9999989322972587,
                0.9999921107383782,
                0.9999984465018784,
                0.9999945777803929,
                0.9999982396569993,
                0.9999955048162916,
                0.9999969105044505,
                0.9999978766212871,
                0.9999969105066606,
                0.9999952149038003
            ],
            [
                1.2098659719757836e-06,
                3.059021175261338e-07,
                2.699577774585891e-07,
                1.6373770576776313e-07,
                2.10243290909724e-07,
                3.4663266243308805e-07,
                7.338212429582604e-07,
                3.9278610661902853e-07,
                5.715005151606823e-07,
                3.4663253846718004e-07
            ],
            [
                0.9999975938968035,
                0.9999687980740243,
                0.9999987121050942,
                3.927862470899887e-07,
                0.9999977396751663,
                0.9999980052709935,
                0.9999991148428593,
                0.9999992188519499,
                0.9999987901346067,
                0.9999989322975135
            ],
            [
                0.9999991148428597,
                0.9999930377437671,
                0.9999960330122017,
                0.9999987901341751,
                0.9999987121041737,
                0.9999964991455939,
                0.9999987901338858,
                0.9999977396759756,
                0.9999970976887139,
                0.9999962733611694
            ],
            [
                0.9999962733607239,
                0.9999982396574194,
                0.9999964991464273,
                0.9999910603047945,
                0.9999949062931827,
                0.9999964991447586,
                0.9999898700054292,
                0.9999925887166229,
                0.999996033013149,
                0.9999877809240245
            ],
            [
                0.9999986290427958,
                0.9999990577549578,
                0.9999987901341741,
                0.9999962733593895,
                0.9999987121041726,
                0.9999969105059261,
                0.9999991148430709,
                0.9999916019249785,
                0.9999978766223003,
                0.9999991684715771
            ],
            [
                1.0129993395217047e-05,
                6.9622587397397306e-06,
                7.88926446679691e-06,
                2.7535694384081332e-05,
                7.88926070489716e-06,
                2.7535681254804434e-05,
                1.994730672668496e-06,
                3.535626336072768e-05,
                3.535626757524533e-05,
                3.120191137659974e-05
            ],
            [
                0.9999985406243017,
                0.9999977396765122,
                0.9999960330136158,
                0.9999989322968763,
                0.999999057755744,
                0.9999972735290816,
                0.9999995262093859,
                0.999998005269329,
                0.9999996940978098,
                0.9999970976876712
            ],
            [
                6.962257079832313e-06,
                1.067703124601679e-06,
                9.422448185534261e-07,
                7.338212429582604e-07,
                1.0129992187253088e-05,
                3.726639284144195e-06,
                6.475947210046347e-07,
                6.962254589851619e-06,
                9.422449308774482e-07,
                5.04347468323289e-07
            ],
            [
                0.9999989322972588,
                0.9999981261250649,
                0.9999938558261424,
                0.9999969105040829,
                0.9999984465022475,
                0.9999967112513317,
                0.9999983463106126,
                0.9999982396561586,
                0.9999962733602755,
                0.9999975938985227
            ],
            [
                0.9999994631248046,
                0.9999962733602804,
                0.9999987901346066,
                0.9999983463104177,
                0.9999989322967495,
                0.9999980052709944,
                0.9999993524049712,
                1.1253506814797596e-07,
                5.422218969858371e-06,
                0.9999984465018764
            ],
            [
                0.9999996072137064,
                0.9999996533674617,
                0.9999995818810777,
                0.9999991148433867,
                0.9999989969861515,
                0.9999995549147891,
                0.9999991684719729,
                0.9999995262094423,
                0.9999989969856734,
                0.9999987901343173
            ],
            [
                1.2751905808881762e-07,
                0.9999989969859127,
                0.9999989322971308,
                8.7642516304188e-08,
                0.9999989322966215,
                0.9999989322973862,
                0.9999988634364259,
                0.9999996072138937,
                0.9999996743688976,
                1.4449798650551755e-07
            ],
            [
                0.9999980052707574,
                0.9999975938970893,
                0.9999985406230849,
                0.9999955048200379,
                0.9999980052705182,
                0.9999977396748959,
                0.9999984465020636,
                0.9999964991439229,
                0.9999967112521162,
                0.9999983463106124
            ],
            [
                1.994730434879465e-06,
                8.315281267861397e-07,
                1.5534975693933505e-06,
                1.994730197090463e-06,
                1.9947292459347367e-06,
                6.475951069985296e-07,
                3.927862002654366e-07,
                9.422450431989127e-07,
                3.059022998576899e-07,
                1.2098661162023305e-06
            ],
            [
                0.9999989969857934,
                0.999999266179108,
                0.9999974387168761,
                0.9999986290429582,
                0.9999984465022498,
                0.9999967112521143,
                0.9999987121044791,
                0.9999970976876729,
                0.9999985406241303,
                0.9999982396567924
            ],
            [
                0.9999993106387906,
                0.9999997126313098,
                0.9999982396565782,
                0.9999997126315499,
                0.9999989322975127,
                0.9999996940976638,
                0.9999989322967487,
                0.9999995549147892,
                0.9999989322968768,
                0.9999993106387906
            ],
            [
                2.3823693839290317e-07,
                2.3823688159291947e-07,
                1.1253516205489029e-07,
                1.275191036933194e-07,
                6.475949526003845e-07,
                1.8553903548231313e-07,
                2.1024339116134898e-07,
                2.3823702359290413e-07,
                9.93118503859575e-08,
                1.275190276859705e-07
            ],
            [
                0.9999995262094987,
                0.9999987901340298,
                0.9999991148433877,
                0.9999992661791952,
                0.9999982396572089,
                0.9999991684721714,
                0.999999428499758,
                0.9999991148428595,
                0.999999266179108,
                0.9999992188512984
            ],
            [
                2.5612812947240366e-06,
                5.422217030747413e-06,
                2.561282210729555e-06,
                3.927860597935108e-07,
                2.5612828213352452e-06,
                6.144175334418252e-06,
                1.3709573702822306e-06,
                6.96225873967641e-06,
                4.2228324377740105e-06,
                1.4738981972564636e-05
            ],
            [
                0.9999984465018767,
                0.9999967112493692,
                0.9999916019299804,
                0.9999987121043247,
                0.9999990577550701,
                0.9999993524052023,
                6.475946438055299e-07,
                0.9999992661791077,
                0.9999986290424686,
                0.999998932297004
            ],
            [
                2.2603242978871282e-06,
                3.05902190458764e-07,
                0.9999964991460073,
                9.422442569290178e-07,
                1.012999218776902e-05,
                0.9999978766220478,
                3.120190765625026e-05,
                1.8925152753790864e-05,
                0.9999949062938029,
                0.9999960330121979
            ],
            [
                0.9999970976880166,
                0.9999962733598313,
                0.9999969105062915,
                0.9999990577552946,
                0.999997876621034,
                0.9999934595651206,
                0.9999991684715768,
                0.9999964991468419,
                0.9999949062937875,
                0.9999945777810366
            ],
            [
                0.9999970976887146,
                0.9999938558268763,
                0.9999984465015092,
                0.9999984465026194,
                0.9999985406239558,
                0.9999986290423077,
                0.999994577779104,
                0.9999980052707602,
                0.9999955048200463,
                0.9999930377462624
            ],
            [
                0.9999978766207848,
                0.9999991684722708,
                0.9999975938968054,
                0.9999974387171843,
                0.9999985406234336,
                0.9999974387171847,
                0.9999938558261409,
                0.9999930377437658,
                0.9999984465026199,
                0.9999975938968059
            ],
            [
                7.338208930460318e-07,
                4.4508494582405734e-07,
                7.338208930460318e-07,
                0.9999972735294069,
                0.9999957771680701,
                7.338210680021253e-07,
                1.0677027427624903e-06,
                1.3709568799919866e-06,
                0.9999975938979495,
                0.999990483747186
            ],
            [
                8.315280276607289e-07,
                8.315284241650899e-07,
                0.9999994631250607,
                2.5612812947508257e-06,
                0.9999955048184309,
                2.9023112932177327e-06,
                0.99999787662078,
                3.0590226339061185e-07,
                0.9999972735284319,
                1.8553910183649565e-07
            ],
            [
                0.9999978766220454,
                0.9999972735300575,
                0.9999974387174896,
                0.9999989322973861,
                0.999995214906662,
                0.9999981261246191,
                0.999998446501878,
                0.9999975938979506,
                0.9999969105048216,
                0.999994906296827
            ],
            [
                0.9999977396754371,
                0.9999984465026176,
                0.9999997463981939,
                0.9999990577557439,
                0.9999962733598374,
                0.9999975938982361,
                0.9999955048173564,
                0.9999989969862723,
                0.9999992188519495,
                0.9999987901347505
            ],
            [
                0.9999977396757067,
                0.9999986290429578,
                0.9999964991447584,
                0.9999957771660578,
                0.9999984465018773,
                0.9999985406232594,
                0.999999114842754,
                0.9999925887228004,
                0.9999991148428601,
                0.9999983463096278
            ],
            [
                0.9999957771650592,
                0.9999986290423067,
                0.9999942280820495,
                0.9999964991464302,
                0.9999988634366982,
                0.9999952149066643,
                0.9999991148428603,
                0.9999955048162896,
                0.9999952149072254,
                0.9999974387171834
            ],
            [
                0.9999972735284313,
                0.9999955048173558,
                0.999999168471973,
                0.9999992661789325,
                0.9999957771645467,
                0.9999993916411813,
                0.9999989322975129,
                0.9999992188516699,
                0.999994228079294,
                0.9999993524053564
            ],
            [
                1.7603427936335396e-06,
                0.9999945777810377,
                5.422218969895357e-06,
                9.422447062294175e-07,
                0.999991060304779,
                1.9947304348862686e-06,
                1.3709567165617364e-06,
                2.561282516066741e-06,
                1.994729483723626e-06,
                2.260323758987159e-06
            ],
            [
                0.9999975938979521,
                0.9999962733598329,
                0.9999972735287591,
                0.9999957771650533,
                0.9999925887192567,
                0.9999985406237826,
                0.9999987901344624,
                0.9999984465016919,
                0.9999964991460084,
                0.9999975938970884
            ],
            [
                0.9999989969861521,
                0.9999975938979518,
                0.9999990577550701,
                0.9999989322975129,
                0.9999990577557434,
                0.9999981261252906,
                0.9999989969855549,
                0.9999989322967496,
                0.9999989969857935,
                0.9999992188519493
            ],
            [
                0.9999993106392017,
                0.9999992188513906,
                0.9999991148429651,
                0.9999962733593879,
                0.9999967112509419,
                0.9999985406236077,
                0.9999994631248045,
                0.9999993106386263,
                0.9999978766210343,
                0.9999985406237812
            ],
            [
                1.0677026154806063e-06,
                1.8553905760024476e-07,
                4.450848927650143e-07,
                3.9278634073732336e-07,
                2.1024329090867228e-07,
                2.69957906184239e-07,
                4.4508494582405734e-07,
                2.3823690999290963e-07,
                9.422442569315887e-07,
                2.102434412871794e-07
            ],
            [
                0.9999993106391197,
                0.9999986290426311,
                0.999999114842965,
                0.9999964991451747,
                0.9999985406243033,
                0.9999994631249967,
                0.9999986290424683,
                0.9999991684720726,
                0.999997273530383,
                0.9999984465020624
            ],
            [
                0.9999967112513297,
                0.999999607213753,
                0.9999997463982241,
                0.9999989322971308,
                0.9999978766215388,
                0.9999993524052795,
                0.9999996743686259,
                0.9999988634365615,
                0.9999991148429649,
                0.9999978766222989
            ],
            [
                0.9999982396563708,
                0.9999978766205293,
                0.9999892166865417,
                0.9999975938976654,
                0.9999974387181042,
                0.9999974387174886,
                0.9999972735290834,
                0.9999983463100224,
                2.753569110256289e-05,
                0.9999964991451769
            ],
            [
                0.9999983463100223,
                0.9999962733593886,
                0.9999967112513329,
                0.9999989322972587,
                0.9999969105055612,
                0.9999960330126718,
                0.9999938558232121,
                0.9999972735300655,
                0.9999957771675695,
                0.9999960330150385
            ],
            [
                1.1478772231086046e-05,
                0.9999990577551825,
                0.9999987121046323,
                0.9999985406232597,
                0.9999975938976635,
                0.9999974387187093,
                0.9999974387174874,
                0.9999974387165713,
                0.9999978766207809,
                0.9999988634357492
            ],
            [
                3.7266406168624155e-06,
                0.999997876621544,
                0.9999989322975136,
                0.9999991148428596,
                0.9999987121041712,
                0.9999960330140908,
                1.2098659719757836e-06,
                0.9999993106392017,
                0.9999987901343176,
                0.999998629042795
            ],
            [
                0.9999991148430707,
                0.9999972735303841,
                1.5534973842076057e-06,
                5.043473480777865e-07,
                0.9999938558261459,
                6.47595107001401e-07,
                2.2603248367949354e-06,
                0.9999977396765146,
                0.9999969105059239,
                6.962258739796719e-06
            ],
            [
                1.5534975693979422e-06,
                5.04347287955046e-07,
                2.699577774585891e-07,
                3.05902190458764e-07,
                1.0677026154806063e-06,
                3.2887506336235617e-06,
                1.4738983729535602e-05,
                1.8553905760062447e-07,
                1.4738978458623327e-05,
                1.3709575337159875e-06
            ],
            [
                1.3007126914245925e-05,
                2.1444948414321717e-05,
                6.96225873967641e-06,
                0.9999930377429296,
                0.9999977396765124,
                6.14417753171671e-06,
                1.1478772231086046e-05,
                1.89251527534122e-05,
                0.00015843616030417933,
                5.144223205871514e-05
            ],
            [
                0.9999967112521163,
                0.9999987901337407,
                0.9999987121043257,
                0.9999885212360063,
                0.9999952149055212,
                0.9999962733589464,
                0.9999987901338855,
                0.9999982396559491,
                0.9999987121047857,
                1.2098659719757836e-06
            ],
            [
                1.7603434231777837e-06,
                0.9999989969859129,
                3.4663249714451116e-07,
                4.4508505193932864e-07,
                0.9999993106392021,
                0.9999992188515769,
                0.9999991684718746,
                0.9999988634362906,
                0.999999391640964,
                0.9999987121049388
            ],
            [
                2.102433159721477e-07,
                3.288748673376478e-06,
                1.5534977545886537e-06,
                1.5534979397740895e-06,
                1.637376276909393e-07,
                6.475947982022763e-07,
                6.475947210046347e-07,
                4.450850519403407e-07,
                4.4508510499849186e-07,
                2.382368531929327e-07
            ],
            [
                0.9999957771650532,
                0.9999960330155104,
                0.9999910603037232,
                0.9999934595620116,
                0.9999892166852525,
                0.9999934595604468,
                0.9999892166839616,
                0.9999930377454279,
                0.9999974387171845,
                0.9999945777784665
            ],
            [
                5.715005151606823e-07,
                6.962259569750576e-06,
                1.2098653950692178e-06,
                5.04347528446051e-07,
                3.466325797896173e-07,
                3.46632497145457e-07,
                1.0677032518785256e-06,
                3.2887482813149375e-06,
                7.338213304363436e-07,
                5.715005832886879e-07
            ],
            [
                1.209866260432471e-06,
                5.043474081993875e-07,
                1.3709572068522336e-06,
                1.0677032518748838e-06,
                1.5534975693792215e-06,
                1.7603436330259153e-06,
                1.9947299592933255e-06,
                3.0590226339061185e-07,
                7.338209805224048e-07,
                1.3007123813382511e-05
            ],
            [
                1.2098661162056318e-06,
                0.9999955048200369,
                0.9999974387165724,
                0.9999832985742574,
                0.9999987901344622,
                0.9999934595604449,
                1.7603427936335396e-06,
                0.9999970976869823,
                0.9999982396569994,
                0.9999984465020617
            ],
            [
                0.9999982396565797,
                0.9999832985702152,
                0.9999988634366976,
                0.9999983463106132,
                0.9999990577557444,
                0.9999945777810421,
                0.9999988634364265,
                0.9999987121049391,
                0.9999974387181022,
                0.9999988634364265
            ],
            [
                0.9999992188518563,
                0.9999977396748959,
                0.9999985406230847,
                1.760343003481596e-06,
                0.9999977396765137,
                0.9999987121050934,
                0.9999984465015072,
                4.2228334445658276e-06,
                0.9999962733598304,
                6.144175334468545e-06
            ],
            [
                4.4508526417298334e-07,
                2.3823702359138736e-07,
                1.5534975693979422e-06,
                3.466325384661554e-07,
                2.5612834320563895e-06,
                7.73441946488886e-08,
                6.475950297993789e-07,
                6.475945666063607e-07,
                3.466327037512053e-07,
                9.422443692555439e-07
            ],
            [
                0.9999952149038049,
                0.9999982396563688,
                0.9999977396757062,
                0.9999974387168772,
                0.9999869928669634,
                0.9999904837471999,
                0.9999962733598314,
                0.9999972735287601,
                0.9999977396759754,
                0.9999981261248416
            ],
            [
                0.9999988634365627,
                0.9999982396567901,
                0.9999988634357494,
                0.9999957771675702,
                0.9999986290427956,
                0.999998446502803,
                0.9999960330140939,
                0.9999981261243969,
                0.9999934595627853,
                0.9999982396565795
            ],
            [
                4.222833444590791e-06,
                1.2098652508424818e-06,
                1.5534981249697903e-06,
                0.9999986290431225,
                1.5534975693979422e-06,
                1.9947304348862686e-06,
                1.5534973842076057e-06,
                3.7266410611296085e-06,
                0.9999623635395954,
                1.2098655392871682e-06
            ],
            [
                2.90231094723893e-06,
                2.5612834320470717e-06,
                2.5612825160271407e-06,
                6.605214468549049e-05,
                NaN,
                0.9999938558261371,
                8.939696304213768e-06,
                3.2887478892683997e-06,
                6.144176066901277e-06,
                7.889266347786918e-06
            ],
            [
                0.9999952149060826,
                0.9999982396561605,
                0.9999985406243035,
                0.9999983463108109,
                0.9999974387168824,
                0.9999982396561604,
                0.9999972735287589,
                0.9999916019299974,
                0.9999972735297369,
                0.9999975938968056
            ],
            [
                3.927863875616689e-07,
                1.8553910183649565e-07,
                2.3823682479292225e-07,
                8.764252675194995e-08,
                2.102434412875379e-07,
                6.475948754028718e-07,
                3.4663266243308805e-07,
                9.422447062270609e-07,
                4.450848927658745e-07,
                9.422445939054222e-07
            ],
            [
                0.9999982396574195,
                0.9999989969855549,
                0.9999962733589433,
                0.9999964991439254,
                0.9999930377412825,
                9.931190958076104e-08,
                0.9999985406239572,
                0.999995214905514,
                0.9999985406243049,
                0.9999942280820499
            ],
            [
                0.9999972735294111,
                0.9999986290424698,
                0.9999980052698094,
                0.999996910504091,
                0.9999989969861516,
                0.9999983463096281,
                0.9999974387177984,
                0.9999983463110079,
                0.9999984465028051,
                0.9999974387165738
            ],
            [
                8.315280276626197e-07,
                4.450852111148132e-07,
                0.9999938558246769,
                3.466327863983311e-07,
                0.9999993524050479,
                3.2887482813149375e-06,
                1.0677027427600627e-06,
                1.8553916819032217e-07,
                3.726637951387472e-06,
                7.338209805240734e-07
            ],
            [
                6.605216044933028e-05,
                1.7603438428800754e-06,
                4.006370652067535e-05,
                0.9999989322970032,
                3.120190021759579e-05,
                3.288749065423109e-06,
                1.1478764020883773e-05,
                1.300712846477255e-05,
                7.889260704968913e-06,
                1.994729483723626e-06
            ],
            [
                0.9999990577551827,
                0.9999987121052485,
                0.9999990577554073,
                0.9999989322972587,
                0.9999987121044801,
                0.9999989969856735,
                0.9999974387184035,
                0.9999977396759758,
                0.9999983463102201,
                0.9999987121050948
            ],
            [
                3.466326624336003e-07,
                6.144175334418252e-06,
                2.699577774585891e-07,
                3.2887502415767434e-06,
                2.3823688159291947e-07,
                9.931202796957073e-08,
                3.7266383955882547e-06,
                2.3823690999290963e-07,
                9.422445939054222e-07,
                4.450849988811838e-07
            ],
            [
                1.0677024881980089e-06,
                8.315283250371857e-07,
                1.5534984953453635e-06,
                8.315278294072958e-07,
                5.71500515159253e-07,
                7.338207180864763e-07,
                1.0677029973192638e-06,
                1.3709568799760888e-06,
                3.726638395611981e-06,
                6.475947210031623e-07
            ],
            [
                0.9999989969856741,
                0.9999990577556318,
                0.9999993916408912,
                0.9999992188514839,
                0.9999993916411086,
                0.9999991684719732,
                0.9999985406232597,
                0.9999991684715764,
                0.9999993916406738,
                0.9999992661792824
            ],
            [
                5.04347468323289e-07,
                2.6995784182140636e-07,
                7.338212429582604e-07,
                2.382370235922541e-07,
                5.043473480777865e-07,
                2.1024334103505245e-07,
                2.3823688159291947e-07,
                3.466326211113502e-07,
                7.338212429582604e-07,
                4.450850519403407e-07
            ],
            [
                4.222834451382849e-06,
                1.0677024882009222e-06,
                4.4508526417298334e-07,
                2.1024336609843824e-07,
                3.9278605979534166e-07,
                4.222833444590791e-06,
                2.1024331597262577e-07,
                2.1024341622426268e-07,
                8.315284241650899e-07,
                3.059022269250683e-07
            ],
            [
                0.9999994956525922,
                0.9999978766207817,
                0.9999981261241718,
                0.999999114842965,
                0.9999985406234326,
                0.9999978766212897,
                0.9999970976869832,
                0.9999988634357486,
                0.9999970976880169,
                0.9999986290426311
            ],
            [
                4.785095065132354e-06,
                0.9999949062968331,
                1.994730197090463e-06,
                7.889259764273619e-06,
                4.222833947960866e-06,
                0.9999964991455949,
                0.999994906293189,
                0.9999967112509389,
                0.9999957771665607,
                4.222832941111319e-06
            ],
            [
                0.9999978766210362,
                0.9999452402505637,
                0.9999978766215394,
                0.9999960330145651,
                0.9999991148429651,
                0.9999623635441233,
                2.2603242978213447e-06,
                7.338209805170655e-07,
                0.9999921107393193,
                0.9999960330155108
            ],
            [
                0.9999994631251249,
                3.9278610661822475e-07,
                0.9999990577552952,
                0.999999391641109,
                0.9999990577554072,
                0.9999993524053568,
                0.9999993106391193,
                0.9999983463100217,
                0.9999989969862718,
                0.9999993916408914
            ],
            [
                1.275190276859705e-07,
                1.637377448057981e-07,
                3.927862002663297e-07,
                1.3709572068478697e-06,
                5.422219616265831e-06,
                3.0590237279032884e-07,
                7.734421308914719e-08,
                5.715004470313855e-07,
                1.637377448057981e-07,
                3.4663266243308805e-07
            ],
            [
                0.9999977396746271,
                0.9999988634365619,
                0.9999991148429652,
                0.9999989969856741,
                0.9999992661787579,
                0.9999993106386266,
                0.9999992188519495,
                0.9999974387174867,
                0.9999984465018767,
                0.9999993916408914
            ],
            [
                6.962257079775324e-06,
                NaN,
                4.22283394786293e-06,
                5.422218323487975e-06,
                7.88926070489716e-06,
                1.1478770862067849e-05,
                1.0677029973192638e-06,
                9.422450431954847e-07,
                6.475947210031623e-07,
                2.9023119851781017e-06
            ],
            [
                0.9999970976883664,
                0.9999988634364255,
                0.9999987121052482,
                0.999998346310021,
                0.9999962733602765,
                0.9999990577554072,
                0.9999972735307093,
                0.9999978766205267,
                0.999997593896519,
                0.9999988634364259
            ],
            [
                0.9999955048168201,
                0.9999970976866346,
                0.9999985406230855,
                0.9999960330131454,
                0.9999969105059238,
                0.9999989969854344,
                0.9999960330136166,
                0.9999986290424677,
                0.9999877809284001,
                7.73441946488886e-08
            ],
            [
                0.9999991148432816,
                0.9999975938985235,
                0.9999985406236065,
                0.9999970976890549,
                0.9999989322967486,
                0.999999266178933,
                0.0001233945603033627,
                0.9999994284996216,
                0.9999983463098238,
                0.9999985406237798
            ],
            [
                0.9999986290429604,
                0.9999962733602799,
                0.9999985406230855,
                0.999998446501879,
                0.9999978766217971,
                0.9999981261243974,
                0.9999987901340298,
                0.9999970976890661,
                0.9999984465024342,
                0.9999981261243966
            ],
            [
                0.9999977396765141,
                0.9999984465024335,
                0.9999982396569991,
                4.222835458175145e-06,
                0.999999057755744,
                0.9999987121043254,
                0.9999991148428597,
                0.9999991148432815,
                0.9999988634361554,
                0.9999987901346067
            ],
            [
                0.9999989969859125,
                0.9999987121052456,
                0.9999972735294063,
                0.9999988634360194,
                0.9999991148431756,
                0.9999986290429578,
                0.9999989969862711,
                0.9999995262092731,
                0.9999997126315154,
                0.9999983463102178
            ],
            [
                0.9999921107336746,
                0.9999955048173543,
                0.9999991148431759,
                0.9999987901346059,
                0.9999991148430709,
                0.9999993916407462,
                0.9999988634361551,
                0.9999984465020624,
                0.9999970976887095,
                0.9999930377412739
            ],
            [
                3.726639728370556e-06,
                4.222833444590791e-06,
                1.7603440527286572e-06,
                7.338209805224048e-07,
                4.450850519403407e-07,
                1.2098659719788098e-06,
                1.5534971990126997e-06,
                1.0129993395336818e-05,
                2.5612812947508257e-06,
                7.338209805224048e-07
            ],
            [
                6.605216832236121e-05,
                0.9999938558268975,
                0.9999957771650491,
                0.9999949062943985,
                0.9999822214504426,
                0.999986992873142,
                0.9999964991455932,
                0.9999960330126726,
                0.9999992661791075,
                0.9999993106387087
            ],
            [
                0.9999970976880174,
                0.9999993524053569,
                0.999995504820033,
                0.9999955048189642,
                0.9999969105051894,
                0.9999986290432843,
                1.1478765389368729e-05,
                0.9999970976883648,
                4.785093353940187e-06,
                0.9999987121050924
            ],
            [
                0.9999993106389551,
                0.9999990577557437,
                0.9999987121052466,
                0.9999967112505463,
                0.9999993916406738,
                0.9999981261243946,
                0.9999982396561589,
                0.999998863435884,
                0.9999969105044535,
                0.9999993524050479
            ],
            [
                0.9999964991455909,
                0.999998790134751,
                0.9999987121052467,
                0.9999962733598364,
                0.9999990577549586,
                0.9999969105051889,
                0.9999949062943985,
                0.9999989969854347,
                0.9999975938968034,
                0.999993459565141
            ],
            [
                2.382370235933104e-07,
                1.6373776432509826e-07,
                0.9999996743687034,
                9.931198061405701e-08,
                1.6373764721072816e-07,
                6.825600469412533e-08,
                1.1253508156363576e-07,
                9.931189774187203e-08,
                2.3823682479292225e-07,
                1.444980209564556e-07
            ],
            [
                0.999999352405434,
                0.9999989322966217,
                0.9999972735287567,
                0.9999938558224767,
                0.9999990577549578,
                0.9999977396746261,
                0.9999991684722707,
                0.9999960330136166,
                0.9999975938973761,
                0.9999980052707581
            ],
            [
                5.422220908925639e-06,
                1.012999581021488e-05,
                2.902312331170226e-06,
                1.0677032518785256e-06,
                1.300713001508642e-05,
                2.6995784182140636e-07,
                1.2098655392871682e-06,
                5.829127944863308e-05,
                5.715002426475718e-07,
                5.422218323487975e-06
            ],
            [
                0.9999952149038066,
                0.9999972735284387,
                0.9999972735287597,
                0.9999972735284363,
                0.9999980052700451,
                0.9999980052695675,
                0.9999952149060841,
                0.9999987121049406,
                0.9999986290423055,
                0.9999972735284378
            ],
            [
                0.9999992661788454,
                0.999998790134463,
                0.9999962733616146,
                0.9999988634361554,
                0.9999991684722708,
                0.9999989969854353,
                0.9999989322971318,
                0.9999985406237812,
                0.9999978766205306,
                0.9999992661792827
            ],
            [
                0.9999987121049398,
                0.9999978766205285,
                0.999999310638709,
                0.9999992188517635,
                0.9999993106390371,
                0.999999266178933,
                0.9999960330145641,
                0.9999994284996898,
                0.9999987901338853,
                0.9999994631248686
            ],
            [
                0.9999995818813768,
                0.9999993916408186,
                0.999999428499417,
                0.9999993916406736,
                0.9999996940977732,
                0.9999996072137532,
                0.9999995549150545,
                0.9999996743687035,
                0.9999997126313442,
                0.999999526209273
            ],
            [
                0.9999921107336647,
                0.9999942280792965,
                1.370957860576702e-06,
                0.9999980052705191,
                0.9999982396559496,
                0.9999972735294063,
                0.9999978766210337,
                0.9999938558268766,
                0.9999970976866349,
                0.9999972735294071
            ],
            [
                0.9999984465022466,
                0.9999955048184263,
                0.9999983463096273,
                0.9999969105048188,
                0.9999960330136145,
                0.9999972735294077,
                0.9999991148431759,
                0.9999980052707564,
                0.9999994956527725,
                0.999999057755744
            ],
            [
                0.9999984465024326,
                0.9999938558268827,
                0.9999952149038148,
                0.9999989322967505,
                0.9999942280792958,
                0.9999983463108114,
                0.9999984465024343,
                0.9999984465018779,
                0.9999986290432844,
                0.9999980052709981
            ],
            [
                0.9999994631248046,
                0.9999969105040847,
                0.9999992661791952,
                0.999999526209386,
                0.999999526209386,
                0.9999990577554076,
                0.9999993106392018,
                0.9999992188517639,
                0.9999991148429651,
                0.9999988634357485
            ],
            [
                8.315282259138311e-07,
                0.9999977396759739,
                2.2603242978871282e-06,
                7.889261645427538e-06,
                0.9999991148430708,
                0.9999945777784593,
                8.315277302841894e-07,
                0.9999989322970042,
                5.422220262599396e-06,
                1.7603434231777837e-06
            ],
            [
                8.315283250260307e-07,
                9.422450431989127e-07,
                1.7603425837702984e-06,
                7.889265407177056e-06,
                6.475947982002148e-07,
                3.05902117523595e-07,
                8.315281267861397e-07,
                9.422450431954847e-07,
                1.5534971990126997e-06,
                6.475950297971703e-07
            ],
            [
                0.9999974387174883,
                0.999999266178933,
                0.9999989322970043,
                0.9999972735297333,
                0.9999989322973857,
                0.9999957771660596,
                0.9999991684717752,
                0.9999989969855547,
                0.999999218851577,
                0.9999989322973859
            ]
        ]
    },
    {
        "q_id": "9142_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.927862470899887e-07,
                1.994730434879465e-06,
                4.450848927650143e-07,
                1.7603436330259153e-06,
                3.927862470899887e-07,
                3.9278605979534166e-07,
                2.382368531929327e-07,
                5.715003107767143e-07,
                4.450851049959619e-07,
                4.4508494582405734e-07
            ],
            [
                3.927862002663297e-07,
                4.450848927650143e-07,
                2.2603237589676295e-06,
                1.3709570434178922e-06,
                4.7850950649408664e-06,
                1.2098653950656417e-06,
                2.7535694384882703e-05,
                4.450850519403407e-07,
                1.0677032518814388e-06,
                4.785092783519724e-06
            ],
            [
                8.315281267800897e-07,
                3.059021175247079e-07,
                4.450849988798682e-07,
                5.04347468318358e-07,
                3.9278605979534166e-07,
                5.715005151606823e-07,
                1.6373762769138607e-07,
                3.05902226923399e-07,
                9.4224425692559e-07,
                5.04347348075149e-07
            ],
            [
                1.0677026154730804e-06,
                3.9278634073732336e-07,
                2.2603253756956754e-06,
                1.760343423160973e-06,
                1.2098652508347793e-06,
                2.5612819054028872e-06,
                1.0677026154730804e-06,
                6.144175334468545e-06,
                0.0008040857681122694,
                2.5612812947380135e-06
            ],
            [
                1.2098655392811161e-06,
                6.475947210012481e-07,
                1.9947297214544894e-06,
                1.3709567165461505e-06,
                6.475948753847607e-07,
                6.1441731370702875e-06,
                3.9278605979011705e-07,
                7.338212429307298e-07,
                9.422442569208767e-07,
                3.927862002625787e-07
            ],
            [
                9.422448185510695e-07,
                7.338209805224048e-07,
                6.475947210031623e-07,
                1.0677024881980089e-06,
                5.422220909009474e-06,
                1.209865539295696e-06,
                2.260324836776948e-06,
                8.939695238536645e-06,
                1.2098659719757836e-06,
                9.422449308774482e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                9.422448185534261e-07,
                NaN,
                1.9947292459265734e-06,
                5.715003107767143e-07,
                NaN,
                2.9023119851635836e-06
            ],
            [
                4.450848927658745e-07,
                3.466326624336003e-07,
                1.8553910183674878e-07,
                2.382370235933104e-07,
                4.222834451403972e-06,
                1.6373764721072816e-07,
                5.715003107767143e-07,
                3.466326211113502e-07,
                4.450852111155216e-07,
                5.715005151606823e-07
            ],
            [
                5.043475284350422e-07,
                2.102434162245973e-07,
                3.4663249714451116e-07,
                NaN,
                7.338207180898968e-07,
                1.994729008145876e-06,
                1.0677027427340866e-06,
                3.2887506336235617e-06,
                3.7266383956509585e-06,
                1.0677027427624903e-06
            ],
            [
                5.715002426486762e-07,
                3.4663266243111764e-07,
                2.6995777745711594e-07,
                1.9947306726594253e-06,
                3.0590237279032884e-07,
                2.3823685319244518e-07,
                2.3823682479181176e-07,
                5.715007195447234e-07,
                1.7603430034743913e-06,
                2.6995777745711594e-07
            ],
            [
                3.4663266242969896e-07,
                2.3823688159069855e-07,
                7.338212429582604e-07,
                4.450849458218309e-07,
                9.4224425692559e-07,
                3.927860597935108e-07,
                NaN,
                4.450848927658745e-07,
                3.927860597945825e-07,
                8.315281267834927e-07
            ],
            [
                7.889266347786918e-06,
                1.9947299593014888e-06,
                2.382368815932174e-07,
                1.553498124964492e-06,
                5.422218969895357e-06,
                6.475947210031623e-07,
                8.315277302841894e-07,
                1.3709575337159875e-06,
                6.144173869603344e-06,
                1.067703124601679e-06
            ],
            [
                NaN,
                8.315280276626197e-07,
                9.422443692574719e-07,
                2.260323758987159e-06,
                9.422450432014836e-07,
                6.475947210046347e-07,
                NaN,
                5.422220262636381e-06,
                NaN,
                1.9947304348862686e-06
            ],
            [
                1.3709576971425944e-06,
                1.9947297215125433e-06,
                1.3709567165617364e-06,
                7.338213304363436e-07,
                9.422444815792981e-07,
                8.315278294114555e-07,
                4.785096776499213e-06,
                2.2603248367949354e-06,
                2.9023119851781017e-06,
                NaN
            ],
            [
                1.760344052650207e-06,
                6.475947209985977e-07,
                3.535624227734284e-05,
                1.5534981249697903e-06,
                9.4224425692559e-07,
                4.785096205973894e-06,
                1.994729483666479e-06,
                1.067702615468225e-06,
                4.222834954461155e-06,
                1.7603432132912532e-06
            ],
            [
                1.2098652508424818e-06,
                9.422443692574719e-07,
                1.9947301970972664e-06,
                3.288749849529972e-06,
                7.889265407255982e-06,
                3.72663883989755e-06,
                NaN,
                1.994729483723626e-06,
                NaN,
                NaN
            ],
            [
                1.8553916819032217e-07,
                1.2751899728311609e-07,
                7.734423152941018e-08,
                7.73441946488886e-08,
                9.422450431954847e-07,
                3.466327037548308e-07,
                2.3823699519290042e-07,
                3.726638839878908e-06,
                2.1024331597262577e-07,
                1.6373770576776313e-07
            ],
            [
                1.855391239544352e-07,
                1.6373770576776313e-07,
                NaN,
                5.715005151606823e-07,
                1.855391239544352e-07,
                2.9023116391978967e-06,
                1.760343003481596e-06,
                3.288749849498565e-06,
                1.994730672668496e-06,
                3.288749849498565e-06
            ],
            [
                5.043475885696228e-07,
                3.466327037539638e-07,
                4.450852111148132e-07,
                3.0590215399183813e-07,
                4.450852111148132e-07,
                3.466327037548308e-07,
                8.315282259138311e-07,
                2.382369951932796e-07,
                2.1024326584639497e-07,
                7.338208055680009e-07
            ],
            [
                3.2887478892683997e-06,
                2.6995790618252024e-07,
                8.315279285370317e-07,
                9.422444815792981e-07,
                0.00012339455927639072,
                5.144223819041771e-05,
                NaN,
                5.144222583232244e-05,
                5.4222209089700225e-06,
                1.8553905759969634e-07
            ],
            [
                1.8553907971855875e-07,
                3.726639728370556e-06,
                2.699577774585891e-07,
                1.6373770576776313e-07,
                3.2887482813149375e-06,
                2.4300240731964193e-05,
                7.338212429582604e-07,
                7.734423152941018e-08,
                5.715003107767143e-07,
                4.4508494582405734e-07
            ],
            [
                3.288750241561788e-06,
                4.222833444590791e-06,
                2.5612822107167428e-06,
                1.3709578605729614e-06,
                5.043474683204221e-07,
                2.382368531929327e-07,
                1.760343003481596e-06,
                2.9023109472244114e-06,
                1.5534983101602148e-06,
                5.043475885674441e-07
            ],
            [
                5.715003107755449e-07,
                7.338210680021253e-07,
                1.6373772528704005e-07,
                6.475946438055299e-07,
                8.315284241650899e-07,
                6.475950298011458e-07,
                6.475947210012481e-07,
                3.466327863961242e-07,
                3.466326624336003e-07,
                2.5612819054133693e-06
            ],
            [
                6.475947982037486e-07,
                3.4663249714612693e-07,
                3.466327450756327e-07,
                3.9278629391427843e-07,
                1.4449800373065699e-07,
                7.338208930460318e-07,
                1.275190884913241e-07,
                7.338207180898968e-07,
                5.043475885696228e-07,
                1.8553919030858602e-07
            ],
            [
                1.855391239544352e-07,
                1.2098656835252174e-06,
                3.466327037553825e-07,
                3.927863875616689e-07,
                2.699578096403948e-07,
                1.2751908849167202e-07,
                1.2751901248391176e-07,
                2.3823690999323465e-07,
                NaN,
                2.5612834320214477e-06
            ],
            [
                2.6995774527718623e-07,
                4.450852111155216e-07,
                2.102434412875379e-07,
                2.6995784182140636e-07,
                3.0590219045914655e-07,
                3.0590237279032884e-07,
                3.466325797896173e-07,
                2.6995784182183607e-07,
                2.102434412871794e-07,
                2.6995774527577444e-07
            ],
            [
                6.475947982037486e-07,
                3.466325797888292e-07,
                2.1024326584639497e-07,
                2.69957906184239e-07,
                8.315280276626197e-07,
                5.043472278322555e-07,
                2.2603240284371276e-06,
                9.422442569290178e-07,
                4.450850519403407e-07,
                2.1024339116010604e-07
            ],
            [
                2.902310947190096e-06,
                1.7603438428188364e-06,
                1.7603432133136672e-06,
                1.2098661161927025e-06,
                NaN,
                1.2098656835136636e-06,
                8.315277302588544e-07,
                1.0677032518700286e-06,
                8.315284241333265e-07,
                1.553498124964492e-06
            ],
            [
                7.338212429537553e-07,
                4.2228349546493465e-06,
                6.475949525981759e-07,
                2.4300252321904572e-05,
                2.7535694384081332e-05,
                1.0677026154551157e-06,
                1.8925157265332104e-05,
                2.7535697666401535e-05,
                1.3709570434178922e-06,
                8.93969950132721e-06
            ],
            [
                1.5534973842076057e-06,
                1.6373774480605869e-07,
                NaN,
                3.059022998576899e-07,
                4.4508494582405734e-07,
                4.450848927650143e-07,
                5.715003107767143e-07,
                NaN,
                1.7603438428740716e-06,
                1.2098659719757836e-06
            ],
            [
                2.699578740011634e-07,
                3.059023727894942e-07,
                5.04347468318358e-07,
                9.422450431860582e-07,
                1.2751901248391176e-07,
                1.855391681898159e-07,
                9.422450432014836e-07,
                1.8553907971682908e-07,
                9.422444815765128e-07,
                5.04347528446051e-07
            ],
            [
                2.2603234895372223e-06,
                3.288747889284851e-06,
                3.927863875616689e-07,
                NaN,
                2.561281294760143e-06,
                1.2098662604291696e-06,
                7.889264466868659e-06,
                9.422445939054222e-07,
                8.315281267882195e-07,
                8.31528325040778e-07
            ],
            [
                1.0677026154827912e-06,
                2.902313023101807e-06,
                5.715003789033962e-07,
                1.760343632854606e-06,
                2.9023119851635836e-06,
                6.475947982002148e-07,
                1.7603427935678977e-06,
                3.0590215399183813e-07,
                2.2603242978778778e-06,
                4.222834451327159e-06
            ],
            [
                9.422443692555439e-07,
                1.209865827752005e-06,
                NaN,
                7.338212429582604e-07,
                2.5612834320563895e-06,
                2.5612834320563895e-06,
                2.561283126728994e-06,
                3.72663883989755e-06,
                1.3709568799919866e-06,
                5.715002426486762e-07
            ],
            [
                3.927860597935108e-07,
                9.422443692489024e-07,
                9.422443692489024e-07,
                4.4508494582405734e-07,
                4.785093924389007e-06,
                2.6995790618350237e-07,
                7.338207180864763e-07,
                NaN,
                2.2603253756956754e-06,
                1.5534984953552536e-06
            ],
            [
                4.450851580555361e-07,
                4.785095635655362e-06,
                6.1441746020359e-06,
                2.2603234895176927e-06,
                1.994729483729522e-06,
                NaN,
                6.962255419931625e-06,
                1.012998977264307e-05,
                8.939693107190907e-06,
                3.7266410611296085e-06
            ],
            [
                NaN,
                5.715002426486762e-07,
                3.05902336324494e-07,
                4.222832437798974e-06,
                2.5612831267202583e-06,
                NaN,
                5.043475885696228e-07,
                7.338209805240734e-07,
                2.9023119851899796e-06,
                9.422442569290178e-07
            ],
            [
                7.338208055613267e-07,
                2.902312677150514e-06,
                9.422443692555439e-07,
                NaN,
                8.315284241560147e-07,
                3.927862470899887e-07,
                5.04347528446051e-07,
                2.3823690999160957e-07,
                1.7603438428800754e-06,
                1.760343003481596e-06
            ],
            [
                NaN,
                6.475947982037486e-07,
                4.450849458218309e-07,
                6.475947210031623e-07,
                4.450848927650143e-07,
                1.0677024881980089e-06,
                1.7603425837855082e-06,
                1.0677024881980089e-06,
                1.5534975693869924e-06,
                5.04347348070562e-07
            ],
            [
                2.699577774585891e-07,
                8.939698435226916e-06,
                5.422220262636381e-06,
                8.315279285370317e-07,
                3.05902190458764e-07,
                1.8925143728749452e-05,
                NaN,
                8.315279285351409e-07,
                1.5534973842076057e-06,
                3.4663253846718004e-07
            ],
            [
                NaN,
                1.0129987357407137e-05,
                NaN,
                5.043474081993875e-07,
                1.1478772231232203e-05,
                4.450850519403407e-07,
                5.715002426486762e-07,
                2.5612828213934817e-06,
                NaN,
                5.715007195447234e-07
            ],
            [
                2.561281294760143e-06,
                3.466327037548308e-07,
                5.422217030747413e-06,
                9.422444815814404e-07,
                1.30071315662049e-05,
                2.382368531929327e-07,
                5.715005832886879e-07,
                5.715003107767143e-07,
                5.715003107755449e-07,
                8.315281267861397e-07
            ],
            [
                1.6373764721072816e-07,
                3.0590215399183813e-07,
                2.6995784182140636e-07,
                1.8553907971855875e-07,
                3.0590215399183813e-07,
                1.637377448057981e-07,
                2.6995771309523475e-07,
                1.444980209564556e-07,
                5.715003107767143e-07,
                2.1024341622368903e-07
            ],
            [
                4.4508494582405734e-07,
                2.6995784182140636e-07,
                7.889259764359722e-06,
                3.927862002663297e-07,
                8.315280276626197e-07,
                3.927862470899887e-07,
                6.475946438055299e-07,
                2.1024341622426268e-07,
                4.450850519403407e-07,
                8.315280276626197e-07
            ],
            [
                5.04347287955046e-07,
                1.0677032518814388e-06,
                1.0677028700422047e-06,
                1.2098659719788098e-06,
                1.0677031245990084e-06,
                1.760342793638743e-06,
                4.450852641737424e-07,
                2.2603251062450327e-06,
                6.475947982037486e-07,
                5.715005151606823e-07
            ],
            [
                2.561282210729555e-06,
                5.043474683220276e-07,
                7.88926446679691e-06,
                3.288749849477628e-06,
                1.3709576971425944e-06,
                7.88926446679691e-06,
                8.315277302788957e-07,
                2.5612825160562587e-06,
                2.26032402841657e-06,
                1.9947306726594253e-06
            ],
            [
                1.855390576008354e-07,
                NaN,
                3.466327037553825e-07,
                7.338209805240734e-07,
                2.6995784182183607e-07,
                1.855391239547094e-07,
                NaN,
                1.209865827752005e-06,
                6.47595107001401e-07,
                5.715003107767143e-07
            ],
            [
                4.450849458200093e-07,
                NaN,
                2.561282210740037e-06,
                5.043475284430694e-07,
                2.9023112932177327e-06,
                NaN,
                6.475945666063607e-07,
                5.71500719545698e-07,
                2.902312677150514e-06,
                2.5612819054133693e-06
            ],
            [
                1.2098656835224664e-06,
                5.422217030747413e-06,
                3.927863407379485e-07,
                5.043473480777865e-07,
                6.96225956921868e-06,
                1.2098652508424818e-06,
                5.043473480777865e-07,
                3.4663249714612693e-07,
                4.785094494811783e-06,
                4.2228324377740105e-06
            ],
            [
                8.315284241597959e-07,
                5.422219616228845e-06,
                NaN,
                1.3709570434178922e-06,
                4.222832437798974e-06,
                1.0677027427600627e-06,
                NaN,
                4.2228339479858295e-06,
                5.715006514176113e-07,
                NaN
            ],
            [
                5.715003107738556e-07,
                6.475946437996402e-07,
                9.422443692555439e-07,
                1.7603427935342762e-06,
                7.338208055536515e-07,
                2.2603251061849014e-06,
                1.7603432133136672e-06,
                5.043474683204221e-07,
                7.338212429307298e-07,
                6.47594798194325e-07
            ],
            [
                4.450850519403407e-07,
                7.338209805240734e-07,
                1.6373770576776313e-07,
                3.9278610661902853e-07,
                3.0590215399183813e-07,
                6.475949526020042e-07,
                2.6995784182140636e-07,
                3.927863407379485e-07,
                2.102434412875379e-07,
                2.382368531929327e-07
            ],
            [
                1.855391239547094e-07,
                5.315780536011123e-08,
                7.338207180898968e-07,
                1.1253524254650944e-07,
                4.450852641737424e-07,
                1.0677024881941248e-06,
                1.370957860567974e-06,
                2.2603242978871282e-06,
                1.0677032518814388e-06,
                1.275190124846946e-07
            ],
            [
                1.3709567165617364e-06,
                5.043476486915964e-07,
                3.466325797896173e-07,
                1.209865827752005e-06,
                5.043472278322555e-07,
                5.715003789033962e-07,
                9.422443692574719e-07,
                8.315281267861397e-07,
                9.422448185534261e-07,
                1.0677027427600627e-06
            ],
            [
                3.9278605979534166e-07,
                NaN,
                NaN,
                1.4449800373118268e-07,
                1.0677028700422047e-06,
                1.067703124601679e-06,
                3.4663249714325014e-07,
                9.93120161306789e-08,
                NaN,
                3.2887502415438413e-06
            ],
            [
                3.466327863983311e-07,
                1.3709576971425944e-06,
                2.6995774527718623e-07,
                8.939696304311336e-06,
                5.715003789046955e-07,
                8.315281267861397e-07,
                1.2098653950656417e-06,
                NaN,
                7.338212429582604e-07,
                2.382370235922541e-07
            ],
            [
                NaN,
                2.102434412875379e-07,
                9.931195693628605e-08,
                2.699578096393206e-07,
                3.466325797896173e-07,
                9.931198061405701e-08,
                2.1024329090867228e-07,
                3.2887482807182155e-06,
                7.88926070489716e-06,
                3.059023363221292e-07
            ],
            [
                1.5534981249697903e-06,
                7.338207180898968e-07,
                1.5534981249496567e-06,
                8.315281267882195e-07,
                5.043472879504592e-07,
                7.338212429582604e-07,
                2.382368531929327e-07,
                6.475947982037486e-07,
                9.4224425692559e-07,
                2.561282516066741e-06
            ],
            [
                2.561283431888668e-06,
                2.2603242978871282e-06,
                2.9023119851899796e-06,
                1.994729483705484e-06,
                1.3709572068522336e-06,
                3.72663883989755e-06,
                3.0590237279085045e-07,
                1.5534977545497995e-06,
                1.7603430034743913e-06,
                9.422448185510695e-07
            ],
            [
                8.7642526752214e-08,
                1.9947297214944016e-06,
                9.931200429212718e-08,
                1.4449805540763184e-07,
                1.275190124846946e-07,
                3.9278629391427843e-07,
                1.8553907971758842e-07,
                2.699578096403948e-07,
                7.338208930460318e-07,
                1.4449800373118268e-07
            ],
            [
                NaN,
                6.144176799227922e-06,
                2.2603237589676295e-06,
                1.3709576971425944e-06,
                NaN,
                4.785095635655362e-06,
                1.6701423835624208e-05,
                NaN,
                1.0129988565084915e-05,
                1.553498124964492e-06
            ],
            [
                1.3709573702856596e-06,
                2.382368815932174e-07,
                5.043475885696228e-07,
                7.734414854823498e-08,
                9.422443692574719e-07,
                3.9278620026686556e-07,
                5.043472278322555e-07,
                1.370957860576702e-06,
                1.7603425837903113e-06,
                5.715006514176113e-07
            ],
            [
                6.962258739068529e-06,
                6.9622537576631295e-06,
                7.338209805224048e-07,
                5.043472278280699e-07,
                4.222833947820683e-06,
                1.3709573702822306e-06,
                6.14417460073947e-06,
                2.9023133690980155e-06,
                4.450851580555361e-07,
                7.338207180864763e-07
            ],
            [
                9.422448185534261e-07,
                2.69957906184239e-07,
                2.699576809143613e-07,
                9.422444815792981e-07,
                8.315279285351409e-07,
                8.315283250394546e-07,
                5.04347528446051e-07,
                1.5534971990126997e-06,
                3.927862470899887e-07,
                1.7603425837855082e-06
            ],
            [
                1.2098659719788098e-06,
                2.9023116392097746e-06,
                1.0677029973192638e-06,
                1.5534975693869924e-06,
                1.0677027427600627e-06,
                NaN,
                NaN,
                5.71500719545698e-07,
                8.31528325040778e-07,
                1.0677024882029858e-06
            ],
            [
                3.927862939126708e-07,
                7.338208055664991e-07,
                9.422448185510695e-07,
                5.715003789046955e-07,
                1.0677031245990084e-06,
                5.715006514151423e-07,
                6.475949525878687e-07,
                1.3709567165579959e-06,
                1.0677033791583005e-06,
                3.466327863983311e-07
            ],
            [
                1.0677027427624903e-06,
                1.0677027427525368e-06,
                9.422442569315887e-07,
                1.5534971990169383e-06,
                1.0677028700422047e-06,
                1.7603438428800754e-06,
                8.939693107190907e-06,
                1.0,
                1.0677027427471959e-06,
                3.4663278639892215e-07
            ],
            [
                1.012999218776902e-05,
                5.04347468318358e-07,
                2.90231094723893e-06,
                9.422448185478557e-07,
                2.5612834320470717e-06,
                7.338212429537553e-07,
                7.338209805200689e-07,
                2.9023112932177327e-06,
                1.9947306726213275e-06,
                7.338209805170655e-07
            ],
            [
                1.2098661162023305e-06,
                1.1253506814842375e-07,
                2.9023133690188264e-06,
                1.4449805540651476e-07,
                5.315789407666425e-08,
                9.422442569315887e-07,
                1.994729008105057e-06,
                2.2603234894745224e-06,
                9.931190958076104e-08,
                8.315278294038928e-07
            ],
            [
                1.067703124601679e-06,
                1.3709567165617364e-06,
                2.6995774527718623e-07,
                2.902313369111213e-06,
                7.338209805240734e-07,
                1.0677033791612137e-06,
                4.450848927658745e-07,
                9.422442569315887e-07,
                3.466326211113502e-07,
                1.209866260432471e-06
            ],
            [
                8.315281267834927e-07,
                7.889263526345123e-06,
                6.475951069932288e-07,
                4.7850933534310035e-06,
                1.3709570434122812e-06,
                2.699577452746696e-07,
                1.892514371900746e-05,
                2.102432658440048e-07,
                1.2098659719757836e-06,
                6.475946438022905e-07
            ],
            [
                8.315281267834927e-07,
                1.3709575337078829e-06,
                9.422442569208767e-07,
                8.315284241560147e-07,
                1.0677024881829577e-06,
                5.715006514105942e-07,
                8.315284241560147e-07,
                1.5534983101393749e-06,
                2.2603251062450327e-06,
                1.9947292459347367e-06
            ],
            [
                2.260324567227179e-06,
                2.902311984989368e-06,
                8.315281267037064e-07,
                6.475945665900901e-07,
                1.7603440527046419e-06,
                1.0677026153919963e-06,
                2.902311984989368e-06,
                1.067703251769523e-06,
                3.288749457432399e-06,
                1.3709575336530204e-06
            ],
            [
                2.902312331170226e-06,
                3.927862002663297e-07,
                1.3709568799919866e-06,
                8.315281267882195e-07,
                6.144177531767002e-06,
                1.2098656835224664e-06,
                3.466327037539638e-07,
                5.715006514167015e-07,
                8.315278294038928e-07,
                3.059022269250683e-07
            ],
            [
                1.1253510839355284e-07,
                3.927860597945825e-07,
                1.8553903548231313e-07,
                1.6373770576776313e-07,
                3.0590237279032884e-07,
                2.382369383923073e-07,
                8.315277302857965e-07,
                2.699576809143613e-07,
                1.2751904288739315e-07,
                1.6373766672888118e-07
            ],
            [
                2.902310947208574e-06,
                1.6373766672973748e-07,
                1.27519088491875e-07,
                1.300713466685723e-05,
                7.338209805224048e-07,
                1.2098653950606901e-06,
                1.2098653950403334e-06,
                2.6995790618350237e-07,
                1.553497199007048e-06,
                1.5534973841154145e-06
            ],
            [
                1.0677029973219343e-06,
                3.9278629391427843e-07,
                2.5612834320563895e-06,
                7.338209805240734e-07,
                7.338209805240734e-07,
                7.338208930443633e-07,
                2.9023126771227976e-06,
                NaN,
                NaN,
                7.338208055680009e-07
            ],
            [
                1.7603425837606927e-06,
                1.9947304348703948e-06,
                5.043475284430694e-07,
                1.4738985486265496e-05,
                3.726638839806038e-06,
                9.422448185478557e-07,
                2.9023119851781017e-06,
                1.3709573702647743e-06,
                1.3709567165530083e-06,
                3.288749849498565e-06
            ],
            [
                5.422218323231539e-06,
                1.0677029973219343e-06,
                1.9947297215125433e-06,
                8.315278294114555e-07,
                8.939696304311336e-06,
                1.0677029973192638e-06,
                NaN,
                8.315277302841894e-07,
                8.315282259138311e-07,
                1.3709567165617364e-06
            ],
            [
                1.2098662604192665e-06,
                6.475946437781423e-07,
                2.2603237589676295e-06,
                5.715002426254813e-07,
                2.260324567337161e-06,
                1.3709570433979422e-06,
                1.0677028700053041e-06,
                5.715007195275709e-07,
                1.0677032518209896e-06,
                1.5534979397677313e-06
            ],
            [
                1.5534971990126997e-06,
                4.4508515805199415e-07,
                5.043472278280699e-07,
                2.6995774527577444e-07,
                5.043472879540142e-07,
                1.275190884913241e-07,
                5.043475885674441e-07,
                1.6373774480404828e-07,
                5.715007195447234e-07,
                2.699577774560111e-07
            ],
            [
                5.043472879525233e-07,
                4.450848927650143e-07,
                NaN,
                1.3709572068522336e-06,
                3.466327863983311e-07,
                2.2603237589542675e-06,
                NaN,
                4.450852111148132e-07,
                8.315280276626197e-07,
                NaN
            ],
            [
                6.475949526020042e-07,
                6.144177530146464e-06,
                7.338209805224048e-07,
                1.9947294837154625e-06,
                6.144173868983067e-06,
                1.994729245917502e-06,
                3.2887506334560605e-06,
                1.0677031245990084e-06,
                1.760343213322473e-06,
                4.4508510499849186e-07
            ],
            [
                1.6373774480535133e-07,
                7.338210680021253e-07,
                5.715003789017068e-07,
                3.05902263391829e-07,
                3.927862939126708e-07,
                9.422447062294175e-07,
                1.370957860576702e-06,
                2.260323758987159e-06,
                5.043472879540142e-07,
                6.475949526020042e-07
            ],
            [
                2.2603248367949354e-06,
                1.5534983101478522e-06,
                4.450852111148132e-07,
                1.855391239539711e-07,
                7.338212429582604e-07,
                1.0677028700422047e-06,
                3.059022998581767e-07,
                2.382369383923073e-07,
                3.4663249714451116e-07,
                2.3823699519290042e-07
            ],
            [
                NaN,
                5.715005151606823e-07,
                1.994729008145876e-06,
                1.4449800373118268e-07,
                5.04347287955046e-07,
                1.8553919030858602e-07,
                3.059022998576899e-07,
                9.422444815814404e-07,
                2.1024339116168358e-07,
                6.825609419848033e-08
            ],
            [
                4.222833947960866e-06,
                3.0590237279085045e-07,
                2.699578096403948e-07,
                3.9278610661902853e-07,
                3.9278610661902853e-07,
                7.338208930460318e-07,
                NaN,
                5.04347528446051e-07,
                3.7266406167827664e-06,
                1.9947301970972664e-06
            ],
            [
                7.338209805240734e-07,
                1.7603434231833873e-06,
                4.785094494783494e-06,
                1.994730672668496e-06,
                8.315280276546789e-07,
                1.0677033791612137e-06,
                3.927860597935108e-07,
                1.3709567165617364e-06,
                NaN,
                5.715002426486762e-07
            ],
            [
                2.5612819054028872e-06,
                2.902312677150514e-06,
                1.994730672668496e-06,
                1.5534981249697903e-06,
                8.76424013786396e-08,
                2.2603253756956754e-06,
                2.902311639183378e-06,
                1.370957860567974e-06,
                NaN,
                4.2228324377740105e-06
            ],
            [
                4.222834954753043e-06,
                2.9023133690637e-06,
                1.9947292459406333e-06,
                NaN,
                1.3709575337159875e-06,
                4.450852111155216e-07,
                1.0129989772532511e-05,
                NaN,
                3.4663278639892215e-07,
                NaN
            ],
            [
                7.88926446679691e-06,
                1.7603432133136672e-06,
                8.93969950132721e-06,
                1.4738983729053029e-05,
                1.3007126914245925e-05,
                1.994730434847717e-06,
                1.5534975693792215e-06,
                4.222833444506298e-06,
                1.8925157265332104e-05,
                1.760342793583908e-06
            ],
            [
                2.5612822106654943e-06,
                6.475945666063607e-07,
                NaN,
                9.422447061953531e-07,
                8.315277302857965e-07,
                1.760344052714248e-06,
                9.422445939002803e-07,
                1.9947292458930106e-06,
                3.2887486733420804e-06,
                1.7603425837903113e-06
            ],
            [
                1.7603430034743913e-06,
                NaN,
                8.315280276626197e-07,
                5.715005151606823e-07,
                8.315281267861397e-07,
                2.6995774527718623e-07,
                2.9023119851635836e-06,
                1.8553919030858602e-07,
                2.561282210701601e-06,
                6.962257909842961e-06
            ],
            [
                7.889264466868659e-06,
                4.450848927658745e-07,
                1.5534975693979422e-06,
                1.5534971990126997e-06,
                7.338208055664991e-07,
                1.3709572068522336e-06,
                7.338207180864763e-07,
                4.785096206076165e-06,
                1.5534983101602148e-06,
                1.760342793638743e-06
            ],
            [
                1.275190884913241e-07,
                2.6995790618350237e-07,
                2.3823682479181176e-07,
                2.3823702359290413e-07,
                3.05902336324494e-07,
                1.0677031245990084e-06,
                5.043472879540142e-07,
                2.102433410343832e-07,
                1.6373770576776313e-07,
                2.1024341622426268e-07
            ],
            [
                NaN,
                4.222833948008874e-06,
                2.2603253756956754e-06,
                1.2098656835224664e-06,
                NaN,
                1.670141786325573e-05,
                1.994729008105057e-06,
                1.7603430034867993e-06,
                2.90231094723893e-06,
                1.7603436330091044e-06
            ],
            [
                2.902311639183378e-06,
                1.5534979397740895e-06,
                1.1478769494250387e-05,
                2.5612812947508257e-06,
                2.382369667914917e-07,
                1.2098652508424818e-06,
                NaN,
                4.450848927658745e-07,
                3.927862002663297e-07,
                5.715005832886879e-07
            ],
            [
                2.902312331081799e-06,
                1.5534979397740895e-06,
                8.315283250371857e-07,
                3.46632497145457e-07,
                1.9947299593014888e-06,
                4.785092783519724e-06,
                NaN,
                2.1024341622368903e-07,
                3.7266383955882547e-06,
                2.699576809143613e-07
            ],
            [
                3.059021904571643e-07,
                1.4449805540740185e-07,
                6.475948754012522e-07,
                4.450848927637999e-07,
                5.043475284430694e-07,
                5.715004470313855e-07,
                4.4508505193791187e-07,
                8.315278294072958e-07,
                6.475946437996402e-07,
                7.338211554783522e-07
            ],
            [
                NaN,
                NaN,
                1.6373770576776313e-07,
                NaN,
                0.999569442919477,
                NaN,
                NaN,
                2.6995784182183607e-07,
                3.9278610661366994e-07,
                4.7850933539684755e-06
            ],
            [
                1.7603436330259153e-06,
                1.2751899728311609e-07,
                1.444980209564556e-07,
                6.825601283086733e-08,
                1.3709568799760888e-06,
                2.3823693839290317e-07,
                9.422449308716635e-07,
                2.260325106237323e-06,
                1.444980209564556e-07,
                6.47594643784032e-07
            ],
            [
                2.902311639183378e-06,
                1.275190732904469e-07,
                1.2098659719716573e-06,
                1.6373764721072816e-07,
                3.288750241410738e-06,
                3.288749849529972e-06,
                5.04347287955046e-07,
                2.902312331170226e-06,
                2.6995790618469934e-07,
                1.7603427936335396e-06
            ],
            [
                2.9023133690821773e-06,
                5.043475885606781e-07,
                2.3823690999236795e-07,
                2.1024329090867228e-07,
                6.475950297942253e-07,
                2.260324567337161e-06,
                1.7603425837791042e-06,
                9.422447062270609e-07,
                7.338207180864763e-07,
                5.71500242637956e-07
            ],
            [
                8.315281267861397e-07,
                1.0677032518814388e-06,
                2.6995784182140636e-07,
                5.043472879540142e-07,
                2.69957906184239e-07,
                1.3709567165530083e-06,
                2.382368531929327e-07,
                1.4449796927932878e-07,
                3.4663249714325014e-07,
                1.6373766672973748e-07
            ],
            [
                4.450848927637999e-07,
                1.3007130015677909e-05,
                2.699578096403948e-07,
                1.147876812620341e-05,
                NaN,
                NaN,
                2.2603234895372223e-06,
                1.7603434231833873e-06,
                3.5356238073889594e-05,
                NaN
            ],
            [
                1.0677028700422047e-06,
                1.0677029973192638e-06,
                1.5534971990126997e-06,
                7.338207180898968e-07,
                3.9278634073732336e-07,
                3.466326211113502e-07,
                2.1024339116168358e-07,
                7.338209805224048e-07,
                5.04347287955046e-07,
                5.043472278312808e-07
            ],
            [
                2.699577452746696e-07,
                3.059023363221292e-07,
                3.466327863983311e-07,
                2.3823685319244518e-07,
                1.994729008145876e-06,
                1.0677032518814388e-06,
                6.144176799283803e-06,
                7.338209805240734e-07,
                1.9947299592933255e-06,
                7.338210679979539e-07
            ],
            [
                1.2098652508287273e-06,
                2.561282516042282e-06,
                1.5534971990126997e-06,
                2.260324297853209e-06,
                5.715005832853093e-07,
                7.338208055664991e-07,
                1.0677029973192638e-06,
                1.209866260432471e-06,
                4.222834451382849e-06,
                5.04347528446051e-07
            ],
            [
                4.450848927637999e-07,
                5.422218323487975e-06,
                9.422444815792981e-07,
                2.1444953527476883e-05,
                1.7603425837791042e-06,
                1.3709576971379186e-06,
                1.7603427935678977e-06,
                4.450851580555361e-07,
                5.043472278255469e-07,
                1.5534983101602148e-06
            ],
            [
                3.927862470899887e-07,
                6.475947210046347e-07,
                1.8553914607267268e-07,
                1.994729483729522e-06,
                9.422450432014836e-07,
                4.450852111148132e-07,
                2.1024331597262577e-07,
                5.04347468323289e-07,
                1.0677028700422047e-06,
                3.0590237279085045e-07
            ],
            [
                3.2887506336235617e-06,
                6.475951069985296e-07,
                9.42244930862237e-07,
                2.5612819054028872e-06,
                5.715004470313855e-07,
                4.450849988798682e-07,
                2.2603234895289998e-06,
                4.785093353909723e-06,
                2.2603234895372223e-06,
                8.315278294072958e-07
            ],
            [
                1.3709570433979422e-06,
                1.3709567164962755e-06,
                2.9023116389761676e-06,
                1.5534975693601474e-06,
                1.3709578605455302e-06,
                1.5534975693601474e-06,
                1.7603434231385591e-06,
                1.760343003481596e-06,
                1.2098661161927025e-06,
                1.9947306725451314e-06
            ],
            [
                3.466325797900508e-07,
                7.338209805240734e-07,
                NaN,
                6.144172404738491e-06,
                1.4738983729535602e-05,
                1.3709575337159875e-06,
                2.561281294760143e-06,
                7.338208930460318e-07,
                7.338210680021253e-07,
                1.209866260432471e-06
            ],
            [
                8.315283250371857e-07,
                7.338213304363436e-07,
                2.1024336609843824e-07,
                4.2228319344021954e-06,
                1.8553905760062447e-07,
                2.382368531929327e-07,
                6.14417753171671e-06,
                1.2098656835224664e-06,
                1.0677032518814388e-06,
                3.4663253846718004e-07
            ],
            [
                NaN,
                NaN,
                0.0004305569897133733,
                3.927862002663297e-07,
                6.144173869603344e-06,
                3.2887478892683997e-06,
                5.043472278322555e-07,
                7.338210680002898e-07,
                7.338209805240734e-07,
                2.260323758987159e-06
            ],
            [
                1.2098653950656417e-06,
                2.9023133690980155e-06,
                6.144173869603344e-06,
                2.9023119851781017e-06,
                4.785093924156175e-06,
                1.1478764021029928e-05,
                3.7266406168624155e-06,
                7.889259764445822e-06,
                9.422447062202052e-07,
                1.5534973841895917e-06
            ],
            [
                1.0677029973192638e-06,
                8.939695238634211e-06,
                1.3709570434219446e-06,
                1.9947299593078385e-06,
                4.7850967763512445e-06,
                NaN,
                3.288748281329893e-06,
                1.0677032518814388e-06,
                1.760343213335281e-06,
                1.670142980920999e-05
            ],
            [
                1.553498124964492e-06,
                1.9947299593014888e-06,
                5.043472278322555e-07,
                3.466326211113502e-07,
                2.699577452775239e-07,
                NaN,
                1.2098655392921197e-06,
                3.9278615344178325e-07,
                1.9947299593078385e-06,
                3.726638839878908e-06
            ],
            [
                1.2098662604247682e-06,
                NaN,
                2.4300232043369055e-05,
                1.2098662604247682e-06,
                1.2098653950656417e-06,
                2.699578096393206e-07,
                3.0590226339061185e-07,
                3.7266406168827523e-06,
                1.3709575337078829e-06,
                9.931186222523604e-08
            ],
            [
                1.012999581057419e-05,
                2.5612825160096693e-06,
                1.5534984953552536e-06,
                1.0129993394811673e-05,
                NaN,
                4.7850933534310035e-06,
                NaN,
                4.222833444467892e-06,
                NaN,
                2.5612834320563895e-06
            ],
            [
                1.0677029973192638e-06,
                3.0590226339061185e-07,
                1.2098656835224664e-06,
                1.2098662604291696e-06,
                8.315277302841894e-07,
                4.222834954753043e-06,
                1.2098659719757836e-06,
                7.338213304363436e-07,
                7.338209805224048e-07,
                1.0129990980100021e-05
            ],
            [
                7.33821330437595e-07,
                8.315278294114555e-07,
                4.450852641737424e-07,
                5.043475885696228e-07,
                2.382370235933104e-07,
                2.6995771309523475e-07,
                3.05902336324494e-07,
                5.715006514176113e-07,
                NaN,
                7.338207180898968e-07
            ],
            [
                3.4663278639892215e-07,
                NaN,
                NaN,
                NaN,
                1.5534973842076057e-06,
                6.144173137170873e-06,
                6.144175334468545e-06,
                5.422217030781934e-06,
                7.338208055680009e-07,
                3.288749457469787e-06
            ],
            [
                NaN,
                1.0677027427600627e-06,
                6.475950297971703e-07,
                7.338212429582604e-07,
                1.5534984953552536e-06,
                1.0677033791437343e-06,
                1.209866260432471e-06,
                1.0677024882009222e-06,
                2.260324567337161e-06,
                6.475948754012522e-07
            ],
            [
                8.315278294001114e-07,
                4.450849988758202e-07,
                1.5534979397677313e-06,
                3.059022998581767e-07,
                1.2098656835076114e-06,
                1.5534981249496567e-06,
                3.9278634073732336e-07,
                6.47594952595231e-07,
                1.5534977545603963e-06,
                5.043474081993875e-07
            ]
        ]
    },
    {
        "q_id": "9098_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            23,
            24,
            26,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            66,
            67,
            70,
            71,
            72,
            73,
            75,
            77,
            79,
            80,
            83,
            84,
            85,
            88,
            90,
            91,
            92,
            93,
            96,
            97,
            99,
            100,
            104,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.7266406168827523e-06,
                1.2098659719788098e-06,
                1.0677027427600627e-06,
                1.6373774480605869e-07,
                3.288747889284851e-06,
                1.8553914607267268e-07,
                3.466327037539638e-07,
                5.043473480777865e-07,
                2.1024339116168358e-07,
                1.370957860576702e-06
            ],
            [
                2.5612812947380135e-06,
                1.9947306726594253e-06,
                1.7603434231777837e-06,
                1.7603440527222532e-06,
                8.481104138976795e-05,
                2.382369383923073e-07,
                6.1441731370702875e-06,
                1.3709568799760888e-06,
                7.484624512911504e-05,
                4.0063696969564425e-05
            ],
            [
                6.475947981975644e-07,
                1.3709568799760888e-06,
                5.715004470313855e-07,
                2.5612828213690224e-06,
                7.889260704968913e-06,
                1.0129988565084915e-05,
                1.9947306726594253e-06,
                1.0677028700363782e-06,
                4.4508494582314646e-07,
                3.7266401726359486e-06
            ],
            [
                7.338208055680009e-07,
                NaN,
                0.9999987901341727,
                NaN,
                0.9999987901343169,
                2.699577452775239e-07,
                3.2887506336235617e-06,
                0.9999989322971305,
                2.3823693839325527e-07,
                2.699577774589574e-07
            ],
            [
                5.715003789046955e-07,
                1.27519088491875e-07,
                4.450851049991497e-07,
                2.5612834320563895e-06,
                1.760343213335281e-06,
                1.5534971990169383e-06,
                4.4508515805735777e-07,
                1.637376862489725e-07,
                2.699577774585891e-07,
                1.637376862489725e-07
            ],
            [
                6.962257079889302e-06,
                1.7603430034867993e-06,
                5.043473480777865e-07,
                2.753569766795419e-05,
                1.209866260432471e-06,
                2.3823690999323465e-07,
                2.90231094723893e-06,
                7.338208930460318e-07,
                1.209866260432471e-06,
                1.760343213335281e-06
            ],
            [
                2.260324567337161e-06,
                1.7603436330179102e-06,
                3.288749849477628e-06,
                4.785095635655362e-06,
                9.610242648063708e-05,
                1.9947299593014888e-06,
                1.3007126914435202e-05,
                1.4738980213985297e-05,
                6.475950298011458e-07,
                5.422217030032353e-06
            ],
            [
                4.222832941072913e-06,
                3.288748281329893e-06,
                1.3007125363908762e-05,
                6.475945666051092e-07,
                1.0677031245990084e-06,
                4.785093353940187e-06,
                6.144174601991196e-06,
                1.3709570434219446e-06,
                1.3709572068522336e-06,
                2.5612812947240366e-06
            ],
            [
                1.1478765389368729e-05,
                2.26032402841657e-06,
                4.450849988811838e-07,
                5.4222176771176554e-06,
                6.475951069985296e-07,
                3.726637951387472e-06,
                3.726638839878908e-06,
                2.753568453712307e-05,
                3.726639728370556e-06,
                4.785093353909723e-06
            ],
            [
                2.5612825160562587e-06,
                NaN,
                4.785094494750855e-06,
                1.9947297215043796e-06,
                8.93969950132721e-06,
                2.90231094723893e-06,
                1.0129995810343862e-05,
                5.144220140264605e-05,
                1.4738976701411704e-05,
                1.0129990980100021e-05
            ],
            [
                1.3709572068522336e-06,
                1.0677024882009222e-06,
                4.222832437677995e-06,
                3.726638395611981e-06,
                3.2887498495150166e-06,
                2.902312677137316e-06,
                2.9023112931688987e-06,
                4.006369219233375e-05,
                2.430024652854702e-05,
                1.7603438428660665e-06
            ],
            [
                3.927860597945825e-07,
                6.47595107001401e-07,
                4.450848927650143e-07,
                4.4508526417298334e-07,
                1.3709575337159875e-06,
                2.3823699519290042e-07,
                2.3823682479292225e-07,
                3.05902190458764e-07,
                7.889260704968913e-06,
                2.1024341622426268e-07
            ],
            [
                1.2098662604291696e-06,
                9.422444815765128e-07,
                2.9023116392097746e-06,
                8.939695238634211e-06,
                3.120190393794438e-05,
                2.699577452746696e-07,
                3.466327037553825e-07,
                2.5612819054133693e-06,
                5.715003107738556e-07,
                5.043475885634304e-07
            ],
            [
                2.2603251062450327e-06,
                1.012998977264307e-05,
                1.760342793638743e-06,
                9.422448185534261e-07,
                6.962258739796719e-06,
                2.902313023130843e-06,
                4.4508494582405734e-07,
                3.4663278639892215e-07,
                1.9947299593078385e-06,
                1.209865827752005e-06
            ],
            [
                1.0677027427624903e-06,
                8.315280276626197e-07,
                9.422444815814404e-07,
                8.315281267861397e-07,
                9.422444815814404e-07,
                3.4663266243308805e-07,
                NaN,
                6.962257909785973e-06,
                5.043474081993875e-07,
                6.475945666051092e-07
            ],
            [
                9.422447062294175e-07,
                3.4663278639892215e-07,
                5.715006514176113e-07,
                1.6373776432509826e-07,
                2.6995784182183607e-07,
                6.47594952603035e-07,
                1.637376862489725e-07,
                2.6995771309523475e-07,
                1.8553914607267268e-07,
                2.699577774585891e-07
            ],
            [
                2.699578740011634e-07,
                4.450849988811838e-07,
                8.315282259009745e-07,
                2.3823690999063455e-07,
                4.450848927650143e-07,
                1.5534973841592143e-06,
                2.69957906184239e-07,
                7.338209805170655e-07,
                4.450852111148132e-07,
                5.04347528440776e-07
            ],
            [
                1.2098656835224664e-06,
                5.715007195447234e-07,
                3.288750241500471e-06,
                1.0677028700363782e-06,
                1.2098661161927025e-06,
                1.7603432133136672e-06,
                1.3709578605617394e-06,
                1.5534975693707442e-06,
                3.059021175261338e-07,
                1.0677026154730804e-06
            ],
            [
                6.605216832236121e-05,
                1.892515049819277e-05,
                1.2098659719788098e-06,
                2.2603242978871282e-06,
                1.0677028700422047e-06,
                0.9999898700090866,
                3.726639284144195e-06,
                5.422220909009474e-06,
                5.04347528446051e-07,
                6.962257909842961e-06
            ],
            [
                3.9278624708775595e-07,
                2.90231094723893e-06,
                6.475945666051092e-07,
                5.043474081993875e-07,
                8.315281267834927e-07,
                3.0590226339061185e-07,
                1.760343213335281e-06,
                3.466327037539638e-07,
                8.315279285351409e-07,
                1.2098659719788098e-06
            ],
            [
                7.338209805240734e-07,
                1.3709567165530083e-06,
                1.0677024881980089e-06,
                2.2603242978778778e-06,
                3.927860597945825e-07,
                1.067702615468225e-06,
                2.382369951932796e-07,
                3.9278615344178325e-07,
                2.2603253756956754e-06,
                1.99472924590571e-06
            ],
            [
                9.422442569315887e-07,
                NaN,
                1.3709567165579959e-06,
                5.71500378896509e-07,
                3.466327037548308e-07,
                7.338209805200689e-07,
                9.422450431989127e-07,
                5.043473480777865e-07,
                8.315283250371857e-07,
                2.260324567337161e-06
            ],
            [
                2.1024339116168358e-07,
                5.715007195447234e-07,
                1.0677033791612137e-06,
                9.422448185534261e-07,
                1.2098653950692178e-06,
                1.0677028700422047e-06,
                6.962257909785973e-06,
                9.422445939054222e-07,
                5.422217677152175e-06,
                1.7603438428800754e-06
            ],
            [
                1.2098655392811161e-06,
                5.715007195447234e-07,
                6.475947210046347e-07,
                7.889259764445822e-06,
                7.338209805224048e-07,
                1.067703251864202e-06,
                5.422218323290717e-06,
                4.539787406003298e-05,
                8.315281267834927e-07,
                1.0677024881829577e-06
            ],
            [
                3.466327450765785e-07,
                5.715002426460124e-07,
                8.315278294001114e-07,
                5.715004470313855e-07,
                4.450852111148132e-07,
                1.0677031245710902e-06,
                7.338212429464139e-07,
                1.2098656835136636e-06,
                2.6995790618252024e-07,
                3.2887482811220126e-06
            ],
            [
                1.2098662604291696e-06,
                4.785095065171522e-06,
                6.475948754012522e-07,
                3.7266401726359486e-06,
                4.450848927650143e-07,
                3.9278615344178325e-07,
                5.715005832886879e-07,
                4.785096776468749e-06,
                1.3709573702822306e-06,
                5.715005832872586e-07
            ],
            [
                3.4663278639892215e-07,
                3.059022998581767e-07,
                1.1253509497883659e-07,
                1.855391681906175e-07,
                1.6373766672994222e-07,
                2.382369667929001e-07,
                2.1024334103581732e-07,
                1.855390576008354e-07,
                1.275191036933194e-07,
                1.855391239547094e-07
            ],
            [
                4.222834451382849e-06,
                1.0677032518785256e-06,
                6.144172404738491e-06,
                2.2603234895372223e-06,
                3.2887498495150166e-06,
                2.902312677150514e-06,
                2.2603253756956754e-06,
                6.144176799334096e-06,
                2.2603251062450327e-06,
                1.3709572068522336e-06
            ],
            [
                2.7535681254003062e-05,
                4.785095635592258e-06,
                6.1441731370702875e-06,
                3.726639284103523e-06,
                2.753569110256289e-05,
                5.4222176771176554e-06,
                1.7603427936335396e-06,
                4.78509278348926e-06,
                2.260324836787226e-06,
                5.829126555256903e-05
            ],
            [
                3.05902336324494e-07,
                6.82560779249779e-08,
                1.6373770576776313e-07,
                1.1253525596174225e-07,
                6.023578501513224e-08,
                0.9999945777810352,
                2.1024334103581732e-07,
                1.2098652508424818e-06,
                1.1253525596174225e-07,
                0.9999949062962147
            ],
            [
                9.422449308673789e-07,
                6.475951070002966e-07,
                1.2098656835224664e-06,
                5.422217677152175e-06,
                5.715005832886879e-07,
                1.2098655392921197e-06,
                3.535625071730638e-05,
                9.422450431989127e-07,
                3.059023363221292e-07,
                1.6701421845361053e-05
            ],
            [
                2.6995774527718623e-07,
                8.315281267882195e-07,
                3.9278634073732336e-07,
                3.059021175261338e-07,
                3.0590237279085045e-07,
                3.4663249714612693e-07,
                6.475947210046347e-07,
                3.466326624336003e-07,
                5.04347287955046e-07,
                3.05902263391829e-07
            ],
            [
                1.9947304348862686e-06,
                1.5534975693933505e-06,
                1.1478770862735993e-05,
                1.1478769494396542e-05,
                1.147877359957198e-05,
                1.012998977264307e-05,
                1.0129989772532511e-05,
                5.422218323487975e-06,
                NaN,
                4.222834954778007e-06
            ],
            [
                2.1024341622426268e-07,
                2.102434412871794e-07,
                1.1253520230052635e-07,
                2.6995774527718623e-07,
                6.825598028392069e-08,
                2.699577774589574e-07,
                1.8553905760024476e-07,
                1.444979692800516e-07,
                6.475949526020042e-07,
                1.855391681906175e-07
            ],
            [
                1.0677027427600627e-06,
                1.9947292459347367e-06,
                3.927862002663297e-07,
                6.475947210031623e-07,
                1.067703379154416e-06,
                7.484624512911504e-05,
                0.0004305571822548241,
                8.315283250371857e-07,
                5.715002426486762e-07,
                1.3709573702822306e-06
            ],
            [
                2.2603234895289998e-06,
                6.962254589978262e-06,
                6.144173869603344e-06,
                8.939700567094277e-06,
                1.3709568799919866e-06,
                2.6995790618469934e-07,
                1.5534973842076057e-06,
                1.1253516205489029e-07,
                NaN,
                1.7603427936335396e-06
            ],
            [
                2.1024331597262577e-07,
                9.422443692574719e-07,
                1.370957860576702e-06,
                3.7266410611296085e-06,
                7.889260704968913e-06,
                8.939693107190907e-06,
                7.484624511223438e-05,
                1.6701425827133152e-05,
                1.7603425837855082e-06,
                4.2228324377740105e-06
            ],
            [
                5.043476486924565e-07,
                6.475946438055299e-07,
                NaN,
                1.209865827752005e-06,
                1.9947297215043796e-06,
                1.209865827752005e-06,
                1.5534975693933505e-06,
                2.5612834320563895e-06,
                5.71500515161527e-07,
                8.315279285370317e-07
            ],
            [
                2.902312331170226e-06,
                6.144176799334096e-06,
                1.012998977264307e-05,
                1.147877359957198e-05,
                2.561282210729555e-06,
                1.3007125363908762e-05,
                NaN,
                3.1201926253802263e-05,
                NaN,
                7.338209805240734e-07
            ],
            [
                1.275190276859705e-07,
                4.450852641737424e-07,
                1.1253522913127183e-07,
                1.6373766672994222e-07,
                2.3823690999323465e-07,
                3.05902336324494e-07,
                8.764252675194995e-08,
                2.9023119851899796e-06,
                1.1253508156363576e-07,
                1.1253506814842375e-07
            ],
            [
                1.855391681906175e-07,
                1.209865539295696e-06,
                4.785094494811783e-06,
                2.1024336609843824e-07,
                6.475949526020042e-07,
                4.22283545819819e-06,
                3.4663274507713016e-07,
                9.931186222523604e-08,
                4.785093924389007e-06,
                NaN
            ],
            [
                2.5612825160271407e-06,
                NaN,
                4.785094494672519e-06,
                6.144173137126169e-06,
                3.2887490653872164e-06,
                6.144176066795103e-06,
                7.338213304316717e-07,
                1.7603436330179102e-06,
                8.315282259089153e-07,
                6.475947210012481e-07
            ],
            [
                4.785095635592258e-06,
                7.338212429582604e-07,
                3.9278634073732336e-07,
                5.715005832886879e-07,
                8.315278294097538e-07,
                2.5612812947508257e-06,
                1.3709568799919866e-06,
                3.726638839878908e-06,
                3.466327037539638e-07,
                1.1478764020560142e-05
            ],
            [
                8.315278293899016e-07,
                1.0677028700363782e-06,
                NaN,
                1.3709568799823232e-06,
                1.3709573702722555e-06,
                4.2228324377740105e-06,
                2.5612831267086116e-06,
                5.043475284430694e-07,
                1.2098662604192665e-06,
                3.927863875584984e-07
            ],
            [
                NaN,
                5.422220262636381e-06,
                2.9023133690980155e-06,
                8.315277302788957e-07,
                6.962257079705671e-06,
                1.2098656835224664e-06,
                2.561282516066741e-06,
                1.0677028700363782e-06,
                1.3007126914435202e-05,
                5.043475885674441e-07
            ],
            [
                5.422217030747413e-06,
                3.9278615344178325e-07,
                NaN,
                2.69957906184239e-07,
                1.4449798650569826e-07,
                8.939696304311336e-06,
                6.47594798194325e-07,
                0.0,
                5.3157811697009444e-08,
                2.6995774527718623e-07
            ],
            [
                5.422218969858371e-06,
                1.3007133116732079e-05,
                3.466326624336003e-07,
                6.1441746020359e-06,
                3.0590219045914655e-07,
                1.6373776432509826e-07,
                3.2887498495150166e-06,
                3.9278629391427843e-07,
                1.6701425827133152e-05,
                6.475949526020042e-07
            ],
            [
                3.059021175261338e-07,
                3.466325797896173e-07,
                1.4449795205429202e-07,
                4.450850519403407e-07,
                3.05902336324494e-07,
                6.023577783447482e-08,
                2.382369667929001e-07,
                2.1024341622426268e-07,
                6.475947982037486e-07,
                9.422447062294175e-07
            ],
            [
                2.3823693839325527e-07,
                9.931187406410953e-08,
                9.422443692574719e-07,
                1.5534971990169383e-06,
                5.422221555414699e-06,
                5.043475885696228e-07,
                1.9947292459406333e-06,
                3.535624228313077e-05,
                2.3823696679327928e-07,
                1.27519088491875e-07
            ],
            [
                1.4738987243236881e-05,
                6.475945666051092e-07,
                3.288747889284851e-06,
                4.2228319344021954e-06,
                1.0677028700363782e-06,
                8.315281267834927e-07,
                8.315278294072958e-07,
                4.785092783519724e-06,
                1.5534973842076057e-06,
                1.2098653950692178e-06
            ],
            [
                7.338210680021253e-07,
                NaN,
                6.475949526020042e-07,
                2.102434412875379e-07,
                5.715003107767143e-07,
                5.4222183235249605e-06,
                8.315278294114555e-07,
                3.927863407379485e-07,
                3.9278634073732336e-07,
                3.4663278639892215e-07
            ],
            [
                1.275190732904469e-07,
                5.043475885696228e-07,
                NaN,
                3.2887506336235617e-06,
                3.9278634073732336e-07,
                1.8553914607267268e-07,
                2.382369667929001e-07,
                1.5534971990169383e-06,
                4.2228319344021954e-06,
                6.475946438055299e-07
            ],
            [
                2.699577774585891e-07,
                2.1444950971601277e-05,
                8.764242227418718e-08,
                7.734424996987981e-08,
                6.962253760024999e-06,
                1.6373764721072816e-07,
                2.3823693839325527e-07,
                1.855391239547094e-07,
                4.450852111148132e-07,
                0.00020342690101849269
            ],
            [
                2.102434162245973e-07,
                1.275190276859705e-07,
                7.338212429594283e-07,
                1.0677026154827912e-06,
                1.8553910183674878e-07,
                1.5534975693979422e-06,
                3.927863875616689e-07,
                5.043474683240344e-07,
                8.315278294114555e-07,
                5.043475885696228e-07
            ],
            [
                1.6701421845057263e-05,
                1.0129993395336818e-05,
                1.0129989772532511e-05,
                2.260324028427877e-06,
                4.450848927621807e-07,
                1.7603427936335396e-06,
                8.315281267834927e-07,
                3.288748673360027e-06,
                2.7535691101761522e-05,
                7.889262585886274e-06
            ],
            [
                3.288749457409966e-06,
                6.475948754012522e-07,
                5.422217030747413e-06,
                1.0129987357407137e-05,
                3.7266401726359486e-06,
                6.962254589914941e-06,
                6.962256249821764e-06,
                6.962257909722651e-06,
                1.4738976701170414e-05,
                1.1478772230929451e-05
            ],
            [
                4.222834954778007e-06,
                8.315284241597959e-07,
                1.3709576971425944e-06,
                4.78509278348926e-06,
                7.88926446679691e-06,
                5.043475885674441e-07,
                8.315284241597959e-07,
                1.2098659719757836e-06,
                1.3709576971425944e-06,
                1.0677024881980089e-06
            ],
            [
                4.0063677865600476e-05,
                1.0677029973192638e-06,
                NaN,
                3.288749065423109e-06,
                4.785095635655362e-06,
                4.006369219073056e-05,
                2.10243290909724e-07,
                3.288750241561788e-06,
                5.715005151606823e-07,
                5.715003107755449e-07
            ],
            [
                0.9999997897565588,
                0.9999998555020135,
                0.9999998144608762,
                0.9999998642567028,
                3.059022998576899e-07,
                2.561281905376098e-06,
                2.699577774585891e-07,
                0.99999886343629,
                0.9999998461827139,
                0.9999997897566089
            ],
            [
                5.043473480784173e-07,
                NaN,
                2.902312677150514e-06,
                2.3823693839325527e-07,
                0.9999741325726184,
                1.3709575337159875e-06,
                1.3709576971463352e-06,
                7.338210680021253e-07,
                1.0677028700422047e-06,
                NaN
            ],
            [
                5.043474081993875e-07,
                6.475951069961737e-07,
                1.2098659719601033e-06,
                3.927862002654366e-07,
                2.102434412871794e-07,
                3.9278624708775595e-07,
                8.315279285370317e-07,
                2.5612812947240366e-06,
                1.855391239547094e-07,
                3.0590215399183813e-07
            ],
            [
                7.338212429582604e-07,
                2.260324567337161e-06,
                3.726637951387472e-06,
                3.120191881525687e-05,
                1.5534971990126997e-06,
                1.5534979397500702e-06,
                1.0677026154730804e-06,
                1.2098659719757836e-06,
                1.994729008145876e-06,
                1.7603425837855082e-06
            ],
            [
                7.338212429537553e-07,
                1.3709575336947905e-06,
                9.422447062270609e-07,
                1.9947297214182054e-06,
                9.422443692489024e-07,
                1.994729721482609e-06,
                4.450850519403407e-07,
                4.450849458218309e-07,
                6.475947982002148e-07,
                8.315284241597959e-07
            ],
            [
                3.46632497145457e-07,
                1.5534975693979422e-06,
                1.3709576971425944e-06,
                1.3709572068522336e-06,
                1.3709567165617364e-06,
                2.5612831267202583e-06,
                2.902313369111213e-06,
                1.3709567165461505e-06,
                3.72664061681327e-06,
                6.962253760024999e-06
            ],
            [
                1.1253526937656726e-07,
                1.0677026154806063e-06,
                3.466325797896173e-07,
                7.338212429582604e-07,
                NaN,
                3.466326624336003e-07,
                1.760342793638743e-06,
                1.209865827752005e-06,
                9.422447062294175e-07,
                6.475949526020042e-07
            ],
            [
                1.8553916819032217e-07,
                5.715005151606823e-07,
                1.4449795205472734e-07,
                8.315278294114555e-07,
                2.3823693839325527e-07,
                3.0590237279032884e-07,
                3.059022998581767e-07,
                1.1253516205489029e-07,
                1.3709568799823232e-06,
                2.5612819054133693e-06
            ],
            [
                2.382370235933104e-07,
                1.5534975693979422e-06,
                1.0677027427624903e-06,
                NaN,
                1.855391239547094e-07,
                2.69957906184239e-07,
                3.9278605979534166e-07,
                2.902312330891746e-06,
                6.023579219579052e-08,
                1.2751899728286965e-07
            ],
            [
                3.4663249714325014e-07,
                1.7603430034867993e-06,
                6.144173869603344e-06,
                5.043474081993875e-07,
                8.315277302841894e-07,
                1.3709575337159875e-06,
                4.450851049959619e-07,
                1.3709567165617364e-06,
                6.962256249885085e-06,
                1.0677024882009222e-06
            ],
            [
                1.2098662604247682e-06,
                6.475947210046347e-07,
                3.05902336324494e-07,
                7.338210680021253e-07,
                3.288749849477628e-06,
                8.939696304116203e-06,
                2.902310947208574e-06,
                1.5534979397500702e-06,
                1.3709570434219446e-06,
                1.5534983101393749e-06
            ],
            [
                3.927862939126708e-07,
                2.6995784182140636e-07,
                1.8553905760024476e-07,
                2.1024339116134898e-07,
                3.05902263391829e-07,
                2.699577452775239e-07,
                2.1024344128660572e-07,
                1.855391239544352e-07,
                2.6995784182140636e-07,
                5.043475885657239e-07
            ],
            [
                5.043473480777865e-07,
                1.0677032518785256e-06,
                1.4449803818215767e-07,
                3.059022269254856e-07,
                2.6995784182183607e-07,
                1.855391681906175e-07,
                1.8553907971879076e-07,
                2.3823693839325527e-07,
                3.466325797888292e-07,
                6.47595107001401e-07
            ],
            [
                6.962253759828703e-06,
                6.962253759904688e-06,
                8.315278294072958e-07,
                6.1441760667392215e-06,
                1.3007123813382511e-05,
                1.0129987357287368e-05,
                1.1478773599425825e-05,
                3.726641061109272e-06,
                2.9023119851781017e-06,
                0.0002034270464616072
            ],
            [
                1.209866260432471e-06,
                6.962257909785973e-06,
                1.2098658277335738e-06,
                8.315284241597959e-07,
                1.6701421845057263e-05,
                3.7266397283231055e-06,
                8.315284241650899e-07,
                2.6995784182140636e-07,
                1.994730197090463e-06,
                7.338213304363436e-07
            ],
            [
                1.1253512180925583e-07,
                2.3823690999290963e-07,
                2.3823688159291947e-07,
                1.855391681906175e-07,
                1.6373776432509826e-07,
                2.699577774585891e-07,
                1.8553910183674878e-07,
                1.4449802095666915e-07,
                1.8553916819032217e-07,
                1.6373772528677946e-07
            ],
            [
                1.1253512180925583e-07,
                1.637377057673536e-07,
                8.76424013786396e-08,
                3.9278634073625165e-07,
                4.4508494582405734e-07,
                1.6373766672973748e-07,
                1.8553907971855875e-07,
                5.715007195431641e-07,
                1.855391239544352e-07,
                2.1024341622426268e-07
            ],
            [
                1.3709572068522336e-06,
                3.7266397283908927e-06,
                1.9947292459347367e-06,
                2.1024334103505245e-07,
                5.715003107755449e-07,
                4.4508494582405734e-07,
                2.699576809143613e-07,
                7.338207180864763e-07,
                2.902313023101807e-06,
                4.222835458175145e-06
            ],
            [
                2.3823688159291947e-07,
                2.3823702359290413e-07,
                3.9278605979534166e-07,
                5.715004470326849e-07,
                1.0677026154806063e-06,
                1.760343213335281e-06,
                4.450850519403407e-07,
                6.475945666063607e-07,
                8.315280276626197e-07,
                9.422447062294175e-07
            ],
            [
                1.2751901248454963e-07,
                3.0590237279032884e-07,
                2.3823688159291947e-07,
                5.715005151606823e-07,
                3.05902190458764e-07,
                3.059022998576899e-07,
                5.043474081993875e-07,
                5.043472278322555e-07,
                3.927863407379485e-07,
                3.0590237279032884e-07
            ],
            [
                2.561282516066741e-06,
                9.422445939054222e-07,
                1.209866260432471e-06,
                1.7603438428800754e-06,
                1.6701425827133152e-05,
                NaN,
                2.5612819054133693e-06,
                2.2603253756956754e-06,
                1.760342793638743e-06,
                4.53978632394714e-05
            ],
            [
                1.553497754583709e-06,
                1.5534971990169383e-06,
                5.422217030747413e-06,
                6.144176799283803e-06,
                5.715005151606823e-07,
                1.5534975693869924e-06,
                3.726638395611981e-06,
                0.0007096703843227284,
                4.785092783519724e-06,
                1.4738987243478167e-05
            ],
            [
                6.475945666051092e-07,
                3.466325797896173e-07,
                2.382369667929001e-07,
                8.315277302841894e-07,
                3.466325384661554e-07,
                6.475949526003845e-07,
                6.475945666051092e-07,
                5.043476486915964e-07,
                6.47595107001401e-07,
                2.5612834320563895e-06
            ],
            [
                6.475948754028718e-07,
                8.315279285351409e-07,
                0.9999798543164848,
                5.715005151606823e-07,
                1.5534979397790343e-06,
                1.3709567165617364e-06,
                8.315284241650899e-07,
                5.04347528446051e-07,
                5.043475885688201e-07,
                6.962253760024999e-06
            ],
            [
                1.3007125363908762e-05,
                5.043472879540142e-07,
                1.012999098021058e-05,
                2.5612831267202583e-06,
                6.962254589781966e-06,
                2.5612812947240366e-06,
                7.338211554801876e-07,
                1.4738981972082061e-05,
                1.067702870039777e-06,
                2.1444948412722418e-05
            ],
            [
                1.9947301970972664e-06,
                7.889266347786918e-06,
                1.8925157266089433e-05,
                0.9999974387184054,
                3.46632497145457e-07,
                2.2603240284371276e-06,
                1.1253509497883659e-07,
                NaN,
                2.561281600086738e-06,
                2.561282210740037e-06
            ],
            [
                1.9947299593078385e-06,
                2.2603253756956754e-06,
                5.422217030747413e-06,
                5.71500719545698e-07,
                1.3709572068522336e-06,
                2.561282516066741e-06,
                1.0677026154806063e-06,
                1.3709575337125585e-06,
                5.043474082005342e-07,
                6.144175334468545e-06
            ],
            [
                7.338208930421943e-07,
                2.9023109472244114e-06,
                5.71500515159253e-07,
                7.889260704968913e-06,
                6.14417533430649e-06,
                2.90231094723893e-06,
                1.2098653950656417e-06,
                5.422218969895357e-06,
                7.484620943960125e-05,
                5.715003789046955e-07
            ],
            [
                4.785095065232451e-06,
                9.422450432014836e-07,
                1.2098653950692178e-06,
                3.9278629391427843e-07,
                2.2603234895372223e-06,
                1.2098661162056318e-06,
                2.1024331597262577e-07,
                2.699577774585891e-07,
                4.2228319344021954e-06,
                3.726638839878908e-06
            ],
            [
                NaN,
                1.0129989772412744e-05,
                3.535624228698939e-05,
                7.48462005189952e-05,
                6.962255419868303e-06,
                4.785093353909723e-06,
                4.785093353940187e-06,
                NaN,
                7.889265407255982e-06,
                1.209865250822125e-06
            ],
            [
                7.338211554758494e-07,
                4.2228334445370225e-06,
                6.475946438022905e-07,
                3.726637951387472e-06,
                5.043472879540142e-07,
                7.889262585886274e-06,
                1.067703379154416e-06,
                8.939700566907275e-06,
                2.5612819054028872e-06,
                6.144173869446876e-06
            ],
            [
                2.2603242978871282e-06,
                1.3007130015677909e-05,
                5.043475885674441e-07,
                1.3709568799919866e-06,
                1.3709578605729614e-06,
                8.315282259089153e-07,
                3.9278610661366994e-07,
                5.043475885696228e-07,
                1.994730672675753e-06,
                1.5534975693979422e-06
            ],
            [
                2.2603245673443566e-06,
                1.994729483729522e-06,
                0.9999852610181458,
                1.5534984953552536e-06,
                2.561282516066741e-06,
                0.9999741325599631,
                0.9999962733598332,
                5.71500719545698e-07,
                3.05902336324494e-07,
                2.6995784182183607e-07
            ],
            [
                4.222831934379152e-06,
                3.7266401726173067e-06,
                9.422448185510695e-07,
                2.2603234895176927e-06,
                2.2603234895289998e-06,
                1.0677029973192638e-06,
                1.5534981249496567e-06,
                4.4508526417298334e-07,
                NaN,
                6.144172404520556e-06
            ],
            [
                1.760342793638743e-06,
                8.315279285351409e-07,
                2.2603234895372223e-06,
                8.315279285351409e-07,
                1.99472900813862e-06,
                7.338207180884785e-07,
                4.222834954778007e-06,
                9.422445939054222e-07,
                9.422447062294175e-07,
                6.475945666051092e-07
            ],
            [
                7.338208055680009e-07,
                2.1444945858485726e-05,
                9.422450431989127e-07,
                1.3709570434178922e-06,
                9.422445939032799e-07,
                1.7603425837791042e-06,
                1.0129990980100021e-05,
                1.4738989000422955e-05,
                1.8553905760062447e-07,
                5.4222183235249605e-06
            ],
            [
                1.3709573702822306e-06,
                9.422449308774482e-07,
                4.4508510499849186e-07,
                1.5534971990126997e-06,
                6.475945666051092e-07,
                7.338213304363436e-07,
                9.422445939032799e-07,
                8.315282259138311e-07,
                1.5534975693979422e-06,
                1.067703124601679e-06
            ],
            [
                5.71500651413193e-07,
                1.067703124601679e-06,
                5.715002426475718e-07,
                1.5534979397790343e-06,
                3.059022998576899e-07,
                5.715002426486762e-07,
                5.715003107767143e-07,
                3.288749065423109e-06,
                4.222834954778007e-06,
                3.466327037553825e-07
            ],
            [
                7.338210680021253e-07,
                1.9947290081286418e-06,
                2.2603237589779086e-06,
                4.785096776499213e-06,
                1.2098656835224664e-06,
                3.05902336324494e-07,
                1.0677027427600627e-06,
                4.222833444590791e-06,
                2.5612812947077304e-06,
                1.760343633031919e-06
            ],
            [
                1.2751905808881762e-07,
                3.9278629391427843e-07,
                7.338208055680009e-07,
                6.47595107001401e-07,
                0.9999687980963065,
                1.4449795205429202e-07,
                1.4449795205429202e-07,
                0.9999982396569981,
                0.9999938558246779,
                8.315282259051341e-07
            ],
            [
                1.7603440527334603e-06,
                1.994729483729522e-06,
                0.9999960330126738,
                7.33821330437595e-07,
                2.9023112932296107e-06,
                2.3823696679327928e-07,
                1.4449803818215767e-07,
                5.715006514176113e-07,
                1.3709575337159875e-06,
                1.300712536408621e-05
            ],
            [
                5.715007195431641e-07,
                4.450849988811838e-07,
                1.2098659719757836e-06,
                7.338213304343413e-07,
                6.475947982037486e-07,
                3.466326624322211e-07,
                6.475945666051092e-07,
                7.338209805200689e-07,
                3.46632497145457e-07,
                1.5534973842076057e-06
            ],
            [
                1.8553903548113195e-07,
                3.466326211105621e-07,
                2.561281294760143e-06,
                2.902313369111213e-06,
                5.04347528446051e-07,
                3.927862470899887e-07,
                3.4663253846718004e-07,
                5.04347408197782e-07,
                1.6373766672936518e-07,
                7.338209805240734e-07
            ],
            [
                5.043472278322555e-07,
                3.9278629391427843e-07,
                1.2751902768612997e-07,
                6.475949526003845e-07,
                4.22283545808297e-06,
                3.927862470899887e-07,
                3.466326624336003e-07,
                3.46632497145457e-07,
                4.222834954801051e-06,
                5.715003789033962e-07
            ]
        ]
    },
    {
        "q_id": "10193_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            13,
            14,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            58,
            59,
            62,
            63,
            64,
            65,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                2.144495864106235e-05,
                1.012998977264307e-05,
                0.00013982212424495333,
                2.5612834320563895e-06,
                3.7266397283908927e-06,
                0.00012339454558103757,
                3.120191881616493e-05,
                1.994729721518893e-06,
                5.715006514176113e-07,
                1.8553910183674878e-07
            ],
            [
                1.3709568799879344e-06,
                1.3709575337125585e-06,
                1.9947301970972664e-06,
                4.539787406217992e-05,
                1.3709575337125585e-06,
                9.422448185534261e-07,
                3.726637951387472e-06,
                5.422219616265831e-06,
                9.422442569315887e-07,
                2.260324567337161e-06
            ],
            [
                5.715002426486762e-07,
                1.1478766757718129e-05,
                3.288748281329893e-06,
                7.33821330437595e-07,
                6.962254589978262e-06,
                7.889265407327733e-06,
                6.9622595696935874e-06,
                1.3007130015488633e-05,
                4.22283545819819e-06,
                8.939693107190907e-06
            ],
            [
                0.9999970976887075,
                0.9999998144609645,
                4.450852641737424e-07,
                0.999993037744583,
                2.1444945858953813e-05,
                0.9999995262094986,
                2.7535694385633984e-05,
                0.9999998724808964,
                0.999999900688055,
                1.0129993395336818e-05
            ],
            [
                2.561281600086738e-06,
                3.466327037548308e-07,
                1.4738983729294318e-05,
                2.90231094723893e-06,
                1.994730434879465e-06,
                1.0129993395336818e-05,
                8.315284241650899e-07,
                8.315282259138311e-07,
                9.422443692574719e-07,
                2.144495608424996e-05
            ],
            [
                5.715003789046955e-07,
                2.9023133690980155e-06,
                1.7603434231833873e-06,
                6.475951069985296e-07,
                3.53562549305363e-05,
                3.4663253846718004e-07,
                2.69957906184239e-07,
                2.902312677150514e-06,
                0.00012339454556667436,
                7.338209805224048e-07
            ],
            [
                3.224188555067886e-08,
                0.9999998362623529,
                0.9999977396759736,
                6.023577065381482e-08,
                4.691167157146029e-08,
                1.3709575337159875e-06,
                1.3709567165617364e-06,
                1.2098661162056318e-06,
                6.962257079832313e-06,
                3.7266397283908927e-06
            ],
            [
                3.927862002641863e-07,
                8.939696304311336e-06,
                5.043476486915964e-07,
                1.855390576008354e-07,
                4.785095065232451e-06,
                1.9947299593078385e-06,
                3.927860597945825e-07,
                2.102434162245973e-07,
                2.5612819054133693e-06,
                1.8553910183674878e-07
            ],
            [
                6.475947982037486e-07,
                9.422443692555439e-07,
                3.466325797896173e-07,
                9.422445939054222e-07,
                6.962256249885085e-06,
                1.1478772231232203e-05,
                1.1478770862882149e-05,
                9.422449308774482e-07,
                2.260324836776948e-06,
                8.315282259138311e-07
            ],
            [
                4.222834451403972e-06,
                1.067703124601679e-06,
                4.222834451403972e-06,
                2.9023116392097746e-06,
                1.2098659719788098e-06,
                4.22283545819819e-06,
                3.288749065423109e-06,
                2.699578096403948e-07,
                1.300712536408621e-05,
                9.422447062294175e-07
            ],
            [
                4.785096776499213e-06,
                2.9023116392097746e-06,
                2.1024341622426268e-07,
                1.2098653950692178e-06,
                6.475947210031623e-07,
                5.422218969895357e-06,
                1.370957860576702e-06,
                2.9023116392097746e-06,
                8.315281267882195e-07,
                8.939698435657833e-06
            ],
            [
                5.144221366623174e-05,
                5.422220909009474e-06,
                1.9947292459347367e-06,
                1.5534973842076057e-06,
                3.535626757524533e-05,
                2.5612828213934817e-06,
                7.889261645427538e-06,
                1.0677029973219343e-06,
                5.422217677152175e-06,
                NaN
            ],
            [
                1.0677026154806063e-06,
                2.2603253756956754e-06,
                6.144173869603344e-06,
                NaN,
                6.962255419931625e-06,
                6.962254589978262e-06,
                NaN,
                6.475947982022763e-07,
                3.288749065423109e-06,
                7.889261645355786e-06
            ],
            [
                6.605217618626244e-05,
                8.315281267861397e-07,
                2.9023119851635836e-06,
                3.059022269250683e-07,
                4.2228349547223175e-06,
                1.5534979397740895e-06,
                2.5612819054028872e-06,
                0.0001088969482847688,
                3.4663249714612693e-07,
                2.9023119851781017e-06
            ],
            [
                6.144172404693786e-06,
                1.1478769494396542e-05,
                4.539786864876098e-05,
                8.93969950132721e-06,
                4.222834451355964e-06,
                2.1444953523537147e-05,
                6.9622537599680095e-06,
                8.939700567004841e-06,
                3.726638395634011e-06,
                3.9278610661902853e-07
            ],
            [
                3.927863407379485e-07,
                2.5612834320563895e-06,
                4.2228324377740105e-06,
                3.466326624336003e-07,
                1.9947292459347367e-06,
                1.9947299593078385e-06,
                1.7603430034867993e-06,
                4.22283545819819e-06,
                1.2098656835224664e-06,
                NaN
            ],
            [
                7.734416698849138e-08,
                8.764241182641775e-08,
                9.93120161310289e-08,
                6.825600469412533e-08,
                1.1253509497883659e-07,
                7.734418542875216e-08,
                7.73441946488886e-08,
                2.6995790618469934e-07,
                1.1253512180925583e-07,
                8.764242227418718e-08
            ],
            [
                1.3709568799919866e-06,
                5.043475885696228e-07,
                9.422449308774482e-07,
                5.715002426486762e-07,
                1.760343003481596e-06,
                NaN,
                5.71500719545698e-07,
                2.561282210740037e-06,
                9.422445939054222e-07,
                7.338209805240734e-07
            ],
            [
                NaN,
                6.47595107001401e-07,
                7.889265407327733e-06,
                4.22283545819819e-06,
                2.9023119851899796e-06,
                1.855391239547094e-07,
                NaN,
                7.338208055680009e-07,
                1.5534973842076057e-06,
                7.889262585886274e-06
            ],
            [
                1.7603430034867993e-06,
                1.2751902768612997e-07,
                5.04347468323289e-07,
                5.71500719545698e-07,
                1.8553914607267268e-07,
                8.315278294072958e-07,
                1.7603425837903113e-06,
                1.7603425837903113e-06,
                NaN,
                2.10243290909724e-07
            ],
            [
                3.059022998576899e-07,
                1.7603434231833873e-06,
                7.338208930460318e-07,
                1.209866260432471e-06,
                1.5534973842076057e-06,
                6.475947982037486e-07,
                4.22283545819819e-06,
                1.3709576971463352e-06,
                1.6373766672973748e-07,
                1.5534983101644536e-06
            ],
            [
                2.9023119851899796e-06,
                1.994729721518893e-06,
                5.715002426486762e-07,
                2.2603245673443566e-06,
                8.315284241650899e-07,
                3.927860597945825e-07,
                1.5534973842076057e-06,
                5.715002426475718e-07,
                5.715003107767143e-07,
                2.382368531929327e-07
            ],
            [
                4.222834954801051e-06,
                3.466325797900508e-07,
                1.5534984953552536e-06,
                1.5534975693979422e-06,
                1.067703124601679e-06,
                5.715003107767143e-07,
                6.9622595696935874e-06,
                5.043474082012222e-07,
                1.892515049819277e-05,
                3.927862470905692e-07
            ],
            [
                8.764241182641775e-08,
                1.1253513522447425e-07,
                8.315280276626197e-07,
                3.059021175255426e-07,
                3.466327037553825e-07,
                7.734418542875216e-08,
                9.931195693628605e-08,
                1.8553905760062447e-07,
                9.931189774187203e-08,
                1.8553910183674878e-07
            ],
            [
                6.475945666063607e-07,
                6.962253760024999e-06,
                NaN,
                7.889265407327733e-06,
                6.144173137170873e-06,
                5.422221555414699e-06,
                1.012999218776902e-05,
                2.382368531929327e-07,
                4.785094494783494e-06,
                1.9947304348862686e-06
            ],
            [
                1.3709572068522336e-06,
                4.222835458148261e-06,
                1.9947292459265734e-06,
                1.0677024882009222e-06,
                0.9999986290429576,
                0.999998346310218,
                9.931195693628605e-08,
                1.3709567165617364e-06,
                5.715003107767143e-07,
                0.9998204720360444
            ],
            [
                6.144175334468545e-06,
                5.04347287955046e-07,
                2.382368531929327e-07,
                2.699577774585891e-07,
                1.3709567165617364e-06,
                3.059022998576899e-07,
                2.102433660979124e-07,
                1.8553919030858602e-07,
                2.902313023130843e-06,
                4.4508510499849186e-07
            ],
            [
                1.444980726324838e-07,
                2.1024334103505245e-07,
                1.637377448057981e-07,
                2.382368531929327e-07,
                9.931190958076104e-08,
                1.8553903548231313e-07,
                9.931189774187203e-08,
                1.1253516205489029e-07,
                2.1024326584639497e-07,
                9.931189774187203e-08
            ],
            [
                1.3709576971463352e-06,
                6.962257909842961e-06,
                0.957912276139514,
                5.715003789046955e-07,
                1.2098656835224664e-06,
                7.338207180898968e-07,
                5.144220140264605e-05,
                5.715002426486762e-07,
                7.889259764517575e-06,
                1.5534983101644536e-06
            ],
            [
                6.144176066901277e-06,
                8.939700566907275e-06,
                3.726637951387472e-06,
                4.5397857828200684e-05,
                5.422219616265831e-06,
                1.3709570434219446e-06,
                1.1478764021029928e-05,
                4.222831934379152e-06,
                1.2098652508424818e-06,
                NaN
            ],
            [
                1.6373764721072816e-07,
                4.2228339479858295e-06,
                3.4663278639892215e-07,
                1.27519088491875e-07,
                4.450852641737424e-07,
                2.382370235933104e-07,
                1.637377057680051e-07,
                1.2751899728311609e-07,
                3.4663274507713016e-07,
                3.05902336324494e-07
            ],
            [
                3.7266401726359486e-06,
                4.785094494811783e-06,
                8.939697369980456e-06,
                0.9999990577554065,
                0.999998005270042,
                0.9999983463096264,
                0.9999983463104153,
                0.9999957771655507,
                0.9999978766222987,
                0.999993855825404
            ],
            [
                6.475945666051092e-07,
                9.422445939054222e-07,
                3.0590226339061185e-07,
                1.3709573702822306e-06,
                5.715005832886879e-07,
                5.04347528446051e-07,
                9.422442569315887e-07,
                3.927860597945825e-07,
                8.315281267834927e-07,
                7.33821330437595e-07
            ],
            [
                1.3709567165617364e-06,
                0.9999974387180971,
                4.785095635655362e-06,
                8.939699501229642e-06,
                1.3709573702822306e-06,
                8.481102118021275e-05,
                0.9999910603069138,
                1.0677024882009222e-06,
                2.1444940745839484e-05,
                2.561282516066741e-06
            ],
            [
                3.4663253846718004e-07,
                6.475947210031623e-07,
                NaN,
                7.889266347786918e-06,
                6.475947982037486e-07,
                2.902312677150514e-06,
                1.0129987357517693e-05,
                3.2887506336235617e-06,
                8.315284241650899e-07,
                1.7603430034867993e-06
            ],
            [
                6.962255419931625e-06,
                4.222833948008874e-06,
                9.610238067382736e-05,
                2.2603248367949354e-06,
                1.3709567165617364e-06,
                1.5534971990169383e-06,
                6.475945666063607e-07,
                4.450851049991497e-07,
                1.275190428875671e-07,
                6.962258739796719e-06
            ],
            [
                8.315281267861397e-07,
                2.561282516042282e-06,
                6.144175334418252e-06,
                5.4222183234485234e-06,
                1.3709573702822306e-06,
                3.726639728370556e-06,
                1.7603432133296774e-06,
                1.2098662604247682e-06,
                9.422449308748773e-07,
                1.9947292459347367e-06
            ],
            [
                2.5612812947508257e-06,
                1.7603440527286572e-06,
                1.8925157265710765e-05,
                1.7603432133296774e-06,
                5.04347528446051e-07,
                2.2603240284371276e-06,
                9.422448185510695e-07,
                1.5534975693933505e-06,
                1.5534981249697903e-06,
                5.422217030747413e-06
            ],
            [
                4.785092783519724e-06,
                7.73442776303243e-08,
                6.475945666063607e-07,
                3.7266406168827523e-06,
                4.2228319344021954e-06,
                2.561281600086738e-06,
                3.288749849529972e-06,
                4.785093353940187e-06,
                2.5612819054133693e-06,
                1.6373774480605869e-07
            ],
            [
                5.043475885696228e-07,
                3.726639728348526e-06,
                1.2098661162056318e-06,
                2.90231094723893e-06,
                4.450852641737424e-07,
                0.9999687980889166,
                0.9999832985822094,
                1.5534984953510149e-06,
                5.043475885696228e-07,
                0.9999756997535832
            ],
            [
                3.059022269250683e-07,
                1.7603438428848787e-06,
                1.8553910183649565e-07,
                4.4508510499849186e-07,
                3.9278610661902853e-07,
                3.059022998576899e-07,
                5.043476486915964e-07,
                3.927860597945825e-07,
                9.422448185510695e-07,
                3.46632497145457e-07
            ],
            [
                7.734423152941018e-08,
                4.691160446380562e-08,
                7.734421308914719e-08,
                7.734415776836702e-08,
                3.224189323773857e-08,
                8.764245361752286e-08,
                5.3157837044597743e-08,
                8.764254764780641e-08,
                4.139934092760465e-08,
                3.224184327183648e-08
            ],
            [
                1.5534973842076057e-06,
                2.902312331170226e-06,
                1.7603430034867993e-06,
                2.430024652854702e-05,
                9.931200429212718e-08,
                5.715002426486762e-07,
                3.2887506336235617e-06,
                2.2603251062450327e-06,
                2.3823690999290963e-07,
                2.3823690999323465e-07
            ],
            [
                2.90231094723893e-06,
                2.9023133690821773e-06,
                4.785096776499213e-06,
                8.939696304311336e-06,
                4.2228319344021954e-06,
                5.422220262636381e-06,
                2.9023112932177327e-06,
                2.430024073461624e-05,
                3.7266397283908927e-06,
                0.0002305066881357914
            ],
            [
                7.338210680021253e-07,
                7.338209805240734e-07,
                3.4663274507713016e-07,
                1.6373774480605869e-07,
                1.1253509497883659e-07,
                6.47595107001401e-07,
                1.275190732904469e-07,
                1.0677028700422047e-06,
                8.315278294114555e-07,
                2.6995774527718623e-07
            ],
            [
                8.315280276626197e-07,
                1.0129989772532511e-05,
                2.5612819054133693e-06,
                2.561282210740037e-06,
                1.7603425837903113e-06,
                1.3007134667259441e-05,
                3.288748673376478e-06,
                3.7266406168827523e-06,
                1.2098661162056318e-06,
                4.785095065232451e-06
            ],
            [
                1.6373766672973748e-07,
                1.4449805540763184e-07,
                9.931185038635267e-08,
                9.931186222523604e-08,
                9.931195693628605e-08,
                7.734418542875216e-08,
                7.73441946488886e-08,
                8.764241182641775e-08,
                7.734421308914719e-08,
                8.764253720001207e-08
            ],
            [
                1.5534975693933505e-06,
                2.6995771309523475e-07,
                6.475947210012481e-07,
                7.338209805224048e-07,
                1.2098659719757836e-06,
                1.0677032518785256e-06,
                9.422444815814404e-07,
                3.535625493182252e-05,
                4.222834954778007e-06,
                5.715004470313855e-07
            ],
            [
                1.9947292459406333e-06,
                2.3823688159291947e-07,
                7.338207180898968e-07,
                3.466325797888292e-07,
                2.699578740032504e-07,
                1.994729483729522e-06,
                1.209866260432471e-06,
                4.222832437798974e-06,
                1.3709567165617364e-06,
                8.315281267882195e-07
            ],
            [
                9.422448185478557e-07,
                1.8925143729575624e-05,
                4.006370652067535e-05,
                1.0677024881980089e-06,
                1.6701421845361053e-05,
                1.3709573702722555e-06,
                4.785095635592258e-06,
                7.889262585814522e-06,
                1.2098662604247682e-06,
                1.9947292459265734e-06
            ],
            [
                1.4449803818215767e-07,
                4.4508494582405734e-07,
                1.8553919030858602e-07,
                1.4449807263312446e-07,
                1.6373772528704005e-07,
                2.1024336609874897e-07,
                5.715006514176113e-07,
                1.855391681906175e-07,
                2.699578740032504e-07,
                1.8553914607267268e-07
            ],
            [
                1.5534983101602148e-06,
                2.902312331170226e-06,
                4.785094494811783e-06,
                8.939694172957213e-06,
                1.7603434231833873e-06,
                3.7266401726359486e-06,
                4.785095065232451e-06,
                1.5534971990169383e-06,
                2.90231094723893e-06,
                6.962259569750576e-06
            ],
            [
                1.2751899728311609e-07,
                3.4663274507713016e-07,
                2.10243290909724e-07,
                8.764244316973974e-08,
                1.8553905760062447e-07,
                2.1024336609843824e-07,
                1.6373776432509826e-07,
                3.466325797896173e-07,
                2.6995784182183607e-07,
                1.4449803818215767e-07
            ],
            [
                1.994729008145876e-06,
                1.6373764721072816e-07,
                3.466325384678894e-07,
                1.067703124601679e-06,
                0.9999599362985095,
                0.9999485577743548,
                1.444979692800516e-07,
                1.5534984953552536e-06,
                0.9998766054113759,
                9.422447062294175e-07
            ],
            [
                2.1024336609874897e-07,
                2.3823696679327928e-07,
                1.275190580890061e-07,
                1.6373762769138607e-07,
                1.0677032518814388e-06,
                1.8553910183674878e-07,
                1.4738983729535602e-05,
                7.734415776836702e-08,
                6.825598842065202e-08,
                2.753569110256289e-05
            ],
            [
                3.927860597945825e-07,
                9.422442569334097e-07,
                7.338209805240734e-07,
                3.059022998581767e-07,
                1.275190732904469e-07,
                2.9023133690980155e-06,
                2.260324567337161e-06,
                5.422218969895357e-06,
                7.338210680021253e-07,
                2.260325106237323e-06
            ],
            [
                0.00010889696125141565,
                3.2887506336235617e-06,
                7.889263526345123e-06,
                3.7266401726359486e-06,
                4.222833444590791e-06,
                2.2603253756874524e-06,
                8.939694172867777e-06,
                2.1444943302181958e-05,
                4.006367786720367e-05,
                1.7603440527222532e-06
            ],
            [
                5.422219616265831e-06,
                2.561281905390075e-06,
                8.315278294072958e-07,
                1.9947297215043796e-06,
                1.3709575337078829e-06,
                2.6995784182140636e-07,
                9.422448185478557e-07,
                1.7603434231705793e-06,
                1.5534975693869924e-06,
                7.338212429537553e-07
            ],
            [
                7.338209805224048e-07,
                2.699578096403948e-07,
                1.4449800373065699e-07,
                3.466327863983311e-07,
                5.043472278322555e-07,
                1.5534983101644536e-06,
                7.338208930460318e-07,
                2.3823702359290413e-07,
                5.715003789046955e-07,
                6.475945666063607e-07
            ],
            [
                9.931198061405701e-08,
                9.931193325852072e-08,
                2.6995790618350237e-07,
                2.1024326584639497e-07,
                1.6373766672973748e-07,
                8.764249540862797e-08,
                2.1024326584639497e-07,
                1.1253516205489029e-07,
                1.4449800373065699e-07,
                8.764254764780641e-08
            ],
            [
                1.0677029973219343e-06,
                3.4663274507713016e-07,
                1.9947299593078385e-06,
                2.430023204460668e-05,
                1.6701425827133152e-05,
                5.043472278322555e-07,
                3.7266410611296085e-06,
                0.9999869928684861,
                3.4663278639892215e-07,
                6.475945666051092e-07
            ],
            [
                4.450848927658745e-07,
                3.927863875616689e-07,
                2.5612819054133693e-06,
                1.8553905760062447e-07,
                7.338207180898968e-07,
                7.338212429582604e-07,
                4.785096776499213e-06,
                1.4449807263312446e-07,
                9.422444815814404e-07,
                3.4663278639892215e-07
            ],
            [
                1.553497754577351e-06,
                4.785096776468749e-06,
                1.2098659719716573e-06,
                4.450852111148132e-07,
                2.2603251062270446e-06,
                5.043472879540142e-07,
                1.0677029973192638e-06,
                3.2887490653872164e-06,
                3.927862002663297e-07,
                5.043472879525233e-07
            ],
            [
                2.2603240284371276e-06,
                3.059022269250683e-07,
                2.2603242978871282e-06,
                3.288747889284851e-06,
                2.3823685319244518e-07,
                6.475947210046347e-07,
                1.5534973842076057e-06,
                1.670142980893658e-05,
                2.902312677150514e-06,
                3.2887502415767434e-06
            ],
            [
                0.0001795279449767558,
                3.288748673376478e-06,
                1.1478769494542698e-05,
                1.994729008151319e-06,
                4.785096206076165e-06,
                3.120190393896595e-05,
                3.726639284144195e-06,
                1.3709567165617364e-06,
                1.9947299593078385e-06,
                1.0677028700422047e-06
            ],
            [
                1.1253506814797596e-07,
                6.825600469412533e-08,
                5.315789407685159e-08,
                4.691168275606451e-08,
                6.825606978822427e-08,
                1.1253517547010071e-07,
                1.8553910183548312e-07,
                1.275190732904469e-07,
                8.764252675194995e-08,
                7.734416698849138e-08
            ],
            [
                5.715003107715166e-07,
                1.5534975693601474e-06,
                1.760344052714248e-06,
                1.7603432133136672e-06,
                2.2603234895176927e-06,
                4.22283394786293e-06,
                2.9023116391978967e-06,
                2.260325106237323e-06,
                5.715005832886879e-07,
                7.889259764517575e-06
            ],
            [
                2.382370235933104e-07,
                2.699577774585891e-07,
                6.475946438055299e-07,
                7.338209805240734e-07,
                1.6373770576776313e-07,
                1.6373774480605869e-07,
                3.288749457469787e-06,
                2.6995784182183607e-07,
                1.855391681906175e-07,
                3.927862002663297e-07
            ],
            [
                5.4222183235249605e-06,
                1.8553907971879076e-07,
                2.2603253756956754e-06,
                NaN,
                8.764242227418718e-08,
                2.699577774589574e-07,
                3.0590219045914655e-07,
                0.5621765008857982,
                4.450848927658745e-07,
                6.962258739796719e-06
            ],
            [
                4.4508505193791187e-07,
                1.2098655392871682e-06,
                7.338208055664991e-07,
                6.475948754012522e-07,
                7.338212429537553e-07,
                6.475949525981759e-07,
                3.927862939126708e-07,
                9.4224425692559e-07,
                5.715007195447234e-07,
                7.338209805200689e-07
            ],
            [
                3.059022269250683e-07,
                1.8553907971855875e-07,
                1.1253516205489029e-07,
                1.6373770576776313e-07,
                1.2751901248454963e-07,
                1.1253516205489029e-07,
                2.1024336609874897e-07,
                1.6373776432509826e-07,
                1.6373768624837685e-07,
                1.4449805540740185e-07
            ],
            [
                5.04347468323289e-07,
                7.338209805240734e-07,
                NaN,
                1.7603430034867993e-06,
                6.475950298011458e-07,
                4.450850519403407e-07,
                1.3709575337159875e-06,
                2.2603251062450327e-06,
                3.2887506336235617e-06,
                3.2887502415767434e-06
            ],
            [
                2.699576809143613e-07,
                3.05902190458764e-07,
                4.450848927658745e-07,
                6.475947210031623e-07,
                7.734416698849138e-08,
                1.0677029973219343e-06,
                6.475947982037486e-07,
                3.0590237279032884e-07,
                2.699577774585891e-07,
                2.382368531929327e-07
            ],
            [
                2.3823696679327928e-07,
                1.6701423836262173e-05,
                9.422444815814404e-07,
                NaN,
                1.3007133116909523e-05,
                1.4449795205472734e-07,
                2.699578740032504e-07,
                1.1253524254650944e-07,
                1.4738978458623327e-05,
                0.0015011819862647004
            ],
            [
                4.4508515805735777e-07,
                3.05902336324494e-07,
                8.315284241650899e-07,
                1.3709576971463352e-06,
                6.47595107001401e-07,
                5.043476486924565e-07,
                2.90231094723893e-06,
                1.994729008145876e-06,
                8.315279285370317e-07,
                3.927863407379485e-07
            ],
            [
                1.4738981972564636e-05,
                7.889266347786918e-06,
                5.8291293348093234e-05,
                2.902312331170226e-06,
                2.75356812556058e-05,
                NaN,
                1.0129993395336818e-05,
                3.05902263391829e-07,
                3.2887506336235617e-06,
                NaN
            ],
            [
                2.144495608424996e-05,
                2.260325375664839e-06,
                2.5612831267202583e-06,
                5.043473480777865e-07,
                9.422448185534261e-07,
                7.889263526345123e-06,
                6.962254589978262e-06,
                3.726639284144195e-06,
                2.1444948415296896e-05,
                4.785095065232451e-06
            ],
            [
                1.3709575337159875e-06,
                9.422450432014836e-07,
                4.4508515805735777e-07,
                1.637377057680051e-07,
                1.2098653950692178e-06,
                1.5534979397500702e-06,
                1.0677032518814388e-06,
                1.0677031245990084e-06,
                2.6995790618469934e-07,
                3.726641061058432e-06
            ],
            [
                0.9999967112497715,
                0.9999989322970047,
                0.9999942280792933,
                0.9999964991460111,
                0.9999964991468455,
                0.9999942280813843,
                0.9999967112513322,
                0.9999832985722086,
                0.9999910603047895,
                0.9999921107364854
            ],
            [
                4.785092783519724e-06,
                9.931195693628605e-08,
                6.962257909842961e-06,
                2.69957906184239e-07,
                3.7266406168827523e-06,
                4.450848927658745e-07,
                2.561283126728994e-06,
                2.1024336609843824e-07,
                0.999983298584174,
                1.9947299593078385e-06
            ],
            [
                3.288749065423109e-06,
                1.3007126914612648e-05,
                4.785092783519724e-06,
                2.5612828213934817e-06,
                1.5534971990169383e-06,
                5.715002426475718e-07,
                5.4222183235249605e-06,
                1.3709576971425944e-06,
                1.4449800373118268e-07,
                1.9947292459406333e-06
            ],
            [
                1.3709568799919866e-06,
                6.475950298011458e-07,
                3.466325797888292e-07,
                1.3709573702856596e-06,
                2.102434412875379e-07,
                3.4663249714612693e-07,
                1.2098653950656417e-06,
                6.475946438055299e-07,
                2.699576809143613e-07,
                2.6995784182140636e-07
            ],
            [
                1.3007123813382511e-05,
                2.561281600086738e-06,
                1.370957860576702e-06,
                1.370957860576702e-06,
                1.2751901248454963e-07,
                3.927863875616689e-07,
                7.889262585886274e-06,
                7.889266347715168e-06,
                1.0129990980100021e-05,
                3.927862002663297e-07
            ],
            [
                9.422444815814404e-07,
                1.8925148241872038e-05,
                3.059022998576899e-07,
                1.0677028700363782e-06,
                9.422450431989127e-07,
                7.338208930460318e-07,
                6.475947210046347e-07,
                2.10243290909724e-07,
                5.715003789046955e-07,
                1.994730434879465e-06
            ],
            [
                1.4449795205429202e-07,
                3.0590226339061185e-07,
                1.6373770576776313e-07,
                3.4663262110945863e-07,
                3.466327037548308e-07,
                2.561281905390075e-06,
                7.338210680021253e-07,
                2.699578096393206e-07,
                2.6995790618469934e-07,
                3.0590215399183813e-07
            ],
            [
                9.422448185534261e-07,
                8.315279285370317e-07,
                2.6995790618469934e-07,
                1.3709575337159875e-06,
                9.931189774187203e-08,
                6.475945666063607e-07,
                2.561283126728994e-06,
                5.715006514176113e-07,
                9.422443692574719e-07,
                1.275190580890061e-07
            ],
            [
                5.715002426486762e-07,
                3.05902190458764e-07,
                0.9999706884652066,
                6.1441746020359e-06,
                0.9999910603016089,
                0.00015843627371237145,
                7.889260704968913e-06,
                1.0129994602895546e-05,
                7.338212429582604e-07,
                6.1441746020359e-06
            ],
            [
                9.422443692574719e-07,
                4.222835458175145e-06,
                4.785096206047877e-06,
                1.760343633031919e-06,
                3.0590237279085045e-07,
                NaN,
                1.8925148241872038e-05,
                2.430024942462891e-05,
                4.222831934379152e-06,
                1.3007134667259441e-05
            ],
            [
                1.855391239547094e-07,
                2.699578096403948e-07,
                9.931187406410953e-08,
                2.2603234895372223e-06,
                3.120191881616493e-05,
                1.4449803818215767e-07,
                3.05902190458764e-07,
                1.3709573702822306e-06,
                1.4449800373118268e-07,
                5.043473480777865e-07
            ],
            [
                1.2751905808881762e-07,
                9.931193325852072e-08,
                3.05902263391829e-07,
                6.023572038912295e-08,
                1.637377448057981e-07,
                1.1253508156363576e-07,
                9.931190958076104e-08,
                1.855391239547094e-07,
                7.734418542875216e-08,
                8.764245361752286e-08
            ],
            [
                8.939696304311336e-06,
                5.043472278322555e-07,
                1.7603425837855082e-06,
                1.5534971990169383e-06,
                9.422445939054222e-07,
                2.9023116392097746e-06,
                5.043473480777865e-07,
                5.71500719545698e-07,
                8.315283250394546e-07,
                3.05902336324494e-07
            ],
            [
                2.561281600086738e-06,
                2.3823690999323465e-07,
                3.466326624336003e-07,
                1.892515501014656e-05,
                6.144176066943187e-06,
                3.05902336324494e-07,
                1.9947299593078385e-06,
                1.012998977264307e-05,
                0.00015843619818758247,
                6.023578501513224e-08
            ],
            [
                2.5110011880337063e-08,
                4.139936066832438e-08,
                6.023571320847322e-08,
                7.734421308914719e-08,
                3.224189323773857e-08,
                6.023572038912295e-08,
                1.637376862489725e-07,
                9.931198061405701e-08,
                1.637376862489725e-07,
                3.2241847115356483e-08
            ],
            [
                7.338210680021253e-07,
                1.5534983101602148e-06,
                4.4508494582405734e-07,
                6.475947210046347e-07,
                8.315279285351409e-07,
                1.5534973842076057e-06,
                1.760343633031919e-06,
                5.04347528446051e-07,
                1.0677029973192638e-06,
                1.3709567165617364e-06
            ],
            [
                1.855391681906175e-07,
                5.715006514176113e-07,
                3.466327037553825e-07,
                5.422219616265831e-06,
                5.04347287955046e-07,
                2.90231094723893e-06,
                1.855391239547094e-07,
                5.04347287955046e-07,
                NaN,
                1.5534973842076057e-06
            ],
            [
                5.422220262636381e-06,
                2.902313369111213e-06,
                6.962258739796719e-06,
                4.450850519403407e-07,
                1.5534973842076057e-06,
                8.315281267882195e-07,
                6.962254589978262e-06,
                6.962256249885085e-06,
                0.00015843625480754269,
                1.760343213335281e-06
            ],
            [
                4.785092783519724e-06,
                4.450849458200093e-07,
                1.6701421845361053e-05,
                1.0677029973192638e-06,
                5.04347528446051e-07,
                5.043473480777865e-07,
                6.475948753991907e-07,
                8.315278294072958e-07,
                7.338213304316717e-07,
                2.1444958640087166e-05
            ],
            [
                2.3823696679327928e-07,
                1.7603434231833873e-06,
                5.04347287955046e-07,
                2.1444950971601277e-05,
                5.04347287955046e-07,
                5.715003107767143e-07,
                3.288749849498565e-06,
                1.0677026154806063e-06,
                1.7603438428800754e-06,
                2.6995771309523475e-07
            ],
            [
                9.931198061405701e-08,
                3.4663274507713016e-07,
                8.764242227418718e-08,
                8.315280276626197e-07,
                5.04347287955046e-07,
                2.7535694384882703e-05,
                1.637376862489725e-07,
                NaN,
                1.6373774480605869e-07,
                6.475945666063607e-07
            ],
            [
                2.2603234895372223e-06,
                2.2603245673443566e-06,
                3.2887502415767434e-06,
                4.4508515805735777e-07,
                2.561281600086738e-06,
                2.561281600086738e-06,
                1.9947301970972664e-06,
                1.3709567165617364e-06,
                5.422218969895357e-06,
                1.3709572068522336e-06
            ],
            [
                1.7603434231833873e-06,
                1.855391681906175e-07,
                3.059022998581767e-07,
                3.05902336324494e-07,
                9.422448185534261e-07,
                1.1478770862882149e-05,
                1.8925157266089433e-05,
                2.699577774589574e-07,
                1.8553907971855875e-07,
                3.2887498495150166e-06
            ],
            [
                1.1253513522447425e-07,
                1.4449800373118268e-07,
                9.422443692574719e-07,
                1.7603440527286572e-06,
                0.9999978766215396,
                1.0677027427624903e-06,
                NaN,
                6.47595107001401e-07,
                6.475947210031623e-07,
                4.6911638017556955e-08
            ],
            [
                1.1253518888531272e-07,
                3.059021175261338e-07,
                3.466326624336003e-07,
                1.6373764721072816e-07,
                1.8553919030858602e-07,
                1.4449805540740185e-07,
                9.931193325852072e-08,
                1.2751905808881762e-07,
                1.1253512180925583e-07,
                3.9278610661902853e-07
            ],
            [
                8.315281267882195e-07,
                5.043475885696228e-07,
                3.288749849529972e-06,
                3.059022998581767e-07,
                1.2098652508424818e-06,
                9.422443692574719e-07,
                1.9947299593078385e-06,
                3.288749065436569e-06,
                3.9278629391427843e-07,
                4.450848927658745e-07
            ],
            [
                0.9999977396751646,
                6.475949526020042e-07,
                0.9999798543092405,
                2.90231094723893e-06,
                2.699576809143613e-07,
                1.7603440527286572e-06,
                7.338212429582604e-07,
                NaN,
                2.69957906184239e-07,
                4.450852111155216e-07
            ],
            [
                0.9999975938968019,
                0.9999985406243022,
                0.9999984465020615,
                0.9999988634361543,
                0.9999964991439199,
                0.9999980052700422,
                0.9999987121050924,
                0.999997438717181,
                0.9999984465026167,
                0.9999885212264232
            ],
            [
                3.4663278639892215e-07,
                3.466326624336003e-07,
                7.73442776303243e-08,
                3.466325384678894e-07,
                1.855391239547094e-07,
                5.71500719545698e-07,
                1.6373772528704005e-07,
                3.466327037548308e-07,
                3.4663257978638593e-07,
                1.855391239547094e-07
            ],
            [
                3.7266401726359486e-06,
                2.561282210740037e-06,
                3.288748281329893e-06,
                2.3823693839325527e-07,
                1.209866260432471e-06,
                2.5612819054133693e-06,
                4.785095635655362e-06,
                7.338209805224048e-07,
                2.9023112932177327e-06,
                1.6701427817730953e-05
            ],
            [
                3.726639284125553e-06,
                8.315283250371857e-07,
                1.5534984953453635e-06,
                2.2603242978665707e-06,
                1.9947299593014888e-06,
                1.7603427936335396e-06,
                6.144176799334096e-06,
                2.7535704229340197e-05,
                5.422218969858371e-06,
                7.889260704968913e-06
            ],
            [
                6.962259569750576e-06,
                3.726639284144195e-06,
                4.450850519403407e-07,
                5.4222209089700225e-06,
                4.2228334445658276e-06,
                4.785095635624897e-06,
                9.422443692555439e-07,
                1.855391681906175e-07,
                5.715002426486762e-07,
                1.5534981249697903e-06
            ],
            [
                3.9278629391427843e-07,
                1.1478765389368729e-05,
                5.422219616265831e-06,
                8.315281267861397e-07,
                3.466327037553825e-07,
                NaN,
                1.8925145985895816e-05,
                3.466327863983311e-07,
                1.012998977264307e-05,
                1.5534979397790343e-06
            ],
            [
                4.4508515805735777e-07,
                1.3709576971463352e-06,
                4.785095065232451e-06,
                7.338209805240734e-07,
                5.71500719545698e-07,
                2.3823693839325527e-07,
                3.4663249714612693e-07,
                8.315278294114555e-07,
                1.370957860576702e-06,
                9.422447062294175e-07
            ],
            [
                1.0677028700363782e-06,
                3.0590237279032884e-07,
                4.450852111135988e-07,
                8.315281267882195e-07,
                8.315279285351409e-07,
                6.475945666051092e-07,
                8.315281267861397e-07,
                9.422448185478557e-07,
                1.5534975693869924e-06,
                1.7603434231777837e-06
            ],
            [
                5.3157900413760374e-08,
                6.825600469412533e-08,
                4.139935079796334e-08,
                8.764241182641775e-08,
                3.653479031538012e-08,
                4.691160446380562e-08,
                4.691168275606451e-08,
                4.139941002027314e-08,
                4.691162683297406e-08,
                4.691162124067829e-08
            ]
        ]
    },
    {
        "q_id": "9335_mmlu_physics",
        "cot_ids": [
            0,
            2,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            15,
            17,
            19,
            22,
            25,
            27,
            28,
            30,
            32,
            33,
            36,
            37,
            38,
            39,
            40,
            43,
            45,
            47,
            49,
            51,
            53,
            55,
            56,
            57,
            59,
            63,
            64,
            66,
            69,
            71,
            73,
            76,
            78,
            81,
            83,
            86,
            92,
            93,
            94,
            98,
            103,
            104,
            106,
            108,
            110,
            112,
            115,
            116,
            119,
            121,
            122,
            123,
            124
        ],
        "rewards": [
            [
                5.043475284468537e-07,
                5.71500515161527e-07,
                4.450850519409479e-07,
                5.715003789054103e-07,
                6.47594952603035e-07,
                6.47594952603035e-07,
                5.043474683240344e-07,
                NaN,
                NaN,
                2.3823682479317953e-07
            ],
            [
                2.561282516066741e-06,
                1.0677026154806063e-06,
                1.3709568799919866e-06,
                7.338208055664991e-07,
                5.715005151606823e-07,
                4.2228319344021954e-06,
                3.0590237279085045e-07,
                5.422220909009474e-06,
                1.3709568799919866e-06,
                1.370957860576702e-06
            ],
            [
                3.2887478892683997e-06,
                4.2228324377164004e-06,
                4.5397852414783676e-05,
                1.0129995810343862e-05,
                2.260325106237323e-06,
                1.4738981972323349e-05,
                6.475947210046347e-07,
                4.0063677865600476e-05,
                1.5534983101602148e-06,
                7.889266347636241e-06
            ],
            [
                7.484625404482555e-05,
                1.3007125363908762e-05,
                2.7535704231844484e-05,
                4.006370652067535e-05,
                7.889259764445822e-06,
                6.962255419868303e-06,
                0.0003799844413700916,
                1.0129990980100021e-05,
                2.5612819054028872e-06,
                NaN
            ],
            [
                8.315279285351409e-07,
                7.338207180898968e-07,
                2.3823702359138736e-07,
                1.3709567165617364e-06,
                2.3823682479292225e-07,
                1.8553912395338048e-07,
                2.6995784182073116e-07,
                5.043475885696228e-07,
                1.760343213335281e-06,
                3.0590219045914655e-07
            ],
            [
                5.422218969858371e-06,
                1.2098658277451275e-06,
                1.553497754577351e-06,
                7.338209805240734e-07,
                NaN,
                2.5612812947508257e-06,
                5.043474081993875e-07,
                2.2603242978871282e-06,
                1.3709576971425944e-06,
                2.5612819054028872e-06
            ],
            [
                9.422445939054222e-07,
                8.315280276607289e-07,
                4.785095065132354e-06,
                2.6995768091383957e-07,
                3.9278634073732336e-07,
                3.7266406168624155e-06,
                9.422447062294175e-07,
                3.927862470899887e-07,
                1.7603430034867993e-06,
                4.222833947960866e-06
            ],
            [
                5.043476486924565e-07,
                1.209865827752005e-06,
                1.0677024882029858e-06,
                9.422443692574719e-07,
                NaN,
                8.315280276626197e-07,
                NaN,
                8.315278294114555e-07,
                NaN,
                1.3709576971463352e-06
            ],
            [
                3.2887482812745586e-06,
                4.222834954753043e-06,
                NaN,
                2.9023133690980155e-06,
                8.315277302841894e-07,
                NaN,
                8.315278294097538e-07,
                1.553497754577351e-06,
                3.1201911375578156e-05,
                1.3709567165530083e-06
            ],
            [
                3.2887478892504536e-06,
                1.012999097997104e-05,
                NaN,
                1.4738985486265496e-05,
                1.9947294837154625e-06,
                4.785092783454444e-06,
                1.7603427936183298e-06,
                1.067703379154416e-06,
                1.0677032518785256e-06,
                1.2098661162023305e-06
            ],
            [
                2.699578740032504e-07,
                2.699578740032504e-07,
                7.734428685047173e-08,
                1.994729483729522e-06,
                9.422443692574719e-07,
                2.1024331597262577e-07,
                1.7603434231833873e-06,
                4.450852641737424e-07,
                1.637376862489725e-07,
                4.4508515805735777e-07
            ],
            [
                8.939695238333382e-06,
                7.889260704818233e-06,
                2.1444940744864302e-05,
                6.1441767990323395e-06,
                4.5397874057886045e-05,
                1.4738978458382043e-05,
                5.4222215552470286e-06,
                3.535625492217596e-05,
                7.889265407004852e-06,
                2.2603251062147097e-06
            ],
            [
                9.422447062294175e-07,
                2.699577774589574e-07,
                2.3823682479292225e-07,
                7.338210680021253e-07,
                1.0677029973219343e-06,
                6.962259569630266e-06,
                2.382369951932796e-07,
                1.4449807263312446e-07,
                1.1253525596174225e-07,
                1.2098659719788098e-06
            ],
            [
                3.7266410611296085e-06,
                3.7266406168624155e-06,
                4.785092783519724e-06,
                2.90231094723893e-06,
                NaN,
                5.4222183235249605e-06,
                1.0677032518785256e-06,
                5.715003107715166e-07,
                6.962256249885085e-06,
                1.3709573702778664e-06
            ],
            [
                1.5534973842076057e-06,
                NaN,
                1.5534977545886537e-06,
                NaN,
                1.3709575337159875e-06,
                4.785095635655362e-06,
                3.466326624336003e-07,
                7.338212429594283e-07,
                1.994729483729522e-06,
                8.315278294114555e-07
            ],
            [
                NaN,
                9.422442569334097e-07,
                9.422442569334097e-07,
                5.71500515161527e-07,
                6.475950298021765e-07,
                NaN,
                2.3823685319320354e-07,
                5.715006514176113e-07,
                9.422443692574719e-07,
                3.288747889284851e-06
            ],
            [
                2.1024334103581732e-07,
                8.315277302857965e-07,
                4.450850519409479e-07,
                2.3823693839325527e-07,
                8.315278294114555e-07,
                7.338207180898968e-07,
                9.422443692574719e-07,
                1.370957860576702e-06,
                9.422442569334097e-07,
                8.315279285370317e-07
            ],
            [
                4.785093353940187e-06,
                3.120191137455659e-05,
                2.5612828213690224e-06,
                4.222834954778007e-06,
                3.2887494574518405e-06,
                1.2098659719524008e-06,
                3.726639284125553e-06,
                7.889266347636241e-06,
                1.5534984953510149e-06,
                1.7603440527286572e-06
            ],
            [
                0.00010889687035420022,
                1.5534975693869924e-06,
                NaN,
                6.962255419728997e-06,
                1.0129994602057158e-05,
                2.902312677137316e-06,
                4.222831934352267e-06,
                3.535626335686906e-05,
                1.4738988998117324e-05,
                2.9023109472244114e-06
            ],
            [
                4.785093924330255e-06,
                8.315281267834927e-07,
                1.2098662604247682e-06,
                1.4738983728784933e-05,
                7.889264466545779e-06,
                2.753568453712307e-05,
                4.222835458175145e-06,
                1.5534975693792215e-06,
                2.9023119851266288e-06,
                2.2603242978665707e-06
            ],
            [
                2.430024942462891e-05,
                1.99472900813862e-06,
                4.222834451382849e-06,
                1.994729483705484e-06,
                1.5534984953510149e-06,
                0.00012339460439135077,
                1.5534975693792215e-06,
                1.7603425837606927e-06,
                2.9023130230846496e-06,
                1.2098661162056318e-06
            ],
            [
                7.889266347636241e-06,
                6.144172404587612e-06,
                1.0129989772274546e-05,
                1.1478766757561534e-05,
                2.2603242978665707e-06,
                8.315283250371857e-07,
                7.889262585642319e-06,
                6.144172404520556e-06,
                4.785094494463623e-06,
                1.7603427936183298e-06
            ],
            [
                2.5612834320563895e-06,
                3.05902263391829e-07,
                1.147877359957198e-05,
                1.3709572068553509e-06,
                NaN,
                2.2603248367949354e-06,
                1.2098661162056318e-06,
                6.475950298021765e-07,
                4.006368263437623e-05,
                8.315284241650899e-07
            ],
            [
                8.939699501132077e-06,
                6.144176799166453e-06,
                1.5534977545603963e-06,
                3.2887490653408545e-06,
                2.561283126679493e-06,
                6.144177531532303e-06,
                5.422219616228845e-06,
                2.5612812946681295e-06,
                3.288748673295719e-06,
                1.7603436330091044e-06
            ],
            [
                3.2887506334201674e-06,
                3.726639284103523e-06,
                NaN,
                3.726641061058432e-06,
                2.4300243616508983e-05,
                1.0677026154774503e-06,
                1.0129995810343862e-05,
                2.90231233114251e-06,
                1.3709575337016483e-06,
                7.889263525405172e-06
            ],
            [
                7.889261645090304e-06,
                6.475947210012481e-07,
                1.7603436330179102e-06,
                2.7535697666401535e-05,
                NaN,
                2.9023126771227976e-06,
                1.3709567165579959e-06,
                3.288749849477628e-06,
                5.422218969769604e-06,
                2.9023109471689794e-06
            ],
            [
                2.753569110256289e-05,
                2.430023204460668e-05,
                2.9023119851266288e-06,
                5.04347528446051e-07,
                4.785092783519724e-06,
                3.288748673360027e-06,
                1.5534975693933505e-06,
                1.994730197090463e-06,
                2.90231094723893e-06,
                5.4222183235249605e-06
            ],
            [
                NaN,
                NaN,
                3.059021175261338e-07,
                NaN,
                2.699578096403948e-07,
                NaN,
                NaN,
                5.043476486924565e-07,
                1.5534975693979422e-06,
                2.382368815932174e-07
            ],
            [
                7.338207180864763e-07,
                3.288748281295496e-06,
                8.939696304311336e-06,
                8.315277302857965e-07,
                1.5534973842076057e-06,
                7.338209805200689e-07,
                5.715004470295662e-07,
                3.2887506335906595e-06,
                1.9947294837154625e-06,
                5.715003789017068e-07
            ],
            [
                2.10243290909724e-07,
                7.889261645269683e-06,
                1.4738981972323349e-05,
                1.760343213322473e-06,
                1.99472900813862e-06,
                1.5534983101549167e-06,
                4.785094494750855e-06,
                1.0677032518814388e-06,
                8.315283250371857e-07,
                3.726639284125553e-06
            ],
            [
                1.7603432133136672e-06,
                3.288748673319648e-06,
                4.785095635592258e-06,
                4.785092783454444e-06,
                0.00010889687027972941,
                6.962253759904688e-06,
                NaN,
                3.2887482813149375e-06,
                1.892514598551715e-05,
                1.1478768126057254e-05
            ],
            [
                4.785095065232451e-06,
                1.994729008151319e-06,
                NaN,
                NaN,
                5.144222593244026e-05,
                0.0,
                1.3709572068553509e-06,
                NaN,
                NaN,
                1.2098656835252174e-06
            ],
            [
                3.466327037553825e-07,
                2.6995790618469934e-07,
                2.699578740032504e-07,
                1.0677026154806063e-06,
                3.4663253846718004e-07,
                7.338213304363436e-07,
                1.444979692800516e-07,
                1.8553907971855875e-07,
                8.315283250371857e-07,
                2.6995774527718623e-07
            ],
            [
                NaN,
                NaN,
                5.422220262636381e-06,
                0.0003353502709532356,
                0.000626334257685222,
                1.5534975693601474e-06,
                8.93969950132721e-06,
                NaN,
                1.6701423836262173e-05,
                7.889265407327733e-06
            ],
            [
                2.9023130231176453e-06,
                2.6995784182073116e-07,
                9.422445939032799e-07,
                5.715006514167015e-07,
                4.785093924362895e-06,
                3.7266383955882547e-06,
                3.927862002654366e-07,
                3.927861534406222e-07,
                1.5534971990169383e-06,
                2.5612819054028872e-06
            ],
            [
                3.2887502415767434e-06,
                5.422219616265831e-06,
                2.561282516042282e-06,
                1.760343213335281e-06,
                2.260325375664839e-06,
                1.0129987357407137e-05,
                NaN,
                8.315283250343497e-07,
                8.939697369882888e-06,
                8.939699501229642e-06
            ],
            [
                2.382369951932796e-07,
                5.715003789046955e-07,
                1.0677027427600627e-06,
                1.9947290081286418e-06,
                1.2098659719788098e-06,
                7.338209805240734e-07,
                3.927862470899887e-07,
                2.6995774527718623e-07,
                1.2098661162056318e-06,
                2.382369951932796e-07
            ],
            [
                2.699577774589574e-07,
                2.2603251062450327e-06,
                1.0677028700422047e-06,
                9.422442569334097e-07,
                NaN,
                2.5612819054133693e-06,
                7.338208930460318e-07,
                5.043475885696228e-07,
                1.7603425837903113e-06,
                NaN
            ],
            [
                7.338207180898968e-07,
                2.699577452775239e-07,
                3.726639284144195e-06,
                1.994729483729522e-06,
                6.47595107001401e-07,
                1.5534984953552536e-06,
                2.699578096403948e-07,
                4.450850519409479e-07,
                1.5534971990169383e-06,
                5.043476486924565e-07
            ],
            [
                6.475947210031623e-07,
                9.422450431954847e-07,
                2.561281294760143e-06,
                1.5534979397740895e-06,
                3.927863407379485e-07,
                2.6995784182183607e-07,
                5.71500719545698e-07,
                1.5534973842076057e-06,
                3.059021175261338e-07,
                5.715003107767143e-07
            ],
            [
                3.9278629391427843e-07,
                2.1024336609874897e-07,
                9.422444815814404e-07,
                1.637377057680051e-07,
                6.47595107001401e-07,
                2.3823690999323465e-07,
                9.422450432030903e-07,
                3.059022269254856e-07,
                1.855391681906175e-07,
                3.466326624336003e-07
            ],
            [
                5.422217030707961e-06,
                5.422220262505697e-06,
                2.9023130231176453e-06,
                1.0129987357407137e-05,
                9.422447062270609e-07,
                2.260324028427877e-06,
                1.300713156582635e-05,
                4.222834451382849e-06,
                1.5534979397740895e-06,
                1.9947292459265734e-06
            ],
            [
                2.2603248367949354e-06,
                1.9947304348862686e-06,
                5.043472879525233e-07,
                3.7266406168624155e-06,
                1.067702615468225e-06,
                5.043476486924565e-07,
                3.2887490653872164e-06,
                3.4663249714612693e-07,
                9.422447062202052e-07,
                1.3709576971463352e-06
            ],
            [
                NaN,
                7.889260704968913e-06,
                5.715005832886879e-07,
                8.939693107190907e-06,
                2.2603251062450327e-06,
                3.4663253846316044e-07,
                3.927862002641863e-07,
                1.7603434231833873e-06,
                3.4663278639892215e-07,
                2.902313023130843e-06
            ],
            [
                1.0677026154827912e-06,
                9.422442569315887e-07,
                1.3709575337016483e-06,
                7.338208930460318e-07,
                1.7603432133296774e-06,
                6.475947210046347e-07,
                7.338210680021253e-07,
                1.0677027427600627e-06,
                3.05902190458764e-07,
                1.0677029973192638e-06
            ],
            [
                1.0677033791583005e-06,
                1.4738981972564636e-05,
                NaN,
                4.785094494811783e-06,
                6.1441767993788005e-06,
                3.7266383956509585e-06,
                1.994730672675753e-06,
                4.450849458200093e-07,
                3.288747889284851e-06,
                6.475945666063607e-07
            ],
            [
                5.043474683204221e-07,
                9.422445939032799e-07,
                2.902312331125353e-06,
                1.994729483705484e-06,
                2.2603248367173307e-06,
                7.338208930391909e-07,
                1.0677031245905116e-06,
                2.260324567268294e-06,
                9.422447062202052e-07,
                6.144177531532303e-06
            ],
            [
                4.222833444590791e-06,
                1.3709576971425944e-06,
                1.0129988564974359e-05,
                5.4222183235249605e-06,
                NaN,
                1.553497199007048e-06,
                1.6701421845361053e-05,
                1.670141786295194e-05,
                1.5534975693869924e-06,
                2.5612825160562587e-06
            ],
            [
                9.422450431989127e-07,
                1.2098655392811161e-06,
                1.0677028700203557e-06,
                1.2098653950480359e-06,
                9.422448185388577e-07,
                7.338209805200689e-07,
                4.450848927637999e-07,
                3.4663266242969896e-07,
                2.5612834319655406e-06,
                1.994730434847717e-06
            ],
            [
                0.00013982205753511605,
                1.3007123813559956e-05,
                1.3007126914435202e-05,
                7.889259764273619e-06,
                0.9820137930646488,
                5.144222592963322e-05,
                3.7266397282926013e-06,
                6.962258739530771e-06,
                7.889266347715168e-06,
                8.939696304213768e-06
            ],
            [
                8.315282259117513e-07,
                7.338208930391909e-07,
                5.043476486883855e-07,
                5.715003107755449e-07,
                9.4224425692559e-07,
                2.5612819054133693e-06,
                1.0677028700363782e-06,
                1.2098659719757836e-06,
                1.2098658277451275e-06,
                5.043472879525233e-07
            ],
            [
                1.0677032518814388e-06,
                6.144173137170873e-06,
                3.288749849529972e-06,
                1.209865827752005e-06,
                1.2098653950692178e-06,
                3.72663883989755e-06,
                1.370957860576702e-06,
                7.33821330437595e-07,
                NaN,
                2.1444940745839484e-05
            ],
            [
                2.260324836776948e-06,
                7.338207180864763e-07,
                1.2098662604247682e-06,
                3.4663249714451116e-07,
                5.043474081993875e-07,
                7.338209805224048e-07,
                8.315278294072958e-07,
                5.043476486833397e-07,
                3.466326624322211e-07,
                1.7603432133136672e-06
            ],
            [
                4.222834954801051e-06,
                5.422217677152175e-06,
                2.90231094723893e-06,
                7.338208055664991e-07,
                2.2603251062450327e-06,
                6.144177531811707e-06,
                6.144177531811707e-06,
                5.715005832886879e-07,
                1.300712536408621e-05,
                4.4508494582405734e-07
            ],
            [
                8.315279285351409e-07,
                2.2603245673279107e-06,
                9.422449308748773e-07,
                8.31527928532683e-07,
                1.4738981972082061e-05,
                7.338209805224048e-07,
                2.2603240284371276e-06,
                5.043475885674441e-07,
                1.9947306726594253e-06,
                9.422448185510695e-07
            ],
            [
                1.994729483723626e-06,
                1.5534971990126997e-06,
                1.0677032518785256e-06,
                2.260325106237323e-06,
                1.2098652508391807e-06,
                1.553498124964492e-06,
                9.422444815792981e-07,
                1.760343213322473e-06,
                1.5534971990126997e-06,
                9.422442569315887e-07
            ],
            [
                3.726638839878908e-06,
                6.144175334468545e-06,
                5.043476486915964e-07,
                9.422444815563743e-07,
                1.994729245917502e-06,
                1.067703379154416e-06,
                4.785095635592258e-06,
                1.9947297214544894e-06,
                2.260325375634003e-06,
                1.7603438428660665e-06
            ],
            [
                4.450852641737424e-07,
                NaN,
                NaN,
                4.450852111148132e-07,
                1.7603434231833873e-06,
                NaN,
                NaN,
                NaN,
                5.715006514176113e-07,
                2.561282210740037e-06
            ],
            [
                3.288749457432399e-06,
                1.9947297215043796e-06,
                9.422445939002803e-07,
                1.994729483705484e-06,
                1.0677028700363782e-06,
                1.012999460278499e-05,
                1.9947301970813926e-06,
                7.889266347786918e-06,
                1.3007133116542802e-05,
                8.315278294072958e-07
            ],
            [
                6.962257079705671e-06,
                6.475945666051092e-07,
                6.47595107001401e-07,
                7.338210680021253e-07,
                2.430024942462891e-05,
                6.962258739796719e-06,
                3.535625914492432e-05,
                1.370957860576702e-06,
                4.450851580566494e-07,
                5.71500719545698e-07
            ],
            [
                1.994729008145876e-06,
                1.1478764020883773e-05,
                3.288749457469787e-06,
                1.0677027427600627e-06,
                1.3709576971425944e-06,
                6.962254589978262e-06,
                4.785096206047877e-06,
                2.9023119851781017e-06,
                6.9622587397397306e-06,
                2.5612819054028872e-06
            ],
            [
                1.2098652508391807e-06,
                3.2887506336086064e-06,
                2.2603245673279107e-06,
                2.2603248367656408e-06,
                1.0677027427525368e-06,
                3.726638395611981e-06,
                1.2098652508391807e-06,
                1.1478769494396542e-05,
                2.260324836776948e-06,
                1.3709573702778664e-06
            ]
        ]
    },
    {
        "q_id": "10233_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                1.5534981249397663e-06,
                4.222831934286977e-06,
                7.338212429464139e-07,
                1.5534979397394734e-06,
                0.9999992188515765,
                1.3709578605542582e-06,
                6.47594566597747e-07,
                1.76034300345598e-06,
                0.9999994631251243,
                1.994729959270648e-06
            ],
            [
                0.9999991148431757,
                0.9999962733589416,
                0.9999998144608098,
                0.9999945777823307,
                0.9999994956527123,
                0.9999998257020799,
                0.9999996310115039,
                0.9999957771645479,
                0.9999998362622553,
                0.999984310448439
            ],
            [
                0.9999957771660541,
                0.9999977396748948,
                0.999999631011416,
                0.9999998555019275,
                3.9278634072866033e-07,
                0.9999997300423191,
                0.9999987121047851,
                0.9999993524053565,
                0.999999894283061,
                0.9999972735297309
            ],
            [
                0.9999985406232588,
                0.9999995262096117,
                0.999998126124172,
                0.9999996533673376,
                0.9999996072137531,
                0.9999989322972578,
                0.9999994284996896,
                0.9999996072137064,
                0.9999983463106127,
                0.9999991684719727
            ],
            [
                0.9999964991443374,
                0.9999974387180965,
                0.9999969105048188,
                0.9999952149066509,
                0.999995214904938,
                0.9999994284995534,
                0.9999981261252877,
                0.9999982396567879,
                0.9999990577552943,
                0.9999955048173531
            ],
            [
                0.9999994284992811,
                0.9999985406230842,
                0.9999990577557439,
                0.9999975938973781,
                0.9999978766207809,
                0.9999992188513905,
                0.9999970976890554,
                0.9999996743688586,
                0.9999967112501542,
                0.9999986290423033
            ],
            [
                0.9999978766217936,
                0.999999906705061,
                0.9999983463104152,
                0.999999581881327,
                0.9999997761971582,
                0.9999999123575674,
                0.9999999123574733,
                0.9999993106392018,
                0.9999999273417923,
                0.9999999067051499
            ],
            [
                0.9999997761970782,
                0.9999991684719727,
                0.999997593896802,
                0.9999993106387083,
                0.999998239656578,
                0.9999997897566841,
                0.9999989322970035,
                0.9999989969857928,
                0.9999996940978462,
                0.9999987901341728
            ],
            [
                0.9999938558246707,
                0.9999981261239476,
                0.9999980052707557,
                0.9999998461826771,
                0.9999957771650496,
                0.9999945777803889,
                0.9999989322967487,
                0.9999885212277959,
                0.9999925887201369,
                0.9999996940977002
            ],
            [
                0.9999994956524116,
                1.0677032518785256e-06,
                0.9999992188514835,
                0.999999746398073,
                0.9999993524054337,
                3.653481209178873e-08,
                0.9999417087069492,
                2.102433159721477e-07,
                6.475947982037486e-07,
                2.10243290909724e-07
            ],
            [
                2.102434412875379e-07,
                2.382369667929001e-07,
                1.637377448057981e-07,
                1.8553910183607374e-07,
                3.0590237279032884e-07,
                5.043473480777865e-07,
                7.338207180864763e-07,
                1.6373766672973748e-07,
                3.466326624322211e-07,
                4.4508510499849186e-07
            ],
            [
                0.999995214906083,
                0.9999960330145629,
                0.9999885212359875,
                0.9999957771680713,
                0.9999925887227943,
                0.9999997300420939,
                0.9999989969856731,
                0.9999995262096116,
                0.999999310638626,
                0.999999730042094
            ],
            [
                4.222835458148261e-06,
                0.999998446501506,
                0.9999934595612221,
                0.999997273529082,
                2.561282821352716e-06,
                0.9999982396563679,
                2.5612825159677387e-06,
                0.999997739675435,
                1.9947292458930106e-06,
                1.0677027427471959e-06
            ],
            [
                3.2887498494551953e-06,
                1.0677027427471959e-06,
                2.5612812947077304e-06,
                3.2887502415438413e-06,
                2.2603234894745224e-06,
                2.5612822107167428e-06,
                5.715003107689177e-07,
                2.260323758939877e-06,
                2.5612812947077304e-06,
                1.5534981249397663e-06
            ],
            [
                0.9999997761970248,
                0.999999712631344,
                0.9999996310115039,
                0.9999997463982241,
                0.9999995818810776,
                0.999999900687984,
                0.999999554914736,
                0.9999992661790198,
                0.9999998257022046,
                0.9999998144608319
            ],
            [
                0.9999986290424686,
                0.9999916019299909,
                0.9999984465020626,
                0.9999997126313098,
                0.9999989969861514,
                0.9999970976887114,
                0.999999526209273,
                0.9999994631249967,
                0.9999997761971849,
                0.9999995262094422
            ],
            [
                0.9999974387187072,
                0.9999995549151075,
                0.9999982396567879,
                0.999999631011372,
                0.9999994631251884,
                0.9999990577555188,
                0.9999981261248412,
                0.9999997617631469,
                0.9999986290426301,
                0.9999985406237797
            ],
            [
                3.466325797888292e-07,
                2.1024341622426268e-07,
                8.315284241650899e-07,
                3.0590237279032884e-07,
                2.1024331597262577e-07,
                5.715003789046955e-07,
                2.6995787400208416e-07,
                3.0590237279032884e-07,
                2.69957906184239e-07,
                0.9999986290426314
            ],
            [
                0.9999938558261359,
                0.9999989969859121,
                0.9999885212264098,
                0.9999957771680692,
                0.9999952149049397,
                0.9999984465024311,
                0.9999885212291474,
                0.9999952149072182,
                0.9999952149049379,
                0.9999975938973762
            ],
            [
                0.9999993916411086,
                0.9999998144608098,
                0.9999987121046321,
                0.9999997126315153,
                0.9999994631249323,
                0.999999310639037,
                0.9999992188518559,
                0.9999991148433868,
                0.999999352405125,
                0.9999994956524119
            ],
            [
                5.715006514151423e-07,
                4.450851580555361e-07,
                4.4508505193791187e-07,
                7.338209805200689e-07,
                3.726638395527247e-06,
                5.715004470313855e-07,
                7.338207180864763e-07,
                1.067702615468225e-06,
                5.043474081993875e-07,
                2.260324836776948e-06
            ],
            [
                0.9999993916411085,
                0.9999988634360194,
                0.9999904837505901,
                0.9999949062956137,
                0.9999996310115039,
                0.9999930377437558,
                0.999997593896514,
                0.9999982396559479,
                0.9999997126313784,
                0.9999980052698042
            ],
            [
                0.9999925887219079,
                2.1024326584639497e-07,
                3.0590226339061185e-07,
                5.71500719545698e-07,
                3.0590237279085045e-07,
                2.69957906184239e-07,
                3.927863875616689e-07,
                8.315280276626197e-07,
                4.450848927658745e-07,
                4.450851049991497e-07
            ],
            [
                0.999999631011372,
                0.9999994631249324,
                0.9999952149043684,
                0.999988521231895,
                0.9999997761971049,
                0.9999992188515767,
                0.999999495652592,
                0.9999996072138936,
                0.9999990577551818,
                0.9999949062962156
            ],
            [
                5.04347468323289e-07,
                2.1024336609874897e-07,
                8.315283250371857e-07,
                3.466327037548308e-07,
                4.450851580555361e-07,
                3.4663249714612693e-07,
                9.93118503859575e-08,
                3.059022269250683e-07,
                1.4449796927932878e-07,
                2.3823693839290317e-07
            ],
            [
                0.9999998461826956,
                0.9999997617630617,
                0.9999998555019619,
                0.9999978766205269,
                0.9999952149037977,
                0.9999998461826588,
                0.9999994284995533,
                0.999999495652652,
                0.9999987901341728,
                0.9999997897565588
            ],
            [
                1.8553905759969634e-07,
                1.4449798650265913e-07,
                3.9278605979011705e-07,
                6.475951069985296e-07,
                9.931190958026426e-08,
                2.102434162220159e-07,
                4.450851580555361e-07,
                9.93120161306789e-08,
                1.8553905759969634e-07,
                2.3823699519143784e-07
            ],
            [
                0.9999987901343174,
                0.999999631011372,
                0.9999998362623138,
                0.999999631011592,
                0.9999984465018763,
                0.9999997300421261,
                0.9999994956526522,
                0.9999995818810776,
                0.999999581881277,
                0.9999998802069302
            ],
            [
                0.9999997126314468,
                0.9999993916408911,
                0.9999977396762435,
                0.9999996310115479,
                0.9999984465020618,
                0.9999985406232584,
                0.9999981261246184,
                0.9999993916408187,
                0.9999994631250604,
                0.9999990577555191
            ],
            [
                0.9999938558276017,
                0.9999980052707563,
                0.9999996072136594,
                0.9999987121041711,
                0.9999977396746257,
                0.9999925887192651,
                0.9999962733620538,
                0.9999996072138936,
                0.9999991684721709,
                0.999996033013145
            ],
            [
                1.3709573702822306e-06,
                1.9947306726358406e-06,
                7.338212429537553e-07,
                8.315278293838516e-07,
                4.450848927650143e-07,
                1.3709575336947905e-06,
                1.7603432132912532e-06,
                5.043475885674441e-07,
                1.2098659719441482e-06,
                1.0677031245851707e-06
            ],
            [
                0.9999978766222978,
                0.9999997761970248,
                0.9999992188518559,
                0.9999997463980125,
                0.9999993106391191,
                0.99999879013374,
                0.9999997897566841,
                0.9999989322971307,
                0.9999994956525919,
                0.9999990577549573
            ],
            [
                2.1024344128584085e-07,
                0.9999991684717744,
                0.9999997761971049,
                3.288749457469787e-06,
                3.726637951387472e-06,
                2.4300232045225487e-05,
                2.9023116392097746e-06,
                7.889259764517575e-06,
                3.059022998569248e-07,
                3.288747889284851e-06
            ],
            [
                0.9999952149066522,
                0.9999949062943949,
                0.9999992188517637,
                0.9999990577549576,
                0.9999996072139404,
                0.9999980052693317,
                0.9999994631250607,
                0.9999952149055112,
                0.9999987901346074,
                0.9999998724809571
            ],
            [
                0.9999987121043247,
                0.9999962733589425,
                0.9999998461826771,
                1.0129993395217047e-05,
                0.9999970976866335,
                0.9999997761970781,
                0.999997739676512,
                0.9999978766215393,
                0.9999993524051249,
                0.9999982396574175
            ],
            [
                0.9999999273418703,
                0.9999998555019274,
                0.9999993916408185,
                0.9999999176675142,
                0.999999746398073,
                0.9999997300422228,
                0.9999996743686645,
                0.9999987121049386,
                0.9999998362622358,
                0.9999996940976272
            ],
            [
                0.9999996072136594,
                0.9999957771660551,
                0.9999972735287566,
                0.999999631011636,
                0.9999989322971308,
                0.9999967112497615,
                0.9999990577557438,
                0.9999987901346057,
                0.9999978766205264,
                0.999999761763005
            ],
            [
                3.2887482812745586e-06,
                0.9999994631248684,
                1.2098652508424818e-06,
                0.999998446502061,
                0.9999989969854344,
                0.9999977396746269,
                0.9999981261246188,
                0.999999554914736,
                0.9999991148429651,
                0.9999997463980731
            ],
            [
                0.9999992661786697,
                7.734424996967756e-08,
                0.9999993106390375,
                2.38237023590304e-07,
                2.1024344128660572e-07,
                0.9999998555019447,
                0.9999810748427657,
                0.9999990577552943,
                4.450850519403407e-07,
                0.9999942280786006
            ],
            [
                8.764254764749753e-08,
                3.9278605979208185e-07,
                1.3007123812980299e-05,
                1.8553907971682908e-07,
                5.04347468323289e-07,
                4.450851580555361e-07,
                1.8553907971682908e-07,
                1.4449798650476187e-07,
                1.8553905759969634e-07,
                1.637377643243723e-07
            ],
            [
                8.7642516304188e-08,
                1.2751901248454963e-07,
                1.1253518888464745e-07,
                8.764244316933122e-08,
                9.931192141912081e-08,
                1.637377643243723e-07,
                6.825604537781398e-08,
                1.8553910183548312e-07,
                1.1253510839355284e-07,
                1.1253526937656726e-07
            ],
            [
                9.931199245292204e-08,
                1.637377448057981e-07,
                9.931189774140912e-08,
                1.4449796927932878e-07,
                1.0677029973219343e-06,
                6.825601283086733e-08,
                9.931202796957073e-08,
                1.4449795205429202e-07,
                1.2751904288710323e-07,
                1.2751908849167202e-07
            ],
            [
                0.9999993106387903,
                0.9999997300420939,
                0.9999992661788452,
                0.9999994284996894,
                0.9999994631248041,
                0.9999995549149482,
                0.9999997126315497,
                0.9999977396754341,
                0.999999310639037,
                0.9999996940976638
            ],
            [
                0.9999985406234316,
                0.9999992188512972,
                0.9999987121047853,
                0.999997273528756,
                0.9999997126314468,
                0.9999997300422548,
                0.9999952149060801,
                0.9999978766215386,
                0.9999984465026165,
                0.999999631011592
            ],
            [
                0.999999607213753,
                2.9023119851781017e-06,
                0.9999984465024313,
                0.9999972735303806,
                0.9999972735294052,
                3.7266401726359486e-06,
                0.9999945777810342,
                2.561281600086738e-06,
                0.9999981261243941,
                2.5612834320563895e-06
            ],
            [
                0.9999989969856735,
                0.9999991684717743,
                0.9999997300423192,
                0.9999998642567028,
                0.9999970976873258,
                0.9999974387168759,
                0.9999995262093294,
                0.9999997897565588,
                0.9999949062937916,
                0.9999997617629766
            ],
            [
                1.0677026154806063e-06,
                3.05902190458764e-07,
                1.7603425837855082e-06,
                4.222834954778007e-06,
                1.2098659719757836e-06,
                5.715003789046955e-07,
                2.5612831267202583e-06,
                2.1444948415296896e-05,
                1.9947301970972664e-06,
                1.2098661162056318e-06
            ],
            [
                3.0590237279032884e-07,
                2.382370235922541e-07,
                6.1441746020359e-06,
                2.7535694384081332e-05,
                2.1024331597152624e-07,
                3.726637951387472e-06,
                8.31528126775552e-07,
                9.422448185510695e-07,
                3.466325797888292e-07,
                2.1024329090867228e-07
            ],
            [
                0.9999997761971849,
                0.9999997897565839,
                0.999999825702059,
                0.9999992661791074,
                0.9999998144608762,
                0.9999972735287567,
                0.9999999006880314,
                0.9999999123575778,
                0.9999998362622747,
                0.9999995262094988
            ],
            [
                6.475947210012481e-07,
                3.466324971415162e-07,
                7.889266347715168e-06,
                0.9999984465020608,
                1.7603425837702984e-06,
                6.475947209985977e-07,
                4.4508526417014975e-07,
                0.9999981261241708,
                9.422444815563743e-07,
                0.9999991148427537
            ],
            [
                8.93969950132721e-06,
                1.4738981972564636e-05,
                8.939695238634211e-06,
                1.994730672675753e-06,
                0.9999980052698045,
                0.999998712104478,
                1.9947299593014888e-06,
                1.012998977264307e-05,
                0.9999996310115481,
                6.144173869603344e-06
            ],
            [
                1.6701419854156377e-05,
                3.726637951387472e-06,
                2.5612819054133693e-06,
                1.6701417863559525e-05,
                2.5612828213934817e-06,
                7.338208930460318e-07,
                3.726639284144195e-06,
                0.9999985406234322,
                2.7535700950274782e-05,
                2.5612831267202583e-06
            ],
            [
                2.561282210740037e-06,
                1.3007128465151102e-05,
                3.7266397283908927e-06,
                1.670142980893658e-05,
                2.902312677150514e-06,
                1.1478764021029928e-05,
                6.144172404738491e-06,
                1.3007126914612648e-05,
                3.72663883989755e-06,
                4.785096206076165e-06
            ],
            [
                0.9999984465028022,
                0.9999916019239817,
                0.9999997300421904,
                0.9999975938970889,
                0.9999995262096116,
                0.9999996310116358,
                0.9999957771650508,
                0.9999997761972117,
                0.9999996743688588,
                0.999999746398194
            ],
            [
                0.9999996743688199,
                0.9999998461826037,
                5.715003789046955e-07,
                7.338208930460318e-07,
                6.962253760024999e-06,
                0.9999997761971315,
                4.2228319344021954e-06,
                2.5612834320563895e-06,
                5.043473480777865e-07,
                0.9999998555019619
            ],
            [
                3.4663266242969896e-07,
                1.855391239505118e-07,
                1.2098656834834034e-06,
                1.4449805540585765e-07,
                1.275190884903093e-07,
                1.4449805540585765e-07,
                1.6373774480479287e-07,
                1.1253525596055243e-07,
                2.3823702359138736e-07,
                2.6995784181551376e-07
            ],
            [
                0.9999992188518558,
                0.9999996310113719,
                0.9999993916409635,
                0.9999996310115039,
                0.9999985406243014,
                0.9999995818812272,
                0.9999991148429644,
                0.999999554914736,
                0.9999987901343169,
                0.9999852610198355
            ],
            [
                1.370957860576702e-06,
                7.889259764517575e-06,
                1.1478770862882149e-05,
                0.9999997463982241,
                1.5534973842076057e-06,
                4.785093924389007e-06,
                3.7266401726359486e-06,
                8.939696304311336e-06,
                6.962259569750576e-06,
                8.315277302857965e-07
            ],
            [
                0.9999987901346058,
                0.9999986290429573,
                0.9999988634361545,
                0.9999998144609646,
                0.999999825702163,
                0.9999980052702806,
                0.999999825702059,
                0.9999996072137529,
                0.9999996940977002,
                0.9999964991460057
            ],
            [
                1.4449805540740185e-07,
                7.338212429582604e-07,
                2.6995774527718623e-07,
                1.2751905808881762e-07,
                3.927862002663297e-07,
                1.1253521571574156e-07,
                6.475947210031623e-07,
                9.422448185534261e-07,
                8.315277302841894e-07,
                2.10243290909724e-07
            ],
            [
                0.9999916019249692,
                0.9999938558246693,
                0.9999997463981939,
                0.9999992188514835,
                0.9999996072137062,
                0.9999993524052019,
                0.9999996310115039,
                0.9999934595596603,
                0.9999995818811773,
                0.9999997761970248
            ],
            [
                0.9999998461826954,
                0.9999996743688586,
                0.9999998555019791,
                0.9999996940976273,
                0.9999997761971049,
                0.9999997300420939,
                0.9999997617630333,
                0.9999999176675731,
                0.9999998362623334,
                0.999999894282998
            ],
            [
                0.9999972735290799,
                0.9999999067049832,
                0.999992588719253,
                0.9999957771645435,
                0.9999822214481775,
                0.9999938558268671,
                0.9999970976890544,
                0.9999982396559484,
                0.999998996985673,
                0.9999955048178879
            ],
            [
                0.9999984465015068,
                0.9999942280806637,
                8.939693107288474e-06,
                5.422217677152175e-06,
                7.889261645427538e-06,
                1.3007123813382511e-05,
                7.889266347786918e-06,
                5.422217677152175e-06,
                2.260323758987159e-06,
                3.7266410611296085e-06
            ],
            [
                1.2098659719788098e-06,
                2.9023119851899796e-06,
                0.9999904837460506,
                4.785093924389007e-06,
                4.222833444590791e-06,
                1.1478768125911099e-05,
                4.222834451355964e-06,
                0.9999960330145621,
                8.315279285370317e-07,
                2.382369667929001e-07
            ],
            [
                6.825597214718257e-08,
                4.139938534423022e-08,
                9.931187406410953e-08,
                8.764249540862797e-08,
                8.764247451307293e-08,
                6.825606165129312e-08,
                6.825600469412533e-08,
                6.023578501491997e-08,
                0.9999993524052021,
                4.691162124067829e-08
            ],
            [
                0.9999990577551823,
                0.9999993524053565,
                0.9999996940976638,
                0.9999990577550699,
                0.9999975938973762,
                0.9999955048189615,
                0.9999988634364259,
                0.999999631011416,
                0.9999991684718743,
                0.999998446502061
            ],
            [
                8.764242227418718e-08,
                0.9999986290427941,
                2.5612828213690224e-06,
                1.3007130015488633e-05,
                7.73441946488886e-08,
                1.5534984953453635e-06,
                2.260324567302214e-06,
                0.9999977396762424,
                1.6373770576683237e-07,
                1.6373776432509826e-07
            ],
            [
                6.023576347299818e-08,
                1.275190124842887e-07,
                6.825604537781398e-08,
                6.023569166629634e-08,
                8.764247451307293e-08,
                0.9999980052700421,
                9.931198061405701e-08,
                0.999998126125064,
                9.931202796957073e-08,
                8.764254764749753e-08
            ],
            [
                0.9999995262095551,
                0.9999996743688586,
                0.9999977396762431,
                0.9999993524048932,
                0.9999996940976638,
                0.9999985406232585,
                0.9999991148433867,
                0.9999998024947037,
                0.9999996533674202,
                0.9999997617631753
            ],
            [
                0.9999996310115479,
                0.9999995549149483,
                0.9999995549148422,
                0.9999989322971303,
                0.9999998024946801,
                0.9999993916411811,
                0.9999949062956118,
                0.9999999006880195,
                0.9999989322970034,
                0.9999997300423191
            ],
            [
                8.939695238439078e-06,
                2.9023130230846496e-06,
                1.3709578605617394e-06,
                1.5534981249574276e-06,
                7.338207180864763e-07,
                3.927860597935108e-07,
                2.902310947208574e-06,
                5.043472278280699e-07,
                2.2603242978665707e-06,
                5.043472278280699e-07
            ],
            [
                0.99999926617902,
                0.9999832985742014,
                0.9999986290432845,
                0.9999945777784524,
                0.9999993524049705,
                0.9999978766205262,
                0.9999989322966216,
                2.69957906184239e-07,
                0.9999985406243017,
                0.9999984465028018
            ],
            [
                0.9999904837483253,
                0.9999981261243943,
                0.9999982396563682,
                5.422218969858371e-06,
                1.3007133116353526e-05,
                0.9999972735303831,
                0.9999938558261406,
                0.9999980052698042,
                0.9999996072137062,
                0.9999984465020617
            ],
            [
                2.382369667929001e-07,
                2.6995774527718623e-07,
                0.9999869928684467,
                2.6995768091383957e-07,
                0.9999991148430698,
                7.73441946488886e-08,
                1.2751899728286965e-07,
                4.4508510499849186e-07,
                4.450850519403407e-07,
                4.4508494582405734e-07
            ],
            [
                9.422448185264317e-07,
                7.338211554783522e-07,
                9.422448185478557e-07,
                1.99472900813862e-06,
                9.422445938728576e-07,
                1.0677029973158649e-06,
                6.475947210012481e-07,
                1.7603436330179102e-06,
                8.315277302841894e-07,
                6.475945666051092e-07
            ],
            [
                1.1478769494542698e-05,
                4.785094494811783e-06,
                2.2603253756956754e-06,
                1.994729483729522e-06,
                1.370957860576702e-06,
                3.288747889284851e-06,
                4.785093924389007e-06,
                1.5534984953552536e-06,
                3.72663883989755e-06,
                9.422450431989127e-07
            ],
            [
                0.9999989969861515,
                0.9999962733611633,
                0.9999938558268682,
                0.9999992661789323,
                0.9999987901337405,
                0.9999945777823277,
                0.9999987121049384,
                0.9999975938973752,
                0.9999982396567877,
                0.999999310639037
            ],
            [
                0.9999996533675031,
                0.9999993106392013,
                0.9999996940978098,
                0.9999994631249963,
                0.999998996985434,
                0.9999992661787575,
                0.9999996743687812,
                0.9999997300420941,
                0.9999996310115479,
                0.9999994956524118
            ],
            [
                1.7603425837903113e-06,
                1.5534984953552536e-06,
                3.7266379514061143e-06,
                3.726639284144195e-06,
                1.5534975693979422e-06,
                0.9999952149072218,
                6.475949526020042e-07,
                0.999995504817356,
                2.9023119851899796e-06,
                5.715005832886879e-07
            ],
            [
                0.9999967112493691,
                7.734423152941018e-08,
                0.9999996940977003,
                0.9999975938976622,
                0.9999978766210335,
                0.9999974387184012,
                0.9999987121041708,
                0.9999981261239477,
                0.9999992661790198,
                0.9999957771675654
            ],
            [
                1.6373770576683237e-07,
                2.1024329090781183e-07,
                1.855391681891831e-07,
                2.3823685319244518e-07,
                3.927860597935108e-07,
                2.382370235922541e-07,
                1.2751902768478173e-07,
                2.699576809121209e-07,
                1.2751901248391176e-07,
                2.3823699519143784e-07
            ],
            [
                0.9999994956524114,
                0.9999982396565777,
                1.6373762769138607e-07,
                0.9999997300423191,
                0.9999992661789322,
                0.9999994631250603,
                0.9999996533674205,
                0.9999994631251242,
                0.9999989969862708,
                0.9999952149072184
            ],
            [
                3.927862939126708e-07,
                5.043474081993875e-07,
                2.1024329090867228e-07,
                3.059021904571643e-07,
                9.422447062094932e-07,
                5.043472278280699e-07,
                5.043472879504592e-07,
                7.338212429504183e-07,
                2.69957906184239e-07,
                6.962259569750576e-06
            ],
            [
                0.9999986290432844,
                0.9999994956527122,
                0.9999995818811276,
                0.9999995262096116,
                0.9999989322968763,
                0.9999996743686257,
                0.9999997463980729,
                0.9999996743687422,
                0.9999980052707559,
                0.9999996072136125
            ],
            [
                0.9999995262093858,
                0.9999989322967487,
                0.9999996072139403,
                0.9999997463981939,
                0.9999975938965138,
                0.9999955048173529,
                0.9999997463982241,
                0.999999607213753,
                NaN,
                0.9999998802068873
            ],
            [
                6.023573475041126e-08,
                4.139935079796334e-08,
                6.825602910433871e-08,
                2.2159473432612064e-08,
                6.023573475041126e-08,
                8.764247451307293e-08,
                7.734421308914719e-08,
                6.825606165129312e-08,
                3.653482080235082e-08,
                6.023576347299818e-08
            ],
            [
                0.9999993106386265,
                0.9999996743687424,
                0.999999114843071,
                0.9999993106390375,
                0.999999266178845,
                0.9999974387174869,
                0.999998239655949,
                0.9999934595651245,
                0.999999391640819,
                0.9999977396754349
            ],
            [
                0.9999980052705173,
                0.9999972735294081,
                0.9999967112509369,
                0.9999989322966212,
                0.9999995818811773,
                0.999999391640746,
                0.9999978766210336,
                0.999998346310021,
                0.9999957771655524,
                0.9999962733616075
            ],
            [
                0.9999975938979488,
                8.315282259138311e-07,
                0.9999934595619995,
                0.9999785550414299,
                0.9999957771670626,
                0.9999975938985219,
                0.9999942280786042,
                2.561282210740037e-06,
                1.2098659719788098e-06,
                0.9999952149066511
            ],
            [
                0.9999978766212861,
                0.9999996743686647,
                0.9999991148427538,
                0.9999996310114599,
                0.9999957771645461,
                0.9999996310115039,
                0.9999974387177907,
                0.9999997761971317,
                0.999999631011416,
                0.9999975938970884
            ],
            [
                3.4663249714451116e-07,
                8.764247451307293e-08,
                1.0677032518748838e-06,
                8.315278294114555e-07,
                3.059023363221292e-07,
                2.6995790618469934e-07,
                1.1478765389368729e-05,
                9.931186222523604e-08,
                2.102434162245973e-07,
                1.855391681898159e-07
            ],
            [
                9.422448185435711e-07,
                3.466327450744504e-07,
                3.059023727894942e-07,
                2.1024336609724313e-07,
                3.0590226338838606e-07,
                2.6995780963588326e-07,
                4.450851049890802e-07,
                3.92786340734912e-07,
                3.466327863961242e-07,
                3.927862002625787e-07
            ],
            [
                0.9999981261252892,
                0.9999938558254131,
                0.9999938558276115,
                0.9999980052709956,
                0.9999925887227938,
                0.9999997897565839,
                0.9999964991468419,
                0.9999991684719735,
                0.9999957771660636,
                0.9999921107374246
            ],
            [
                3.059022269250683e-07,
                5.043476486915964e-07,
                0.9999967112517221,
                3.466326211113502e-07,
                0.9999945777810372,
                6.475947210046347e-07,
                3.466326211113502e-07,
                6.475950298011458e-07,
                4.450849988811838e-07,
                1.0677027427600627e-06
            ],
            [
                0.9999998802069302,
                0.9999998802069302,
                0.9999998461826406,
                0.9999989969862714,
                0.9999998024946566,
                0.999997593898523,
                0.9999987121047862,
                0.9999997126315153,
                0.9999998362622358,
                0.9999994631250603
            ],
            [
                1.4449798650551755e-07,
                8.764247451307293e-08,
                1.4449798650551755e-07,
                3.0590215399183813e-07,
                1.8553916819032217e-07,
                1.2751899728286965e-07,
                2.382370235933104e-07,
                1.7603440527286572e-06,
                1.1253526937656726e-07,
                3.466327450765785e-07
            ],
            [
                0.9999994956527725,
                0.9999967112493697,
                0.9999985406234316,
                0.9999998802069873,
                0.9999996310116359,
                0.9999998362623724,
                0.9999992188512971,
                0.9999994956524116,
                0.9999938558276023,
                0.999998005270518
            ],
            [
                0.9999993916408185,
                0.9999989322966214,
                0.9999996743688586,
                0.9999998024946095,
                0.9999997300421583,
                0.9999997463980729,
                0.9999996940978096,
                0.9999975938979482,
                0.9999998257020798,
                0.9999996743686257
            ],
            [
                9.931193325852072e-08,
                8.764247451307293e-08,
                8.764247451307293e-08,
                9.931189774187203e-08,
                5.315780536011123e-08,
                4.691160446380562e-08,
                6.825598842065202e-08,
                5.315784971839039e-08,
                9.931189774187203e-08,
                1.6373766672973748e-07
            ],
            [
                7.338207180761315e-07,
                2.2603245672497918e-06,
                2.699578739999358e-07,
                7.338213304196583e-07,
                1.0677028699858827e-06,
                9.42244930862237e-07,
                5.043472879525233e-07,
                2.260324567227179e-06,
                6.475945665741875e-07,
                3.9278638755671223e-07
            ],
            [
                0.9999994284997576,
                0.9999993106388729,
                0.9999985406232582,
                0.9999994631251247,
                0.999996499146426,
                0.9999992661789326,
                0.999998446502247,
                0.9999997463981334,
                0.9999975938973754,
                0.9999997761971582
            ],
            [
                3.288749457469787e-06,
                0.999998446501691,
                2.902313023130843e-06,
                0.999998932297258,
                1.5534971990169383e-06,
                1.3709568799919866e-06,
                1.012999218776902e-05,
                8.939700567094277e-06,
                9.422448185534261e-07,
                2.9023116392097746e-06
            ],
            [
                2.3823690999290963e-07,
                0.9999967112501523,
                2.1024329090929374e-07,
                1.6373768624837685e-07,
                0.9999978766220451,
                9.931186222482958e-08,
                1.4449796927932878e-07,
                1.4449798650417048e-07,
                1.125352291309328e-07,
                1.1253518888531272e-07
            ],
            [
                0.9999977396748967,
                0.9999992188516703,
                0.9999990577556315,
                0.9999949062950025,
                0.9999988634361545,
                0.9999970976866338,
                0.9999983463104154,
                0.999998126125065,
                0.9999987121046318,
                0.9999983463098239
            ],
            [
                0.9999996940978461,
                1.0677027427600627e-06,
                2.6995784182140636e-07,
                2.102434412871794e-07,
                1.6373768624837685e-07,
                6.475947210046347e-07,
                1.209865539295696e-06,
                6.475946438055299e-07,
                1.6373766672888118e-07,
                5.715002426475718e-07
            ],
            [
                1.0677027427600627e-06,
                5.715003789046955e-07,
                1.2751908849167202e-07,
                2.1024326584639497e-07,
                2.3823690999290963e-07,
                9.931198061405701e-08,
                1.1253513522447425e-07,
                1.6373768624837685e-07,
                1.4449803818156628e-07,
                3.059021175247079e-07
            ],
            [
                0.9999957771665603,
                0.999992110735543,
                0.9999843104559168,
                0.9999977396746259,
                0.9999962733593867,
                0.9999980052700422,
                0.9999977396746255,
                0.9999952149043673,
                0.9999930377454256,
                0.9999989322966216
            ],
            [
                1.8553916819032217e-07,
                2.699578740011634e-07,
                6.825602910433871e-08,
                1.2098656835224664e-06,
                1.2751901248454963e-07,
                1.2751904288739315e-07,
                0.9999972735300561,
                1.8553903548231313e-07,
                1.637377448057981e-07,
                1.6373764720990908e-07
            ],
            [
                2.845333710449759e-08,
                4.691164360958274e-08,
                4.139938534423022e-08,
                3.2241881707064475e-08,
                6.023568448565689e-08,
                7.734421308914719e-08,
                6.825608606148807e-08,
                9.931189774187203e-08,
                6.023572038912295e-08,
                8.764255809528314e-08
            ],
            [
                0.9999997463981334,
                0.9999985406234322,
                0.9999975938965165,
                0.9999992661789325,
                0.9999970976890554,
                0.9999982396574185,
                0.999998863436019,
                0.999998446501691,
                0.9999988634366963,
                0.9999994284996218
            ],
            [
                0.9999984465024327,
                0.9999984465028018,
                0.9999992661788448,
                0.9999988634364256,
                0.999999802494633,
                0.999998126123948,
                1.553497754577351e-06,
                1.3709575337078829e-06,
                0.9999998024946095,
                0.9999998024947273
            ],
            [
                2.382370235922541e-07,
                4.450849988780466e-07,
                3.059023363221292e-07,
                5.043472879504592e-07,
                1.1253517546946102e-07,
                3.0590237278838124e-07,
                3.9278624708775595e-07,
                4.450849458179853e-07,
                1.4449798650417048e-07,
                3.0590226339061185e-07
            ],
            [
                0.9999985406230836,
                0.9999993106386262,
                0.9999995262094987,
                0.9999991148427533,
                0.9999996743687811,
                0.9999984465015058,
                0.999997593897375,
                0.9999997300421904,
                0.9999997126313783,
                0.9999977396746262
            ],
            [
                0.9999994284996895,
                0.9999996533672963,
                0.999999168471874,
                0.9999992188519491,
                0.9999987901343176,
                0.9999991684720724,
                0.9999992188515768,
                0.9999994284996897,
                0.9999991148429644,
                0.9999981261250653
            ],
            [
                3.653482951291499e-08,
                6.023569884718319e-08,
                7.73442776300517e-08,
                3.653482951291499e-08,
                3.6534807736504303e-08,
                2.3823682479181176e-07,
                4.691164920214251e-08,
                6.825608606148807e-08,
                0.9999986290421404,
                7.734414854792722e-08
            ],
            [
                1.637377643243723e-07,
                2.6995771309523475e-07,
                3.0590215399183813e-07,
                1.3709568799760888e-06,
                3.4663249714451116e-07,
                2.3823699519290042e-07,
                6.475949525981759e-07,
                5.043475885674441e-07,
                5.715005832853093e-07,
                4.450849458179853e-07
            ],
            [
                1.2751908849167202e-07,
                2.1024341622368903e-07,
                2.1024331597152624e-07,
                1.6373772528636992e-07,
                2.102434412871794e-07,
                2.3823699519225038e-07,
                2.1024341622426268e-07,
                1.6373770576776313e-07,
                0.9999997126313784,
                3.927863875616689e-07
            ],
            [
                0.9999986290424672,
                0.9999962733602771,
                0.9999960330150365,
                0.9999992188512975,
                0.9999984465020619,
                0.9999925887174883,
                0.9999997126314811,
                0.9999984465016915,
                0.9999997761971317,
                0.9999983463100213
            ],
            [
                0.9999993106387082,
                0.9999981261237237,
                0.9999986290424676,
                0.9999980052693285,
                0.9999995549149483,
                0.9999990577549572,
                0.9999987901340288,
                0.9999987121046314,
                0.9999972735300563,
                0.9999987901343173
            ],
            [
                0.9999987121049387,
                0.9999989969856733,
                0.9999998144608541,
                0.9999998144609203,
                0.9999997897566841,
                0.9999993524049704,
                0.9999983463106126,
                0.9999992188518563,
                0.9999988634362912,
                0.9999996310115921
            ],
            [
                1.4449805540740185e-07,
                0.9999997761971317,
                1.4449805540740185e-07,
                6.023574911170301e-08,
                8.764244316933122e-08,
                0.9999996743688199,
                1.637377448057981e-07,
                1.1253509497883659e-07,
                9.931195693628605e-08,
                2.1024341622368903e-07
            ],
            [
                0.999999554914789,
                0.9999981261241706,
                0.9999991684715761,
                8.7642516304188e-08,
                0.9999987121044777,
                0.9999993524048932,
                0.9999980052700427,
                0.9999991684716751,
                0.9999972735290809,
                0.9999994631248683
            ]
        ]
    },
    {
        "q_id": "9516_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.99999905775507,
                0.9999998802069445,
                0.9999994284993492,
                0.9999986290429579,
                0.9999993106391194,
                0.9999994956525923,
                0.9999992188513908,
                0.9999994284995535,
                0.9999996743686259,
                0.9999997300423192
            ],
            [
                0.9999999123575255,
                0.9999999397642437,
                0.9999999067050276,
                0.9999998724809723,
                0.9999998802069874,
                0.999999958600659,
                1.0,
                0.9999999530883508,
                1.0,
                0.9999998257020591
            ],
            [
                0.9999993106386261,
                0.9999991684717745,
                0.9999987121047852,
                0.9999977396759734,
                0.999999872480942,
                0.9999998802069302,
                0.9999999559305681,
                0.9999992661790201,
                0.9999995818812772,
                0.999997593898236
            ],
            [
                0.9999998555019964,
                0.9999983463108103,
                0.9999997126314469,
                0.9999997897566341,
                0.9999997897566341,
                0.9999994956527725,
                0.9999999586006344,
                0.9999986290429586,
                0.9999992661788452,
                0.9999996310114161
            ],
            [
                0.9999994956524118,
                0.9999998257021007,
                0.9999998362623138,
                0.9999970976866349,
                0.9999997300421261,
                0.9999989322968762,
                0.999999746398194,
                0.9999997300421261,
                0.9999998144608319,
                0.9999957771645475
            ],
            [
                0.9999998144609205,
                0.9999999226557316,
                0.999999114843387,
                0.9999998874648515,
                0.9999987121044782,
                0.9999984465015059,
                0.9999995818810777,
                0.9999989969856734,
                0.9999998942829981,
                0.9999994631248044
            ],
            [
                0.999999906705072,
                0.9999997126314468,
                0.999999935879425,
                1.0,
                0.9999997897567342,
                0.9999998802069587,
                0.9999994284997576,
                0.999999730042287,
                0.9999997761970516,
                0.9999996072139404
            ],
            [
                0.9999997617630901,
                0.9999998362622358,
                0.9999996940977005,
                0.9999998461826406,
                1.0,
                0.9999998724810029,
                0.9999998802069588,
                1.0,
                0.999999894282935,
                0.9999998942830485
            ],
            [
                0.9999989969857933,
                0.9999989969857929,
                0.9999999317439546,
                0.9999995549150544,
                0.9999989969854343,
                0.9999995262095552,
                0.9999996940978099,
                0.9999991684715764,
                0.9999998144609205,
                0.9999999358794021
            ],
            [
                0.9999998024946332,
                0.9999992188513905,
                0.9999998257021213,
                0.9999994956527124,
                1.0,
                0.9999998144608098,
                0.9999991148431757,
                0.9999997300423192,
                0.9999999358793944,
                0.9999999358793409
            ],
            [
                0.999996499146842,
                0.999998863435884,
                0.9999994284997578,
                0.9999992188518564,
                0.9999998024946567,
                0.9999985406243025,
                0.9999993524048937,
                3.059022269250683e-07,
                0.9999994284993491,
                0.999999114843282
            ],
            [
                0.9999996533672139,
                0.9999993916411812,
                0.9999997897566841,
                0.999999526209273,
                0.9999995818812273,
                0.9999998257021422,
                0.9999997463980428,
                0.9999997463981637,
                0.9999997300421262,
                0.9999998024946801
            ],
            [
                1.0,
                0.999999674368781,
                0.9999998724809116,
                0.9999996940978826,
                0.9999998642567028,
                0.999999789756659,
                0.9999997463981032,
                0.9999995262092729,
                0.9999997463981636,
                0.999999931743979
            ],
            [
                0.9999998874647977,
                0.9999998362622553,
                0.9999999176675044,
                0.9999998461827323,
                0.9999998802069302,
                0.9999999123574942,
                0.9999998642567353,
                0.9999999123575882,
                1.0,
                0.9999998874647844
            ],
            [
                0.9999991684718741,
                0.9999991148427537,
                0.9999995262092729,
                0.9999981261250669,
                0.999999776197025,
                0.999999887464771,
                0.9999999067050387,
                0.9999969105044528,
                0.9999994956527126,
                0.999999631011372
            ],
            [
                0.9999999226558423,
                0.9999988634364262,
                0.9999998942830485,
                0.9999992661791954,
                0.9999996310115481,
                0.999999802494586,
                0.9999991148426485,
                0.9999998874647978,
                0.9999999273417662,
                0.9999998724809877
            ],
            [
                0.9999996533672139,
                0.9999997761971583,
                0.9999997300422226,
                0.9999972735290836,
                0.9999955048173577,
                0.9999972735284316,
                0.9999978766205272,
                0.9999997300421262,
                0.999999653367255,
                0.9999988634362907
            ],
            [
                0.9999997463981637,
                0.9999996743686648,
                0.9999995262094424,
                0.9999997300422871,
                0.9999995262094993,
                0.9999996743687813,
                0.9999996940977368,
                0.999999730042255,
                0.999999789756584,
                0.9999995549148953
            ],
            [
                0.9999990577550699,
                0.999998712104171,
                0.9999985406236057,
                0.9999982396565782,
                0.9999989322966213,
                0.9999997897567343,
                0.9999997300422226,
                0.9999986290424672,
                0.9999995262094987,
                0.9999998024947273
            ],
            [
                0.9999999273418182,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.999999814460876,
                0.9999999468421059,
                0.9999998555020307,
                1.0
            ],
            [
                0.9999999067050721,
                0.9999995818812771,
                0.9999998642566866,
                0.999999922655787,
                0.9999998144608762,
                0.9999995549147891,
                0.9999999273418962,
                0.9999994631250604,
                1.0,
                0.9999999358794402
            ],
            [
                0.9999996940977733,
                0.9999983463098238,
                0.9999994284996214,
                0.9999998144609646,
                0.9999998024947273,
                0.9999999006881496,
                0.9999995262093293,
                0.9999993524053564,
                0.9999995549148953,
                0.9999996072136126
            ],
            [
                0.9999998362622943,
                1.0,
                0.9999998802069445,
                0.9999999273418096,
                0.9999999273417837,
                0.9999998257021838,
                1.0,
                0.9999999434137907,
                0.9999998024946095,
                0.9999998642566543
            ],
            [
                0.9999992188518563,
                0.9999992188513906,
                0.999999789756659,
                0.9999989322975124,
                0.9999998802069302,
                0.9999993524052022,
                0.9999999123575151,
                0.9999999317440279,
                0.9999987901346058,
                0.9999991148427536
            ],
            [
                0.9999993916410362,
                0.9999994631251243,
                0.9999992188512974,
                0.9999998874648246,
                0.9999995262094422,
                0.9999999468421883,
                0.9999998257021422,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999972735297326,
                0.9999978766207804,
                0.9999988634360195,
                0.9999996533674619,
                0.999999266178933,
                0.9999964991443426,
                0.999998996985793,
                0.9999967112513297,
                0.9999991148431757,
                0.9999987121047857
            ],
            [
                0.9999998024946332,
                0.9999999434137368,
                0.9999999176674552,
                0.9999977396765126,
                0.9999998642566866,
                1.0,
                0.999999864256622,
                0.9999998724809115,
                0.9999999397642365,
                0.9999997617630617
            ],
            [
                0.9999997463980427,
                0.9999990577554069,
                0.9999970976880196,
                0.9999997897567343,
                0.9999999006880312,
                0.9999980052702806,
                0.999999057754958,
                0.9999997897566091,
                0.9999999006880195,
                0.9999997126313785
            ],
            [
                0.9999990577549573,
                0.9999999317440116,
                0.9999999067050387,
                0.9999992188516698,
                0.9999998555020307,
                0.99999926617867,
                0.9999989322971308,
                1.0,
                0.9999997463982241,
                0.9999990577550696
            ],
            [
                0.999999653367503,
                0.9999998144609424,
                0.9999996533673792,
                1.0,
                0.9999998144608098,
                0.9999998942829099,
                0.9999997761970515,
                0.9999998942829981,
                0.9999999176675632,
                1.0
            ],
            [
                0.9999998874649185,
                0.9999998802069587,
                0.9999994631248044,
                0.9999993524048935,
                0.9999996072138936,
                1.0,
                0.9999995262094987,
                0.9999994956524718,
                0.9999994284997576,
                0.9999997126314812
            ],
            [
                0.9999998555020481,
                0.9999999006881141,
                0.9999991148427539,
                0.9999998257021422,
                0.9999995262092165,
                0.9999995818812771,
                0.9999998362622358,
                0.999999730042094,
                0.999999776197185,
                0.9999997126313785
            ],
            [
                0.9999991684715764,
                0.9999998724809723,
                0.9999998144608319,
                0.9999998724809571,
                0.999999802494633,
                0.9999990577555192,
                0.9999997897565588,
                0.9999994284994171,
                0.9999994631248045,
                0.9999978766222992
            ],
            [
                0.9999997617630334,
                0.9999998362622553,
                0.9999997300420941,
                0.9999998555019447,
                0.9999994956524718,
                0.9999980052698054,
                0.9999994631248047,
                0.9999997463981637,
                0.999999352405125,
                0.9999998362622357
            ],
            [
                0.9999997761971315,
                0.9999996743687811,
                0.9999997761970782,
                0.9999997897566091,
                0.9999997300422871,
                0.9999999006881497,
                0.9999998257021214,
                0.9999999397642653,
                0.9999999358793409,
                0.9999994631249968
            ],
            [
                3.0590226339061185e-07,
                5.043474683220276e-07,
                3.466325384661554e-07,
                3.059023727894942e-07,
                5.04347348075149e-07,
                8.315279285351409e-07,
                3.9278624708775595e-07,
                3.9278615343901467e-07,
                2.6995784182140636e-07,
                9.422448185435711e-07
            ],
            [
                0.9999991684720723,
                0.999999631011328,
                0.9999998144608763,
                0.9999994956524719,
                0.9999998257021837,
                0.9999996310114162,
                0.9999994956525922,
                0.9999988634357484,
                0.99999971263131,
                0.9999997761971584
            ],
            [
                6.144173869603344e-06,
                1.0129993395217047e-05,
                3.05902226923399e-07,
                2.3823696679230424e-07,
                1.2098662604192665e-06,
                1.9947306726594253e-06,
                1.3709573702778664e-06,
                2.430024073523505e-05,
                2.102434412875379e-07,
                2.3823702359138736e-07
            ],
            [
                0.9999998362623138,
                0.9999997761970784,
                1.0,
                0.9999994631249325,
                0.9999999358794096,
                0.9999997126313784,
                0.9999999006880549,
                0.9999989969862711,
                0.9999998024947274,
                0.9999997300421906
            ],
            [
                0.9999998642566866,
                0.9999996940977368,
                0.9999994956527726,
                0.9999986290432848,
                0.9999987121046321,
                0.9999996743687811,
                0.9999993916411812,
                0.999999825702059,
                0.9999998461826038,
                0.9999999317439872
            ],
            [
                0.999999825702059,
                0.9999997126314468,
                0.9999998362622748,
                1.9947294837154625e-06,
                0.9999998461826038,
                0.9999992188513904,
                0.9999997897567343,
                0.9999993106389549,
                0.9999995262092163,
                0.999999114843281
            ],
            [
                0.9999998461826406,
                0.9999998461826038,
                0.9999993106386265,
                0.9999994956527124,
                0.9999997300422228,
                0.9999975938968017,
                0.9999987901338849,
                0.9999992661791951,
                0.9999995818813768,
                0.9999992661787576
            ],
            [
                0.9999996310113282,
                0.9999982396572107,
                0.9999998024946332,
                0.9999995549148423,
                0.9999998724808964,
                0.9999998144609205,
                0.9999995262096119,
                0.9999993916406738,
                0.9999996072137531,
                0.9999998362622944
            ],
            [
                0.9999999500628035,
                0.999999789756634,
                0.9999997761972116,
                0.9999996940978462,
                0.9999998724809723,
                1.0,
                0.9999999358794479,
                0.9999999397642725,
                0.9999999317440035,
                0.9999996072138467
            ],
            [
                0.9999997617630334,
                0.9999998724810027,
                0.9999993916410361,
                0.9999982396565783,
                0.9999988634366966,
                0.9999998461826588,
                0.9999999530883172,
                0.9999998461826038,
                0.9999996310115918,
                0.9999981261239476
            ],
            [
                0.9999998461826038,
                1.0,
                0.9999998642566542,
                0.9999997617631186,
                0.9999995262092165,
                0.9999999317440197,
                0.999999887464744,
                0.9999991684722704,
                0.9999998874649185,
                0.9999999468421946
            ],
            [
                0.9999985406232583,
                0.9999987121047864,
                0.9999997300421263,
                0.9999993916406739,
                0.9999964991447678,
                0.9999969105048271,
                0.9999982396563708,
                0.9999996743687424,
                0.999999352405126,
                0.9999996072137066
            ],
            [
                0.9999995262092729,
                0.9999997300421904,
                0.9999998362622358,
                0.9999998942829225,
                0.9999998942829224,
                0.9999997617631186,
                1.0,
                0.9999998942830485,
                0.9999995549151076,
                0.9999984465020618
            ],
            [
                0.99999926617867,
                1.0,
                0.9999989322975126,
                0.9999999317439384,
                0.9999995549148951,
                0.9999998942830107,
                0.9999980052702803,
                0.999999789756634,
                0.9999996940976275,
                0.9999999123575359
            ],
            [
                0.9999998642566543,
                0.9999995818811773,
                0.9999998024946095,
                0.9999998724809723,
                0.9999996310113279,
                0.9999995818812272,
                0.9999998144609646,
                0.9999997617631753,
                0.9999996743686645,
                0.9999997463980729
            ],
            [
                9.422444815814404e-07,
                2.2603240284371276e-06,
                2.2603234895372223e-06,
                1.5534981249697903e-06,
                1.067703124601679e-06,
                6.962254589978262e-06,
                1.0677032518785256e-06,
                8.315284241650899e-07,
                9.422448185534261e-07,
                3.288750241561788e-06
            ],
            [
                0.9999974387171824,
                0.9999987901338866,
                0.9999994631248049,
                0.999996711252117,
                0.999999310638709,
                0.999989870005461,
                0.9999992188519513,
                0.9999980052705207,
                0.9999982396569995,
                0.9999974387174878
            ],
            [
                0.9999997463981031,
                0.9999992188518562,
                0.9999998724809268,
                0.9999994956523517,
                0.9999997617631754,
                0.9999994631250604,
                0.9999997126314126,
                0.9999997300423193,
                0.9999995818813768,
                0.9999997761970248
            ],
            [
                0.9999998802068873,
                0.9999988634361546,
                0.999999761763005,
                0.9999999176674357,
                0.9999999273417662,
                0.9999998874649051,
                0.9999998461827139,
                0.9999999006881378,
                0.999997438718708,
                0.9999999123575674
            ],
            [
                0.9999999397642294,
                0.9999999123575046,
                0.9999998362622747,
                0.999999939764258,
                0.9999998555019619,
                0.9999999317439303,
                0.9999999358793409,
                0.9999999434137098,
                0.9999975938973746,
                0.9999998874647441
            ],
            [
                1.0677029973219343e-06,
                1.994729483729522e-06,
                2.382369951932796e-07,
                NaN,
                9.422448185534261e-07,
                1.2098661162056318e-06,
                3.466327450756327e-07,
                1.0677028700422047e-06,
                5.043475885696228e-07,
                7.338208055680009e-07
            ],
            [
                0.9999994284995535,
                0.9999962733620521,
                0.9999999176675338,
                0.9999995262096116,
                0.9999992661787576,
                0.9999996940978826,
                0.9999987121052457,
                0.9999987901344615,
                0.9999997897566089,
                0.9999995549147891
            ],
            [
                0.9999999434137098,
                0.9999989322970035,
                0.9999999611088766,
                0.9999998802069445,
                0.9999997761971849,
                0.9999998555020307,
                0.9999998257021007,
                0.9999993916410361,
                0.9999993916410362,
                0.9999999067051499
            ],
            [
                1.9947299593078385e-06,
                0.999999526209386,
                0.9999998642566543,
                0.9999992188512974,
                0.9999983463106127,
                0.9999989322972581,
                0.9999997126314127,
                0.9999992188515768,
                0.9999995549149485,
                0.9999993106390371
            ],
            [
                1.0,
                0.9999998942830359,
                0.9999999006879958,
                0.999999939764294,
                0.999999789756659,
                1.0,
                0.9999997897566841,
                1.0,
                0.9999998024945624,
                0.9999996743688976
            ],
            [
                0.9999982396559495,
                0.9999995262094425,
                0.9999998024946801,
                0.9999991684722707,
                0.9999981261241715,
                0.9999995262093295,
                0.9999996533672966,
                0.9999987901346062,
                0.9999992188513908,
                0.9999993916410364
            ],
            [
                0.9999975938965181,
                0.9999985406237806,
                0.9999988634360202,
                0.9999994956524119,
                0.9999977396748977,
                0.9999988634362906,
                0.9999996940977735,
                0.9999982396561606,
                0.9999995262092164,
                0.9999977396754368
            ],
            [
                0.9999993916408191,
                0.9999996310115041,
                0.999998996985674,
                0.9999991148432821,
                0.9999994631251884,
                0.9999994956526524,
                0.9999995549149486,
                0.9999995262093296,
                0.9999994284993493,
                0.9999981261252889
            ],
            [
                0.9999998874647307,
                0.9999996072138468,
                0.9999996310115481,
                0.9999998024945861,
                0.9999997463981637,
                0.9999998024947273,
                0.9999993524054337,
                0.9999998642566866,
                0.9999997300420941,
                0.9999996743686257
            ],
            [
                0.9999999123575674,
                0.9999998362623138,
                0.9999995818813269,
                0.9999998362623138,
                0.9999998724810029,
                0.9999994284994174,
                0.9999999123575882,
                0.9999997463981032,
                0.9999986290426311,
                0.9999998874648112
            ],
            [
                0.999999814460832,
                0.9999995262093294,
                0.9999997126314126,
                0.999999631011328,
                1.0,
                0.9999997126313784,
                0.9999989969860322,
                0.9999999358793639,
                1.0,
                0.999999927341801
            ],
            [
                0.9999995262096117,
                0.9999997463981032,
                0.9999998144608098,
                0.9999991684719728,
                0.9999998724809723,
                0.9999997761971584,
                0.9999998144608541,
                0.9999997463981637,
                1.0,
                0.9999999176675338
            ],
            [
                0.9999995262096119,
                0.9999991148428593,
                0.9999998555020309,
                0.9999998257021631,
                0.9999994284994855,
                0.9999996743688587,
                0.9999997617631753,
                0.9999992661786702,
                0.9999997761972117,
                0.9999990577557444
            ],
            [
                0.9999999500627739,
                0.9999996743688976,
                0.999999746398073,
                0.9999993916406736,
                0.9999996310115481,
                0.9999998555019275,
                0.9999999226558238,
                0.9999996310113282,
                0.9999999226557316,
                0.9999980052702803
            ],
            [
                0.9999997463981033,
                0.9999997300422229,
                0.9999995549150545,
                0.9999998555019791,
                0.9999998642566705,
                0.9999996940977004,
                0.9999987901344622,
                0.9999985406239555,
                0.9999991148430706,
                0.9999996533673793
            ],
            [
                0.9999996310114599,
                0.9999998555019446,
                0.9999997897567091,
                0.9999996940978461,
                0.9999995549151075,
                0.9999998461826038,
                0.999999946842163,
                0.9999987901338844,
                0.9999998802069873,
                0.9999995818813269
            ],
            [
                0.999999789756584,
                0.9999998144609646,
                0.9999997761972117,
                0.9999994956527126,
                0.9999997463980126,
                0.9999996072137064,
                0.9999994284995538,
                0.9999974387168789,
                0.9999996533672966,
                0.9999994631251246
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999998874648246,
                0.9999998362623723,
                0.999999922655833,
                1.0,
                1.0,
                0.9999998144608763,
                0.999999931743971
            ],
            [
                0.9999996743687424,
                1.0,
                1.0,
                0.9999993524052024,
                0.9999998874647977,
                0.9999995262096119,
                0.9999998024946332,
                0.9999994956526523,
                0.9999996940978099,
                0.9999998724809116
            ],
            [
                0.9999999123575465,
                0.9999997463981033,
                0.9999996940977733,
                0.9999999123574629,
                1.0,
                0.9999997617631187,
                0.9999999006879957,
                0.9999998942829099,
                0.9999996940978828,
                0.9999996072138003
            ],
            [
                0.99999967436882,
                0.9999998724809875,
                0.9999995818813769,
                0.9999996940978099,
                0.9999997300423193,
                0.9999997463980429,
                0.9999998802068875,
                0.9999997617630618,
                0.9999993106392017,
                0.9999998642566705
            ],
            [
                0.999999352405048,
                0.9999996533672963,
                0.9999997617630617,
                0.9999996743688588,
                0.9999998362622943,
                0.9999992661788453,
                0.999999730042255,
                0.9999995549148954,
                0.9999992188517629,
                0.9999994956527126
            ],
            [
                0.9999994284993492,
                0.9999994956527726,
                0.9999991684718741,
                0.9999991148432813,
                0.9999993916408912,
                0.999999114842648,
                0.9999994631249967,
                0.9999957771670677,
                2.9023133690637e-06,
                9.422449308748773e-07
            ],
            [
                0.9999999067051054,
                0.9999999226557132,
                0.9999998144609203,
                0.9999993106388728,
                0.9999996940977003,
                0.9999998942829981,
                1.0,
                0.9999996310113279,
                0.9999997761971849,
                0.9999999317439303
            ],
            [
                1.0,
                1.0,
                0.9999999317439628,
                0.9999999067050387,
                0.999999887464932,
                0.9999998555020307,
                0.9999998874648917,
                1.0,
                0.9999993524053568,
                1.0
            ],
            [
                0.9999962733593871,
                0.9999995549149483,
                0.9999991148430702,
                0.9999999358793332,
                0.9999998942830106,
                0.9999987901338845,
                0.9999987121052459,
                0.9999998642566543,
                0.9999999226557501,
                0.999999855502048
            ],
            [
                0.9999998257021631,
                0.9999998555019619,
                0.9999998144608099,
                0.999999746398073,
                0.9999998874649051,
                0.9999999067049943,
                0.999999872480942,
                0.9999998257022046,
                0.999999887464932,
                0.9999998802069874
            ],
            [
                0.9999998724809571,
                0.9999996533673378,
                0.9999999273418355,
                1.0,
                0.9999998724808964,
                0.9999982396563684,
                0.9999981261241714,
                0.999999631011636,
                0.9999921107336729,
                0.9999999226557685
            ],
            [
                0.9999992661791952,
                0.9999955048194983,
                0.9999987121052459,
                0.9999945777823301,
                0.9999987121046315,
                0.9999995818814266,
                0.9999964991439216,
                0.9999960330126704,
                0.9999978766222984,
                0.9999983463108095
            ],
            [
                0.9999999226557684,
                0.9999999358793867,
                0.9999999397642653,
                0.9999993106388726,
                0.9999990577552942,
                0.9999999468421567,
                0.9999999123574733,
                0.9999996743687422,
                0.9999989969860319,
                0.9999998724809723
            ],
            [
                0.9999998461827139,
                0.9999999067049942,
                0.9999998642567028,
                0.9999997463981334,
                0.9999998874647843,
                1.0,
                0.9999998362622944,
                0.9999999530883844,
                0.9999998802069445,
                0.9999997126313441
            ],
            [
                0.9999975938970918,
                0.9999984465028023,
                0.9999989969857933,
                0.9999998555019275,
                0.9999992188512977,
                0.9999998362623724,
                0.9999993106392016,
                0.999999114842754,
                0.9999969105044498,
                0.9999998555020136
            ],
            [
                0.9999996533672552,
                0.9999993524048942,
                0.9999998461826772,
                0.9999995262092731,
                0.9999987901347508,
                0.9999993916411088,
                0.9999994956527726,
                0.9999985406243026,
                0.9999997126314129,
                0.9999991148428595
            ],
            [
                5.04347408197782e-07,
                2.1444943302181958e-05,
                3.2887506335906595e-06,
                1.3709567165579959e-06,
                2.75356878194421e-05,
                0.9999938558261341,
                2.7535700948722127e-05,
                0.9999970976883625,
                1.7603438428800754e-06,
                0.9999989322975126
            ],
            [
                1.0,
                0.999999939764294,
                1.0,
                0.9999998144608098,
                0.9999999176674946,
                0.9999999006880904,
                0.999999495652592,
                0.9999998461826589,
                0.9999977396751661,
                0.999999218851856
            ],
            [
                0.9999998024946332,
                0.9999998555019447,
                0.9999998461826589,
                0.9999989969854344,
                0.9999998461826772,
                0.9999998555019791,
                0.9999991148427537,
                0.9999999123574838,
                0.9999998942830737,
                0.9999999176675338
            ],
            [
                0.9999995262092164,
                0.9999992188518565,
                0.9999996310114603,
                0.999999880206916,
                0.9999998461827323,
                0.9999998024947038,
                0.9999998555019447,
                0.9999998257021214,
                0.9999998362622748,
                0.9999998461826772
            ],
            [
                0.9999999006880904,
                0.9999998144608319,
                0.9999999697115407,
                0.9999997617630333,
                0.9999998257020799,
                0.9999993524054337,
                0.9999997126314812,
                0.9999999358794327,
                0.9999999226557685,
                0.9999999500628513
            ],
            [
                0.9999996533673791,
                0.9999998461826772,
                0.9999997761971317,
                0.9999998942830737,
                0.9999998461827322,
                0.9999998724809115,
                0.9999997897566592,
                0.9999996743687423,
                0.9999998144608541,
                0.9999998257020591
            ],
            [
                0.9999995549148423,
                0.9999999500628333,
                0.9999993524053568,
                0.9999998144609425,
                0.9999998802069874,
                0.9999998257021422,
                0.9999997463981032,
                0.9999998024947272,
                0.9999992661789325,
                0.9999998362623138
            ],
            [
                0.9999998024946566,
                0.9999998461826405,
                0.9999998257021631,
                0.9999998642567351,
                0.9999996072137531,
                0.999999653367255,
                0.9999996940977003,
                0.9999996940978096,
                0.9999998642566704,
                0.9999998024947273
            ],
            [
                1.0,
                0.9999999176674652,
                0.9999995549150545,
                0.9999998555019274,
                0.9999996072138466,
                0.9999999067051499,
                0.9999999226557408,
                0.9999996072137531,
                0.9999997761971049,
                0.9999997126313099
            ],
            [
                0.9999995549150015,
                0.9999998642566704,
                1.0,
                1.0,
                1.0,
                0.9999999123575674,
                0.99999963101146,
                0.999999802494586,
                0.9999998802069588,
                1.0
            ],
            [
                0.9999991148430702,
                0.9999998724810027,
                0.9999998874648917,
                0.999999872480942,
                0.9999997300421584,
                0.9999998024947038,
                0.9999996940978462,
                0.9999998257021007,
                0.9999997761971583,
                0.9999984465028022
            ],
            [
                0.999999428499281,
                0.9999995262095553,
                0.999998932297004,
                0.9999996743688588,
                0.9999997761971583,
                0.9999997897567092,
                0.9999998555019792,
                0.9999996310115481,
                0.9999986290431214,
                0.9999998642567028
            ],
            [
                0.9999995262092166,
                0.9999994631250604,
                0.999999872480942,
                0.9999998874648246,
                0.9999997761971849,
                0.9999997463980126,
                0.9999997126314812,
                0.9999999006879957,
                0.9999998724809268,
                0.999999912357442
            ],
            [
                0.999999814460832,
                0.9999994284996218,
                0.9999998461826406,
                0.9999987901340297,
                0.9999996743688977,
                0.9999998642566542,
                0.9999999434137232,
                0.9999999317439953,
                0.999999776197025,
                0.9999998024946096
            ],
            [
                0.9999999434137907,
                0.9999992188514835,
                0.9999998257020798,
                0.9999995262096117,
                0.9999997617630617,
                0.9999991148428592,
                0.9999995262092729,
                0.9999998144608983,
                0.9999996940978463,
                0.9999992661791074
            ],
            [
                0.999999872480942,
                0.9999999226558146,
                0.9999998024945861,
                0.9999997897565588,
                0.9999994956527726,
                0.9999999226557962,
                0.9999996940978098,
                0.9999998942829225,
                0.999999631011372,
                0.9999998461826405
            ],
            [
                0.999999789756609,
                0.9999969105048185,
                0.999999761763147,
                0.9999993106387908,
                0.9999995818812273,
                0.9999998874648782,
                0.9999990577552947,
                0.999999802494586,
                0.9999997300421261,
                0.9999991684717748
            ],
            [
                0.9999999468421821,
                0.9999998257020798,
                0.9999998362623334,
                0.9999998802069587,
                0.9999996743688199,
                0.9999999656787243,
                0.9999999559305628,
                0.9999999500627799,
                0.9999998802069445,
                0.9999989969854346
            ],
            [
                0.9999999634651574,
                0.9999999226557961,
                0.9999999273418528,
                0.9999993524050476,
                0.999999927341853,
                0.9999996743686645,
                0.9999998724809571,
                0.9999995818813269,
                0.9999997617631186,
                0.9999991684720718
            ],
            [
                0.9999998024946802,
                0.9999999006879957,
                0.999999653367255,
                1.0,
                0.9999999226558238,
                0.9999997463981033,
                0.9999998024945624,
                0.9999998874649185,
                0.9999998257021838,
                0.9999998642567028
            ],
            [
                0.9999995818813767,
                0.9999998802069017,
                0.9999992661788449,
                0.9999999611088626,
                0.9999998802069302,
                0.9999998144608098,
                1.0,
                0.9999996940976638,
                1.0,
                0.9999995262093858
            ],
            [
                0.9999999397643083,
                1.0,
                0.9999995549149484,
                1.0,
                0.9999987121044781,
                0.999999730042255,
                0.9999993106388728,
                0.999999946842144,
                0.9999997463981939,
                0.9999989322972578
            ],
            [
                0.9999994284996213,
                0.9999994284996213,
                0.9999993916409636,
                0.999998629042631,
                0.9999987121041712,
                0.999999352405125,
                0.9999998642566705,
                0.9999992188515767,
                0.9999988634366966,
                0.9999990577557435
            ],
            [
                0.9999991148429654,
                0.9999985406241283,
                0.9999998942830738,
                0.9999994284995538,
                0.9999997617631471,
                0.999998932296622,
                0.999999880206916,
                0.999998126124172,
                0.9999998257021423,
                0.9999992661791077
            ],
            [
                0.9999995549148952,
                0.999999864256622,
                0.9999994284997578,
                0.9999998555020307,
                0.9999998642566543,
                0.9999993106386263,
                0.9999999358793485,
                0.9999999500628453,
                0.9999994631249324,
                0.999999730042287
            ],
            [
                0.999998239656789,
                0.9999994956524119,
                0.9999998362622553,
                0.9999987901338849,
                0.9999994284995534,
                0.9999998642567028,
                0.9999998802069302,
                0.9999997463981032,
                0.9999988634358841,
                0.9999990577551824
            ],
            [
                0.9999992661791074,
                3.2887498495150166e-06,
                0.9999995818814267,
                1.0677027427525368e-06,
                1.5534984953453635e-06,
                0.9999969105048178,
                0.9999980052707563,
                0.9999985406232585,
                3.120190765522868e-05,
                0.9999969105051865
            ],
            [
                0.9999994956523519,
                0.9999990577554081,
                0.9999996533675035,
                0.9999993106388738,
                0.9999996310114163,
                0.9999992188519496,
                0.999999168472271,
                0.9999988634366972,
                0.9999957771675869,
                0.999999581881078
            ],
            [
                0.9999998257022046,
                0.9999992661790202,
                0.9999996940977732,
                0.9999989322970039,
                5.715005151606823e-07,
                0.9999992188512974,
                0.9999994956525922,
                0.9999986290426308,
                0.9999938558261402,
                0.00023050679810176722
            ],
            [
                0.9999996940976273,
                1.0,
                1.0,
                0.9999998555019619,
                1.0,
                0.9999991684722703,
                0.9999987121050926,
                0.999999917667573,
                0.9999998724810027,
                0.9999999123574419
            ],
            [
                0.9999485577680924,
                0.9999964991460055,
                0.9999978766217921,
                0.9999991684718738,
                3.466325384678894e-07,
                0.9999978766215402,
                0.9999995818814266,
                1.6373770576776313e-07,
                0.999993855823207,
                1.6373764721039308e-07
            ],
            [
                0.9999998724809724,
                0.9999996533672555,
                0.9999998257022045,
                0.9999999273418356,
                0.9999998257021007,
                0.9999997300421584,
                0.9999996940977733,
                0.9999997761970248,
                0.9999998724809116,
                0.9999997300422871
            ],
            [
                0.9999992661792826,
                0.9999986290424675,
                1.8553903548231313e-07,
                1.6373770576776313e-07,
                3.059021539909339e-07,
                2.1024341622426268e-07,
                1.444979692800516e-07,
                0.9999996310114598,
                0.9999986290426313,
                1.0677029973158649e-06
            ],
            [
                0.999999730042287,
                0.9999996072138,
                0.9999994631248685,
                0.9999998555019791,
                0.9999981261241712,
                0.9999996072137063,
                0.9999997463981033,
                0.9999994956523515,
                0.9999999358793332,
                0.9999996533673378
            ],
            [
                0.9999996533674619,
                0.9999996743686647,
                0.999999746398073,
                0.9999996940978463,
                0.9999996940976275,
                0.9999996310113282,
                0.9999997617629766,
                0.9999995549151078,
                0.9999995549148953,
                0.999999730042287
            ],
            [
                0.9999999226558423,
                0.9999987901344615,
                0.9999996310116359,
                0.99999994341373,
                0.9999998642566543,
                1.0,
                0.9999996072138937,
                0.9999998461827139,
                0.999999922655787,
                1.0
            ],
            [
                0.9999989969857931,
                0.9999999123574629,
                0.9999998555019619,
                1.0,
                1.0,
                0.9999998942829477,
                0.9999996310115039,
                0.9999998942829729,
                1.0677031245990084e-06,
                0.999999554914736
            ],
            [
                0.9999987901343184,
                0.9999996310115482,
                0.9999998461826222,
                0.9999975938973767,
                0.9999984465020623,
                0.9999975938968041,
                0.9999987121052462,
                0.9999957771665602,
                0.9999972735294084,
                0.9999945777797439
            ],
            [
                0.9999998144608541,
                0.9999991148431759,
                0.9999998555019963,
                1.0,
                1.0,
                0.9999994284995533,
                1.0,
                0.9999997300421906,
                0.9999998942830106,
                0.9999977396751658
            ],
            [
                0.9999994284997578,
                0.9999999559305733,
                0.9999991148428594,
                0.9999999530883285,
                1.0,
                0.9999999317439383,
                0.9999999317440279,
                0.9999999530883228,
                0.9999999397643083,
                0.9999999397642294
            ]
        ]
    },
    {
        "q_id": "10068_mmlu_physics",
        "cot_ids": [
            4,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            43,
            44,
            47,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            70,
            71,
            73,
            74,
            76,
            77,
            78,
            80,
            81,
            83,
            84,
            86,
            87,
            88,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            100,
            103,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                5.04347287955046e-07,
                0.9999999434137907,
                0.9999997897567342,
                0.9999999358793332,
                0.9999998024946801,
                0.9999999559305891,
                0.9999993106389549,
                0.9999999176675829,
                0.999996910504082,
                0.9999999397642437
            ],
            [
                3.05902263391829e-07,
                6.962258739796719e-06,
                3.1201922535494165e-05,
                6.475947982037486e-07,
                2.3823690999290963e-07,
                7.338213304363436e-07,
                1.7603430034867993e-06,
                1.0129987357517693e-05,
                3.1201926253802263e-05,
                4.4508515805735777e-07
            ],
            [
                6.962253759904688e-06,
                2.9023116391978967e-06,
                1.3709567165461505e-06,
                1.6701419853518415e-05,
                1.1478769494250387e-05,
                6.144176799334096e-06,
                3.7266406168827523e-06,
                2.1444943301674863e-05,
                8.939696304213768e-06,
                0.00010889692232771249
            ],
            [
                0.9999996940978826,
                0.9999998144609645,
                0.999999391641181,
                0.9999997463981031,
                0.999999789756684,
                0.9999997463981032,
                0.9999998362622748,
                0.9999997300422226,
                0.9999996072139404,
                0.999999653367379
            ],
            [
                0.9999995262095553,
                1.3709576971463352e-06,
                9.422444815792981e-07,
                0.9999996743688976,
                3.466325797896173e-07,
                7.338213304363436e-07,
                8.315280276626197e-07,
                1.892515501014656e-05,
                3.0590237279085045e-07,
                1.9947304348862686e-06
            ],
            [
                2.2603248367512505e-06,
                8.315284241597959e-07,
                7.88926446679691e-06,
                1.2098662604192665e-06,
                8.315284241597959e-07,
                2.5612828213934817e-06,
                9.4224425692559e-07,
                8.315280276546789e-07,
                7.338208930391909e-07,
                1.0677028700363782e-06
            ],
            [
                8.315282259089153e-07,
                1.7603432133296774e-06,
                3.466327863983311e-07,
                8.939693107190907e-06,
                7.338212429582604e-07,
                6.144172404693786e-06,
                8.939700567004841e-06,
                3.288749849498565e-06,
                1.067703379154416e-06,
                1.3709567165530083e-06
            ],
            [
                0.9999987901344615,
                0.9999996533675033,
                0.9999994631250604,
                0.9999993106388729,
                0.9999990577557444,
                0.999998629042469,
                0.9999988634361558,
                0.9999989969855553,
                0.9999987121052465,
                0.999998446501692
            ],
            [
                0.9999810748495187,
                0.9999964991455889,
                0.9999972735287562,
                0.9999984465026172,
                0.9999998144609645,
                0.999999825702163,
                0.9999996533674202,
                0.9999999006880195,
                0.9999989969856734,
                0.9999993524054336
            ],
            [
                0.999999653367379,
                0.9999995818813768,
                0.9999998802069731,
                0.9999993916408186,
                0.999999776197105,
                0.9999990577557443,
                0.9999994284995534,
                0.9999997761971583,
                0.999999114843387,
                0.9999994956527124
            ],
            [
                1.3709578605617394e-06,
                1.9947304348703948e-06,
                1.209865250822125e-06,
                2.5612816000145246e-06,
                2.902311639183378e-06,
                2.5612834320214477e-06,
                1.0129994602656007e-05,
                1.3007130014873483e-05,
                5.422217030663578e-06,
                2.561283432035425e-06
            ],
            [
                1.9947297215043796e-06,
                7.338209805240734e-07,
                0.999998126124619,
                4.222834451327159e-06,
                4.222831934352267e-06,
                1.994730197071414e-06,
                2.5612831266946347e-06,
                1.3709576971379186e-06,
                1.0677032518700286e-06,
                1.994729245917502e-06
            ],
            [
                0.9999991148427535,
                0.999999674368781,
                0.9999994956527724,
                0.9999990577554069,
                0.999998932297258,
                0.9999998724809724,
                0.9999994956524718,
                0.9999995549147891,
                0.9999996533674205,
                0.9999996940976639
            ],
            [
                2.5612828213934817e-06,
                7.88926446679691e-06,
                1.0677028700363782e-06,
                3.7266410611296085e-06,
                4.222831934379152e-06,
                5.422220262636381e-06,
                1.7603432133296774e-06,
                6.962259569750576e-06,
                6.475950298011458e-07,
                5.043472879525233e-07
            ],
            [
                0.9999994284996895,
                0.9999993916409637,
                0.9999987121047854,
                0.9999989969861516,
                0.9999995549148953,
                0.9999988634366965,
                0.9999994284994169,
                0.9999993106388725,
                0.9999992661790201,
                0.9999993916406734
            ],
            [
                0.9999916019300193,
                1.012999581021488e-05,
                0.9999938558239616,
                0.9999938558268726,
                0.9999969105048219,
                1.6701427817730953e-05,
                0.9999892166903832,
                0.9999949062968527,
                0.9999892166826918,
                0.9999967112509387
            ],
            [
                0.999999581881277,
                0.9999993916409634,
                0.9999997617630049,
                0.9999994956523516,
                0.9999995818813269,
                0.9999996533674204,
                0.9999993916409635,
                0.9999996533674204,
                0.999999855502048,
                0.9999998642566219
            ],
            [
                0.9999996743688199,
                0.9999986290426307,
                0.999999168472171,
                0.9999994956527123,
                0.9999991148431756,
                0.9999988634358834,
                0.9999994956527725,
                0.9999995262094423,
                0.9999989322970039,
                0.999999352405125
            ],
            [
                0.9999996940977002,
                0.9999993106390371,
                0.9999987901341734,
                0.9999993916411813,
                0.9999985406236068,
                0.9999997897567342,
                0.9999995818812273,
                0.9999991148428591,
                0.9999987901343174,
                0.9999993106392017
            ],
            [
                0.9999992661790209,
                0.9999992661792834,
                0.9999987121046339,
                0.999998932297004,
                0.9999972735287634,
                0.99999759389767,
                0.9999980052695722,
                0.9999980052693345,
                0.9999992188512977,
                0.9999993106390378
            ],
            [
                0.9999988634361549,
                0.9999994956524718,
                0.9999989969855537,
                0.9999993524053568,
                0.9999991148431757,
                0.999999674368781,
                0.9999989322975128,
                0.9999991148432811,
                0.99999926617867,
                0.9999997617630617
            ],
            [
                2.2603240283888175e-06,
                2.2603242978665707e-06,
                0.999997438717491,
                5.144220752910515e-05,
                4.785093924330255e-06,
                0.9999910603048057,
                1.670142383595838e-05,
                7.88926070489716e-06,
                7.889264466545779e-06,
                1.4738987243236881e-05
            ],
            [
                1.3709573702822306e-06,
                4.222832941193893e-06,
                2.5612834320470717e-06,
                2.2603234895372223e-06,
                3.2887482813149375e-06,
                7.338209805240734e-07,
                1.3709576971379186e-06,
                1.3007123813382511e-05,
                8.315282259138311e-07,
                7.338207180864763e-07
            ],
            [
                1.2098661162023305e-06,
                3.927860597945825e-07,
                8.315283250343497e-07,
                1.9947301970813926e-06,
                8.315281267861397e-07,
                1.0677032518785256e-06,
                2.6995771309523475e-07,
                1.0677031245953668e-06,
                3.46632497145457e-07,
                3.9278610661822475e-07
            ],
            [
                7.889263526093993e-06,
                1.1478772230407462e-05,
                4.222831934379152e-06,
                3.5356254926549066e-05,
                1.300712536258383e-05,
                6.144172404693786e-06,
                2.9023126771227976e-06,
                1.8925152752138513e-05,
                2.4300252319959737e-05,
                4.006370651207639e-05
            ],
            [
                3.2887502415767434e-06,
                2.102434412875379e-07,
                4.222832437798974e-06,
                8.315278294114555e-07,
                5.715003789046955e-07,
                9.422447062294175e-07,
                1.8553905760062447e-07,
                8.939700567094277e-06,
                1.760343213335281e-06,
                9.422443692555439e-07
            ],
            [
                0.999999730042287,
                0.99999967436882,
                0.9999994284996898,
                0.9999975938973752,
                3.288749457432399e-06,
                0.9999997300423192,
                0.9999994631251246,
                0.9999938558232045,
                0.9999996310114599,
                0.9999975938968011
            ],
            [
                3.05902117523595e-07,
                3.059022998569248e-07,
                5.04347528440776e-07,
                5.04347648686092e-07,
                4.450849458218309e-07,
                8.315278294038928e-07,
                3.9278605979208185e-07,
                5.043475284430694e-07,
                7.338210679949506e-07,
                4.450849988780466e-07
            ],
            [
                0.9999987901343176,
                0.9999993106389552,
                0.9999995818813269,
                0.9999995262094424,
                0.9999997617630902,
                0.9999994284995534,
                0.9999997761972116,
                0.999999730042094,
                2.2603248367949354e-06,
                0.9999994631250606
            ],
            [
                0.9999998802069302,
                0.9999999067049943,
                0.9999994631250606,
                0.999999927341775,
                0.9999995549150548,
                0.9999994631248685,
                0.9999995262094992,
                0.9999993916406735,
                0.9999999176675534,
                0.999999776197185
            ],
            [
                0.9999994956523518,
                0.9999995549150015,
                0.9999997617630049,
                0.9999998724809724,
                0.9999982396574183,
                0.9999993916407462,
                0.9999998802069731,
                0.9999997897566089,
                0.9999994956525922,
                0.9999992188518565
            ],
            [
                8.939700566435704e-06,
                1.994729483694599e-06,
                6.962255419653012e-06,
                1.5534975693792215e-06,
                3.288747889178668e-06,
                4.785094494716039e-06,
                6.144173137014406e-06,
                2.5612812947077304e-06,
                2.2603248367512505e-06,
                5.422218323290717e-06
            ],
            [
                2.561283432035425e-06,
                6.475951069985296e-07,
                1.209865539295696e-06,
                1.7603436330259153e-06,
                8.315278294072958e-07,
                1.5534979397740895e-06,
                1.3709575337078829e-06,
                4.222831934352267e-06,
                3.2887490653872164e-06,
                7.338209805224048e-07
            ],
            [
                8.939700567004841e-06,
                0.9999993916407462,
                0.9999975938982361,
                1.0129988564845378e-05,
                0.9999995549151076,
                3.535626757524533e-05,
                2.753568782024347e-05,
                0.9999978766220463,
                0.9999983463100215,
                4.539786323732447e-05
            ],
            [
                0.9999995262093863,
                0.9999992188512977,
                0.9999985406239542,
                0.9999996533672966,
                0.9999995262093296,
                0.9999945777790938,
                0.9999993916408187,
                0.9999993916411816,
                0.9999989969859129,
                0.9999992661790202
            ],
            [
                3.12019002122609e-05,
                0.9988304898966363,
                1.2098653950656417e-06,
                1.7603427936183298e-06,
                8.315278294072958e-07,
                6.962253759828703e-06,
                1.3709575337078829e-06,
                3.7266379512857925e-06,
                4.78509563550957e-06,
                9.422448185510695e-07
            ],
            [
                3.2887478892683997e-06,
                7.889262585886274e-06,
                3.726637951387472e-06,
                9.422442569315887e-07,
                6.962254589978262e-06,
                4.222831934352267e-06,
                4.2228324377740105e-06,
                2.5612834320470717e-06,
                4.785094494783494e-06,
                6.962255419931625e-06
            ],
            [
                1.067702870039777e-06,
                1.2098662604291696e-06,
                1.3709578605617394e-06,
                1.3709567165530083e-06,
                1.5534975693869924e-06,
                1.5534971990169383e-06,
                5.715003107755449e-07,
                NaN,
                1.6701421844753466e-05,
                1.0677024881980089e-06
            ],
            [
                2.9023133690980155e-06,
                2.753569110256289e-05,
                6.9622537599680095e-06,
                6.144176066901277e-06,
                1.994730672668496e-06,
                1.0677024881980089e-06,
                8.315282259051341e-07,
                6.47594566597747e-07,
                2.5612819054028872e-06,
                1.012999460278499e-05
            ],
            [
                0.9999997617631186,
                0.9999996072136127,
                0.9999997897566341,
                0.9999996743687811,
                0.9999997126313441,
                0.999998629043122,
                0.9999993524051253,
                0.999999495652472,
                0.9999997761970248,
                0.9999998024947274
            ],
            [
                7.338208055680009e-07,
                2.6995784182140636e-07,
                1.6373770576776313e-07,
                1.275190276859705e-07,
                8.315282259138311e-07,
                2.3823690999323465e-07,
                1.6373764721072816e-07,
                1.855391239544352e-07,
                1.1478765389368729e-05,
                2.102434412871794e-07
            ],
            [
                4.78509278348926e-06,
                1.4738981972323349e-05,
                8.315278294114555e-07,
                NaN,
                4.450848927658745e-07,
                1.0129987357407137e-05,
                1.7603430034867993e-06,
                5.715003107755449e-07,
                1.760343003481596e-06,
                3.288749065423109e-06
            ],
            [
                0.9999975938985224,
                0.9999987121049395,
                2.7535697667202906e-05,
                0.9999978766223,
                0.9999984465016915,
                0.9999993524049707,
                0.9999990577557438,
                1.1478770862589836e-05,
                0.9999996533674618,
                0.9999984465026175
            ],
            [
                0.9999998362623528,
                0.9999996310115479,
                0.9999989969855545,
                0.9999998555020307,
                0.9999998362623528,
                0.9999998257021214,
                0.9999997897565588,
                0.9999997126315496,
                0.999999730042094,
                0.9999997126314811
            ],
            [
                0.9999991148428591,
                0.9999998024947038,
                0.9999997617629766,
                0.9999994956524119,
                0.9999996940978827,
                0.9999997897567343,
                0.9999994956527724,
                0.9999991148433871,
                0.9999998362622358,
                0.999998932296749
            ],
            [
                0.9999995262094428,
                0.9999994284997583,
                0.9999996743686645,
                0.9999982396565795,
                0.9999978766210369,
                0.9999984465020625,
                0.9999972735297378,
                0.999998239656789,
                0.9999989969856747,
                0.9999981261243956
            ],
            [
                3.726638839878908e-06,
                9.422444815726566e-07,
                7.338207180838067e-07,
                1.99472900813862e-06,
                3.2887490653872164e-06,
                1.9947292459347367e-06,
                6.962254589914941e-06,
                5.422221555380179e-06,
                5.043475284447896e-07,
                3.2887502415438413e-06
            ],
            [
                0.9999995818813767,
                0.999999730042287,
                0.9999998257022045,
                0.9999995262095555,
                0.99999963101146,
                0.999999900687984,
                0.9999996310115918,
                0.9999997897565588,
                0.9999997761970781,
                0.9999989969855537
            ],
            [
                0.9999993524053573,
                0.9999987901343173,
                0.9999995549149482,
                0.9999995549148956,
                0.9999996310113721,
                0.999998932297258,
                0.9999989969862716,
                0.9999993916408916,
                0.9999995818811278,
                0.99999931063912
            ],
            [
                0.9999972735294067,
                0.999995214904938,
                0.9999982396561594,
                0.9999996743687811,
                0.9999983463100212,
                0.9999904837517332,
                0.9999993106389552,
                0.999999631011592,
                0.999996273359388,
                0.9999991684715772
            ],
            [
                1.553497754577351e-06,
                0.9999989969861519,
                0.9999993524052021,
                0.9999988634362899,
                0.9999974387184015,
                0.9999994631248043,
                0.9999994631251244,
                0.9999980052702804,
                0.9999988634361544,
                0.9999991148427537
            ],
            [
                2.9023119851899796e-06,
                2.9023116392097746e-06,
                8.315280276626197e-07,
                5.043475885696228e-07,
                3.288749849529972e-06,
                6.962257909842961e-06,
                1.6701425827133152e-05,
                2.902312331170226e-06,
                3.120191509592808e-05,
                4.785093924389007e-06
            ],
            [
                1.6701427818034747e-05,
                6.962254589978262e-06,
                1.994730197090463e-06,
                1.670141587174774e-05,
                5.422218323487975e-06,
                4.222834954687752e-06,
                1.209865827740176e-06,
                1.1478772230929451e-05,
                2.7535691100960147e-05,
                0.9999785550593026
            ],
            [
                0.9999981261246188,
                0.9999992661790202,
                0.9999994284996218,
                0.9999997897566842,
                0.9999993524054342,
                0.999999218851391,
                0.9999995818810776,
                0.999998239657419,
                0.9999990577554073,
                0.9999987121050927
            ],
            [
                1.55349775456958e-06,
                1.7603427936263351e-06,
                6.1441731370702875e-06,
                2.5612825160271407e-06,
                0.9999921107393132,
                0.9999910603069154,
                2.5612812947240366e-06,
                7.889260704732132e-06,
                2.5612812947240366e-06,
                3.72664061681327e-06
            ],
            [
                0.9999998144608983,
                0.9999995549147891,
                0.9999995818814266,
                0.9999997300421584,
                0.9999989322975126,
                0.999999495652592,
                0.9999995262093294,
                0.9999995549150545,
                0.9999996533672137,
                0.9999993916408186
            ],
            [
                0.9999993916409637,
                0.9999997126313784,
                0.9999996310114161,
                0.9999995549150545,
                0.999999864256622,
                0.9999996743686257,
                0.9999995818812272,
                0.9999996743688588,
                0.9999991684715764,
                0.9999998555020135
            ],
            [
                0.9999992188516696,
                0.9999993106387907,
                0.9999996072138,
                0.9999994956527725,
                0.9999995262096119,
                0.9999998461826222,
                0.9999994956527725,
                0.9999997617630901,
                0.9999993106391193,
                0.9999997126313441
            ],
            [
                2.902311639183378e-06,
                2.7535697666401535e-05,
                7.889266347715168e-06,
                7.338210679979539e-07,
                4.222831934352267e-06,
                1.3709570434054234e-06,
                1.7603436330091044e-06,
                1.1478764020883773e-05,
                1.8925145985895816e-05,
                8.939696304213768e-06
            ],
            [
                0.9999984465020622,
                0.9999996743687812,
                0.9999997761972116,
                0.9999992661786701,
                0.9999985406234325,
                0.9999987121050932,
                0.9999997617630901,
                0.9999997761971315,
                0.9999987901344622,
                0.9999997463981031
            ],
            [
                7.338212429537553e-07,
                1.0677029973192638e-06,
                5.422220262555012e-06,
                1.2098658277451275e-06,
                1.99472900813862e-06,
                1.6701427818034747e-05,
                5.043476486915964e-07,
                3.288748673360027e-06,
                7.338208055664991e-07,
                1.0677029973219343e-06
            ],
            [
                0.9999995549150543,
                0.9999996533673791,
                0.9999989322966217,
                0.9999995549150013,
                0.9999995549150014,
                0.9999993106388727,
                0.9999997463980125,
                0.999999789756659,
                0.9999989969854343,
                0.9999996310113721
            ],
            [
                1.5534975693869924e-06,
                6.144175334367959e-06,
                1.670141786231398e-05,
                1.8925145983795953e-05,
                5.144221979793211e-05,
                3.120190021339598e-05,
                2.430024073333442e-05,
                6.962255419804982e-06,
                1.89251527534122e-05,
                5.829128637885414e-05
            ],
            [
                3.4663249714612693e-07,
                1.067702870039777e-06,
                5.04347528446051e-07,
                7.338210680021253e-07,
                6.475946438042047e-07,
                2.102434412875379e-07,
                8.315282259138311e-07,
                1.5534977545886537e-06,
                1.7603440527286572e-06,
                2.5612834320563895e-06
            ],
            [
                5.043475885696228e-07,
                2.3823693839325527e-07,
                3.466326624336003e-07,
                1.6373770576776313e-07,
                3.927862470899887e-07,
                2.102434162245973e-07,
                3.05902336324494e-07,
                1.8553914607267268e-07,
                1.2751901248454963e-07,
                2.102434162245973e-07
            ],
            [
                0.9999995262096117,
                0.9999988634362912,
                0.9999988634360201,
                0.9999996940977733,
                0.9999995262094991,
                0.9999991684717752,
                0.9999994631248688,
                0.9999994956526524,
                0.9999989969860323,
                0.9999994631251887
            ],
            [
                0.9999987901340298,
                0.9999981261246194,
                0.999998932297004,
                0.9999986290429582,
                0.9999989969861528,
                0.9999957771655538,
                0.9999991684719742,
                0.9999991684715768,
                0.9999991148432817,
                0.9999989969859135
            ],
            [
                2.561281294760143e-06,
                1.3709575337159875e-06,
                1.3007126914612648e-05,
                1.0129987357517693e-05,
                8.939699501416646e-06,
                1.0129988565084915e-05,
                5.422217030747413e-06,
                4.222834954801051e-06,
                1.994729721518893e-06,
                1.2098659719788098e-06
            ],
            [
                2.561281905390075e-06,
                1.9947297215125433e-06,
                7.338208055664991e-07,
                6.144173137126169e-06,
                4.785095635624897e-06,
                2.2603242978871282e-06,
                1.5534975693933505e-06,
                1.994729483723626e-06,
                1.7603440527286572e-06,
                1.7603427936263351e-06
            ],
            [
                6.144175334468545e-06,
                5.043472278312808e-07,
                3.466326211113502e-07,
                3.0590237279032884e-07,
                3.05902190458764e-07,
                2.5612834320563895e-06,
                1.1253516205489029e-07,
                2.10243290909724e-07,
                5.043472879540142e-07,
                NaN
            ],
            [
                2.2603242978871282e-06,
                2.260324836787226e-06,
                1.0677032518785256e-06,
                2.902313369111213e-06,
                3.05902190458764e-07,
                6.475950298011458e-07,
                6.144176799334096e-06,
                1.8925157266089433e-05,
                2.10243290909724e-07,
                4.222832941193893e-06
            ],
            [
                0.9999991148428594,
                0.999999730042255,
                0.9999995549150014,
                0.999999114842965,
                0.9999992661789324,
                0.9999997126315497,
                0.9999994631247405,
                0.9999996310115922,
                0.9999994956526522,
                0.9999997126315496
            ],
            [
                0.9999987901341736,
                0.9999986290431212,
                0.9999972735294084,
                0.9999993524049706,
                0.999998996985913,
                2.561281294760143e-06,
                0.9999993916411087,
                0.9999987901338857,
                0.9999994284993488,
                0.9999993916408912
            ],
            [
                1.8553907971682908e-07,
                1.637376862471855e-07,
                1.855391681873269e-07,
                2.699577452733192e-07,
                3.0590229985449037e-07,
                2.1024336609638268e-07,
                2.1024329090685577e-07,
                3.4663274507287414e-07,
                2.699577774560111e-07,
                1.1253520229983549e-07
            ],
            [
                2.3823702359138736e-07,
                5.043474081957179e-07,
                2.102433410343832e-07,
                4.4508515805735777e-07,
                1.2751901248454963e-07,
                1.855390354818069e-07,
                3.0590237279032884e-07,
                5.715002426486762e-07,
                2.1024339116082313e-07,
                2.6995784182140636e-07
            ],
            [
                0.9999991684717755,
                0.9999991684715774,
                0.9999993524052027,
                0.9999986290423067,
                0.9999993106388738,
                0.9999987901343199,
                0.999999554915055,
                0.9999992661792831,
                0.9999983463108129,
                0.9999998024946568
            ],
            [
                0.9999994284993492,
                0.9999994956527122,
                0.9999997463982241,
                0.9999994631251883,
                0.9999996743688199,
                0.999999352404971,
                0.9999998144608983,
                0.999999653367255,
                0.9999993106390372,
                0.9999996310115921
            ],
            [
                0.9999952149055256,
                0.9999981261248424,
                0.9999960330131596,
                5.043474081993875e-07,
                0.9999945777804169,
                0.999996499144339,
                4.450852111135988e-07,
                0.9999972735297403,
                0.9999975938973777,
                0.999996033013624
            ],
            [
                1.670141786325573e-05,
                2.902312331170226e-06,
                2.9023119851899796e-06,
                3.7266397283908927e-06,
                1.2098652508424818e-06,
                3.927862470899887e-07,
                6.144172404738491e-06,
                2.561282516066741e-06,
                3.288749849529972e-06,
                2.561283126728994e-06
            ],
            [
                4.222832941193893e-06,
                1.3709568799919866e-06,
                7.734418542875216e-08,
                2.6995784182183607e-07,
                5.71500719545698e-07,
                2.699578096403948e-07,
                1.760342793638743e-06,
                2.3823690999290963e-07,
                3.466326624336003e-07,
                2.1024336609874897e-07
            ],
            [
                1.5534984953453635e-06,
                1.2098658277451275e-06,
                3.2887506336086064e-06,
                8.315277302819205e-07,
                3.288749457469787e-06,
                9.422448185510695e-07,
                1.9947301970813926e-06,
                1.760344052714248e-06,
                9.422447062270609e-07,
                2.561283432035425e-06
            ],
            [
                0.999999114843387,
                0.9999996072137063,
                0.999999776197105,
                0.9999986290421409,
                0.9999984465020619,
                0.9999994631249965,
                0.9999993106386263,
                0.9999989322975122,
                0.9999994956524118,
                0.9999993524054339
            ],
            [
                6.1441731370702875e-06,
                3.7266388398585725e-06,
                4.785095635592258e-06,
                3.726639284103523e-06,
                9.422449308673789e-07,
                2.5612828213690224e-06,
                9.422443692527585e-07,
                4.2228324377740105e-06,
                2.5612819054028872e-06,
                2.2603245673279107e-06
            ],
            [
                0.9999998144608097,
                5.043475885696228e-07,
                1.9947299593078385e-06,
                4.539787947559951e-05,
                7.338207180898968e-07,
                4.785093924389007e-06,
                1.0677032518814388e-06,
                1.7603425837903113e-06,
                7.338210680021253e-07,
                1.8553916819032217e-07
            ],
            [
                2.260325375664839e-06,
                1.994729721482609e-06,
                1.3709578605617394e-06,
                3.726641061085547e-06,
                3.288749849477628e-06,
                2.2603248367358324e-06,
                1.760344052714248e-06,
                1.5534975693869924e-06,
                2.260325375664839e-06,
                9.422444815765128e-07
            ],
            [
                0.9999993524049705,
                0.9999999067050387,
                0.9999997126314125,
                0.9999997300422226,
                0.9999994956527725,
                0.9999995549150545,
                0.9999998555020135,
                0.9999993106392016,
                0.9999997897565588,
                0.9999997897566841
            ],
            [
                0.999999631011372,
                0.9999993524050483,
                0.9999996940978826,
                0.9999995262096121,
                0.9999996743687812,
                0.9999996310116362,
                0.9999938558276102,
                0.9999997463980428,
                0.9999996743688199,
                0.9999997463980127
            ],
            [
                1.994730434879465e-06,
                5.715003107755449e-07,
                1.2098658277451275e-06,
                1.3007123813382511e-05,
                3.726639728370556e-06,
                6.475948754012522e-07,
                1.994730197090463e-06,
                3.9278610661366994e-07,
                1.0677024881980089e-06,
                2.260325106237323e-06
            ],
            [
                0.9999997761972117,
                0.999999872480942,
                0.9999996072136595,
                0.9999998024946802,
                0.9999993916408911,
                0.9999998362622748,
                0.9999998024946332,
                0.9999997463981637,
                0.9999998874647441,
                0.9999996072136595
            ],
            [
                0.9999997761971849,
                4.22283545819819e-06,
                2.753569110256289e-05,
                1.760342793638743e-06,
                3.726639284144195e-06,
                1.3007123813559956e-05,
                3.726639284144195e-06,
                3.2887502415767434e-06,
                NaN,
                1.3709567165617364e-06
            ],
            [
                0.9999998257021837,
                0.9999991684717745,
                0.9999999358793333,
                0.9999996533674617,
                1.0,
                0.9999998555019963,
                0.9999994284996895,
                0.9999996072137064,
                0.9999999434137907,
                0.9999994631249963
            ],
            [
                2.9023112932177327e-06,
                1.7603427936183298e-06,
                1.8925145985895816e-05,
                5.422217030707961e-06,
                4.785093353940187e-06,
                7.889265407255982e-06,
                2.902312677137316e-06,
                1.0677033791495609e-06,
                8.315278294097538e-07,
                4.2228324377740105e-06
            ]
        ]
    },
    {
        "q_id": "9359_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998724809724,
                0.9999999067050276,
                0.9999998874649318,
                0.9999997897567092,
                0.9999998942829729,
                0.9999999123575046,
                0.9999998461826038,
                0.9999999397642653,
                0.9999999611088627,
                0.9999999559305733
            ],
            [
                2.260323758987159e-06,
                3.059021175261338e-07,
                0.9999997761971317,
                2.561281294760143e-06,
                0.9999993524048936,
                1.370957860576702e-06,
                1.5534983101644536e-06,
                2.561281294760143e-06,
                3.2887506336235617e-06,
                2.2603248367949354e-06
            ],
            [
                0.9999999123575778,
                0.9999998555020309,
                0.9999998461827322,
                0.9999998257021007,
                0.9999998724809723,
                0.9999997617629766,
                0.9999998642567028,
                0.9999998724809268,
                0.9999999123574524,
                0.9999998642566381
            ],
            [
                0.9999997761970515,
                0.9999997761970515,
                0.9999998144608098,
                0.9999998362622359,
                0.9999997897567343,
                0.9999994956524119,
                0.9999996310115481,
                0.9999998802069302,
                0.9999997300421263,
                0.999999746398194
            ],
            [
                0.9999999006880194,
                0.9999999468421883,
                0.9999998362623334,
                0.9999999317439221,
                0.9999996072136593,
                0.999999958600595,
                0.9999998802069873,
                0.999999939764215,
                0.9999999067050831,
                0.9999998257021007
            ],
            [
                0.999999855501979,
                0.9999997126314468,
                0.9999998257022046,
                0.9999998461826037,
                0.9999998802069445,
                0.9999998942829098,
                0.9999999317439872,
                0.9999999273417923,
                0.9999998257021422,
                0.9999998024945624
            ],
            [
                0.9999999559305681,
                0.9999998874648648,
                1.0,
                0.9999997761971049,
                1.0,
                0.999999931743914,
                1.0,
                0.9999998802069445,
                1.0,
                0.9999998362623723
            ],
            [
                0.9999998144608319,
                0.9999997617630049,
                0.9999992188514836,
                0.9999997463981939,
                0.9999996940978098,
                0.9999996310114599,
                0.9999997897565839,
                0.9999992661791076,
                0.9999998942829477,
                0.9999997617630901
            ],
            [
                0.9999987901338843,
                0.999999900688126,
                0.9999996072137062,
                8.315281267861397e-07,
                0.9999999067051054,
                0.9999998555020307,
                4.450852641717689e-07,
                0.9999998942829477,
                0.9999987121043242,
                3.0590237279032884e-07
            ],
            [
                0.9999998362623723,
                0.9999998874647709,
                0.9999997761971315,
                0.9999998555019619,
                0.9999998942830106,
                0.9999999226557501,
                0.9999999123575046,
                0.9999999397643011,
                0.9999999123575987,
                0.999999855501979
            ],
            [
                0.9999998144609646,
                0.9999999006880786,
                0.9999998024945624,
                0.9999997300421262,
                0.9999998362623724,
                0.9999999176674848,
                0.9999997897565839,
                0.9999997761970782,
                0.9999999176674946,
                0.9999998874648112
            ],
            [
                1.012999218776902e-05,
                4.2228319344021954e-06,
                3.7266379514061143e-06,
                2.5612834320563895e-06,
                4.222834451403972e-06,
                2.144495864106235e-05,
                5.422221555414699e-06,
                3.7266410611465547e-06,
                1.3007126914612648e-05,
                0.9999998724810027
            ],
            [
                0.9999999123575882,
                0.9999998555019446,
                0.9999997300421262,
                0.9999998642566381,
                0.9999998942829224,
                0.9999998461826222,
                0.9999998555020135,
                0.9999997463980125,
                0.9999998362622357,
                0.9999999176674454
            ],
            [
                0.9999999176674651,
                0.9999999397642796,
                0.9999999176674651,
                0.9999998724809572,
                0.9999998555019274,
                0.9999999358794402,
                0.9999999006881142,
                0.9999999468421567,
                0.9999998874648917,
                0.9999998724809116
            ],
            [
                0.9999998642566219,
                0.9999999176675535,
                0.9999999123575986,
                0.9999996533674204,
                0.9999999358794021,
                1.0,
                0.999999958600659,
                0.9999999176675239,
                0.9999999006880549,
                0.9999998942828973
            ],
            [
                0.9999999358793562,
                0.9999997300422548,
                0.9999997463980427,
                0.9999996940976639,
                0.9999999358794021,
                0.9999999123574523,
                0.9999996743686645,
                0.9999997300423193,
                0.9999998461827323,
                0.9999996940977732
            ],
            [
                2.4300246526646385e-05,
                1.3709576971425944e-06,
                8.939693107288474e-06,
                6.475950298011458e-07,
                1.7603430034743913e-06,
                1.0677032518700286e-06,
                2.5612831267202583e-06,
                1.0677024881980089e-06,
                1.5534971989907999e-06,
                1.5534983101478522e-06
            ],
            [
                0.9999998802068873,
                0.999999814460854,
                0.9999998257021006,
                0.9999999123574941,
                0.9999998642566704,
                0.9999999006881259,
                0.9999999273417922,
                0.999999825702059,
                0.9999998555019791,
                0.999999789756634
            ],
            [
                2.1024339116082313e-07,
                0.9999997617630333,
                2.260324836787226e-06,
                0.9999987901347501,
                5.715004470313855e-07,
                6.475948753991907e-07,
                2.3823702359290413e-07,
                2.561281600076256e-06,
                1.4449802095609418e-07,
                0.9999997617630617
            ],
            [
                0.9999998874648649,
                0.9999998257021214,
                0.999999912357442,
                0.9999999434137434,
                0.999999939764251,
                0.9999998942829477,
                0.9999999317439872,
                0.9999999358793638,
                0.9999998362623138,
                0.9999998024946332
            ],
            [
                4.222833444590791e-06,
                1.3007130015677909e-05,
                0.9999998802069731,
                0.9999998874649184,
                0.9999999434137773,
                0.9999998024946801,
                0.9999999067050165,
                0.9999997463981637,
                4.222834954801051e-06,
                2.5612819054133693e-06
            ],
            [
                0.9999999273418355,
                0.9999998461826589,
                0.9999997897567342,
                0.9999998555019963,
                0.9999998144609645,
                0.9999998802069587,
                0.9999998362622357,
                0.9999998802069016,
                0.999999887464905,
                0.9999998362623138
            ],
            [
                0.9999992188518559,
                1.2098653950606901e-06,
                0.9999995549150543,
                0.9999904837483146,
                0.9999998024945624,
                0.9999972735307067,
                0.9999983463096264,
                0.9999997300421583,
                0.9999985406230841,
                0.9999985406241279
            ],
            [
                0.9999992661790197,
                0.999999931743914,
                0.9999998642566866,
                0.9999998362622553,
                0.9999998024946801,
                0.9999998257021007,
                0.9999996743688586,
                0.9999999176674946,
                0.9999998642566704,
                0.999999825702059
            ],
            [
                0.9999999006881497,
                0.9999997126315154,
                0.9999996533672552,
                0.9999993916408912,
                0.9999997897567343,
                0.9999996072136595,
                0.9999995818811277,
                9.422448185534261e-07,
                0.9999998024947273,
                0.9999997761971849
            ],
            [
                0.9999999358793944,
                0.9999999317439872,
                1.0,
                0.9999999397642508,
                0.9999999397642366,
                1.0,
                0.9999999697115551,
                0.9999999226557776,
                0.9999999273418443,
                0.9999998874647843
            ],
            [
                0.9999997126314811,
                0.9999998257022045,
                0.9999995818813767,
                0.9999998461826588,
                0.999999730042287,
                0.9999998642567028,
                0.9999999006879721,
                0.9999997761971315,
                0.9999998362622747,
                0.9999998642567028
            ],
            [
                0.9999999273418703,
                1.0,
                0.9999998642566219,
                0.9999999176674946,
                0.9999998555019446,
                0.9999997761970782,
                0.9999998802069444,
                0.9999999123575674,
                0.9999998024946566,
                0.9999998642566543
            ],
            [
                0.999999581881377,
                0.9999994631249326,
                0.9999996072136128,
                0.9999999123575465,
                0.9999999006880668,
                0.9999995262095556,
                0.9999998802069731,
                0.9999997761971583,
                0.9999998724809875,
                0.9999999067050387
            ],
            [
                0.9999989322966216,
                0.9999978766217937,
                0.9999983463096271,
                0.9999988634357486,
                0.9999993524052794,
                0.9999999273418355,
                0.9999980052707568,
                0.9999999176675142,
                0.999998863435748,
                0.999999653367503
            ],
            [
                0.9999998555020307,
                0.9999996533673379,
                0.9999993916406738,
                0.9999997761970516,
                0.9999998555019447,
                0.9999998461826405,
                0.9999999226557776,
                0.9999997300421261,
                0.9999994956527124,
                0.999999712631481
            ],
            [
                0.9999998802069587,
                0.9999998802069445,
                0.9999998362622943,
                0.9999998144609203,
                0.999999730042287,
                0.9999998144608097,
                0.9999998942830358,
                0.9999999067050388,
                0.9999996533674204,
                0.9999998942829981
            ],
            [
                0.9999998874647575,
                0.9999996072138467,
                0.9999998802069731,
                0.9999999500627917,
                0.9999996940978826,
                0.9999998144608762,
                0.9999995262096119,
                0.9999995818812772,
                0.9999999317440197,
                0.9999998362623724
            ],
            [
                0.9999999468421313,
                0.9999998802069731,
                0.9999999273417749,
                0.9999998724809875,
                0.9999998724809723,
                0.9999996743688199,
                0.9999999006880195,
                0.9999998555020307,
                0.9999999273418961,
                0.9999998724809115
            ],
            [
                0.9999999006881142,
                0.9999999067050387,
                0.999999931743979,
                1.0,
                1.0,
                1.0,
                0.9999998942828973,
                0.9999999123575882,
                0.9999999358793638,
                0.999999900688055
            ],
            [
                0.9999998461826956,
                0.9999998724808963,
                0.9999998257021214,
                0.9999999006880195,
                0.9999998942830485,
                0.9999999006879957,
                0.9999998144609645,
                0.9999999358794021,
                0.9999998874647978,
                0.9999998642566704
            ],
            [
                0.9999998024946801,
                0.999999631011372,
                0.9999999358793944,
                0.999999802494586,
                0.999999825702163,
                0.9999999273418615,
                0.9999998802068873,
                0.9999997897567092,
                0.9999998942829981,
                0.9999998362623138
            ],
            [
                6.144172404738491e-06,
                2.2603248367949354e-06,
                0.9999997126313098,
                0.9999996743688976,
                4.785093924389007e-06,
                0.9999999176674357,
                0.9999997126315154,
                7.338207180898968e-07,
                1.994729008151319e-06,
                0.9999996743687811
            ],
            [
                1.994729483723626e-06,
                0.9999998555019274,
                6.962258739796719e-06,
                0.9999999226558146,
                3.288749849529972e-06,
                0.9999997761970515,
                7.338213304363436e-07,
                4.222832437798974e-06,
                7.338210680021253e-07,
                4.785093924389007e-06
            ],
            [
                0.9999998362622943,
                0.9999998802069159,
                0.9999998257021214,
                0.9999998362622553,
                0.9999999123575777,
                0.9999999530883285,
                0.9999999500628095,
                0.9999999006881496,
                0.9999998362623528,
                0.9999999273418615
            ],
            [
                0.9999999358794097,
                0.9999999273418703,
                0.9999998257020799,
                0.9999998362623529,
                0.9999998461826956,
                0.9999998724809116,
                0.9999998874648648,
                0.9999999358793792,
                0.9999998461827322,
                0.9999996940977732
            ],
            [
                0.9999998874648917,
                0.9999999123575987,
                0.9999998724809268,
                1.0,
                0.9999998802069587,
                0.9999999123574836,
                0.9999999006880668,
                0.9999997897566341,
                0.9999999067050832,
                0.9999998942829477
            ],
            [
                0.9999999123575256,
                0.9999998362623529,
                0.9999998362622553,
                0.9999999006881497,
                0.999999864256719,
                0.9999999176675535,
                0.9999998942830233,
                0.9999998257021837,
                0.9999999006880668,
                0.9999998257021214
            ],
            [
                0.9999999176675829,
                0.9999997617631753,
                1.0,
                0.9999999434137704,
                0.9999999317439464,
                0.9999999358793944,
                0.9999999273418009,
                1.0,
                0.999999939764294,
                0.9999999226557593
            ],
            [
                0.9999998802069159,
                0.9999998024946802,
                0.9999999273418962,
                0.9999998942828972,
                1.0,
                1.0,
                0.9999998642566381,
                0.999999872480942,
                1.0,
                0.9999998257022045
            ],
            [
                0.9999999273418702,
                0.9999999358794173,
                0.999999746398073,
                0.9999997126313783,
                0.9999997126314812,
                0.9999998874648112,
                0.9999998642566543,
                0.999999631011328,
                0.999999922655787,
                0.9999998257021006
            ],
            [
                0.9999998724809267,
                0.9999997463981637,
                0.9999999006880194,
                0.9999998724809419,
                0.9999999123575882,
                0.9999999273418096,
                0.9999998802069017,
                0.9999997463982241,
                0.999999802494586,
                0.9999998024947038
            ],
            [
                5.4222183235249605e-06,
                1.3709567165617364e-06,
                0.9999998724810027,
                2.2603234895372223e-06,
                1.7603430034867993e-06,
                6.475947982037486e-07,
                1.2098661162056318e-06,
                1.9947304348862686e-06,
                2.561281600086738e-06,
                2.2603248367949354e-06
            ],
            [
                0.9999996533675031,
                0.9999997126314812,
                0.999999789756634,
                0.999999802494586,
                0.9999995549151076,
                0.9999997126315496,
                0.9999997126314811,
                0.9999996940978096,
                0.9999999226558423,
                0.9999999006880076
            ],
            [
                0.9999998802069017,
                0.9999999123575672,
                0.9999999176674848,
                0.9999998874647307,
                0.9999998802069302,
                0.9999998144608983,
                0.9999999123575255,
                0.9999996533672965,
                0.9999998144608541,
                0.999999887464932
            ],
            [
                0.9999892166865034,
                3.4663270375278157e-07,
                0.9999981261248405,
                0.9999980052705176,
                0.9999993916409637,
                8.315277302841894e-07,
                0.9999975938968022,
                0.9999983463100209,
                0.9999977396765116,
                0.9999955048194976
            ],
            [
                0.9999998874648782,
                1.0,
                0.9999999273418875,
                0.999999814460876,
                0.9999999397642653,
                0.9999999176674454,
                0.9999999468421756,
                0.9999999273418096,
                0.9999999500628513,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999123574942,
                0.9999998874647977,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999397642078
            ],
            [
                0.9999994956527124,
                0.9999996940977367,
                0.9999992661788449,
                1.0,
                0.999999526209386,
                0.9999992188519493,
                0.9999993524051249,
                0.9999993916411088,
                0.99999963101146,
                0.9999998555020135
            ],
            [
                0.999999761763005,
                0.9999996072137999,
                0.9999995818813768,
                0.9999998461826589,
                0.9999996072138467,
                0.9999999067050165,
                0.9999997617630617,
                0.9999998802069874,
                0.9999996072137063,
                0.9999999123574733
            ],
            [
                0.9999999123575569,
                0.9999998724809875,
                0.9999999317440278,
                0.9999999226558054,
                0.9999988634365607,
                0.9999998257021213,
                0.9999998555020135,
                0.9999999317439627,
                0.9999999358794021,
                0.9999998024946095
            ],
            [
                3.059022998558814e-07,
                0.9999998802069159,
                1.9947299593078385e-06,
                0.9999998555019275,
                0.9999996940976272,
                0.9999998144608319,
                1.3709567165617364e-06,
                0.9999998942829854,
                0.9999998724810027,
                1.0
            ],
            [
                2.5612834320563895e-06,
                2.9023119851899796e-06,
                0.9999998362622943,
                4.785095065232451e-06,
                6.962253760024999e-06,
                0.9999997463981938,
                3.2887494574832472e-06,
                1.7603440527286572e-06,
                0.9999998461826772,
                0.9999998257020798
            ],
            [
                0.9999998257020798,
                0.9999995818811773,
                0.9999998024945624,
                0.9999998024947273,
                0.9999998257021007,
                0.9999999006881496,
                0.9999996072138468,
                0.9999998461827139,
                0.9999996743687035,
                0.9999998461826038
            ],
            [
                1.0,
                0.9999998642567189,
                1.0,
                1.0,
                0.999999939764258,
                1.0,
                0.9999999434137773,
                1.0,
                0.9999999273418182,
                0.9999999317440279
            ],
            [
                0.9999997463980428,
                0.9999998802069017,
                0.9999998724809723,
                0.9999998362623528,
                0.9999998942829098,
                0.9999998874648515,
                0.9999998461826954,
                0.9999998362622358,
                0.9999999226557593,
                0.999999887464771
            ],
            [
                0.9999996072138468,
                0.9999997463981939,
                0.9999996533673792,
                0.9999997617630617,
                0.9999994284992807,
                0.9999998257020591,
                0.9999999067049943,
                0.9999997761971849,
                0.9999995549148423,
                0.999999761763147
            ],
            [
                0.9999996072137063,
                0.9999998362623724,
                0.999999789756609,
                0.999999917667524,
                8.315278294114555e-07,
                2.2603248367949354e-06,
                0.9999996743687034,
                0.9999998144609424,
                0.9999995549150015,
                2.2603248367949354e-06
            ],
            [
                0.9999999123575046,
                0.9999998724810027,
                0.9999999123575882,
                0.999999825702163,
                0.9999998024947273,
                0.9999998942830106,
                0.9999999226558515,
                0.9999998874648379,
                0.9999998461827139,
                0.9999999176674946
            ],
            [
                0.9999998555019447,
                0.9999999176674848,
                0.9999999123574628,
                0.9999999226558238,
                0.9999998257021007,
                0.9999999317439221,
                0.999999943413757,
                0.9999999067050387,
                0.999999931743979,
                0.9999999176674946
            ],
            [
                0.9999998802069731,
                0.9999998642566381,
                0.9999999176675829,
                0.999999789756609,
                0.9999996940978098,
                0.9999998461826037,
                0.9999999067050832,
                0.9999998942830106,
                0.9999999358794021,
                0.9999998802069159
            ],
            [
                3.0590237279085045e-07,
                3.288749849529972e-06,
                0.9999999006881142,
                8.315278294097538e-07,
                4.785095635655362e-06,
                0.9999998362623138,
                1.0677031245990084e-06,
                6.144175334468545e-06,
                0.9999998362622747,
                5.422220909009474e-06
            ],
            [
                4.450852111155216e-07,
                0.9999998802069017,
                0.9999998362623724,
                1.0677026154827912e-06,
                5.043475885696228e-07,
                1.209865827752005e-06,
                8.315278294114555e-07,
                2.902312331170226e-06,
                0.999999428499417,
                4.222833948008874e-06
            ],
            [
                0.9999997617630617,
                0.9999995549150013,
                1.0,
                0.9999994956527123,
                0.9999993524049707,
                0.9999996940978462,
                0.9999997761971849,
                0.9999998724809419,
                0.9999995262096119,
                0.9999996940978096
            ],
            [
                0.999999887464838,
                0.9999999176675437,
                0.9999999434137637,
                0.9999998461827139,
                0.9999998724810027,
                0.9999998874649051,
                0.9999999273418528,
                0.9999998942830233,
                0.9999999397642437,
                0.9999999123575986
            ],
            [
                0.9999995818814266,
                0.9999998144609205,
                1.370957860576702e-06,
                0.9999998362622358,
                2.561282210740037e-06,
                3.288748281329893e-06,
                7.889260704968913e-06,
                7.338208055664991e-07,
                0.9999989969856732,
                1.067703124601679e-06
            ],
            [
                1.0677032518814388e-06,
                6.47595107001401e-07,
                0.9999998461826772,
                0.9999998461826222,
                3.288749849529972e-06,
                2.902312677150514e-06,
                0.9999998461827322,
                1.3007133116909523e-05,
                1.3709573702856596e-06,
                0.9999999397643156
            ],
            [
                0.9999996743687422,
                0.9999997463981032,
                0.9999999006880312,
                0.9999999317439465,
                0.9999998024945624,
                0.9999998257021837,
                0.9999998257021214,
                0.9999997126314811,
                0.9999998874648917,
                0.9999999273418009
            ],
            [
                0.9999999067051054,
                0.9999995818814268,
                0.9999998461826406,
                0.9999999226558515,
                0.9999997126315154,
                0.9999998874647977,
                0.9999991684716754,
                0.9999996072137064,
                0.9999995262094987,
                0.9999991148433868
            ],
            [
                0.9999997126314811,
                0.9999996940977004,
                0.9999998874647977,
                0.999999761763005,
                0.9999997617629766,
                0.9999998461826588,
                0.999999746398073,
                0.9999998362622358,
                0.9999996533674618,
                0.9999997126314126
            ],
            [
                0.9999998461826222,
                0.9999999273418962,
                0.9999999317440279,
                0.9999999176674848,
                0.9999998461826038,
                0.9999998724810027,
                0.999999864256719,
                0.9999998461827139,
                0.9999997897565588,
                1.0
            ],
            [
                0.9999998144609646,
                0.9999996310115041,
                0.999999730042094,
                0.9999999123575151,
                0.9999998802069731,
                0.9999997126314469,
                0.9999998257021837,
                0.9999998461826956,
                0.9999998362622359,
                0.9999998555020307
            ],
            [
                0.9999999226557225,
                0.9999998942829224,
                0.9999997463981031,
                0.9999998024946095,
                0.9999997126315496,
                0.9999998362622357,
                0.9999996310114598,
                0.9999999317439303,
                0.9999998724810027,
                0.9999999226557685
            ],
            [
                1.0677029973219343e-06,
                2.561282210729555e-06,
                2.561281600076256e-06,
                0.9999981261250639,
                0.9999986290427935,
                1.2098662604291696e-06,
                7.338210680021253e-07,
                3.726638839878908e-06,
                1.4449798650551755e-07,
                0.9999997463980427
            ],
            [
                0.9999997463980729,
                0.9999999006881259,
                0.9999992188517628,
                0.9999997126314126,
                0.9999998362623723,
                0.9999997463982241,
                0.9999997761970781,
                0.9999996072137999,
                0.9999995818811773,
                0.9999998942829981
            ],
            [
                0.9999998642567189,
                0.9999987121052454,
                0.9999990577552941,
                0.9999997300423192,
                0.9999999358794021,
                0.9999998874649051,
                0.9999992661786699,
                0.9999999067050721,
                0.9999998724809267,
                0.9999993106388727
            ],
            [
                0.9999998802069587,
                0.9999998257021007,
                0.999999946842125,
                0.9999999123575568,
                0.9999999559305787,
                0.9999998642566219,
                0.9999998874647575,
                0.9999999006880904,
                0.9999998942829099,
                0.9999999434137435
            ],
            [
                0.9999999317439465,
                0.9999991684715761,
                0.9999998257021422,
                0.9999998555019618,
                0.9999997300422226,
                0.999999922655833,
                0.9999999358794097,
                0.9999999273418269,
                0.9999999123575778,
                0.9999998802069302
            ],
            [
                0.9999998024945624,
                0.9999997126313097,
                0.9999993106386261,
                0.9999999226558146,
                0.9999997126314126,
                0.9999997761970248,
                0.9999998555019275,
                0.9999998874648246,
                0.9999997126315154,
                0.9999997463981939
            ],
            [
                0.9999999226558515,
                1.0,
                0.9999999226557592,
                0.9999999123575882,
                1.0,
                0.9999999273417749,
                0.9999999397643083,
                0.9999999434138043,
                0.9999999176675142,
                1.0
            ],
            [
                0.9999995818814266,
                0.9999995262093859,
                0.9999997126315496,
                0.9999996743686645,
                0.9999996533672963,
                0.9999994284994171,
                0.9999997126314468,
                0.9999994631250604,
                0.9999996533674618,
                0.9999997463980125
            ],
            [
                0.9999999358794097,
                1.0,
                0.9999998942829602,
                1.0,
                0.999999887464838,
                0.9999999397642078,
                0.9999999176674848,
                1.0,
                0.9999999006880431,
                0.9999999006880312
            ],
            [
                0.9999996533673791,
                0.9999999226558423,
                0.9999999067050498,
                0.9999998461826956,
                0.9999998642566866,
                0.9999998362622357,
                0.999999631011416,
                0.9999999067050165,
                0.9999998724809571,
                0.9999998874647307
            ],
            [
                0.9999988634357482,
                0.9999994631249964,
                6.475948754012522e-07,
                0.9999982396567878,
                1.855391681906175e-07,
                2.3823696679327928e-07,
                3.927862470899887e-07,
                2.1024339116082313e-07,
                0.9999987901347499,
                0.9999869928762285
            ],
            [
                2.5612834320563895e-06,
                5.422220262636381e-06,
                1.994729483729522e-06,
                0.9999994631249963,
                0.9999996533672137,
                6.144172404738491e-06,
                3.726639284144195e-06,
                2.9023112932296107e-06,
                0.9999996072137532,
                0.9999999123574942
            ],
            [
                0.9999999468421377,
                0.9999999273418615,
                0.9999998724809724,
                0.9999999067050276,
                0.9999999358793333,
                0.9999998874648112,
                0.9999999176675829,
                0.9999999273418355,
                0.9999999317439628,
                0.9999999006880195
            ],
            [
                0.9999999067049832,
                0.9999994284992807,
                0.9999998257021838,
                0.9999997897566841,
                0.9999997463980125,
                0.9999998942829098,
                0.9999998024947273,
                0.9999998874648379,
                0.9999998144609425,
                0.9999998874648648
            ],
            [
                0.9999999226557224,
                0.9999998257021006,
                0.999999802494586,
                0.9999999067050943,
                0.9999998642566866,
                0.999999789756659,
                0.9999998802069444,
                0.9999998257020798,
                0.9999998257022045,
                0.9999999067050944
            ],
            [
                0.9999998144609203,
                0.999999631011372,
                0.9999998144609425,
                0.9999997463980126,
                0.9999997897566341,
                0.9999998144608098,
                0.9999995818811277,
                0.9999995549148952,
                0.9999998144608983,
                0.999999825702163
            ],
            [
                0.9999997617631754,
                0.9999997463980428,
                0.9999998802069017,
                0.9999996072139404,
                0.9999998024945861,
                0.9999996533672965,
                0.9999998555020481,
                0.9999998024945624,
                0.9999998362623334,
                0.9999998024947038
            ],
            [
                0.999999825702059,
                0.9999999397642653,
                0.999999917667573,
                0.9999998362623723,
                0.9999999123575151,
                0.9999998461827138,
                0.9999999358793791,
                1.0,
                0.9999999123575882,
                0.9999997300421583
            ],
            [
                0.9999995549147891,
                0.9999997126315496,
                0.9999996533673379,
                0.9999997463981636,
                0.999999761763005,
                0.9999997761971049,
                0.9999993524048933,
                0.9999997126315153,
                0.9999995549148953,
                0.9999997897566841
            ],
            [
                0.9999999273417663,
                0.9999995549150015,
                0.9999997897566089,
                0.9999997300421262,
                0.9999997617631186,
                0.9999997897566592,
                0.9999998461826038,
                1.0,
                0.9999999006880549,
                0.9999999006880786
            ],
            [
                0.9999998942829225,
                1.0,
                0.9999998874647575,
                0.999999825702163,
                0.9999997897566841,
                0.9999997300421262,
                0.9999996310116358,
                0.999999953088334,
                0.99999976176309,
                0.9999999176675044
            ],
            [
                0.999999581881277,
                0.9999999317440278,
                0.9999998144608983,
                0.9999999358794327,
                0.9999999226558238,
                0.9999998024947272,
                0.9999999176675142,
                0.9999998555019619,
                0.9999999273418615,
                0.9999999006880668
            ],
            [
                0.9999998724809268,
                0.9999999176675338,
                1.0,
                0.9999999358793639,
                0.9999998942829098,
                0.9999999067050943,
                0.9999998802068873,
                0.9999998724809116,
                0.9999999067049831,
                0.9999999530883843
            ],
            [
                0.9999999273418443,
                0.9999998144608981,
                1.0,
                0.9999998362623723,
                0.9999999358793485,
                0.9999998257021837,
                0.9999999067050943,
                0.9999998802069731,
                0.9999999397643083,
                0.9999999123575569
            ],
            [
                0.9999998144608098,
                0.9999998461827322,
                0.9999999358794402,
                0.9999999273418703,
                0.9999998555019446,
                0.9999999434137705,
                0.9999999500628215,
                0.9999999123575778,
                0.9999998724809723,
                0.999999939764215
            ],
            [
                0.9999998874648246,
                0.9999997463980428,
                0.9999997897566592,
                0.999999864256719,
                0.9999998642566705,
                0.9999998642566867,
                0.9999998724809875,
                0.9999998802069874,
                0.9999997617631754,
                0.9999998642566219
            ],
            [
                0.9999994956524116,
                0.9999998024946566,
                0.9999986290432842,
                3.726641061109272e-06,
                0.9999972735290805,
                4.539786862811735e-05,
                0.9999942280806634,
                0.9999952149066513,
                1.3007126913820052e-05,
                0.9999978766222984
            ],
            [
                0.9999998874647977,
                0.9999999006880905,
                0.9999999067050165,
                0.9999999067050276,
                0.9999999317439627,
                0.9999999317439302,
                0.9999998942829225,
                0.9999999176674454,
                0.9999998362622358,
                1.0
            ],
            [
                0.9999999358793867,
                0.9999999397642365,
                0.999999900688126,
                0.9999999123575151,
                1.0,
                0.9999998144608983,
                0.9999998555020309,
                0.9999999067049943,
                0.9999998724809115,
                0.9999999067049942
            ],
            [
                0.9999999226557132,
                0.9999998802069302,
                0.9999998461827322,
                0.9999998257022045,
                0.9999998942830485,
                0.9999999123575882,
                0.9999998642566543,
                0.9999999006881142,
                0.9999998461826956,
                0.9999998144609425
            ],
            [
                0.9999998144608981,
                0.999999946842125,
                0.9999999434137502,
                0.999999927341827,
                0.9999998257020799,
                0.9999998461826222,
                0.9999999273418702,
                0.999999894282935,
                0.9999998802069731,
                0.9999998642566219
            ],
            [
                0.9999998144608981,
                0.9999998874647709,
                0.9999998555019791,
                0.9999998362623137,
                0.9999999067050387,
                0.9999997761971049,
                0.9999998724809723,
                0.9999998942829854,
                0.9999997897566841,
                0.999999730042094
            ],
            [
                0.9999998257021837,
                1.0,
                0.9999998555020135,
                0.9999999067051499,
                0.9999998874648379,
                1.0,
                0.9999999176674454,
                0.9999999123575778,
                0.9999999530883843,
                0.9999999006880668
            ],
            [
                0.9999996533673791,
                0.9999997463980428,
                0.9999994284995534,
                0.9999997126313098,
                0.9999992188516698,
                0.9999998555019447,
                0.999999746398194,
                0.9999999123575359,
                0.9999996743686645,
                0.9999999358793715
            ],
            [
                0.99999994341373,
                0.9999995549149482,
                0.9999998555019274,
                0.9999999559305576,
                0.9999999586006048,
                0.9999998802069016,
                0.9999991684720718,
                0.9999998461826956,
                0.9999999067051277,
                0.9999998724808964
            ],
            [
                0.9999999273418615,
                0.9999998144608983,
                0.9999997463981032,
                0.9999994284996895,
                0.9999996310115481,
                0.9999993524053568,
                0.9999997300421906,
                0.9999996072137064,
                0.9999997300421583,
                0.9999997761971849
            ],
            [
                1.3709573702856596e-06,
                6.475950298021765e-07,
                3.2887506336235617e-06,
                3.288748673376478e-06,
                5.715003789046955e-07,
                3.2887502415767434e-06,
                1.0677032518814388e-06,
                9.422444815814404e-07,
                9.422445939054222e-07,
                8.315279285370317e-07
            ],
            [
                0.9999998257020799,
                0.9999998144608762,
                0.9999996743688976,
                0.9999997300421906,
                0.9999997300421906,
                0.9999998642566381,
                0.999999730042255,
                0.9999998461826589,
                0.9999998024947273,
                0.9999996940978826
            ],
            [
                0.9999998461826038,
                0.9999999123575986,
                0.9999995549151075,
                0.9999999176674456,
                0.9999994956524121,
                0.9999996743687424,
                0.9999996743687035,
                0.999999631011548,
                0.9999995818813271,
                0.9999998362622747
            ],
            [
                0.999999900687984,
                1.0,
                0.9999999273418703,
                1.0,
                1.0,
                0.9999999176675143,
                0.9999999067050165,
                1.0,
                0.9999999397642868,
                0.9999999067050943
            ],
            [
                0.9999997300423192,
                0.9999998942830485,
                0.999999912357442,
                0.9999998024947038,
                0.9999998555020309,
                0.9999998024946566,
                0.9999994956527725,
                0.9999999434137503,
                0.9999995262093295,
                0.9999998362623334
            ],
            [
                0.9999998362622944,
                0.9999999226557501,
                0.9999997897565588,
                0.9999998724809875,
                0.9999996940978096,
                0.999999802494586,
                0.9999997463981032,
                0.9999998362622747,
                0.9999999006881378,
                0.999999900687984
            ],
            [
                0.9999999067051054,
                0.9999998024945624,
                0.9999998461827322,
                0.9999998724809419,
                0.9999997897565839,
                0.9999998642566543,
                0.999999746398073,
                0.9999998024947038,
                0.9999999123575986,
                0.9999998461826772
            ],
            [
                0.9999999123575046,
                0.9999999067051165,
                0.9999999123575568,
                0.9999999123575151,
                1.0,
                0.9999998802069159,
                1.0,
                0.9999998802069159,
                0.9999998724808963,
                0.9999998942830358
            ],
            [
                0.9999998144608098,
                1.0,
                0.9999997300422548,
                0.9999998724809875,
                1.0,
                0.9999998724809875,
                0.9999997897567343,
                0.9999999273418788,
                0.9999999434137502,
                0.9999998802069159
            ],
            [
                0.9999999586006394,
                0.9999998024947037,
                0.9999998942830358,
                0.9999998802069444,
                0.9999998802069445,
                0.9999997761972116,
                0.9999996310115039,
                0.9999998555019274,
                0.9999998362622748,
                0.9999999397643154
            ],
            [
                0.9999998942830862,
                0.9999998257021422,
                0.9999998802069731,
                0.9999997761970515,
                0.999999887464905,
                0.9999999358793944,
                0.9999998024946566,
                0.9999998144608541,
                0.9999998802069302,
                0.999999900687984
            ],
            [
                0.9999998024946095,
                0.9999996310116359,
                0.9999999273418182,
                0.999999802494633,
                0.9999998555019618,
                0.9999998024946801,
                0.9999998802069731,
                0.9999997617629764,
                0.9999999123575881,
                0.9999998257021422
            ],
            [
                0.9999997761971849,
                0.9999997761972116,
                0.999999802494633,
                0.9999998642566543,
                0.9999998024947272,
                0.9999998724809571,
                0.9999996940978096,
                0.9999999317439058,
                0.9999999226558146,
                0.9999997761970515
            ],
            [
                0.9999998144609424,
                0.9999998024947038,
                0.9999995818812771,
                0.9999996533674204,
                0.9999995818810776,
                0.9999992661791951,
                0.9999997126314469,
                0.9999998257021631,
                0.9999995262093294,
                0.9999996940977004
            ]
        ]
    },
    {
        "q_id": "9224_mmlu_physics",
        "cot_ids": [
            3,
            4,
            5,
            7,
            11,
            12,
            13,
            14,
            16,
            17,
            18,
            20,
            21,
            23,
            25,
            28,
            29,
            33,
            35,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            50,
            53,
            54,
            55,
            64,
            65,
            66,
            68,
            69,
            70,
            72,
            73,
            75,
            78,
            80,
            81,
            82,
            83,
            86,
            88,
            89,
            91,
            92,
            94,
            96,
            97,
            100,
            101,
            102,
            103,
            104,
            106,
            110,
            111,
            112,
            113,
            115,
            116,
            120,
            121,
            122,
            124,
            125,
            127
        ],
        "rewards": [
            [
                3.466326624336003e-07,
                5.422218969895357e-06,
                7.889266347715168e-06,
                0.9999339478580691,
                NaN,
                5.715006514176113e-07,
                8.315278294114555e-07,
                NaN,
                3.288748673360027e-06,
                9.422445939032799e-07
            ],
            [
                4.4508515805735777e-07,
                2.699578096403948e-07,
                1.637376862489725e-07,
                5.043475885696228e-07,
                1.637376862489725e-07,
                7.889263526345123e-06,
                1.4449798650569826e-07,
                1.760342793638743e-06,
                8.315284241665078e-07,
                2.699577452775239e-07
            ],
            [
                5.422217677152175e-06,
                2.5612831267202583e-06,
                2.3823690999323465e-07,
                3.059022269250683e-07,
                1.1253506814842375e-07,
                9.422443692574719e-07,
                2.9023119851899796e-06,
                1.637376862489725e-07,
                6.144177531811707e-06,
                1.8553910183674878e-07
            ],
            [
                5.043475885674441e-07,
                1.147876675686207e-05,
                5.043472278322555e-07,
                2.3823693839154895e-07,
                1.2098653950656417e-06,
                1.5534981249574276e-06,
                2.1024326584639497e-07,
                1.994729483705484e-06,
                2.10243290909724e-07,
                2.7535697666401535e-05
            ],
            [
                NaN,
                2.1024334103581732e-07,
                1.4449798650569826e-07,
                6.825598842065202e-08,
                1.8553914607237736e-07,
                3.6534838223576766e-08,
                6.825606978822427e-08,
                1.6373764721091427e-07,
                7.734428685047173e-08,
                5.315789407685159e-08
            ],
            [
                5.8291272493815044e-05,
                1.7603434231241496e-06,
                1.3709570434122812e-06,
                7.889263526266196e-06,
                3.535624650150453e-05,
                0.0002959572059428831,
                0.01243165354016317,
                3.4663249714612693e-07,
                NaN,
                1.4738981972323349e-05
            ],
            [
                2.5612812947508257e-06,
                9.422442569290178e-07,
                7.889259764445822e-06,
                7.338210680021253e-07,
                8.315280276626197e-07,
                4.222831934156396e-06,
                1.9947304348862686e-06,
                1.3709570434178922e-06,
                1.9947299593078385e-06,
                7.484623618563417e-05
            ],
            [
                1.8925143729575624e-05,
                NaN,
                1.9947297215125433e-06,
                6.1441746020359e-06,
                1.0677028700422047e-06,
                2.2603253756956754e-06,
                5.715003789046955e-07,
                NaN,
                3.288749849498565e-06,
                1.2098653950692178e-06
            ],
            [
                3.9278634073732336e-07,
                1.9947292459347367e-06,
                3.2887498495150166e-06,
                7.338209805133949e-07,
                9.422450431989127e-07,
                5.043474683220276e-07,
                1.6373770576776313e-07,
                9.422447062202052e-07,
                6.9622537599680095e-06,
                NaN
            ],
            [
                6.475950298011458e-07,
                5.422219616265831e-06,
                7.338209805240734e-07,
                3.9278634073732336e-07,
                9.422448185534261e-07,
                6.475945666051092e-07,
                2.1024339116168358e-07,
                2.382368531929327e-07,
                5.043476486915964e-07,
                4.450849988811838e-07
            ],
            [
                6.475947210012481e-07,
                1.637376862489725e-07,
                3.927863875616689e-07,
                7.338210680002898e-07,
                1.637376862489725e-07,
                9.422442569315887e-07,
                2.3823690999160957e-07,
                2.699577774589574e-07,
                2.6995768091383957e-07,
                3.4663266242969896e-07
            ],
            [
                1.5534981249697903e-06,
                NaN,
                2.6995784182073116e-07,
                3.466327037539638e-07,
                1.0677033791612137e-06,
                3.05902226923399e-07,
                NaN,
                1.444979692797559e-07,
                2.2603251062450327e-06,
                3.059021175255426e-07
            ],
            [
                1.994729721518893e-06,
                1.7603425837855082e-06,
                7.338211554801876e-07,
                6.1441746020359e-06,
                5.715002426475718e-07,
                3.0590219045914655e-07,
                9.422448185510695e-07,
                9.422443692574719e-07,
                3.288747889284851e-06,
                8.315283250394546e-07
            ],
            [
                2.6995774527718623e-07,
                0.9999970976887106,
                1.2098659719788098e-06,
                2.10243290909724e-07,
                1.855391681906175e-07,
                0.9999980052702816,
                9.931200429212718e-08,
                0.9999986290421411,
                0.9999978766210328,
                2.2603253756874524e-06
            ],
            [
                1.5534983101602148e-06,
                7.88926634755014e-06,
                1.553498124964492e-06,
                1.6701427817427163e-05,
                8.939696304213768e-06,
                1.209865539295696e-06,
                2.2603253756874524e-06,
                6.962257909785973e-06,
                1.5534971990126997e-06,
                3.7266397283908927e-06
            ],
            [
                8.315283250394546e-07,
                1.3709576971425944e-06,
                9.422443692574719e-07,
                9.422449308716635e-07,
                9.422443692555439e-07,
                3.9278629391427843e-07,
                2.2603234895372223e-06,
                1.3709575337016483e-06,
                7.338209805240734e-07,
                3.05902263391829e-07
            ],
            [
                1.2098659719788098e-06,
                1.760343213335281e-06,
                9.422450431954847e-07,
                2.5612828213934817e-06,
                5.422221555414699e-06,
                0.9999485578057012,
                3.05902190458764e-07,
                1.3709575337159875e-06,
                1.7603438428800754e-06,
                5.829127944863308e-05
            ],
            [
                1.8553910183674878e-07,
                0.9999599363086848,
                3.466326624336003e-07,
                2.699577774589574e-07,
                1.637376862489725e-07,
                2.9023119851899796e-06,
                2.1024334103581732e-07,
                6.962255419931625e-06,
                0.9999985406243019,
                0.9999942280813544
            ],
            [
                NaN,
                3.288749457383046e-06,
                1.7603434231833873e-06,
                9.422449308716635e-07,
                2.9023123311055552e-06,
                4.222835458148261e-06,
                2.561282210729555e-06,
                9.931200429181105e-08,
                2.9023133690637e-06,
                1.5534975693601474e-06
            ],
            [
                1.4738980215352592e-05,
                3.7266379514061143e-06,
                5.715005832886879e-07,
                2.2603251062450327e-06,
                1.5534971990169383e-06,
                6.475946438055299e-07,
                1.760342793638743e-06,
                2.753569766795419e-05,
                NaN,
                3.4663278639892215e-07
            ],
            [
                1.5534979397740895e-06,
                3.927862002663297e-07,
                6.144173137170873e-06,
                2.90231094723893e-06,
                NaN,
                1.1478766757404937e-05,
                3.7266383956509585e-06,
                6.475946437966953e-07,
                4.785094494811783e-06,
                1.0677029973219343e-06
            ],
            [
                4.4508510499849186e-07,
                5.04347468323289e-07,
                6.144172404693786e-06,
                8.315281267882195e-07,
                4.450850519403407e-07,
                1.2098652508391807e-06,
                4.785095065232451e-06,
                1.0677029973192638e-06,
                5.04347287955046e-07,
                6.1441746020359e-06
            ],
            [
                6.962257909785973e-06,
                2.382368531929327e-07,
                3.05902190458764e-07,
                2.3823690999323465e-07,
                1.012999098021058e-05,
                1.2751902768612997e-07,
                3.2887502415767434e-06,
                2.699577774585891e-07,
                8.315279285370317e-07,
                2.699576809143613e-07
            ],
            [
                4.450852111155216e-07,
                1.1253509497883659e-07,
                3.05902336324494e-07,
                9.93120161310289e-08,
                5.043476486924565e-07,
                2.3823690999323465e-07,
                5.043475885696228e-07,
                3.466326211113502e-07,
                1.855390576008354e-07,
                2.699576809143613e-07
            ],
            [
                0.9992903294413976,
                0.9999877809255213,
                1.2098652508424818e-06,
                0.9999942280772325,
                8.315282259138311e-07,
                1.147877359957198e-05,
                1.209866260432471e-06,
                0.9999516743690458,
                2.902312331170226e-06,
                8.939696304311336e-06
            ],
            [
                1.7603425837702984e-06,
                2.2603251062270446e-06,
                1.5534975693933505e-06,
                3.288749849498565e-06,
                1.0677026154730804e-06,
                1.7603440527222532e-06,
                9.422448185510695e-07,
                1.5534975693933505e-06,
                3.288749849498565e-06,
                3.726639284103523e-06
            ],
            [
                1.4449798650569826e-07,
                1.8553919030858602e-07,
                1.27519088491875e-07,
                1.8553907971855875e-07,
                9.93120161310289e-08,
                1.1253525596174225e-07,
                1.637376862489725e-07,
                1.4449805540763184e-07,
                1.855391239547094e-07,
                1.275190580884987e-07
            ],
            [
                5.715007195431641e-07,
                3.9278605979208185e-07,
                4.450848927658745e-07,
                4.450851580566494e-07,
                4.450849988780466e-07,
                NaN,
                9.422447062294175e-07,
                1.9947297215125433e-06,
                4.4508515805735777e-07,
                3.4663262111182307e-07
            ],
            [
                7.338213304363436e-07,
                2.699578096403948e-07,
                5.3157887739943563e-08,
                5.04347528446051e-07,
                2.3823693839325527e-07,
                1.2751902768612997e-07,
                3.927863407379485e-07,
                2.1024336609874897e-07,
                1.6373764721091427e-07,
                7.338209805240734e-07
            ],
            [
                3.0590219045914655e-07,
                2.6995774527718623e-07,
                6.475945666063607e-07,
                5.715002426486762e-07,
                6.475946438055299e-07,
                6.475946438055299e-07,
                3.466326624336003e-07,
                1.6373764721091427e-07,
                1.2098655392921197e-06,
                4.450850519409479e-07
            ],
            [
                3.9278634073732336e-07,
                4.785095065232451e-06,
                1.125352291309328e-07,
                1.2098653950692178e-06,
                3.05902190458764e-07,
                2.3823690999290963e-07,
                2.382369667929001e-07,
                1.444979692800516e-07,
                2.6995790618469934e-07,
                3.0590215399183813e-07
            ],
            [
                2.2603251062450327e-06,
                1.9947299593078385e-06,
                4.785093353940187e-06,
                6.1441746020359e-06,
                3.288749065423109e-06,
                1.3709573702778664e-06,
                1.067703379154416e-06,
                4.450851580540182e-07,
                3.927861066170637e-07,
                1.3709572068522336e-06
            ],
            [
                3.927863875616689e-07,
                5.715003107767143e-07,
                2.10243290909724e-07,
                4.4508515805735777e-07,
                1.3709572068522336e-06,
                5.715003107767143e-07,
                1.3709576971463352e-06,
                8.315277302841894e-07,
                3.466327037553825e-07,
                1.7603430034867993e-06
            ],
            [
                2.1444950971601277e-05,
                NaN,
                2.699576809143613e-07,
                1.4738976701652988e-05,
                3.288749065406658e-06,
                7.338208055680009e-07,
                1.9947304348703948e-06,
                NaN,
                5.043473480777865e-07,
                5.043474081993875e-07
            ],
            [
                3.05902263391829e-07,
                2.1024336609874897e-07,
                2.382369951932796e-07,
                2.699578096403948e-07,
                2.699577452775239e-07,
                6.47595107001401e-07,
                2.1024334103581732e-07,
                3.059021175261338e-07,
                5.043476486924565e-07,
                9.422444815814404e-07
            ],
            [
                1.0677029973192638e-06,
                6.475950298021765e-07,
                1.067703124601679e-06,
                5.043475885674441e-07,
                3.0590237279085045e-07,
                4.450852111155216e-07,
                7.338208055579897e-07,
                1.5534975693979422e-06,
                7.338213304363436e-07,
                3.0590237279085045e-07
            ],
            [
                2.2603242978778778e-06,
                1.2098662604291696e-06,
                7.338211554801876e-07,
                2.9023109472494878e-06,
                0.9999955048189634,
                0.9999756997681326,
                0.9999949062937884,
                0.9999990577549572,
                0.9999771720028893,
                0.9999904837506239
            ],
            [
                5.043476486833397e-07,
                6.475950298011458e-07,
                3.7266397283908927e-06,
                1.3709568799760888e-06,
                1.3709575337016483e-06,
                9.422443692574719e-07,
                1.3709576971463352e-06,
                1.2098662604291696e-06,
                3.927862470899887e-07,
                1.0677027427525368e-06
            ],
            [
                4.222834954778007e-06,
                6.962256249885085e-06,
                1.760343003481596e-06,
                1.5534981249697903e-06,
                6.475950297942253e-07,
                1.300713156582635e-05,
                6.962255419868303e-06,
                2.561282516042282e-06,
                1.2098656835076114e-06,
                1.0677032518785256e-06
            ],
            [
                2.382369951932796e-07,
                1.8553910183674878e-07,
                3.466326624336003e-07,
                2.1024334103581732e-07,
                3.9278629391427843e-07,
                4.450850519403407e-07,
                6.1441746020359e-06,
                2.3823685319320354e-07,
                2.3823690999323465e-07,
                3.927863407379485e-07
            ],
            [
                1.5534981249697903e-06,
                5.715003788993679e-07,
                NaN,
                3.726638839833152e-06,
                1.5534973842076057e-06,
                3.0590237279085045e-07,
                3.059021175261338e-07,
                3.9278629391427843e-07,
                8.315281267882195e-07,
                3.288749457469787e-06
            ],
            [
                5.715003788993679e-07,
                6.962253760024999e-06,
                5.04347468323289e-07,
                1.0129992187658463e-05,
                6.475947210046347e-07,
                3.4663266243308805e-07,
                NaN,
                1.760343633031919e-06,
                4.450851580566494e-07,
                1.7603430034867993e-06
            ],
            [
                4.450848927650143e-07,
                1.8553907971758842e-07,
                2.3823690999290963e-07,
                1.1253525596134564e-07,
                1.3709578605729614e-06,
                1.3709568799919866e-06,
                4.450851580555361e-07,
                2.699577774560111e-07,
                3.4663274507713016e-07,
                2.69957906184239e-07
            ],
            [
                2.382370235933104e-07,
                9.422442569290178e-07,
                4.450852111148132e-07,
                2.6995784182183607e-07,
                1.0677032518814388e-06,
                5.71500651413193e-07,
                6.475947210031623e-07,
                6.475947982037486e-07,
                1.0677033791612137e-06,
                1.5534984953510149e-06
            ],
            [
                2.260325375664839e-06,
                5.043474081993875e-07,
                5.043472278312808e-07,
                5.043474683220276e-07,
                1.067703124601679e-06,
                9.422445939002803e-07,
                8.315279285351409e-07,
                5.715006514167015e-07,
                9.422447062270609e-07,
                1.8553914607237736e-07
            ],
            [
                1.5534975693488444e-06,
                1.300713311614059e-05,
                1.3709575337159875e-06,
                9.42244818532859e-07,
                1.3709576971061233e-06,
                1.2098659719601033e-06,
                1.3709572068478697e-06,
                1.7603438428800754e-06,
                1.7603432132784448e-06,
                NaN
            ],
            [
                4.785095065132354e-06,
                3.726641061109272e-06,
                3.288749849477628e-06,
                9.422449308774482e-07,
                5.422220909009474e-06,
                2.7535694383279957e-05,
                2.4300246526646385e-05,
                2.430023494002383e-05,
                NaN,
                1.9947301970587145e-06
            ],
            [
                9.422450432014836e-07,
                1.0677031245905116e-06,
                9.422443692330485e-07,
                8.315281267861397e-07,
                5.043474081993875e-07,
                4.450850519403407e-07,
                1.5534975693792215e-06,
                8.939694172957213e-06,
                1.5534973841592143e-06,
                NaN
            ],
            [
                2.5612825160562587e-06,
                3.7266406168827523e-06,
                1.370957860567974e-06,
                3.535626336072768e-05,
                2.2603237589779086e-06,
                1.8925141472360678e-05,
                1.9947292459265734e-06,
                1.012999218776902e-05,
                2.9023116391675407e-06,
                2.4300234941261454e-05
            ],
            [
                NaN,
                7.33821330437595e-07,
                3.0590237279085045e-07,
                3.927862939126708e-07,
                1.209866260432471e-06,
                1.8553907971879076e-07,
                2.3823682479292225e-07,
                1.2751905808881762e-07,
                3.0590237279085045e-07,
                3.4663278639892215e-07
            ],
            [
                9.931202796993203e-08,
                1.994729483729522e-06,
                5.043473480777865e-07,
                2.102434412875379e-07,
                2.382369667929001e-07,
                1.209865539295696e-06,
                1.8553905760062447e-07,
                3.466327450765785e-07,
                6.144173869558639e-06,
                8.315278294114555e-07
            ],
            [
                2.561281294760143e-06,
                9.422448185534261e-07,
                2.699578740032504e-07,
                4.785092783519724e-06,
                2.3823688159291947e-07,
                3.2887486733420804e-06,
                1.5534984953510149e-06,
                1.7603425837702984e-06,
                1.855391239547094e-07,
                1.4449798650551755e-07
            ],
            [
                1.0677027427624903e-06,
                2.382369951932796e-07,
                9.931185038635267e-08,
                6.144176066943187e-06,
                1.275190580890061e-07,
                2.699576809143613e-07,
                2.6995784182183607e-07,
                2.561282516066741e-06,
                2.3823696679327928e-07,
                5.715007195431641e-07
            ],
            [
                5.422219616140078e-06,
                4.006369696446335e-05,
                3.927863875616689e-07,
                1.3709568799823232e-06,
                7.88926164518358e-06,
                1.0677032518814388e-06,
                2.5612834320214477e-06,
                2.4300232043369055e-05,
                2.144495097113319e-05,
                3.288748673319648e-06
            ],
            [
                6.47595107001401e-07,
                1.6701421845057263e-05,
                1.6701419854156377e-05,
                1.670141786295194e-05,
                2.430025232128576e-05,
                4.785094494783494e-06,
                1.012999218776902e-05,
                2.430024652854702e-05,
                2.5612831267202583e-06,
                2.2603251062450327e-06
            ],
            [
                1.5534984953453635e-06,
                8.315278294072958e-07,
                8.315280276626197e-07,
                1.0677026154806063e-06,
                2.2603234895289998e-06,
                6.144177531767002e-06,
                9.422445939002803e-07,
                9.422448185510695e-07,
                3.2887486733420804e-06,
                1.99472924590571e-06
            ],
            [
                1.7603425837855082e-06,
                2.3823693839325527e-07,
                2.3823693839325527e-07,
                1.4449803818215767e-07,
                3.46632497145457e-07,
                3.059022269254856e-07,
                1.994729721518893e-06,
                1.444980726324838e-07,
                5.04347528446051e-07,
                2.102433410343832e-07
            ],
            [
                7.338207180884785e-07,
                7.338208930421943e-07,
                3.9278610661902853e-07,
                2.699578740032504e-07,
                4.450848927650143e-07,
                1.8553907971879076e-07,
                6.475946438042047e-07,
                5.043476486915964e-07,
                4.450852641737424e-07,
                1.9947297215043796e-06
            ],
            [
                2.2603242978871282e-06,
                6.475947210046347e-07,
                5.04347528446051e-07,
                5.715005832872586e-07,
                4.785096776499213e-06,
                1.6373774480605869e-07,
                5.04347528446051e-07,
                9.422444815792981e-07,
                7.889262585886274e-06,
                6.475946438055299e-07
            ],
            [
                5.715002426486762e-07,
                1.2098662604192665e-06,
                3.927862470861484e-07,
                8.315283250371857e-07,
                3.0590215398968196e-07,
                5.043476486915964e-07,
                3.0590233632400716e-07,
                3.2887482813149375e-06,
                6.475950298011458e-07,
                2.3823688159237777e-07
            ],
            [
                3.7266397283908927e-06,
                1.7603434231777837e-06,
                1.2098655392921197e-06,
                1.2098662604291696e-06,
                3.726638839878908e-06,
                2.902313369111213e-06,
                1.0677032518700286e-06,
                1.9947297215125433e-06,
                6.962257079832313e-06,
                1.0677029973192638e-06
            ],
            [
                1.2098652508287273e-06,
                7.889263526345123e-06,
                NaN,
                2.260325106237323e-06,
                1.2098653950692178e-06,
                1.7603436330091044e-06,
                1.6701419854156377e-05,
                1.7603430034655858e-06,
                2.90231094723893e-06,
                1.3709568799879344e-06
            ],
            [
                1.3709570434178922e-06,
                1.0677026154730804e-06,
                9.422444815792981e-07,
                1.760344052714248e-06,
                9.422444815765128e-07,
                3.2887506336235617e-06,
                2.90231094723893e-06,
                2.3823685319244518e-07,
                4.785094494628999e-06,
                7.338213304363436e-07
            ],
            [
                9.422444815679433e-07,
                4.4508494582405734e-07,
                1.3709567165461505e-06,
                1.0677027427471959e-06,
                5.715007195431641e-07,
                4.450848927658745e-07,
                2.2603234895289998e-06,
                1.760343213322473e-06,
                3.0590237279085045e-07,
                7.338209805224048e-07
            ],
            [
                2.9023119851899796e-06,
                8.315281267882195e-07,
                NaN,
                9.422442569315887e-07,
                3.4663249714612693e-07,
                NaN,
                0.9999861539954885,
                8.939696304311336e-06,
                0.9999822214503244,
                0.9999962733611683
            ],
            [
                1.8553914607267268e-07,
                2.6995790618469934e-07,
                6.47595107001401e-07,
                8.764254764780641e-08,
                3.0590237279085045e-07,
                5.043475885696228e-07,
                1.4449798650551755e-07,
                2.3823693839325527e-07,
                2.382370235933104e-07,
                2.1024334103581732e-07
            ],
            [
                1.067703379136937e-06,
                1.7603436329978976e-06,
                1.3709573702778664e-06,
                1.0677033791437343e-06,
                3.726639728184142e-06,
                9.422444815765128e-07,
                1.3709567165579959e-06,
                1.9947299592570416e-06,
                3.7266401725935817e-06,
                1.2098652508287273e-06
            ],
            [
                2.5612812947508257e-06,
                5.043475284430694e-07,
                2.260325106237323e-06,
                6.9622587397397306e-06,
                1.2098661161789477e-06,
                3.9278615344178325e-07,
                1.9947304348862686e-06,
                2.561282210701601e-06,
                8.939694172770212e-06,
                1.1478772230929451e-05
            ],
            [
                1.6701425827133152e-05,
                1.6701417863559525e-05,
                6.605213683024311e-05,
                1.2098659719788098e-06,
                2.260324567337161e-06,
                1.209865827752005e-06,
                0.00015843623592576802,
                4.785095065232451e-06,
                3.2887502415767434e-06,
                0.9999546021478132
            ],
            [
                1.3709567165617364e-06,
                1.994729483723626e-06,
                1.1253525596174225e-07,
                1.7603430034867993e-06,
                3.9278605979534166e-07,
                1.994729483723626e-06,
                7.889266347356409e-06,
                9.422450432014836e-07,
                3.4663262111182307e-07,
                5.715002426460124e-07
            ]
        ]
    },
    {
        "q_id": "10339_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            15,
            16,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.7603425837903113e-06,
                3.05902336324494e-07,
                5.043475885696228e-07,
                9.931187406410953e-08,
                3.9278629391427843e-07,
                1.0677026154827912e-06,
                7.33821330437595e-07,
                4.450852111155216e-07,
                1.855390576008354e-07,
                1.8553910183674878e-07
            ],
            [
                1.2098656835252174e-06,
                1.0677027427624903e-06,
                5.715005832895975e-07,
                1.5534979397829198e-06,
                8.315277302857965e-07,
                4.450850519409479e-07,
                4.450850519409479e-07,
                3.4663278639892215e-07,
                1.5534979397829198e-06,
                7.338208055680009e-07
            ],
            [
                1.7603434231833873e-06,
                7.338211554813555e-07,
                3.466327450765785e-07,
                1.2098659719757836e-06,
                9.422449308774482e-07,
                2.3823685319244518e-07,
                5.715003107767143e-07,
                NaN,
                1.7603440527286572e-06,
                2.102434162245973e-07
            ],
            [
                7.338209805224048e-07,
                1.7603425837903113e-06,
                1.275190884913241e-07,
                6.47595107001401e-07,
                1.0677028700363782e-06,
                9.422449308748773e-07,
                1.3709578605729614e-06,
                7.338208055664991e-07,
                1.0677033791583005e-06,
                1.444980209564556e-07
            ],
            [
                3.288748673376478e-06,
                1.5534983101602148e-06,
                7.889263526345123e-06,
                8.93969950132721e-06,
                NaN,
                1.067702870039777e-06,
                9.422450431989127e-07,
                2.9023116391978967e-06,
                9.422448185510695e-07,
                1.1478769494396542e-05
            ],
            [
                8.31528325040778e-07,
                2.3823682479317953e-07,
                4.2228319344021954e-06,
                6.47594952603035e-07,
                1.8553910183674878e-07,
                1.2751899728286965e-07,
                2.1024334103581732e-07,
                7.338207180898968e-07,
                7.338208055680009e-07,
                2.5612834320563895e-06
            ],
            [
                3.466325384682834e-07,
                1.637377448057981e-07,
                3.466326624336003e-07,
                3.466326624336003e-07,
                3.9278629391427843e-07,
                9.422443692574719e-07,
                2.9023119851899796e-06,
                3.05902190458764e-07,
                3.059021175261338e-07,
                8.764245361752286e-08
            ],
            [
                2.102434162245973e-07,
                3.05902263391829e-07,
                2.1024334103581732e-07,
                1.6373764721072816e-07,
                2.5612834320563895e-06,
                3.0590219045914655e-07,
                1.637376862489725e-07,
                3.05902263391829e-07,
                4.450850519409479e-07,
                6.825608606172863e-08
            ],
            [
                1.760343003481596e-06,
                7.33821330437595e-07,
                3.05902263391829e-07,
                4.785096206076165e-06,
                4.4508515805735777e-07,
                3.059023363221292e-07,
                1.7603440527334603e-06,
                2.699578740032504e-07,
                3.927863875616689e-07,
                3.059023363221292e-07
            ],
            [
                4.691164920214251e-08,
                6.023571320847322e-08,
                9.931190958076104e-08,
                1.4449803818215767e-07,
                1.855391681906175e-07,
                3.466325384678894e-07,
                7.734423152941018e-08,
                1.1253513522447425e-07,
                6.825602910433871e-08,
                6.825604537781398e-08
            ],
            [
                9.422442569334097e-07,
                7.338212429594283e-07,
                NaN,
                5.715005832895975e-07,
                8.315278294114555e-07,
                7.338211554813555e-07,
                2.2603253756956754e-06,
                6.47595107001401e-07,
                NaN,
                3.7266383956509585e-06
            ],
            [
                3.9278620026686556e-07,
                5.043474082012222e-07,
                5.71500515161527e-07,
                2.699577774589574e-07,
                2.699577130960941e-07,
                2.699577774589574e-07,
                5.043476486924565e-07,
                5.043476486924565e-07,
                2.1024326584702836e-07,
                3.9278620026686556e-07
            ],
            [
                6.1441724046434924e-06,
                1.0677027427600627e-06,
                4.2228329411708495e-06,
                1.6373768624837685e-07,
                9.422443692489024e-07,
                1.7603434231777837e-06,
                6.475947210031623e-07,
                2.260324028427877e-06,
                7.338211554783522e-07,
                8.939695238536645e-06
            ],
            [
                5.043474082012222e-07,
                1.209865827752005e-06,
                4.4508515805735777e-07,
                1.209865539298447e-06,
                1.637377448057981e-07,
                9.93118503859575e-08,
                4.450852111148132e-07,
                0.26894141551050293,
                6.475950298021765e-07,
                7.338209805224048e-07
            ],
            [
                1.209866260432471e-06,
                5.043476486924565e-07,
                1.4449803818215767e-07,
                1.4449803818215767e-07,
                7.338211554813555e-07,
                1.9947299593078385e-06,
                1.4449805540740185e-07,
                1.3709576971463352e-06,
                1.7603438428848787e-06,
                2.3823690999323465e-07
            ],
            [
                3.059022998581767e-07,
                2.102434412875379e-07,
                6.475946438055299e-07,
                5.043476486924565e-07,
                3.9278610661902853e-07,
                4.450852641737424e-07,
                7.338209805240734e-07,
                9.422447062294175e-07,
                1.0677026154806063e-06,
                4.450852111155216e-07
            ],
            [
                2.1024339116168358e-07,
                9.422442569334097e-07,
                1.3709572068553509e-06,
                2.102434162245973e-07,
                3.9278610661902853e-07,
                2.3823690999323465e-07,
                1.4449805540740185e-07,
                3.4663249714612693e-07,
                3.0590237279032884e-07,
                7.338212429582604e-07
            ],
            [
                2.699578096403948e-07,
                NaN,
                7.338210680032098e-07,
                3.466327037553825e-07,
                1.3709573702856596e-06,
                6.47594875403829e-07,
                5.043475885696228e-07,
                6.475950298021765e-07,
                1.3709573702856596e-06,
                6.47595107001401e-07
            ],
            [
                8.315280276626197e-07,
                5.715003789046955e-07,
                5.04347287955046e-07,
                1.5534984953552536e-06,
                3.2887482812745586e-06,
                9.422444815765128e-07,
                4.4508515805735777e-07,
                5.715002426486762e-07,
                1.637377448057981e-07,
                5.04347528446051e-07
            ],
            [
                1.8553903548287212e-07,
                NaN,
                3.0590219045914655e-07,
                1.6373766672994222e-07,
                9.422442569334097e-07,
                3.05902263391829e-07,
                2.2603253756956754e-06,
                2.3823690999323465e-07,
                8.315277302857965e-07,
                3.05902263391829e-07
            ],
            [
                0.9999981261239476,
                0.9999988634358835,
                3.927863875616689e-07,
                0.9999942280772237,
                5.1442225934873024e-05,
                0.9999930377454169,
                5.043476486924565e-07,
                2.2603245673443566e-06,
                0.9999986290432842,
                0.9999989969859123
            ],
            [
                5.043474683240344e-07,
                2.699577130960941e-07,
                5.043475885696228e-07,
                6.475947982037486e-07,
                6.475946438055299e-07,
                1.209865827752005e-06,
                1.209865827740176e-06,
                1.3709575337078829e-06,
                9.422448185187191e-07,
                2.3823696679327928e-07
            ],
            [
                1.2098655392871682e-06,
                9.422448185478557e-07,
                1.067703251864202e-06,
                1.7603434231777837e-06,
                1.7603438428740716e-06,
                7.338209805200689e-07,
                3.466326211113502e-07,
                1.2098655392871682e-06,
                7.338209805200689e-07,
                3.059021175261338e-07
            ],
            [
                5.715005832895975e-07,
                2.3823690999323465e-07,
                1.637376862489725e-07,
                NaN,
                6.47594952603035e-07,
                5.043475284468537e-07,
                2.699577452775239e-07,
                6.023569884718319e-08,
                3.059022269254856e-07,
                2.699577130960941e-07
            ],
            [
                5.422219616184461e-06,
                4.222831934379152e-06,
                6.962256249821764e-06,
                4.222831934321543e-06,
                1.067703379136937e-06,
                4.785095635592258e-06,
                3.927862002625787e-07,
                7.889262585728421e-06,
                6.144173137170873e-06,
                5.043472879540142e-07
            ],
            [
                1.7603438428848787e-06,
                3.927862002663297e-07,
                6.605213683024311e-05,
                3.0590237279085045e-07,
                2.1024331597262577e-07,
                3.4663266243308805e-07,
                6.475945666063607e-07,
                2.699576809143613e-07,
                1.1253506814842375e-07,
                1.6373770576776313e-07
            ],
            [
                5.043476486924565e-07,
                1.2098659719788098e-06,
                4.450850519403407e-07,
                1.209866260432471e-06,
                1.7603434231833873e-06,
                1.3709567165617364e-06,
                3.7266383956509585e-06,
                1.760342793638743e-06,
                5.043475885696228e-07,
                1.0677029973219343e-06
            ],
            [
                3.059021175261338e-07,
                9.422444815814404e-07,
                8.315280276626197e-07,
                1.209865827752005e-06,
                5.422217677152175e-06,
                5.715007195431641e-07,
                5.04347287955046e-07,
                5.04347287955046e-07,
                NaN,
                3.059022269250683e-07
            ],
            [
                9.422444815814404e-07,
                4.785093924389007e-06,
                1.3709575337159875e-06,
                3.466325797900508e-07,
                2.6995771309523475e-07,
                5.715004470334646e-07,
                5.043473480784173e-07,
                3.059022269254856e-07,
                1.5534983101644536e-06,
                6.475950298021765e-07
            ],
            [
                7.338208055680009e-07,
                4.450852111135988e-07,
                3.7266406168827523e-06,
                3.7266397283908927e-06,
                1.0677027427624903e-06,
                6.475947982037486e-07,
                1.7603430034867993e-06,
                8.315277302857965e-07,
                5.043472879540142e-07,
                4.450852641737424e-07
            ],
            [
                1.275190124846946e-07,
                1.2751904288739315e-07,
                4.691161005609407e-08,
                1.275190124846946e-07,
                8.315281267882195e-07,
                2.1024336609874897e-07,
                3.4663278639892215e-07,
                5.715003107767143e-07,
                2.3823693839290317e-07,
                5.043474082012222e-07
            ],
            [
                9.422442569334097e-07,
                4.450852111155216e-07,
                2.3823685319320354e-07,
                5.043476486924565e-07,
                3.466326624336003e-07,
                3.466326624336003e-07,
                2.6995784182183607e-07,
                6.825598842065202e-08,
                1.8553910183674878e-07,
                2.1024334103581732e-07
            ],
            [
                2.6995774527718623e-07,
                9.422449308774482e-07,
                1.4449805540763184e-07,
                3.466325384678894e-07,
                1.7603425837903113e-06,
                5.715003789046955e-07,
                9.931190958076104e-08,
                3.927863875616689e-07,
                2.10243290909724e-07,
                6.962253760024999e-06
            ],
            [
                1.6373776432509826e-07,
                1.6373766672994222e-07,
                7.33821330437595e-07,
                8.315282259151545e-07,
                1.209866260432471e-06,
                5.043475885696228e-07,
                1.4449807263312446e-07,
                2.3823693839325527e-07,
                5.715003107767143e-07,
                3.9278638756099906e-07
            ],
            [
                3.059022269250683e-07,
                1.2751904288710323e-07,
                3.059023727894942e-07,
                2.6995784182183607e-07,
                2.382369951932796e-07,
                4.4508494582405734e-07,
                6.475947982037486e-07,
                1.1253520230052635e-07,
                3.059022269250683e-07,
                2.1024336609874897e-07
            ],
            [
                1.209865827752005e-06,
                9.422444815814404e-07,
                2.1024334103581732e-07,
                6.475949526020042e-07,
                2.699577774589574e-07,
                1.855391681898159e-07,
                3.059021904580685e-07,
                5.715002426475718e-07,
                6.475945666051092e-07,
                8.764249540862797e-08
            ],
            [
                0.9999975938979511,
                0.9999910603026563,
                0.9999974387168757,
                0.9999975938970889,
                0.9999983463100215,
                1.0677028700422047e-06,
                0.9999993916407461,
                0.999995214904941,
                0.9999982396569979,
                0.9999964991447542
            ],
            [
                2.3823690999323465e-07,
                4.4508505193791187e-07,
                6.475949526020042e-07,
                3.059022269250683e-07,
                3.4663278639892215e-07,
                3.927860597935108e-07,
                2.1024326584639497e-07,
                1.2751904288710323e-07,
                8.315278294114555e-07,
                2.3823696679327928e-07
            ],
            [
                4.450850519409479e-07,
                4.450850519409479e-07,
                3.927862470905692e-07,
                5.71500515161527e-07,
                8.315284241665078e-07,
                4.4508515805735777e-07,
                3.9278620026686556e-07,
                2.699577452775239e-07,
                7.338211554813555e-07,
                6.47594952603035e-07
            ],
            [
                1.4449807263312446e-07,
                2.102434412875379e-07,
                2.102434162245973e-07,
                1.370957860576702e-06,
                3.726639284144195e-06,
                4.450848927658745e-07,
                1.444979692800516e-07,
                4.4508494582405734e-07,
                NaN,
                2.6995784182183607e-07
            ],
            [
                3.059021175261338e-07,
                0.9999955048178923,
                7.338209805224048e-07,
                0.9999955048168281,
                0.9999706884688884,
                0.9999960330140916,
                0.9999892166865305,
                0.9999930377462651,
                5.715003789046955e-07,
                0.9999970976876728
            ],
            [
                3.927862470899887e-07,
                3.059022269250683e-07,
                7.338212429582604e-07,
                8.939695238634211e-06,
                3.466327863983311e-07,
                8.315283250371857e-07,
                1.9947304348862686e-06,
                1.5534971990126997e-06,
                3.059022998576899e-07,
                5.715005151606823e-07
            ],
            [
                8.315277302857965e-07,
                1.6373776432509826e-07,
                8.315280276626197e-07,
                3.059022998581767e-07,
                2.5612812947508257e-06,
                2.5612819054133693e-06,
                9.422443692574719e-07,
                4.450848927650143e-07,
                3.4663249714612693e-07,
                5.715005151606823e-07
            ],
            [
                5.715006514167015e-07,
                0.9999964991447584,
                0.9999972735290831,
                0.9999985406234331,
                0.9999978766215396,
                1.994729008145876e-06,
                3.7266383956509585e-06,
                0.9999975938968031,
                1.147877359957198e-05,
                0.9999987901338852
            ],
            [
                7.734418542875216e-08,
                7.734418542875216e-08,
                3.4663262111182307e-07,
                2.699577130960941e-07,
                5.715003107767143e-07,
                9.931187406410953e-08,
                1.9947292459347367e-06,
                1.1253508156363576e-07,
                8.315281267882195e-07,
                8.315278294114555e-07
            ],
            [
                3.059022998581767e-07,
                5.715006514176113e-07,
                5.715006514176113e-07,
                1.760343633036322e-06,
                3.4663274507713016e-07,
                3.9278629391427843e-07,
                4.4508499888275247e-07,
                3.466326624336003e-07,
                1.2098659719788098e-06,
                5.043475284468537e-07
            ],
            [
                1.760342793638743e-06,
                6.475947210012481e-07,
                3.2887502415767434e-06,
                3.9278629391427843e-07,
                2.3823696679327928e-07,
                8.315281267882195e-07,
                2.6995784182183607e-07,
                5.043475885696228e-07,
                3.4663274507713016e-07,
                1.2098659719788098e-06
            ],
            [
                8.764245361752286e-08,
                1.1253521571574156e-07,
                0.9999832985821676,
                3.466327450756327e-07,
                2.3823699519290042e-07,
                0.9999964991460056,
                0.9999810748427485,
                1.8553903548231313e-07,
                0.999981074856318,
                1.2751905808881762e-07
            ],
            [
                3.9278629391427843e-07,
                3.927862002663297e-07,
                2.3823696679327928e-07,
                5.04347528446051e-07,
                6.475947210046347e-07,
                6.825602910433871e-08,
                1.1253513522447425e-07,
                2.1024334103581732e-07,
                3.0590237279085045e-07,
                7.338208930460318e-07
            ],
            [
                1.8553914607128047e-07,
                1.855391681898159e-07,
                1.8553905760062447e-07,
                1.2098653950716937e-06,
                2.3823685319244518e-07,
                1.209865683518615e-06,
                1.8553903548231313e-07,
                1.6373766672888118e-07,
                2.102433660979124e-07,
                2.1024331597262577e-07
            ],
            [
                8.315284241665078e-07,
                8.315277302857965e-07,
                6.475950298021765e-07,
                NaN,
                2.3823685319320354e-07,
                9.422449308673789e-07,
                2.1024334103581732e-07,
                3.466326624336003e-07,
                NaN,
                1.3709572068553509e-06
            ],
            [
                1.1253524254650944e-07,
                9.422443692574719e-07,
                8.315284241665078e-07,
                2.561282821402217e-06,
                2.10243290909963e-07,
                3.466325797900508e-07,
                1.9947292459406333e-06,
                3.927861066194751e-07,
                5.043475885696228e-07,
                6.475945666063607e-07
            ],
            [
                9.422442569290178e-07,
                1.3709576971379186e-06,
                8.939695238536645e-06,
                8.315282259089153e-07,
                1.2098662604247682e-06,
                2.5612828213934817e-06,
                4.785096206013061e-06,
                8.939694172957213e-06,
                8.939699501229642e-06,
                2.561281294760143e-06
            ],
            [
                8.31528325040778e-07,
                1.4449795205472734e-07,
                3.927862470905692e-07,
                2.382368815932174e-07,
                4.4508515805735777e-07,
                1.8553910183674878e-07,
                3.466326624336003e-07,
                4.450852641737424e-07,
                2.2603242978943238e-06,
                3.4663274507713016e-07
            ],
            [
                3.927863407379485e-07,
                6.47594952603035e-07,
                1.637376862489725e-07,
                3.05902263391829e-07,
                2.6995784182183607e-07,
                8.315278294114555e-07,
                1.370957860576702e-06,
                3.9278629391427843e-07,
                5.043476486924565e-07,
                1.7603430034867993e-06
            ],
            [
                2.260324836776948e-06,
                1.855391239547094e-07,
                1.209865827752005e-06,
                2.2603248367949354e-06,
                NaN,
                1.067703124601679e-06,
                1.5534983101644536e-06,
                3.927862470899887e-07,
                2.3823693839325527e-07,
                4.450850519403407e-07
            ],
            [
                5.04347468323289e-07,
                5.715007195447234e-07,
                3.927861066170637e-07,
                NaN,
                1.8553916819032217e-07,
                1.3709576971425944e-06,
                7.338209805240734e-07,
                2.1024341622368903e-07,
                2.1024326584639497e-07,
                1.067702870039777e-06
            ],
            [
                5.715006514176113e-07,
                1.760342793638743e-06,
                7.33821330437595e-07,
                5.043475284468537e-07,
                1.7603430034867993e-06,
                1.2098658277451275e-06,
                9.422447062294175e-07,
                1.370957860567974e-06,
                5.715006514176113e-07,
                2.902312331170226e-06
            ],
            [
                2.699578096403948e-07,
                6.825597214718257e-08,
                6.47594875403829e-07,
                3.0590219045914655e-07,
                5.715002426486762e-07,
                2.1024331597288867e-07,
                2.3823690999323465e-07,
                3.466325797900508e-07,
                2.1024336609874897e-07,
                1.637376862489725e-07
            ],
            [
                5.71500515159253e-07,
                4.450852641737424e-07,
                3.0590226339061185e-07,
                2.6995771309523475e-07,
                9.422443692446175e-07,
                3.927862002641863e-07,
                7.338211554783522e-07,
                5.715005832853093e-07,
                3.927860597935108e-07,
                2.6995771309523475e-07
            ],
            [
                0.9999960330136186,
                4.450852111155216e-07,
                2.382370235933104e-07,
                0.9999949062950072,
                1.0677024881980089e-06,
                NaN,
                1.5534979397500702e-06,
                9.422448185510695e-07,
                0.99994170871415,
                0.9999972735297334
            ],
            [
                1.8553910183674878e-07,
                1.1253508156363576e-07,
                1.637376862489725e-07,
                2.1024334103581732e-07,
                4.4508515805735777e-07,
                1.275190428875671e-07,
                9.931195693628605e-08,
                6.82560779249779e-08,
                1.2751902768612997e-07,
                7.734425919002834e-08
            ],
            [
                1.5534979397790343e-06,
                1.994729483694599e-06,
                1.3709568799879344e-06,
                3.466327037553825e-07,
                9.422445939032799e-07,
                1.9947297215043796e-06,
                5.315780536011123e-08,
                1.3709575337159875e-06,
                0.9999949062962185,
                8.939699501416646e-06
            ],
            [
                2.102434412871794e-07,
                3.927863875616689e-07,
                1.855391239544352e-07,
                NaN,
                5.715006514176113e-07,
                1.855391681906175e-07,
                2.1024334103581732e-07,
                1.760343213335281e-06,
                5.043472278322555e-07,
                3.288750633569722e-06
            ],
            [
                2.561281294760143e-06,
                1.3709573702822306e-06,
                NaN,
                7.33821330437595e-07,
                1.1253509497883659e-07,
                2.3823690999290963e-07,
                5.043475885696228e-07,
                8.315283250371857e-07,
                8.315284241665078e-07,
                2.10243290909963e-07
            ],
            [
                2.699578096403948e-07,
                2.1024334103553052e-07,
                8.315277302857965e-07,
                1.1253512180925583e-07,
                4.4508510499849186e-07,
                8.315281267882195e-07,
                2.2603237589779086e-06,
                5.043474683240344e-07,
                2.3823690999290963e-07,
                1.4449798650551755e-07
            ],
            [
                1.2098659719757836e-06,
                2.102433159721477e-07,
                2.102433660979124e-07,
                1.1253513522447425e-07,
                2.3823685319244518e-07,
                1.2751899728286965e-07,
                1.2751905808881762e-07,
                2.382369667929001e-07,
                2.2603253756956754e-06,
                6.825608606148807e-08
            ],
            [
                1.4449798650551755e-07,
                1.1253506814842375e-07,
                9.931186222523604e-08,
                5.715006514176113e-07,
                7.734416698849138e-08,
                3.4663262111182307e-07,
                6.82560779249779e-08,
                7.73442776303243e-08,
                8.764245361752286e-08,
                6.023568448589658e-08
            ],
            [
                8.764247451307293e-08,
                1.209866260434534e-06,
                NaN,
                2.3823690999323465e-07,
                2.699578096403948e-07,
                1.0677027427624903e-06,
                1.5534983101644536e-06,
                9.422443692574719e-07,
                8.764254764749753e-08,
                2.9023116392097746e-06
            ],
            [
                5.71500719545698e-07,
                7.338207180898968e-07,
                3.927863407379485e-07,
                5.71500719545698e-07,
                1.855391681906175e-07,
                5.3157830707696514e-08,
                9.931193325852072e-08,
                5.043475885696228e-07,
                4.450851049991497e-07,
                2.699578096403948e-07
            ],
            [
                1.3709575337159875e-06,
                1.3709576971425944e-06,
                4.450850519403407e-07,
                5.422219616265831e-06,
                3.466327863983311e-07,
                5.715003107767143e-07,
                3.9278610661902853e-07,
                5.043473480777865e-07,
                9.931190958076104e-08,
                6.475949526020042e-07
            ],
            [
                5.043476486924565e-07,
                1.637376862489725e-07,
                1.8553919030858602e-07,
                6.47594952603035e-07,
                5.715003789046955e-07,
                8.315277302857965e-07,
                2.6995790618469934e-07,
                4.450852111155216e-07,
                3.05902336324494e-07,
                7.33821330437595e-07
            ],
            [
                4.4508494582405734e-07,
                1.6373762769138607e-07,
                3.0590215399183813e-07,
                1.2751902768478173e-07,
                1.0677029973219343e-06,
                3.9278610661902853e-07,
                1.994729721518893e-06,
                3.05902190458764e-07,
                5.715003107767143e-07,
                3.9278605979534166e-07
            ],
            [
                8.315278294114555e-07,
                6.475949526020042e-07,
                6.144176066901277e-06,
                2.699577774585891e-07,
                1.275190580890061e-07,
                2.3823693839290317e-07,
                5.043474081993875e-07,
                6.475947982037486e-07,
                6.475949526020042e-07,
                3.0590237279085045e-07
            ],
            [
                0.9999985406232583,
                0.9999969105051885,
                0.9999970976890591,
                0.9999991684715764,
                2.699578096393206e-07,
                0.999999114843281,
                0.9999151889225207,
                0.9999982396565792,
                0.9999989969856737,
                0.999998126124842
            ],
            [
                6.825609419848033e-08,
                1.3709572068478697e-06,
                2.9023133690980155e-06,
                NaN,
                6.475950298011458e-07,
                2.699578740032504e-07,
                3.0590215398829087e-07,
                4.450849458200093e-07,
                2.3823690999063455e-07,
                3.9278634073312583e-07
            ],
            [
                3.288747889284851e-06,
                1.7603430034867993e-06,
                2.902312331170226e-06,
                1.7603425837903113e-06,
                1.2098661161982042e-06,
                2.9023119851899796e-06,
                9.422450432014836e-07,
                1.3709575337159875e-06,
                8.315280276626197e-07,
                1.370957860576702e-06
            ],
            [
                2.382368531929327e-07,
                8.764249540862797e-08,
                5.043475284468537e-07,
                5.715005832895975e-07,
                1.3709572068553509e-06,
                2.382368815932174e-07,
                2.1024339116168358e-07,
                6.962257909842961e-06,
                6.144172404738491e-06,
                NaN
            ],
            [
                1.3709572068522336e-06,
                1.3709568799879344e-06,
                1.3709567165579959e-06,
                1.1478769494542698e-05,
                7.338211554783522e-07,
                9.4224425692559e-07,
                5.043472879540142e-07,
                1.3709567165617364e-06,
                2.260324836787226e-06,
                3.466327037539638e-07
            ],
            [
                1.6373762769138607e-07,
                1.2751904288710323e-07,
                2.102434412875379e-07,
                2.102434412871794e-07,
                9.931187406410953e-08,
                2.102434412871794e-07,
                2.8453333712602254e-08,
                2.1024344128660572e-07,
                2.382369951932796e-07,
                1.2751904288710323e-07
            ],
            [
                9.422443692574719e-07,
                6.962258739796719e-06,
                7.33821330437595e-07,
                4.450852641737424e-07,
                9.422448185534261e-07,
                3.927863407379485e-07,
                6.475947982037486e-07,
                2.5612828213934817e-06,
                9.422445939054222e-07,
                1.2098661162056318e-06
            ],
            [
                1.855390576008354e-07,
                2.1024331597288867e-07,
                2.3823690999323465e-07,
                1.27519088491875e-07,
                5.043475885696228e-07,
                1.8553910183674878e-07,
                2.1024331597288867e-07,
                2.1024331597288867e-07,
                2.1024326584702836e-07,
                7.338211554813555e-07
            ],
            [
                4.691167716359673e-08,
                9.931189774187203e-08,
                3.466325384678894e-07,
                1.067702870039777e-06,
                4.4508510499849186e-07,
                1.4449803818215767e-07,
                2.2603253756874524e-06,
                5.04347468323289e-07,
                5.715004470326849e-07,
                4.785092783454444e-06
            ],
            [
                0.9999925887166301,
                1.0677024881980089e-06,
                2.5612834320470717e-06,
                0.9999869928700289,
                2.102434162245973e-07,
                1.8553916819032217e-07,
                1.7603438428800754e-06,
                2.5612831267202583e-06,
                1.4449798650551755e-07,
                2.1444953527944967e-05
            ],
            [
                4.53978632394714e-05,
                8.939693107190907e-06,
                5.043474081993875e-07,
                3.726638395611981e-06,
                6.1441746020359e-06,
                4.539789029616496e-05,
                5.4222209089700225e-06,
                1.7603427936335396e-06,
                2.5612819054028872e-06,
                5.043476486915964e-07
            ],
            [
                0.9999962733598321,
                2.9023119851899796e-06,
                4.222834451403972e-06,
                9.422447062294175e-07,
                1.7603430034867993e-06,
                1.3709567165617364e-06,
                0.9999984465018764,
                0.9999955048178925,
                1.2098659719788098e-06,
                0.9999980052693287
            ],
            [
                1.5534979397592542e-06,
                1.3709570434054234e-06,
                0.9999916019299928,
                0.9999892166865332,
                0.9999843104446996,
                0.9999916019309825,
                1.2098653950551882e-06,
                1.3709576970949014e-06,
                0.9999756997535193,
                0.9999910603069168
            ],
            [
                9.422443692574719e-07,
                1.994729008151319e-06,
                1.4449807263312446e-07,
                4.450852111155216e-07,
                6.47595107001401e-07,
                1.5534984953552536e-06,
                1.3709576971463352e-06,
                9.422443692574719e-07,
                5.715006514176113e-07,
                4.450852111155216e-07
            ],
            [
                6.825601283086733e-08,
                1.209865827752005e-06,
                9.422443692574719e-07,
                2.561281294760143e-06,
                4.450850519409479e-07,
                8.315284241665078e-07,
                1.8553910183674878e-07,
                1.0677029973219343e-06,
                NaN,
                5.71500719545698e-07
            ],
            [
                6.475947210046347e-07,
                3.466325797896173e-07,
                9.931186222523604e-08,
                1.5534975693979422e-06,
                8.315277302857965e-07,
                4.450848927658745e-07,
                7.338209805240734e-07,
                2.1024331597262577e-07,
                1.3709575337159875e-06,
                3.4663278639892215e-07
            ],
            [
                3.927862002663297e-07,
                0.9999987901347495,
                0.9999934595612272,
                0.9999960330155068,
                0.9999978766222987,
                0.9999985406243018,
                0.9999869928762359,
                0.9999993106387082,
                3.9278605979534166e-07,
                0.9999869928715723
            ],
            [
                1.4449798650551755e-07,
                6.144175334468545e-06,
                2.3823688159291947e-07,
                8.939693107288474e-06,
                1.8553910183674878e-07,
                1.8553914607267268e-07,
                0.9999988634360194,
                2.699578096403948e-07,
                1.8553910183674878e-07,
                0.9999974387184015
            ],
            [
                7.338209805224048e-07,
                3.0590226339061185e-07,
                6.962255419931625e-06,
                2.6995771309523475e-07,
                4.785095635655362e-06,
                2.1444948414321717e-05,
                4.785095635655362e-06,
                9.422445939032799e-07,
                2.1444953527944967e-05,
                1.1478764021029928e-05
            ],
            [
                3.288749065423109e-06,
                1.2751901248454963e-07,
                7.889265407327733e-06,
                1.8553910183548312e-07,
                3.4663249714612693e-07,
                1.8553910183607374e-07,
                9.931190958076104e-08,
                5.422220909041528e-06,
                4.450852111155216e-07,
                9.931190958076104e-08
            ],
            [
                3.059022269254856e-07,
                1.2751908849167202e-07,
                2.3823693839154895e-07,
                5.04347287955046e-07,
                5.715002426460124e-07,
                8.315283250394546e-07,
                2.3823693839325527e-07,
                4.4508515805735777e-07,
                NaN,
                1.1478772231232203e-05
            ],
            [
                5.715006514176113e-07,
                3.466326624336003e-07,
                4.4508515805735777e-07,
                5.715005832895975e-07,
                8.764254764780641e-08,
                7.338211554813555e-07,
                1.3709575337159875e-06,
                2.699578740032504e-07,
                9.422442569334097e-07,
                5.715006514176113e-07
            ],
            [
                1.0677027427624903e-06,
                4.4508515805735777e-07,
                1.27519088491875e-07,
                6.47595107001401e-07,
                1.994729483723626e-06,
                7.338208055680009e-07,
                7.33821330437595e-07,
                8.31528325040778e-07,
                2.561281294760143e-06,
                6.475950298021765e-07
            ],
            [
                0.9999822214397008,
                5.71500719545698e-07,
                4.4508510499849186e-07,
                3.9278629391427843e-07,
                1.4449800373118268e-07,
                0.999978555046523,
                4.450851049991497e-07,
                3.927863407379485e-07,
                3.466326624336003e-07,
                2.10243290909724e-07
            ],
            [
                1.0677027427624903e-06,
                6.023569166654288e-08,
                5.71500515161527e-07,
                1.6373766672994222e-07,
                2.3823690999323465e-07,
                8.31528325040778e-07,
                1.0677028700422047e-06,
                2.1024331597288867e-07,
                3.9278620026686556e-07,
                2.561282516066741e-06
            ],
            [
                1.637377057680051e-07,
                1.1253521571603583e-07,
                2.2603251062450327e-06,
                1.8553910183674878e-07,
                4.4508499888275247e-07,
                2.699578740032504e-07,
                3.927862470905692e-07,
                2.699577130960941e-07,
                8.315280276626197e-07,
                3.466327037553825e-07
            ],
            [
                0.9999945777816823,
                0.9999921107336633,
                1.0677027427624903e-06,
                0.9999969105051879,
                0.9999967112513288,
                0.999995214907222,
                0.999999114843281,
                5.043475284468537e-07,
                0.9999960330140898,
                0.9999974387171808
            ],
            [
                5.04347468323289e-07,
                4.450849988811838e-07,
                5.043476486915964e-07,
                2.3823690999290963e-07,
                4.450851580566494e-07,
                7.338210680002898e-07,
                6.475951069985296e-07,
                7.338211554725124e-07,
                4.450849988780466e-07,
                7.338211554801876e-07
            ],
            [
                9.4224425692559e-07,
                9.422448185478557e-07,
                6.475949525981759e-07,
                1.994730197071414e-06,
                1.7603432133136672e-06,
                9.422443692489024e-07,
                NaN,
                1.994730434879465e-06,
                1.99472924590571e-06,
                5.043472278322555e-07
            ],
            [
                5.043474082012222e-07,
                1.0677026154806063e-06,
                2.9023123311583482e-06,
                NaN,
                1.8553907971855875e-07,
                4.4508515805735777e-07,
                3.726638395611981e-06,
                1.3709572068553509e-06,
                1.9947297215125433e-06,
                1.1253526937697666e-07
            ],
            [
                3.4663274507713016e-07,
                1.8553919030858602e-07,
                1.0677029973219343e-06,
                3.2887506336235617e-06,
                2.9023119851899796e-06,
                3.4663274507713016e-07,
                2.10243290909724e-07,
                1.6373770576776313e-07,
                9.422443692574719e-07,
                4.4508515805735777e-07
            ],
            [
                1.637377448057981e-07,
                3.0590215399183813e-07,
                1.5534973842076057e-06,
                2.3823693839325527e-07,
                3.4663274507713016e-07,
                3.466327037548308e-07,
                0.5621765008857981,
                1.637377057680051e-07,
                1.209865827752005e-06,
                9.931193325852072e-08
            ],
            [
                3.05902263391829e-07,
                2.699578096403948e-07,
                2.1024331597288867e-07,
                1.2751901248454963e-07,
                5.715006514176113e-07,
                6.023569884718319e-08,
                3.9278620026686556e-07,
                3.927862470905692e-07,
                1.4449798650569826e-07,
                5.3157900413760374e-08
            ],
            [
                4.785095635655362e-06,
                3.288747889284851e-06,
                2.260324836787226e-06,
                1.3709572068522336e-06,
                1.0129989772532511e-05,
                1.9947299593014888e-06,
                8.315282259051341e-07,
                1.067702870039777e-06,
                2.2603242978665707e-06,
                5.043473480777865e-07
            ],
            [
                1.637377448057981e-07,
                1.0677029973219343e-06,
                2.3823696679327928e-07,
                1.6373764721072816e-07,
                2.3823696679327928e-07,
                3.2887478892683997e-06,
                6.47595107001401e-07,
                4.450852641737424e-07,
                2.699576809143613e-07,
                5.043474081993875e-07
            ],
            [
                3.059022269254856e-07,
                1.4449798650569826e-07,
                3.0590219045914655e-07,
                1.6373774480605869e-07,
                5.3157900413760374e-08,
                1.2751902768612997e-07,
                2.5612834320563895e-06,
                1.8553907971879076e-07,
                4.450850519409479e-07,
                5.043474683240344e-07
            ],
            [
                8.315284241650899e-07,
                3.0590215399246414e-07,
                1.0677032518700286e-06,
                1.8553914607267268e-07,
                1.3709572068272963e-06,
                3.0590226339137693e-07,
                7.338213304363436e-07,
                2.3823682479292225e-07,
                3.4663266243308805e-07,
                1.760344052693435e-06
            ],
            [
                9.931185038635267e-08,
                5.043475885696228e-07,
                1.6373764721091427e-07,
                2.3823690999323465e-07,
                5.715005832895975e-07,
                1.1253525596174225e-07,
                6.475947982037486e-07,
                3.4663249714612693e-07,
                1.637377057680051e-07,
                2.6995784182183607e-07
            ],
            [
                3.9278605979534166e-07,
                1.2098656835252174e-06,
                2.3823696679327928e-07,
                1.6373774480605869e-07,
                4.4508515805735777e-07,
                0.9999810748564042,
                2.3823690999323465e-07,
                3.927863407379485e-07,
                5.043475284468537e-07,
                2.699577452775239e-07
            ],
            [
                9.931196877456114e-08,
                7.338209805240734e-07,
                1.7603425837903113e-06,
                4.450852111155216e-07,
                3.059021175261338e-07,
                5.715005832895975e-07,
                2.3823685319320354e-07,
                1.3709573702856596e-06,
                3.059022998581767e-07,
                3.05902336324494e-07
            ],
            [
                NaN,
                1.3709573702856596e-06,
                4.450850519409479e-07,
                2.3823690999323465e-07,
                2.382369951932796e-07,
                2.5612834320563895e-06,
                3.0590219045914655e-07,
                8.315277302857965e-07,
                5.043473480777865e-07,
                7.338209805240734e-07
            ],
            [
                1.6373766672994222e-07,
                1.760342793638743e-06,
                1.7603438428800754e-06,
                1.5534973842076057e-06,
                1.4449798650569826e-07,
                4.450850519409479e-07,
                1.5534984953552536e-06,
                4.450851049991497e-07,
                3.9278629391427843e-07,
                5.715003789033962e-07
            ],
            [
                5.3157830707696514e-08,
                8.7642558095602e-08,
                2.902312331170226e-06,
                1.209865827752005e-06,
                3.7266401726359486e-06,
                5.71500515161527e-07,
                3.72663883989755e-06,
                7.73441946488886e-08,
                9.931190958076104e-08,
                3.927863407379485e-07
            ],
            [
                0.9999964991460052,
                0.9999983463108095,
                6.47595107001401e-07,
                0.9999980052695665,
                0.9999982396561582,
                4.222834451403972e-06,
                7.73442776300517e-08,
                0.9999977396759733,
                3.726639284144195e-06,
                0.9999952149032301
            ],
            [
                4.4508515805735777e-07,
                1.2098653950716937e-06,
                1.760343633036322e-06,
                4.450851580566494e-07,
                7.338207180898968e-07,
                6.475945666063607e-07,
                5.043476486924565e-07,
                8.7642516304188e-08,
                2.6995784182183607e-07,
                7.338211554813555e-07
            ],
            [
                4.450849458200093e-07,
                3.466326211113502e-07,
                5.715003788993679e-07,
                4.450849458218309e-07,
                5.043475284468537e-07,
                9.42244256915735e-07,
                1.3709573702822306e-06,
                2.382368815932174e-07,
                6.475945666033422e-07,
                1.0677032518814388e-06
            ],
            [
                1.0677032518814388e-06,
                6.825609419848033e-08,
                5.043472278299047e-07,
                6.475945666009864e-07,
                7.338211554725124e-07,
                6.475948753991907e-07,
                3.927862002663297e-07,
                1.3709567165617364e-06,
                8.315278294097538e-07,
                5.04347528438253e-07
            ],
            [
                3.0590226339061185e-07,
                2.382369383923073e-07,
                1.7603436330179102e-06,
                2.6995771309523475e-07,
                3.9278615344178325e-07,
                5.715004470313855e-07,
                5.715005151606823e-07,
                9.422448185478557e-07,
                5.043472879525233e-07,
                2.90231094723893e-06
            ],
            [
                1.2098659719788098e-06,
                7.338207180864763e-07,
                3.4663266243308805e-07,
                1.0677027427600627e-06,
                8.315278294114555e-07,
                8.939694172957213e-06,
                2.5612834320563895e-06,
                1.3709567165617364e-06,
                1.2098658277489788e-06,
                5.715003107767143e-07
            ]
        ]
    },
    {
        "q_id": "9327_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            6,
            8,
            11,
            12,
            14,
            15,
            16,
            17,
            18,
            20,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            35,
            36,
            37,
            39,
            41,
            43,
            44,
            46,
            49,
            50,
            51,
            52,
            53,
            55,
            57,
            58,
            59,
            62,
            63,
            66,
            69,
            70,
            73,
            74,
            76,
            77,
            78,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            93,
            94,
            97,
            98,
            99,
            101,
            104,
            105,
            106,
            107,
            108,
            109,
            113,
            114,
            118,
            119,
            120,
            122,
            123
        ],
        "rewards": [
            [
                1.5534973841450852e-06,
                2.2603251062013478e-06,
                1.2098662604291696e-06,
                1.9947292458930106e-06,
                2.902312677137316e-06,
                9.422442569290178e-07,
                1.0677024881829577e-06,
                1.0677032518316716e-06,
                1.7603425837702984e-06,
                1.7603436330091044e-06
            ],
            [
                9.931186222523604e-08,
                6.825598028392069e-08,
                5.315781803390236e-08,
                7.734415776836702e-08,
                1.27519088491875e-07,
                1.8553907971855875e-07,
                1.1253506814842375e-07,
                1.4449807263312446e-07,
                6.825598842065202e-08,
                8.764241182641775e-08
            ],
            [
                7.338207180898968e-07,
                3.9278634073732336e-07,
                5.043472278322555e-07,
                2.1024334103581732e-07,
                1.275191036933194e-07,
                5.715003107767143e-07,
                2.3823696679327928e-07,
                2.3823696679327928e-07,
                2.6995784182183607e-07,
                2.699578740032504e-07
            ],
            [
                4.450848927658745e-07,
                9.422447062270609e-07,
                7.338209805200689e-07,
                5.715007195447234e-07,
                3.466325797896173e-07,
                2.69957906184239e-07,
                7.338208055664991e-07,
                2.382368247924618e-07,
                5.043475885674441e-07,
                1.7603434231705793e-06
            ],
            [
                2.6995771309523475e-07,
                3.9278634073732336e-07,
                3.0590237279032884e-07,
                3.9278634073732336e-07,
                4.450852111155216e-07,
                5.04347287955046e-07,
                2.3823685319244518e-07,
                6.475949526020042e-07,
                3.4663266243308805e-07,
                2.6995774527657245e-07
            ],
            [
                1.444979692800516e-07,
                1.6373764721072816e-07,
                3.0590237279032884e-07,
                9.931193325852072e-08,
                3.9278634073732336e-07,
                3.927862002663297e-07,
                8.7642516304188e-08,
                3.927862002663297e-07,
                8.76424013786396e-08,
                1.6373764721072816e-07
            ],
            [
                2.902312677150514e-06,
                1.3709568799919866e-06,
                7.484626297687326e-05,
                1.7603434231833873e-06,
                2.9023116391978967e-06,
                6.475945666033422e-07,
                3.466325797896173e-07,
                2.5612816000646084e-06,
                2.561282210740037e-06,
                3.535624650021832e-05
            ],
            [
                6.475947210046347e-07,
                4.450848927650143e-07,
                3.059022269250683e-07,
                3.059021175261338e-07,
                4.785096776468749e-06,
                1.5534981249697903e-06,
                1.5534983101602148e-06,
                8.315284241650899e-07,
                7.338208055664991e-07,
                6.475949526020042e-07
            ],
            [
                1.5534977545886537e-06,
                2.2603253756956754e-06,
                6.962259569750576e-06,
                3.72663883989755e-06,
                1.5534977545886537e-06,
                9.422447062294175e-07,
                6.962259569750576e-06,
                1.994729483729522e-06,
                2.260324567337161e-06,
                9.422445939054222e-07
            ],
            [
                1.0677032518785256e-06,
                5.715006514151423e-07,
                1.2098653950656417e-06,
                1.3709572068422585e-06,
                3.4663257978780455e-07,
                1.2098653950656417e-06,
                7.338209805224048e-07,
                1.0677028700363782e-06,
                9.422444815765128e-07,
                9.422442569315887e-07
            ],
            [
                7.734415776836702e-08,
                1.5534983101602148e-06,
                1.6373776432509826e-07,
                5.3157900413760374e-08,
                1.9947297214944016e-06,
                6.023568448589658e-08,
                9.931186222523604e-08,
                7.734418542875216e-08,
                1.0677029973158649e-06,
                7.734414854823498e-08
            ],
            [
                9.931187406410953e-08,
                9.931189774187203e-08,
                5.315789407685159e-08,
                4.139936066832438e-08,
                5.3157830707696514e-08,
                9.931186222523604e-08,
                5.315781803390236e-08,
                6.825598842065202e-08,
                4.691160446380562e-08,
                5.315780536011123e-08
            ],
            [
                2.1024336609843824e-07,
                2.699576809143613e-07,
                1.7603430034867993e-06,
                1.4449798650551755e-07,
                2.69957906184239e-07,
                9.931195693628605e-08,
                2.699577774585891e-07,
                1.8553919030858602e-07,
                1.4449798650551755e-07,
                1.6373770576776313e-07
            ],
            [
                6.475948754012522e-07,
                1.7603440527286572e-06,
                1.0677024881980089e-06,
                1.5534981249697903e-06,
                2.699577774585891e-07,
                8.315282259138311e-07,
                1.2098656835224664e-06,
                1.5534977545886537e-06,
                9.422444815814404e-07,
                5.043474081993875e-07
            ],
            [
                4.2228339479858295e-06,
                4.785093353940187e-06,
                2.260325106237323e-06,
                4.222831934379152e-06,
                2.4300234941261454e-05,
                1.7603427936263351e-06,
                4.222832941193893e-06,
                4.785093924330255e-06,
                2.260325106237323e-06,
                3.288748673360027e-06
            ],
            [
                2.5612828213934817e-06,
                1.5534975693933505e-06,
                8.315278294072958e-07,
                1.7603434231705793e-06,
                1.7603425837791042e-06,
                1.0677032518748838e-06,
                5.04347528440776e-07,
                2.5612812947508257e-06,
                7.338210679979539e-07,
                5.715003107755449e-07
            ],
            [
                5.715005151606823e-07,
                5.04347528446051e-07,
                3.9278615344178325e-07,
                5.043476486915964e-07,
                6.475948754012522e-07,
                1.0677026154806063e-06,
                1.0677027427600627e-06,
                5.715003107755449e-07,
                7.338210680021253e-07,
                4.450852111148132e-07
            ],
            [
                2.2603242978871282e-06,
                1.994729483729522e-06,
                5.422217677152175e-06,
                8.939693107288474e-06,
                7.338209805240734e-07,
                1.9947304348862686e-06,
                1.0677029973219343e-06,
                2.2603234895372223e-06,
                6.475947210046347e-07,
                3.288749849529972e-06
            ],
            [
                1.2098652508424818e-06,
                1.6373764721072816e-07,
                3.4663274507713016e-07,
                5.043475885696228e-07,
                6.962253760024999e-06,
                7.338211554813555e-07,
                5.043472278322555e-07,
                6.475947210046347e-07,
                1.0677029973219343e-06,
                2.2603253756956754e-06
            ],
            [
                8.315280276546789e-07,
                1.9947299593014888e-06,
                1.0677026154730804e-06,
                1.7603438428740716e-06,
                1.209865539295696e-06,
                6.475950298011458e-07,
                7.338209805200689e-07,
                8.315283250371857e-07,
                7.338208930391909e-07,
                1.3709567165530083e-06
            ],
            [
                5.715004470313855e-07,
                5.715006514167015e-07,
                1.3709567165617364e-06,
                2.699578096393206e-07,
                9.422444815814404e-07,
                1.8553903548231313e-07,
                4.4508494582405734e-07,
                7.338209805224048e-07,
                7.338210680021253e-07,
                5.715005832886879e-07
            ],
            [
                4.450848927658745e-07,
                3.927862002663297e-07,
                2.3823702359290413e-07,
                4.4508494582405734e-07,
                6.475951069985296e-07,
                1.8553916819032217e-07,
                2.3823696679230424e-07,
                1.6373762769138607e-07,
                3.0590215399183813e-07,
                2.699578096393206e-07
            ],
            [
                3.466327037553825e-07,
                2.10243290909724e-07,
                1.4449807263312446e-07,
                1.6373766672973748e-07,
                3.726639728370556e-06,
                7.338208055680009e-07,
                1.855391681906175e-07,
                3.927862002663297e-07,
                3.059021175261338e-07,
                1.0129987357407137e-05
            ],
            [
                1.6373776432509826e-07,
                7.73441946488886e-08,
                1.6373770576776313e-07,
                5.3157811697009444e-08,
                1.4449798650551755e-07,
                1.8553919030826963e-07,
                1.4449795205429202e-07,
                4.691161005609407e-08,
                7.73442776303243e-08,
                1.4449803818215767e-07
            ],
            [
                3.653481209178873e-08,
                4.691161005609407e-08,
                4.691167157146029e-08,
                7.734428685047173e-08,
                5.3157811697009444e-08,
                6.825600469412533e-08,
                5.3157837044597743e-08,
                4.691162124067829e-08,
                4.139935079796334e-08,
                1.1253509497883659e-07
            ],
            [
                2.3823702359290413e-07,
                1.0677032518814388e-06,
                5.715006514167015e-07,
                1.9947299593078385e-06,
                1.3709575337159875e-06,
                3.927863875616689e-07,
                1.7603430034867993e-06,
                1.8553905760062447e-07,
                5.043473480777865e-07,
                5.715002426486762e-07
            ],
            [
                5.043474683204221e-07,
                3.9278615344178325e-07,
                6.475951069985296e-07,
                2.382370235922541e-07,
                8.315281267861397e-07,
                3.059021904571643e-07,
                2.382368815916736e-07,
                3.059023727894942e-07,
                3.466327037539638e-07,
                5.715003789017068e-07
            ],
            [
                8.315282259138311e-07,
                7.338209805240734e-07,
                8.315281267882195e-07,
                1.0677026154806063e-06,
                1.0677033791612137e-06,
                3.059022269250683e-07,
                6.475946438055299e-07,
                2.2603234895372223e-06,
                9.422447062294175e-07,
                2.6995774527718623e-07
            ],
            [
                2.102434412875379e-07,
                2.699577774585891e-07,
                3.9278634073732336e-07,
                3.466326211113502e-07,
                2.382369667929001e-07,
                5.715007195447234e-07,
                2.382369667929001e-07,
                2.699576809143613e-07,
                3.4663278639892215e-07,
                2.3823682479292225e-07
            ],
            [
                1.855391681898159e-07,
                2.69957906184239e-07,
                2.1024331597262577e-07,
                1.6373776432509826e-07,
                1.8553905760062447e-07,
                1.855391239544352e-07,
                1.855391681906175e-07,
                1.1253508156363576e-07,
                7.734416698849138e-08,
                1.8553903548231313e-07
            ],
            [
                9.931187406410953e-08,
                1.6373772528704005e-07,
                4.4508515805735777e-07,
                3.4663274507713016e-07,
                2.699576809143613e-07,
                5.71500719545698e-07,
                6.475947982037486e-07,
                5.715003107767143e-07,
                9.422444815814404e-07,
                5.715002426486762e-07
            ],
            [
                8.764249540862797e-08,
                1.1253513522447425e-07,
                2.102434162245973e-07,
                9.931195693628605e-08,
                6.825606165129312e-08,
                1.1253521571574156e-07,
                4.691160446380562e-08,
                1.1253509497883659e-07,
                7.734416698849138e-08,
                1.4449800373118268e-07
            ],
            [
                9.931195693628605e-08,
                5.3157830707696514e-08,
                1.637377057680051e-07,
                1.855391681906175e-07,
                1.4449807263312446e-07,
                1.637377448057981e-07,
                1.444979692800516e-07,
                1.2751905808881762e-07,
                2.10243290909724e-07,
                1.6373776432509826e-07
            ],
            [
                1.2098661161927025e-06,
                9.422450432014836e-07,
                7.338210680021253e-07,
                6.475950298011458e-07,
                5.043472879525233e-07,
                7.338209805224048e-07,
                4.450849988811838e-07,
                8.315283250371857e-07,
                1.0677029973192638e-06,
                5.04347468323289e-07
            ],
            [
                3.059023727894942e-07,
                5.715005832827105e-07,
                1.067703124601679e-06,
                2.69957906184239e-07,
                3.927860597935108e-07,
                5.043472879540142e-07,
                3.0590237279085045e-07,
                7.338213304363436e-07,
                6.475947210012481e-07,
                8.315281267882195e-07
            ],
            [
                1.6373766672973748e-07,
                7.338209805240734e-07,
                8.315284241650899e-07,
                9.422443692555439e-07,
                1.5534971990169383e-06,
                3.4663266243308805e-07,
                5.04347287955046e-07,
                5.715003789033962e-07,
                5.04347468323289e-07,
                7.338207180898968e-07
            ],
            [
                7.734416698849138e-08,
                1.637377448057981e-07,
                8.764245361752286e-08,
                6.023569166654288e-08,
                1.275190732904469e-07,
                7.734416698849138e-08,
                9.931190958076104e-08,
                7.734423152941018e-08,
                7.734415776836702e-08,
                6.023572038912295e-08
            ],
            [
                1.209866260432471e-06,
                2.699576809143613e-07,
                1.1253521571574156e-07,
                8.764249540862797e-08,
                1.8553905760062447e-07,
                2.3823685319244518e-07,
                2.382368531929327e-07,
                3.05902190458764e-07,
                1.6373764721072816e-07,
                3.0590237279085045e-07
            ],
            [
                3.726641061058432e-06,
                8.315278294072958e-07,
                1.3709570434178922e-06,
                7.338209805224048e-07,
                1.4738980214843206e-05,
                1.9947301970813926e-06,
                3.7266406168624155e-06,
                1.5534984953453635e-06,
                1.2098656835224664e-06,
                1.7603427936263351e-06
            ],
            [
                4.450852111135988e-07,
                2.382369667929001e-07,
                1.0677029973192638e-06,
                1.8553916819032217e-07,
                8.315282259138311e-07,
                4.450849988811838e-07,
                6.475950298011458e-07,
                5.043472879540142e-07,
                2.1024331597262577e-07,
                5.043475885674441e-07
            ],
            [
                5.3157830707696514e-08,
                8.764245361752286e-08,
                1.637377448057981e-07,
                3.2241839428313264e-08,
                1.275190580890061e-07,
                4.139936066832438e-08,
                5.315781803390236e-08,
                9.931189774187203e-08,
                4.139941495546278e-08,
                5.315781803390236e-08
            ],
            [
                5.715007195447234e-07,
                2.1024334103505245e-07,
                0.9999938558239557,
                2.2603253756874524e-06,
                8.31527928532683e-07,
                3.726638395634011e-06,
                5.422220262636381e-06,
                2.9023119851781017e-06,
                2.3823699519290042e-07,
                1.209865539295696e-06
            ],
            [
                5.715007195447234e-07,
                7.338208930391909e-07,
                3.0590226339061185e-07,
                6.475947210031623e-07,
                2.1024326584639497e-07,
                5.043474081993875e-07,
                2.260324567337161e-06,
                3.46632497145457e-07,
                5.043474683204221e-07,
                3.927860597935108e-07
            ],
            [
                1.8553916819032217e-07,
                1.4449805540740185e-07,
                2.1024334103505245e-07,
                1.4449803818107344e-07,
                1.1253516205489029e-07,
                1.637377057680051e-07,
                3.927862470899887e-07,
                9.931195693628605e-08,
                1.8553919030776337e-07,
                8.7642516304188e-08
            ],
            [
                4.4508494582405734e-07,
                2.102434412875379e-07,
                9.422442569315887e-07,
                1.6373766672973748e-07,
                3.05902190458764e-07,
                4.450848927650143e-07,
                1.855391239544352e-07,
                1.637377448057981e-07,
                6.475949526020042e-07,
                5.71500719545698e-07
            ],
            [
                2.382368815916736e-07,
                4.450849988811838e-07,
                6.475947982037486e-07,
                8.315277302841894e-07,
                5.043473480777865e-07,
                1.855391681891831e-07,
                3.059022269250683e-07,
                4.450850519403407e-07,
                3.927862939126708e-07,
                3.05902190458764e-07
            ],
            [
                3.927862470899887e-07,
                1.2751902768612997e-07,
                3.059022269250683e-07,
                4.4508505193932864e-07,
                3.9278634073625165e-07,
                3.466327450765785e-07,
                2.699578096393206e-07,
                3.05902190458764e-07,
                2.1024334103553052e-07,
                3.059022269250683e-07
            ],
            [
                2.382369951932796e-07,
                9.931186222523604e-08,
                1.4449803818215767e-07,
                5.715003107767143e-07,
                1.4449800373118268e-07,
                2.3823696679327928e-07,
                1.4449807263312446e-07,
                3.927863875616689e-07,
                1.6373774480605869e-07,
                3.9278629391427843e-07
            ],
            [
                9.931190958076104e-08,
                2.3823688159291947e-07,
                6.825601283086733e-08,
                1.6373766672973748e-07,
                8.764247451307293e-08,
                3.059021175261338e-07,
                1.4449798650551755e-07,
                1.4449805540700758e-07,
                1.8553919030858602e-07,
                2.102434162245973e-07
            ],
            [
                5.043473480777865e-07,
                5.715003107767143e-07,
                3.466326211113502e-07,
                5.04347468323289e-07,
                7.338208930460318e-07,
                3.46632497145457e-07,
                3.46632497145457e-07,
                3.05902190458764e-07,
                3.466325797888292e-07,
                2.6995784182183607e-07
            ],
            [
                2.699578096403948e-07,
                2.699577774585891e-07,
                2.699576809143613e-07,
                3.9278629391427843e-07,
                2.3823688159237777e-07,
                5.043476486915964e-07,
                8.764242227418718e-08,
                5.715006514176113e-07,
                3.05902263391829e-07,
                1.6373770576776313e-07
            ],
            [
                4.450848927650143e-07,
                1.3709567165617364e-06,
                1.5534981249697903e-06,
                3.927862470899887e-07,
                5.715003789033962e-07,
                7.338211554783522e-07,
                6.475947210031623e-07,
                3.927862002663297e-07,
                3.927862002663297e-07,
                7.338207180864763e-07
            ],
            [
                3.726638839878908e-06,
                3.2887506336086064e-06,
                1.6701421845057263e-05,
                1.209866260432471e-06,
                2.4300232043987867e-05,
                1.7603438428800754e-06,
                1.4738989000422955e-05,
                8.939697369980456e-06,
                1.8925143729575624e-05,
                1.2098661162056318e-06
            ],
            [
                9.931189774187203e-08,
                2.1024331597262577e-07,
                1.1253509497883659e-07,
                9.931189774187203e-08,
                9.931195693628605e-08,
                1.1253513522447425e-07,
                2.382370235933104e-07,
                1.4449798650551755e-07,
                2.1024326584639497e-07,
                1.4449798650551755e-07
            ],
            [
                2.561282210729555e-06,
                1.0129994602895546e-05,
                1.0677028700363782e-06,
                1.9947294837154625e-06,
                4.785093353909723e-06,
                5.4222176771176554e-06,
                4.222834451382849e-06,
                1.5534971990126997e-06,
                1.9947299593014888e-06,
                2.561283432035425e-06
            ],
            [
                5.04347468323289e-07,
                5.04347468323289e-07,
                3.0590237279032884e-07,
                6.475950298021765e-07,
                4.450848927658745e-07,
                4.4508510499849186e-07,
                6.475947210046347e-07,
                2.382368531929327e-07,
                4.4508510499849186e-07,
                3.9278610661902853e-07
            ],
            [
                1.3709576971425944e-06,
                4.785095635655362e-06,
                2.902313023130843e-06,
                7.338213304363436e-07,
                1.7603434231833873e-06,
                1.3709568799919866e-06,
                1.2098653950656417e-06,
                3.7266401726359486e-06,
                1.7603438428800754e-06,
                8.315283250394546e-07
            ],
            [
                3.927862939126708e-07,
                3.927862939126708e-07,
                5.715003107738556e-07,
                6.475948754012522e-07,
                6.475951069985296e-07,
                2.2603242978871282e-06,
                8.315284241650899e-07,
                8.315277302819205e-07,
                5.043476486915964e-07,
                3.92786340734912e-07
            ],
            [
                2.5612828213690224e-06,
                7.338209805170655e-07,
                3.726638839878908e-06,
                3.927862470899887e-07,
                2.9023109472244114e-06,
                1.2098661161927025e-06,
                9.422444815792981e-07,
                1.3709573702822306e-06,
                1.209865539295696e-06,
                1.5534975693979422e-06
            ],
            [
                3.059022998576899e-07,
                1.8553919030858602e-07,
                1.637377448057981e-07,
                3.9278615344178325e-07,
                2.69957906184239e-07,
                2.3823693839290317e-07,
                1.4449807263312446e-07,
                1.855391681906175e-07,
                1.4449800373118268e-07,
                2.6995790618350237e-07
            ],
            [
                8.315277302841894e-07,
                3.466326624336003e-07,
                4.4508494582405734e-07,
                3.466325797896173e-07,
                5.043476486915964e-07,
                3.466326211113502e-07,
                2.6995790618469934e-07,
                2.699577774585891e-07,
                3.059021175261338e-07,
                3.466327450765785e-07
            ],
            [
                3.059022998581767e-07,
                8.315277302857965e-07,
                8.315279285251204e-07,
                8.31527928532683e-07,
                1.0677029973158649e-06,
                1.670141786325573e-05,
                1.0677027427600627e-06,
                1.3709576971463352e-06,
                1.994729008145876e-06,
                4.2228319344021954e-06
            ],
            [
                6.475949526020042e-07,
                1.275190732904469e-07,
                2.6995784182140636e-07,
                1.6373766672973748e-07,
                4.4508494582405734e-07,
                6.475951069985296e-07,
                2.1024336609843824e-07,
                2.3823699519290042e-07,
                3.059022269250683e-07,
                3.059021175261338e-07
            ],
            [
                1.8553905760062447e-07,
                9.422442569334097e-07,
                2.699578740032504e-07,
                5.043473480777865e-07,
                2.69957906184239e-07,
                6.475947210046347e-07,
                2.1024336609843824e-07,
                1.209865827752005e-06,
                5.04347468323289e-07,
                6.475947982037486e-07
            ],
            [
                1.2098662604291696e-06,
                6.475949525981759e-07,
                1.5534983101602148e-06,
                2.9023112932177327e-06,
                9.422447062202052e-07,
                9.422448185534261e-07,
                1.7603425837903113e-06,
                2.2603240284371276e-06,
                3.059023727894942e-07,
                1.2098659719757836e-06
            ],
            [
                7.73441946488886e-08,
                6.825598028392069e-08,
                8.76424013786396e-08,
                1.444979692800516e-07,
                7.734428685047173e-08,
                2.8453371023563735e-08,
                1.6373764721072816e-07,
                6.825608606172863e-08,
                9.93120161310289e-08,
                7.734415776836702e-08
            ],
            [
                9.422448185510695e-07,
                7.338208055664991e-07,
                1.3709570434178922e-06,
                3.466326624322211e-07,
                1.2098656835224664e-06,
                1.209865539295696e-06,
                8.31528424162821e-07,
                6.475945666051092e-07,
                7.338210680021253e-07,
                2.69957906184239e-07
            ],
            [
                1.7603427936335396e-06,
                6.475947210031623e-07,
                9.422445939032799e-07,
                1.7603427936335396e-06,
                2.5612825160562587e-06,
                1.0677029973192638e-06,
                1.994729483723626e-06,
                3.46632497145457e-07,
                7.338209805200689e-07,
                9.422444815765128e-07
            ],
            [
                3.927862470899887e-07,
                2.3823688159291947e-07,
                3.927862002663297e-07,
                3.927863407379485e-07,
                2.6995774527718623e-07,
                3.059022998576899e-07,
                9.422447062294175e-07,
                3.059021175261338e-07,
                7.338208055680009e-07,
                3.466326624336003e-07
            ],
            [
                2.699578740032504e-07,
                2.6995790618469934e-07,
                6.475947210031623e-07,
                6.475950297993789e-07,
                6.475947210031623e-07,
                7.338212429562581e-07,
                5.715005151606823e-07,
                7.338209805224048e-07,
                5.043476486902204e-07,
                5.715004470295662e-07
            ],
            [
                1.760342793638743e-06,
                8.315281267882195e-07,
                1.0677032518814388e-06,
                2.3823685319244518e-07,
                3.466327037553825e-07,
                7.338210680021253e-07,
                1.760343633031919e-06,
                1.5534977545886537e-06,
                4.450852641737424e-07,
                6.144173137170873e-06
            ],
            [
                1.8925150497848527e-05,
                1.3709576971425944e-06,
                1.3709576971425944e-06,
                0.9999990577552955,
                3.726638839878908e-06,
                3.12019225345861e-05,
                0.9999967112497631,
                1.89251527534122e-05,
                4.539789029616496e-05,
                1.5534981249697903e-06
            ],
            [
                3.927862002663297e-07,
                2.6995771309523475e-07,
                5.715005832886879e-07,
                3.9278610661902853e-07,
                1.8553903548231313e-07,
                4.450849988811838e-07,
                2.3823702359138736e-07,
                3.9278634073732336e-07,
                2.3823685319244518e-07,
                5.715002426486762e-07
            ],
            [
                8.315281267882195e-07,
                5.715005832886879e-07,
                1.5534981249697903e-06,
                3.9278610661902853e-07,
                2.260324028427877e-06,
                2.561281294760143e-06,
                2.2603240284371276e-06,
                5.715003107767143e-07,
                7.338209805240734e-07,
                4.2228339479858295e-06
            ],
            [
                9.422449308774482e-07,
                3.288748281329893e-06,
                2.2603253756956754e-06,
                2.902312331170226e-06,
                1.9947304348862686e-06,
                2.561282210740037e-06,
                1.5534977545886537e-06,
                5.1442232066762e-05,
                1.2098662604291696e-06,
                3.726639284144195e-06
            ],
            [
                1.8553907971855875e-07,
                1.275190276859705e-07,
                1.855391239547094e-07,
                6.475945666051092e-07,
                2.69957906184239e-07,
                3.466325797896173e-07,
                3.9278634073732336e-07,
                2.699577774585891e-07,
                3.9278634073732336e-07,
                6.475949526020042e-07
            ],
            [
                1.2098662604291696e-06,
                1.3709567165579959e-06,
                2.902311639183378e-06,
                1.2098662604291696e-06,
                7.338210679909462e-07,
                1.760343003481596e-06,
                1.0677024881980089e-06,
                6.475947210031623e-07,
                1.7603425837855082e-06,
                8.315280276607289e-07
            ],
            [
                2.1024336609843824e-07,
                1.2751899728286965e-07,
                3.927862002663297e-07,
                1.2751899728311609e-07,
                1.8553919030858602e-07,
                1.2751901248454963e-07,
                1.8553919030858602e-07,
                1.4449798650551755e-07,
                1.8553919030858602e-07,
                1.8553905760062447e-07
            ]
        ]
    },
    {
        "q_id": "9630_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                4.4508515805735777e-07,
                8.764242227418718e-08,
                6.023571320847322e-08,
                4.139940508508409e-08,
                6.825598028392069e-08,
                6.82560779249779e-08,
                6.825602910433871e-08,
                3.927860597945825e-07,
                5.3157811697009444e-08,
                6.825601283086733e-08
            ],
            [
                1.4449803818215767e-07,
                1.370957860576702e-06,
                0.9999998024945624,
                2.9023119851899796e-06,
                6.47595107001401e-07,
                6.82560779249779e-08,
                0.9999998257021837,
                1.5534984953552536e-06,
                7.734426841017797e-08,
                1.5534979397829198e-06
            ],
            [
                0.999999607213753,
                0.9999999559306259,
                0.9999999123574732,
                0.9999996310115039,
                0.9999999500628334,
                0.9999983463106117,
                8.764241182641775e-08,
                0.9999998724810027,
                0.9999999273418269,
                0.9999999715466528
            ],
            [
                0.9999986290423036,
                0.999996273360719,
                1.275190580884987e-07,
                8.7642516304188e-08,
                0.9999957771670615,
                0.9999997761970781,
                1.444979692800516e-07,
                8.7642516304188e-08,
                0.9999945777803864,
                0.9999885212332588
            ],
            [
                1.4449798650551755e-07,
                1.4449802095666915e-07,
                2.3823702359290413e-07,
                3.4663249714612693e-07,
                5.3157837044597743e-08,
                2.10243290909963e-07,
                2.3823690999323465e-07,
                7.338209805240734e-07,
                6.825602910433871e-08,
                1.855391239544352e-07
            ],
            [
                3.4663249714612693e-07,
                1.5534984953552536e-06,
                0.9999987901344615,
                0.9999984465016909,
                1.5534981249736758e-06,
                8.764242227418718e-08,
                4.691167157146029e-08,
                9.422443692574719e-07,
                6.023569166654288e-08,
                6.023569166654288e-08
            ],
            [
                4.7850933539684755e-06,
                3.9278610661902853e-07,
                1.6373772528704005e-07,
                7.889266347786918e-06,
                1.1253525596174225e-07,
                2.561282821402217e-06,
                4.222834451403972e-06,
                0.9999970976869785,
                1.4449795205472734e-07,
                2.2603251062450327e-06
            ],
            [
                3.466326624336003e-07,
                0.9999997617630333,
                0.9999990577555189,
                0.99999976176309,
                0.9999997617630048,
                0.999999607213753,
                2.2603248367949354e-06,
                0.9999997897567092,
                0.9999996743686257,
                0.9999995549149481
            ],
            [
                0.9999999006879838,
                6.023569884718319e-08,
                1.4449798650569826e-07,
                0.999977171994748,
                0.9999945777790985,
                4.691160446380562e-08,
                7.734426841017797e-08,
                1.1253506814842375e-07,
                1.4449802095666915e-07,
                2.382369667929001e-07
            ],
            [
                1.855391239547094e-07,
                2.69957906184239e-07,
                8.764241182641775e-08,
                0.999998629042957,
                6.825609419848033e-08,
                3.2241839428313264e-08,
                6.825598842065202e-08,
                4.691161005609407e-08,
                3.653479031538012e-08,
                6.023577783447482e-08
            ],
            [
                8.764247451307293e-08,
                3.9278629391427843e-07,
                1.6373770576776313e-07,
                2.6995790618469934e-07,
                9.931200429212718e-08,
                2.102433660979124e-07,
                8.315280276626197e-07,
                2.699576809143613e-07,
                2.699578740032504e-07,
                1.637376862489725e-07
            ],
            [
                4.139935079796334e-08,
                4.139939521470304e-08,
                7.73441946488886e-08,
                3.2887502415767434e-06,
                1.5534984953552536e-06,
                4.139936066832438e-08,
                7.338207180898968e-07,
                2.10243290909724e-07,
                1.8553910183674878e-07,
                0.9999996310116358
            ],
            [
                1.1253526937697666e-07,
                1.1253526937697666e-07,
                1.6373776432509826e-07,
                3.466325797896173e-07,
                9.93120161310289e-08,
                1.7603425837903113e-06,
                5.715005832886879e-07,
                3.4663278639892215e-07,
                3.05902336324494e-07,
                7.734425919002834e-08
            ],
            [
                0.9999992661786699,
                0.9999969105044483,
                5.715002426439334e-07,
                0.9999984465018755,
                6.475946438022905e-07,
                0.9999978766210321,
                0.9999997463981032,
                0.9999994631248043,
                0.9999852610180539,
                1.2098652508287273e-06
            ],
            [
                6.825598028392069e-08,
                6.825598028392069e-08,
                1.6373772528704005e-07,
                5.04347528446051e-07,
                5.3157830707696514e-08,
                2.382369951932796e-07,
                4.691164920214251e-08,
                2.215950777364157e-08,
                3.9278629391427843e-07,
                2.260324028427877e-06
            ],
            [
                1.855391239544352e-07,
                6.825598028392069e-08,
                9.931186222523604e-08,
                6.475947982037486e-07,
                2.382368531929327e-07,
                1.8553919030858602e-07,
                1.1253518888531272e-07,
                1.8553910183674878e-07,
                0.9999981261250641,
                3.9278634073732336e-07
            ],
            [
                6.475945666063607e-07,
                4.4508515805735777e-07,
                1.7603440527222532e-06,
                1.6701429808298613e-05,
                9.422447062294175e-07,
                2.1024331597288867e-07,
                3.9278629391427843e-07,
                6.47595107001401e-07,
                3.466326624336003e-07,
                8.315279285370317e-07
            ],
            [
                9.931193325852072e-08,
                4.139941002027314e-08,
                1.7257833862007743e-08,
                3.224189323773857e-08,
                6.825597214718257e-08,
                3.0590237279032884e-07,
                2.8453360847853877e-08,
                4.139934586278605e-08,
                7.734415776836702e-08,
                9.931189774187203e-08
            ],
            [
                3.6534833868287154e-08,
                7.734415776836702e-08,
                6.82560616514716e-08,
                6.023571320847322e-08,
                3.2241881707148775e-08,
                1.275191036933194e-07,
                1.046740792423576e-08,
                8.764254764780641e-08,
                1.27519088491875e-07,
                1.275191036933194e-07
            ],
            [
                0.9999993916406734,
                0.9999987121043241,
                0.9999986290426303,
                0.9999997897566589,
                0.9999994956527722,
                0.9999991684721707,
                0.9999991684717744,
                0.9999997761971315,
                0.9999977396754337,
                0.9999983463096263
            ],
            [
                0.9999904837517206,
                2.8453326928809566e-08,
                0.9999995549147359,
                0.9999989969862708,
                0.999999814460876,
                6.825600469412533e-08,
                0.9999960330145617,
                0.9999955048184245,
                0.9999996533673376,
                0.9999977396748948
            ],
            [
                0.9999974387165695,
                0.9999987901338843,
                0.9999822214524349,
                0.9999993916406734,
                0.9999988634365607,
                0.9999991148431755,
                0.9999969105040811,
                0.9999986290426306,
                0.99999862904214,
                0.9999987121046313
            ],
            [
                1.1253520230052635e-07,
                1.4449798650551755e-07,
                7.734416698849138e-08,
                9.93120161310289e-08,
                1.8553905760062447e-07,
                1.6373770576776313e-07,
                6.825601283086733e-08,
                1.6373774480605869e-07,
                5.3157811697009444e-08,
                7.73442776303243e-08
            ],
            [
                1.209865539295696e-06,
                8.315278294097538e-07,
                9.422443692574719e-07,
                3.7266397283908927e-06,
                3.927862470905692e-07,
                5.043475885696228e-07,
                1.0677028700422047e-06,
                8.315277302857965e-07,
                0.9999938558268702,
                3.4663274507713016e-07
            ],
            [
                8.764244316973974e-08,
                2.5109999906960648e-08,
                6.825598028392069e-08,
                9.931202796993203e-08,
                6.825597214718257e-08,
                2.8453364239757298e-08,
                3.2241881707148775e-08,
                7.734428685047173e-08,
                4.1399375473868e-08,
                6.023576347299818e-08
            ],
            [
                0.9999970976883635,
                0.9999989322975126,
                0.9999960330131434,
                0.9999969105044496,
                0.9999972735294063,
                0.9999987121047849,
                0.9999993916410361,
                0.999997273529406,
                0.9999987121041711,
                0.9999985406237798
            ],
            [
                0.9999990577554063,
                0.9999992661790198,
                0.9999987121046312,
                0.9999996940977732,
                0.9999977396748947,
                0.9999985406239534,
                0.9999991148433864,
                0.999997593896514,
                0.9999997897567091,
                0.9999982396559481
            ],
            [
                0.9999999067051277,
                0.9999998461826405,
                0.9999998144608098,
                1.637376862489725e-07,
                0.9999998362622357,
                1.1253508156363576e-07,
                1.0,
                1.2751902768612997e-07,
                0.9999999500627916,
                8.764244316973974e-08
            ],
            [
                4.691162683297406e-08,
                7.73442776303243e-08,
                6.825604537781398e-08,
                9.931185038635267e-08,
                6.825597214718257e-08,
                4.6911660386730734e-08,
                9.931188590255539e-08,
                7.734421308914719e-08,
                9.931194509740267e-08,
                8.764247451307293e-08
            ],
            [
                4.0063677865600476e-05,
                6.475948754028718e-07,
                5.715007195447234e-07,
                6.962256249885085e-06,
                6.475947982037486e-07,
                6.475947982037486e-07,
                2.561281294760143e-06,
                5.043472278322555e-07,
                2.7535694384081332e-05,
                4.450848927650143e-07
            ],
            [
                2.3823682479317953e-07,
                0.999998446502246,
                1.5534979397829198e-06,
                1.994729483729522e-06,
                4.4508515805735777e-07,
                4.7850933539684755e-06,
                5.043474683240344e-07,
                2.1024326584702836e-07,
                1.2098659719788098e-06,
                3.9278629391427843e-07
            ],
            [
                0.00017952792358181245,
                1.3709567165579959e-06,
                2.1024336609843824e-07,
                2.561281600086738e-06,
                8.939693107190907e-06,
                1.4449802095666915e-07,
                3.288749065423109e-06,
                3.927862470899887e-07,
                2.699578740032504e-07,
                3.2887506336086064e-06
            ],
            [
                0.9999987121049383,
                0.9999984465026164,
                0.9999985406232578,
                0.9999921107393004,
                0.9999989969859122,
                0.9999974387165693,
                0.9999978766207793,
                0.9999974387171795,
                0.9999982396563677,
                0.9999975938965143
            ],
            [
                0.9999989322973851,
                0.9999999656786915,
                7.338208055680009e-07,
                0.9999945777810327,
                0.9999999434137232,
                1.4449802095609418e-07,
                0.9999999358793715,
                0.999997876620526,
                0.9999994284994169,
                5.315789407685159e-08
            ],
            [
                1.3709573702856596e-06,
                1.4449798650569826e-07,
                0.999999900688043,
                8.764254764780641e-08,
                1.4449798650569826e-07,
                0.9999995262092163,
                6.023577783447482e-08,
                7.338210679979539e-07,
                7.734425919002834e-08,
                6.825608606172863e-08
            ],
            [
                4.691168275606451e-08,
                0.9999967112493701,
                0.999995504816818,
                0.9999877809225471,
                0.9999981261237236,
                0.9999995549150542,
                0.9999997300422869,
                0.9999994956524115,
                0.9999995262092163,
                0.9999984465026165
            ],
            [
                0.9999970976883629,
                1.2751904288710323e-07,
                0.9999987901346055,
                0.9999983463100203,
                0.9999978766205264,
                0.9999832985821582,
                0.9999892166916496,
                0.9999949062937887,
                0.9999983463098233,
                0.9999988634366963
            ],
            [
                0.9999996072137529,
                0.9999991148427533,
                1.5534984953552536e-06,
                0.9999999006879957,
                0.9999999358793561,
                5.715005832895975e-07,
                1.0677027427624903e-06,
                2.3823693839325527e-07,
                0.9999997897566089,
                0.9999996743686257
            ],
            [
                0.9999985406243014,
                0.9999975938979488,
                7.73441946488886e-08,
                1.2751904288710323e-07,
                0.9999969105044487,
                3.4663274507713016e-07,
                0.9999977396746257,
                1.444980209564556e-07,
                0.9999957771675655,
                1.8553907971758842e-07
            ],
            [
                0.9999930377420954,
                0.9999995549151073,
                6.023574911170301e-08,
                3.653479467066246e-08,
                0.9999998257021628,
                0.9999921107336593,
                6.023572038912295e-08,
                0.9999930377437568,
                0.9999987901343167,
                0.9999861539921727
            ],
            [
                0.9999983463102178,
                0.999999653367379,
                0.9999994956527724,
                0.999999802494633,
                0.9999986290429573,
                0.9999997761970248,
                0.999999730042126,
                0.9999997617631753,
                0.9999997300421904,
                0.9999998257020799
            ],
            [
                0.9999997617631752,
                3.466326624336003e-07,
                0.9999977396759729,
                0.9999989969855535,
                0.9999930377462445,
                5.315781803390236e-08,
                0.9999991684716751,
                0.9999993524051248,
                0.9999993106391191,
                0.9999994284997575
            ],
            [
                9.931202796993203e-08,
                1.8553914607267268e-07,
                5.315780536011123e-08,
                1.2751902768612997e-07,
                4.6911677163762064e-08,
                8.764241182641775e-08,
                1.1253514863968147e-07,
                7.734415776836702e-08,
                6.825600469412533e-08,
                5.315789407685159e-08
            ],
            [
                2.2159510415258326e-08,
                1.855391681906175e-07,
                6.023569884718319e-08,
                6.023577783447482e-08,
                0.9999962733616062,
                2.699577130960941e-07,
                6.023579219579052e-08,
                2.845334728018925e-08,
                1.637376862489725e-07,
                9.931190958076104e-08
            ],
            [
                0.9999151889588984,
                1.4449800373065699e-07,
                2.699576809143613e-07,
                2.3823702359138736e-07,
                3.059021175261338e-07,
                1.8553905760024476e-07,
                2.699578740032504e-07,
                3.288749849529972e-06,
                0.9999992661789322,
                0.999991060299441
            ],
            [
                5.043474081993875e-07,
                0.999994906295608,
                0.9999997463981636,
                3.2241850958880614e-08,
                0.9999810748427668,
                0.9999988634364252,
                0.9999978766212853,
                0.9999921107402416,
                0.9999967112509368,
                0.9999996533672962
            ],
            [
                0.9999985406232575,
                2.2603234895372223e-06,
                4.222833948008874e-06,
                4.222834451403972e-06,
                0.9999975938973749,
                6.475946438055299e-07,
                6.475950298021765e-07,
                3.288749849529972e-06,
                0.9999987901338843,
                1.855391239547094e-07
            ],
            [
                1.2751905808881762e-07,
                1.275190580890061e-07,
                0.999998712104171,
                0.9999987121049385,
                0.9999969105044494,
                0.999995504817356,
                4.450848927658745e-07,
                0.9999962733593856,
                0.9999962733616071,
                0.9999991148432809
            ],
            [
                0.9999992188518558,
                0.9999938558254017,
                0.999998239657207,
                4.691159887151251e-08,
                0.9999998555019446,
                0.9999999067051498,
                0.9999996743686257,
                0.9999996072137998,
                0.9999904837505871,
                0.9999988634365607
            ],
            [
                1.6373768624837685e-07,
                2.382368815916736e-07,
                1.855391239544352e-07,
                3.2241889394209404e-08,
                0.9999921107383591,
                6.825598028392069e-08,
                0.9999832985801692,
                0.999941708755929,
                3.9278624708775595e-07,
                0.9999910603037008
            ],
            [
                0.9999989322966213,
                0.99999976176309,
                0.9999992661786699,
                3.9278610661902853e-07,
                0.9999997761970781,
                0.9999987901343169,
                0.999998932297385,
                0.999998346310612,
                0.9999982396567876,
                6.825606165129312e-08
            ],
            [
                2.845333032070409e-08,
                8.7642526752214e-08,
                1.3440422588263833e-08,
                6.825598028392069e-08,
                2.845333032070409e-08,
                1.5229974066077245e-08,
                2.5109975960189263e-08,
                1.6373774480605869e-07,
                5.315781803390236e-08,
                2.8453360847853877e-08
            ],
            [
                5.315788140303327e-08,
                1.0677032518814388e-06,
                1.2751902768612997e-07,
                7.734418542875216e-08,
                6.023572038912295e-08,
                1.6373772528704005e-07,
                7.734428685047173e-08,
                6.825598028392069e-08,
                4.139941495546278e-08,
                9.931200429181105e-08
            ],
            [
                1.1253506814842375e-07,
                0.9999994631248682,
                0.9999991148427534,
                1.1253513522447425e-07,
                7.734414854823498e-08,
                0.9999992661792821,
                0.9999998362622553,
                0.9999988634358834,
                0.999999825702059,
                0.9999991684718735
            ],
            [
                1.6373772528704005e-07,
                7.734418542875216e-08,
                1.637377057680051e-07,
                2.382370235933104e-07,
                8.76424013786396e-08,
                6.825601283086733e-08,
                1.0677028700422047e-06,
                0.999999391641036,
                1.8553919030858602e-07,
                0.999999391641181
            ],
            [
                7.734418542875216e-08,
                3.653482080235082e-08,
                8.315281267882195e-07,
                1.637377057673536e-07,
                6.023578501513224e-08,
                6.825597214718257e-08,
                0.9999996940977366,
                1.1253525596174225e-07,
                1.855391681906175e-07,
                9.931187406410953e-08
            ],
            [
                5.3157811697009444e-08,
                1.8553905759969634e-07,
                7.734421308872513e-08,
                1.3709576971463352e-06,
                3.224184327183648e-08,
                1.7603438428848787e-06,
                3.466325797900508e-07,
                4.691162683297406e-08,
                3.7266383956509585e-06,
                4.691167716359673e-08
            ],
            [
                1.855391681906175e-07,
                2.6995790618469934e-07,
                2.1024339116168358e-07,
                6.023578501513224e-08,
                8.764242227418718e-08,
                1.275190276859705e-07,
                2.3823685319244518e-07,
                1.1253514863968147e-07,
                1.275190580890061e-07,
                1.275191036933194e-07
            ],
            [
                0.9999986290431208,
                0.9999998024946095,
                0.9999998362623724,
                0.9999986290429573,
                0.999999855501979,
                0.9999998461827321,
                0.99999879013374,
                0.9999999226557409,
                0.9999994956527724,
                0.9999986290424666
            ],
            [
                1.3709576971425944e-06,
                2.260323758987159e-06,
                0.9999993524050477,
                0.9999992661788448,
                0.9999987901340285,
                NaN,
                0.9999994284995531,
                0.9999997617630049,
                0.9999995818813268,
                2.3823702359290413e-07
            ],
            [
                0.9999952149055085,
                0.999999168471576,
                0.9999952149060769,
                0.999998005270517,
                0.9999980052700413,
                0.9999989969856729,
                0.9999989322968759,
                0.9999994631251242,
                6.023578501491997e-08,
                0.9999998362622747
            ],
            [
                6.825608606172863e-08,
                6.023578501513224e-08,
                5.315789407685159e-08,
                1.637376862489725e-07,
                2.845337441546675e-08,
                7.33821330437595e-07,
                3.9278629391427843e-07,
                1.2751901248454963e-07,
                5.315780536011123e-08,
                8.764242227418718e-08
            ],
            [
                1.8553914607267268e-07,
                3.05902263391829e-07,
                2.3823690999323465e-07,
                2.102434412875379e-07,
                4.450852111155216e-07,
                6.47594952603035e-07,
                1.0677024882029858e-06,
                5.715005832895975e-07,
                2.699576809143613e-07,
                NaN
            ],
            [
                1.5534973842030142e-06,
                8.315280276626197e-07,
                3.7266397283908927e-06,
                1.855391681906175e-07,
                6.475949526020042e-07,
                1.855391681906175e-07,
                0.9999957771680733,
                1.067703124601679e-06,
                0.9999974387174864,
                5.715006514176113e-07
            ],
            [
                4.139941002027314e-08,
                0.9999998802069731,
                0.9999992661789323,
                5.3157887739943563e-08,
                0.9999999176675535,
                5.3157811697009444e-08,
                4.1399400149893274e-08,
                1.0677026154806063e-06,
                4.691159887151251e-08,
                1.955569236151977e-08
            ],
            [
                1.8553907971758842e-07,
                2.6995768091310296e-07,
                3.059022998576899e-07,
                0.9999885212305117,
                3.05902190458764e-07,
                0.9999885212305222,
                7.73441946488886e-08,
                0.9999832985781731,
                1.637377057673536e-07,
                6.825597214718257e-08
            ],
            [
                8.764241182641775e-08,
                8.31528325040778e-07,
                1.855391681906175e-07,
                9.422443692574719e-07,
                3.65348425788669e-08,
                8.764254764780641e-08,
                5.043475885696228e-07,
                3.7266383956509585e-06,
                6.023577783447482e-08,
                2.5612831267202583e-06
            ],
            [
                0.9999997126314468,
                0.9999998942829098,
                9.931202796993203e-08,
                0.9999991148431755,
                8.764254764780641e-08,
                1.6373766672994222e-07,
                3.653479467066246e-08,
                2.8453360847853877e-08,
                0.9999988634358834,
                0.9999985406232579
            ],
            [
                3.288749849529972e-06,
                9.931193325852072e-08,
                9.422445939054222e-07,
                2.1024331597262577e-07,
                3.9278634073625165e-07,
                1.6373764721072816e-07,
                3.059022998576899e-07,
                4.450848927658745e-07,
                6.475945666063607e-07,
                2.1444943301674863e-05
            ],
            [
                0.9999987901344609,
                0.9999962733589404,
                0.9999998024947272,
                0.9999938558254012,
                2.902312677150514e-06,
                0.9999756997679764,
                0.9999990577551816,
                6.962259569750576e-06,
                2.9023109472494878e-06,
                0.9999980052700413
            ],
            [
                0.9999995818810776,
                1.4449807263312446e-07,
                1.2751908849167202e-07,
                0.9999964991455879,
                1.275190580884987e-07,
                0.9999852610145328,
                0.9999960330155065,
                0.9999989969860317,
                0.9999967112497612,
                0.9999960330145603
            ],
            [
                0.9999998144609203,
                0.9999999273418269,
                3.653482080235082e-08,
                1.0677026154827912e-06,
                6.144173869603344e-06,
                0.9999999006880312,
                8.315284241665078e-07,
                0.9999982396563679,
                0.9999999273418356,
                0.9999992661790197
            ],
            [
                7.338211554801876e-07,
                9.422444815765128e-07,
                1.0677028700422047e-06,
                1.760343213322473e-06,
                7.338213304363436e-07,
                6.475946438022905e-07,
                8.315280276607289e-07,
                7.338208930443633e-07,
                0.9999999559306312,
                1.4449803818215767e-07
            ],
            [
                0.999996033012669,
                2.102433410343832e-07,
                0.9999962733611633,
                1.8553914607267268e-07,
                2.2603251062450327e-06,
                8.764247451307293e-08,
                1.2751904288710323e-07,
                3.0590215399183813e-07,
                0.9999977396748954,
                0.9999993916406733
            ],
            [
                8.764249540862797e-08,
                0.999998239657417,
                6.023578501513224e-08,
                0.9999942280806621,
                1.994729483729522e-06,
                0.9999885212277811,
                0.9999930377429337,
                0.9999785550414371,
                0.9999843104540629,
                1.9555671380533023e-08
            ],
            [
                8.939693107288474e-06,
                1.8553905760062447e-07,
                3.288749849529972e-06,
                2.260324028443809e-06,
                1.4449803818215767e-07,
                2.1024336609874897e-07,
                1.1253525596174225e-07,
                1.275190732904469e-07,
                3.7266397283908927e-06,
                1.6373764721091427e-07
            ],
            [
                1.2751910369275402e-07,
                9.931187406410953e-08,
                1.6373776432509826e-07,
                3.059022269254856e-07,
                0.9999994956527722,
                2.3823702359290413e-07,
                9.93120161310289e-08,
                1.6373770576776313e-07,
                1.1253508156363576e-07,
                0.9999996940977367
            ],
            [
                0.9999998257021837,
                2.1024344128660572e-07,
                0.9999996072138466,
                0.9999981261243936,
                0.9999992661786697,
                0.9999975938965143,
                0.9999998942829351,
                4.139936066832438e-08,
                0.9999996533672963,
                7.734418542875216e-08
            ],
            [
                7.338208930460318e-07,
                5.315780536011123e-08,
                3.653485564473625e-08,
                1.8553919030858602e-07,
                2.699578740032504e-07,
                2.382368815932174e-07,
                1.637376862489725e-07,
                3.224189323773857e-08,
                1.2098656835252174e-06,
                5.715006514176113e-07
            ],
            [
                3.059021175261338e-07,
                0.00012339454559719625,
                2.5612834320563895e-06,
                5.3157811697009444e-08,
                7.734418542875216e-08,
                1.3709575337159875e-06,
                9.931198061405701e-08,
                7.734416698849138e-08,
                5.3157837044597743e-08,
                9.931193325852072e-08
            ],
            [
                0.9999992661791948,
                0.9999999067050498,
                1.637376862489725e-07,
                9.931199245322124e-08,
                9.931200429212718e-08,
                8.764253720001207e-08,
                7.734426841017797e-08,
                6.023577065381482e-08,
                9.93120161310289e-08,
                0.9999998874648112
            ],
            [
                2.382369667929001e-07,
                3.2887506336235617e-06,
                5.315788140303327e-08,
                2.2603248367949354e-06,
                1.760342793638743e-06,
                0.9999960330145599,
                8.315277302857965e-07,
                1.0677026154827912e-06,
                1.7603440527334603e-06,
                7.734415776836702e-08
            ],
            [
                0.9999998642566704,
                0.9999724643155111,
                0.9999978766212857,
                0.9999998642566704,
                1.1253506814842375e-07,
                0.9999993524048932,
                0.999999653367255,
                6.825608606172863e-08,
                0.9999974387171804,
                0.9999998144608319
            ],
            [
                1.8553905760062447e-07,
                0.9999974387184011,
                0.9999997617630048,
                9.422444815814404e-07,
                9.422450432030903e-07,
                8.315277302857965e-07,
                4.1399400149893274e-08,
                1.994729483729522e-06,
                5.715006514176113e-07,
                1.5534984953552536e-06
            ],
            [
                1.3709575337078829e-06,
                1.27519088491875e-07,
                4.691159887151251e-08,
                7.338212429562581e-07,
                2.260323758987159e-06,
                1.2751901248454963e-07,
                4.691159887151251e-08,
                3.224189323773857e-08,
                8.764253720001207e-08,
                8.31527928532683e-07
            ],
            [
                0.9999997126314468,
                0.9999949062956075,
                6.825606165129312e-08,
                0.9999997126313441,
                0.9999998874648245,
                0.999999814460876,
                0.9999996940976636,
                0.9999995549149481,
                0.9999974387187065,
                0.9999982396569971
            ],
            [
                0.9999996072137062,
                0.999999789756634,
                0.9999997617630334,
                0.9999957771670622,
                0.9999967112509364,
                0.9999995262093857,
                0.9999485577621464,
                0.9999998724809875,
                0.9999994631248682,
                0.9999998942829602
            ],
            [
                2.382369383923073e-07,
                1.444980726324838e-07,
                1.8553905760062447e-07,
                1.275190428875671e-07,
                0.999996273359831,
                3.9278610661902853e-07,
                1.4738980215593877e-05,
                1.444979692800516e-07,
                8.315278294114555e-07,
                1.8553905760062447e-07
            ],
            [
                5.043473480730849e-07,
                0.9999964991447537,
                1.994730197090463e-06,
                9.422449308673789e-07,
                0.9999843104484313,
                0.9999832985781901,
                0.9999962733611628,
                7.889266347636241e-06,
                0.9999904837494511,
                4.22283394786293e-06
            ],
            [
                7.734426841017797e-08,
                1.0677027427624903e-06,
                3.72663883989755e-06,
                6.825597214718257e-08,
                1.2098661162056318e-06,
                1.2098656835252174e-06,
                0.9999996940978826,
                1.209865539298447e-06,
                8.764242227418718e-08,
                8.764253720001207e-08
            ],
            [
                0.9999980052709925,
                0.999996033014087,
                0.9999975938985219,
                2.9023116392097746e-06,
                1.6373770576776313e-07,
                3.7266383956509585e-06,
                8.939697370069891e-06,
                1.8553916819032217e-07,
                1.2751902768612997e-07,
                4.4508494582405734e-07
            ],
            [
                8.31528325040778e-07,
                6.023577783447482e-08,
                3.22418970812682e-08,
                9.422443692574719e-07,
                4.691159887151251e-08,
                3.653485564473625e-08,
                1.0677027427624903e-06,
                6.82560779249779e-08,
                9.422449308774482e-07,
                2.5109975960189263e-08
            ],
            [
                0.9999974387174857,
                0.9999955048178913,
                0.9999960330145614,
                3.927862470899887e-07,
                0.9999969105040816,
                0.9999942280772285,
                0.9999985406236055,
                6.47595107001401e-07,
                0.9999981261246177,
                0.9999972735300566
            ],
            [
                1.5534971990169383e-06,
                9.4224425692559e-07,
                1.7603425837903113e-06,
                1.994729483729522e-06,
                4.785094494811783e-06,
                7.889264466868659e-06,
                1.9947292459406333e-06,
                1.4449805540763184e-07,
                1.994729008151319e-06,
                2.5612834320563895e-06
            ],
            [
                0.9999984465016905,
                0.9999934595635592,
                0.9999993106391192,
                0.9999990577557434,
                1.1253508156363576e-07,
                0.9999898700114399,
                0.999999495652652,
                0.9999974387177908,
                0.9999998724809419,
                0.9999970976883622
            ],
            [
                1.370957860576702e-06,
                6.023577065381482e-08,
                3.224187786361915e-08,
                3.466327037553825e-07,
                7.734426841017797e-08,
                1.209865827752005e-06,
                5.715005832895975e-07,
                6.023578501513224e-08,
                6.023568448589658e-08,
                5.3157887739943563e-08
            ],
            [
                0.9999877809269082,
                1.8553907971855875e-07,
                6.023569884718319e-08,
                1.6373770576776313e-07,
                1.6373772528704005e-07,
                0.9999957771670626,
                5.04347287955046e-07,
                6.475947982037486e-07,
                0.9999898700126498,
                1.6373766672973748e-07
            ],
            [
                5.043474683204221e-07,
                1.9947306725868575e-06,
                0.9999955048168181,
                6.144172404380855e-06,
                0.9999938558232055,
                0.9999982396563679,
                0.999999802494633,
                2.7535681241281285e-05,
                1.0677028700266676e-06,
                0.9999997126314811
            ],
            [
                0.9999852610127743,
                0.9999988634365607,
                0.9999997300422548,
                1.8553907971855875e-07,
                6.023571320847322e-08,
                4.6911638017556955e-08,
                7.73441946488886e-08,
                0.9999998362623528,
                1.2751899728311609e-07,
                0.9999994631249963
            ],
            [
                1.6373774480605869e-07,
                NaN,
                6.023569884718319e-08,
                1.4449803818215767e-07,
                1.1253521571574156e-07,
                1.855391239544352e-07,
                1.4449807263312446e-07,
                1.637376862489725e-07,
                7.734415776836702e-08,
                2.6995774527718623e-07
            ],
            [
                2.5612834320563895e-06,
                3.7266383956509585e-06,
                1.7603425837903113e-06,
                1.3709572068553509e-06,
                0.9999978766210327,
                0.9999984465015055,
                1.5534983101644536e-06,
                3.72663883989755e-06,
                0.9999967112513287,
                3.2887486733899378e-06
            ],
            [
                0.9999921107364815,
                1.125352291309328e-07,
                0.9999977396765111,
                1.6373774480605869e-07,
                0.9999981261250641,
                7.734421308914719e-08,
                0.9999952149055075,
                6.825601283086733e-08,
                0.9999988634364252,
                0.9999990577551816
            ],
            [
                0.9999904837449136,
                2.102434162245973e-07,
                0.9999925887210205,
                0.9999983463108089,
                0.9999930377445836,
                4.691162124067829e-08,
                0.9999977396746254,
                0.9999949062925731,
                3.927860597945825e-07,
                0.9999822214502956
            ],
            [
                3.9278629391427843e-07,
                2.561282516066741e-06,
                0.9999996940978461,
                0.9999898700054111,
                1.3709570434178922e-06,
                1.5534984953510149e-06,
                9.93120161310289e-08,
                8.315281267861397e-07,
                2.102434412875379e-07,
                1.0677029973158649e-06
            ],
            [
                0.9999991684720717,
                0.999999352405202,
                0.9999995262094987,
                0.9999996072137998,
                0.9999996072137062,
                0.9999987121047849,
                0.999999653367503,
                0.9999964991455894,
                0.9999995818814265,
                0.9999998724809875
            ],
            [
                1.637377643243723e-07,
                9.422448185534261e-07,
                5.715002426486762e-07,
                2.1024334103352274e-07,
                2.6995790618350237e-07,
                1.8553905760062447e-07,
                2.382370235922541e-07,
                1.8553910183607374e-07,
                4.6911665979156514e-08,
                1.855391239539711e-07
            ],
            [
                6.023569166654288e-08,
                6.825600469412533e-08,
                3.05902263389638e-07,
                4.691160446380562e-08,
                2.6995790618469934e-07,
                1.444979692800516e-07,
                2.382368531929327e-07,
                1.637377448057981e-07,
                5.315784971839039e-08,
                6.825608606172863e-08
            ],
            [
                0.9999921107374271,
                0.9999997761971848,
                9.931200429212718e-08,
                0.9999996940977732,
                0.9999996743688975,
                3.9278629391427843e-07,
                0.9999998874648915,
                0.9999996533674204,
                0.9999998874648112,
                0.9999997617630616
            ],
            [
                8.764245361752286e-08,
                8.764242227418718e-08,
                2.3823690999290963e-07,
                2.1024326584639497e-07,
                0.9999962733607184,
                0.9999955048189606,
                1.275189972832538e-07,
                0.9999898700054046,
                1.2751904288739315e-07,
                2.3823699519143784e-07
            ],
            [
                0.9999999176674945,
                7.734414854823498e-08,
                1.3709568799919866e-06,
                4.691161005609407e-08,
                2.102434162245973e-07,
                0.9999991684722701,
                4.691167157146029e-08,
                7.73442776303243e-08,
                0.9999999468421502,
                0.999999946842144
            ],
            [
                0.9999983463100206,
                0.9999999123575045,
                0.9999998642567351,
                0.9999992661787572,
                0.9999972735297304,
                0.9999981261248407,
                0.9999994956527122,
                0.9999994284994169,
                0.9999983463102173,
                0.9999994956524717
            ],
            [
                6.475947210046347e-07,
                1.275190580890061e-07,
                7.734416698849138e-08,
                2.3823690999323465e-07,
                1.5534984953453635e-06,
                7.73442776303243e-08,
                5.315789407685159e-08,
                1.209865827752005e-06,
                4.691159887151251e-08,
                1.8553910183674878e-07
            ],
            [
                4.450848927658745e-07,
                0.9999938558268675,
                0.9999972735284304,
                0.9999984465016903,
                0.9999985406234313,
                0.9999985406237794,
                0.9999970976866323,
                0.9999964991443359,
                1.1253526937656726e-07,
                0.999998346309626
            ],
            [
                8.315282259151545e-07,
                0.9999999226557778,
                0.9999998461827322,
                0.9999990577552943,
                0.99999916847227,
                0.9999998942829603,
                0.9999996072136594,
                0.9999998362622747,
                0.9999999123575777,
                0.9999999176675043
            ],
            [
                0.9999998362623529,
                0.9999991148428589,
                0.999999631011372,
                0.9999995549151076,
                0.9999982396563685,
                0.9999997300422547,
                0.9999997126313784,
                0.9999998144609424,
                0.9999975938985224,
                0.999999802494633
            ],
            [
                2.382368531929327e-07,
                0.9999852610145264,
                1.6373762769138607e-07,
                1.1253508156317518e-07,
                0.9999985406230838,
                0.9999982396563675,
                0.9999975938979484,
                7.734416698815724e-08,
                0.9999970976873241,
                6.825600469412533e-08
            ],
            [
                0.99999992265575,
                0.9999998642567028,
                0.9999999123574942,
                0.9999999468421756,
                0.9999999611088766,
                1.5534973842076057e-06,
                1.994729721518893e-06,
                0.999999802494633,
                6.475950298021765e-07,
                0.9999997761970248
            ],
            [
                0.9999910603037028,
                0.9999997300422548,
                0.9999957771660539,
                0.9999978766210321,
                0.9999970976880167,
                0.9999960330140875,
                0.9999980052702793,
                NaN,
                0.9999975938985219,
                0.9999798543116071
            ],
            [
                8.315280276626197e-07,
                0.9999741325690118,
                0.9999998724809723,
                2.1024336609843824e-07,
                3.466326211113502e-07,
                0.9999999358793484,
                7.338211554783522e-07,
                5.715002426475718e-07,
                1.3709578605729614e-06,
                7.3382080556433e-07
            ],
            [
                6.475947982002148e-07,
                2.7535694384882703e-05,
                1.012998977264307e-05,
                8.939700567004841e-06,
                2.7535700949523498e-05,
                1.7603438428740716e-06,
                1.7603434231705793e-06,
                7.338210680002898e-07,
                8.315281267861397e-07,
                2.2603237589676295e-06
            ],
            [
                0.9999989322967484,
                0.9999960330140879,
                1.4449805540763184e-07,
                NaN,
                0.9999967112517204,
                0.9999994956525918,
                0.9999898700114423,
                0.9999974387177905,
                0.999998629043284,
                0.999997876622298
            ],
            [
                1.5534979397829198e-06,
                3.05902263391829e-07,
                2.699578096403948e-07,
                0.999999653367379,
                1.0677024882029858e-06,
                2.6995784182183607e-07,
                9.422450432030903e-07,
                1.0677027427624903e-06,
                1.5534979397829198e-06,
                2.260324028443809e-06
            ],
            [
                0.9999998555020307,
                0.9999987121043242,
                3.2887494574832472e-06,
                0.9999994284994169,
                2.5612834320563895e-06,
                3.726639284144195e-06,
                0.9999983463100205,
                1.7603430034867993e-06,
                4.785094494811783e-06,
                1.209865827752005e-06
            ],
            [
                8.764254764780641e-08,
                3.6534833868287154e-08,
                2.215950249040774e-08,
                2.5109981946866052e-08,
                4.6911638017556955e-08,
                2.215950249040774e-08,
                1.1253513522447425e-07,
                6.825600469412533e-08,
                8.7642526752214e-08,
                3.224188555067886e-08
            ],
            [
                0.9999970976880173,
                0.9999960330121963,
                0.9999975938965144,
                0.9999983463110063,
                0.9999980052705174,
                0.9999993916408909,
                0.9999984465016907,
                0.9999955048189608,
                0.9999945777803869,
                0.9999974387187069
            ],
            [
                0.9999991148429644,
                8.764244316973974e-08,
                0.9999998942829981,
                0.9999934595651165,
                2.3823682479317953e-07,
                0.9999910603037021,
                0.999999391640891,
                0.9999997463981334,
                0.9999987121046313,
                0.9999991684722699
            ],
            [
                2.699578096403948e-07,
                1.275190732904469e-07,
                7.73441946488886e-08,
                3.059022998581767e-07,
                3.653481209178873e-08,
                1.1253509497883659e-07,
                1.1253526937697666e-07,
                7.73441946488886e-08,
                1.275190732904469e-07,
                7.338207180898968e-07
            ],
            [
                0.9999995262094987,
                0.9999999006880075,
                0.9999987901340286,
                0.9999988634361543,
                0.999999846182622,
                0.9999982396574174,
                0.9999987901344614,
                0.9999989322967487,
                0.9999993524052792,
                0.9999995262093858
            ]
        ]
    },
    {
        "q_id": "9713_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                3.288750241561788e-06,
                5.715006514167015e-07,
                3.72663883989755e-06,
                1.0129995810343862e-05,
                1.7603440527286572e-06,
                1.3709576971425944e-06,
                2.260324836787226e-06,
                7.338212429582604e-07,
                3.4663253846718004e-07,
                3.2887506335906595e-06
            ],
            [
                1.444980726324838e-07,
                2.1024334103581732e-07,
                2.382370235922541e-07,
                1.5534981249697903e-06,
                2.561281294760143e-06,
                4.450851049991497e-07,
                2.1024339116082313e-07,
                8.315281267882195e-07,
                2.3823690999290963e-07,
                5.043476486924565e-07
            ],
            [
                1.7603430034867993e-06,
                5.715006514176113e-07,
                2.1024334103581732e-07,
                4.4508494582405734e-07,
                3.059022269254856e-07,
                1.27519088491875e-07,
                2.699578740032504e-07,
                6.47595107001401e-07,
                5.715005832895975e-07,
                2.6995784182183607e-07
            ],
            [
                7.734416698849138e-08,
                0.9999972735297324,
                2.1024336609874897e-07,
                3.4663278639892215e-07,
                2.102434162245973e-07,
                2.102434412875379e-07,
                0.999996033014567,
                4.450851049991497e-07,
                2.1024331597262577e-07,
                4.450852111155216e-07
            ],
            [
                0.9999982396572077,
                0.9999975938976616,
                0.9999969105044514,
                0.9999930377454179,
                0.9999930377445848,
                3.7266379514061143e-06,
                2.2603253756956754e-06,
                0.9999546021261739,
                0.9999975938976621,
                0.9999974387174874
            ],
            [
                2.5612831267202583e-06,
                7.889265407327733e-06,
                1.3007125363908762e-05,
                1.9947294837154625e-06,
                1.0677027427569065e-06,
                6.144172404738491e-06,
                2.2603240284371276e-06,
                6.144172404738491e-06,
                3.2887482813149375e-06,
                2.1444953527944967e-05
            ],
            [
                3.4663274507713016e-07,
                1.5534971990169383e-06,
                5.043474683240344e-07,
                2.382368815932174e-07,
                5.043474082012222e-07,
                1.8553919030858602e-07,
                3.05902263391829e-07,
                5.04347287955046e-07,
                7.338211554801876e-07,
                6.475950298021765e-07
            ],
            [
                0.9999687980999108,
                0.9999975938965153,
                0.99999916847227,
                0.999985261021573,
                0.9999573525321029,
                0.9999925887192616,
                0.999993855826869,
                0.9999843104559659,
                0.999998712104171,
                0.9999985406243016
            ],
            [
                4.450852111120808e-07,
                3.4663266242780743e-07,
                3.466325384661554e-07,
                3.9278634073312583e-07,
                4.450852111120808e-07,
                4.222834954801051e-06,
                5.043474081993875e-07,
                9.422450431912e-07,
                4.450852111100568e-07,
                4.4508505193791187e-07
            ],
            [
                4.4508499888275247e-07,
                1.5534983101644536e-06,
                7.33821330437595e-07,
                4.450850519409479e-07,
                5.043475885696228e-07,
                1.2098656835252174e-06,
                4.785095635655362e-06,
                6.47594952603035e-07,
                4.450850519403407e-07,
                8.315284241665078e-07
            ],
            [
                1.7603438428800754e-06,
                2.3823688159291947e-07,
                2.6995777745711594e-07,
                6.475946438055299e-07,
                6.475948754028718e-07,
                1.9947304348862686e-06,
                5.043472278322555e-07,
                4.450850519403407e-07,
                5.043474082005342e-07,
                1.3709570434178922e-06
            ],
            [
                2.699578740032504e-07,
                1.637377057680051e-07,
                2.699578740032504e-07,
                4.450848927658745e-07,
                3.059021175261338e-07,
                3.9278620026686556e-07,
                1.275190428875671e-07,
                2.1024331597288867e-07,
                3.05902263391829e-07,
                2.699577452775239e-07
            ],
            [
                1.9947299593078385e-06,
                9.422443692574719e-07,
                1.9947299593078385e-06,
                6.47595107001401e-07,
                9.422442569334097e-07,
                9.422445939032799e-07,
                2.699576809143613e-07,
                8.939699501416646e-06,
                4.4508494582405734e-07,
                2.2603248367949354e-06
            ],
            [
                8.315279285370317e-07,
                8.315280276626197e-07,
                4.450850519403407e-07,
                1.370957860576702e-06,
                1.3709570434122812e-06,
                2.10243290909724e-07,
                2.3823688159291947e-07,
                2.382370235933104e-07,
                8.939700567094277e-06,
                6.475950298011458e-07
            ],
            [
                1.6373764721091427e-07,
                1.855391239547094e-07,
                9.931186222523604e-08,
                2.3823685319320354e-07,
                9.931193325852072e-08,
                1.4449800373118268e-07,
                3.9278634073732336e-07,
                2.1024336609843824e-07,
                2.102434412871794e-07,
                3.9278620026686556e-07
            ],
            [
                2.3823693839325527e-07,
                3.4663262111182307e-07,
                1.1253526937697666e-07,
                3.927863875616689e-07,
                1.855391239547094e-07,
                2.699577452775239e-07,
                2.3823693839325527e-07,
                1.6373776432509826e-07,
                6.475945666063607e-07,
                5.715006514176113e-07
            ],
            [
                3.0590219045914655e-07,
                3.9278620026686556e-07,
                5.715005832895975e-07,
                1.4738976701652988e-05,
                3.466325797900508e-07,
                8.315277302857965e-07,
                0.01098694327827096,
                0.9997965731041876,
                4.4508515805735777e-07,
                3.9278605979534166e-07
            ],
            [
                0.9999992661792827,
                6.47595107001401e-07,
                1.855391681906175e-07,
                6.475945666063607e-07,
                5.715004470326849e-07,
                1.5534983101644536e-06,
                1.0677027427624903e-06,
                4.450850519403407e-07,
                2.69957906184239e-07,
                1.8925141473978602e-05
            ],
            [
                3.4663274507713016e-07,
                1.637376862489725e-07,
                7.338207180898968e-07,
                2.2603251062450327e-06,
                1.5534973842076057e-06,
                1.2098659719757836e-06,
                2.3823688159291947e-07,
                7.338207180898968e-07,
                1.8553919030858602e-07,
                8.315283250394546e-07
            ],
            [
                9.422443692574719e-07,
                7.889261645427538e-06,
                4.139934586278605e-08,
                3.9278629391427843e-07,
                1.7603430034867993e-06,
                3.9278620026686556e-07,
                9.931189774187203e-08,
                5.71500515161527e-07,
                3.466326624336003e-07,
                1.012998977264307e-05
            ],
            [
                6.475947210046347e-07,
                1.9947292459347367e-06,
                1.5534983101478522e-06,
                4.222831934321543e-06,
                1.3007126914435202e-05,
                7.338211554783522e-07,
                7.338212429537553e-07,
                1.0129987357407137e-05,
                4.222834954778007e-06,
                1.7603427936335396e-06
            ],
            [
                1.855391681898159e-07,
                3.9278634073625165e-07,
                2.6995784182073116e-07,
                2.3823702359138736e-07,
                3.059021539909339e-07,
                6.475947982022763e-07,
                5.71500515159253e-07,
                3.9278634073625165e-07,
                9.422443692527585e-07,
                3.46632497145457e-07
            ],
            [
                1.067702870039777e-06,
                2.260323758987159e-06,
                1.8925143729954285e-05,
                7.338212429562581e-07,
                2.9023123311583482e-06,
                8.315279285351409e-07,
                2.902312677150514e-06,
                0.9999942280813544,
                1.9947292459347367e-06,
                5.715005832895975e-07
            ],
            [
                5.043475885696228e-07,
                1.994729721518893e-06,
                3.466325384678894e-07,
                1.6373764721072816e-07,
                1.3709572068553509e-06,
                0.9999994631249323,
                7.33821330437595e-07,
                3.4663262111182307e-07,
                4.450850519409479e-07,
                3.927863407379485e-07
            ],
            [
                3.466327450765785e-07,
                7.338209805240734e-07,
                8.315281267861397e-07,
                2.3823693839057394e-07,
                3.7266397283908927e-06,
                1.994729008145876e-06,
                3.466327037539638e-07,
                3.9278605979534166e-07,
                2.2603245673443566e-06,
                1.4449805540763184e-07
            ],
            [
                1.0677033791583005e-06,
                1.7603430034655858e-06,
                0.9999955048200382,
                1.0677024882009222e-06,
                2.5612828213934817e-06,
                6.144173869603344e-06,
                0.9998911030465585,
                5.715007195410849e-07,
                9.422445939002803e-07,
                2.260324567337161e-06
            ],
            [
                1.4449807263312446e-07,
                1.125352291309328e-07,
                5.043473480777865e-07,
                2.2603234895372223e-06,
                1.8553910183674878e-07,
                9.93118503859575e-08,
                8.7642558095602e-08,
                1.6373766672973748e-07,
                6.47594566597747e-07,
                5.715007195431641e-07
            ],
            [
                6.475945666063607e-07,
                2.3823696679327928e-07,
                2.3823685319320354e-07,
                2.902312331170226e-06,
                5.71500719545698e-07,
                1.8553907971879076e-07,
                3.927862470905692e-07,
                1.855391239547094e-07,
                1.3709576971463352e-06,
                2.699578096403948e-07
            ],
            [
                5.043474082005342e-07,
                9.931193325852072e-08,
                3.927860597935108e-07,
                3.46632497145457e-07,
                3.4663266243308805e-07,
                1.8553919030826963e-07,
                3.0590237279085045e-07,
                3.927862002663297e-07,
                1.6373764721072816e-07,
                9.422448185534261e-07
            ],
            [
                2.3823682479292225e-07,
                8.315282259089153e-07,
                9.422450432014836e-07,
                2.3823690999160957e-07,
                6.475949526020042e-07,
                9.422445939032799e-07,
                6.475951069961737e-07,
                1.3709567165530083e-06,
                4.450852641717689e-07,
                5.715005832886879e-07
            ],
            [
                2.2603234895372223e-06,
                1.3709567165579959e-06,
                8.315281267861397e-07,
                6.475947210031623e-07,
                1.3709570434219446e-06,
                5.715002426475718e-07,
                1.2098658277451275e-06,
                7.338207180864763e-07,
                1.2098652508391807e-06,
                4.222832437798974e-06
            ],
            [
                1.6701429808632785e-05,
                1.5534971990169383e-06,
                1.30071315662049e-05,
                1.9947301970972664e-06,
                9.422447062294175e-07,
                1.5534973842076057e-06,
                4.222834954801051e-06,
                7.338210680021253e-07,
                1.7603434231833873e-06,
                7.338208930460318e-07
            ],
            [
                1.4449807263312446e-07,
                2.1024334103581732e-07,
                2.6995790618469934e-07,
                2.699577452775239e-07,
                1.8553910183674878e-07,
                3.059022998581767e-07,
                3.466326624336003e-07,
                3.466325797888292e-07,
                1.125351083940518e-07,
                5.043476486924565e-07
            ],
            [
                6.475946438055299e-07,
                NaN,
                2.382368247924618e-07,
                9.422445939002803e-07,
                NaN,
                1.444980209564556e-07,
                NaN,
                2.1024334103581732e-07,
                3.059021175261338e-07,
                2.2603248367949354e-06
            ],
            [
                7.33821330437595e-07,
                5.715002426486762e-07,
                9.422444815814404e-07,
                1.444979692800516e-07,
                2.382368815932174e-07,
                1.6373764721072816e-07,
                1.5534984953552536e-06,
                5.715006514176113e-07,
                1.4449800373118268e-07,
                3.9278620026686556e-07
            ],
            [
                5.71500719545698e-07,
                9.422450432030903e-07,
                7.338211554813555e-07,
                3.726639284125553e-06,
                1.209866260432471e-06,
                1.8553903548287212e-07,
                3.7266379514061143e-06,
                6.475945666063607e-07,
                3.927862002663297e-07,
                3.2887502415767434e-06
            ],
            [
                1.0677026154806063e-06,
                3.726639728348526e-06,
                1.7603430034867993e-06,
                2.5612831266946347e-06,
                1.9947292459347367e-06,
                3.7266388398585725e-06,
                9.422449308774482e-07,
                3.9278620026686556e-07,
                5.043472278322555e-07,
                1.3709576971379186e-06
            ],
            [
                1.5534975693979422e-06,
                9.422442569315887e-07,
                4.222832941193893e-06,
                2.2603242978871282e-06,
                5.715005832895975e-07,
                5.71500515159253e-07,
                5.715007195447234e-07,
                3.9278629391427843e-07,
                6.475949526020042e-07,
                2.6995790618469934e-07
            ],
            [
                1.0677027427600627e-06,
                1.209866260432471e-06,
                3.059021175255426e-07,
                5.043474683220276e-07,
                5.04347528446051e-07,
                3.466326211113502e-07,
                2.382370235933104e-07,
                8.315277302841894e-07,
                1.7603425837903113e-06,
                7.338207180898968e-07
            ],
            [
                0.9999988634361546,
                0.9999822214439597,
                2.9023116392097746e-06,
                1.8553914607267268e-07,
                0.9999945777829792,
                0.9999987121052456,
                0.9999978766205264,
                0.9999983463100205,
                0.999997739675974,
                0.9999967112497617
            ],
            [
                5.422217030747413e-06,
                1.3709576971463352e-06,
                1.9947301970972664e-06,
                1.1478768126057254e-05,
                4.450852641737424e-07,
                1.3709576971463352e-06,
                7.889263526345123e-06,
                1.2098661162056318e-06,
                2.6995771309523475e-07,
                1.9947292459406333e-06
            ],
            [
                0.9999916019259749,
                0.9999994956526521,
                0.9999994284994169,
                0.9999967112521124,
                0.9999962733602751,
                0.9999984465015056,
                7.338208055680009e-07,
                0.9999982396574167,
                3.05902190458764e-07,
                0.9999960330136175
            ],
            [
                2.561281600086738e-06,
                3.2887506336235617e-06,
                5.715005832886879e-07,
                1.8553910183674878e-07,
                0.999933947879456,
                0.9999916019239741,
                4.450848927658745e-07,
                2.1024331597262577e-07,
                3.9278605979534166e-07,
                3.4663262111182307e-07
            ],
            [
                2.6995771309523475e-07,
                5.715006514176113e-07,
                7.338207180898968e-07,
                0.9999983463108096,
                4.450852641737424e-07,
                2.3823693839325527e-07,
                1.209865827752005e-06,
                3.466326624336003e-07,
                3.4663262111182307e-07,
                3.46632497145457e-07
            ],
            [
                1.994729721518893e-06,
                2.3823682479317953e-07,
                6.144173137170873e-06,
                7.338207180898968e-07,
                1.8553919030858602e-07,
                3.927862470899887e-07,
                3.7266397283908927e-06,
                7.338208055680009e-07,
                1.5534983101644536e-06,
                1.3709573702822306e-06
            ],
            [
                8.315284241665078e-07,
                2.3823688159291947e-07,
                2.699577774589574e-07,
                8.315277302857965e-07,
                2.10243290909963e-07,
                2.3823696679327928e-07,
                2.6995784182183607e-07,
                3.466326624336003e-07,
                3.9278620026686556e-07,
                4.4508515805735777e-07
            ],
            [
                5.715005832895975e-07,
                2.144495864106235e-05,
                3.05902263391829e-07,
                3.466325797900508e-07,
                7.338208930460318e-07,
                2.3823693839325527e-07,
                4.450851580566494e-07,
                3.0590215399183813e-07,
                1.8553910183674878e-07,
                0.9999957771655562
            ],
            [
                3.4663266243111764e-07,
                3.4663278639892215e-07,
                1.6373766672973748e-07,
                3.927863875616689e-07,
                2.6995771309523475e-07,
                3.0590215399183813e-07,
                1.8553916819032217e-07,
                1.855391460719133e-07,
                5.043475885674441e-07,
                3.4663249714612693e-07
            ],
            [
                7.338211554801876e-07,
                9.422443692527585e-07,
                3.927862470899887e-07,
                8.315280276546789e-07,
                1.0677032518785256e-06,
                8.315280276546789e-07,
                1.3709573702822306e-06,
                1.3709567165579959e-06,
                4.2228349547223175e-06,
                1.5534979397790343e-06
            ],
            [
                3.05902263391829e-07,
                3.4663278639892215e-07,
                4.450852641737424e-07,
                1.370957860576702e-06,
                3.927863875616689e-07,
                2.1024339116168358e-07,
                5.715003107767143e-07,
                2.6995784182140636e-07,
                1.4449805540763184e-07,
                6.47595107001401e-07
            ],
            [
                4.4508515805735777e-07,
                2.6995790618469934e-07,
                2.5612834320563895e-06,
                1.7603425837903113e-06,
                1.5534983101644536e-06,
                2.5612834320563895e-06,
                8.315278294114555e-07,
                9.422445939054222e-07,
                2.561281600086738e-06,
                2.3823693839325527e-07
            ],
            [
                1.855391239544352e-07,
                7.338209805240734e-07,
                3.05902190458764e-07,
                3.466327037553825e-07,
                1.067703124601679e-06,
                7.338209805240734e-07,
                1.760342793638743e-06,
                4.785093924389007e-06,
                2.10243290909963e-07,
                2.561281294760143e-06
            ],
            [
                4.4508515805735777e-07,
                3.927862470905692e-07,
                3.9278620026686556e-07,
                5.043475885696228e-07,
                9.422450432030903e-07,
                2.3823696679327928e-07,
                6.475945666063607e-07,
                3.0590215399281185e-07,
                5.715004470334646e-07,
                2.699577452775239e-07
            ],
            [
                1.444980209564556e-07,
                1.6373774480605869e-07,
                1.1253517547010071e-07,
                1.2751901248454963e-07,
                1.6373770576776313e-07,
                1.637377057680051e-07,
                1.637377057680051e-07,
                1.27519088491875e-07,
                1.4449807263312446e-07,
                2.6995784182183607e-07
            ],
            [
                6.47594952603035e-07,
                5.71500515161527e-07,
                3.927862470905692e-07,
                1.3709576971463352e-06,
                7.33821330437595e-07,
                1.3709575337159875e-06,
                1.6373762769187936e-07,
                3.466325797900508e-07,
                2.561282516066741e-06,
                3.927862470905692e-07
            ],
            [
                6.475950298021765e-07,
                5.715005832895975e-07,
                2.1024326584702836e-07,
                2.561283126728994e-06,
                9.422444815814404e-07,
                3.0590237279085045e-07,
                1.0677027427624903e-06,
                3.7266379514061143e-06,
                3.466326624336003e-07,
                5.71500515161527e-07
            ],
            [
                1.4449800373118268e-07,
                3.927863875616689e-07,
                1.6373764721072816e-07,
                1.4449796928021588e-07,
                1.1253506814842375e-07,
                1.6373766672973748e-07,
                1.4449800373118268e-07,
                2.699578740032504e-07,
                2.1024334103581732e-07,
                5.043475284468537e-07
            ],
            [
                1.9947292459265734e-06,
                4.785095635624897e-06,
                1.2098662604291696e-06,
                1.5534973841895917e-06,
                1.0129988564845378e-05,
                2.9023112932045342e-06,
                7.88926070489716e-06,
                1.3007130015488633e-05,
                4.222834954753043e-06,
                3.2887478892683997e-06
            ],
            [
                1.8553914607267268e-07,
                3.9278629391427843e-07,
                0.9999785550542024,
                1.6373772528704005e-07,
                3.05902263391829e-07,
                5.71500515161527e-07,
                0.9999938558239456,
                3.4663262111182307e-07,
                1.8553914607267268e-07,
                0.9999978766215389
            ],
            [
                2.3823685319320354e-07,
                9.93120161310289e-08,
                1.637377057680051e-07,
                1.8553910183674878e-07,
                6.475945666063607e-07,
                2.1024334103581732e-07,
                2.382370235933104e-07,
                2.699578096403948e-07,
                1.4449803818215767e-07,
                2.10243290909963e-07
            ],
            [
                5.71500719545698e-07,
                5.043475885696228e-07,
                2.3823690999290963e-07,
                1.9947299593078385e-06,
                1.3709567165617364e-06,
                5.715002426486762e-07,
                1.994729721518893e-06,
                1.0677026154806063e-06,
                3.0590219045914655e-07,
                1.2098659719788098e-06
            ],
            [
                1.855391681906175e-07,
                9.93120161310289e-08,
                6.47595107001401e-07,
                1.1253525596174225e-07,
                1.0677028700422047e-06,
                2.382369951932796e-07,
                5.043475885696228e-07,
                1.6373772528704005e-07,
                1.4449802095666915e-07,
                7.734428685047173e-08
            ],
            [
                1.5534984953552536e-06,
                6.475945666063607e-07,
                3.059022269250683e-07,
                5.715003107767143e-07,
                1.209865539295696e-06,
                2.10243290909963e-07,
                3.466325797896173e-07,
                4.450852111148132e-07,
                2.382369667929001e-07,
                3.46632497145457e-07
            ],
            [
                5.422218969895357e-06,
                4.785095635655362e-06,
                1.5534984953552536e-06,
                7.889260704818233e-06,
                7.88926446679691e-06,
                9.610241502683509e-05,
                8.939695238634211e-06,
                4.222834954778007e-06,
                1.3007126914435202e-05,
                1.994730672675753e-06
            ],
            [
                3.2887502415767434e-06,
                1.275189972832538e-07,
                6.475947210046347e-07,
                3.059022269250683e-07,
                3.4663249714612693e-07,
                4.4508510499849186e-07,
                1.275190428875671e-07,
                1.4449805540763184e-07,
                3.0590222692437275e-07,
                4.4508499888219586e-07
            ],
            [
                1.7603430034867993e-06,
                9.422450432014836e-07,
                NaN,
                4.450850519403407e-07,
                5.043475885696228e-07,
                2.3823688159291947e-07,
                1.370957860576702e-06,
                6.1441767993788005e-06,
                1.0129993395336818e-05,
                5.715005151606823e-07
            ],
            [
                6.47594875403829e-07,
                4.450852641737424e-07,
                5.715002426486762e-07,
                3.653479031538012e-08,
                3.466327037553825e-07,
                3.466327450765785e-07,
                3.927862939126708e-07,
                5.71500719545698e-07,
                8.315283250371857e-07,
                2.3823688159291947e-07
            ],
            [
                4.450850519409479e-07,
                1.1253520230052635e-07,
                3.466327450765785e-07,
                3.466326211113502e-07,
                5.043475885696228e-07,
                2.699578096403948e-07,
                2.5612819054133693e-06,
                2.1024339116168358e-07,
                4.4508515805735777e-07,
                2.3823688159291947e-07
            ],
            [
                3.927862939136532e-07,
                1.1253509497883659e-07,
                6.475950298021765e-07,
                1.4449800373118268e-07,
                4.450851049991497e-07,
                4.4508515805735777e-07,
                5.043475284468537e-07,
                3.9278610661902853e-07,
                5.043475284468537e-07,
                3.05902336324494e-07
            ],
            [
                8.315277302841894e-07,
                1.6701415872659116e-05,
                0.9999969105055595,
                1.3709573702856596e-06,
                0.9999993106390376,
                5.043475885696228e-07,
                2.699578740032504e-07,
                5.04347287955046e-07,
                5.043476486924565e-07,
                0.9999990577554075
            ],
            [
                4.222834954801051e-06,
                1.370957860576702e-06,
                1.2098661162056318e-06,
                9.422444815792981e-07,
                2.902312331170226e-06,
                1.2098659719757836e-06,
                1.5534983101602148e-06,
                1.1478765389368729e-05,
                3.288749457469787e-06,
                3.7266397283908927e-06
            ],
            [
                2.3823688159237777e-07,
                9.931186222523604e-08,
                1.6373766672973748e-07,
                2.6995774527657245e-07,
                2.699576809143613e-07,
                1.6373762769138607e-07,
                3.927863407379485e-07,
                1.275191036933194e-07,
                3.466326624336003e-07,
                2.3823696679327928e-07
            ],
            [
                6.475945666063607e-07,
                1.0677028700422047e-06,
                1.3709573702856596e-06,
                1.6373772528704005e-07,
                8.31528325040778e-07,
                1.6373766672973748e-07,
                7.338208055680009e-07,
                9.422447062294175e-07,
                7.734423152941018e-08,
                5.715006514176113e-07
            ],
            [
                4.450852111155216e-07,
                1.8925157266089433e-05,
                3.2887494574832472e-06,
                0.9999980052707549,
                2.9023119851899796e-06,
                6.605216832620571e-05,
                7.338212429594283e-07,
                2.561281294760143e-06,
                5.715005832895975e-07,
                1.9947299593078385e-06
            ],
            [
                1.8553910183674878e-07,
                5.043475885696228e-07,
                4.450851049991497e-07,
                5.04347287955046e-07,
                3.927863407379485e-07,
                4.450852641737424e-07,
                8.315280276626197e-07,
                3.72663883989755e-06,
                7.338208055680009e-07,
                5.043475885696228e-07
            ],
            [
                5.043475885696228e-07,
                1.0677024882029858e-06,
                1.209865539298447e-06,
                1.8553907971855875e-07,
                NaN,
                1.855391239547094e-07,
                3.05902263391829e-07,
                1.3709576971463352e-06,
                6.475947210046347e-07,
                4.4508515805735777e-07
            ],
            [
                1.067703124601679e-06,
                4.4508505193932864e-07,
                3.466325797896173e-07,
                4.450850519403407e-07,
                4.4508494582314646e-07,
                7.338209805224048e-07,
                6.475947210046347e-07,
                6.475946438042047e-07,
                4.4508515805735777e-07,
                3.927862002663297e-07
            ],
            [
                1.4449805540740185e-07,
                4.450848927658745e-07,
                1.6373776432509826e-07,
                2.3823685319320354e-07,
                1.637376862489725e-07,
                6.47594952603035e-07,
                5.715004470326849e-07,
                2.699577452775239e-07,
                6.475948754012522e-07,
                1.637377057680051e-07
            ],
            [
                4.22283545819819e-06,
                2.3823690999290963e-07,
                2.382370235933104e-07,
                2.2603240284371276e-06,
                1.0677027427600627e-06,
                3.927863875616689e-07,
                3.7266397283908927e-06,
                3.466325797888292e-07,
                2.561282210740037e-06,
                2.902313369111213e-06
            ],
            [
                1.5534984953552536e-06,
                3.288749849529972e-06,
                1.209866260432471e-06,
                1.3709573702856596e-06,
                1.209865827752005e-06,
                4.785095065232451e-06,
                1.9947299593078385e-06,
                2.2603248367949354e-06,
                3.726639284125553e-06,
                1.2098656835252174e-06
            ],
            [
                2.902313369111213e-06,
                6.475947982037486e-07,
                2.561282516066741e-06,
                2.260324567337161e-06,
                2.260324567337161e-06,
                1.0677024882009222e-06,
                2.260323758987159e-06,
                1.2098659719601033e-06,
                3.2887506336235617e-06,
                1.0129988564974359e-05
            ],
            [
                2.1024326584680133e-07,
                3.059022998581767e-07,
                1.3709576971425944e-06,
                2.699578096403948e-07,
                3.466326624336003e-07,
                2.6995790618469934e-07,
                5.71500515161527e-07,
                6.47594952603035e-07,
                3.9278629391427843e-07,
                1.8553910183674878e-07
            ],
            [
                3.927862470899887e-07,
                9.93120161310289e-08,
                1.855391239547094e-07,
                8.764244316973974e-08,
                7.338207180898968e-07,
                3.9278629391427843e-07,
                1.1253525596174225e-07,
                1.275190732904469e-07,
                1.6373772528581146e-07,
                7.734416698849138e-08
            ],
            [
                1.3709572068553509e-06,
                9.422445939054222e-07,
                4.4508494582405734e-07,
                1.760342793638743e-06,
                1.9947304348703948e-06,
                2.3823682479317953e-07,
                8.315277302841894e-07,
                3.05902336324494e-07,
                4.4508499888275247e-07,
                3.466326624336003e-07
            ],
            [
                2.26032402841657e-06,
                1.0129990980100021e-05,
                7.889260704968913e-06,
                6.144173869603344e-06,
                1.994730197071414e-06,
                1.4738983729535602e-05,
                5.422220262636381e-06,
                1.0129988564974359e-05,
                1.1478768126057254e-05,
                1.4738989000422955e-05
            ],
            [
                3.9278620026686556e-07,
                1.637376862489725e-07,
                3.059022269254856e-07,
                2.699577774589574e-07,
                3.927862470905692e-07,
                1.8553910183674878e-07,
                2.102434412875379e-07,
                2.10243290909963e-07,
                9.422450432030903e-07,
                7.338212429594283e-07
            ],
            [
                1.994729483729522e-06,
                1.0677029973219343e-06,
                4.4508515805735777e-07,
                5.715005832895975e-07,
                1.2098659719788098e-06,
                1.9947299593078385e-06,
                1.0677028700422047e-06,
                3.2887494574832472e-06,
                2.2603251062450327e-06,
                1.209865827752005e-06
            ],
            [
                5.715005832886879e-07,
                6.47594952603035e-07,
                1.370957860576702e-06,
                1.9947299593078385e-06,
                2.699578740032504e-07,
                2.561282210740037e-06,
                1.7603440527334603e-06,
                8.315277302857965e-07,
                3.0590219045914655e-07,
                6.144173869603344e-06
            ],
            [
                1.6373764721072816e-07,
                1.637377057673536e-07,
                4.4508515805735777e-07,
                2.3823696679327928e-07,
                4.450852641737424e-07,
                5.04347468323289e-07,
                3.466327037539638e-07,
                3.927862002663297e-07,
                3.466327037553825e-07,
                8.315279285351409e-07
            ],
            [
                3.05902117523595e-07,
                8.31528424162821e-07,
                8.315283250394546e-07,
                8.939698435560267e-06,
                1.637377643243723e-07,
                9.422443692489024e-07,
                1.0677032518814388e-06,
                3.4663249714451116e-07,
                1.2098659719757836e-06,
                3.9278615343901467e-07
            ],
            [
                9.422443692574719e-07,
                8.764242227418718e-08,
                0.0001795280091563771,
                2.902312331170226e-06,
                8.315280276626197e-07,
                5.043473480777865e-07,
                6.475946438055299e-07,
                1.275190276859705e-07,
                9.931190958076104e-08,
                1.5534984953510149e-06
            ],
            [
                1.9947299593078385e-06,
                1.5534981249736758e-06,
                1.994729483729522e-06,
                2.2603245673443566e-06,
                2.699578096403948e-07,
                9.422442569334097e-07,
                7.338207180898968e-07,
                5.71500515161527e-07,
                3.0590219045914655e-07,
                3.9278629391427843e-07
            ],
            [
                3.05902190458764e-07,
                2.699578740032504e-07,
                3.059022269254856e-07,
                6.825609419848033e-08,
                1.8553905760024476e-07,
                2.3823696679327928e-07,
                1.6373762769187936e-07,
                2.1024339116168358e-07,
                1.4449807263312446e-07,
                2.699577774589574e-07
            ],
            [
                1.0677028700422047e-06,
                1.2098653950656417e-06,
                1.5534975693933505e-06,
                3.2887506335906595e-06,
                2.561281294760143e-06,
                1.5534981249574276e-06,
                1.5534984953453635e-06,
                1.3709572068272963e-06,
                1.5534975693933505e-06,
                1.5534983101549167e-06
            ],
            [
                9.422444815765128e-07,
                1.0677032518748838e-06,
                4.222833444590791e-06,
                1.5534975693979422e-06,
                1.7603425837791042e-06,
                7.889263526345123e-06,
                2.2603245673279107e-06,
                3.288748281329893e-06,
                4.2228319344021954e-06,
                3.726638839878908e-06
            ],
            [
                4.4508515805735777e-07,
                4.450852111148132e-07,
                1.2098659719788098e-06,
                6.475950298021765e-07,
                6.47595107001401e-07,
                3.288749065423109e-06,
                2.699578096403948e-07,
                5.715003107767143e-07,
                2.6995790618469934e-07,
                5.043475885696228e-07
            ],
            [
                1.855391681906175e-07,
                1.27519088491875e-07,
                3.059022269250683e-07,
                2.1024339116168358e-07,
                1.2751910369275402e-07,
                3.059022998581767e-07,
                2.3823690999323465e-07,
                2.699578740032504e-07,
                1.637377057680051e-07,
                1.637376862489725e-07
            ],
            [
                6.475948754028718e-07,
                1.3709573702856596e-06,
                8.315277302857965e-07,
                2.9023130231176453e-06,
                8.315284241665078e-07,
                1.7603438428800754e-06,
                5.715006514176113e-07,
                1.5534983101602148e-06,
                8.93969843573914e-06,
                1.0677026154827912e-06
            ],
            [
                7.338208055680009e-07,
                8.315277302841894e-07,
                1.067703124601679e-06,
                2.6995774527577444e-07,
                1.0677026154806063e-06,
                8.315282259138311e-07,
                1.7603440527286572e-06,
                3.466325797896173e-07,
                5.715006514176113e-07,
                1.2098659719661556e-06
            ],
            [
                1.5534983101602148e-06,
                1.067703124601679e-06,
                9.422450432014836e-07,
                1.5534971989696065e-06,
                1.0677024882009222e-06,
                5.043474683204221e-07,
                5.043472879540142e-07,
                4.450851580555361e-07,
                1.2098652508391807e-06,
                3.05902263391829e-07
            ],
            [
                1.0677026154827912e-06,
                1.370957860576702e-06,
                1.5534984953552536e-06,
                3.9278629391427843e-07,
                2.699577774589574e-07,
                1.209865827752005e-06,
                4.4508515805735777e-07,
                3.05902263391829e-07,
                5.715006514176113e-07,
                2.699578740032504e-07
            ],
            [
                1.1253520230052635e-07,
                4.4508494582405734e-07,
                1.637377448057981e-07,
                8.315282259117513e-07,
                3.927862002654366e-07,
                2.1024344128584085e-07,
                1.8553905760024476e-07,
                3.927862002663297e-07,
                1.8553905760062447e-07,
                9.931196877517082e-08
            ],
            [
                1.0677032518814388e-06,
                9.931193325852072e-08,
                1.637376862489725e-07,
                2.699578740032504e-07,
                3.059022998576899e-07,
                3.9278629391427843e-07,
                1.3709567165617364e-06,
                2.382369667929001e-07,
                3.05902263391829e-07,
                3.927863407379485e-07
            ],
            [
                1.147877359957198e-05,
                2.902313023130843e-06,
                1.209866260432471e-06,
                5.71500515159253e-07,
                5.043475885696228e-07,
                8.315278294114555e-07,
                8.315278294114555e-07,
                9.422450432030903e-07,
                2.699576809143613e-07,
                0.0031726830795912294
            ],
            [
                1.3709572068522336e-06,
                5.04347348075149e-07,
                6.475947982022763e-07,
                3.120191881423529e-05,
                0.9999756997622188,
                0.9999978766205261,
                3.4663249714325014e-07,
                0.9999706884545607,
                1.2098652508391807e-06,
                0.9999974387165695
            ],
            [
                1.275191036933194e-07,
                2.3823682479317953e-07,
                1.855390576008354e-07,
                2.699577452775239e-07,
                1.3709576971463352e-06,
                1.3709572068553509e-06,
                2.3823693839325527e-07,
                1.4449798650569826e-07,
                2.2603234895372223e-06,
                5.043475885696228e-07
            ],
            [
                7.734418542875216e-08,
                1.0677028700422047e-06,
                3.726639284144195e-06,
                1.5534971990169383e-06,
                1.444980209564556e-07,
                1.067703124601679e-06,
                7.734414854823498e-08,
                8.764242227418718e-08,
                4.6911638017556955e-08,
                4.450852111155216e-07
            ],
            [
                7.338207180898968e-07,
                2.1024334103581732e-07,
                1.8553914607267268e-07,
                1.5534971990169383e-06,
                0.9999981261239471,
                0.9999925887201382,
                6.962256249935742e-06,
                2.9023112932296107e-06,
                0.9999967112509368,
                3.9278620026686556e-07
            ],
            [
                2.2603248367949354e-06,
                3.927863407379485e-07,
                1.994729483723626e-06,
                3.466327450765785e-07,
                5.043472278312808e-07,
                5.715003789033962e-07,
                4.4508505193932864e-07,
                4.785094494783494e-06,
                8.315281267861397e-07,
                9.422445939032799e-07
            ],
            [
                4.539786864876098e-05,
                1.5534984953510149e-06,
                3.9278605979534166e-07,
                5.422218323487975e-06,
                1.7603427936183298e-06,
                1.760343213335281e-06,
                8.315277302788957e-07,
                4.4508499888219586e-07,
                1.9947299592933255e-06,
                1.6701427818034747e-05
            ],
            [
                1.6373766672994222e-07,
                5.043475885696228e-07,
                2.1024336609874897e-07,
                3.466326624336003e-07,
                4.450851049991497e-07,
                2.10243290909724e-07,
                2.699576809143613e-07,
                1.275191036933194e-07,
                3.059022998581767e-07,
                3.4663262111182307e-07
            ],
            [
                1.8553919030826963e-07,
                1.209865827752005e-06,
                0.9999921107393097,
                9.422444815814404e-07,
                1.3709575337159875e-06,
                1.0677032518814388e-06,
                2.699578096393206e-07,
                2.1024341622426268e-07,
                6.144175334510455e-06,
                8.764242227380856e-08
            ],
            [
                2.3823693839325527e-07,
                5.043475885696228e-07,
                6.825598028392069e-08,
                2.3823696679327928e-07,
                1.4449805540763184e-07,
                9.931187406410953e-08,
                9.931202796993203e-08,
                9.422442569334097e-07,
                2.6995771309523475e-07,
                1.3709573702856596e-06
            ],
            [
                6.47595107001401e-07,
                5.715004470326849e-07,
                2.5612834320563895e-06,
                1.5534984953552536e-06,
                3.9278629391427843e-07,
                1.0677026154827912e-06,
                0.9999877809254617,
                1.9947299593078385e-06,
                3.9278620026686556e-07,
                5.043476486924565e-07
            ],
            [
                1.855391681906175e-07,
                2.3823682479292225e-07,
                2.102434162245973e-07,
                2.3823688159291947e-07,
                2.382368815932174e-07,
                1.4449802095666915e-07,
                3.466325384682834e-07,
                3.05902336324494e-07,
                1.6373764721072816e-07,
                2.1024334103581732e-07
            ],
            [
                1.7603436330259153e-06,
                9.422442569290178e-07,
                1.7603438428740716e-06,
                1.012999098021058e-05,
                6.14417753171671e-06,
                4.785096776468749e-06,
                1.3007126914435202e-05,
                3.288749849498565e-06,
                2.5612828213934817e-06,
                1.7603425837791042e-06
            ],
            [
                5.71500719545698e-07,
                3.927863875616689e-07,
                3.9278610661902853e-07,
                3.466326624336003e-07,
                6.47595107001401e-07,
                3.927863875616689e-07,
                3.9278605979534166e-07,
                1.5534983101644536e-06,
                1.275190580890061e-07,
                2.1024334103581732e-07
            ],
            [
                9.422444815814404e-07,
                1.8553907971855875e-07,
                5.043472278322555e-07,
                1.6373764721072816e-07,
                3.0590226339137693e-07,
                2.1024336609874897e-07,
                1.8553914607267268e-07,
                1.855391681906175e-07,
                4.450848927658745e-07,
                3.05902263391829e-07
            ],
            [
                6.475948754028718e-07,
                6.475945666051092e-07,
                7.338208930460318e-07,
                7.338213304363436e-07,
                2.5612819054133693e-06,
                7.338212429582604e-07,
                1.3709568799919866e-06,
                1.6373766672973748e-07,
                6.475949526020042e-07,
                1.2751908849167202e-07
            ],
            [
                8.315277302857965e-07,
                8.315282259151545e-07,
                3.0590219045914655e-07,
                7.33821330437595e-07,
                1.209865827752005e-06,
                8.315279285370317e-07,
                9.422444815814404e-07,
                3.9278620026686556e-07,
                3.9278629391427843e-07,
                1.8553910183674878e-07
            ],
            [
                2.699576809143613e-07,
                1.4449798650551755e-07,
                3.4663266243308805e-07,
                2.382369667929001e-07,
                3.726637951367137e-06,
                1.0677032518814388e-06,
                1.6373770576776313e-07,
                5.715002426475718e-07,
                3.059023363231725e-07,
                3.2887506336086064e-06
            ],
            [
                2.3823693839325527e-07,
                6.47595107001401e-07,
                1.1253516205489029e-07,
                1.6373772528704005e-07,
                2.3823685319320354e-07,
                5.043474683240344e-07,
                1.5534973842076057e-06,
                3.05902263391829e-07,
                1.855391239547094e-07,
                4.450850519409479e-07
            ],
            [
                4.4508494582314646e-07,
                3.466326624336003e-07,
                5.04347348075149e-07,
                6.475950298021765e-07,
                4.2228339479858295e-06,
                8.315278294114555e-07,
                3.927862939126708e-07,
                3.05902263391829e-07,
                8.315278294038928e-07,
                6.475945666051092e-07
            ],
            [
                0.9999960330145624,
                0.9999982396559488,
                0.9999942280792876,
                0.9999972735307056,
                0.9999934595596646,
                0.9999877809239989,
                0.9999934595627789,
                0.9999942280799766,
                0.9999974387171798,
                0.9999974387187064
            ]
        ]
    },
    {
        "q_id": "9462_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            9,
            11,
            12,
            13,
            14,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            28,
            29,
            30,
            33,
            34,
            37,
            41,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            55,
            58,
            59,
            60,
            61,
            63,
            66,
            68,
            69,
            70,
            72,
            78,
            79,
            80,
            81,
            82,
            88,
            89,
            90,
            92,
            94,
            95,
            96,
            97,
            100,
            101,
            102,
            103,
            104,
            105,
            108,
            109,
            110,
            111,
            114,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            125,
            127,
            64,
            65
        ],
        "rewards": [
            [
                1.9947297215043796e-06,
                1.2098662604291696e-06,
                3.7266410611296085e-06,
                1.7603440527222532e-06,
                9.422443692527585e-07,
                4.785096205973894e-06,
                3.7266410611296085e-06,
                3.72663883989755e-06,
                3.288748281295496e-06,
                2.5612828213934817e-06
            ],
            [
                NaN,
                1.8553914607267268e-07,
                6.962259569750576e-06,
                1.4738978458140753e-05,
                1.5534979397790343e-06,
                9.422444815765128e-07,
                1.0677032518748838e-06,
                4.785095635655362e-06,
                7.889262585886274e-06,
                5.715006514151423e-07
            ],
            [
                1.2098653950656417e-06,
                3.726639728370556e-06,
                1.5534975693933505e-06,
                9.422442569208767e-07,
                1.7603434231705793e-06,
                3.2887494573232236e-06,
                9.422450431989127e-07,
                2.561283126679493e-06,
                2.2603240284371276e-06,
                6.475951069985296e-07
            ],
            [
                2.260325375677174e-06,
                2.430024073461624e-05,
                6.144174601935314e-06,
                6.962257909722651e-06,
                0.9999978766210335,
                0.9999972735294067,
                0.9999852610180633,
                2.9023112932045342e-06,
                3.7266410611296085e-06,
                3.535624650150453e-05
            ],
            [
                0.999998863436562,
                0.9999997897566592,
                0.9999982396569987,
                0.999998712104325,
                0.9999983463110071,
                0.9999969105044545,
                0.9999975938982397,
                0.9999962733607267,
                0.9999996533674207,
                0.9999921107402546
            ],
            [
                2.260324028427877e-06,
                6.475947210031623e-07,
                1.760343003481596e-06,
                4.539787406003298e-05,
                1.012999460278499e-05,
                5.422217030707961e-06,
                8.315283250371857e-07,
                9.422445939032799e-07,
                9.422448185510695e-07,
                1.7603430034743913e-06
            ],
            [
                3.927860597945825e-07,
                1.0677029973192638e-06,
                5.422220262636381e-06,
                0.9984988176335037,
                4.222832941034507e-06,
                2.699577774589574e-07,
                7.889259764517575e-06,
                3.059022998569248e-07,
                NaN,
                1.670142582682936e-05
            ],
            [
                3.466326211113502e-07,
                1.3709567165617364e-06,
                1.2098656835224664e-06,
                1.7603434231833873e-06,
                3.7266397283908927e-06,
                3.0590237279085045e-07,
                2.90231094723893e-06,
                3.46632497145457e-07,
                NaN,
                1.2098659719788098e-06
            ],
            [
                0.999975699759374,
                4.539785782390681e-05,
                0.9999706884581169,
                3.466326624336003e-07,
                0.9999785550593698,
                6.962259569630266e-06,
                0.9999910603069082,
                0.9999756997564915,
                2.699577130960941e-07,
                0.999983298578184
            ],
            [
                6.144173137126169e-06,
                4.785093924330255e-06,
                2.5612812947508257e-06,
                2.260325106237323e-06,
                2.9023119851635836e-06,
                NaN,
                1.670142383595838e-05,
                3.2887506336086064e-06,
                2.260325106237323e-06,
                1.1478768125911099e-05
            ],
            [
                1.4449798650551755e-07,
                9.931198061405701e-08,
                1.8553916819032217e-07,
                1.6373770576776313e-07,
                6.475945666051092e-07,
                9.422444815814404e-07,
                5.715005832886879e-07,
                7.73441946488886e-08,
                1.275190276859705e-07,
                5.715003107767143e-07
            ],
            [
                0.9999994631248685,
                0.9999989322972586,
                0.9999949062944016,
                0.9999972735294095,
                1.444980726324838e-07,
                0.9999885212360617,
                0.9999981261237252,
                0.9999962733593967,
                0.9999987121044785,
                0.9999985406230849
            ],
            [
                2.561281905390075e-06,
                8.315283250371857e-07,
                1.5534973841895917e-06,
                1.3709575336947905e-06,
                9.422448185478557e-07,
                6.962254589851619e-06,
                9.422448185478557e-07,
                1.994730434879465e-06,
                1.0677027427600627e-06,
                1.9947297215043796e-06
            ],
            [
                1.553498310118888e-06,
                0.999998346310417,
                5.422217030747413e-06,
                NaN,
                2.382369951932796e-07,
                0.9999861539971221,
                0.9999980052693284,
                0.9999885212360079,
                0.9999741325629217,
                0.9999972735290832
            ],
            [
                6.023577783447482e-08,
                0.999993459565121,
                0.9999969105055548,
                1.6701423836262173e-05,
                0.9978172837022192,
                0.9998911031307312,
                3.9278605979534166e-07,
                0.9999952149060799,
                0.9999970976869792,
                0.9997694932589922
            ],
            [
                6.475949526020042e-07,
                7.338207180864763e-07,
                3.7266383956509585e-06,
                1.067703379154416e-06,
                3.7266397283908927e-06,
                1.994730672668496e-06,
                NaN,
                2.1024336609843824e-07,
                6.962259569750576e-06,
                2.9023112932177327e-06
            ],
            [
                8.315280276626197e-07,
                0.9999898700066315,
                6.475951069985296e-07,
                0.9999599363080647,
                1.0677026154806063e-06,
                1.2098652508424818e-06,
                0.9999949062968284,
                0.9999974387171825,
                0.9999967112509387,
                0.9999921107336793
            ],
            [
                1.0677026154806063e-06,
                1.4738981972082061e-05,
                5.043476486915964e-07,
                4.785095065132354e-06,
                3.7266383954560706e-06,
                7.338209805200689e-07,
                3.2887498495150166e-06,
                5.715004470295662e-07,
                1.0677032518748838e-06,
                1.1478770862735993e-05
            ],
            [
                8.315281267882195e-07,
                1.3709570434178922e-06,
                1.0677026154730804e-06,
                4.785093353874907e-06,
                1.7603427936263351e-06,
                5.422217030707961e-06,
                1.0677026154730804e-06,
                1.0677026154730804e-06,
                1.0677024881980089e-06,
                9.422448185478557e-07
            ],
            [
                2.2603234895176927e-06,
                1.3007134667259441e-05,
                4.222832941142044e-06,
                8.93969950101825e-06,
                2.2603242978871282e-06,
                5.422220909009474e-06,
                6.144173869502757e-06,
                0.9999957771670868,
                1.3007126914435202e-05,
                NaN
            ],
            [
                NaN,
                1.6701423836262173e-05,
                1.670141985446017e-05,
                1.0129995810463632e-05,
                3.7266397283908927e-06,
                1.7603434231705793e-06,
                2.260325106237323e-06,
                1.2098662604291696e-06,
                4.2228324377740105e-06,
                6.144176799334096e-06
            ],
            [
                8.939693107190907e-06,
                1.0677032518785256e-06,
                5.715003107755449e-07,
                2.5612822107167428e-06,
                1.5534984953453635e-06,
                5.04347348075149e-07,
                2.5612819054028872e-06,
                2.9023133690637e-06,
                8.315283250371857e-07,
                5.715003107767143e-07
            ],
            [
                NaN,
                NaN,
                1.2098661162056318e-06,
                NaN,
                2.5612834320563895e-06,
                4.785096776433933e-06,
                2.260324836787226e-06,
                1.5534984953510149e-06,
                1.5534984953453635e-06,
                5.715003107767143e-07
            ],
            [
                2.2603234895176927e-06,
                1.5534983101602148e-06,
                3.2887502415767434e-06,
                1.370957860576702e-06,
                3.288748673376478e-06,
                1.1478773599425825e-05,
                6.9622595696935874e-06,
                2.561282516066741e-06,
                5.043476486924565e-07,
                9.422448185534261e-07
            ],
            [
                0.9999984465026167,
                0.9999981261246182,
                1.2098662604247682e-06,
                3.059022998581767e-07,
                0.999999428499349,
                1.3709576971463352e-06,
                1.553498495338299e-06,
                7.338208930460318e-07,
                9.610242648972629e-05,
                4.450850519409479e-07
            ],
            [
                8.315279285370317e-07,
                1.9947299593078385e-06,
                1.1478772231086046e-05,
                1.7603434231833873e-06,
                4.785093924362895e-06,
                5.4222183235249605e-06,
                NaN,
                1.5534971990169383e-06,
                2.561282210740037e-06,
                6.1441746020359e-06
            ],
            [
                2.90231233114251e-06,
                0.9999885212360033,
                1.0677032518785256e-06,
                0.9999921107355554,
                3.7266401726173067e-06,
                0.9993736658477201,
                3.288749457469787e-06,
                0.9997965729566846,
                0.9999038975974491,
                0.9999898700078569
            ],
            [
                3.726637951387472e-06,
                3.120190021759579e-05,
                1.7603440527286572e-06,
                4.450852111135988e-07,
                2.5612819054028872e-06,
                9.422449308716635e-07,
                4.78509563550957e-06,
                6.9622595696935874e-06,
                NaN,
                3.9278615344178325e-07
            ],
            [
                8.939698435657833e-06,
                5.8291286393273546e-05,
                0.9999916019299858,
                1.3007123813193233e-05,
                4.2228339479858295e-06,
                2.5612816000646084e-06,
                NaN,
                5.829124470847917e-05,
                8.481101107142626e-05,
                3.726639728370556e-06
            ],
            [
                NaN,
                5.4222183235249605e-06,
                1.7603440527222532e-06,
                2.5612828213934817e-06,
                1.067703124601679e-06,
                2.561281600086738e-06,
                2.260324028427877e-06,
                8.315282259151545e-07,
                1.760342793638743e-06,
                NaN
            ],
            [
                1.2098662604291696e-06,
                1.8553919030858602e-07,
                2.902313023101807e-06,
                9.931196877517082e-08,
                1.3709575337125585e-06,
                2.382370235933104e-07,
                0.9999985406241277,
                0.9998911031304761,
                6.475947982037486e-07,
                0.9999990577551819
            ],
            [
                2.699578096403948e-07,
                4.450849988811838e-07,
                8.315281267882195e-07,
                NaN,
                3.059022269250683e-07,
                3.466326211113502e-07,
                2.3823690999323465e-07,
                9.422444815814404e-07,
                5.715003107767143e-07,
                3.927862939126708e-07
            ],
            [
                1.0677026154827912e-06,
                8.764254764749753e-08,
                9.422447062294175e-07,
                2.902313023130843e-06,
                1.27519088491875e-07,
                1.5534971990169383e-06,
                2.102434412875379e-07,
                1.4449798650551755e-07,
                3.927862470899887e-07,
                3.0590237279032884e-07
            ],
            [
                2.9023119851781017e-06,
                3.2887502415438413e-06,
                2.2603248367949354e-06,
                8.315283250371857e-07,
                1.7603434231833873e-06,
                6.962257079832313e-06,
                6.144173869558639e-06,
                2.90231094723893e-06,
                3.288748673376478e-06,
                4.2228319344021954e-06
            ],
            [
                0.9999798543140564,
                0.9999724642991294,
                0.9999974387180982,
                0.9999251538000897,
                0.9999970976869802,
                0.9999970976869815,
                4.78509278348926e-06,
                0.9999962733611671,
                4.53978632394714e-05,
                0.9999942280820446
            ],
            [
                5.422217030707961e-06,
                2.902310947208574e-06,
                2.5612831267086116e-06,
                8.939693107190907e-06,
                4.785094494716039e-06,
                0.00015843629221379494,
                5.144221979793211e-05,
                5.043475885674441e-07,
                2.5612812947508257e-06,
                1.5534971990169383e-06
            ],
            [
                1.2098656835224664e-06,
                1.3709572068522336e-06,
                3.466327037553825e-07,
                4.450849988811838e-07,
                8.315278294072958e-07,
                3.927862470899887e-07,
                1.370957860576702e-06,
                8.315279285351409e-07,
                5.715002426486762e-07,
                8.315277302841894e-07
            ],
            [
                1.2098662604291696e-06,
                6.1441746020359e-06,
                6.47595107001401e-07,
                6.962257909842961e-06,
                3.288749457469787e-06,
                0.999954602120768,
                1.1478768126057254e-05,
                3.12019039369228e-05,
                3.726637951387472e-06,
                2.90231094723893e-06
            ],
            [
                4.4508515805735777e-07,
                5.715005832895975e-07,
                NaN,
                5.71500719545698e-07,
                NaN,
                0.9999843104484678,
                4.785092783519724e-06,
                8.315278294097538e-07,
                NaN,
                9.422445939054222e-07
            ],
            [
                8.939695238634211e-06,
                1.5534977545886537e-06,
                7.889260704968913e-06,
                3.726639284144195e-06,
                1.994729721518893e-06,
                1.9947301970972664e-06,
                2.2603240284371276e-06,
                1.5534971990169383e-06,
                4.222834954801051e-06,
                3.72663883989755e-06
            ],
            [
                3.059022998581767e-07,
                5.71500719545698e-07,
                9.931194509740267e-08,
                1.637376862489725e-07,
                3.4663278639892215e-07,
                8.315277302857965e-07,
                1.0677027427624903e-06,
                0.9999996310115042,
                3.0590237279085045e-07,
                2.699578740032504e-07
            ],
            [
                NaN,
                0.9999516743449642,
                6.962258739796719e-06,
                0.2018132126589859,
                0.99999911484307,
                9.61024150359243e-05,
                0.0002959570650765635,
                1.892515049819277e-05,
                3.535623807260338e-05,
                1.892514598551715e-05
            ],
            [
                2.6995774527718623e-07,
                9.422448185534261e-07,
                1.1253518888531272e-07,
                2.699577774585891e-07,
                2.1024334103581732e-07,
                2.3823702359290413e-07,
                9.93120161310289e-08,
                3.0590237279032884e-07,
                NaN,
                2.102433159721477e-07
            ],
            [
                2.1444953527476883e-05,
                3.288749065423109e-06,
                6.144177531811707e-06,
                NaN,
                0.9999785550567928,
                0.9999667857933785,
                0.999860177927803,
                0.9999646437578918,
                1.1478769494396542e-05,
                0.9999771719974861
            ],
            [
                2.5612812946681295e-06,
                5.043475284430694e-07,
                6.475948754012522e-07,
                6.962256249885085e-06,
                1.3709575337078829e-06,
                3.726639284103523e-06,
                5.043472879525233e-07,
                2.561281905390075e-06,
                4.450848927637999e-07,
                5.422218323487975e-06
            ],
            [
                4.539787406003298e-05,
                1.4738978458382043e-05,
                4.006371129615879e-05,
                5.4222176771176554e-06,
                4.785092783519724e-06,
                6.144175334468545e-06,
                1.5534983101644536e-06,
                0.00023050668823639762,
                2.4300237837960777e-05,
                3.120191881094355e-05
            ],
            [
                1.0677032518785256e-06,
                7.338208055680009e-07,
                2.3823690999323465e-07,
                9.422447062294175e-07,
                1.1253506814842375e-07,
                5.043473480777865e-07,
                3.466327037553825e-07,
                NaN,
                2.1024339116168358e-07,
                5.715006514176113e-07
            ],
            [
                0.9999975938970891,
                0.0001233946191118875,
                0.999991601931004,
                0.9999962733616125,
                2.9023126771227976e-06,
                1.994729483729522e-06,
                2.2603251062450327e-06,
                0.9999974387165702,
                0.9914225152832379,
                0.9999938558246803
            ],
            [
                5.715007195384861e-07,
                6.144175334418252e-06,
                5.715006514105942e-07,
                8.939699501229642e-06,
                1.670142582682936e-05,
                1.670141786231398e-05,
                6.962255419868303e-06,
                1.2098662604291696e-06,
                2.5612819054133693e-06,
                1.0677027427525368e-06
            ],
            [
                3.2887506336235617e-06,
                3.535625493182252e-05,
                1.4738983729535602e-05,
                1.209865539295696e-06,
                1.7603436330259153e-06,
                NaN,
                8.939695238634211e-06,
                2.260324567337161e-06,
                8.939700566907275e-06,
                2.902312331125353e-06
            ],
            [
                1.4738989000422955e-05,
                0.9999972735294093,
                0.999998446501692,
                3.288749457469787e-06,
                0.9999987901344629,
                1.5534979397740895e-06,
                3.12019039369228e-05,
                2.902312677150514e-06,
                NaN,
                0.9999957771680745
            ],
            [
                3.466326211113502e-07,
                6.475950297993789e-07,
                9.931190958076104e-08,
                2.1024341622368903e-07,
                6.475947982037486e-07,
                2.2603242978871282e-06,
                6.475947982037486e-07,
                9.422448185534261e-07,
                2.1024331597262577e-07,
                5.043472278299047e-07
            ],
            [
                1.30071315662049e-05,
                NaN,
                1.4738989000422955e-05,
                6.962254589978262e-06,
                1.370957860576702e-06,
                1.2098655392921197e-06,
                1.9947292459347367e-06,
                1.0129990980100021e-05,
                1.9947292459347367e-06,
                4.785095065204162e-06
            ],
            [
                0.9999904837494679,
                0.9999516743626059,
                3.4663262111182307e-07,
                2.430023204460668e-05,
                6.475947982037486e-07,
                0.9999861539988052,
                0.9999861539988246,
                3.9278629391427843e-07,
                0.9999852610198725,
                1.7603434231833873e-06
            ],
            [
                4.222834451382849e-06,
                0.00012339457500953096,
                2.3823702359290413e-07,
                2.1024339116168358e-07,
                2.90231094723893e-06,
                1.637377057680051e-07,
                3.2887482813149375e-06,
                7.889262585886274e-06,
                2.1444943302181958e-05,
                1.2098662604291696e-06
            ],
            [
                6.1441746020359e-06,
                1.3709578605729614e-06,
                5.715005151606823e-07,
                1.0677027427600627e-06,
                5.715005151606823e-07,
                7.338210680021253e-07,
                5.4222183235249605e-06,
                4.450849988811838e-07,
                6.144173869558639e-06,
                3.059022998576899e-07
            ],
            [
                6.475949526020042e-07,
                1.3709567165579959e-06,
                7.338211554783522e-07,
                0.0002611904339341055,
                4.5397852401406606e-05,
                8.315283250371857e-07,
                1.9947299593014888e-06,
                1.3709576971425944e-06,
                2.9023133690980155e-06,
                9.422443692555439e-07
            ],
            [
                1.5534975693933505e-06,
                1.5534979397740895e-06,
                2.4300234940642642e-05,
                1.5534975693869924e-06,
                3.0590226339061185e-07,
                3.059022998581767e-07,
                1.3007130015677909e-05,
                2.2603234895176927e-06,
                3.0590215399183813e-07,
                1.9947294837154625e-06
            ],
            [
                1.2098659719757836e-06,
                7.338207180838067e-07,
                3.288750241561788e-06,
                NaN,
                1.0677024881980089e-06,
                1.99473067264854e-06,
                0.00033535027007513217,
                9.422445939054222e-07,
                1.3709570434054234e-06,
                5.422220909009474e-06
            ],
            [
                7.889260704818233e-06,
                0.9999925887175004,
                NaN,
                1.3007128464559612e-05,
                7.889263526266196e-06,
                1.6701423836262173e-05,
                3.5356242285703183e-05,
                1.0129992187658463e-05,
                2.7535694384882703e-05,
                6.96225873967641e-06
            ],
            [
                1.2098662604247682e-06,
                5.043475885674441e-07,
                1.370956716529941e-06,
                1.5534975693933505e-06,
                9.422450431989127e-07,
                6.475947210012481e-07,
                1.3709573702778664e-06,
                9.4224425692559e-07,
                9.422444815765128e-07,
                1.7603438428800754e-06
            ],
            [
                NaN,
                2.699577774589574e-07,
                1.9947297215125433e-06,
                3.2887506336235617e-06,
                8.315283250371857e-07,
                2.699578740032504e-07,
                9.422445939054222e-07,
                9.422447062294175e-07,
                5.043475885696228e-07,
                1.637376862489725e-07
            ],
            [
                4.450849988811838e-07,
                3.2887482813149375e-06,
                7.338209805240734e-07,
                1.1478769494250387e-05,
                2.6995790618469934e-07,
                4.450848927637999e-07,
                2.561281600049467e-06,
                6.144173136952939e-06,
                3.726639728370556e-06,
                8.315279285370317e-07
            ],
            [
                1.994729483729522e-06,
                0.9999251538001431,
                0.999997438716571,
                7.338208055680009e-07,
                3.9278629391427843e-07,
                4.785095635655362e-06,
                2.382369951932796e-07,
                4.222832941072913e-06,
                1.2098661162056318e-06,
                9.422447062294175e-07
            ],
            [
                1.994730434879465e-06,
                1.0677026154806063e-06,
                5.04347287955046e-07,
                5.715005151606823e-07,
                9.422450432014836e-07,
                2.260325375664839e-06,
                3.927862002663297e-07,
                4.450849988811838e-07,
                1.2098653950692178e-06,
                3.9278610661902853e-07
            ],
            [
                2.5612834320470717e-06,
                2.9023116392097746e-06,
                0.9999892166878142,
                1.30071315662049e-05,
                2.5612834320470717e-06,
                5.422218969895357e-06,
                0.9998766053832401,
                6.962256249935742e-06,
                2.1444950971601277e-05,
                0.9997040429112434
            ],
            [
                3.927863875584984e-07,
                1.27519088491875e-07,
                2.1024344128660572e-07,
                2.1024329090781183e-07,
                7.889261644875049e-06,
                2.3823693839290317e-07,
                4.450851049941403e-07,
                3.059021904571643e-07,
                1.6373768624837685e-07,
                1.4449805540651476e-07
            ],
            [
                5.715004470313855e-07,
                2.699576809121209e-07,
                3.0590215399183813e-07,
                5.043475885696228e-07,
                9.422450432030903e-07,
                1.7603438428800754e-06,
                5.422217030781934e-06,
                3.927862939126708e-07,
                2.5612828213934817e-06,
                4.450848927650143e-07
            ],
            [
                1.7603438428800754e-06,
                4.222834451355964e-06,
                3.4663249714612693e-07,
                0.9999934595596691,
                0.9968273169734263,
                3.05902336324494e-07,
                0.9980732655368116,
                3.726637951387472e-06,
                4.450852111148132e-07,
                2.699576809143613e-07
            ],
            [
                0.9999987121047852,
                0.9999975938982366,
                0.9999993916411088,
                1.6701427818034747e-05,
                0.9999892166865092,
                0.9999945777816849,
                0.9999945777797459,
                0.9999970976876719,
                0.9999949062925744,
                0.9999916019309849
            ],
            [
                1.0677032518814388e-06,
                6.475947982037486e-07,
                3.05902190458764e-07,
                3.059021175261338e-07,
                3.466325797896173e-07,
                3.4663274507713016e-07,
                2.430024073461624e-05,
                2.5612834320470717e-06,
                3.7266406168827523e-06,
                2.3823688159291947e-07
            ],
            [
                0.9999945777791046,
                1.5534971990169383e-06,
                0.9999945777823355,
                0.9999843104485736,
                1.4738989000422955e-05,
                5.715003107767143e-07,
                3.7266401726359486e-06,
                0.9999861539954895,
                3.466326624336003e-07,
                2.902313023130843e-06
            ],
            [
                6.144173869502757e-06,
                1.670142980893658e-05,
                1.6701427817730953e-05,
                1.3007123813193233e-05,
                1.012998977213635e-05,
                1.147876812538911e-05,
                4.785096776303374e-06,
                3.726639284017094e-06,
                NaN,
                3.288750633518874e-06
            ],
            [
                3.7266410611296085e-06,
                1.1478773599425825e-05,
                9.422447062294175e-07,
                1.5534973842030142e-06,
                8.315284241650899e-07,
                3.726641061109272e-06,
                9.422449308774482e-07,
                4.2228319344021954e-06,
                9.422443692574719e-07,
                8.481102117280838e-05
            ],
            [
                8.939698435560267e-06,
                2.5612825160562587e-06,
                7.338213304363436e-07,
                NaN,
                9.422444815792981e-07,
                1.9947299593014888e-06,
                2.2603245673279107e-06,
                8.315281267882195e-07,
                2.561281905390075e-06,
                0.9999151889189865
            ],
            [
                0.9999955048173538,
                0.999998239657208,
                0.9999452402374848,
                0.9999995818812272,
                8.315281267882195e-07,
                5.043476486915964e-07,
                0.9999843104428316,
                8.315277302857965e-07,
                0.9999985406237802,
                0.9999945777810453
            ],
            [
                8.315278294072958e-07,
                1.2098652508424818e-06,
                2.2603245673443566e-06,
                2.699576809143613e-07,
                7.338211554783522e-07,
                1.5534981249697903e-06,
                9.422442569315887e-07,
                1.2098652508424818e-06,
                1.6701421843720577e-05,
                5.715003107755449e-07
            ],
            [
                1.3709575337159875e-06,
                6.47595107001401e-07,
                2.430025232247918e-05,
                1.5534983101644536e-06,
                8.939697369980456e-06,
                NaN,
                2.561281600086738e-06,
                3.7266406168827523e-06,
                1.9947299593078385e-06,
                1.3709576971463352e-06
            ],
            [
                0.9924227578707229,
                0.9999646437582725,
                0.9940889320138948,
                0.999909719581675,
                0.997199073253986,
                0.9982992774509979,
                0.9999706884618819,
                0.999977171994804,
                0.9999706884689391,
                NaN
            ],
            [
                NaN,
                5.715007195447234e-07,
                0.00015843619816453063,
                5.4222183235249605e-06,
                6.144176799283803e-06,
                2.9023116391675407e-06,
                1.760343213335281e-06,
                4.222834954778007e-06,
                NaN,
                1.2098653950551882e-06
            ],
            [
                1.0677027427471959e-06,
                1.7603425837791042e-06,
                5.715004470313855e-07,
                2.902313369111213e-06,
                8.315281267861397e-07,
                7.338209805224048e-07,
                5.715007195447234e-07,
                2.260324028427877e-06,
                6.475947210012481e-07,
                3.288750241561788e-06
            ],
            [
                0.9999485577884615,
                0.999876605397221,
                0.9999930377404639,
                0.9999994631251247,
                0.9999885212332612,
                7.338208930460318e-07,
                0.9999969105040838,
                0.999997097686635,
                0.9992903294716138,
                0.9997965731046078
            ],
            [
                1.994729483723626e-06,
                1.3007126913583456e-05,
                7.889266347715168e-06,
                1.5534983101602148e-06,
                NaN,
                NaN,
                2.430024652792821e-05,
                NaN,
                5.422218969818919e-06,
                2.5612819054133693e-06
            ],
            [
                1.3709576971425944e-06,
                2.1444943301674863e-05,
                1.3709572068422585e-06,
                0.999974132560239,
                6.144174601935314e-06,
                NaN,
                2.9023119851635836e-06,
                1.209866260432471e-06,
                0.9999938558246876,
                1.5534975693979422e-06
            ],
            [
                1.994729483705484e-06,
                1.3709575336860625e-06,
                5.422217030555087e-06,
                1.5534983101393749e-06,
                1.760343213322473e-06,
                9.422448185435711e-07,
                7.889264466639056e-06,
                9.422443692527585e-07,
                1.2098655392662613e-06,
                8.315280276580819e-07
            ]
        ]
    },
    {
        "q_id": "9852_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            7,
            8,
            9,
            11,
            12,
            13,
            15,
            16,
            19,
            22,
            24,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            49,
            50,
            51,
            52,
            54,
            55,
            58,
            59,
            60,
            62,
            63,
            64,
            67,
            68,
            69,
            70,
            73,
            74,
            75,
            77,
            82,
            83,
            86,
            89,
            91,
            92,
            93,
            95,
            96,
            99,
            100,
            101,
            102,
            105,
            106,
            107,
            109,
            110,
            111,
            113,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            124,
            125,
            127
        ],
        "rewards": [
            [
                6.962254589914941e-06,
                1.1478768125911099e-05,
                4.222832941193893e-06,
                2.4300234941261454e-05,
                7.889265407090955e-06,
                5.422220262636381e-06,
                3.2887498495150166e-06,
                2.5612828213934817e-06,
                1.209865539295696e-06,
                4.785096206047877e-06
            ],
            [
                5.715005151606823e-07,
                6.475948754012522e-07,
                1.760343213335281e-06,
                3.466326211113502e-07,
                0.9999945777804113,
                0.9999904837473246,
                3.535624650279074e-05,
                4.450852641737424e-07,
                0.1403362494900832,
                5.043472278322555e-07
            ],
            [
                2.90231094723893e-06,
                1.4738981972564636e-05,
                4.2228339479858295e-06,
                3.059022269250683e-07,
                1.5534983101478522e-06,
                1.0677024881980089e-06,
                1.9947292459347367e-06,
                3.2887506336086064e-06,
                2.2603234895289998e-06,
                6.144174601991196e-06
            ],
            [
                3.288748673376478e-06,
                0.00023050671544367406,
                6.144174601991196e-06,
                2.1024334103581732e-07,
                1.2098659719788098e-06,
                5.043472278322555e-07,
                5.715005151606823e-07,
                9.422444815792981e-07,
                4.785092783519724e-06,
                5.715005151606823e-07
            ],
            [
                0.0004305569894503386,
                0.00023050682556727942,
                1.012999218776902e-05,
                1.760343003481596e-06,
                0.0005527786830705686,
                6.144173869603344e-06,
                3.120190765625026e-05,
                5.715006514176113e-07,
                NaN,
                5.144220753172505e-05
            ],
            [
                5.715005151574337e-07,
                4.785095065204162e-06,
                5.043472879540142e-07,
                1.0677032518785256e-06,
                9.4224425692559e-07,
                1.5534983101602148e-06,
                3.2887506336086064e-06,
                7.88926446679691e-06,
                1.2098655392921197e-06,
                1.5534973842076057e-06
            ],
            [
                1.3709575337159875e-06,
                8.93969950132721e-06,
                5.422221555380179e-06,
                4.222834451382849e-06,
                9.610241501774589e-05,
                1.6701425827133152e-05,
                2.1444948414321717e-05,
                4.785093353909723e-06,
                3.2887482813149375e-06,
                2.90231233114251e-06
            ],
            [
                6.962254589978262e-06,
                3.7266410611296085e-06,
                4.2228339479858295e-06,
                7.889259764517575e-06,
                6.475947982037486e-07,
                2.9023119851899796e-06,
                1.994730672668496e-06,
                4.2228339479858295e-06,
                1.2098662604291696e-06,
                1.6701421845361053e-05
            ],
            [
                9.422443692574719e-07,
                7.33821330437595e-07,
                0.9999985406243028,
                5.043475885696228e-07,
                6.1441767993788005e-06,
                4.785093924389007e-06,
                2.2603245673443566e-06,
                1.7603440527334603e-06,
                6.475947982037486e-07,
                3.2887502415767434e-06
            ],
            [
                3.726639728348526e-06,
                0.010986945069505025,
                4.222831934379152e-06,
                5.422217677152175e-06,
                5.422218323487975e-06,
                6.962257909785973e-06,
                1.994729008145876e-06,
                3.288749065423109e-06,
                6.962255419931625e-06,
                3.288750241561788e-06
            ],
            [
                1.0677024881980089e-06,
                2.5612828213690224e-06,
                2.5612812947508257e-06,
                1.9947292459347367e-06,
                1.3709575337016483e-06,
                1.5534973841895917e-06,
                3.288750241561788e-06,
                3.726641061058432e-06,
                1.5534983101393749e-06,
                2.260324836776948e-06
            ],
            [
                2.3823696679327928e-07,
                1.1253506814842375e-07,
                0.9999996743688586,
                0.9999992661786701,
                0.9999997897566841,
                0.9999987901343176,
                2.1024331597262577e-07,
                1.1253516205489029e-07,
                1.637377057680051e-07,
                0.9999986290421404
            ],
            [
                4.450850519403407e-07,
                3.466327450756327e-07,
                3.9278638756099906e-07,
                2.382369383878655e-07,
                9.422449308716635e-07,
                2.9023112932296107e-06,
                2.6995790618350237e-07,
                5.715005832872586e-07,
                2.1024326584639497e-07,
                3.7266410611296085e-06
            ],
            [
                5.4222183235249605e-06,
                7.338208055664991e-07,
                3.288749457469787e-06,
                2.902313369111213e-06,
                2.9023126771227976e-06,
                2.5612831267202583e-06,
                2.5612812947508257e-06,
                4.785093924362895e-06,
                8.939698435657833e-06,
                1.3007130015677909e-05
            ],
            [
                7.484625404482555e-05,
                4.539786323319574e-05,
                7.484625403339028e-05,
                4.006368741670684e-05,
                4.785094494783494e-06,
                8.93969950132721e-06,
                5.829127944863308e-05,
                NaN,
                7.889263526266196e-06,
                1.3709575337125585e-06
            ],
            [
                1.994730672668496e-06,
                4.222832941142044e-06,
                1.2098661161982042e-06,
                4.0063692185483734e-05,
                1.0677027427600627e-06,
                2.9023133690425823e-06,
                4.785092783519724e-06,
                5.715002426486762e-07,
                1.2098658277451275e-06,
                NaN
            ],
            [
                8.939693107190907e-06,
                9.422442569315887e-07,
                3.288749065423109e-06,
                2.2603234895176927e-06,
                1.7603434231777837e-06,
                4.785095065204162e-06,
                NaN,
                3.726639284103523e-06,
                NaN,
                8.315280276626197e-07
            ],
            [
                2.902310947208574e-06,
                4.450850519403407e-07,
                2.902312677150514e-06,
                6.60521446989462e-05,
                2.2603242978871282e-06,
                1.8925148241872038e-05,
                1.4738981972323349e-05,
                3.288750241561788e-06,
                3.2887482813149375e-06,
                3.0590237279032884e-07
            ],
            [
                3.288748673360027e-06,
                1.0677026154806063e-06,
                3.927863875616689e-07,
                9.422448185510695e-07,
                1.7603430034743913e-06,
                1.3709575337078829e-06,
                2.5612831266946347e-06,
                1.553497199007048e-06,
                1.7603434231777837e-06,
                NaN
            ],
            [
                0.9999988634362905,
                0.9999987121043247,
                4.222834954801051e-06,
                1.637377057680051e-07,
                0.9999996072139404,
                0.9046505402422645,
                0.0028009272532596003,
                1.2098656835252174e-06,
                6.962257909842961e-06,
                1.3709567165617364e-06
            ],
            [
                2.10243290909724e-07,
                5.315781803390236e-08,
                7.338208930460318e-07,
                3.4663274507713016e-07,
                2.699578096403948e-07,
                6.475948754028718e-07,
                3.9278615344178325e-07,
                1.4449795205457127e-07,
                2.1024331597262577e-07,
                2.1024341622426268e-07
            ],
            [
                6.475945666033422e-07,
                3.7266401725935817e-06,
                6.475947210046347e-07,
                1.3709573702722555e-06,
                1.1478772231086046e-05,
                1.5534983101549167e-06,
                1.760343423160973e-06,
                3.2887486733420804e-06,
                6.47594566597747e-07,
                5.4222183234485234e-06
            ],
            [
                1.1478765389368729e-05,
                1.8553919030858602e-07,
                3.9278634073732336e-07,
                4.785092783519724e-06,
                1.7603434231777837e-06,
                2.382370235933104e-07,
                6.475947210046347e-07,
                1.1478765389368729e-05,
                2.1024339116168358e-07,
                1.3709576971379186e-06
            ],
            [
                1.370957860567974e-06,
                5.04347528446051e-07,
                NaN,
                2.90231094723893e-06,
                1.2098658277264215e-06,
                NaN,
                8.315281267861397e-07,
                1.27519088491875e-07,
                2.260324028372372e-06,
                8.3152792852928e-07
            ],
            [
                5.315789407685159e-08,
                9.931200429212718e-08,
                3.7266406168403854e-06,
                NaN,
                9.931202796993203e-08,
                4.691159887151251e-08,
                NaN,
                5.3157811697009444e-08,
                9.93120161310289e-08,
                NaN
            ],
            [
                3.726639728370556e-06,
                7.338207180898968e-07,
                1.370957860576702e-06,
                NaN,
                2.6995771309523475e-07,
                3.927862002663297e-07,
                2.9023119851899796e-06,
                2.6995790618469934e-07,
                2.2603242978778778e-06,
                1.7603430034867993e-06
            ],
            [
                3.05902263391829e-07,
                NaN,
                2.902313023130843e-06,
                3.927860597945825e-07,
                NaN,
                1.7603430034867993e-06,
                1.067703124601679e-06,
                2.561281294760143e-06,
                2.699578096403948e-07,
                1.370957860576702e-06
            ],
            [
                3.4663278639892215e-07,
                2.3823693839325527e-07,
                2.9023119851899796e-06,
                NaN,
                NaN,
                5.422217677152175e-06,
                9.422444815814404e-07,
                8.315277302857965e-07,
                2.382369951932796e-07,
                7.338210680021253e-07
            ],
            [
                4.5397863235342677e-05,
                1.8925145985895816e-05,
                5.422218969858371e-06,
                4.785093924362895e-06,
                6.144176066901277e-06,
                0.00017952792355046838,
                4.539785782605375e-05,
                1.3007133116542802e-05,
                2.9023112932177327e-06,
                2.1444950971601277e-05
            ],
            [
                0.00020342702218063233,
                3.535623807260338e-05,
                2.4300243630653244e-05,
                1.3007123813382511e-05,
                4.785095635624897e-06,
                2.7535681254804434e-05,
                2.5612831267202583e-06,
                7.48462183607529e-05,
                1.3007125363908762e-05,
                1.3007130015488633e-05
            ],
            [
                1.6373772528704005e-07,
                1.275190732904469e-07,
                3.466327037539638e-07,
                2.1024336609843824e-07,
                3.4663249714325014e-07,
                1.8553914607267268e-07,
                3.059022998581767e-07,
                8.764244316973974e-08,
                1.855391239544352e-07,
                8.315277302841894e-07
            ],
            [
                6.825601283086733e-08,
                4.785096206076165e-06,
                2.10243290909724e-07,
                1.1253526937697666e-07,
                3.466326211113502e-07,
                3.05902336324494e-07,
                1.209865827752005e-06,
                NaN,
                1.1253506814842375e-07,
                2.3823696679327928e-07
            ],
            [
                5.715006514176113e-07,
                7.889259764517575e-06,
                2.561281600086738e-06,
                4.4508505193932864e-07,
                4.450850519403407e-07,
                8.315277302857965e-07,
                7.338210680021253e-07,
                3.9278610661902853e-07,
                3.927862470861484e-07,
                NaN
            ],
            [
                6.144177531811707e-06,
                1.8553919030858602e-07,
                3.927863407379485e-07,
                1.209866260432471e-06,
                8.315281267882195e-07,
                3.05902263391829e-07,
                3.05902336324494e-07,
                2.902312331170226e-06,
                3.288748281329893e-06,
                3.927862470899887e-07
            ],
            [
                3.05902190458764e-07,
                1.8553905760062447e-07,
                3.466327037553825e-07,
                3.05902190458764e-07,
                2.3823690999323465e-07,
                2.6995784182140636e-07,
                2.1024341622426268e-07,
                2.3823685319244518e-07,
                2.382370235933104e-07,
                1.6373770576776313e-07
            ],
            [
                1.209866260432471e-06,
                NaN,
                3.05902263391829e-07,
                3.9278634073732336e-07,
                NaN,
                5.715003107767143e-07,
                1.5534979397740895e-06,
                5.715002426486762e-07,
                NaN,
                2.1024334103581732e-07
            ],
            [
                0.9999992188516701,
                0.999998005269807,
                0.9999995262093861,
                0.9999983463108129,
                4.785095635655362e-06,
                0.9999985406230855,
                0.9999982396559517,
                0.9999988634365623,
                0.9999996940976639,
                0.9999994284996221
            ],
            [
                0.9999987901344631,
                0.9999993106392018,
                0.9999993524053569,
                1.2751902768612997e-07,
                0.9999991148432816,
                0.9999993106391195,
                0.9999987901340291,
                0.9999990577552946,
                3.466327037553825e-07,
                1.4449798650551755e-07
            ],
            [
                1.8553916819032217e-07,
                1.2098659719716573e-06,
                2.69957906184239e-07,
                6.475946438055299e-07,
                2.699578740032504e-07,
                1.4449805540740185e-07,
                1.6373764721072816e-07,
                2.6995787400208416e-07,
                3.92786340734912e-07,
                1.0677029973192638e-06
            ],
            [
                2.2603253756956754e-06,
                NaN,
                6.144173137170873e-06,
                NaN,
                1.5534973842076057e-06,
                4.78509392429544e-06,
                NaN,
                1.0677027427525368e-06,
                1.0677027427624903e-06,
                1.444979692800516e-07
            ],
            [
                0.9999978766212873,
                0.9999982396572086,
                0.9999987121052477,
                0.9999898700126594,
                0.9999987121050943,
                6.605217619491253e-05,
                0.9999977396746268,
                0.9999989322970039,
                0.9999989969854347,
                0.9999980052702813
            ],
            [
                1.3007130015488633e-05,
                5.422217030747413e-06,
                1.4738981972323349e-05,
                8.939696304311336e-06,
                1.3709568799919866e-06,
                3.2887502415767434e-06,
                1.0677027427600627e-06,
                8.939699501416646e-06,
                8.939696304311336e-06,
                NaN
            ],
            [
                3.927860597935108e-07,
                5.715004470313855e-07,
                1.9947304348862686e-06,
                4.450849988811838e-07,
                6.475948754012522e-07,
                5.715004470313855e-07,
                3.466327037548308e-07,
                8.315280276580819e-07,
                NaN,
                1.3709576971316842e-06
            ],
            [
                0.9999990577556332,
                0.9999991684717751,
                0.9999981261243956,
                0.9999980052709987,
                9.422449308774482e-07,
                0.9999991684717754,
                8.315282259138311e-07,
                0.9999978766205303,
                0.9999995549150548,
                2.902313369111213e-06
            ],
            [
                8.315279285370317e-07,
                NaN,
                5.422220262599396e-06,
                NaN,
                5.422217030747413e-06,
                3.288747889284851e-06,
                1.0129988564974359e-05,
                5.422220909009474e-06,
                2.7535694384882703e-05,
                1.760343213335281e-06
            ],
            [
                1.0677033791612137e-06,
                1.9947297215125433e-06,
                6.475947982037486e-07,
                1.300712536350655e-05,
                1.3709567165579959e-06,
                1.0677032518785256e-06,
                6.962254589914941e-06,
                1.5534975693979422e-06,
                1.3709567165579959e-06,
                1.7603425837855082e-06
            ],
            [
                1.5534973842076057e-06,
                8.315277302841894e-07,
                5.422217677152175e-06,
                4.450848927658745e-07,
                3.05902336324494e-07,
                1.994729008145876e-06,
                3.466327037548308e-07,
                3.9278605979534166e-07,
                3.726638839878908e-06,
                1.370957860576702e-06
            ],
            [
                NaN,
                1.3007123813382511e-05,
                3.2887502415767434e-06,
                1.3709573702822306e-06,
                5.043473480777865e-07,
                4.450848927621807e-07,
                NaN,
                6.47595107001401e-07,
                8.315277302857965e-07,
                4.222834954778007e-06
            ],
            [
                5.715005151606823e-07,
                6.475947982037486e-07,
                7.734415776836702e-08,
                3.120190021759579e-05,
                5.715005151606823e-07,
                NaN,
                5.715003107755449e-07,
                1.6373776432509826e-07,
                NaN,
                NaN
            ],
            [
                3.72663883989755e-06,
                2.561282210740037e-06,
                3.726639284125553e-06,
                1.9947301970972664e-06,
                6.962255419931625e-06,
                1.7603438428740716e-06,
                3.2887482813149375e-06,
                4.22283545819819e-06,
                6.475949526020042e-07,
                5.4222176771176554e-06
            ],
            [
                3.535624228441698e-05,
                1.4738981972082061e-05,
                4.785093924330255e-06,
                3.2887502415438413e-06,
                1.8925157265332104e-05,
                1.3007125363908762e-05,
                1.0677027427471959e-06,
                2.4300232043987867e-05,
                1.300713001508642e-05,
                4.785094494750855e-06
            ],
            [
                7.338208055664991e-07,
                2.102434162245973e-07,
                6.475947210046347e-07,
                1.067703124601679e-06,
                1.6701419854156377e-05,
                NaN,
                4.4508494582405734e-07,
                2.5612812947508257e-06,
                1.1253509497883659e-07,
                1.2098653950692178e-06
            ],
            [
                2.2603253756956754e-06,
                6.144173137170873e-06,
                3.120191881525687e-05,
                1.9947299593078385e-06,
                5.422221555380179e-06,
                2.7535704232595768e-05,
                1.5534973842076057e-06,
                4.785096776499213e-06,
                3.288748673376478e-06,
                7.889265407327733e-06
            ],
            [
                5.422217030707961e-06,
                2.5612828213934817e-06,
                2.260325106237323e-06,
                6.475951069985296e-07,
                1.3709568799760888e-06,
                NaN,
                1.2098655392871682e-06,
                1.760343003481596e-06,
                6.475951069985296e-07,
                3.1201922535494165e-05
            ],
            [
                3.2887506336086064e-06,
                2.6995790618469934e-07,
                2.5612819054133693e-06,
                5.043474683240344e-07,
                8.315279285370317e-07,
                3.05902263391829e-07,
                NaN,
                1.2751905808881762e-07,
                1.855391239544352e-07,
                3.059021175261338e-07
            ],
            [
                1.5534973842076057e-06,
                4.450849988758202e-07,
                1.4738983729535602e-05,
                2.561281905376098e-06,
                5.043474081993875e-07,
                1.994730672675753e-06,
                7.338208055680009e-07,
                5.715007195447234e-07,
                4.222832941193893e-06,
                5.043472278280699e-07
            ],
            [
                2.5612834320563895e-06,
                2.1024334103581732e-07,
                5.422217677152175e-06,
                5.043475885696228e-07,
                1.6373774480605869e-07,
                0.9999986290424678,
                5.043476486924565e-07,
                7.338208055680009e-07,
                4.450852111148132e-07,
                9.931190958076104e-08
            ],
            [
                1.3709575337159875e-06,
                3.059022998581767e-07,
                2.102434412875379e-07,
                2.3823702359290413e-07,
                1.2098652508287273e-06,
                5.715005151606823e-07,
                1.275190428875671e-07,
                NaN,
                9.931195693628605e-08,
                6.475950298011458e-07
            ],
            [
                NaN,
                1.0129994602895546e-05,
                1.275189972832538e-07,
                1.1478766757718129e-05,
                2.753569110256289e-05,
                3.7266401726359486e-06,
                4.785094494811783e-06,
                1.3007130015677909e-05,
                4.785095635655362e-06,
                1.012999218776902e-05
            ],
            [
                2.699577774585891e-07,
                4.5397874064161706e-05,
                2.3823693839290317e-07,
                1.9947304348862686e-06,
                5.04347528446051e-07,
                4.450848927637999e-07,
                3.927863407379485e-07,
                3.059021175261338e-07,
                2.382370235933104e-07,
                4.450852111155216e-07
            ],
            [
                1.3007126914245925e-05,
                1.012999460278499e-05,
                3.7266406168624155e-06,
                1.1478772231086046e-05,
                5.829126555256903e-05,
                2.9023112932177327e-06,
                7.889265407255982e-06,
                2.430024942462891e-05,
                1.3709576971425944e-06,
                2.4300252319296727e-05
            ],
            [
                5.71500719545698e-07,
                3.0590237279085045e-07,
                2.3823702359290413e-07,
                3.9278629391427843e-07,
                1.2751902768612997e-07,
                1.855391681906175e-07,
                1.1253524254650944e-07,
                3.0590237279085045e-07,
                9.931186222523604e-08,
                7.338207180898968e-07
            ],
            [
                6.475946438055299e-07,
                4.222834451382849e-06,
                8.315279285370317e-07,
                1.6373766672973748e-07,
                8.315282259138311e-07,
                1.9947299593078385e-06,
                3.466326211113502e-07,
                1.9947304348862686e-06,
                1.3709576971463352e-06,
                3.927863407379485e-07
            ],
            [
                2.2603234895289998e-06,
                8.939693107190907e-06,
                5.715005151606823e-07,
                9.422443692489024e-07,
                3.466326624336003e-07,
                6.475945666063607e-07,
                3.466327863983311e-07,
                3.7266406168827523e-06,
                7.338207180898968e-07,
                NaN
            ],
            [
                5.422218969895357e-06,
                2.3823688159291947e-07,
                4.222834954778007e-06,
                3.9278610661902853e-07,
                5.715006514176113e-07,
                5.043474683204221e-07,
                1.067703124601679e-06,
                2.1024339116168358e-07,
                NaN,
                NaN
            ],
            [
                5.04347528446051e-07,
                4.222832437798974e-06,
                4.450852111148132e-07,
                3.726639284125553e-06,
                2.2603248367949354e-06,
                2.902312677137316e-06,
                1.3709567165579959e-06,
                0.9999945777816874,
                4.222834451382849e-06,
                2.5612819054028872e-06
            ],
            [
                4.53978632394714e-05,
                1.9947299592933255e-06,
                5.422217030707961e-06,
                NaN,
                2.144494841482881e-05,
                1.7603434231777837e-06,
                1.3709573702822306e-06,
                8.48110514911537e-05,
                2.9023126771227976e-06,
                NaN
            ],
            [
                5.422220262599396e-06,
                6.605212107553962e-05,
                1.4738978458382043e-05,
                NaN,
                1.3007130015488633e-05,
                1.9947297215043796e-06,
                6.962255419931625e-06,
                2.9023112932177327e-06,
                4.2228339479858295e-06,
                3.2887506336086064e-06
            ],
            [
                1.1253525596174225e-07,
                1.6373772528704005e-07,
                1.855390576008354e-07,
                1.0677033791612137e-06,
                1.2751904288739315e-07,
                6.023569166654288e-08,
                1.209865827752005e-06,
                1.1253506814842375e-07,
                2.3823693839325527e-07,
                8.76424013786396e-08
            ],
            [
                1.7603425837903113e-06,
                3.466325797896173e-07,
                1.6373764721072816e-07,
                1.27519088491875e-07,
                2.430024652792821e-05,
                0.9999706884551585,
                1.855391681906175e-07,
                3.0590215399183813e-07,
                6.475947210012481e-07,
                NaN
            ],
            [
                2.382368531929327e-07,
                5.715002426486762e-07,
                8.315284241650899e-07,
                9.422449308748773e-07,
                7.338210680021253e-07,
                9.931189774187203e-08,
                1.30071315662049e-05,
                2.2603234895372223e-06,
                2.7535700950274782e-05,
                NaN
            ],
            [
                3.7266406168403854e-06,
                NaN,
                1.8925155009767892e-05,
                3.288748673376478e-06,
                1.4738987243478167e-05,
                1.994730672668496e-06,
                5.422220909009474e-06,
                NaN,
                3.726639728348526e-06,
                2.90231094723893e-06
            ],
            [
                NaN,
                1.760343003481596e-06,
                3.4663249714612693e-07,
                2.10243290909724e-07,
                7.338212429582604e-07,
                6.475947210046347e-07,
                2.699578740032504e-07,
                1.3709567165579959e-06,
                3.466325797896173e-07,
                2.1024331597262577e-07
            ],
            [
                1.27519088491875e-07,
                1.4449796928021588e-07,
                2.2603245673443566e-06,
                1.4449795205472734e-07,
                8.764249540862797e-08,
                2.1024336609874897e-07,
                5.043475885696228e-07,
                1.0677028700422047e-06,
                2.382369667929001e-07,
                1.275190428875671e-07
            ],
            [
                NaN,
                1.7603425837855082e-06,
                6.475947210031623e-07,
                1.5534983101602148e-06,
                NaN,
                8.315282259138311e-07,
                1.6373776432509826e-07,
                4.222831934379152e-06,
                6.475947982022763e-07,
                2.1024326584639497e-07
            ],
            [
                1.2098661162056318e-06,
                1.0677033791612137e-06,
                2.2603245673279107e-06,
                NaN,
                3.726638839878908e-06,
                3.7266406168827523e-06,
                1.012998977264307e-05,
                5.043475885696228e-07,
                6.962256249885085e-06,
                3.2887502415767434e-06
            ],
            [
                NaN,
                0.9999987901346071,
                1.1478772231086046e-05,
                6.475946438055299e-07,
                3.4663249714612693e-07,
                9.422442569334097e-07,
                NaN,
                5.043476486924565e-07,
                6.962257909785973e-06,
                2.430024073523505e-05
            ],
            [
                1.5534977545886537e-06,
                8.315279285351409e-07,
                7.338209805240734e-07,
                5.715005832886879e-07,
                8.315281267882195e-07,
                4.785096776468749e-06,
                1.4449803818215767e-07,
                2.9023112932177327e-06,
                4.785094494750855e-06,
                2.2603253756956754e-06
            ],
            [
                6.144173869446876e-06,
                7.889262585886274e-06,
                4.4508510499849186e-07,
                1.9947292459347367e-06,
                1.0677032518814388e-06,
                4.785095635624897e-06,
                4.222832437798974e-06,
                NaN,
                NaN,
                1.553497199007048e-06
            ],
            [
                2.699577774585891e-07,
                5.04347528446051e-07,
                3.927860597945825e-07,
                1.6373764721072816e-07,
                3.7266397283908927e-06,
                3.059021175261338e-07,
                1.5534984953552536e-06,
                3.059022998581767e-07,
                3.4663274507713016e-07,
                7.338208930460318e-07
            ],
            [
                3.466327863983311e-07,
                1.4449798650569826e-07,
                1.637376862489725e-07,
                3.927863875616689e-07,
                1.637376862489725e-07,
                2.3823696679327928e-07,
                5.043472278322555e-07,
                1.8553910183674878e-07,
                3.4663249714612693e-07,
                1.275189972832538e-07
            ],
            [
                7.338213304363436e-07,
                0.0005527787481587043,
                1.994729008145876e-06,
                3.726638839878908e-06,
                4.4508510499849186e-07,
                2.9023126771227976e-06,
                4.78509278348926e-06,
                8.315280276546789e-07,
                8.315284241597959e-07,
                1.3709578605617394e-06
            ],
            [
                1.5534975693869924e-06,
                5.715002426486762e-07,
                2.9023119851635836e-06,
                7.338212429582604e-07,
                1.3007130015488633e-05,
                1.0129987357287368e-05,
                4.2228339479858295e-06,
                2.260324836787226e-06,
                1.7603427936263351e-06,
                1.99472900813862e-06
            ],
            [
                NaN,
                1.0677032518700286e-06,
                8.315281267861397e-07,
                2.90231233114251e-06,
                1.3709575337016483e-06,
                7.338212429562581e-07,
                1.0677028700320085e-06,
                4.785095635624897e-06,
                6.475948753991907e-07,
                1.0677028700363782e-06
            ],
            [
                3.7266410611296085e-06,
                NaN,
                3.2887478892683997e-06,
                6.962255419868303e-06,
                7.889261645427538e-06,
                9.610238066473817e-05,
                2.5612819054133693e-06,
                2.5612831267202583e-06,
                1.1478770862735993e-05,
                2.902313369111213e-06
            ],
            [
                3.05902263391829e-07,
                1.067703124601679e-06,
                4.4508526417298334e-07,
                NaN,
                3.927862939126708e-07,
                4.222831934379152e-06,
                3.466326624336003e-07,
                4.450852641737424e-07,
                3.9278629391427843e-07,
                1.3709575337159875e-06
            ]
        ]
    },
    {
        "q_id": "10078_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            21,
            22,
            23,
            24,
            25,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            59,
            60,
            61,
            62,
            64,
            65,
            66,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            109,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            107,
            108
        ],
        "rewards": [
            [
                9.93120161310289e-08,
                2.2603240284371276e-06,
                1.275190276859705e-07,
                9.931189774187203e-08,
                1.994729008145876e-06,
                1.4449800373118268e-07,
                1.4449798650551755e-07,
                2.1024336609843824e-07,
                1.275190580890061e-07,
                3.466327450756327e-07
            ],
            [
                5.715005151606823e-07,
                3.4663253846718004e-07,
                1.8553910183674878e-07,
                1.994729008151319e-06,
                0.0001233946191424094,
                3.466327037553825e-07,
                1.8553916819032217e-07,
                2.9023119851899796e-06,
                5.422220262636381e-06,
                2.102434412875379e-07
            ],
            [
                1.209866260432471e-06,
                2.9023123311583482e-06,
                0.9999997300421584,
                0.9999934595604443,
                7.338210680021253e-07,
                0.9999741325693567,
                6.82560779249779e-08,
                5.715002426486762e-07,
                6.47595107001401e-07,
                0.9999974387174887
            ],
            [
                0.9999996072139403,
                2.2603253756956754e-06,
                0.9999981261243943,
                0.9999989969859122,
                3.7266383955882547e-06,
                0.9999892166852435,
                3.9278629391427843e-07,
                1.855391681906175e-07,
                0.9999985406234323,
                6.962259569750576e-06
            ],
            [
                3.059022269250683e-07,
                0.9999885212278105,
                0.9999916019269817,
                0.9999974387165709,
                0.9999949062944071,
                0.9999822214439316,
                0.9999938558246765,
                6.475947982037486e-07,
                2.561281294760143e-06,
                NaN
            ],
            [
                4.450851049991497e-07,
                NaN,
                1.4738985486506781e-05,
                3.9278629391427843e-07,
                1.012999218776902e-05,
                1.637376862489725e-07,
                5.715002426486762e-07,
                2.10243290909963e-07,
                8.93969950132721e-06,
                8.315279285370317e-07
            ],
            [
                1.4449798650569826e-07,
                6.825609419848033e-08,
                2.699577774585891e-07,
                0.999997438718707,
                1.8553910183674878e-07,
                2.699577774589574e-07,
                0.9999934595604411,
                1.275190732904469e-07,
                1.6373766672994222e-07,
                7.73442776303243e-08
            ],
            [
                0.9999706884685433,
                1.5534975693979422e-06,
                5.043475885696228e-07,
                0.9999485577684193,
                1.7603427936335396e-06,
                2.561282516066741e-06,
                9.422442569315887e-07,
                0.9999980052698043,
                0.9999989969857928,
                0.9999985406239535
            ],
            [
                1.8925148242250705e-05,
                2.382369383923073e-07,
                3.288749849529972e-06,
                6.475947210046347e-07,
                5.043472879540142e-07,
                9.422448185534261e-07,
                2.9023112932177327e-06,
                3.7266410611296085e-06,
                2.902312677137316e-06,
                7.338209805224048e-07
            ],
            [
                0.9999785550439794,
                3.059022998581767e-07,
                9.931193325852072e-08,
                7.734428685047173e-08,
                9.931185038635267e-08,
                1.4449805540763184e-07,
                0.9999990577557436,
                3.466327037553825e-07,
                6.023568448589658e-08,
                6.023571320847322e-08
            ],
            [
                1.760342793638743e-06,
                0.9999969105044522,
                0.9998766054262131,
                0.9999930377420992,
                1.3007131473317599e-05,
                2.260324567337161e-06,
                0.9999972735297333,
                4.450852111155216e-07,
                0.9999980052707567,
                1.209865539295696e-06
            ],
            [
                7.734425919002834e-08,
                1.8553903548287212e-07,
                0.9999949062943982,
                1.855390576008354e-07,
                2.3823693839325527e-07,
                1.6373772528704005e-07,
                1.2098659719788098e-06,
                4.4508515805735777e-07,
                2.6995784182183607e-07,
                5.715006514176113e-07
            ],
            [
                9.422444815792981e-07,
                0.9999970976876728,
                0.999998629042631,
                0.9999996940978826,
                1.3709576971463352e-06,
                1.0677026154806063e-06,
                0.9999989969856733,
                0.9999999123574942,
                1.0677026154806063e-06,
                6.475951070002966e-07
            ],
            [
                3.7266410611296085e-06,
                1.9947301970972664e-06,
                5.715006514176113e-07,
                1.0677024881980089e-06,
                2.4300243630653244e-05,
                7.338207180898968e-07,
                1.994730434879465e-06,
                1.2098652508424818e-06,
                0.9999771719974365,
                3.7266410611296085e-06
            ],
            [
                9.422447062294175e-07,
                0.9999993524053563,
                0.9999997126315153,
                6.144177531660828e-06,
                0.9998601778779969,
                0.999994228078609,
                5.043474082005342e-07,
                0.9999964991447595,
                0.9999869928653431,
                0.999998996985434
            ],
            [
                3.2887502415767434e-06,
                2.260324567337161e-06,
                3.726639284144195e-06,
                3.726637951387472e-06,
                5.422220909009474e-06,
                2.5612834320214477e-06,
                8.939694172957213e-06,
                1.4738981972564636e-05,
                0.9999861539954654,
                3.466326211113502e-07
            ],
            [
                1.3709567165617364e-06,
                9.422442569315887e-07,
                5.043476486924565e-07,
                8.315277302819205e-07,
                1.209865539295696e-06,
                9.422442569315887e-07,
                NaN,
                7.338212429562581e-07,
                NaN,
                2.2603240284371276e-06
            ],
            [
                8.315277302857965e-07,
                0.9999996940978461,
                4.139941495546278e-08,
                7.338207180864763e-07,
                0.9999999006880668,
                3.05902263391829e-07,
                1.9947304348862686e-06,
                6.475950298021765e-07,
                6.475945666063607e-07,
                NaN
            ],
            [
                3.059022269250683e-07,
                3.4663262111182307e-07,
                7.338208055680009e-07,
                1.8553910183674878e-07,
                2.699578096393206e-07,
                1.4449805540740185e-07,
                2.3823690999323465e-07,
                5.043474683204221e-07,
                2.6995784182140636e-07,
                2.3823696679327928e-07
            ],
            [
                0.9999994956523515,
                9.422448185534261e-07,
                0.9999485577805157,
                0.9999969105044508,
                0.9999997761971583,
                1.0677033791612137e-06,
                0.999999922655833,
                7.338208055680009e-07,
                0.9999996310114599,
                0.9999994631248683
            ],
            [
                1.5534983101478522e-06,
                9.422447062270609e-07,
                8.315280276626197e-07,
                0.9999981261241706,
                1.3709575337125585e-06,
                0.9999987121047857,
                6.475947210031623e-07,
                0.9999974387177915,
                5.715002426486762e-07,
                0.9999962733611629
            ],
            [
                1.8553916819032217e-07,
                2.6995774527718623e-07,
                5.043475885696228e-07,
                1.4738987243478167e-05,
                0.999948557799418,
                5.715003789033962e-07,
                1.4449805540740185e-07,
                3.927862470861484e-07,
                3.05902226923399e-07,
                0.9999861539888758
            ],
            [
                0.9999969105048191,
                0.9999974387165702,
                3.9278629391427843e-07,
                8.315281267882195e-07,
                3.05902263391829e-07,
                0.9999977396751676,
                5.043472278322555e-07,
                3.466327037548308e-07,
                9.931185038635267e-08,
                3.4663278639892215e-07
            ],
            [
                1.6373770576776313e-07,
                2.2603251062013478e-06,
                1.2098661162056318e-06,
                5.04347528446051e-07,
                1.7603430034867993e-06,
                5.4222183235249605e-06,
                6.475951069985296e-07,
                1.3709568799919866e-06,
                1.760342793638743e-06,
                6.475946438055299e-07
            ],
            [
                3.466325384678894e-07,
                6.475945666063607e-07,
                7.338213304363436e-07,
                8.315284241665078e-07,
                1.994730672675753e-06,
                1.7603438428800754e-06,
                2.699576809143613e-07,
                4.22283545819819e-06,
                1.9947304348862686e-06,
                5.715003107767143e-07
            ],
            [
                NaN,
                NaN,
                3.927861534431675e-07,
                9.931189774187203e-08,
                2.9023116392097746e-06,
                NaN,
                5.715005832895975e-07,
                9.422447062294175e-07,
                NaN,
                NaN
            ],
            [
                3.927862470899887e-07,
                0.9999977396751649,
                4.450851049991497e-07,
                6.475949526020042e-07,
                5.422217030747413e-06,
                1.0677024882009222e-06,
                0.9999987121041707,
                0.999999900687972,
                0.9999962733598318,
                0.9999996533674617
            ],
            [
                0.9999485577804745,
                NaN,
                1.275190732904469e-07,
                4.785092783519724e-06,
                NaN,
                6.023577065381482e-08,
                6.82560616514716e-08,
                0.9999945777816823,
                0.9999993106390368,
                0.9999974387177917
            ],
            [
                5.715006514151423e-07,
                4.222835458175145e-06,
                1.3007133116542802e-05,
                7.338210680021253e-07,
                3.059021175247079e-07,
                1.7603438428740716e-06,
                2.6995784182140636e-07,
                9.422447062270609e-07,
                1.3709578605729614e-06,
                7.338211554758494e-07
            ],
            [
                2.699578096403948e-07,
                0.999998126124395,
                3.2887502415767434e-06,
                3.7266401726359486e-06,
                3.4663274507713016e-07,
                0.9999996072139405,
                1.0677024882009222e-06,
                1.067703124601679e-06,
                3.535626336072768e-05,
                5.422219616265831e-06
            ],
            [
                1.760343213322473e-06,
                0.9999991148432812,
                0.9999996310113279,
                0.0011695100058592013,
                0.9999667857974389,
                0.9999989322966216,
                6.47594952603035e-07,
                0.9999978766217925,
                0.9999955048162847,
                0.9999972735287582
            ],
            [
                9.422444815765128e-07,
                7.338213304363436e-07,
                7.338210680021253e-07,
                1.3709568799919866e-06,
                7.338210680021253e-07,
                5.422221555380179e-06,
                3.726638839878908e-06,
                9.422447062294175e-07,
                1.1253516205489029e-07,
                1.3709567165617364e-06
            ],
            [
                0.9999898700102438,
                2.2603240284371276e-06,
                0.9999980052707551,
                9.422442569334097e-07,
                7.338208055680009e-07,
                1.8925157266089433e-05,
                0.9999646437535755,
                1.670142980893658e-05,
                8.481101107142626e-05,
                0.9999957771665603
            ],
            [
                7.33821330437595e-07,
                5.043472278322555e-07,
                2.5612819054133693e-06,
                1.3709572068522336e-06,
                6.962254589914941e-06,
                1.2098659719757836e-06,
                5.04347468323289e-07,
                NaN,
                NaN,
                2.5612828213934817e-06
            ],
            [
                3.0590237279085045e-07,
                6.475947210046347e-07,
                8.315278294114555e-07,
                1.8553903548231313e-07,
                9.93120161310289e-08,
                1.1253516205489029e-07,
                1.2751899728311609e-07,
                1.275190732904469e-07,
                1.8553905760024476e-07,
                2.1024331597262577e-07
            ],
            [
                2.902312331170226e-06,
                NaN,
                4.785094494783494e-06,
                4.785095635624897e-06,
                1.6701419854156377e-05,
                9.422449308673789e-07,
                2.2603240284371276e-06,
                6.962253759904688e-06,
                4.785095635624897e-06,
                4.4508510499849186e-07
            ],
            [
                0.9999993524052021,
                0.9999982396569981,
                0.9999980052695675,
                0.9999977396748966,
                3.726639284144195e-06,
                9.422447062294175e-07,
                7.338207180884785e-07,
                0.9999995818813768,
                NaN,
                0.9999987121047855
            ],
            [
                1.0677031245990084e-06,
                7.73441946488886e-08,
                0.9999967112513297,
                6.962254589914941e-06,
                1.0677033791583005e-06,
                0.9999990577554067,
                8.939700566801578e-06,
                NaN,
                2.90231094723893e-06,
                0.9999996743688975
            ],
            [
                9.422448185510695e-07,
                7.889266347715168e-06,
                1.637376862489725e-07,
                3.288748673376478e-06,
                6.475945666063607e-07,
                5.71500719545698e-07,
                3.927862002663297e-07,
                1.2098659719788098e-06,
                5.715003789033962e-07,
                1.275190124846946e-07
            ],
            [
                0.9999974387187066,
                0.9999998555020135,
                0.9999996743688975,
                0.9999997761972116,
                0.9999995262092163,
                0.9999998257021213,
                0.9999977396759724,
                9.422444815792981e-07,
                1.0,
                0.9999998555020307
            ],
            [
                1.6373770576776313e-07,
                2.382369951932796e-07,
                1.8553903548231313e-07,
                6.825606165129312e-08,
                2.699577774585891e-07,
                1.1253518888531272e-07,
                NaN,
                2.6995771309523475e-07,
                2.1024326584582131e-07,
                1.6373768624837685e-07
            ],
            [
                0.9999987901340289,
                0.9999975938982371,
                5.715006514176113e-07,
                9.931189774187203e-08,
                0.9999989322968763,
                0.9999980052700418,
                0.9999945777797471,
                4.450850519409479e-07,
                0.9999986290426307,
                0.9999970976869799
            ],
            [
                1.855390576008354e-07,
                1.444979692797559e-07,
                NaN,
                1.4449807263325588e-07,
                1.4449796928021588e-07,
                2.102434412875379e-07,
                3.4663249714612693e-07,
                1.4449795205472734e-07,
                1.1478765389368729e-05,
                8.764247451307293e-08
            ],
            [
                9.422448185534261e-07,
                3.927862002663297e-07,
                1.3709573702822306e-06,
                1.3709567165617364e-06,
                1.3709570434219446e-06,
                4.450849988811838e-07,
                7.338212429582604e-07,
                4.006369219233375e-05,
                2.1024336609843824e-07,
                6.475947210046347e-07
            ],
            [
                NaN,
                1.0677029973219343e-06,
                7.338208055680009e-07,
                1.5534979397829198e-06,
                NaN,
                NaN,
                3.466326624336003e-07,
                8.315280276626197e-07,
                6.475946438055299e-07,
                NaN
            ],
            [
                1.994729008145876e-06,
                1.0677032518814388e-06,
                7.338208930460318e-07,
                1.7603425837791042e-06,
                9.422447062294175e-07,
                3.9278610661902853e-07,
                1.5534973841154145e-06,
                1.7603438428800754e-06,
                3.4663249714451116e-07,
                1.0129993395336818e-05
            ],
            [
                0.9999987901338846,
                0.9999910603037071,
                4.139936066832438e-08,
                1.1253512180925583e-07,
                2.1024339116168358e-07,
                0.9999989969855536,
                0.9999994631251883,
                0.9999983463108099,
                3.466325384678894e-07,
                4.1399400149893274e-08
            ],
            [
                1.855391681906175e-07,
                1.6373774480605869e-07,
                0.9999756997478022,
                5.715002426486762e-07,
                3.9278629391427843e-07,
                NaN,
                4.5397884876138115e-05,
                2.9023112931873767e-06,
                1.637377057680051e-07,
                9.422443692489024e-07
            ],
            [
                1.8553907971879076e-07,
                0.9999991148426479,
                0.999999554914842,
                0.9999996072138467,
                0.9999987901343174,
                0.9999945777797417,
                0.9999999397642222,
                1.2751902768612997e-07,
                0.9999997300422548,
                0.9999999434137232
            ],
            [
                0.9999885212264218,
                5.71500719545698e-07,
                2.1024336609874897e-07,
                0.9999967112493686,
                0.9999832985722178,
                2.6995774527718623e-07,
                1.1253509497883659e-07,
                5.422220262599396e-06,
                0.9999861539921876,
                1.8553919030858602e-07
            ],
            [
                1.275190732904469e-07,
                4.4508515805735777e-07,
                5.715003107755449e-07,
                5.315788140303327e-08,
                0.9999967112509381,
                NaN,
                0.9999996310115039,
                6.825600469412533e-08,
                3.726638395634011e-06,
                1.2751899728311609e-07
            ],
            [
                1.1478770862735993e-05,
                1.275190124846946e-07,
                1.6701425827133152e-05,
                9.422442569315887e-07,
                NaN,
                1.8553910183674878e-07,
                1.1253522913127183e-07,
                8.939693107288474e-06,
                2.5612834320563895e-06,
                1.1253525596174225e-07
            ],
            [
                1.3709567165617364e-06,
                8.315281267882195e-07,
                0.9999985406239539,
                0.9999978766207801,
                6.475947210046347e-07,
                0.9999955048173584,
                0.9999984465018762,
                0.9999988634358834,
                7.734426841017797e-08,
                4.4508515805735777e-07
            ],
            [
                6.475946438055299e-07,
                5.715003107767143e-07,
                1.7603427936335396e-06,
                0.9999995262092728,
                0.9999989322975126,
                7.338208930460318e-07,
                9.422450432014836e-07,
                0.9999998642566219,
                1.3709572068422585e-06,
                2.5612834320563895e-06
            ],
            [
                0.00043055704001563315,
                0.9999960330121973,
                0.9999998642567028,
                0.9999785550567669,
                0.9999993524053566,
                0.9999999317440279,
                2.699577774585891e-07,
                1.8553919030826963e-07,
                0.9999955048162824,
                6.825606978822427e-08
            ],
            [
                0.999999814460854,
                1.5534971990169383e-06,
                0.9999991684717744,
                1.067702870039777e-06,
                8.315278294097538e-07,
                0.9999981261246185,
                1.7603438428800754e-06,
                1.9947292459347367e-06,
                1.3709576971463352e-06,
                7.338212429594283e-07
            ],
            [
                0.9999994631249962,
                3.466326624336003e-07,
                0.9999417087555893,
                7.338210680021253e-07,
                1.760343633031919e-06,
                8.315284241650899e-07,
                0.9999998024946801,
                1.0677024882009222e-06,
                0.999988521233273,
                0.9999997126314811
            ],
            [
                1.370957860576702e-06,
                2.5612831267202583e-06,
                0.9999687980849776,
                0.04742586947505113,
                0.9999798543116131,
                0.00010889688340323103,
                1.209866260432471e-06,
                7.338212429582604e-07,
                3.7266406168827523e-06,
                7.338208055680009e-07
            ],
            [
                1.8553919030858602e-07,
                2.69957906184239e-07,
                0.9999251537732452,
                0.9999987901341729,
                0.9999921107393102,
                0.9999957771655534,
                2.3823690999290963e-07,
                8.315279285370317e-07,
                5.04347287955046e-07,
                0.9999724642958431
            ],
            [
                1.5534981249697903e-06,
                3.059022998576899e-07,
                4.2228319344021954e-06,
                2.69957906184239e-07,
                2.10243290909724e-07,
                1.4449805540740185e-07,
                6.475946438055299e-07,
                1.8553905760062447e-07,
                3.4663253846718004e-07,
                6.475947982037486e-07
            ],
            [
                6.023576347315567e-08,
                2.3823696679327928e-07,
                1.8553910183674878e-07,
                5.715006514176113e-07,
                1.0677026154827912e-06,
                0.9999991148432813,
                9.422448185534261e-07,
                2.699578740032504e-07,
                NaN,
                6.475946438055299e-07
            ],
            [
                1.1253516205489029e-07,
                7.73441946488886e-08,
                1.9947299593014888e-06,
                1.99472900813862e-06,
                1.0677024882009222e-06,
                4.139934092760465e-08,
                8.764245361752286e-08,
                1.6373774480605869e-07,
                1.4449802095666915e-07,
                6.825609419848033e-08
            ],
            [
                5.715003789046955e-07,
                8.764249540862797e-08,
                7.484620052444058e-05,
                1.3709568799919866e-06,
                1.994729008145876e-06,
                4.4508510499849186e-07,
                3.9278634073732336e-07,
                2.6995784182140636e-07,
                2.6995774527718623e-07,
                9.422445939032799e-07
            ],
            [
                2.1024334103581732e-07,
                7.338208055680009e-07,
                3.466327037553825e-07,
                1.4449803818107344e-07,
                1.2751899728311609e-07,
                6.475947210046347e-07,
                5.715005832798517e-07,
                9.931193325852072e-08,
                1.8553916819032217e-07,
                NaN
            ],
            [
                6.475946438042047e-07,
                0.9999997126313784,
                5.715003107767143e-07,
                0.999999631011416,
                7.338210680021253e-07,
                3.9278615344267634e-07,
                0.9999970976880155,
                3.9278605979534166e-07,
                1.370957860576702e-06,
                0.9999997300422869
            ],
            [
                1.275190124846946e-07,
                6.144177531767002e-06,
                0.9999996743686257,
                0.9999991684717745,
                9.931186222523604e-08,
                8.764254764780641e-08,
                0.9999988634360185,
                0.9999988634358837,
                2.699578096403948e-07,
                2.382368531929327e-07
            ],
            [
                3.9278610661902853e-07,
                0.9999993524053563,
                1.1253509497883659e-07,
                7.734414854823498e-08,
                4.691159887151251e-08,
                2.382369667929001e-07,
                9.931202796993203e-08,
                0.999975699768061,
                5.3157900413760374e-08,
                0.9999986290432844
            ],
            [
                5.422218969895357e-06,
                3.7266383956509585e-06,
                6.962257909842961e-06,
                6.962257909842961e-06,
                1.6701423836262173e-05,
                7.338207180898968e-07,
                NaN,
                1.7603438428848787e-06,
                2.2603242978943238e-06,
                1.3709573702856596e-06
            ],
            [
                7.734414854823498e-08,
                0.9999996533674202,
                1.1253514863968147e-07,
                0.9999934595612239,
                2.3823696679327928e-07,
                0.9999993916409635,
                2.6995774527718623e-07,
                2.6995784182183607e-07,
                9.931200429212718e-08,
                8.7642526752214e-08
            ],
            [
                0.9999960330121973,
                0.9999955048184258,
                2.5612816000646084e-06,
                0.0003353499910822861,
                4.785092783454444e-06,
                3.0590215399183813e-07,
                2.260324836787226e-06,
                2.1444948412722418e-05,
                1.0129989772274546e-05,
                5.144221979793211e-05
            ],
            [
                2.1024334103581732e-07,
                2.699578740032504e-07,
                1.855390576008354e-07,
                8.764253720001207e-08,
                9.422444815814404e-07,
                NaN,
                8.764244316973974e-08,
                1.209865827752005e-06,
                8.7642558095602e-08,
                2.1024336609874897e-07
            ],
            [
                2.9023109472244114e-06,
                0.9999452402111245,
                2.3823696679327928e-07,
                0.9999998024946095,
                0.9999990577550699,
                2.3823690999323465e-07,
                6.023577783447482e-08,
                1.1253525596174225e-07,
                3.65348425788669e-08,
                7.73442776303243e-08
            ],
            [
                3.726637951387472e-06,
                1.7603434231833873e-06,
                3.927863407379485e-07,
                0.9999987901347497,
                0.9996200155731559,
                2.382369667929001e-07,
                0.9999852610145455,
                0.9999993524050477,
                0.9999379495195926,
                0.9999151889491308
            ],
            [
                0.9999996310115918,
                0.9999957771645467,
                7.734428685047173e-08,
                8.315280276626197e-07,
                9.931185038635267e-08,
                0.9999985406241279,
                0.9999925887183737,
                0.999996711250938,
                0.9999960330126701,
                0.9999995262092728
            ],
            [
                8.76424013786396e-08,
                1.2751901248454963e-07,
                9.931189774187203e-08,
                2.430024652854702e-05,
                6.475947982037486e-07,
                3.9278605979534166e-07,
                7.73442776303243e-08,
                3.224189323773857e-08,
                9.931185038635267e-08,
                1.855391681906175e-07
            ],
            [
                1.0129993395336818e-05,
                0.9999885212359936,
                0.999997876622045,
                5.043475885696228e-07,
                3.4663274507713016e-07,
                0.9999964991451706,
                0.9999516743396185,
                0.9999869928730988,
                1.1478764021029928e-05,
                6.82560779249779e-08
            ],
            [
                3.4663274507713016e-07,
                0.9999916019249747,
                0.9999977396765122,
                6.144177531767002e-06,
                1.7603430034867993e-06,
                0.9999921107383755,
                0.9999975938976616,
                0.999994906296219,
                1.209866260432471e-06,
                0.9999985406243013
            ],
            [
                2.102434162245973e-07,
                0.9999981261239475,
                0.9999756997651039,
                1.275190732904469e-07,
                9.931190958076104e-08,
                0.9999989322966216,
                0.9999960330140881,
                2.102434162245973e-07,
                0.9999916019299875,
                4.450850519403407e-07
            ],
            [
                8.939698435454571e-06,
                0.001032231089934077,
                2.9023119851899796e-06,
                NaN,
                1.1478766757561534e-05,
                NaN,
                3.120191509592808e-05,
                1.7603427936079236e-06,
                1.1478766757718129e-05,
                3.120190393487965e-05
            ],
            [
                7.338209805240734e-07,
                2.699578096403948e-07,
                2.699578096403948e-07,
                4.222834954801051e-06,
                1.855390576008354e-07,
                1.1253512180925583e-07,
                9.422442569334097e-07,
                1.3709576971463352e-06,
                7.338212429582604e-07,
                4.450850519403407e-07
            ],
            [
                0.9999810748427803,
                0.999999391641036,
                1.2098661162056318e-06,
                3.9278605979534166e-07,
                7.73441946488886e-08,
                2.6995774527718623e-07,
                2.699578096403948e-07,
                0.9999987121043243,
                7.734418542875216e-08,
                0.9999986290424671
            ],
            [
                NaN,
                1.5534973842076057e-06,
                1.4738985486506781e-05,
                5.3157811697009444e-08,
                5.04347468323289e-07,
                4.785095065232451e-06,
                8.315281267882195e-07,
                NaN,
                5.04347468323289e-07,
                1.209865539295696e-06
            ],
            [
                0.9999998724808964,
                0.9999992661786699,
                0.9999986290424675,
                8.315284241650899e-07,
                0.9999990577556309,
                6.144177531767002e-06,
                8.315280276626197e-07,
                0.9999756997478355,
                3.9278629391427843e-07,
                0.9999892166903857
            ],
            [
                0.9999969105059254,
                1.0677029973219343e-06,
                1.7603438428800754e-06,
                0.9999998461827139,
                0.9999960330126717,
                0.9999990577551823,
                0.9999861539888832,
                1.2098653950692178e-06,
                8.315278294114555e-07,
                7.338212429582604e-07
            ],
            [
                6.475946438055299e-07,
                9.422444815814404e-07,
                0.9999995262095552,
                0.9999667858023987,
                6.475948754028718e-07,
                0.9999995549150542,
                0.9999999273418703,
                0.9999996310113279,
                5.715006514176113e-07,
                2.561282516042282e-06
            ],
            [
                2.561281600086738e-06,
                2.144495864059426e-05,
                1.2098658277451275e-06,
                4.450849988811838e-07,
                1.4738985486506781e-05,
                2.6995768091310296e-07,
                8.315284241650899e-07,
                1.0677032518785256e-06,
                1.3007134667259441e-05,
                8.93969950132721e-06
            ],
            [
                0.9999993524051247,
                0.9999993106387904,
                0.9999957771650526,
                0.9999992188516698,
                0.00029595720602899244,
                0.9999992661791073,
                0.9999998461826222,
                NaN,
                0.999994228079291,
                2.102434162245973e-07
            ],
            [
                5.04347468323289e-07,
                1.2098659719757836e-06,
                1.3709576971425944e-06,
                6.144173137126169e-06,
                1.2098652508347793e-06,
                1.2098661162056318e-06,
                5.04347468323289e-07,
                1.6701421845361053e-05,
                8.939696304311336e-06,
                6.962255419931625e-06
            ],
            [
                0.9999982396574172,
                0.9999998257021422,
                0.9999916019269707,
                0.9999646437536464,
                0.9999995262093859,
                3.653485564473625e-08,
                6.47595107001401e-07,
                0.999999887464771,
                0.9999756997622059,
                0.9999997897567091
            ],
            [
                6.144173137126169e-06,
                0.9999978766215388,
                0.9999996743687422,
                8.315277302841894e-07,
                0.9999997126313441,
                1.5534975693979422e-06,
                1.0677026154806063e-06,
                2.2603237589779086e-06,
                2.5612831267202583e-06,
                1.3007125363719486e-05
            ],
            [
                2.6995774527718623e-07,
                4.785092783519724e-06,
                1.6701415872385704e-05,
                0.9999852610110652,
                3.2887482813149375e-06,
                0.9999417087350513,
                0.9999981261252888,
                1.3007134667259441e-05,
                6.144175334367959e-06,
                4.006371129615879e-05
            ],
            [
                0.9999995262095551,
                0.9999997617631752,
                0.9999949062962162,
                0.9999982396559487,
                0.999948557805035,
                0.9999992188517627,
                0.9999993524051249,
                0.999999789756634,
                0.999999057755631,
                0.9999599362985574
            ],
            [
                0.9999667858173442,
                5.829124471187197e-05,
                0.9999822214460643,
                0.9999832985761751,
                1.30071315662049e-05,
                0.9999967112513306,
                0.0003353500713116092,
                0.9999934595612245,
                5.829127945202588e-05,
                1.147877359957198e-05
            ],
            [
                4.785096776499213e-06,
                1.7603434231777837e-06,
                9.422444815765128e-07,
                1.3709567165579959e-06,
                3.2887486733420804e-06,
                6.962255419931625e-06,
                0.0001584362925687936,
                1.3007126914245925e-05,
                7.338207180864763e-07,
                2.260324836776948e-06
            ],
            [
                7.734414854823498e-08,
                0.9999993106387903,
                6.023579219579052e-08,
                0.9999978766207798,
                1.6373764721072816e-07,
                0.9999955048173543,
                8.764244316973974e-08,
                0.9999964991460052,
                0.999998863436561,
                8.764241182641775e-08
            ],
            [
                1.6373766672994222e-07,
                0.9999981261243939,
                8.315279285351409e-07,
                NaN,
                6.475945666063607e-07,
                3.9278605979534166e-07,
                1.760342793638743e-06,
                0.00015843616032953635,
                9.422444815814404e-07,
                9.931187406410953e-08
            ],
            [
                0.9999667858171837,
                6.475947210031623e-07,
                0.9999998362622358,
                1.3709573702822306e-06,
                1.7603430034867993e-06,
                0.9999997761971849,
                1.2098661162056318e-06,
                9.422450432014836e-07,
                6.475947982037486e-07,
                0.9999998555019275
            ],
            [
                0.9999995818813269,
                0.9999998257020798,
                0.9999995262092728,
                5.71500719545698e-07,
                0.9999996072137062,
                0.9999996310115918,
                0.999999631011372,
                0.9999977396746262,
                0.9999991684720718,
                0.9999972735303831
            ],
            [
                5.422217677152175e-06,
                1.3709572068522336e-06,
                3.466325797896173e-07,
                8.31528325040778e-07,
                3.059022269250683e-07,
                7.338209805240734e-07,
                1.3709576971463352e-06,
                2.382370235933104e-07,
                8.315282259138311e-07,
                3.288749849529972e-06
            ],
            [
                0.9999998555019619,
                NaN,
                0.9999980052698045,
                0.9999998874647709,
                1.0,
                0.9999997761971582,
                1.4449798650569826e-07,
                0.9999843104485401,
                0.9999995549150544,
                0.9999996940977367
            ],
            [
                3.466326624336003e-07,
                1.6373772528704005e-07,
                3.05902190458764e-07,
                4.4508515805735777e-07,
                0.9999296881751849,
                2.6995784182183607e-07,
                0.9999942280779126,
                1.1253525596174225e-07,
                3.466327037553825e-07,
                1.4449805540763184e-07
            ],
            [
                0.9999987901337399,
                0.999897700149686,
                1.2098652508424818e-06,
                1.5534979397790343e-06,
                0.9999970976883636,
                0.999999391641181,
                0.9999980052707561,
                6.144175334468545e-06,
                2.1024341622426268e-07,
                1.6373762769138607e-07
            ],
            [
                5.043473480777865e-07,
                1.444980209564556e-07,
                5.71500719545698e-07,
                7.338207180898968e-07,
                2.3823696679327928e-07,
                1.209866260432471e-06,
                6.475947210046347e-07,
                6.82560779249779e-08,
                8.764245361752286e-08,
                6.475945666051092e-07
            ],
            [
                1.6373766672994222e-07,
                NaN,
                5.3157887739943563e-08,
                3.466326624336003e-07,
                1.4449796928021588e-07,
                6.023578501513224e-08,
                6.023569884718319e-08,
                0.9999967112521135,
                0.9999599363175037,
                0.9999999397643083
            ],
            [
                0.9999990577552946,
                7.734414854823498e-08,
                7.73442776303243e-08,
                9.931200429212718e-08,
                1.8553916819032217e-07,
                1.275191036933194e-07,
                1.275190276859705e-07,
                9.931199245322124e-08,
                2.5110005893648856e-08,
                1.1253525596174225e-07
            ],
            [
                0.9999981261239476,
                0.9999994284996895,
                0.9999975938985225,
                1.0677029973192638e-06,
                1.2098659719788098e-06,
                5.043475885696228e-07,
                1.0677026154806063e-06,
                1.370957860576702e-06,
                2.2603253756956754e-06,
                0.9999970976880176
            ],
            [
                1.4449800373118268e-07,
                2.7535694384882703e-05,
                1.9947304348862686e-06,
                2.3823690999323465e-07,
                0.9999991684720718,
                0.9999972735300574,
                0.9999251537373134,
                0.9999962733620524,
                0.9999771720001799,
                0.9999993106391191
            ],
            [
                0.9999974387177911,
                9.931202796993203e-08,
                2.382370235933104e-07,
                6.475945666063607e-07,
                0.9999989969862711,
                0.9999993106387906,
                1.637377057680051e-07,
                1.637377057680051e-07,
                8.764242227418718e-08,
                2.102434412875379e-07
            ],
            [
                2.2603234895176927e-06,
                1.3709568799760888e-06,
                1.760344052714248e-06,
                5.422218323487975e-06,
                2.2603234895289998e-06,
                0.9999877809240467,
                3.7266401726173067e-06,
                4.78509563555309e-06,
                1.370957860567974e-06,
                4.785096776499213e-06
            ],
            [
                0.9999972735290822,
                0.9999987121046314,
                1.3709567165617364e-06,
                0.999998996986032,
                0.9999998555019274,
                0.9999998144609645,
                0.9999998642566542,
                0.9999942280806688,
                9.422447062294175e-07,
                2.5612812947508257e-06
            ],
            [
                2.5612828213934817e-06,
                3.2887486733420804e-06,
                3.7266406168827523e-06,
                1.9947297215043796e-06,
                1.0677026154730804e-06,
                1.1478769494396542e-05,
                1.760343003481596e-06,
                1.8925157265710765e-05,
                5.715006514176113e-07,
                6.9622595696935874e-06
            ],
            [
                3.7266401726359486e-06,
                5.715005832895975e-07,
                0.999998712104325,
                3.059022998581767e-07,
                4.4508526417298334e-07,
                8.764244316973974e-08,
                0.9999756997564421,
                0.9999969105051874,
                1.209865827752005e-06,
                1.637376862489725e-07
            ],
            [
                0.9999964991443367,
                7.338208055680009e-07,
                5.715002426486762e-07,
                5.04347468323289e-07,
                0.99999879013374,
                0.9999985406243017,
                5.715002426475718e-07,
                0.9999970976869799,
                3.4663278639892215e-07,
                0.999999554914736
            ],
            [
                0.9999993524050477,
                0.9999995262092164,
                0.9999983463096265,
                0.9999994631248683,
                0.9999952149060781,
                NaN,
                0.999999168472171,
                0.999998540623954,
                0.999998629042141,
                0.9999987901343171
            ],
            [
                9.93120161310289e-08,
                0.9999989969861515,
                8.764253720001207e-08,
                9.931186222523604e-08,
                0.9999949062937875,
                3.9278605979534166e-07,
                1.1253524254650944e-07,
                1.275190124846946e-07,
                0.999997438717792,
                0.9999964991460065
            ],
            [
                3.927862470905692e-07,
                0.9999981261239486,
                4.450852111155216e-07,
                5.71500719545698e-07,
                5.043476486924565e-07,
                1.0677026154806063e-06,
                0.9999724643024137,
                0.9999982396565782,
                2.1024339116168358e-07,
                0.9999978766215402
            ],
            [
                0.9999983463106122,
                1.8553905759969634e-07,
                1.275190732904469e-07,
                0.9999994284996894,
                0.9999990577552941,
                0.999998996985434,
                5.043475885696228e-07,
                0.9999995818810776,
                0.9999756997477584,
                0.9999985406234317
            ],
            [
                NaN,
                1.4449798650569826e-07,
                0.999897700135587,
                0.999986153988973,
                0.9998601778788311,
                0.9999573525272656,
                1.3709572068522336e-06,
                0.9999964991443396,
                0.9999296881333094,
                2.5612819054028872e-06
            ],
            [
                8.315284241650899e-07,
                1.5534971990126997e-06,
                2.3823696679327928e-07,
                2.2603234895372223e-06,
                1.275190732904469e-07,
                1.7603438428800754e-06,
                3.927862470899887e-07,
                4.4508526417298334e-07,
                3.288749065423109e-06,
                1.8925145985895816e-05
            ],
            [
                1.5534983101602148e-06,
                1.3709567165579959e-06,
                0.9999996533674204,
                2.561282516066741e-06,
                0.9999991684715763,
                9.422449308774482e-07,
                0.9999251537554039,
                0.9999987121046314,
                8.315277302841894e-07,
                8.315279285351409e-07
            ]
        ]
    },
    {
        "q_id": "9090_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            102,
            103,
            104,
            105,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                6.962254589978262e-06,
                1.7603430034867993e-06,
                0.9999822214524591,
                3.0590226339137693e-07,
                0.9999964991443386,
                0.9999904837494658,
                0.9999869928654075,
                8.939695238536645e-06,
                0.999995214904946,
                0.9999972735294123
            ],
            [
                0.9999977396748959,
                0.9999995262094422,
                0.9999998024947038,
                0.9999997300421904,
                0.9999996310116359,
                0.9999964991447529,
                0.9999949062968234,
                0.9999978766215383,
                0.9999998024946566,
                0.9999982396563681
            ],
            [
                0.9999942280806711,
                0.9999970976880201,
                0.9999667858171183,
                0.9999982396559502,
                0.9999969105044528,
                0.9999952149060887,
                0.9999646437452181,
                0.9999945777784582,
                0.9999972735284305,
                0.9999921107393102
            ],
            [
                0.9999997300422547,
                0.9999998555019791,
                0.9999997617629764,
                0.9999994631250603,
                2.10243290909724e-07,
                0.9999998144609203,
                0.9999997300422548,
                0.9999996310115918,
                0.9999992188515765,
                0.9999986290429577
            ],
            [
                0.9999989322975126,
                0.9999892166877946,
                0.9999798543019918,
                0.9999970976887118,
                0.9999916019299824,
                0.9999925887210228,
                0.9999861539971193,
                0.9999983463096268,
                3.7266410611296085e-06,
                3.927862470899887e-07
            ],
            [
                1.994729008151319e-06,
                1.0677028700422047e-06,
                2.699577774589574e-07,
                1.994729483729522e-06,
                1.0677026154827912e-06,
                1.0677028700422047e-06,
                6.475950298021765e-07,
                9.422442569334097e-07,
                5.715005832895975e-07,
                8.315282259151545e-07
            ],
            [
                0.99999886343629,
                0.9999989969857926,
                0.9999998874648648,
                0.9999990577551817,
                0.9999978766205264,
                0.9999998724809268,
                0.999994906293786,
                0.9999998874649185,
                0.999998863435748,
                0.9999996533672137
            ],
            [
                0.9999885212291787,
                1.3709570434219446e-06,
                0.000626334183322172,
                6.144176066901277e-06,
                0.9999706884650494,
                0.9999970976880177,
                6.144177531811707e-06,
                1.994729483723626e-06,
                3.7266397283908927e-06,
                1.5534979397790343e-06
            ],
            [
                0.9999972735303821,
                0.999998629042795,
                0.9999984465015063,
                0.9999987901338849,
                0.9999969105048203,
                0.9999996533672966,
                0.9999983463102188,
                0.999998239656159,
                0.9999984465015067,
                0.9999986290424678
            ],
            [
                3.4663278639892215e-07,
                3.059021175261338e-07,
                1.209865827752005e-06,
                5.043472278322555e-07,
                1.3709570434219446e-06,
                1.0677029973219343e-06,
                9.422450432030903e-07,
                2.561282821402217e-06,
                5.043472278322555e-07,
                1.0677028700422047e-06
            ],
            [
                0.9999960330145611,
                0.999996711249762,
                0.9999957771655542,
                0.9999987121044783,
                0.9999983463108093,
                0.9999949062943954,
                0.9999972735287557,
                0.999998932296876,
                0.9999990577557435,
                0.9999869928715617
            ],
            [
                2.2603234895372223e-06,
                0.9999995549148956,
                0.9999967112505492,
                7.889265407327733e-06,
                0.9999986290427944,
                0.9999996310115479,
                0.9999984465015059,
                0.9999988634358835,
                0.9999983463108094,
                0.9999998802069731
            ],
            [
                0.9999972735297329,
                0.999997739676512,
                0.9999982396565777,
                0.9999980052700422,
                0.9999969105044498,
                0.999997593896802,
                0.9999949062950079,
                0.9999982396561593,
                0.9999989969859128,
                0.999998446502246
            ],
            [
                0.9999991684720718,
                0.9999970976883643,
                0.9999964991460065,
                0.9999994631251244,
                0.9999982396572085,
                0.9999952149066538,
                0.9999982396561589,
                0.9999991148428596,
                0.9999978766212863,
                0.9999942280772306
            ],
            [
                0.9999997463981032,
                0.9999999123575465,
                0.9999996743686257,
                0.999999653367255,
                0.9999996743688199,
                0.9999998555020309,
                0.9999997617631468,
                0.9999991684717745,
                0.9999988634365609,
                0.9999998024947038
            ],
            [
                0.9999898700066148,
                7.338208055680009e-07,
                0.9999995549151075,
                0.9999957771660557,
                0.9999945777829773,
                0.9999861539971124,
                0.9999970976873251,
                0.9999960330155079,
                0.9999998555019274,
                0.9999998144608762
            ],
            [
                0.9999985406234323,
                0.9999975938968027,
                0.9999339478241627,
                0.9999955048194985,
                0.999999730042287,
                0.9999934595635649,
                0.999996273361164,
                0.9999955048194983,
                0.9999986290429579,
                0.999998239657207
            ],
            [
                0.9999981261248412,
                0.9999991148430699,
                0.9999994631251244,
                0.9999988634358838,
                0.9999984465026172,
                0.9999983463096268,
                0.9999987121050925,
                0.9999942280786059,
                0.9999982396574172,
                0.9999993106387084
            ],
            [
                0.9999997761970515,
                0.9999990577550696,
                0.9999993106387904,
                0.9999991148429644,
                0.9999992661791073,
                0.9999997897567091,
                0.9999991684718734,
                0.9999981261252876,
                0.9999994631251883,
                0.9999997617631184
            ],
            [
                0.9999986290432857,
                2.5612831267202583e-06,
                5.422218323487975e-06,
                0.9999960330155083,
                0.999994906296219,
                9.610239212762526e-05,
                0.9999945777797442,
                0.0002959571002522352,
                0.9999938558232132,
                0.9999832985742074
            ],
            [
                5.715002426475718e-07,
                3.927862939126708e-07,
                1.760343003481596e-06,
                6.144176799334096e-06,
                2.260324567337161e-06,
                5.04347348075149e-07,
                1.994729483723626e-06,
                1.3709575337125585e-06,
                5.043473480766399e-07,
                1.5534975693979422e-06
            ],
            [
                0.9999546021153097,
                4.785095065232451e-06,
                0.9999998555019274,
                0.9999988634357482,
                0.999997438718097,
                0.999997739675165,
                0.9999992188519492,
                4.450852641737424e-07,
                0.9999996940976272,
                0.999999900688126
            ],
            [
                3.927863875616689e-07,
                6.475947982037486e-07,
                2.2603248367949354e-06,
                2.1024339116134898e-07,
                5.71500719545698e-07,
                4.785093353940187e-06,
                1.209866260432471e-06,
                1.3709572068553509e-06,
                2.561282516066741e-06,
                2.2603251062450327e-06
            ],
            [
                0.9999975938970888,
                0.9999987901347505,
                0.9999980052709949,
                0.9999991684718736,
                0.9999989969856736,
                0.9999987121043242,
                0.999998712104478,
                0.9999994631251244,
                0.9999978766220454,
                0.9999980052700425
            ],
            [
                0.9999980052693281,
                0.9999998144608981,
                0.9999989322972574,
                0.999999814460854,
                0.999999428499485,
                0.9999993524049705,
                0.9999990577549572,
                0.9999998362623529,
                0.9999962733598297,
                0.9999997897565838
            ],
            [
                0.9999997761971049,
                0.9999993106387085,
                0.9999983463104161,
                0.9999974387184023,
                0.999996033014092,
                0.9999977396759749,
                0.9999987121050927,
                0.9999992188516703,
                0.9999987901346062,
                0.9999992188512978
            ],
            [
                1.3709573702722555e-06,
                0.9999945777803917,
                0.9999987901340289,
                0.999997739674627,
                9.422448185510695e-07,
                1.99472924590571e-06,
                4.006370652067535e-05,
                0.9999832985782054,
                2.4300237837960777e-05,
                0.9999969105059232
            ],
            [
                3.9278610661902853e-07,
                8.315284241650899e-07,
                3.05902336324494e-07,
                7.338210680021253e-07,
                6.475946438055299e-07,
                4.785095635655362e-06,
                3.059021175261338e-07,
                1.0677029973219343e-06,
                3.7266410611296085e-06,
                1.2098661162056318e-06
            ],
            [
                0.9999983463110066,
                0.9999986290429583,
                0.9999251537559835,
                0.9999970976873244,
                0.9999980052700426,
                0.9999967112513309,
                3.059021175261338e-07,
                0.9999822214482098,
                0.999996033013144,
                0.9999970976887101
            ],
            [
                0.9999984465022471,
                0.9999969105066592,
                0.9999982396561589,
                0.9999995549150014,
                0.9999994284997578,
                0.9999982396572074,
                0.9999945777784506,
                0.9999957771665615,
                0.9999974387184026,
                0.9999989969861514
            ],
            [
                4.450850519409479e-07,
                1.9947292459406333e-06,
                2.699578740032504e-07,
                2.561281600086738e-06,
                2.2603242978943238e-06,
                2.9023116392097746e-06,
                3.288747889284851e-06,
                4.785094494811783e-06,
                2.561281294760143e-06,
                1.3709575337159875e-06
            ],
            [
                0.999999789756634,
                0.9999997300421261,
                0.9999996940978826,
                0.9999997126315495,
                0.9999974387168746,
                0.9999983463102178,
                0.9999930377462469,
                0.9999967112513286,
                0.9999945777784486,
                0.9999885212318854
            ],
            [
                4.222834451355964e-06,
                2.144495097113319e-05,
                3.726639728348526e-06,
                1.3007123813382511e-05,
                3.2887502415243994e-06,
                1.1478773599425825e-05,
                8.939696304002375e-06,
                8.939694172867777e-06,
                6.144174601935314e-06,
                8.939696304213768e-06
            ],
            [
                0.9999986290429581,
                0.9999982396569981,
                0.9999972735300581,
                0.9999978766222991,
                0.9999996743686645,
                0.9999987901338842,
                0.9999990577552946,
                0.9999969105040825,
                0.9999988634366961,
                0.9999994284993488
            ],
            [
                0.9999987901347502,
                6.475947982037486e-07,
                1.994730672675753e-06,
                9.422442569315887e-07,
                0.9999977396746261,
                0.00013982202424632715,
                9.610238067382736e-05,
                9.422445939054222e-07,
                0.9999987901347497,
                0.9999983463096268
            ],
            [
                8.939699501416646e-06,
                2.2603234895372223e-06,
                1.1478766757853845e-05,
                3.7266383956509585e-06,
                5.4222202626709005e-06,
                2.5612834320563895e-06,
                1.0129988565084915e-05,
                2.561281600086738e-06,
                0.0005527785509648304,
                1.0677024882029858e-06
            ],
            [
                0.00010889692232771249,
                0.9999987121043256,
                0.9999982396565807,
                3.0590237279032884e-07,
                0.9999984465024329,
                0.9999546021213186,
                0.9999982396561599,
                0.9999982396565781,
                0.9999938558268799,
                0.9999945777816888
            ],
            [
                0.9999938558246713,
                0.9999970976869792,
                0.9999898700090352,
                0.9999978766217923,
                0.9999972735290809,
                0.9999910603026414,
                0.9999989969856737,
                0.9999991148433867,
                0.9999955048184272,
                0.9999982396569985
            ],
            [
                0.9999972735290831,
                0.9999980052700426,
                0.9999975938965158,
                0.9999904837483241,
                0.9999993106386262,
                0.999999428499417,
                0.9999991148431755,
                0.9999984465020612,
                0.9999967112513313,
                0.9999981261241718
            ],
            [
                0.9999967112493745,
                0.9999974387165719,
                0.9999975938973766,
                0.999995777167571,
                0.9999964991468465,
                0.999998005270285,
                0.9999983463104154,
                0.9999952149060852,
                0.9999904837506001,
                0.9999981261246198
            ],
            [
                0.9999991684715764,
                0.9999962733611641,
                0.9999952149066538,
                0.9999994631247403,
                0.9999991148433868,
                0.9999985406243017,
                0.9999925887210196,
                0.9999969105055552,
                0.9999930377454173,
                0.9999977396765133
            ],
            [
                0.9999955048168211,
                0.9999977396748998,
                0.999998712104785,
                0.9999810748563194,
                0.9999962733607218,
                0.9999339478795309,
                0.9999942280820413,
                0.00010889688339134737,
                0.9999970976876724,
                0.9999980052702807
            ],
            [
                0.999999352405202,
                0.9999988634365613,
                0.999999631011592,
                0.9999988634357484,
                0.9999978766207802,
                0.9999995262094987,
                0.9999995818810777,
                0.9999989969856732,
                0.9999981261237236,
                0.9999991148432817
            ],
            [
                9.93118503859575e-08,
                0.9999861539905326,
                0.999998346310219,
                0.9999987121043247,
                1.5534979397740895e-06,
                0.9999843104484611,
                0.9999967112517221,
                2.3823702359290413e-07,
                0.9999949062944026,
                0.9999989969861525
            ],
            [
                1.994729483729522e-06,
                6.144176066943187e-06,
                5.422217030781934e-06,
                5.715006514176113e-07,
                8.315277302857965e-07,
                1.5534981249697903e-06,
                3.288749849529972e-06,
                1.6701425827133152e-05,
                2.5612834320563895e-06,
                2.2603251062450327e-06
            ],
            [
                0.9999994631248043,
                0.9999985406239539,
                0.9999972735294076,
                0.999999352405202,
                0.9999997300422869,
                0.9999990577555188,
                0.9999994956526522,
                0.9999999123574732,
                0.9999964991451715,
                0.9999969105055556
            ],
            [
                4.4508510499849186e-07,
                0.9999930377420999,
                0.9999957771645475,
                0.9999997300422548,
                4.785095635655362e-06,
                0.9999980052693285,
                0.999999802494586,
                0.9999962733598313,
                0.9999967112501534,
                0.999996711252113
            ],
            [
                1.5534971990169383e-06,
                0.9999599363174929,
                1.3709568799879344e-06,
                5.043476486915964e-07,
                1.8553905760062447e-07,
                1.3709567165617364e-06,
                2.3823685319244518e-07,
                3.05902336324494e-07,
                6.475949526020042e-07,
                1.067703124601679e-06
            ],
            [
                6.475948754012522e-07,
                1.370957860576702e-06,
                7.338207180898968e-07,
                8.315278294114555e-07,
                1.2098661162056318e-06,
                5.715005832886879e-07,
                5.043473480777865e-07,
                1.370957860576702e-06,
                5.043476486915964e-07,
                1.7603438428800754e-06
            ],
            [
                0.9999892166877941,
                0.9999997300422548,
                0.9999989969861515,
                0.9999997126314469,
                0.9999977396746257,
                0.9999997126314468,
                0.9999785550490615,
                0.999999653367379,
                0.9999997761971582,
                0.9999989322971304
            ],
            [
                0.9999945777803908,
                0.999994577779748,
                0.999998629042304,
                0.9999990577555189,
                0.9999992188512974,
                0.9999993524050479,
                0.9999981261239477,
                0.9999993916409639,
                0.9999952149055121,
                0.9999992661790201
            ],
            [
                0.9999998144609424,
                0.9999982396567878,
                0.9999952149032263,
                0.9999962733598291,
                0.999994228078602,
                0.9999996072139403,
                0.9999995262093292,
                0.9999998874648515,
                0.9999999006880312,
                0.9999990577555189
            ],
            [
                1.7603425837903113e-06,
                1.0677028700422047e-06,
                4.222834451403972e-06,
                1.5534981249697903e-06,
                1.209865539298447e-06,
                6.47594952603035e-07,
                2.1024336609874897e-07,
                7.33821330437595e-07,
                1.0677033791630344e-06,
                9.422443692574719e-07
            ],
            [
                5.715003789033962e-07,
                6.475949526020042e-07,
                5.715005832895975e-07,
                1.2098656835252174e-06,
                5.715003789046955e-07,
                3.4663249714612693e-07,
                6.475947982037486e-07,
                1.6373766672994222e-07,
                1.6373776432509826e-07,
                5.715006514176113e-07
            ],
            [
                0.999999631011592,
                0.9999977396759729,
                0.9999785550516243,
                0.9999986290426308,
                0.9999994956523514,
                0.9999996940978095,
                0.9999996743687034,
                0.9999996310113719,
                0.9999996533674617,
                0.9999997300423192
            ],
            [
                0.9999995818811277,
                0.9999996533672137,
                0.9999985406232581,
                0.9999982396563695,
                0.9999986290429587,
                0.9999986290426309,
                0.9999995262092729,
                0.999999814460854,
                0.999999789756634,
                0.9999949062931803
            ],
            [
                0.999999802494633,
                0.999999057755519,
                0.9999970976869802,
                0.9999151889290415,
                1.370957860576702e-06,
                5.04347468323289e-07,
                0.9999960330155074,
                0.9999934595596713,
                2.3823688159291947e-07,
                0.9999992661791947
            ],
            [
                0.9999960330126706,
                0.9999984465016911,
                0.9999996940977731,
                0.9999989969854337,
                0.9999994956527725,
                0.999999653367503,
                0.9999987121052456,
                0.999998446502617,
                0.9999998144608983,
                0.9999995818811275
            ],
            [
                0.9999987121049397,
                0.9999993916411815,
                0.9999980052702802,
                0.9999962733589475,
                0.999996273362052,
                0.9999980052705183,
                2.5612812947380135e-06,
                0.9999942280772292,
                0.9999957771655542,
                0.9999417087279875
            ],
            [
                0.999997438717792,
                0.999999631011592,
                0.9999960330136175,
                0.9999983463098241,
                0.9999974387184024,
                0.9999967112513302,
                0.999993855822477,
                3.288748281329893e-06,
                3.9278615344178325e-07,
                0.9999978766217927
            ],
            [
                1.553497754577351e-06,
                0.9999832985742014,
                5.715005832872586e-07,
                0.9999930377412684,
                1.2098662604291696e-06,
                0.9999970976873251,
                0.999970688468556,
                0.9999994956527727,
                6.475947981975644e-07,
                0.9999934595627809
            ],
            [
                3.288748281329893e-06,
                5.715005832853093e-07,
                6.475949526020042e-07,
                3.466325384678894e-07,
                7.338212429582604e-07,
                1.3709568799919866e-06,
                2.102434412871794e-07,
                5.715007195431641e-07,
                5.043475885674441e-07,
                6.475949526020042e-07
            ],
            [
                7.889262585886274e-06,
                9.931187406410953e-08,
                7.73442776300517e-08,
                7.889261645427538e-06,
                0.9999989969857926,
                0.9999998144609646,
                4.785094494811783e-06,
                0.9999993916408909,
                0.9999967112505443,
                2.699577774585891e-07
            ],
            [
                2.902313023130843e-06,
                0.999998446502247,
                0.9999996533673791,
                1.8553907971855875e-07,
                0.9999967112509403,
                0.999998540623084,
                0.9999964991460063,
                5.043473480777865e-07,
                0.9999977396759732,
                0.9999977396765115
            ],
            [
                3.466325384682834e-07,
                2.699578096403948e-07,
                3.466326624336003e-07,
                9.422444815814404e-07,
                2.699577130960941e-07,
                3.4663278639892215e-07,
                4.450851049991497e-07,
                2.1024339116168358e-07,
                4.4508510499849186e-07,
                9.422450432030903e-07
            ],
            [
                0.9999991684718735,
                0.9999986290423037,
                0.9999999067050388,
                0.9999995262093293,
                3.9278610661902853e-07,
                0.9999991684717746,
                0.9999942280792895,
                0.9999962733593861,
                0.9999989322973849,
                0.9999967112493682
            ],
            [
                4.785093924389007e-06,
                0.9999904837437806,
                6.144172404738491e-06,
                0.9999982396559484,
                0.999997876620527,
                4.450848927658745e-07,
                0.9998766054556901,
                0.9999981261243942,
                1.0677028700422047e-06,
                0.999992110733661
            ],
            [
                1.3709572068553509e-06,
                5.715006514176113e-07,
                1.2098656835252174e-06,
                7.338212429582604e-07,
                9.422443692574719e-07,
                1.012999098021058e-05,
                NaN,
                1.2098659719788098e-06,
                3.2887482813149375e-06,
                1.0677033791612137e-06
            ],
            [
                5.043472879525233e-07,
                3.2887494574832472e-06,
                1.0129994602895546e-05,
                1.3709567165617364e-06,
                5.043475885696228e-07,
                9.422444815814404e-07,
                8.315277302857965e-07,
                8.315281267834927e-07,
                2.2603242978778778e-06,
                8.315281267861397e-07
            ],
            [
                0.9999987121044778,
                0.9999978766207791,
                0.9999993524048931,
                0.9999994956524718,
                0.9999991684721709,
                0.9999972735287564,
                0.99999905775507,
                0.9999969105051877,
                0.9999993106388729,
                0.999996033013142
            ],
            [
                0.9999964991455881,
                0.9999980052698042,
                0.9999980052702796,
                5.715005832886879e-07,
                0.9999992188513902,
                0.9999930377462453,
                0.9999995262094986,
                0.9999925887210183,
                0.999997739675703,
                0.9999962733598305
            ],
            [
                0.9999898700126718,
                0.9999967112497614,
                0.9999987121046314,
                0.9999957771675664,
                1.012999218776902e-05,
                0.9999982396569975,
                0.9999974387168751,
                0.9999949062962158,
                0.9999810748472833,
                0.9999785550414643
            ],
            [
                6.475949526020042e-07,
                4.785096776499213e-06,
                0.9999987121043247,
                0.9999925887210199,
                4.222834451403972e-06,
                0.999998629043121,
                0.999999554914736,
                8.315280276626197e-07,
                0.9999339478635023,
                0.9999983463100207
            ],
            [
                0.9999646437368396,
                0.9999986290431213,
                1.7603440527286572e-06,
                0.9999687980924876,
                0.9999992188514836,
                0.9999964991439193,
                0.9999967112501542,
                0.9999975938968014,
                1.3709567165617364e-06,
                0.9999938558224782
            ],
            [
                0.9999991148433867,
                0.9999987121049384,
                0.999994577781036,
                0.9999987901344611,
                0.9999992188513902,
                0.9999989969854343,
                0.9999988634361547,
                0.9999972735303831,
                0.9999990577551823,
                0.9999993106387904
            ],
            [
                0.9999998942830862,
                0.999999887464932,
                0.9999995262093293,
                0.9999997300421583,
                0.9999998461826222,
                0.9999990577549573,
                0.9999998874647307,
                0.9999988634361543,
                0.9999998257021214,
                0.9999998461827322
            ],
            [
                2.9023119851899796e-06,
                1.0677028700422047e-06,
                2.9023116392097746e-06,
                1.5534981249736758e-06,
                1.5534983101644536e-06,
                2.699578096403948e-07,
                2.2603245673443566e-06,
                1.3709575337159875e-06,
                1.7603425837903113e-06,
                4.785096776525326e-06
            ],
            [
                0.9999991684721712,
                3.1201922533564516e-05,
                0.9999869928731154,
                9.422447062294175e-07,
                0.9999974387165704,
                0.9999972735290824,
                6.962257909722651e-06,
                0.9999832985742252,
                0.0001398220742354593,
                0.9999970976873263
            ],
            [
                0.9999975938979504,
                0.999999814460832,
                0.9999967112505442,
                0.9999934595604475,
                0.9999987901346057,
                2.2603248367949354e-06,
                0.9999983463104153,
                0.9999957771675673,
                0.9999987901346061,
                0.9999969105040838
            ],
            [
                0.999999712631481,
                0.9999996743686259,
                0.9999998555020307,
                0.999999906705072,
                0.9999998461827139,
                0.9999996533672136,
                0.999999814460876,
                0.999998446502802,
                0.9999998642567351,
                0.9999995549151074
            ],
            [
                0.9999822214439489,
                3.05902190458764e-07,
                2.902312677150514e-06,
                0.9999981261252877,
                0.9999975938973751,
                0.999998996986271,
                0.9999987901340288,
                0.999995504820033,
                0.9998911031183896,
                4.785095635655362e-06
            ],
            [
                0.9999998802069017,
                0.9999994956524718,
                0.99999926617902,
                0.9999967112513313,
                0.9999996310114599,
                0.9999975938979495,
                0.9999974387165713,
                0.9999983463106117,
                0.9999997761971849,
                0.9999991684721711
            ],
            [
                0.9999969105062908,
                0.9999982396559487,
                0.9999987121041712,
                0.9999985406241287,
                0.999994577781036,
                0.9999982396563685,
                0.9999962733593872,
                0.9999983463096268,
                0.9999987121044781,
                0.9999994631251883
            ],
            [
                9.422448185534261e-07,
                1.3709575337159875e-06,
                7.338209805240734e-07,
                3.726638395634011e-06,
                3.466327037553825e-07,
                1.0677028700422047e-06,
                2.2603253756956754e-06,
                2.902313369111213e-06,
                3.288749849529972e-06,
                7.338208055680009e-07
            ],
            [
                0.9999983463104146,
                0.9999997761971315,
                0.9999995818812272,
                0.9999993916406733,
                0.9999986290431208,
                0.9999996072136593,
                0.9999996310114159,
                0.9999952149043678,
                0.9999945777823261,
                0.9999952149060787
            ],
            [
                3.059022998576899e-07,
                3.4663266243308805e-07,
                2.9023116392097746e-06,
                8.315282259138311e-07,
                2.6995771309523475e-07,
                7.338207180898968e-07,
                2.2603245673443566e-06,
                3.927862470890063e-07,
                5.043473480766399e-07,
                3.05902336324494e-07
            ],
            [
                1.3709573702822306e-06,
                6.475947210012481e-07,
                1.3007128464559612e-05,
                1.3709576971425944e-06,
                6.962256249758443e-06,
                3.2887478892683997e-06,
                1.8925152753790864e-05,
                4.222834451355964e-06,
                2.2603234895289998e-06,
                2.561282210740037e-06
            ],
            [
                0.9999986290423036,
                0.9999995549151074,
                0.9999986290426303,
                0.999998446502061,
                0.9999962733607213,
                0.9999993524049707,
                0.9999997300423192,
                0.9999962733616093,
                0.9999974387168769,
                0.9999984465020627
            ],
            [
                1.0677024881980089e-06,
                4.450852111148132e-07,
                3.9278634073625165e-07,
                1.1478764020560142e-05,
                2.1444945858485726e-05,
                0.9999986290432838,
                7.88926070489716e-06,
                2.4300243631272052e-05,
                0.00013982207421714976,
                5.829128639666634e-05
            ],
            [
                4.785092783519724e-06,
                9.422449308774482e-07,
                0.9999957771650566,
                1.5534984953453635e-06,
                1.3709568799760888e-06,
                1.9947304348703948e-06,
                0.9999910603037281,
                1.5534971990126997e-06,
                1.4738980215352592e-05,
                7.338210680021253e-07
            ],
            [
                2.5612831267086116e-06,
                5.422219616228845e-06,
                6.475945666009864e-07,
                4.450849988780466e-07,
                7.338207180838067e-07,
                1.0677024881941248e-06,
                1.209865827740176e-06,
                2.2603245673155757e-06,
                9.422445939002803e-07,
                8.315278294038928e-07
            ],
            [
                0.9999970976873265,
                0.9999992661787575,
                0.9999989322975124,
                0.9999987121047855,
                0.9999986290429578,
                0.9999957771655538,
                0.9999984465026167,
                0.9999992661791076,
                0.9999938558224779,
                0.9999972735290822
            ],
            [
                0.9999843104521804,
                0.999999653367503,
                0.9999999176675436,
                0.999998712104478,
                0.9999996310115918,
                0.9999964991443355,
                0.9999981261250643,
                0.9999967112513283,
                0.9999967112505452,
                0.9999952149037987
            ],
            [
                0.9999957771665617,
                0.9999852610162961,
                0.9999861539938124,
                0.9999993916411812,
                0.9999996940976273,
                0.9999994956527722,
                0.9999771719947397,
                0.999999653367379,
                0.9999987901341731,
                0.9999972735307066
            ],
            [
                5.715005832895975e-07,
                2.561283126728994e-06,
                2.1024339116082313e-07,
                5.043475885696228e-07,
                1.0677027427624903e-06,
                6.47595107001401e-07,
                3.466327863983311e-07,
                5.715003107767143e-07,
                1.760342793638743e-06,
                3.927862002663297e-07
            ],
            [
                9.422442569315887e-07,
                1.4738987243478167e-05,
                1.3007123813382511e-05,
                1.067703379154416e-06,
                1.760343633031919e-06,
                4.785095635624897e-06,
                1.7603434231777837e-06,
                8.939696304311336e-06,
                2.2603242978871282e-06,
                2.2603242978871282e-06
            ],
            [
                0.999997593896515,
                0.9999997617630333,
                0.999999581881078,
                0.9999994284992806,
                0.9999998362622747,
                0.9999989322970038,
                0.9999998555020481,
                0.9999962733602756,
                0.9999997463981637,
                0.9999970976869809
            ],
            [
                8.315277302857965e-07,
                3.0590219045914655e-07,
                7.338207180898968e-07,
                8.315277302857965e-07,
                8.315278294114555e-07,
                4.450851049991497e-07,
                6.47595107001401e-07,
                1.9947292459406333e-06,
                6.47595107001401e-07,
                1.8553907971855875e-07
            ],
            [
                4.78509278348926e-06,
                1.7603438428660665e-06,
                8.31527928532683e-07,
                0.999995214905511,
                1.7603434231777837e-06,
                2.9023112932177327e-06,
                3.927860597945825e-07,
                0.9999945777784518,
                1.670142383595838e-05,
                1.5534979397740895e-06
            ],
            [
                0.9999982396569981,
                0.9999989969860322,
                0.9999977396754343,
                0.9999994631248684,
                0.9999986290427948,
                0.9999996310114599,
                0.9999996940976273,
                0.9999988634364253,
                0.999995214905509,
                0.999998540623606
            ],
            [
                0.9999996533672136,
                0.999998346310021,
                0.9999998257021837,
                0.9999996940977732,
                0.9999925887201394,
                0.9999989322967487,
                0.9999969105040822,
                0.999999730042094,
                0.9999996310115039,
                0.9999964991464227
            ],
            [
                0.9999962733602756,
                0.9999985406239541,
                2.2603234895289998e-06,
                0.9999251537466,
                2.699576809143613e-07,
                0.9999975938973767,
                0.9999977396765118,
                5.715002426475718e-07,
                6.962258739796719e-06,
                1.370957860576702e-06
            ],
            [
                0.9999997300421262,
                0.999998239657208,
                0.9999989322975124,
                0.9999978766215399,
                0.9999972735290816,
                0.99999671125133,
                0.9999599363176336,
                0.9999957771675673,
                0.9999646437578743,
                0.9999972735287567
            ],
            [
                0.999998790134173,
                0.9999990577551819,
                0.9999997761971583,
                0.9999998144608098,
                0.9999998555019274,
                0.9999978766207801,
                0.999998712104478,
                0.9999994956527122,
                0.999999730042094,
                0.9999989322971305
            ],
            [
                0.9999987901344609,
                0.9999998362622747,
                2.2603242978871282e-06,
                0.9999994284992806,
                0.9999993106388726,
                0.9999998362622748,
                0.9999997617630616,
                0.9999992188518559,
                0.9999997897566089,
                0.9999977396751644
            ],
            [
                0.9999978766217928,
                0.9999967112505457,
                0.9999898700090352,
                6.1441746018123775e-06,
                3.2887502415438413e-06,
                0.9999974387165722,
                0.999998239657211,
                1.7603425837702984e-06,
                4.222834451355964e-06,
                0.9999984465020614
            ],
            [
                0.999997593897376,
                0.9999991148432813,
                0.9999949062950032,
                0.9999985406239539,
                0.9999964991451715,
                0.9999996743687423,
                0.9999960330131432,
                0.9999967112513297,
                0.9999970976866348,
                0.9999934595620045
            ],
            [
                0.9999978766217926,
                0.9999977396757037,
                0.9999980052705174,
                1.8553914607267268e-07,
                7.338210680021253e-07,
                0.9999977396759736,
                1.994729483729522e-06,
                0.999988521233266,
                0.9999997761971583,
                2.2603245673443566e-06
            ],
            [
                1.5534983101602148e-06,
                1.7603440527286572e-06,
                0.9999974387187074,
                5.715002426475718e-07,
                3.927862002663297e-07,
                5.043473480777865e-07,
                6.475945666051092e-07,
                3.9278615344178325e-07,
                6.475945666051092e-07,
                9.422450431989127e-07
            ],
            [
                4.2228329411708495e-06,
                2.5612828213818346e-06,
                1.9947304348595095e-06,
                7.338213304283347e-07,
                1.5534984953298217e-06,
                7.338207180864763e-07,
                7.338212429537553e-07,
                2.561282210729555e-06,
                2.902312677137316e-06,
                1.3709572068272963e-06
            ],
            [
                2.6995784182140636e-07,
                1.0129987357407137e-05,
                0.9999972735300573,
                0.999997876621287,
                0.9999957771665627,
                2.3823690999290963e-07,
                0.9999942280786026,
                5.422217030781934e-06,
                NaN,
                0.9999646437452422
            ],
            [
                0.9999988634366973,
                0.9999974387184015,
                0.9999964991451747,
                0.9999989969856745,
                0.9999984465018772,
                0.9999925887228107,
                0.999998996985913,
                0.9999964991455927,
                0.9999981261252884,
                0.9999974387184032
            ],
            [
                0.9999995549150543,
                0.999999428499417,
                0.9999982396572069,
                0.9999987901347499,
                0.9999989969861512,
                0.9999993524052021,
                0.9999996310115479,
                0.9999988634362897,
                0.9999999067050054,
                0.9999997897567091
            ],
            [
                2.5612812947508257e-06,
                1.7603440527286572e-06,
                1.3709570433979422e-06,
                7.338208930391909e-07,
                5.043472879540142e-07,
                1.2098655392871682e-06,
                1.067702615468225e-06,
                8.315281267800897e-07,
                1.2098656835136636e-06,
                1.7603440527046419e-06
            ],
            [
                0.9999983463108089,
                0.9999975938970881,
                0.9999964991443383,
                0.9999987121049383,
                0.9999983463098232,
                0.9999977396754345,
                0.9999960330131432,
                0.9999981261252878,
                2.430023204460668e-05,
                0.999998239656578
            ],
            [
                6.9622587397397306e-06,
                5.715003789046955e-07,
                4.4508494582405734e-07,
                1.7603438428848787e-06,
                4.785095065232451e-06,
                3.288748281329893e-06,
                1.3709576971463352e-06,
                1.2098661162056318e-06,
                2.561281600086738e-06,
                1.3007125363719486e-05
            ],
            [
                7.889266347786918e-06,
                1.9947297215125433e-06,
                8.315279285351409e-07,
                1.9947301970972664e-06,
                9.422450431989127e-07,
                8.315281267861397e-07,
                3.2887482813149375e-06,
                9.422445939054222e-07,
                1.1478770862735993e-05,
                1.5534983101602148e-06
            ],
            [
                0.9999960330155064,
                0.9999972735294066,
                0.9999967112521135,
                0.9999945777823293,
                0.9999877809269127,
                0.9999993106387904,
                0.9999982396561583,
                0.9999997126313442,
                0.9999960330155083,
                0.9999977396746262
            ],
            [
                9.422450432030903e-07,
                1.1253513522447425e-07,
                5.043475885696228e-07,
                2.5612834320563895e-06,
                1.3709575337159875e-06,
                1.0677027427624903e-06,
                7.33821330437595e-07,
                2.10243290909963e-07,
                3.9278620026686556e-07,
                3.466327037553825e-07
            ],
            [
                0.9999977396751647,
                0.999998239657207,
                0.9999960330126695,
                0.9999986290421402,
                0.9999997300421583,
                0.9999974387184016,
                0.9999949062937855,
                0.9999997897566089,
                0.9999999358794326,
                0.9999964991468397
            ]
        ]
    },
    {
        "q_id": "9156_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            7,
            10,
            11,
            13,
            14,
            16,
            20,
            21,
            22,
            23,
            26,
            27,
            30,
            32,
            33,
            34,
            35,
            36,
            42,
            43,
            45,
            47,
            49,
            50,
            52,
            54,
            56,
            57,
            58,
            59,
            60,
            62,
            64,
            65,
            66,
            68,
            70,
            71,
            72,
            78,
            80,
            81,
            82,
            85,
            88,
            89,
            90,
            92,
            93,
            97,
            98,
            100,
            101,
            102,
            103,
            105,
            106,
            113,
            114,
            115,
            116,
            117,
            118,
            121,
            123,
            124,
            125,
            127
        ],
        "rewards": [
            [
                4.450850519403407e-07,
                1.7603440527222532e-06,
                6.1441746020359e-06,
                9.422442569290178e-07,
                2.260324836776948e-06,
                8.315278294072958e-07,
                4.4508494582405734e-07,
                1.1478773599425825e-05,
                1.0677032518785256e-06,
                1.7603434231777837e-06
            ],
            [
                1.6701427817730953e-05,
                2.430024073461624e-05,
                1.994730672668496e-06,
                2.2603234895372223e-06,
                4.222832941142044e-06,
                0.00010889696126329929,
                NaN,
                1.4738978458382043e-05,
                NaN,
                1.2098656835224664e-06
            ],
            [
                6.475946438055299e-07,
                NaN,
                NaN,
                2.2603251062450327e-06,
                NaN,
                1.2098659719757836e-06,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                4.785092783519724e-06,
                2.7535697667202906e-05,
                3.0590215399183813e-07,
                NaN,
                3.7266401726173067e-06,
                1.3709575337125585e-06,
                7.338208055664991e-07,
                2.6995784182140636e-07,
                3.726639728370556e-06,
                3.288748281329893e-06
            ],
            [
                6.962257079775324e-06,
                NaN,
                2.5612819054028872e-06,
                NaN,
                NaN,
                1.4738978458382043e-05,
                1.892515501014656e-05,
                2.90231094723893e-06,
                3.7266406168624155e-06,
                NaN
            ],
            [
                7.338210680021253e-07,
                NaN,
                NaN,
                NaN,
                3.927860597945825e-07,
                3.7266388398585725e-06,
                1.0677032518814388e-06,
                8.315278294114555e-07,
                4.450848927658745e-07,
                NaN
            ],
            [
                1.7603434231777837e-06,
                7.338209805224048e-07,
                1.3709570434219446e-06,
                1.2098652508144226e-06,
                5.715007195447234e-07,
                6.475945666051092e-07,
                9.422450432014836e-07,
                8.315281267882195e-07,
                3.927860597945825e-07,
                9.422443692527585e-07
            ],
            [
                8.315280276607289e-07,
                1.855391681906175e-07,
                5.043472879525233e-07,
                1.2098659719757836e-06,
                1.3709570434178922e-06,
                1.2098655392921197e-06,
                1.3709568799823232e-06,
                4.222834954778007e-06,
                6.47594952595231e-07,
                1.0677032518748838e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                7.338213304363436e-07,
                NaN,
                5.043472879540142e-07,
                4.2228319344021954e-06,
                3.4663249714451116e-07,
                5.715003789033962e-07,
                1.3709576971425944e-06
            ],
            [
                9.422444815814404e-07,
                6.475946438055299e-07,
                2.6995784182183607e-07,
                1.2098661162056318e-06,
                NaN,
                3.059021175261338e-07,
                5.043472278322555e-07,
                8.315281267861397e-07,
                NaN,
                7.338207180898968e-07
            ],
            [
                NaN,
                7.338208055664991e-07,
                NaN,
                5.4222183234485234e-06,
                NaN,
                7.889261645427538e-06,
                1.0677026154806063e-06,
                1.0677032518785256e-06,
                1.067703124601679e-06,
                3.4663253846718004e-07
            ],
            [
                2.90231094723893e-06,
                NaN,
                2.2603234895372223e-06,
                NaN,
                5.043476486924565e-07,
                NaN,
                1.7603430034867993e-06,
                NaN,
                NaN,
                7.338209805240734e-07
            ],
            [
                NaN,
                3.288747889284851e-06,
                4.222832941193893e-06,
                9.422442569315887e-07,
                1.9947297215125433e-06,
                NaN,
                NaN,
                2.902311639183378e-06,
                NaN,
                NaN
            ],
            [
                3.927860597945825e-07,
                2.69957906184239e-07,
                4.450852111148132e-07,
                3.927863875616689e-07,
                5.715007195431641e-07,
                3.726638395527247e-06,
                5.715002426475718e-07,
                7.338212429582604e-07,
                9.422450431989127e-07,
                2.382369951932796e-07
            ],
            [
                NaN,
                4.785096776468749e-06,
                1.5534971990169383e-06,
                9.422442569290178e-07,
                9.422443692527585e-07,
                1.5534979397740895e-06,
                NaN,
                NaN,
                5.4222209089700225e-06,
                5.422220909009474e-06
            ],
            [
                NaN,
                2.2603240283888175e-06,
                9.422444815765128e-07,
                1.067703379154416e-06,
                4.785095065232451e-06,
                7.338209805240734e-07,
                8.315281267800897e-07,
                7.889260704968913e-06,
                7.889263526345123e-06,
                9.422448185534261e-07
            ],
            [
                NaN,
                2.9023112932177327e-06,
                4.785095065093186e-06,
                2.430024073399743e-05,
                NaN,
                2.144495608327478e-05,
                NaN,
                1.0129993395217047e-05,
                1.9947304348862686e-06,
                9.610246083366117e-05
            ],
            [
                2.2603248367512505e-06,
                8.315277302788957e-07,
                2.5612812947508257e-06,
                2.260325375677174e-06,
                3.726638395611981e-06,
                2.26032402841657e-06,
                1.2098662604291696e-06,
                5.04347528446051e-07,
                6.1441746020359e-06,
                4.2228329411708495e-06
            ],
            [
                5.04347287955046e-07,
                5.715005151606823e-07,
                NaN,
                NaN,
                1.2751905808881762e-07,
                4.785095065232451e-06,
                NaN,
                6.475947210046347e-07,
                2.382369951932796e-07,
                3.05902190458764e-07
            ],
            [
                6.14417533430649e-06,
                7.889264466725156e-06,
                6.144176066850984e-06,
                NaN,
                NaN,
                2.260325106237323e-06,
                NaN,
                1.0129995810463632e-05,
                1.994730197090463e-06,
                NaN
            ],
            [
                NaN,
                3.059021175261338e-07,
                5.715002426486762e-07,
                2.102434162245973e-07,
                NaN,
                NaN,
                1.5534983101602148e-06,
                2.2603253756956754e-06,
                4.450852111155216e-07,
                9.422448185534261e-07
            ],
            [
                1.2098656835224664e-06,
                3.7266406168827523e-06,
                2.5612828213818346e-06,
                9.422450432014836e-07,
                1.1478765389368729e-05,
                9.422447062294175e-07,
                1.0677033791612137e-06,
                1.0129987357407137e-05,
                1.760343213335281e-06,
                2.2603240284371276e-06
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                2.9023109472244114e-06,
                4.450851580566494e-07,
                9.422442569315887e-07,
                9.422445939054222e-07,
                NaN
            ],
            [
                3.288748281329893e-06,
                NaN,
                NaN,
                1.2098652508424818e-06,
                2.2603251062450327e-06,
                1.5534971990169383e-06,
                1.7603425837903113e-06,
                4.785092783519724e-06,
                NaN,
                3.288747889284851e-06
            ],
            [
                1.994729721436347e-06,
                1.5534979397740895e-06,
                6.475947982037486e-07,
                NaN,
                6.475949526003845e-07,
                6.1441746020359e-06,
                6.475951069985296e-07,
                5.04347528446051e-07,
                6.475949526020042e-07,
                4.222834451355964e-06
            ],
            [
                NaN,
                NaN,
                1.0677028700363782e-06,
                6.144176799334096e-06,
                1.760343213335281e-06,
                3.535625913952226e-05,
                5.715003107755449e-07,
                2.902311985146426e-06,
                1.1478772230929451e-05,
                4.2228329411708495e-06
            ],
            [
                NaN,
                1.7603432133296774e-06,
                3.726638395611981e-06,
                1.5534973842076057e-06,
                1.3709573702722555e-06,
                3.726638395634011e-06,
                NaN,
                4.222834451382849e-06,
                1.7603425837855082e-06,
                NaN
            ],
            [
                NaN,
                7.734415776836702e-08,
                8.76424013786396e-08,
                1.1253508156363576e-07,
                6.82560779249779e-08,
                1.8553905760062447e-07,
                3.05902336324494e-07,
                5.715005832872586e-07,
                3.059022998581767e-07,
                1.8553910183674878e-07
            ],
            [
                4.2228329411708495e-06,
                1.760343003481596e-06,
                1.8925148242250705e-05,
                3.288747889229516e-06,
                2.902313023130843e-06,
                2.5612812947508257e-06,
                NaN,
                3.535625071602016e-05,
                9.422450432014836e-07,
                8.939698435657833e-06
            ],
            [
                3.059022269254856e-07,
                4.4508515805735777e-07,
                3.4663266243308805e-07,
                0.022977369491872766,
                1.8553910183674878e-07,
                5.043473480777865e-07,
                2.9023119851899796e-06,
                NaN,
                0.004609571393103682,
                NaN
            ],
            [
                1.0677027427525368e-06,
                1.7603430034743913e-06,
                1.553498495295912e-06,
                2.5612816000145246e-06,
                4.222833444590791e-06,
                4.785094494811783e-06,
                3.288749065423109e-06,
                2.699577774585891e-07,
                6.47595107001401e-07,
                2.5612819054028872e-06
            ],
            [
                1.2098659719757836e-06,
                1.0677028700363782e-06,
                2.260324836776948e-06,
                8.315283250371857e-07,
                8.939698435657833e-06,
                2.9023119851635836e-06,
                2.260325375677174e-06,
                NaN,
                1.5534984953453635e-06,
                5.4222209089700225e-06
            ],
            [
                4.222834451403972e-06,
                NaN,
                1.4449795205472734e-07,
                1.0677024882009222e-06,
                3.0590237279085045e-07,
                2.5612819054133693e-06,
                1.5534973842076057e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                1.3709575337016483e-06,
                9.422444815814404e-07,
                6.475945666033422e-07,
                1.5534984953552536e-06,
                NaN,
                NaN,
                9.42244818532859e-07,
                4.222832941193893e-06,
                1.9947297215125433e-06,
                1.9947292459347367e-06
            ],
            [
                NaN,
                NaN,
                2.2603242978778778e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                2.260325375664839e-06,
                2.9023112932177327e-06,
                4.785095065204162e-06
            ],
            [
                7.88926070489716e-06,
                3.288748673376478e-06,
                7.338209805224048e-07,
                4.785094494783494e-06,
                5.715006514151423e-07,
                NaN,
                NaN,
                1.9947304348703948e-06,
                1.670141786325573e-05,
                7.338209805240734e-07
            ],
            [
                NaN,
                1.553498124964492e-06,
                8.315283250394546e-07,
                1.209865827740176e-06,
                1.0677032518814388e-06,
                2.260324836787226e-06,
                1.76034300345598e-06,
                NaN,
                6.475945666051092e-07,
                NaN
            ],
            [
                2.561282516066741e-06,
                5.422217030747413e-06,
                1.5534971990126997e-06,
                3.7266410611296085e-06,
                6.475945666051092e-07,
                1.4738987243478167e-05,
                3.726638839878908e-06,
                1.3709567165579959e-06,
                8.315283250371857e-07,
                9.422447062270609e-07
            ],
            [
                4.2228334445370225e-06,
                1.3007123813193233e-05,
                1.1478765389222573e-05,
                3.2887494574518405e-06,
                4.785094494716039e-06,
                3.288749065423109e-06,
                6.144172404587612e-06,
                5.422218969858371e-06,
                NaN,
                4.222834451382849e-06
            ],
            [
                NaN,
                2.38237023590304e-07,
                3.05902190458764e-07,
                2.6995771309523475e-07,
                2.699576809143613e-07,
                3.466325797896173e-07,
                1.4449807263312446e-07,
                2.382369383923073e-07,
                2.6995784182140636e-07,
                1.0677028700422047e-06
            ],
            [
                7.88926070489716e-06,
                1.6701425826191394e-05,
                2.4300243631272052e-05,
                7.48462005189952e-05,
                7.889264466725156e-06,
                1.760344052714248e-06,
                1.2098655392871682e-06,
                1.3709576971316842e-06,
                4.222832437798974e-06,
                3.2887502415243994e-06
            ],
            [
                2.2603234895289998e-06,
                2.382368531929327e-07,
                2.2603240284371276e-06,
                8.315280276626197e-07,
                2.260324567337161e-06,
                3.288750241561788e-06,
                5.04347348070562e-07,
                9.422442569315887e-07,
                4.222833947960866e-06,
                7.338209805170655e-07
            ],
            [
                9.422448185510695e-07,
                0.9999892166890845,
                NaN,
                1.2098659719601033e-06,
                6.475946438055299e-07,
                1.0677027427600627e-06,
                0.00015843625480754269,
                1.0677028700363782e-06,
                5.043472278312808e-07,
                0.9999203270205568
            ],
            [
                1.3709567165530083e-06,
                1.0677031245990084e-06,
                NaN,
                9.422450431989127e-07,
                2.2603242978871282e-06,
                6.475946438042047e-07,
                1.6373764720990908e-07,
                5.043476486924565e-07,
                5.043473480777865e-07,
                3.927860597945825e-07
            ],
            [
                1.0129994602656007e-05,
                1.2098658277451275e-06,
                4.222831934379152e-06,
                7.88926446679691e-06,
                1.2098662604247682e-06,
                3.7266401726173067e-06,
                1.0129992187658463e-05,
                9.422450431954847e-07,
                2.5612822107167428e-06,
                2.7535694384882703e-05
            ],
            [
                2.902312677150514e-06,
                1.2098662604291696e-06,
                NaN,
                4.4508494582405734e-07,
                6.475945666051092e-07,
                NaN,
                1.2098661162056318e-06,
                NaN,
                2.2603234895372223e-06,
                1.2098652508424818e-06
            ],
            [
                5.043472278322555e-07,
                7.889262585814522e-06,
                4.450848927650143e-07,
                1.0677032518700286e-06,
                3.0590226339061185e-07,
                7.889266347715168e-06,
                1.760343213227212e-06,
                2.9023112931688987e-06,
                3.059022998569248e-07,
                6.475949525981759e-07
            ],
            [
                2.902312331081799e-06,
                1.994730434735237e-06,
                1.7603432132912532e-06,
                1.2098662604126641e-06,
                1.553497754577351e-06,
                7.889265407177056e-06,
                4.222832941142044e-06,
                1.3709570434178922e-06,
                1.5534975693792215e-06,
                1.3709567165461505e-06
            ],
            [
                NaN,
                6.475947210031623e-07,
                1.5534981249697903e-06,
                1.0677033791612137e-06,
                4.0063682641226247e-05,
                2.2603234895372223e-06,
                2.1444953527944967e-05,
                NaN,
                7.338208055664991e-07,
                9.422447062270609e-07
            ],
            [
                NaN,
                5.422220262636381e-06,
                2.2603234895289998e-06,
                5.71500242637956e-07,
                NaN,
                3.2887482813149375e-06,
                3.726639284125553e-06,
                2.9023123311583482e-06,
                6.96225873967641e-06,
                8.315281267882195e-07
            ],
            [
                NaN,
                NaN,
                1.8553919030858602e-07,
                NaN,
                5.715003107767143e-07,
                2.1024334103581732e-07,
                1.855391681906175e-07,
                NaN,
                1.8553914607267268e-07,
                3.466326624336003e-07
            ],
            [
                NaN,
                8.764254764780641e-08,
                3.059022998581767e-07,
                2.1024339116168358e-07,
                6.475948754028718e-07,
                3.059021175261338e-07,
                8.315277302857965e-07,
                5.715002426486762e-07,
                1.370957860576702e-06,
                NaN
            ],
            [
                1.0677032518785256e-06,
                1.067703379154416e-06,
                1.9947297215043796e-06,
                1.2098662604291696e-06,
                4.2228319344021954e-06,
                1.9947292459347367e-06,
                1.0677028700363782e-06,
                1.9947294837154625e-06,
                2.561283432035425e-06,
                NaN
            ],
            [
                3.927863407379485e-07,
                4.0063701490430115e-05,
                2.561282210729555e-06,
                8.315279285370317e-07,
                NaN,
                2.5612828213934817e-06,
                2.2603242978871282e-06,
                NaN,
                NaN,
                1.3007126914245925e-05
            ],
            [
                2.1024336609874897e-07,
                NaN,
                7.338207180884785e-07,
                6.825597214718257e-08,
                NaN,
                8.315282259138311e-07,
                NaN,
                1.6373772528704005e-07,
                1.370957860576702e-06,
                NaN
            ],
            [
                5.422220262636381e-06,
                3.726641061085547e-06,
                2.9023133690821773e-06,
                2.2603248367656408e-06,
                1.7603427936263351e-06,
                2.5612831266946347e-06,
                1.7603438428660665e-06,
                1.3709575337078829e-06,
                3.726638395611981e-06,
                3.2887482812745586e-06
            ],
            [
                2.260323758939877e-06,
                4.785096205973894e-06,
                7.889261645269683e-06,
                2.5612834320214477e-06,
                1.1478764020560142e-05,
                3.726641061085547e-06,
                5.422218323399208e-06,
                3.2887502415438413e-06,
                NaN,
                6.144175334418252e-06
            ],
            [
                NaN,
                6.962257079553702e-06,
                2.2603234895176927e-06,
                1.5534975693933505e-06,
                6.144173137126169e-06,
                6.962256249885085e-06,
                7.338212429537553e-07,
                3.288748281295496e-06,
                3.726641061085547e-06,
                3.288749065423109e-06
            ],
            [
                1.994730197090463e-06,
                9.422448185510695e-07,
                3.726638395611981e-06,
                1.5534973842076057e-06,
                6.9622587397397306e-06,
                8.939693107093343e-06,
                1.7603427936263351e-06,
                2.2603242978778778e-06,
                1.0677026154806063e-06,
                1.3709575337078829e-06
            ],
            [
                4.222831934321543e-06,
                NaN,
                1.3007130015488633e-05,
                1.4738983729535602e-05,
                3.12019225345861e-05,
                4.222831934379152e-06,
                1.209865539295696e-06,
                NaN,
                1.9947304348703948e-06,
                1.6373770576776313e-07
            ],
            [
                NaN,
                NaN,
                7.889263526266196e-06,
                4.785095065204162e-06,
                NaN,
                4.222835458148261e-06,
                NaN,
                NaN,
                1.7603434231777837e-06,
                NaN
            ],
            [
                1.8553919030858602e-07,
                9.422444815792981e-07,
                3.927863407379485e-07,
                3.4663249714612693e-07,
                2.1024336609874897e-07,
                1.994729483729522e-06,
                7.338210680021253e-07,
                NaN,
                NaN,
                8.315281267882195e-07
            ],
            [
                3.466325797896173e-07,
                1.2098652508424818e-06,
                3.466326211113502e-07,
                1.6373776432509826e-07,
                4.785096206076165e-06,
                NaN,
                5.04347287955046e-07,
                5.715005832886879e-07,
                5.715005151606823e-07,
                5.043473480777865e-07
            ],
            [
                1.2098656835224664e-06,
                NaN,
                NaN,
                1.3007125363719486e-05,
                1.5534983101602148e-06,
                NaN,
                NaN,
                3.466327863983311e-07,
                NaN,
                NaN
            ],
            [
                NaN,
                3.05902336324494e-07,
                3.05902190458764e-07,
                1.8553907971855875e-07,
                9.931190958076104e-08,
                3.927862470905692e-07,
                1.2751901248454963e-07,
                6.825604537781398e-08,
                4.4508510499849186e-07,
                NaN
            ],
            [
                NaN,
                1.7603430034655858e-06,
                NaN,
                1.9947297214944016e-06,
                5.715006514176113e-07,
                NaN,
                NaN,
                NaN,
                2.561281600086738e-06,
                NaN
            ],
            [
                NaN,
                3.7266410611296085e-06,
                1.3709567165579959e-06,
                8.315279285370317e-07,
                1.7603438428800754e-06,
                2.902312677137316e-06,
                3.2887498495150166e-06,
                1.3709572068522336e-06,
                4.785094494783494e-06,
                6.475948754028718e-07
            ],
            [
                NaN,
                1.9947299592933255e-06,
                1.0677028700363782e-06,
                4.785095635592258e-06,
                NaN,
                1.5534971990126997e-06,
                4.222834451355964e-06,
                1.7603427936335396e-06,
                9.422442569208767e-07,
                1.3709576971425944e-06
            ],
            [
                5.715003107767143e-07,
                3.7266388398585725e-06,
                NaN,
                7.338208930460318e-07,
                1.5534977545886537e-06,
                6.475949526020042e-07,
                2.9023116391978967e-06,
                1.7603425837855082e-06,
                1.209865539295696e-06,
                1.3709570434122812e-06
            ],
            [
                5.043474683204221e-07,
                4.450852111148132e-07,
                NaN,
                3.2887506336235617e-06,
                NaN,
                1.2098655392921197e-06,
                1.3709567165579959e-06,
                1.5534975693979422e-06,
                1.553497754583709e-06,
                5.043474081993875e-07
            ],
            [
                5.715005832886879e-07,
                6.9622587397397306e-06,
                5.71500515159253e-07,
                5.04347528446051e-07,
                1.3709567165617364e-06,
                7.338209805240734e-07,
                NaN,
                9.422445939054222e-07,
                1.067703124601679e-06,
                4.4508515805735777e-07
            ]
        ]
    },
    {
        "q_id": "10285_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            5,
            6,
            9,
            11,
            13,
            16,
            20,
            22,
            24,
            25,
            28,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            45,
            48,
            49,
            52,
            53,
            56,
            58,
            59,
            60,
            64,
            65,
            66,
            67,
            70,
            71,
            74,
            75,
            76,
            77,
            79,
            82,
            83,
            84,
            85,
            90,
            91,
            93,
            94,
            95,
            98,
            100,
            102,
            104,
            105,
            106,
            108,
            110,
            113,
            115,
            117,
            118,
            121,
            123,
            126
        ],
        "rewards": [
            [
                3.0590226339061185e-07,
                5.043475885674441e-07,
                6.475951069985296e-07,
                NaN,
                3.288749457469787e-06,
                1.3007125362820425e-05,
                5.715002426439334e-07,
                5.043474081993875e-07,
                6.475946437966953e-07,
                3.4663270374947136e-07
            ],
            [
                1.5534975693933505e-06,
                8.315277302841894e-07,
                2.902310947208574e-06,
                8.315280276546789e-07,
                1.3709576971425944e-06,
                9.422449308716635e-07,
                7.338209805200689e-07,
                7.338209805224048e-07,
                2.9023133690980155e-06,
                3.4663262110945863e-07
            ],
            [
                2.5612819054028872e-06,
                3.0590222691880844e-07,
                1.5534979397740895e-06,
                2.5612812947508257e-06,
                1.5534984953453635e-06,
                5.422221555296344e-06,
                1.9947297215043796e-06,
                1.9947304348703948e-06,
                3.7266392840781026e-06,
                1.300713001508642e-05
            ],
            [
                2.5612831267086116e-06,
                1.5534971990126997e-06,
                1.9947304348703948e-06,
                2.902313023101807e-06,
                4.785095635592258e-06,
                2.382370235933104e-07,
                8.939698435657833e-06,
                1.209865539295696e-06,
                6.962255419804982e-06,
                2.5612822107167428e-06
            ],
            [
                1.3709572068522336e-06,
                NaN,
                7.338210680021253e-07,
                NaN,
                5.043474081993875e-07,
                6.475947210031623e-07,
                9.422447062270609e-07,
                7.338213304363436e-07,
                2.382369383923073e-07,
                NaN
            ],
            [
                7.889261645427538e-06,
                3.2887498495150166e-06,
                1.9947299593014888e-06,
                2.902312677137316e-06,
                5.715004470313855e-07,
                1.5534973842076057e-06,
                1.5534979397740895e-06,
                6.475951069985296e-07,
                5.4222176771176554e-06,
                5.715005151606823e-07
            ],
            [
                6.9622587396067566e-06,
                3.2887478892683997e-06,
                1.7603438428740716e-06,
                3.288748673295719e-06,
                5.715004470313855e-07,
                1.5534975693933505e-06,
                1.3709578605617394e-06,
                9.422444815765128e-07,
                7.889261645427538e-06,
                1.0677028700363782e-06
            ],
            [
                7.338209805240734e-07,
                4.450850519360903e-07,
                3.2887478892683997e-06,
                NaN,
                1.012999218776902e-05,
                1.7603438428800754e-06,
                2.902312677137316e-06,
                5.715004470295662e-07,
                NaN,
                1.0677028700363782e-06
            ],
            [
                2.260324836776948e-06,
                1.553498124964492e-06,
                1.2098661161927025e-06,
                8.31528126775552e-07,
                6.144176066795103e-06,
                4.222834451382849e-06,
                1.5534975693792215e-06,
                1.2098655392871682e-06,
                1.7603436330259153e-06,
                1.2098655392871682e-06
            ],
            [
                8.315283250371857e-07,
                2.9023116391675407e-06,
                3.9278624708775595e-07,
                1.760343213322473e-06,
                2.90231233114251e-06,
                1.0677028700130727e-06,
                2.2603242978871282e-06,
                1.5534975693792215e-06,
                3.726638839833152e-06,
                1.2098656835076114e-06
            ],
            [
                4.2228339479858295e-06,
                4.4508510499737865e-07,
                6.475951069961737e-07,
                1.3709578605729614e-06,
                6.475948754012522e-07,
                3.466326211113502e-07,
                3.0590237279085045e-07,
                2.382368815916736e-07,
                4.450851580540182e-07,
                3.927861066170637e-07
            ],
            [
                5.715007195447234e-07,
                1.760344052693435e-06,
                3.2887478892504536e-06,
                2.9023119851781017e-06,
                NaN,
                2.561283432035425e-06,
                7.338207180864763e-07,
                1.7603432132912532e-06,
                2.1444940745371397e-05,
                2.561282821352716e-06
            ],
            [
                2.5612812947508257e-06,
                1.5534979397740895e-06,
                7.338208055664991e-07,
                NaN,
                8.315280276607289e-07,
                1.4738978458382043e-05,
                1.7603427936335396e-06,
                3.927860597935108e-07,
                3.288748673376478e-06,
                2.260323758939877e-06
            ],
            [
                4.450852641656969e-07,
                6.475947210031623e-07,
                3.927862002625787e-07,
                1.3709576971425944e-06,
                2.1024334103247107e-07,
                2.2603234895372223e-06,
                NaN,
                6.144173136729416e-06,
                5.04347348070562e-07,
                3.4663278639265633e-07
            ],
            [
                2.5612819054028872e-06,
                9.422450432014836e-07,
                1.5534973841895917e-06,
                9.4224425692559e-07,
                2.902313023101807e-06,
                1.0677031245990084e-06,
                1.067702615468225e-06,
                1.7603438428740716e-06,
                8.315282259117513e-07,
                3.288750241561788e-06
            ],
            [
                7.338211554783522e-07,
                1.855391681898159e-07,
                1.855391681906175e-07,
                3.288749849498565e-06,
                1.3709570434122812e-06,
                1.0677028700363782e-06,
                1.0677032518748838e-06,
                1.7603434231777837e-06,
                1.3709576971425944e-06,
                3.059022269250683e-07
            ],
            [
                1.2098659719757836e-06,
                2.5612831267086116e-06,
                9.422448185478557e-07,
                1.0677024881980089e-06,
                NaN,
                2.5612828213690224e-06,
                3.7266401726173067e-06,
                NaN,
                2.9023119851781017e-06,
                NaN
            ],
            [
                NaN,
                2.5612828213934817e-06,
                7.889261645427538e-06,
                2.6995771309523475e-07,
                4.785092783519724e-06,
                NaN,
                8.939693107190907e-06,
                6.144172404693786e-06,
                6.144176799283803e-06,
                1.5534975693979422e-06
            ],
            [
                3.059022998576899e-07,
                8.315283250371857e-07,
                1.5534975693707442e-06,
                1.0677027427471959e-06,
                NaN,
                2.1024341622426268e-07,
                9.422443692489024e-07,
                NaN,
                9.93120161306789e-08,
                3.059023727894942e-07
            ],
            [
                NaN,
                1.012999218776902e-05,
                5.04347468323289e-07,
                1.5534979397740895e-06,
                1.3709575336947905e-06,
                1.5534981249496567e-06,
                6.475949526020042e-07,
                1.0677026154806063e-06,
                NaN,
                8.315283250371857e-07
            ],
            [
                7.338208055664991e-07,
                2.90231094723893e-06,
                6.144177531767002e-06,
                NaN,
                1.5534981249574276e-06,
                1.7603432133296774e-06,
                1.8925145985895816e-05,
                4.785093924330255e-06,
                2.2603234895176927e-06,
                1.9947297215043796e-06
            ],
            [
                1.4738976700661033e-05,
                2.3823690999236795e-07,
                1.6701423835320418e-05,
                1.994729483705484e-06,
                1.7603427936263351e-06,
                2.260324567337161e-06,
                5.043472879525233e-07,
                4.222834954778007e-06,
                7.889265407090955e-06,
                6.962256249758443e-06
            ],
            [
                1.7603434231777837e-06,
                4.450848927658745e-07,
                3.059023727894942e-07,
                5.715005832827105e-07,
                8.939698435560267e-06,
                1.0677029973158649e-06,
                3.726639728370556e-06,
                1.9947292459347367e-06,
                5.422217676925328e-06,
                3.1201922535494165e-05
            ],
            [
                3.2887494574518405e-06,
                2.2603237589676295e-06,
                NaN,
                8.315283250371857e-07,
                NaN,
                NaN,
                5.422220908925639e-06,
                3.2887490653647836e-06,
                NaN,
                2.260324028427877e-06
            ],
            [
                7.338213304363436e-07,
                1.9947297215125433e-06,
                8.315279285351409e-07,
                1.7603434231833873e-06,
                NaN,
                1.3709575337078829e-06,
                1.0677033791583005e-06,
                2.9023133690980155e-06,
                1.2098653950656417e-06,
                1.9947290081286418e-06
            ],
            [
                1.0677027427600627e-06,
                1.7603427936335396e-06,
                1.9947297215125433e-06,
                2.5612819054133693e-06,
                5.043475885674441e-07,
                5.04347528446051e-07,
                NaN,
                1.3709570434178922e-06,
                7.338213304363436e-07,
                NaN
            ],
            [
                8.939700566907275e-06,
                3.927860597935108e-07,
                8.315281267882195e-07,
                1.6701423836262173e-05,
                1.3007123813382511e-05,
                3.726638839878908e-06,
                2.2603234895289998e-06,
                3.726639728348526e-06,
                1.5534979397790343e-06,
                5.422218969858371e-06
            ],
            [
                1.0677026154730804e-06,
                3.2887506335906595e-06,
                6.962257079705671e-06,
                2.5612812947508257e-06,
                6.475951069985296e-07,
                9.422443692555439e-07,
                5.715007195447234e-07,
                1.3709570434178922e-06,
                1.7603425837702984e-06,
                4.785096776468749e-06
            ],
            [
                1.2098658277451275e-06,
                2.10243290909724e-07,
                4.222835458044565e-06,
                5.422217030707961e-06,
                1.3709567165530083e-06,
                1.2098662604247682e-06,
                5.422220262599396e-06,
                1.7603427936263351e-06,
                1.2098662604291696e-06,
                2.9023119851781017e-06
            ],
            [
                1.4738988999940381e-05,
                2.2603234895176927e-06,
                2.561283432005142e-06,
                1.99472924590571e-06,
                NaN,
                1.5534975693792215e-06,
                3.535625913514915e-05,
                2.1444953527476883e-05,
                6.144173869446876e-06,
                1.99473067264854e-06
            ],
            [
                1.3709570434178922e-06,
                6.962257079775324e-06,
                4.222831934352267e-06,
                NaN,
                1.3007131566015624e-05,
                5.422217677152175e-06,
                NaN,
                1.4738987243478167e-05,
                3.2887494574518405e-06,
                3.2887478892683997e-06
            ],
            [
                7.889259764359722e-06,
                2.1024326584639497e-07,
                9.422450432014836e-07,
                3.927862939126708e-07,
                1.8553907971855875e-07,
                3.059022998576899e-07,
                6.475947210031623e-07,
                2.260325106237323e-06,
                6.475948754012522e-07,
                3.4663278639738526e-07
            ],
            [
                9.422444815765128e-07,
                4.222834451382849e-06,
                6.962254589914941e-06,
                1.0677026154730804e-06,
                2.2603234895289998e-06,
                NaN,
                2.260325106237323e-06,
                NaN,
                1.9947299592933255e-06,
                1.5534979397740895e-06
            ],
            [
                1.7603438428800754e-06,
                2.5612819054133693e-06,
                2.902312677150514e-06,
                1.5534984953510149e-06,
                3.288749065423109e-06,
                3.2887478892683997e-06,
                2.2603234895289998e-06,
                1.0677032518748838e-06,
                2.5612822107167428e-06,
                8.315283250371857e-07
            ],
            [
                1.0677032518785256e-06,
                1.0677026154806063e-06,
                7.338209805200689e-07,
                5.715007195447234e-07,
                6.475951069985296e-07,
                1.0677029973192638e-06,
                7.338209805240734e-07,
                1.994730672668496e-06,
                3.9278634073625165e-07,
                5.043474683204221e-07
            ],
            [
                1.994730434879465e-06,
                1.9947292459347367e-06,
                8.315277302841894e-07,
                NaN,
                8.939700567004841e-06,
                NaN,
                5.715007195447234e-07,
                NaN,
                1.5534981249697903e-06,
                1.9947292459347367e-06
            ],
            [
                1.5534983101602148e-06,
                1.3709570434178922e-06,
                2.699578096393206e-07,
                9.422449308716635e-07,
                1.637377448057981e-07,
                1.7603425837606927e-06,
                1.2098659719757836e-06,
                NaN,
                1.3709567165579959e-06,
                NaN
            ],
            [
                2.260324567268294e-06,
                4.222834451355964e-06,
                2.902312677137316e-06,
                8.939697369980456e-06,
                3.2887478892504536e-06,
                NaN,
                2.9023109472244114e-06,
                4.4508505193791187e-07,
                NaN,
                1.6373766672973748e-07
            ],
            [
                1.7603425837606927e-06,
                1.760343423160973e-06,
                1.3709568799760888e-06,
                2.1024344128584085e-07,
                5.04347348070562e-07,
                1.9947299593014888e-06,
                4.450848927650143e-07,
                9.422447062240614e-07,
                3.059021904571643e-07,
                1.994729008105057e-06
            ],
            [
                NaN,
                6.475948754012522e-07,
                2.9023123311583482e-06,
                2.2603237589542675e-06,
                8.315281267834927e-07,
                9.422448185510695e-07,
                1.2098656835224664e-06,
                5.04347528446051e-07,
                1.5534975693869924e-06,
                NaN
            ],
            [
                NaN,
                1.3709572068422585e-06,
                1.300712536350655e-05,
                1.067702615468225e-06,
                3.726638839806038e-06,
                2.561281905390075e-06,
                1.0129995810343862e-05,
                1.5534983101478522e-06,
                2.9023119851635836e-06,
                2.2603234895176927e-06
            ],
            [
                2.5612825160562587e-06,
                NaN,
                5.043476486915964e-07,
                6.475947210031623e-07,
                8.939699501229642e-06,
                1.2098662604291696e-06,
                2.5612819054133693e-06,
                1.2098656835224664e-06,
                NaN,
                NaN
            ],
            [
                3.4663274507713016e-07,
                8.315281267834927e-07,
                3.288749457469787e-06,
                1.6373770576776313e-07,
                1.760343423160973e-06,
                1.8553910183607374e-07,
                1.4449805540763184e-07,
                1.7603425837855082e-06,
                5.043474081993875e-07,
                2.1024326584639497e-07
            ],
            [
                2.699578740011634e-07,
                5.043476486915964e-07,
                3.927862939126708e-07,
                1.5534981249697903e-06,
                1.444980209564556e-07,
                5.04347528440776e-07,
                6.475947210012481e-07,
                4.450848927637999e-07,
                3.059021175247079e-07,
                2.699577774585891e-07
            ],
            [
                1.2098656835224664e-06,
                2.3823696679327928e-07,
                6.475945666051092e-07,
                1.0677027427600627e-06,
                1.209865539295696e-06,
                2.102434412875379e-07,
                3.466326211113502e-07,
                6.1441746020359e-06,
                3.059022998576899e-07,
                3.05902190458764e-07
            ],
            [
                NaN,
                2.2603242978871282e-06,
                1.3709567165579959e-06,
                1.7603440527222532e-06,
                3.2887502415438413e-06,
                NaN,
                1.3709572068522336e-06,
                8.939693107190907e-06,
                2.260325106237323e-06,
                5.715003107767143e-07
            ],
            [
                6.9622595696935874e-06,
                3.288749457469787e-06,
                1.5534971990126997e-06,
                1.0677024882009222e-06,
                1.5534975693933505e-06,
                4.785095065204162e-06,
                1.5534973841895917e-06,
                NaN,
                NaN,
                9.422447062240614e-07
            ],
            [
                2.5612828213818346e-06,
                1.3709567165579959e-06,
                6.144176066901277e-06,
                3.7266410611296085e-06,
                2.2603234895176927e-06,
                8.315278294072958e-07,
                1.0677024881980089e-06,
                3.726639728370556e-06,
                6.475951069985296e-07,
                1.5534984953453635e-06
            ],
            [
                5.422218323290717e-06,
                2.382368815916736e-07,
                6.47594952595231e-07,
                3.288748673360027e-06,
                2.2603242978377903e-06,
                6.475949525981759e-07,
                5.715005151574337e-07,
                1.0677031245905116e-06,
                6.962254589781966e-06,
                1.6373762769138607e-07
            ],
            [
                2.561282210729555e-06,
                1.3709570434178922e-06,
                2.902312677137316e-06,
                1.2098661161789477e-06,
                8.315278294072958e-07,
                2.9023133690980155e-06,
                9.422450431860582e-07,
                1.3709567165579959e-06,
                1.0677033791583005e-06,
                2.9023130230846496e-06
            ],
            [
                NaN,
                1.994729483694599e-06,
                2.561282210701601e-06,
                1.4449805540740185e-07,
                7.338208055664991e-07,
                2.1024336609843824e-07,
                5.043472879525233e-07,
                8.764247451307293e-08,
                1.4449805540740185e-07,
                3.927863407379485e-07
            ],
            [
                9.422445939002803e-07,
                4.2228334445658276e-06,
                1.553497754577351e-06,
                1.0677029973158649e-06,
                1.7603432133296774e-06,
                7.338208930391909e-07,
                6.475949526020042e-07,
                3.288749065406658e-06,
                2.561283432005142e-06,
                7.338207180864763e-07
            ],
            [
                NaN,
                1.9947304348703948e-06,
                5.422217030663578e-06,
                3.2887498494551953e-06,
                2.3823690999236795e-07,
                NaN,
                9.422450431989127e-07,
                3.927862470899887e-07,
                2.3823693839290317e-07,
                3.2887486733420804e-06
            ],
            [
                2.5612812947508257e-06,
                2.902312677137316e-06,
                NaN,
                NaN,
                1.5534979397790343e-06,
                3.05902263391829e-07,
                1.0677029973219343e-06,
                6.962257909785973e-06,
                8.315280276607289e-07,
                1.0129993395088066e-05
            ],
            [
                1.5534983101478522e-06,
                2.2603248367656408e-06,
                2.2603242978213447e-06,
                9.422448185388577e-07,
                6.475951069985296e-07,
                9.422449308716635e-07,
                2.2603242978213447e-06,
                9.422448185388577e-07,
                1.0677029973192638e-06,
                7.338207180761315e-07
            ],
            [
                6.475949525981759e-07,
                2.2603234895176927e-06,
                1.5534984953453635e-06,
                7.338207180864763e-07,
                2.902311639183378e-06,
                2.9023109472244114e-06,
                3.2887494574518405e-06,
                4.78509392429544e-06,
                1.760343003481596e-06,
                1.3007130015488633e-05
            ],
            [
                3.059021175261338e-07,
                1.0677027427600627e-06,
                1.8553919030858602e-07,
                2.6995790618469934e-07,
                5.043475284430694e-07,
                NaN,
                1.0677026154806063e-06,
                3.059022998576899e-07,
                2.5612825160562587e-06,
                7.338210679949506e-07
            ],
            [
                3.726638395634011e-06,
                1.3709570434178922e-06,
                1.3709570434178922e-06,
                8.315277302819205e-07,
                9.422449308748773e-07,
                1.0677026154730804e-06,
                7.338209805224048e-07,
                3.059022998581767e-07,
                5.715005832886879e-07,
                6.475947210031623e-07
            ],
            [
                4.222834451355964e-06,
                4.450852111135988e-07,
                2.1444950971601277e-05,
                2.9023112931873767e-06,
                1.5534981249574276e-06,
                3.2887498495150166e-06,
                1.6701419854156377e-05,
                6.475950298011458e-07,
                1.0677032518785256e-06,
                1.7603427936263351e-06
            ],
            [
                1.2098655392871682e-06,
                NaN,
                3.288750241561788e-06,
                5.043472879525233e-07,
                1.9947297215125433e-06,
                2.2603234895372223e-06,
                7.338212429537553e-07,
                8.315281267834927e-07,
                1.209866260432471e-06,
                NaN
            ],
            [
                9.422442569208767e-07,
                8.315279285351409e-07,
                1.0677027427600627e-06,
                3.466326211113502e-07,
                4.450851580555361e-07,
                8.315281267861397e-07,
                2.3823690999236795e-07,
                4.450849988811838e-07,
                7.338207180864763e-07,
                1.2098653950656417e-06
            ],
            [
                4.450851580555361e-07,
                4.450851580555361e-07,
                6.475947210012481e-07,
                6.47594952595231e-07,
                2.6995771309523475e-07,
                2.699577452746696e-07,
                7.338212429537553e-07,
                5.715003107755449e-07,
                1.2098655392871682e-06,
                6.475951069985296e-07
            ],
            [
                2.2603234895176927e-06,
                3.288749065406658e-06,
                8.939700567004841e-06,
                2.561283432035425e-06,
                2.9023112932177327e-06,
                5.422221555296344e-06,
                6.962257079705671e-06,
                1.9947299592933255e-06,
                NaN,
                1.2098662604247682e-06
            ],
            [
                NaN,
                3.288748673360027e-06,
                2.260323758987159e-06,
                1.7603434231705793e-06,
                2.260324028427877e-06,
                1.3709572068522336e-06,
                2.5612825160562587e-06,
                2.2603234895289998e-06,
                NaN,
                5.04347528446051e-07
            ],
            [
                1.994730434879465e-06,
                5.043476486915964e-07,
                1.209866260432471e-06,
                3.05902190458764e-07,
                7.338209805224048e-07,
                9.422448185510695e-07,
                6.475950298011458e-07,
                1.3709576971425944e-06,
                3.927860597945825e-07,
                6.475947210031623e-07
            ],
            [
                4.2228339479858295e-06,
                2.902311639183378e-06,
                6.475947982037486e-07,
                1.2098655392871682e-06,
                NaN,
                NaN,
                NaN,
                1.7603440527286572e-06,
                4.785093924362895e-06,
                1.5534977545886537e-06
            ],
            [
                3.927862002663297e-07,
                1.067702870039777e-06,
                7.88926446679691e-06,
                5.043472278322555e-07,
                1.5534975693979422e-06,
                5.715003107767143e-07,
                NaN,
                6.475945666063607e-07,
                3.059021175261338e-07,
                7.338208930460318e-07
            ]
        ]
    },
    {
        "q_id": "10176_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                7.338210680021253e-07,
                3.4663266243308805e-07,
                1.3709572068522336e-06,
                7.338212429582604e-07,
                2.3823688159291947e-07,
                8.315282259138311e-07,
                7.338212429582604e-07,
                2.3823690999290963e-07,
                2.382369667929001e-07,
                1.5534975693979422e-06
            ],
            [
                4.785095635655362e-06,
                9.422448185534261e-07,
                1.3007130015677909e-05,
                3.9278605979534166e-07,
                0.999999495652532,
                1.7603438428800754e-06,
                3.288749065423109e-06,
                1.2751902768612997e-07,
                1.6701425827133152e-05,
                5.422217030747413e-06
            ],
            [
                1.209865827740176e-06,
                1.1253526937656726e-07,
                5.043473480766399e-07,
                2.382369667929001e-07,
                3.9278634073625165e-07,
                2.102433159721477e-07,
                1.4449805540763184e-07,
                1.6373772528704005e-07,
                2.3823702359138736e-07,
                2.3823685319244518e-07
            ],
            [
                3.726641061109272e-06,
                3.9278605979534166e-07,
                0.9999997300422548,
                0.999999114842648,
                0.9999993916411811,
                0.9999998724809875,
                0.9999998802069017,
                0.9999999273417662,
                0.999999814460854,
                0.999997438718096
            ],
            [
                3.9278629391427843e-07,
                1.2751905808881762e-07,
                3.9278629391427843e-07,
                2.6995790618469934e-07,
                2.699578096403948e-07,
                3.4663249714612693e-07,
                8.315280276626197e-07,
                9.422444815814404e-07,
                2.699578096403948e-07,
                2.10243290909724e-07
            ],
            [
                0.999993855825404,
                0.9999991148431755,
                0.9999980052693285,
                0.9999996940978461,
                0.9999810748517849,
                0.9999986290426306,
                0.9999999123574942,
                0.9999996743688586,
                0.9999964991447542,
                0.9999981261252877
            ],
            [
                5.715005832886879e-07,
                5.715005832886879e-07,
                3.9278615344267634e-07,
                3.4663249714612693e-07,
                1.0677027427600627e-06,
                1.2098656835076114e-06,
                4.450848927658745e-07,
                5.043475885688201e-07,
                6.475947210031623e-07,
                1.5534983101393749e-06
            ],
            [
                8.764247451307293e-08,
                8.7642558095602e-08,
                4.691160446380562e-08,
                1.4449800373118268e-07,
                8.764244316973974e-08,
                9.931187406410953e-08,
                8.764245361752286e-08,
                5.315780536011123e-08,
                8.764241182641775e-08,
                7.734414854823498e-08
            ],
            [
                0.9999987901344615,
                0.999999554914842,
                0.9999997126313441,
                0.999999581881277,
                0.9999997761970782,
                0.9999997761971583,
                0.9999995818813269,
                2.430024652854702e-05,
                0.9999998257021837,
                0.9999997463981032
            ],
            [
                0.9999996743688976,
                0.9999998802069587,
                0.9999970976876711,
                0.9999998802069587,
                0.9999997126314469,
                0.9999997126313098,
                1.0,
                0.9999998942830106,
                0.9999999358793944,
                0.9999999067051276
            ],
            [
                1.1253525596174225e-07,
                1.444980209564556e-07,
                1.6373770576776313e-07,
                1.6373774480605869e-07,
                2.382368531929327e-07,
                8.764254764780641e-08,
                1.8553905760062447e-07,
                1.4449803818215767e-07,
                2.3823696679327928e-07,
                1.6373772528704005e-07
            ],
            [
                8.315280276546789e-07,
                8.315278294072958e-07,
                3.466327037548308e-07,
                1.3709567165579959e-06,
                2.2603248367949354e-06,
                1.0677029973219343e-06,
                3.927862470899887e-07,
                4.4508505193932864e-07,
                3.466327450765785e-07,
                3.9278634073625165e-07
            ],
            [
                0.9995121429018827,
                0.9999989322970035,
                0.999999428499349,
                0.9999921107336781,
                0.999998126123725,
                0.9999997617630617,
                0.9999989969857934,
                0.999998346310613,
                7.338212429537553e-07,
                6.962253760024999e-06
            ],
            [
                9.422445939054222e-07,
                6.475945666063607e-07,
                4.22283545819819e-06,
                9.422448185534261e-07,
                8.315283250394546e-07,
                9.422445939054222e-07,
                6.475945666063607e-07,
                4.222834954801051e-06,
                3.4663274507713016e-07,
                1.2098661162056318e-06
            ],
            [
                3.9278610661902853e-07,
                5.715005151606823e-07,
                5.043472278322555e-07,
                5.043472278322555e-07,
                3.466325797896173e-07,
                5.04347287955046e-07,
                3.059021175261338e-07,
                3.927863875616689e-07,
                4.4508515805735777e-07,
                4.4508494582314646e-07
            ],
            [
                8.93969950132721e-06,
                7.889263526409699e-06,
                1.4738978458623327e-05,
                2.902313023130843e-06,
                6.962255419868303e-06,
                0.9999982396565782,
                2.9023112932177327e-06,
                0.9999955048162831,
                4.785096206047877e-06,
                3.2887478892683997e-06
            ],
            [
                0.9999996743687424,
                1.8553916819032217e-07,
                0.9999985406237809,
                2.3823688159237777e-07,
                0.9999996940978826,
                0.9999990577555191,
                0.9999980052702806,
                0.9999646437579337,
                0.9999992661787576,
                0.9999996072136127
            ],
            [
                3.4663278639892215e-07,
                1.8553910183607374e-07,
                1.4449807263312446e-07,
                1.855391239547094e-07,
                1.4449807263312446e-07,
                2.1024331597262577e-07,
                6.825601283086733e-08,
                5.715003107767143e-07,
                1.855391239544352e-07,
                9.931198061405701e-08
            ],
            [
                0.9999960330121985,
                0.9999990577556316,
                0.9999977396759737,
                0.9999962733607226,
                2.430024073461624e-05,
                0.00012339463381806274,
                0.9999960330121985,
                0.9999957771650532,
                0.9999916019269797,
                0.9999960330155088
            ],
            [
                3.05902263391829e-07,
                5.715006514176113e-07,
                7.33821330437595e-07,
                5.043475885696228e-07,
                1.0677027427624903e-06,
                3.927863407379485e-07,
                3.05902263391829e-07,
                3.466326624336003e-07,
                4.4508515805735777e-07,
                6.47595107001401e-07
            ],
            [
                0.9999992661791947,
                0.9999996743687811,
                0.999999168472072,
                0.9999991684715762,
                0.9999975938965152,
                0.9999999006880904,
                0.9999993106391194,
                0.9999964991455916,
                0.9999964991451736,
                3.059022998569248e-07
            ],
            [
                1.27519088491875e-07,
                8.764244316973974e-08,
                9.931189774187203e-08,
                1.1253509497883659e-07,
                1.1253506814842375e-07,
                1.8553914607267268e-07,
                1.2751905808881762e-07,
                2.3823693839325527e-07,
                7.73441946488886e-08,
                2.3823690999323465e-07
            ],
            [
                0.999999789756609,
                0.9999998642566219,
                0.9999993916407459,
                0.9999998257021214,
                0.9999994631248682,
                0.9999994284995531,
                0.9999997617630901,
                1.8553916819032217e-07,
                0.9999999067050499,
                0.9999998555019791
            ],
            [
                0.9999993916408911,
                0.9999981261248412,
                0.9999994631251886,
                0.9999997126314811,
                0.9999992661792824,
                0.9999989969861519,
                0.9999999067050054,
                0.9999983463098238,
                0.9999998362622943,
                0.9999993106387906
            ],
            [
                2.6995790618469934e-07,
                2.699576809143613e-07,
                2.699576809143613e-07,
                2.1024336609843824e-07,
                4.4508515805735777e-07,
                1.6373774480605869e-07,
                2.382369667929001e-07,
                5.715005151606823e-07,
                2.382369951932796e-07,
                2.1024334103553052e-07
            ],
            [
                6.475949526020042e-07,
                1.994729721518893e-06,
                8.315279285351409e-07,
                2.1024336609843824e-07,
                3.9278605979534166e-07,
                9.422450432014836e-07,
                2.3823690999290963e-07,
                4.4508494582405734e-07,
                1.067703124601679e-06,
                5.715005832886879e-07
            ],
            [
                1.6373766672973748e-07,
                9.422450432014836e-07,
                3.927862002663297e-07,
                5.043472278322555e-07,
                2.699578740032504e-07,
                2.5612828213934817e-06,
                3.466326624336003e-07,
                1.6701415872385704e-05,
                1.0677028700422047e-06,
                2.6995774527718623e-07
            ],
            [
                0.9999991148433867,
                0.9999989322973853,
                0.9999994631249324,
                0.9999985406232585,
                0.9999995262093294,
                0.9999989969860319,
                0.9999993106390371,
                1.6373766672973748e-07,
                0.9999989969857926,
                0.9999994631249964
            ],
            [
                5.715004470313855e-07,
                3.9278605979534166e-07,
                3.927862470899887e-07,
                5.04347528446051e-07,
                5.715003789046955e-07,
                1.2098656835252174e-06,
                3.05902190458764e-07,
                2.6995774527718623e-07,
                3.059022998576899e-07,
                5.043476486915964e-07
            ],
            [
                0.9999994956524718,
                0.9999989322971305,
                0.9999998144609203,
                0.9999996533672137,
                0.9999996533672137,
                0.9999997761970781,
                0.9999997897567091,
                0.9999986290424668,
                0.9999994284997575,
                0.9999993106387906
            ],
            [
                2.1024339116168358e-07,
                2.102434162245973e-07,
                4.450852641737424e-07,
                3.059022998576899e-07,
                4.450848927658745e-07,
                5.043475885696228e-07,
                3.927862002663297e-07,
                3.05902263391829e-07,
                2.2603253756956754e-06,
                1.0677027427600627e-06
            ],
            [
                1.855391681906175e-07,
                2.3823693839325527e-07,
                9.931190958076104e-08,
                3.466327037553825e-07,
                1.4449807263312446e-07,
                3.466327037553825e-07,
                1.8553907971879076e-07,
                1.2751901248454963e-07,
                4.222833444590791e-06,
                1.4449802095666915e-07
            ],
            [
                0.9999996743688975,
                0.9999994284996895,
                0.9999994956527123,
                0.9999998874648515,
                1.0,
                0.9999999226557962,
                0.9999999006881142,
                0.9999996310115039,
                0.999998712104171,
                0.9999991148433868
            ],
            [
                0.9999994956524718,
                0.999999428499417,
                8.939696304311336e-06,
                0.9999996533675031,
                0.9999994956526521,
                0.9999993106386261,
                0.9999998461827322,
                2.9023119851899796e-06,
                0.999997876622298,
                0.9999996743686259
            ],
            [
                1.8553907971855875e-07,
                2.10243290909724e-07,
                2.10243290909724e-07,
                2.10243290909724e-07,
                2.6995774527718623e-07,
                2.3823690999290963e-07,
                5.043473480777865e-07,
                1.8553907971855875e-07,
                1.6373772528704005e-07,
                2.699576809143613e-07
            ],
            [
                0.999999653367503,
                0.9999985406243017,
                0.9999987901347499,
                0.9999992661786699,
                0.9999995818811777,
                0.9999993916410361,
                0.999997593896516,
                2.3823690999290963e-07,
                0.9999995262092729,
                0.9999995818811774
            ],
            [
                2.3823690999323465e-07,
                8.315280276626197e-07,
                2.1024326584639497e-07,
                2.3823688159291947e-07,
                1.8553910183674878e-07,
                1.855390576008354e-07,
                2.699578740032504e-07,
                2.382368815932174e-07,
                5.043475885696228e-07,
                2.3823693839325527e-07
            ],
            [
                1.0,
                0.9999999273418615,
                0.9999999176675632,
                0.9999999500628453,
                0.9999999067051499,
                0.9999998257021214,
                0.9999998362622748,
                0.9999998942829981,
                1.0,
                0.9999999123574941
            ],
            [
                0.9999996072136594,
                0.9999991148431755,
                0.9999995549148951,
                0.9999998362622358,
                0.9999885212278059,
                0.9999989969854343,
                0.9999994631249962,
                0.9999993524053564,
                1.8553910183607374e-07,
                0.9999985406234317
            ],
            [
                6.475946438055299e-07,
                9.931186222523604e-08,
                2.6995784182183607e-07,
                1.4449807263312446e-07,
                1.275190732904469e-07,
                2.3823696679327928e-07,
                3.466326624336003e-07,
                2.3823693839325527e-07,
                1.8553914607267268e-07,
                1.4449805540763184e-07
            ],
            [
                8.764245361752286e-08,
                4.4508494582405734e-07,
                7.338212429582604e-07,
                7.338209805240734e-07,
                8.315284241650899e-07,
                1.3709573702822306e-06,
                1.3709568799823232e-06,
                8.315284241650899e-07,
                8.315277302841894e-07,
                1.0677028700363782e-06
            ],
            [
                2.2603248367949354e-06,
                3.927863407379485e-07,
                2.9023112932296107e-06,
                3.7266397283908927e-06,
                2.5612834320470717e-06,
                1.209866260432471e-06,
                1.7603434231833873e-06,
                1.7603434231833873e-06,
                1.7603440527334603e-06,
                2.9023119851899796e-06
            ],
            [
                1.8553919030858602e-07,
                7.338212429582604e-07,
                1.444979692800516e-07,
                3.0590237279085045e-07,
                3.059022998576899e-07,
                4.4508510499849186e-07,
                8.315281267882195e-07,
                9.931185038635267e-08,
                3.9278610661902853e-07,
                6.825608606172863e-08
            ],
            [
                3.466326211113502e-07,
                5.043475885696228e-07,
                2.10243290909724e-07,
                5.715006514176113e-07,
                3.9278610661902853e-07,
                1.8553907971855875e-07,
                1.6373772528704005e-07,
                2.1024336609843824e-07,
                9.931193325852072e-08,
                5.043476486924565e-07
            ],
            [
                2.6995784182183607e-07,
                3.9278620026686556e-07,
                3.059022998581767e-07,
                7.338207180898968e-07,
                2.1024336609874897e-07,
                2.6995784182183607e-07,
                4.4508515805735777e-07,
                1.4449802095666915e-07,
                5.043476486924565e-07,
                9.422443692574719e-07
            ],
            [
                0.9999991148426479,
                0.9999992661791072,
                0.999999825702059,
                0.9999987901338842,
                0.99999916847227,
                0.9999994284993488,
                0.9999997761971583,
                0.9999998724809419,
                5.043476486924565e-07,
                0.9999997897567091
            ],
            [
                0.9999994956527726,
                0.9999993524048933,
                0.9999997897565839,
                0.9999998362622554,
                0.9999998874648112,
                0.999999917667573,
                0.9999998942829729,
                0.9999999067050054,
                0.999999057755519,
                0.9999998642566543
            ],
            [
                1.760343213335281e-06,
                5.715003107767143e-07,
                2.9023119851899796e-06,
                1.209866260432471e-06,
                4.785093353940187e-06,
                3.927862002663297e-07,
                5.043476486915964e-07,
                2.6995771309523475e-07,
                3.0590237279085045e-07,
                6.475947982037486e-07
            ],
            [
                3.059022269254856e-07,
                2.3823688159291947e-07,
                6.825598028392069e-08,
                3.9278629391427843e-07,
                1.1253509497883659e-07,
                1.3709575337016483e-06,
                1.444980209564556e-07,
                2.102434162245973e-07,
                1.4449803818215767e-07,
                2.1024336609874897e-07
            ],
            [
                0.9999989969862714,
                0.9999993524052021,
                0.9999986290423034,
                0.9999993106392013,
                0.9999993106389549,
                2.430023493936082e-05,
                0.9999724643056755,
                0.99999921885167,
                0.9999992661791949,
                0.9999993524052793
            ],
            [
                9.931185038635267e-08,
                3.927863875616689e-07,
                1.6373766672973748e-07,
                6.023571320847322e-08,
                1.6373770576776313e-07,
                1.6373764721072816e-07,
                7.734425919002834e-08,
                2.3823690999290963e-07,
                9.931186222523604e-08,
                3.059021175261338e-07
            ],
            [
                1.4738985486506781e-05,
                2.430024652792821e-05,
                2.1444953527944967e-05,
                1.670141985446017e-05,
                1.4738983729535602e-05,
                6.962256249885085e-06,
                2.382369667929001e-07,
                8.315283250343497e-07,
                4.222831934379152e-06,
                0.00010889693530623988
            ],
            [
                1.7603440527286572e-06,
                2.6995774527718623e-07,
                8.315278294072958e-07,
                1.3709572068422585e-06,
                5.04347287955046e-07,
                6.475949526020042e-07,
                7.338209805200689e-07,
                9.422443692555439e-07,
                9.4224425692559e-07,
                6.475945666051092e-07
            ],
            [
                1.0,
                0.9999997463980125,
                0.9999999067050387,
                1.0,
                0.999997876621793,
                0.9999999176675632,
                0.9999995262095553,
                0.9999997761972116,
                0.999999935879425,
                0.9999999434137434
            ],
            [
                1.3007126914612648e-05,
                0.9999982396561585,
                0.9999974387174858,
                0.9999996533672552,
                0.9999972735297322,
                3.466325384678894e-07,
                0.9999910602994538,
                0.9999987901338844,
                0.9999974387171814,
                0.9999998362623529
            ],
            [
                0.9999985406234317,
                9.610238067382736e-05,
                0.9999810748540635,
                6.605215257197525e-05,
                0.9999975938979501,
                0.9999981261246174,
                1.3007123813382511e-05,
                2.1444950971601277e-05,
                0.9999877809210826,
                8.481104140395962e-05
            ],
            [
                6.475947210031623e-07,
                0.9999877809211105,
                2.2603240284371276e-06,
                0.9999988634364257,
                0.9999996940976638,
                1.3709573702822306e-06,
                4.450848927650143e-07,
                0.9999983463100207,
                5.715002426460124e-07,
                2.5612828213934817e-06
            ],
            [
                1.0,
                0.9999994631251244,
                0.9999999123574733,
                0.9999999358794173,
                0.9999999176674652,
                1.0,
                0.9999999500628215,
                0.9999998724809875,
                0.9999989969856733,
                1.0
            ],
            [
                0.9999998942830233,
                0.999999894282935,
                0.9999999226558238,
                0.9999982396572082,
                0.9999998942830106,
                0.9999999067050054,
                0.9999998802069017,
                0.9999998942830862,
                0.9999997761970516,
                0.9999999006881378
            ],
            [
                1.8553919030776337e-07,
                1.637376862489725e-07,
                3.4663274507713016e-07,
                3.05902263391829e-07,
                5.043472879525233e-07,
                3.9278610661902853e-07,
                3.927862002663297e-07,
                1.6373772528704005e-07,
                8.315277302857965e-07,
                3.9278634073625165e-07
            ],
            [
                3.9278605979534166e-07,
                4.450848927658745e-07,
                3.9278610661902853e-07,
                6.475946438055299e-07,
                5.715006514176113e-07,
                3.0590237279085045e-07,
                5.715003107767143e-07,
                2.699578096403948e-07,
                5.043472278322555e-07,
                2.699577774585891e-07
            ],
            [
                0.9999980052695665,
                0.9999999317439954,
                1.27519088491875e-07,
                1.275190732904469e-07,
                0.9999999176675535,
                0.9999993524050477,
                9.422444815792981e-07,
                3.466325797896173e-07,
                0.999999631011416,
                4.4508510499849186e-07
            ],
            [
                1.7603434231777837e-06,
                2.260325106237323e-06,
                2.561281905390075e-06,
                6.475949526020042e-07,
                3.288749849477628e-06,
                1.5534975693933505e-06,
                2.5612812947508257e-06,
                2.753568453712307e-05,
                1.0677024881980089e-06,
                2.2603234895289998e-06
            ],
            [
                0.9999994956526521,
                0.9999999067051387,
                9.93118503859575e-08,
                0.9999998942830862,
                1.0,
                0.9999995549150545,
                0.99999926617902,
                0.999999168472171,
                1.0,
                1.0
            ],
            [
                2.1024336609843824e-07,
                2.6995784182183607e-07,
                1.6373770576776313e-07,
                4.450852111155216e-07,
                1.855391681906175e-07,
                3.466325797896173e-07,
                3.05902263391829e-07,
                2.102433159721477e-07,
                3.466325384661554e-07,
                0.9999992188515767
            ],
            [
                0.9999960330131477,
                0.999998239657208,
                0.999998932296876,
                0.9999994631249325,
                0.9999981261246181,
                0.9999945777816835,
                0.999999581881327,
                0.9999990577556317,
                0.9999999358794097,
                0.9999994956527725
            ],
            [
                2.699576809143613e-07,
                4.450848927658745e-07,
                2.2603251062450327e-06,
                2.1024331597262577e-07,
                1.209865539295696e-06,
                6.475946438055299e-07,
                7.338208930460318e-07,
                7.338208055680009e-07,
                5.043476486924565e-07,
                1.067703124601679e-06
            ],
            [
                5.043476486915964e-07,
                3.2887478892683997e-06,
                4.222834451292594e-06,
                1.0677027427600627e-06,
                0.9999955048184275,
                9.422449308716635e-07,
                2.3823690999290963e-07,
                2.260324836787226e-06,
                6.475945666051092e-07,
                0.999999712631344
            ],
            [
                0.9999994284997576,
                0.9999993524051248,
                0.9999994631250602,
                0.9999996743688587,
                2.382369951932796e-07,
                0.9999995262096117,
                0.9999995818811774,
                0.9999998144609645,
                0.9999993916410361,
                0.9999967112509391
            ],
            [
                1.4449795205472734e-07,
                2.3823685319320354e-07,
                4.450850519409479e-07,
                3.059022269254856e-07,
                1.1253513522447425e-07,
                2.382369951932796e-07,
                3.927863407379485e-07,
                3.05902336324494e-07,
                NaN,
                1.6373764721072816e-07
            ],
            [
                0.999998126125065,
                0.9999999468421567,
                0.9999999067051165,
                0.9999993524051248,
                1.0,
                0.9999998942830358,
                0.9999999397642293,
                2.102433159721477e-07,
                0.9999998874649318,
                0.9999999397642653
            ],
            [
                2.10243290909724e-07,
                3.466327037553825e-07,
                1.4449803818215767e-07,
                2.382370235933104e-07,
                3.4663249714612693e-07,
                3.05902336324494e-07,
                2.3823696679327928e-07,
                3.059022998576899e-07,
                2.6995790618469934e-07,
                3.059021175261338e-07
            ],
            [
                3.927863875616689e-07,
                6.825604537781398e-08,
                5.043472278322555e-07,
                1.855391681906175e-07,
                2.382369667929001e-07,
                3.927863407379485e-07,
                4.450852641737424e-07,
                2.382369951932796e-07,
                3.05902263391829e-07,
                3.4663274507713016e-07
            ],
            [
                0.9999987121041715,
                0.9999995818813769,
                0.9999990577552952,
                0.9999980052700441,
                5.715006514105942e-07,
                0.999998932297513,
                0.9999985406232587,
                0.9999986290421413,
                0.9999995549150545,
                0.9999994956524119
            ],
            [
                0.9999995262093858,
                0.999998790134173,
                0.9999997761970247,
                0.9999998461827322,
                0.9999987901346059,
                0.9999997126315153,
                0.9999997463980125,
                0.9999996940978462,
                0.9999998461826222,
                0.9999998144608319
            ],
            [
                5.315780536011123e-08,
                2.8453364239757298e-08,
                9.931187406410953e-08,
                5.3157811697009444e-08,
                4.691168275606451e-08,
                7.734416698849138e-08,
                0.9999998802069159,
                4.6911677163762064e-08,
                6.825598028392069e-08,
                2.215950777364157e-08
            ],
            [
                0.99937366578232,
                0.9999999006880195,
                0.9999955048189618,
                0.9999981261243943,
                1.8553916819032217e-07,
                0.9999993106387906,
                0.999998540624128,
                1.8553916819032217e-07,
                0.999996273362053,
                0.9999984465022475
            ],
            [
                1.8553910183674878e-07,
                1.855390576008354e-07,
                1.637376862489725e-07,
                2.699578740032504e-07,
                3.05902263391829e-07,
                1.8553910183674878e-07,
                1.637377057680051e-07,
                5.043475885696228e-07,
                5.715005832895975e-07,
                1.8553910183674878e-07
            ],
            [
                1.6373774480605869e-07,
                3.4663249714612693e-07,
                1.275190732904469e-07,
                1.8553905760062447e-07,
                1.275191036933194e-07,
                1.6373772528704005e-07,
                1.855391681906175e-07,
                6.825600469412533e-08,
                1.1253509497883659e-07,
                9.931185038635267e-08
            ],
            [
                0.9999998724810027,
                0.9999945777829743,
                0.9999970976880166,
                0.9999999530883508,
                0.9999999434137773,
                7.734428685019034e-08,
                1.0,
                0.9999999317439303,
                0.9999999123574524,
                0.9999999006879957
            ],
            [
                1.5534975693979422e-06,
                1.7603425837855082e-06,
                1.0677024881941248e-06,
                1.0677027427600627e-06,
                1.3709572068522336e-06,
                1.9947299593078385e-06,
                1.2098659719788098e-06,
                8.315284241650899e-07,
                8.315279285370317e-07,
                8.315277302841894e-07
            ],
            [
                0.9999996743686257,
                0.999999653367255,
                0.9999997126313441,
                0.9999991148432813,
                0.9999978766215395,
                0.9999996940978462,
                0.999999428499485,
                0.9999997897565588,
                0.9999998724810027,
                0.9999997300422228
            ],
            [
                0.9999885212332607,
                0.9999998362623723,
                0.9999994956527123,
                0.9999993916406734,
                0.9999987121041707,
                0.9999995818812769,
                0.0001088969482847688,
                1.1253512180925583e-07,
                0.9999996310114159,
                0.9999998874647709
            ],
            [
                7.338208930443633e-07,
                5.715003789033962e-07,
                1.0677027427600627e-06,
                9.422443692555439e-07,
                2.2603240284371276e-06,
                5.715005151606823e-07,
                1.5534975693979422e-06,
                8.315281267861397e-07,
                1.5534975693933505e-06,
                3.7266406168827523e-06
            ],
            [
                3.466327037539638e-07,
                2.5612812947508257e-06,
                8.315279285351409e-07,
                1.7603434231833873e-06,
                0.9999980052693287,
                9.422448185510695e-07,
                1.3709576971425944e-06,
                0.9999989322973856,
                2.2603234895372223e-06,
                1.3709573702822306e-06
            ],
            [
                1.855391681906175e-07,
                2.6995784182140636e-07,
                8.315277302857965e-07,
                1.6373772528704005e-07,
                1.1253526937697666e-07,
                2.699576809143613e-07,
                3.4663274507713016e-07,
                1.275191036933194e-07,
                2.1024341622426268e-07,
                1.855391239547094e-07
            ],
            [
                1.3007133116732079e-05,
                3.535625493182252e-05,
                4.53978902983119e-05,
                8.939693107190907e-06,
                1.4738978458382043e-05,
                8.481107172971651e-05,
                1.0129993395336818e-05,
                4.539788488687281e-05,
                1.670141786325573e-05,
                3.726639284125553e-06
            ],
            [
                4.450848927658745e-07,
                5.04347468323289e-07,
                3.466325384678894e-07,
                2.3823682479292225e-07,
                1.8553905760062447e-07,
                2.1024331597262577e-07,
                2.1024334103581732e-07,
                2.382370235933104e-07,
                2.1024341622426268e-07,
                3.0590237279085045e-07
            ],
            [
                0.999998790134317,
                0.9999995262092163,
                7.338207180898968e-07,
                0.9999998362623138,
                0.9999981261239481,
                0.9999998144608319,
                0.9999998024946095,
                1.0,
                0.9999991148431756,
                5.715003789046955e-07
            ],
            [
                2.382370235933104e-07,
                2.102434412875379e-07,
                1.8553914607267268e-07,
                1.8553914607267268e-07,
                2.1024334103553052e-07,
                1.444979692800516e-07,
                3.05902336324494e-07,
                1.4449807263312446e-07,
                1.6373772528704005e-07,
                1.8553919030858602e-07
            ],
            [
                1.8553914607267268e-07,
                3.059022269250683e-07,
                3.927863407379485e-07,
                2.382370235933104e-07,
                7.338207180898968e-07,
                1.8553905760062447e-07,
                2.3823690999323465e-07,
                1.8553914607267268e-07,
                2.1024331597262577e-07,
                3.4663262111182307e-07
            ],
            [
                4.450849988811838e-07,
                3.4663274507713016e-07,
                2.1024336609843824e-07,
                1.855391239544352e-07,
                3.0590237279085045e-07,
                4.450848927658745e-07,
                7.338209805224048e-07,
                3.9278610661902853e-07,
                2.102434412875379e-07,
                1.8553905760062447e-07
            ],
            [
                0.9999987121046319,
                0.9999992188513905,
                0.9999993106391193,
                7.338209805224048e-07,
                1.855391239544352e-07,
                0.9999982396561586,
                0.9999969105040822,
                0.9999877809254633,
                0.9999975938970886,
                0.9999938558239402
            ],
            [
                5.043473480777865e-07,
                3.466325384661554e-07,
                3.9278634073625165e-07,
                1.7603425837855082e-06,
                3.0590215399183813e-07,
                3.059022269250683e-07,
                7.338208930460318e-07,
                1.2098659719788098e-06,
                2.1024344128660572e-07,
                4.006367786720367e-05
            ],
            [
                3.288749849529972e-06,
                3.05902190458764e-07,
                9.422447062294175e-07,
                9.422442569315887e-07,
                5.715003107767143e-07,
                3.7266406168827523e-06,
                5.715006514167015e-07,
                0.999999730042287,
                0.9999995818813271,
                3.9278634073732336e-07
            ],
            [
                8.315280276626197e-07,
                1.5534983101644536e-06,
                0.9999869928715668,
                8.315277302857965e-07,
                0.9999993106387083,
                5.043476486924565e-07,
                1.2098659719788098e-06,
                1.5534973842076057e-06,
                0.9999997897565839,
                9.422447062294175e-07
            ],
            [
                8.764247451307293e-08,
                2.6995768091310296e-07,
                9.931189774187203e-08,
                9.931202796993203e-08,
                2.10243290909724e-07,
                1.8553907971855875e-07,
                1.444980209564556e-07,
                1.8553914606950867e-07,
                0.9999972735303836,
                9.931187406410953e-08
            ],
            [
                0.9999972735290827,
                0.9999962733616101,
                0.9999945777823307,
                0.9999985406243023,
                0.999998540624128,
                0.999998446502617,
                0.9999921107364993,
                0.999991601924984,
                0.9999904837438013,
                0.9999981261246187
            ],
            [
                2.2603242978871282e-06,
                1.3709568799919866e-06,
                1.3709572068522336e-06,
                0.9999785550414351,
                7.338208055664991e-07,
                9.422444815792981e-07,
                8.315277302841894e-07,
                1.0129994602895546e-05,
                1.5534979397740895e-06,
                0.9999987121041711
            ],
            [
                1.892514598551715e-05,
                NaN,
                0.9999991148433864,
                0.00023050682551362277,
                0.9999934595627767,
                0.9999985406230838,
                4.450849988798682e-07,
                5.04347287955046e-07,
                0.99995993631745,
                3.927860597945825e-07
            ],
            [
                0.999999428499417,
                0.9999998024945624,
                0.9999997126313784,
                0.9999998942829981,
                0.9999978766207803,
                0.9999987121044783,
                0.9999999226558515,
                0.9999996743686645,
                0.9999991684718739,
                0.9999982396565795
            ],
            [
                5.043476486915964e-07,
                5.043476486915964e-07,
                2.69957906184239e-07,
                8.315281267882195e-07,
                7.338209805240734e-07,
                5.715005832886879e-07,
                1.855391239539711e-07,
                6.144173869603344e-06,
                1.7603432133296774e-06,
                3.05902190458764e-07
            ],
            [
                4.4508515805735777e-07,
                9.422444815814404e-07,
                3.059022269254856e-07,
                2.3823693839325527e-07,
                7.338208930460318e-07,
                3.9278629391427843e-07,
                9.422444815814404e-07,
                1.5534984953552536e-06,
                5.71500719545698e-07,
                2.3823682479292225e-07
            ],
            [
                1.0677032518814388e-06,
                2.6995790618469934e-07,
                7.338207180898968e-07,
                2.2603234895372223e-06,
                1.3709575337159875e-06,
                1.0677031245990084e-06,
                4.222833444590791e-06,
                4.4508515805735777e-07,
                1.3007134667259441e-05,
                1.9947292459347367e-06
            ],
            [
                2.9023109472244114e-06,
                1.4738981972082061e-05,
                8.481103127419174e-05,
                2.7535694384882703e-05,
                0.9999785550541901,
                0.9999992188518558,
                0.9999339478713826,
                1.9947292459265734e-06,
                4.0063682641226247e-05,
                8.939694172867777e-06
            ],
            [
                6.47594952603035e-07,
                7.338212429594283e-07,
                9.422450432030903e-07,
                4.4508515805735777e-07,
                8.315280276626197e-07,
                6.475947982037486e-07,
                6.475946438055299e-07,
                8.315278294114555e-07,
                1.209865827752005e-06,
                1.5534975693979422e-06
            ],
            [
                2.382368531929327e-07,
                3.466325797896173e-07,
                1.1253508156363576e-07,
                3.927862939126708e-07,
                2.1024336609874897e-07,
                6.475949526020042e-07,
                2.10243290909724e-07,
                1.7603425837855082e-06,
                2.6995790618469934e-07,
                1.1253508156363576e-07
            ],
            [
                1.2751902768612997e-07,
                1.2751901248454963e-07,
                3.059022998581767e-07,
                8.764242227418718e-08,
                1.6373766672973748e-07,
                1.4449802095609418e-07,
                8.764244316973974e-08,
                7.73442776303243e-08,
                5.315786239218605e-08,
                2.102434162245973e-07
            ],
            [
                0.9999810748518453,
                2.7535700948722127e-05,
                0.9999945777810383,
                0.9999687980850618,
                0.9999938558268723,
                4.4508494582405734e-07,
                1.0129993395336818e-05,
                0.9999938558276075,
                3.1201907657271834e-05,
                0.9999987901341734
            ],
            [
                0.9999996533672965,
                0.9999994956527724,
                0.9999995262093294,
                0.9999998362622747,
                0.99999967436882,
                0.9999942280820453,
                0.9999987901343176,
                0.9999995262093294,
                0.9999996940977003,
                0.9999998024946567
            ],
            [
                0.9999998942829477,
                0.999999846182714,
                0.9999990577551822,
                0.9999992188513908,
                0.9999993524052023,
                0.9999993916408914,
                0.9999995549147364,
                0.9999992188518563,
                0.9999992188515768,
                0.999999814460854
            ],
            [
                0.9999987901344614,
                0.9999999006880786,
                0.9999997300421583,
                0.9999997897566589,
                0.9999996743688199,
                0.999999495652592,
                0.999999057755182,
                0.9999994284997578,
                0.9999996940978826,
                0.9999995262094987
            ],
            [
                1.0129994602895546e-05,
                NaN,
                3.288748673376478e-06,
                1.1478770862882149e-05,
                1.4738976701652988e-05,
                2.4300234941261454e-05,
                2.753568782024347e-05,
                6.144173869603344e-06,
                3.2887498495150166e-06,
                7.889266347786918e-06
            ],
            [
                4.2228319344021954e-06,
                2.3823693839290317e-07,
                7.338213304363436e-07,
                1.0677026154806063e-06,
                3.7266410611296085e-06,
                3.466327037553825e-07,
                2.6995790618469934e-07,
                2.5612819054133693e-06,
                9.422444815814404e-07,
                8.315282259138311e-07
            ],
            [
                0.9999999226558238,
                0.9999998802069874,
                0.9999998555020307,
                0.9999999697115768,
                0.9999987121043248,
                0.9999986290431205,
                0.9999997126313098,
                0.9999972735303819,
                0.9999999358794327,
                0.9999982396559485
            ],
            [
                1.8553905760062447e-07,
                1.6373766672973748e-07,
                1.637377448057981e-07,
                1.1253506814842375e-07,
                2.1024336609843824e-07,
                3.4663249714612693e-07,
                2.1024331597262577e-07,
                2.699578740032504e-07,
                3.0590237279085045e-07,
                3.4663278639892215e-07
            ],
            [
                1.6373766672973748e-07,
                8.764242227418718e-08,
                7.734416698849138e-08,
                7.734416698849138e-08,
                1.8553914607267268e-07,
                4.691162683297406e-08,
                9.931187406410953e-08,
                0.9999904837494537,
                7.734414854823498e-08,
                6.023568448589658e-08
            ],
            [
                0.9999994284995531,
                0.9999998874648917,
                0.9999998874649184,
                0.9999998724809723,
                0.9999995262093293,
                0.9999999358794479,
                0.9999993106387083,
                0.9999999006879957,
                0.9999999273418355,
                0.9999995818813767
            ],
            [
                0.9999996940978826,
                0.999998863436561,
                0.9999981261241714,
                0.9999989969856733,
                0.9999998555019446,
                0.9999989969857929,
                0.9999991148427535,
                0.9999982396565779,
                0.9999989969859125,
                0.9999993524051249
            ],
            [
                0.9999981261241716,
                4.006367786720367e-05,
                2.7535697667202906e-05,
                6.605213683024311e-05,
                5.422218969858371e-06,
                1.1478764021029928e-05,
                3.535626336201389e-05,
                0.00012339463384858465,
                1.670141786325573e-05,
                1.1478770862882149e-05
            ],
            [
                0.9999990577551819,
                0.9999996310114599,
                0.999998790134173,
                0.9999994631247403,
                0.9999988634364252,
                0.9999989969860317,
                0.9999987901338845,
                0.9999994956525919,
                0.9999974387174867,
                0.9999985406236056
            ],
            [
                0.9999985406241287,
                0.999999495652592,
                0.999998346309824,
                0.9999993916407462,
                0.9999991684715767,
                0.9999993916406735,
                0.999998863436561,
                0.999997273529409,
                0.9999991684716754,
                0.9999989322975126
            ]
        ]
    },
    {
        "q_id": "9532_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                7.338210679949506e-07,
                1.1253516205489029e-07,
                9.422449308566668e-07,
                1.3709570433387154e-06,
                1.5534983100595462e-06,
                3.2887490648622804e-06,
                2.2603234893594005e-06,
                6.475947209918244e-07,
                1.3709573702722555e-06,
                2.5612834320214477e-06
            ],
            [
                4.450851049991497e-07,
                1.5534979397829198e-06,
                4.4508499888275247e-07,
                1.3709567165087443e-06,
                4.4508515805735777e-07,
                1.7603438428848787e-06,
                5.422217030781934e-06,
                8.315281267894483e-07,
                1.5534981249736758e-06,
                6.144177531811707e-06
            ],
            [
                8.315283250305684e-07,
                5.715004470295662e-07,
                5.715004470313855e-07,
                1.5534977545497995e-06,
                1.3709572068354007e-06,
                1.2098658277264215e-06,
                1.0677029973158649e-06,
                7.338207180838067e-07,
                1.3709575336654889e-06,
                1.2098655392811161e-06
            ],
            [
                1.994730434816876e-06,
                9.422449308716635e-07,
                1.7603434230921292e-06,
                1.994729008056074e-06,
                2.2603245672867952e-06,
                1.5534981249397663e-06,
                2.9023133690188264e-06,
                1.2098658277335738e-06,
                4.139941002027314e-08,
                4.22283394786293e-06
            ],
            [
                5.043472278312808e-07,
                1.2098659719757836e-06,
                3.9278615344178325e-07,
                3.224188555067886e-08,
                3.9278638756099906e-07,
                1.5534984953298217e-06,
                4.450849988798682e-07,
                4.450851580555361e-07,
                5.715004470295662e-07,
                1.7603430034743913e-06
            ],
            [
                2.2603237589028734e-06,
                1.760344052693435e-06,
                1.5534977545384963e-06,
                4.785092783319532e-06,
                5.043476486924565e-07,
                1.5534979397592542e-06,
                1.0677028700320085e-06,
                6.47594952603035e-07,
                1.994730434847717e-06,
                3.288749065209246e-06
            ],
            [
                1.27519088491875e-07,
                7.734428685047173e-08,
                1.370957860567974e-06,
                1.3709567165386693e-06,
                5.3157811697009444e-08,
                6.023568448589658e-08,
                1.5534983101301911e-06,
                9.931185038635267e-08,
                7.73441946488886e-08,
                1.6373772528704005e-07
            ],
            [
                1.0677029973056687e-06,
                1.7603434231241496e-06,
                5.715005832798517e-07,
                1.7603438428660665e-06,
                1.0677029973114952e-06,
                1.9947306726049992e-06,
                1.994729721396435e-06,
                1.3709568799592562e-06,
                1.7603440526806268e-06,
                1.994730196992497e-06
            ],
            [
                1.9947290080343035e-06,
                7.338207180838067e-07,
                8.3152792852928e-07,
                1.9947301970587145e-06,
                7.338213304283347e-07,
                1.3709578605617394e-06,
                8.315280276580819e-07,
                2.2603237587774727e-06,
                1.2098659719601033e-06,
                1.5534977545384963e-06
            ],
            [
                5.315786239218605e-08,
                9.931187406410953e-08,
                9.422445939002803e-07,
                8.764246406483893e-08,
                3.2241847115356483e-08,
                4.691164920214251e-08,
                8.764247451307293e-08,
                9.931187406410953e-08,
                1.4449805540740185e-07,
                4.691161005609407e-08
            ],
            [
                1.5534975693979422e-06,
                1.209865539295696e-06,
                3.288749849529972e-06,
                1.3709573702822306e-06,
                3.9278634073732336e-07,
                2.902313023130843e-06,
                2.5612834320470717e-06,
                0.999997739675703,
                2.2603245673443566e-06,
                1.4449795205429202e-07
            ],
            [
                1.5534983100595462e-06,
                6.475950297993789e-07,
                1.0677024881941248e-06,
                1.3709573702566696e-06,
                5.422218969720291e-06,
                7.3382080556433e-07,
                1.553498495338299e-06,
                6.475951069932288e-07,
                1.994729245878497e-06,
                9.422443692489024e-07
            ],
            [
                8.315282259089153e-07,
                1.2098653950551882e-06,
                8.315283250343497e-07,
                1.370957860576702e-06,
                1.76034300345598e-06,
                1.7603436329978976e-06,
                5.043476486915964e-07,
                1.067703379154416e-06,
                1.275190428875671e-07,
                1.9947290080343035e-06
            ],
            [
                1.2751910369310194e-07,
                2.1024344128660572e-07,
                1.370957860567974e-06,
                1.2751901248391176e-07,
                1.994729245878497e-06,
                8.315279285351409e-07,
                1.275190276853036e-07,
                3.466325384661554e-07,
                1.370957370247318e-06,
                2.2603248367358324e-06
            ],
            [
                1.067702997240607e-06,
                3.7266397283231055e-06,
                9.42244256915735e-07,
                1.7603436329554703e-06,
                9.422445938917108e-07,
                2.902311292783513e-06,
                1.2098659719661556e-06,
                1.2098662603752517e-06,
                9.42244256915735e-07,
                1.0677033791495609e-06
            ],
            [
                6.825600469412533e-08,
                1.760342793638743e-06,
                3.4663274507713016e-07,
                1.1253516205489029e-07,
                1.2098661162056318e-06,
                3.927862470905692e-07,
                3.466327037548308e-07,
                2.1024339116168358e-07,
                1.760342793638743e-06,
                3.927863875616689e-07
            ],
            [
                0.9999982396569973,
                0.9999983463110063,
                0.999999825702059,
                0.999997273528756,
                0.9999996310114598,
                0.9999972735284304,
                8.3152792852928e-07,
                0.9999970976869785,
                0.9999978766220446,
                0.9999985406234316
            ],
            [
                8.315284241665078e-07,
                1.9947304348862686e-06,
                3.288749849529972e-06,
                7.338208930460318e-07,
                1.7603425837903113e-06,
                1.3709573702856596e-06,
                1.0677027427624903e-06,
                3.288748281329893e-06,
                1.5534981249736758e-06,
                5.043476486924565e-07
            ],
            [
                7.73442776300517e-08,
                1.4449805540740185e-07,
                7.734425918979532e-08,
                3.0590226338838606e-07,
                5.315789407666425e-08,
                1.6373762769138607e-07,
                1.2751899728286965e-07,
                1.8553910183674878e-07,
                9.931195693628605e-08,
                2.699578096393206e-07
            ],
            [
                4.222832941111319e-06,
                9.422443692489024e-07,
                7.338210679949506e-07,
                6.475951069932288e-07,
                1.3709570433885908e-06,
                1.7603440526806268e-06,
                9.422449308673789e-07,
                1.370957860567974e-06,
                8.315282259089153e-07,
                1.5534973841705173e-06
            ],
            [
                1.6373774480479287e-07,
                1.1253509497883659e-07,
                1.8553905760062447e-07,
                2.6995771309523475e-07,
                2.382370235922541e-07,
                1.2751905808881762e-07,
                3.059022998581767e-07,
                2.382368247924618e-07,
                9.422449308789479e-07,
                1.855391239544352e-07
            ],
            [
                7.338208930421943e-07,
                1.3709578605118645e-06,
                8.315279285251204e-07,
                1.2098656835076114e-06,
                1.7603430034439723e-06,
                0.9999955048194966,
                2.902312677084523e-06,
                9.422444815679433e-07,
                8.315282259051341e-07,
                1.3709572068272963e-06
            ],
            [
                8.764244316973974e-08,
                2.3823693839290317e-07,
                3.4663274507713016e-07,
                2.561281600086738e-06,
                7.338212429594283e-07,
                7.33821330437595e-07,
                4.450852111155216e-07,
                9.931185038635267e-08,
                8.764242227418718e-08,
                1.8553905760062447e-07
            ],
            [
                4.139934092760465e-08,
                5.3157811697009444e-08,
                1.1253526937697666e-07,
                1.275190428875671e-07,
                1.8553914607267268e-07,
                7.338211554725124e-07,
                1.0677032518748838e-06,
                2.102434162245973e-07,
                8.315282259089153e-07,
                1.370956716519966e-06
            ],
            [
                1.7603434231505666e-06,
                1.0677029973114952e-06,
                6.475948753991907e-07,
                1.1253516205489029e-07,
                1.2098653950606901e-06,
                5.315784971839039e-08,
                5.715003107755449e-07,
                6.023573475041126e-08,
                1.370957370247318e-06,
                2.69957906184239e-07
            ],
            [
                0.9999998802069587,
                0.9999982396561581,
                0.9999999006881259,
                0.9999998874647977,
                0.9999996743688199,
                0.9999991684720718,
                0.9999992661792821,
                0.9999992661787572,
                0.9999990577556311,
                0.9999989969854338
            ],
            [
                1.994729721469003e-06,
                7.338212429464139e-07,
                1.760344052693435e-06,
                2.1024331597262577e-07,
                9.931187406410953e-08,
                9.931190958076104e-08,
                1.2098659719601033e-06,
                2.9023133689924295e-06,
                1.3709575337016483e-06,
                3.288749457409966e-06
            ],
            [
                7.734418542875216e-08,
                1.637377057680051e-07,
                5.315780536011123e-08,
                1.275190580890061e-07,
                6.825600469412533e-08,
                0.9999999358793867,
                1.855391239547094e-07,
                2.1024339116168358e-07,
                1.2751899728311609e-07,
                0.9999988634362896
            ],
            [
                1.067703379154416e-06,
                8.764250585640737e-08,
                6.825604537781398e-08,
                2.1024339116168358e-07,
                9.931185038635267e-08,
                7.734423152941018e-08,
                6.023574911170301e-08,
                1.4449795205429202e-07,
                1.4449798650551755e-07,
                9.931189774187203e-08
            ],
            [
                1.1253514863968147e-07,
                8.764241182641775e-08,
                5.043473480777865e-07,
                4.139934092760465e-08,
                8.764254764780641e-08,
                1.0677026154806063e-06,
                7.73442776303243e-08,
                9.422442569315887e-07,
                2.102434162245973e-07,
                7.73442776303243e-08
            ],
            [
                9.422449308673789e-07,
                6.475947982002148e-07,
                1.5534981249397663e-06,
                1.994730434816876e-06,
                1.2098662604291696e-06,
                9.422448185264317e-07,
                6.475946438055299e-07,
                2.102434162245973e-07,
                1.0677031245990084e-06,
                1.067703379154416e-06
            ],
            [
                3.059021539909339e-07,
                6.825597214718257e-08,
                2.382368531929327e-07,
                2.699577774585891e-07,
                6.023579219579052e-08,
                7.734416698849138e-08,
                1.4449807263312446e-07,
                6.023568448589658e-08,
                6.825600469412533e-08,
                5.315780536011123e-08
            ],
            [
                0.99999916847227,
                0.9999997617630333,
                0.9999992188515765,
                0.9999994284993488,
                0.9999978766215387,
                0.9999990577550696,
                0.9999990577554065,
                0.9999990577555188,
                0.9999998144609424,
                0.9999996310115039
            ],
            [
                1.5534984953552536e-06,
                4.4508515805735777e-07,
                1.3709570434250617e-06,
                8.31528325040778e-07,
                1.994729483729522e-06,
                6.47594952603035e-07,
                1.0677028700422047e-06,
                1.0677027427624903e-06,
                1.4449800373118268e-07,
                2.902312677150514e-06
            ],
            [
                6.825604537781398e-08,
                9.931190958076104e-08,
                2.6995774527718623e-07,
                1.7603430034743913e-06,
                6.825602910433871e-08,
                1.8553916819032217e-07,
                4.691161005609407e-08,
                1.1253514863909295e-07,
                2.6995784182140636e-07,
                2.3823702359290413e-07
            ],
            [
                0.999998346310612,
                4.6911665979156514e-08,
                0.9999984465016907,
                3.224188555067886e-08,
                5.043474683240344e-07,
                5.043474683240344e-07,
                1.855390576008354e-07,
                9.931200429212718e-08,
                2.699578096403948e-07,
                8.315282259151545e-07
            ],
            [
                9.931187406410953e-08,
                1.1253512180925583e-07,
                9.93118503859575e-08,
                3.2241847115356483e-08,
                6.825606165129312e-08,
                6.023572038882162e-08,
                0.9999991148433865,
                6.023576347299818e-08,
                2.10243290909724e-07,
                1.4449802095609418e-07
            ],
            [
                0.9999989322975124,
                1.5534979397592542e-06,
                3.9278638756099906e-07,
                6.475946437966953e-07,
                3.2887478892055875e-06,
                9.422449308673789e-07,
                1.9947290081286418e-06,
                1.7603425837791042e-06,
                0.9999984465015054,
                8.31528424162821e-07
            ],
            [
                7.734428685019034e-08,
                1.1253508156363576e-07,
                1.2751899728311609e-07,
                9.931195693628605e-08,
                7.734421308914719e-08,
                1.4449805540740185e-07,
                3.46632497145457e-07,
                3.466327450765785e-07,
                1.2751899728286965e-07,
                6.825606165129312e-08
            ],
            [
                1.2098661161982042e-06,
                3.466325797900508e-07,
                2.2603253756956754e-06,
                3.927862470905692e-07,
                1.5534983101644536e-06,
                1.7603438428564603e-06,
                3.0590215399281185e-07,
                2.3823685319320354e-07,
                3.927861534431675e-07,
                4.4508499888275247e-07
            ],
            [
                1.0677032518578904e-06,
                1.0677033791495609e-06,
                1.637377448057981e-07,
                4.139935079796334e-08,
                9.422447062094932e-07,
                0.9999898700066207,
                8.315283250343497e-07,
                7.338208930421943e-07,
                6.475949526003845e-07,
                1.0677033791495609e-06
            ],
            [
                9.4224425692559e-07,
                9.422450431912e-07,
                1.067703379154416e-06,
                4.450850519409479e-07,
                1.0677028700422047e-06,
                3.2887490653109436e-06,
                1.9947301970587145e-06,
                1.55349775456958e-06,
                1.2098653950403334e-06,
                1.2098659719601033e-06
            ],
            [
                2.2603253756956754e-06,
                4.450851580566494e-07,
                2.9023119851899796e-06,
                2.561282821402217e-06,
                1.3709570434250617e-06,
                7.338212429594283e-07,
                5.422220909009474e-06,
                1.994729483729522e-06,
                1.3709572068553509e-06,
                1.2098661162056318e-06
            ],
            [
                0.9999892166852263,
                1.0677027427525368e-06,
                1.9947306726594253e-06,
                1.7603436330179102e-06,
                7.338210680021253e-07,
                2.2603242978377903e-06,
                1.9947306726213275e-06,
                2.9023126770343703e-06,
                1.2098653950606901e-06,
                1.760344052693435e-06
            ],
            [
                8.7642558095602e-08,
                7.338207180838067e-07,
                9.931193325852072e-08,
                7.734416698849138e-08,
                2.1024339116168358e-07,
                7.734426841017797e-08,
                5.315781803390236e-08,
                4.4508515805735777e-07,
                3.059022269254856e-07,
                6.825598028392069e-08
            ],
            [
                8.315282259151545e-07,
                5.71500515161527e-07,
                1.0677024881941248e-06,
                1.0677024881941248e-06,
                7.338208055579897e-07,
                1.0677031245953668e-06,
                3.927862470905692e-07,
                6.475951069932288e-07,
                3.0590219045914655e-07,
                3.0590219045914655e-07
            ],
            [
                4.139938534423022e-08,
                9.931188590255539e-08,
                5.315787506598473e-08,
                4.6911604463613627e-08,
                3.653485128931788e-08,
                1.9555676042962202e-08,
                2.8453354063983556e-08,
                4.139934586261661e-08,
                5.315786239218605e-08,
                1.2751910369275402e-07
            ],
            [
                5.043475885696228e-07,
                4.222835457733473e-06,
                1.2098659719601033e-06,
                1.2098652508056196e-06,
                1.5534975693347152e-06,
                1.760343632920248e-06,
                1.5534977545497995e-06,
                1.760344052693435e-06,
                8.764241182605906e-08,
                1.2098652507957165e-06
            ],
            [
                0.9999974387174857,
                0.9999998362622553,
                0.9999989969854339,
                2.6995774527718623e-07,
                0.9999988634362897,
                0.9999986290427937,
                0.9999988634361544,
                0.9999991148427534,
                0.9999985406237797,
                0.9999974387171802
            ],
            [
                5.715007195447234e-07,
                8.764255809528314e-08,
                4.1399410020127234e-08,
                8.764244316973974e-08,
                4.450850519403407e-07,
                1.2751901248454963e-07,
                7.734421308914719e-08,
                1.8553919030826963e-07,
                5.315781803390236e-08,
                5.315786239218605e-08
            ],
            [
                9.422444815765128e-07,
                1.209865250822125e-06,
                3.288749065436569e-06,
                1.7603434231097403e-06,
                6.475946438055299e-07,
                5.71500651413193e-07,
                9.422448185388577e-07,
                1.5534983101301911e-06,
                5.715004470295662e-07,
                9.422450431912e-07
            ],
            [
                7.889265407255982e-06,
                5.422217677152175e-06,
                3.72663883989755e-06,
                2.2603253756956754e-06,
                5.422217677152175e-06,
                6.962257079889302e-06,
                8.939699501416646e-06,
                3.2887494574832472e-06,
                3.4663274507713016e-07,
                2.9023112932296107e-06
            ],
            [
                0.9999982396572078,
                0.9999978766215383,
                9.931193325852072e-08,
                0.9999984465016905,
                0.9999983463098235,
                0.9999989969861512,
                0.9999989322970031,
                0.9999978766212855,
                0.9999977396748948,
                0.9999998874647574
            ],
            [
                8.315284241650899e-07,
                2.2603253756956754e-06,
                7.73441946488886e-08,
                2.6995774527718623e-07,
                5.043474081993875e-07,
                7.338208055664991e-07,
                2.1024341622426268e-07,
                3.927860597935108e-07,
                6.023569884718319e-08,
                1.2751899728311609e-07
            ],
            [
                1.3709570433885908e-06,
                1.6373768624837685e-07,
                0.9999916019279761,
                3.9278610661902853e-07,
                1.6373770576776313e-07,
                2.9023133689924295e-06,
                0.9999974387180965,
                2.6995784182183607e-07,
                1.3709567165386693e-06,
                2.382368531929327e-07
            ],
            [
                2.845334728018925e-08,
                3.2241839428313264e-08,
                1.7257831804675527e-08,
                8.764252675194995e-08,
                8.764247451307293e-08,
                8.764240137829087e-08,
                1.9555685367819447e-08,
                4.691162683297406e-08,
                4.691168275589384e-08,
                2.8453371023563735e-08
            ],
            [
                8.764254764780641e-08,
                2.8453323536912213e-08,
                6.825600469412533e-08,
                6.825598842065202e-08,
                6.023569166654288e-08,
                7.734428685047173e-08,
                4.691160446380562e-08,
                4.139935079796334e-08,
                6.825602910433871e-08,
                1.275190732904469e-07
            ],
            [
                7.338210680002898e-07,
                2.902312677104321e-06,
                3.927861534406222e-07,
                1.994730197071414e-06,
                3.9278615343901467e-07,
                5.04347528446051e-07,
                1.2098661161927025e-06,
                1.3709575336860625e-06,
                9.422445938917108e-07,
                4.4508510499737865e-07
            ],
            [
                0.9999992188512971,
                0.9999989322966211,
                0.9999989969854338,
                0.9999885212264104,
                0.9999993106390368,
                0.9999998461827321,
                0.9999995549147359,
                0.9999955048178872,
                0.9999984465028016,
                0.9999967112501518
            ],
            [
                1.7603436329978976e-06,
                1.7603438428564603e-06,
                6.023571320847322e-08,
                9.422449308716635e-07,
                2.2603248367358324e-06,
                0.9999993524052021,
                3.288749457409966e-06,
                9.422444815679433e-07,
                1.0677032518578904e-06,
                1.2098653950606901e-06
            ],
            [
                0.9999975938970875,
                0.9999988634360187,
                9.422448185534261e-07,
                1.1253510839355284e-07,
                1.125352291309328e-07,
                1.6373764721072816e-07,
                0.9999994956525319,
                0.9999997126313098,
                5.3157837044597743e-08,
                0.9999995818813268
            ],
            [
                2.9023126768680736e-06,
                1.0677031245710902e-06,
                4.785093353739995e-06,
                8.315280276399315e-07,
                1.370956716519966e-06,
                2.3823690999160957e-07,
                1.370957860567974e-06,
                2.2603234894560207e-06,
                9.93118503859575e-08,
                1.6373770576776313e-07
            ],
            [
                1.2751902768612997e-07,
                2.699578740032504e-07,
                1.6373774480605869e-07,
                2.3823688159291947e-07,
                4.4508515805735777e-07,
                3.4663278639892215e-07,
                1.637376862489725e-07,
                1.4449803818215767e-07,
                1.1253525596174225e-07,
                8.7642558095602e-08
            ],
            [
                2.102433159721477e-07,
                1.2098659719788098e-06,
                1.5534983101602148e-06,
                5.715005151606823e-07,
                1.444980209564556e-07,
                1.2751904288710323e-07,
                1.5534984953552536e-06,
                1.4449802095666915e-07,
                4.691160446380562e-08,
                1.855391681906175e-07
            ],
            [
                5.043474683240344e-07,
                1.275189972832538e-07,
                1.5534984953552536e-06,
                5.043474082012222e-07,
                1.6373772528704005e-07,
                1.0677024882029858e-06,
                2.699577452775239e-07,
                3.9278629391427843e-07,
                1.4449800373118268e-07,
                1.994729721518893e-06
            ],
            [
                1.9947299592570416e-06,
                6.825600469412533e-08,
                3.9278605979534166e-07,
                1.7603438428564603e-06,
                8.315280276607289e-07,
                3.927862002663297e-07,
                4.139938534423022e-08,
                7.338210679949506e-07,
                4.139936066832438e-08,
                7.338207180838067e-07
            ],
            [
                3.2241881707064475e-08,
                3.653479902594117e-08,
                5.315786239218605e-08,
                4.1399375473868e-08,
                6.023573475041126e-08,
                8.764254764749753e-08,
                3.653485128931788e-08,
                6.825598842035714e-08,
                6.825608606148807e-08,
                3.653479031523475e-08
            ],
            [
                2.8453371023563735e-08,
                2.9023119851899796e-06,
                7.338209805250744e-07,
                2.2603248367949354e-06,
                5.422220909041528e-06,
                8.315278294114555e-07,
                2.5612834320563895e-06,
                1.209865539298447e-06,
                4.450850519409479e-07,
                1.5534979397829198e-06
            ],
            [
                1.3709570433885908e-06,
                1.0677033791495609e-06,
                9.422447062270609e-07,
                8.315279285351409e-07,
                2.5612816000331606e-06,
                1.7603436329714805e-06,
                3.2887494572095624e-06,
                1.06770312455264e-06,
                1.2098658277451275e-06,
                2.699578096403948e-07
            ],
            [
                9.931195693628605e-08,
                3.0590237279085045e-07,
                1.0677033791495609e-06,
                5.715006514167015e-07,
                5.715004470313855e-07,
                5.043473480766399e-07,
                1.3709572068179446e-06,
                1.067703251864202e-06,
                1.4449807263312446e-07,
                1.5534977545102382e-06
            ],
            [
                3.2887482811579057e-06,
                2.56128159999123e-06,
                3.2887482811908074e-06,
                8.31527928532683e-07,
                2.902313022984344e-06,
                4.222833947728508e-06,
                1.5534973841309562e-06,
                2.260325375650449e-06,
                2.9023123308072772e-06,
                1.0677029973056687e-06
            ],
            [
                5.715007195447234e-07,
                1.2098661162023305e-06,
                9.422444815726566e-07,
                2.3823693839290317e-07,
                0.999998446502246,
                1.9947294837154625e-06,
                6.825598842065202e-08,
                2.1024336609843824e-07,
                0.999997097688708,
                0.999996033013142
            ],
            [
                6.475947982037486e-07,
                3.0590226339061185e-07,
                4.4508505193932864e-07,
                1.637377643243723e-07,
                2.1024336609843824e-07,
                6.475947210012481e-07,
                2.9023112932177327e-06,
                4.450852111148132e-07,
                2.382370235933104e-07,
                3.9278634073732336e-07
            ],
            [
                6.475946438022905e-07,
                0.9999991148427533,
                3.65348425788669e-08,
                9.422450431912e-07,
                0.9999987901347499,
                7.734418542875216e-08,
                6.475947982037486e-07,
                5.315784971839039e-08,
                0.9999687980924505,
                1.9555697023957287e-08
            ],
            [
                4.450850519409479e-07,
                1.3709573702856596e-06,
                4.4508499888275247e-07,
                3.288749849529972e-06,
                2.2603242978943238e-06,
                2.9023109472494878e-06,
                5.422221555414699e-06,
                2.699577130960941e-07,
                1.760343633036322e-06,
                5.043475885696228e-07
            ],
            [
                4.691162683297406e-08,
                1.4449802095666915e-07,
                0.9999985406239534,
                3.4663274507713016e-07,
                8.315277302857965e-07,
                0.9999960330136152,
                1.4449798650551755e-07,
                0.9999998257021214,
                0.9999957771655515,
                0.9999925887174872
            ],
            [
                3.224187017649346e-08,
                1.1253513522447425e-07,
                2.2159470790999714e-08,
                6.825601283086733e-08,
                7.734421308914719e-08,
                5.3157837044597743e-08,
                7.338210679979539e-07,
                6.023577065363335e-08,
                5.315784971839039e-08,
                1.1253525596174225e-07
            ],
            [
                3.927863875616689e-07,
                5.715006514176113e-07,
                4.450852641737424e-07,
                1.8553914607267268e-07,
                2.3823690999323465e-07,
                1.2751908849167202e-07,
                1.8553905760062447e-07,
                1.637377448057981e-07,
                3.466326624336003e-07,
                3.927862002663297e-07
            ],
            [
                2.699577774589574e-07,
                5.715007195447234e-07,
                1.5534984953298217e-06,
                0.999999814460854,
                7.338211554801876e-07,
                1.6373774480605869e-07,
                9.422443692555439e-07,
                5.715002426460124e-07,
                1.2098659719716573e-06,
                1.7603438428460541e-06
            ],
            [
                4.139941495546278e-08,
                6.825608606172863e-08,
                6.825597214718257e-08,
                8.7642558095602e-08,
                3.0590237279085045e-07,
                1.1253509497883659e-07,
                2.3823690999323465e-07,
                3.653485128944664e-08,
                3.653479902594117e-08,
                1.4449803818215767e-07
            ],
            [
                0.9999986290427936,
                1.3709572068422585e-06,
                8.315283250343497e-07,
                1.4449800373118268e-07,
                7.338211554813555e-07,
                0.9999995262094986,
                0.9999987121043242,
                0.9999980052707548,
                0.999997097686632,
                9.931187406410953e-08
            ],
            [
                6.023573475041126e-08,
                7.338207180838067e-07,
                3.653479031538012e-08,
                1.5534977545603963e-06,
                2.2603245673155757e-06,
                1.994730197071414e-06,
                1.3709576971160984e-06,
                8.315277302701984e-07,
                1.553498495338299e-06,
                1.3709568799679844e-06
            ],
            [
                2.102434162245973e-07,
                9.93120161310289e-08,
                2.699578740032504e-07,
                1.2751902768612997e-07,
                1.275190580890061e-07,
                2.3823690999323465e-07,
                4.4508515805735777e-07,
                4.450852111155216e-07,
                1.27519088491875e-07,
                2.382370235933104e-07
            ],
            [
                2.699576809143613e-07,
                8.315277302841894e-07,
                7.338208930460318e-07,
                1.3709568799919866e-06,
                9.931195693628605e-08,
                6.475949526020042e-07,
                8.764244316973974e-08,
                9.931189774187203e-08,
                1.0677028700422047e-06,
                3.6534807736504303e-08
            ],
            [
                3.2887498494551953e-06,
                5.043476486924565e-07,
                1.994729959270648e-06,
                4.450852641737424e-07,
                4.7850933538313875e-06,
                1.5534975693869924e-06,
                1.6373774480605869e-07,
                8.315283250343497e-07,
                1.9947299592570416e-06,
                3.726640172537657e-06
            ],
            [
                6.825604537781398e-08,
                7.338208930443633e-07,
                9.93120161306789e-08,
                1.370957860567974e-06,
                2.561283431942246e-06,
                1.8553916819032217e-07,
                9.931193325852072e-08,
                7.338211554758494e-07,
                8.764242227418718e-08,
                1.5534975693707442e-06
            ],
            [
                2.5110005893648856e-08,
                1.9555699355175906e-08,
                1.6373766672888118e-07,
                3.653485128931788e-08,
                8.764244316973974e-08,
                2.699577774585891e-07,
                7.734418542875216e-08,
                1.2751904288710323e-07,
                6.023578501491997e-08,
                4.450852641737424e-07
            ],
            [
                1.8553907971758842e-07,
                1.0677029973219343e-06,
                9.422450432030903e-07,
                4.4508526417298334e-07,
                4.450851049991497e-07,
                2.6995784182140636e-07,
                1.9947304348862686e-06,
                3.927863407379485e-07,
                8.315278294114555e-07,
                4.4508515805735777e-07
            ],
            [
                4.1399375473868e-08,
                2.3823690999160957e-07,
                6.023573475041126e-08,
                9.931200429181105e-08,
                6.023569884718319e-08,
                9.931195693628605e-08,
                5.315789407685159e-08,
                5.3157811697009444e-08,
                8.764249540862797e-08,
                7.734421308914719e-08
            ],
            [
                0.9999955048173522,
                1.2098655392662613e-06,
                1.0677029972993568e-06,
                2.2603242978665707e-06,
                1.2098659719716573e-06,
                1.2098655392811161e-06,
                1.2098655392871682e-06,
                1.7603432133032607e-06,
                7.338211554758494e-07,
                1.2098661161927025e-06
            ],
            [
                1.9555694692738946e-08,
                5.3157837044597743e-08,
                4.6911677163762064e-08,
                3.653485564473625e-08,
                6.825609419848033e-08,
                2.511001487368099e-08,
                5.3157830707696514e-08,
                3.653479031538012e-08,
                3.2241889394209404e-08,
                4.1399365603508136e-08
            ],
            [
                2.699577452733192e-07,
                0.9999993916406733,
                0.9999990577549571,
                0.9999989969862709,
                0.9999980052693281,
                0.999998239657207,
                0.9999990577552941,
                0.9999990577557434,
                0.9999994284993488,
                1.8553907971758842e-07
            ],
            [
                1.760344052693435e-06,
                1.55349775456958e-06,
                1.5534983101644536e-06,
                9.42244256915735e-07,
                1.7603430034867993e-06,
                4.4508515805735777e-07,
                9.422443692489024e-07,
                1.5534971990169383e-06,
                1.5534984953552536e-06,
                7.33821330437595e-07
            ],
            [
                2.6995790618469934e-07,
                0.9999964991443351,
                0.9999987901347495,
                0.9999960330131418,
                1.4449803818215767e-07,
                0.999997739676242,
                5.043476486924565e-07,
                0.9999960330145594,
                6.825601283086733e-08,
                3.466325384678894e-07
            ],
            [
                1.2751904288710323e-07,
                8.764249540862797e-08,
                1.6373776432509826e-07,
                2.845334728018925e-08,
                8.764241182641775e-08,
                4.691162124067829e-08,
                6.023576347299818e-08,
                4.1399365603508136e-08,
                6.825601283086733e-08,
                8.764244316973974e-08
            ],
            [
                6.825601283086733e-08,
                3.05902190458764e-07,
                2.1024331597262577e-07,
                1.6373766672973748e-07,
                2.1024331597262577e-07,
                1.8553914607267268e-07,
                2.6995790618469934e-07,
                2.1024329090929374e-07,
                2.382368531929327e-07,
                1.637377057673536e-07
            ],
            [
                7.338210679816025e-07,
                1.7603436329394601e-06,
                1.0677027427569065e-06,
                1.9947306726049992e-06,
                2.260324567268294e-06,
                2.561281294558644e-06,
                7.3382080556433e-07,
                3.2887490652810324e-06,
                4.785096205973894e-06,
                1.3709570434250617e-06
            ],
            [
                2.561282821352716e-06,
                1.2098652508056196e-06,
                2.144494585747154e-05,
                0.999998346310612,
                0.9999949062962169,
                0.9999964991439201,
                2.260325375650449e-06,
                0.9999977396754345,
                2.2603237589028734e-06,
                1.7603434231241496e-06
            ],
            [
                9.422449308673789e-07,
                1.5534983100425914e-06,
                1.3709568799760888e-06,
                1.7603434231097403e-06,
                3.2887482811220126e-06,
                3.288749065209246e-06,
                1.067703379136937e-06,
                2.2603237588597026e-06,
                5.715006514105942e-07,
                1.0677028700422047e-06
            ],
            [
                1.3709576971379186e-06,
                1.0677032518578904e-06,
                1.2098652508347793e-06,
                1.0677031245905116e-06,
                9.422450431989127e-07,
                5.04347468323289e-07,
                2.561283126639892e-06,
                1.3709570434122812e-06,
                1.6373774480605869e-07,
                1.0677029973056687e-06
            ],
            [
                6.47594566597747e-07,
                7.338209805133949e-07,
                1.5534971989907999e-06,
                1.5534983100595462e-06,
                1.3709568799592562e-06,
                5.715005151574337e-07,
                1.3709568799368123e-06,
                1.7603434231385591e-06,
                2.902311984989368e-06,
                7.338207180801359e-07
            ],
            [
                1.4449795205472734e-07,
                3.9278620026686556e-07,
                4.139940508508409e-08,
                1.8553910183674878e-07,
                6.82560779249779e-08,
                2.1024334103581732e-07,
                1.1253525596174225e-07,
                8.315279285370317e-07,
                1.1253526937697666e-07,
                1.5534981249697903e-06
            ],
            [
                0.9999972735300561,
                0.999998346310612,
                0.9999987121052456,
                0.9999984465026165,
                0.999997273529082,
                0.9999974387184012,
                0.9999985406241279,
                0.999998712105092,
                0.9999987121049383,
                7.338210679979539e-07
            ],
            [
                2.260324028404236e-06,
                7.338211554758494e-07,
                9.422450431954847e-07,
                1.2098653950403334e-06,
                2.2603251062147097e-06,
                5.043475885634304e-07,
                3.2887478889513447e-06,
                1.7603425836870455e-06,
                1.2098652508056196e-06,
                7.338207180838067e-07
            ],
            [
                1.1253526937697666e-07,
                9.93120161310289e-08,
                1.275190428875671e-07,
                9.931195693628605e-08,
                2.1024331597262577e-07,
                1.3709572068422585e-06,
                1.4449795205472734e-07,
                1.1253526937697666e-07,
                5.315781803390236e-08,
                2.5612812945889277e-06
            ],
            [
                0.9999991148431755,
                1.4738985482753428e-05,
                0.9999972735307056,
                1.3709575337016483e-06,
                9.422445938917108e-07,
                0.9999925887210216,
                8.315283250343497e-07,
                2.561283126679493e-06,
                4.222831934321543e-06,
                1.994730434798734e-06
            ],
            [
                1.4449805540763184e-07,
                1.637377057680051e-07,
                1.0677027427600627e-06,
                1.8553910183674878e-07,
                1.6373766672973748e-07,
                3.927863875616689e-07,
                1.0677029973219343e-06,
                1.3709575337125585e-06,
                5.715003107767143e-07,
                3.05902190458764e-07
            ],
            [
                9.931202796993203e-08,
                6.023571320847322e-08,
                5.3157900413760374e-08,
                1.27519088491875e-07,
                8.764247451307293e-08,
                5.715005832872586e-07,
                9.931193325852072e-08,
                7.734418542875216e-08,
                1.6373774480605869e-07,
                1.6373764721072816e-07
            ],
            [
                1.4449796928021588e-07,
                1.994729721482609e-06,
                7.734421308914719e-08,
                9.422445939002803e-07,
                7.338213304283347e-07,
                2.9023112931688987e-06,
                1.7603432133136672e-06,
                9.422445938964242e-07,
                1.7603427936079236e-06,
                8.315277302841894e-07
            ],
            [
                0.9999916019249689,
                1.2098653950606901e-06,
                1.5534979397592542e-06,
                1.5534979397592542e-06,
                1.9947306726594253e-06,
                2.1024331597262577e-07,
                1.2751905808881762e-07,
                1.994729483680993e-06,
                1.2098655392871682e-06,
                2.26032402841657e-06
            ],
            [
                2.3823685319244518e-07,
                1.4449798650551755e-07,
                1.637377448057981e-07,
                1.444980726324838e-07,
                3.059021539909339e-07,
                8.764247451307293e-08,
                2.1024344128584085e-07,
                3.05902263389638e-07,
                6.144173869603344e-06,
                1.2751899728286965e-07
            ],
            [
                4.450849458218309e-07,
                0.9999962733598301,
                9.931186222523604e-08,
                0.9999977396765116,
                NaN,
                0.9999967112497603,
                0.9999969105066595,
                0.9999910603037089,
                2.6995784182140636e-07,
                0.9999991684718736
            ],
            [
                1.2098659719716573e-06,
                2.902311639183378e-06,
                2.260325375650449e-06,
                4.222834954687752e-06,
                2.902312677084523e-06,
                1.3709578605617394e-06,
                0.9999992661786697,
                9.422444815679433e-07,
                0.9999985406243014,
                6.47594566597747e-07
            ],
            [
                7.338207180898968e-07,
                6.475946438055299e-07,
                3.927861534431675e-07,
                0.9999997463981938,
                1.444980209564556e-07,
                1.855391239547094e-07,
                1.8553903548231313e-07,
                1.3709575337159875e-06,
                2.382369383923073e-07,
                6.825597214718257e-08
            ],
            [
                1.1253516205489029e-07,
                9.931190958076104e-08,
                1.1253513522447425e-07,
                6.023574911170301e-08,
                6.02357921955714e-08,
                1.2751905808881762e-07,
                9.931193325852072e-08,
                9.931186222523604e-08,
                1.6373770576776313e-07,
                5.3157830707696514e-08
            ],
            [
                0.9999885212264118,
                1.2098652508287273e-06,
                1.7603436330091044e-06,
                2.5612831265630198e-06,
                1.99472924590571e-06,
                8.31527928532683e-07,
                7.734414854823498e-08,
                1.8553919030858602e-07,
                9.931185038635267e-08,
                1.2098662604049616e-06
            ],
            [
                9.422450431860582e-07,
                9.422445938917108e-07,
                8.315282259089153e-07,
                1.0677028700320085e-06,
                1.994730434798734e-06,
                1.0677028700320085e-06,
                1.3709570433885908e-06,
                1.3709578605118645e-06,
                1.2098652508144226e-06,
                2.2603253755949437e-06
            ],
            [
                1.7603425837903113e-06,
                3.059022998576899e-07,
                1.8553907971879076e-07,
                1.209865827752005e-06,
                3.927862470905692e-07,
                7.734426841017797e-08,
                5.715006514176113e-07,
                7.33821330437595e-07,
                3.927863875616689e-07,
                6.475946438055299e-07
            ],
            [
                1.4449803818215767e-07,
                2.699577774589574e-07,
                8.764249540862797e-08,
                3.4663249714612693e-07,
                0.9999982396569973,
                3.05902263391829e-07,
                4.691161005609407e-08,
                7.734428685047173e-08,
                8.764242227418718e-08,
                6.825597214718257e-08
            ],
            [
                6.023576347299818e-08,
                1.0677033791612137e-06,
                1.444980726324838e-07,
                4.139935079796334e-08,
                1.444979692800516e-07,
                2.699576809143613e-07,
                4.1399375473868e-08,
                7.734415776805048e-08,
                8.764240137829087e-08,
                1.1253520229983549e-07
            ],
            [
                0.9999986290427935,
                0.9999999317439303,
                1.27519088491875e-07,
                1.1253514863968147e-07,
                0.9999998555019274,
                1.1253506814842375e-07,
                6.023569166654288e-08,
                1.6373774480605869e-07,
                1.1253524254650944e-07,
                0.9999994284995531
            ],
            [
                5.3157811697009444e-08,
                5.3157900413760374e-08,
                4.4508494582405734e-07,
                1.1253506814842375e-07,
                2.102434162245973e-07,
                0.9999990577549571,
                1.4449805540740185e-07,
                1.855391239544352e-07,
                6.825597214718257e-08,
                1.275191036933194e-07
            ],
            [
                0.9999991684722699,
                0.9999985406230836,
                0.9999995549147359,
                0.9999996743687809,
                0.9999987121041706,
                0.9999981261239468,
                0.9999987121041707,
                0.9999998024946095,
                0.9999993916406733,
                0.9999988634360186
            ],
            [
                7.33821330437595e-07,
                4.785093924389007e-06,
                3.2887494574832472e-06,
                1.0677028700422047e-06,
                7.338211554813555e-07,
                2.2603242978943238e-06,
                7.338207180898968e-07,
                1.994729008151319e-06,
                1.9947292459406333e-06,
                9.422442569334097e-07
            ],
            [
                1.9947301970106386e-06,
                0.999990483751723,
                0.9999955048194968,
                0.999964643757835,
                0.9999996533673378,
                0.9999997463980125,
                0.9999991148428591,
                0.9999990577557434,
                0.9999997126314126,
                0.9999978766205265
            ],
            [
                0.9999981261237235,
                0.999998346309626,
                0.9999990577556309,
                0.999994577781032,
                0.9999983463104146,
                0.9999942280785966,
                0.9999967112517207,
                0.9999996533673376,
                0.9999985406239534,
                0.9999986290432842
            ],
            [
                1.8553919030858602e-07,
                2.3823702359290413e-07,
                1.6373762769138607e-07,
                2.69957906184239e-07,
                2.699578740032504e-07,
                2.6995784182140636e-07,
                2.102434162245973e-07,
                3.927863407379485e-07,
                9.931189774187203e-08,
                2.102434162245973e-07
            ],
            [
                1.9947306726213275e-06,
                9.42244930849811e-07,
                1.2098659719601033e-06,
                1.5534975693347152e-06,
                1.2098653950606901e-06,
                1.7603432133032607e-06,
                1.2098662603862553e-06,
                1.0677024881941248e-06,
                0.9999987901341727,
                1.5534971988904843e-06
            ]
        ]
    },
    {
        "q_id": "9455_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            24,
            25,
            26,
            27,
            29,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            52,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            68,
            69,
            71,
            73,
            75,
            76,
            77,
            78,
            80,
            81,
            82,
            83,
            86,
            87,
            88,
            89,
            90,
            92,
            93,
            94,
            95,
            96,
            98,
            99,
            100,
            101,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            123,
            124,
            127
        ],
        "rewards": [
            [
                2.102434162245973e-07,
                1.4449805540740185e-07,
                1.2751901248454963e-07,
                8.764241182641775e-08,
                1.275190276859705e-07,
                1.1253512180925583e-07,
                9.931189774187203e-08,
                2.102434412875379e-07,
                2.699576809143613e-07,
                2.1024339116168358e-07
            ],
            [
                3.927862939126708e-07,
                1.6373766672973748e-07,
                2.69957906184239e-07,
                5.043474081993875e-07,
                4.450848927658745e-07,
                1.6373766672973748e-07,
                1.1253509497883659e-07,
                2.1024341622426268e-07,
                3.9278605979534166e-07,
                3.466327037539638e-07
            ],
            [
                4.2228334445658276e-06,
                3.726641061109272e-06,
                1.2098655392871682e-06,
                1.7603427936079236e-06,
                4.785093353909723e-06,
                1.0677026154730804e-06,
                1.0677026154806063e-06,
                1.7603427936263351e-06,
                2.9023126771227976e-06,
                4.2228329411708495e-06
            ],
            [
                3.4663274507713016e-07,
                2.1024331597262577e-07,
                1.2751899728286965e-07,
                6.825601283086733e-08,
                2.102433660979124e-07,
                1.4449795205429202e-07,
                1.1253509497835043e-07,
                1.1253520230052635e-07,
                1.1253518888531272e-07,
                1.6373774480535133e-07
            ],
            [
                5.715005151606823e-07,
                3.927861066170637e-07,
                3.927860597945825e-07,
                5.04347528446051e-07,
                1.7603425837855082e-06,
                2.6995784182140636e-07,
                7.338209805224048e-07,
                3.0590226339061185e-07,
                4.450852111148132e-07,
                3.466325797888292e-07
            ],
            [
                1.444980209564556e-07,
                1.4449795205429202e-07,
                1.855391239544352e-07,
                4.691162124067829e-08,
                1.1253513522447425e-07,
                1.1253516205489029e-07,
                1.2751899728286965e-07,
                1.2751908849167202e-07,
                9.931189774187203e-08,
                2.69957906184239e-07
            ],
            [
                5.715005832886879e-07,
                3.9278615344178325e-07,
                6.475950298011458e-07,
                3.466327863983311e-07,
                5.04347528446051e-07,
                3.9278634073732336e-07,
                3.4663249714451116e-07,
                5.043476486915964e-07,
                1.0677032518785256e-06,
                1.3709575337078829e-06
            ],
            [
                1.4449800373065699e-07,
                1.2751908849167202e-07,
                5.315788140303327e-08,
                7.734418542875216e-08,
                3.224184327183648e-08,
                4.691167157146029e-08,
                6.825600469412533e-08,
                2.3823682479292225e-07,
                1.125352291309328e-07,
                4.139941495546278e-08
            ],
            [
                5.315786239218605e-08,
                1.4449798650551755e-07,
                1.444980209564556e-07,
                5.315784971839039e-08,
                9.931189774187203e-08,
                7.734421308914719e-08,
                1.1253513522447425e-07,
                1.2751905808881762e-07,
                3.9278615344178325e-07,
                1.1253512180925583e-07
            ],
            [
                7.338211554783522e-07,
                3.059021904571643e-07,
                2.699578096393206e-07,
                5.043475885674441e-07,
                8.315283250371857e-07,
                8.315279285351409e-07,
                3.927862002641863e-07,
                3.9278615344178325e-07,
                3.466327863983311e-07,
                3.9278615344178325e-07
            ],
            [
                2.902312331170226e-06,
                2.382369667929001e-07,
                2.6995784182140636e-07,
                3.466327450765785e-07,
                1.855391239544352e-07,
                3.9278610661902853e-07,
                3.466326211113502e-07,
                3.4663278639892215e-07,
                4.450852111155216e-07,
                2.699577774585891e-07
            ],
            [
                3.9278610661902853e-07,
                5.715003788993679e-07,
                8.315278294038928e-07,
                5.043476486902204e-07,
                3.466325384661554e-07,
                1.8553907971855875e-07,
                4.450852111135988e-07,
                1.8553919030826963e-07,
                3.059021539909339e-07,
                3.466326211113502e-07
            ],
            [
                1.275190732904469e-07,
                6.023572038912295e-08,
                6.825604537781398e-08,
                6.825602910433871e-08,
                6.825608606148807e-08,
                5.315784971839039e-08,
                4.139938534423022e-08,
                4.6911638017556955e-08,
                4.139935079796334e-08,
                5.3157830707696514e-08
            ],
            [
                4.450848927621807e-07,
                8.315284241597959e-07,
                7.338208930391909e-07,
                5.043475284430694e-07,
                7.338211554783522e-07,
                6.475951069985296e-07,
                9.422448185510695e-07,
                9.422448185478557e-07,
                6.475948753930064e-07,
                6.475948754012522e-07
            ],
            [
                4.4508510499849186e-07,
                2.1024336609843824e-07,
                2.1024341622426268e-07,
                2.102433410343832e-07,
                3.466327037539638e-07,
                3.466327037539638e-07,
                1.8553903548231313e-07,
                1.8553903548231313e-07,
                4.450852111148132e-07,
                2.382370235922541e-07
            ],
            [
                6.475951069985296e-07,
                1.9947304348703948e-06,
                1.994729245917502e-06,
                1.2098658277451275e-06,
                1.9947297215043796e-06,
                1.5534981249574276e-06,
                1.5534975693869924e-06,
                2.9023112932045342e-06,
                2.2603242978665707e-06,
                1.2098662604247682e-06
            ],
            [
                6.825604537781398e-08,
                1.1253521571574156e-07,
                6.825606165129312e-08,
                1.2751899728311609e-07,
                6.825600469412533e-08,
                8.764245361752286e-08,
                6.825598842065202e-08,
                1.1253506814842375e-07,
                9.931193325852072e-08,
                2.102434412875379e-07
            ],
            [
                2.6995784182140636e-07,
                2.382370235922541e-07,
                1.4449805540740185e-07,
                2.699578096393206e-07,
                3.4663262110945863e-07,
                1.8553910183607374e-07,
                1.855391239544352e-07,
                2.3823685319244518e-07,
                3.4663262110945863e-07,
                4.450848927650143e-07
            ],
            [
                2.561283432035425e-06,
                1.7603434231777837e-06,
                1.5534975693869924e-06,
                9.422443692555439e-07,
                3.288750241561788e-06,
                8.315277302841894e-07,
                1.2098659719757836e-06,
                1.3709567165579959e-06,
                2.2603234895289998e-06,
                2.2603234895289998e-06
            ],
            [
                6.475951069961737e-07,
                2.6995784182140636e-07,
                5.043472879540142e-07,
                3.059022269250683e-07,
                3.4663262110945863e-07,
                3.466325797888292e-07,
                7.338209805224048e-07,
                3.0590226339061185e-07,
                8.315278294072958e-07,
                3.9278615344178325e-07
            ],
            [
                8.315281267861397e-07,
                2.6995784182140636e-07,
                1.5534971990126997e-06,
                4.450852111135988e-07,
                3.927862939126708e-07,
                5.043475885674441e-07,
                6.475947210031623e-07,
                1.553497199007048e-06,
                6.475948754012522e-07,
                9.422448185510695e-07
            ],
            [
                1.0677032518748838e-06,
                6.475947210031623e-07,
                7.338209805224048e-07,
                1.0677029973158649e-06,
                9.4224425692559e-07,
                3.927863875584984e-07,
                7.338209805200689e-07,
                3.4663262110945863e-07,
                2.5612812947508257e-06,
                7.338208055664991e-07
            ],
            [
                1.444980209564556e-07,
                1.2751905808881762e-07,
                2.699577774585891e-07,
                1.6373776432509826e-07,
                1.8553905760062447e-07,
                2.102434412871794e-07,
                7.734421308914719e-08,
                5.043475885696228e-07,
                2.3823696679327928e-07,
                2.102434162245973e-07
            ],
            [
                5.043474081993875e-07,
                2.10243290909724e-07,
                5.043473480777865e-07,
                2.10243290909724e-07,
                2.1024331597262577e-07,
                2.6995774527718623e-07,
                3.9278634073732336e-07,
                4.4508494582314646e-07,
                2.382369667929001e-07,
                4.4508510499849186e-07
            ],
            [
                4.691162124067829e-08,
                1.1253506814842375e-07,
                1.6373766672973748e-07,
                6.825598842065202e-08,
                1.8553903548231313e-07,
                4.1399365603508136e-08,
                1.275190276859705e-07,
                8.764242227418718e-08,
                6.825604537781398e-08,
                1.6373762769138607e-07
            ],
            [
                5.315781803390236e-08,
                4.1399375473868e-08,
                6.023569884718319e-08,
                1.8553903548231313e-07,
                9.931189774187203e-08,
                2.102434412875379e-07,
                9.931187406410953e-08,
                1.1253512180925583e-07,
                4.139935079796334e-08,
                3.653479902594117e-08
            ],
            [
                5.715004470313855e-07,
                2.5612812947380135e-06,
                1.5534971990126997e-06,
                6.475948754012522e-07,
                9.422448185510695e-07,
                7.338207180864763e-07,
                8.315281267834927e-07,
                2.561281600076256e-06,
                1.067703124601679e-06,
                1.2098662604291696e-06
            ],
            [
                2.1024341622426268e-07,
                2.102434162245973e-07,
                2.1024331597262577e-07,
                8.764241182641775e-08,
                1.8553907971855875e-07,
                9.931195693628605e-08,
                1.6373766672973748e-07,
                6.825606165129312e-08,
                2.1024336609843824e-07,
                9.931193325852072e-08
            ],
            [
                1.637377057680051e-07,
                1.1253517547010071e-07,
                6.023569884718319e-08,
                1.4449803818215767e-07,
                7.734421308914719e-08,
                1.4449807263312446e-07,
                7.734418542875216e-08,
                3.927862002663297e-07,
                1.1253508156363576e-07,
                1.4449798650551755e-07
            ],
            [
                9.422448185510695e-07,
                1.3709568799919866e-06,
                1.0677032518785256e-06,
                1.2098659719757836e-06,
                5.715007195447234e-07,
                9.422445939032799e-07,
                9.422443692555439e-07,
                6.475945666051092e-07,
                6.475945666051092e-07,
                1.5534983101602148e-06
            ],
            [
                2.1024331597262577e-07,
                1.4449805540740185e-07,
                1.4449798650551755e-07,
                1.4449798650551755e-07,
                1.637377448057981e-07,
                2.3823693839290317e-07,
                3.927862470899887e-07,
                1.2751905808881762e-07,
                2.3823702359290413e-07,
                1.8553907971855875e-07
            ],
            [
                2.3823699519290042e-07,
                3.726639728370556e-06,
                5.043472879525233e-07,
                1.2098659719757836e-06,
                1.3709576971425944e-06,
                5.043474081993875e-07,
                1.0677032518785256e-06,
                1.2098658277451275e-06,
                9.422448185510695e-07,
                6.475948754012522e-07
            ],
            [
                8.764241182641775e-08,
                2.8453326928809566e-08,
                5.315781803390236e-08,
                4.691162124067829e-08,
                2.511001487368099e-08,
                4.1399375473868e-08,
                1.4449800373065699e-07,
                7.734423152941018e-08,
                6.825606165129312e-08,
                8.764245361752286e-08
            ],
            [
                8.764242227418718e-08,
                1.1253518888531272e-07,
                1.855391681906175e-07,
                2.699577774585891e-07,
                1.4449795205429202e-07,
                1.6373766672973748e-07,
                7.734428685047173e-08,
                8.764242227418718e-08,
                1.1253512180925583e-07,
                5.315787506598473e-08
            ],
            [
                2.3823685319244518e-07,
                1.8553916819032217e-07,
                2.102433660979124e-07,
                3.466325797888292e-07,
                3.05902190458764e-07,
                3.927862939126708e-07,
                4.450850519403407e-07,
                1.855391239544352e-07,
                1.2751899728311609e-07,
                2.69957906184239e-07
            ],
            [
                3.05902190458764e-07,
                2.6995784182140636e-07,
                6.475950298011458e-07,
                3.059022998576899e-07,
                5.043472278322555e-07,
                3.466325797888292e-07,
                3.466327863983311e-07,
                3.9278615344178325e-07,
                3.05902190458764e-07,
                3.466325797896173e-07
            ],
            [
                2.260324567337161e-06,
                8.315280276607289e-07,
                1.2098653950656417e-06,
                1.5534975693869924e-06,
                4.450852111135988e-07,
                5.715007195447234e-07,
                7.338208055664991e-07,
                1.7603440527286572e-06,
                9.422445939032799e-07,
                1.0677032518785256e-06
            ],
            [
                5.715007195447234e-07,
                1.5534981249697903e-06,
                1.2098659719757836e-06,
                7.338209805224048e-07,
                6.475947210046347e-07,
                1.209865539295696e-06,
                5.715007195447234e-07,
                3.059021175247079e-07,
                6.475949526020042e-07,
                4.450851580555361e-07
            ],
            [
                4.450851580555361e-07,
                8.315281267882195e-07,
                5.043476486915964e-07,
                3.466325797888292e-07,
                3.466327037539638e-07,
                2.382369667929001e-07,
                1.2098656835224664e-06,
                3.0590215399183813e-07,
                1.2098652508424818e-06,
                1.994729008145876e-06
            ],
            [
                1.8553919030858602e-07,
                2.3823685319244518e-07,
                2.382370235922541e-07,
                2.699578096403948e-07,
                7.734416698849138e-08,
                1.637377448057981e-07,
                7.73441946488886e-08,
                1.1253516205489029e-07,
                1.275190732904469e-07,
                1.1253509497883659e-07
            ],
            [
                1.855391239544352e-07,
                1.2751908849167202e-07,
                2.3823690999290963e-07,
                1.1253508156363576e-07,
                1.1253526937697666e-07,
                9.931193325852072e-08,
                9.931189774187203e-08,
                6.825600469412533e-08,
                3.9278615344178325e-07,
                1.444980209564556e-07
            ],
            [
                1.8553905760062447e-07,
                2.6995771309523475e-07,
                1.7603438428800754e-06,
                2.3823693839290317e-07,
                1.0677033791612137e-06,
                6.475947982037486e-07,
                1.855391239544352e-07,
                3.9278634073732336e-07,
                5.043476486915964e-07,
                3.4663266243308805e-07
            ],
            [
                5.715006514176113e-07,
                4.691159887151251e-08,
                5.04347468323289e-07,
                7.338208930443633e-07,
                1.2751899728311609e-07,
                5.715004470313855e-07,
                6.023578501513224e-08,
                1.4449807263312446e-07,
                3.927862470899887e-07,
                8.315284241650899e-07
            ],
            [
                1.8553905760062447e-07,
                1.275190732904469e-07,
                1.4449805540700758e-07,
                2.1024326584639497e-07,
                1.8553910183607374e-07,
                1.2751908849167202e-07,
                1.1253518888531272e-07,
                1.1253518888531272e-07,
                2.1024331597262577e-07,
                1.8553912395262116e-07
            ],
            [
                2.6995784182140636e-07,
                2.3823688159291947e-07,
                3.059023727894942e-07,
                2.1024326584639497e-07,
                3.059021904571643e-07,
                3.059022998576899e-07,
                1.8553907971855875e-07,
                2.382369951932796e-07,
                2.1024336609843824e-07,
                3.059022269250683e-07
            ],
            [
                3.224185480240153e-08,
                1.1253516205489029e-07,
                3.6534807736504303e-08,
                5.315781803390236e-08,
                1.1253514863909295e-07,
                6.023572038912295e-08,
                1.1253517547010071e-07,
                7.734418542875216e-08,
                4.1399375473868e-08,
                7.734418542875216e-08
            ],
            [
                2.382368531929327e-07,
                9.931195693628605e-08,
                1.2098652508424818e-06,
                9.931195693628605e-08,
                1.8553919030858602e-07,
                1.1253520230052635e-07,
                1.6373764721072816e-07,
                4.450848927658745e-07,
                1.8553914607267268e-07,
                1.8553907971855875e-07
            ],
            [
                7.73441946488886e-08,
                1.1253521571574156e-07,
                1.6373762769138607e-07,
                9.931189774187203e-08,
                1.1253516205489029e-07,
                1.6373766672973748e-07,
                2.10243290909724e-07,
                8.764247451307293e-08,
                1.2751905808881762e-07,
                1.2751899728286965e-07
            ],
            [
                1.8553903548231313e-07,
                7.734418542875216e-08,
                6.825601283086733e-08,
                1.444979692800516e-07,
                7.73441946488886e-08,
                1.2751905808881762e-07,
                9.931190958076104e-08,
                1.1253513522391131e-07,
                7.734418542875216e-08,
                1.275190732904469e-07
            ],
            [
                3.466327037539638e-07,
                9.422450431989127e-07,
                3.0590215399183813e-07,
                2.561282210740037e-06,
                3.927862939126708e-07,
                3.9278615344178325e-07,
                6.475948754012522e-07,
                7.338208930391909e-07,
                3.0590215399183813e-07,
                4.4508505193932864e-07
            ],
            [
                1.6373762769138607e-07,
                1.1253513522447425e-07,
                1.1253518888531272e-07,
                7.734423152941018e-08,
                9.931189774187203e-08,
                1.1253513522447425e-07,
                3.4663266243308805e-07,
                1.6373764721072816e-07,
                8.764244316973974e-08,
                9.931195693628605e-08
            ],
            [
                5.422218969818919e-06,
                8.939695238439078e-06,
                6.144177531660828e-06,
                2.5612822107167428e-06,
                6.144172404693786e-06,
                2.753568453712307e-05,
                1.994729245917502e-06,
                3.288749065406658e-06,
                2.2603242978665707e-06,
                1.3007131566015624e-05
            ],
            [
                3.0590226339061185e-07,
                3.0590237279085045e-07,
                2.6995771309523475e-07,
                3.05902263389638e-07,
                6.475947210012481e-07,
                7.338209805200689e-07,
                4.450852111148132e-07,
                3.0590226339061185e-07,
                3.05902226923399e-07,
                3.466327037539638e-07
            ],
            [
                5.043475885657239e-07,
                9.422443692489024e-07,
                1.0677032518785256e-06,
                1.994730434879465e-06,
                7.338207180864763e-07,
                9.422442569315887e-07,
                1.2098658277451275e-06,
                7.338211554783522e-07,
                4.4508505193932864e-07,
                1.0677032518700286e-06
            ],
            [
                1.1253516205489029e-07,
                1.2751905808881762e-07,
                1.444979692800516e-07,
                2.6995774527718623e-07,
                1.444980209564556e-07,
                3.4663266243308805e-07,
                2.699576809143613e-07,
                2.3823688159291947e-07,
                1.8553916819032217e-07,
                1.855391239544352e-07
            ],
            [
                2.699576809143613e-07,
                2.3823688159291947e-07,
                1.2751908849167202e-07,
                2.10243290909724e-07,
                1.1253518888531272e-07,
                2.6995774527718623e-07,
                1.4449795205429202e-07,
                1.1253521571574156e-07,
                1.6373762769138607e-07,
                6.475945666051092e-07
            ],
            [
                1.5534975693869924e-06,
                7.338207180801359e-07,
                5.715003788993679e-07,
                8.31528126775552e-07,
                6.475949525981759e-07,
                1.2098661161927025e-06,
                8.315278294072958e-07,
                6.9622595694023114e-06,
                3.288748281295496e-06,
                3.7266383955882547e-06
            ],
            [
                1.8553907971855875e-07,
                1.7603438428740716e-06,
                3.466326211113502e-07,
                2.699577774585891e-07,
                2.3823690999290963e-07,
                3.059021175261338e-07,
                4.450850519403407e-07,
                3.9278634073732336e-07,
                2.102434412871794e-07,
                2.69957906184239e-07
            ],
            [
                1.4449796927932878e-07,
                1.8553903548231313e-07,
                5.04347528446051e-07,
                1.1253526937656726e-07,
                2.6995771309523475e-07,
                2.6995784182183607e-07,
                2.1024336609843824e-07,
                2.3823688159291947e-07,
                2.69957906184239e-07,
                8.7642516304188e-08
            ],
            [
                1.444980726324838e-07,
                1.6373774480535133e-07,
                2.902311985146426e-06,
                3.0590226339061185e-07,
                1.275190276859705e-07,
                2.3823685319244518e-07,
                4.53978902983119e-05,
                2.699576809143613e-07,
                1.6373770576776313e-07,
                2.3823696679230424e-07
            ],
            [
                3.466325797888292e-07,
                4.450848927650143e-07,
                3.927860597945825e-07,
                3.9278605979534166e-07,
                4.450849988811838e-07,
                5.715007195431641e-07,
                8.31527928532683e-07,
                3.927860597945825e-07,
                6.475948754012522e-07,
                3.4663266242969896e-07
            ],
            [
                1.637376862489725e-07,
                7.734416698849138e-08,
                1.275190276859705e-07,
                1.8553903548231313e-07,
                7.734414854823498e-08,
                1.855391681906175e-07,
                9.931195693628605e-08,
                1.8553903548231313e-07,
                1.1253516205489029e-07,
                1.1253518888531272e-07
            ],
            [
                9.422448185510695e-07,
                2.3823696679230424e-07,
                5.04347468318358e-07,
                1.3709568799919866e-06,
                5.04347348075149e-07,
                6.475947210012481e-07,
                7.338208055664991e-07,
                7.338209805224048e-07,
                5.71500515159253e-07,
                6.475947210012481e-07
            ],
            [
                1.6373774480605869e-07,
                9.931202796993203e-08,
                1.275190580890061e-07,
                1.444979692800516e-07,
                1.6373774480605869e-07,
                1.637377448057981e-07,
                3.9278610661902853e-07,
                2.6995784182140636e-07,
                8.764242227418718e-08,
                8.76424013786396e-08
            ],
            [
                1.5534984953453635e-06,
                1.5534979397740895e-06,
                4.450851580555361e-07,
                4.785095635592258e-06,
                7.338211554783522e-07,
                1.3709573702722555e-06,
                3.466327037539638e-07,
                1.6701415872385704e-05,
                5.715003789017068e-07,
                9.422448185478557e-07
            ],
            [
                8.764249540862797e-08,
                1.27519088491875e-07,
                9.931196877517082e-08,
                2.102434162245973e-07,
                1.2751901248454963e-07,
                9.931187406410953e-08,
                8.764242227418718e-08,
                6.825598842065202e-08,
                8.764244316973974e-08,
                6.825597214718257e-08
            ],
            [
                1.6373766672973748e-07,
                6.825601283086733e-08,
                1.1253516205489029e-07,
                7.734424996967756e-08,
                2.3823696679327928e-07,
                1.444979692800516e-07,
                1.2751905808881762e-07,
                1.2751905808881762e-07,
                3.466326211113502e-07,
                2.6995774527718623e-07
            ],
            [
                1.1253518888531272e-07,
                1.6373774480605869e-07,
                8.764249540862797e-08,
                1.2751908849167202e-07,
                0.9999990577551837,
                1.637377448057981e-07,
                1.2751901248454963e-07,
                8.764245361752286e-08,
                1.275190580890061e-07,
                1.125352291309328e-07
            ],
            [
                1.444980209564556e-07,
                9.931195693628605e-08,
                1.1253508156363576e-07,
                7.734416698849138e-08,
                1.2751901248454963e-07,
                8.764242227418718e-08,
                1.444979692800516e-07,
                2.1024336609843824e-07,
                7.734416698849138e-08,
                8.764244316973974e-08
            ],
            [
                3.059021539909339e-07,
                1.4449798650551755e-07,
                1.8553903548231313e-07,
                3.92786340734912e-07,
                1.4449798650551755e-07,
                2.3823702359290413e-07,
                2.1024341622426268e-07,
                2.382368531929327e-07,
                2.69957906184239e-07,
                3.059022269250683e-07
            ],
            [
                3.466327037539638e-07,
                2.1024336609843824e-07,
                5.715002426475718e-07,
                6.475950298011458e-07,
                5.715005832886879e-07,
                5.715003789046955e-07,
                2.3823685319244518e-07,
                5.715002426460124e-07,
                5.715002426475718e-07,
                1.5534971990126997e-06
            ],
            [
                3.059021904580685e-07,
                1.8553910183607374e-07,
                2.3823688159291947e-07,
                2.1024336609843824e-07,
                2.3823682479292225e-07,
                2.382369667929001e-07,
                1.4449805540740185e-07,
                3.059021175261338e-07,
                1.6373764721072816e-07,
                3.059022998576899e-07
            ],
            [
                2.3823690999290963e-07,
                9.4224425692559e-07,
                3.927862470899887e-07,
                8.3152792852928e-07,
                3.927863875616689e-07,
                6.475945666033422e-07,
                4.4508510499737865e-07,
                2.6995787400282076e-07,
                6.475947210031623e-07,
                6.475948753991907e-07
            ],
            [
                6.475948754012522e-07,
                3.0590237279032884e-07,
                2.699576809143613e-07,
                1.6373766672973748e-07,
                1.3709575337078829e-06,
                3.466325797896173e-07,
                3.9278610661902853e-07,
                3.059021175261338e-07,
                2.10243290909724e-07,
                3.9278605979534166e-07
            ],
            [
                1.6373762769138607e-07,
                3.466325797888292e-07,
                2.1024336609843824e-07,
                5.715007195447234e-07,
                1.9947292459347367e-06,
                1.8553907971855875e-07,
                1.637377448057981e-07,
                3.0590237279032884e-07,
                6.475947210046347e-07,
                8.315284241650899e-07
            ],
            [
                7.734421308914719e-08,
                8.764247451307293e-08,
                1.4449803818215767e-07,
                7.734423152941018e-08,
                1.6373768624837685e-07,
                2.3823693839290317e-07,
                8.764242227418718e-08,
                8.764247451307293e-08,
                1.4449798650551755e-07,
                4.4508494582405734e-07
            ],
            [
                5.043474683240344e-07,
                NaN,
                NaN,
                1.6373764721091427e-07,
                3.466326624336003e-07,
                1.4449800373118268e-07,
                2.561283126728994e-06,
                9.422443692574719e-07,
                1.2098652508448203e-06,
                8.315277302857965e-07
            ],
            [
                1.2751899728311609e-07,
                1.2751899728286965e-07,
                2.10243290909724e-07,
                3.466327037539638e-07,
                1.8553907971855875e-07,
                3.466325797896173e-07,
                7.734423152941018e-08,
                1.8553919030858602e-07,
                1.1253509497883659e-07,
                3.05902336324494e-07
            ],
            [
                1.855391239544352e-07,
                3.059022269250683e-07,
                3.927862002663297e-07,
                3.466325797896173e-07,
                2.1024331597262577e-07,
                2.6995771309523475e-07,
                1.6373768624837685e-07,
                2.69957906184239e-07,
                6.475948754012522e-07,
                2.6995784182140636e-07
            ],
            [
                2.6995771309523475e-07,
                5.715004470313855e-07,
                5.715004470313855e-07,
                3.059023727894942e-07,
                3.466325384661554e-07,
                6.475951069985296e-07,
                3.9278615344178325e-07,
                3.466327863961242e-07,
                9.422448185510695e-07,
                3.0590237279032884e-07
            ],
            [
                1.8553907971855875e-07,
                2.1024331597262577e-07,
                9.93120161306789e-08,
                1.4449805540763184e-07,
                1.444979692800516e-07,
                3.466325797896173e-07,
                4.4508494582405734e-07,
                3.0590237279032884e-07,
                8.764244316973974e-08,
                1.1253512180925583e-07
            ],
            [
                1.1253512180925583e-07,
                1.275191036933194e-07,
                2.1024331597262577e-07,
                1.4449807263312446e-07,
                8.764244316973974e-08,
                1.2751899728311609e-07,
                2.102434412875379e-07,
                7.734418542875216e-08,
                1.444979692800516e-07,
                1.275190428875671e-07
            ],
            [
                3.927862470899887e-07,
                8.315277302841894e-07,
                2.382369667929001e-07,
                7.338213304363436e-07,
                2.382368531929327e-07,
                2.1024331597262577e-07,
                4.4508494582405734e-07,
                4.450848927658745e-07,
                2.1024329090929374e-07,
                3.466325797888292e-07
            ],
            [
                6.475949525981759e-07,
                1.0677032518748838e-06,
                1.2098658277451275e-06,
                1.3709575337078829e-06,
                7.338207180864763e-07,
                1.2098655392871682e-06,
                1.0677032518748838e-06,
                5.043472879540142e-07,
                1.5534979397740895e-06,
                5.715004470313855e-07
            ],
            [
                1.8553903548231313e-07,
                3.466327450765785e-07,
                2.382369667929001e-07,
                3.0590237279032884e-07,
                3.0590237279085045e-07,
                1.8553916819032217e-07,
                7.338212429582604e-07,
                1.4449800373065699e-07,
                2.10243290909724e-07,
                1.8553905760062447e-07
            ],
            [
                3.927862002663297e-07,
                2.1024336609843824e-07,
                3.466327450765785e-07,
                8.315281267882195e-07,
                1.637377448057981e-07,
                1.8553903548231313e-07,
                2.6995771309523475e-07,
                2.3823685319244518e-07,
                5.715007195447234e-07,
                1.6373768624837685e-07
            ],
            [
                3.059022998576899e-07,
                2.1024331597262577e-07,
                1.4449798650551755e-07,
                9.931193325852072e-08,
                2.699578096403948e-07,
                5.715005151606823e-07,
                3.927860597945825e-07,
                2.6995771309523475e-07,
                1.6373770576776313e-07,
                1.6373766672973748e-07
            ],
            [
                5.043475885696228e-07,
                3.466327037553825e-07,
                5.043476486902204e-07,
                2.6995784182140636e-07,
                3.4663249714451116e-07,
                1.8553919030858602e-07,
                7.338212429582604e-07,
                2.6995784182140636e-07,
                3.059021175261338e-07,
                3.9278634073732336e-07
            ],
            [
                1.8553910183607374e-07,
                2.699578096393206e-07,
                2.1024326584639497e-07,
                5.043474683204221e-07,
                2.1024341622426268e-07,
                1.6373762769138607e-07,
                1.637377448057981e-07,
                1.637377448057981e-07,
                2.3823688159291947e-07,
                2.1024336609843824e-07
            ],
            [
                1.2751901248454963e-07,
                2.1024339116134898e-07,
                1.6373772528704005e-07,
                1.2751899728286965e-07,
                8.764241182641775e-08,
                2.102434162245973e-07,
                4.450852111155216e-07,
                2.1024326584639497e-07,
                1.8553910183674878e-07,
                2.1024336609843824e-07
            ],
            [
                1.1253509497883659e-07,
                2.1024331597262577e-07,
                1.4449798650569826e-07,
                1.27519088491875e-07,
                9.931193325852072e-08,
                8.764245361752286e-08,
                1.855391681906175e-07,
                9.931195693628605e-08,
                1.4449800373065699e-07,
                1.4449802095666915e-07
            ],
            [
                6.475947210046347e-07,
                2.1024336609843824e-07,
                3.0590226339061185e-07,
                2.699578740032504e-07,
                1.8553916819032217e-07,
                2.6995774527718623e-07,
                3.4663274507713016e-07,
                2.6995774527718623e-07,
                4.450852111155216e-07,
                5.715005151606823e-07
            ],
            [
                3.0590215399183813e-07,
                3.466326211113502e-07,
                2.382368531929327e-07,
                1.0677032518785256e-06,
                5.715007195431641e-07,
                8.315277302841894e-07,
                3.466325797888292e-07,
                5.043475885688201e-07,
                3.9278634073732336e-07,
                7.338208055664991e-07
            ],
            [
                6.962257909785973e-06,
                6.47594952603035e-07,
                1.275190428875671e-07,
                5.715006514176113e-07,
                3.9278629391427843e-07,
                3.9278629391427843e-07,
                7.338207180898968e-07,
                4.4508515805735777e-07,
                7.338207180898968e-07,
                2.1024334103581732e-07
            ],
            [
                2.2603242978778778e-06,
                5.043472879504592e-07,
                2.260325106237323e-06,
                2.5612831266946347e-06,
                1.2098652508287273e-06,
                1.994729483705484e-06,
                4.2228334445658276e-06,
                7.338213304283347e-07,
                1.2098652508347793e-06,
                1.3709570434054234e-06
            ],
            [
                5.315784971839039e-08,
                7.734418542875216e-08,
                5.315784971839039e-08,
                4.1399375473868e-08,
                4.691161005609407e-08,
                1.6373764721072816e-07,
                8.764242227418718e-08,
                5.315784971839039e-08,
                9.931185038635267e-08,
                4.139935079796334e-08
            ],
            [
                8.315281267861397e-07,
                6.475948754012522e-07,
                3.927862939126708e-07,
                5.715007195431641e-07,
                6.475947210031623e-07,
                1.2098658277451275e-06,
                3.9278634073732336e-07,
                2.6995774527577444e-07,
                8.315278294072958e-07,
                7.338210679979539e-07
            ],
            [
                3.059022998576899e-07,
                5.04347528446051e-07,
                2.1024336609843824e-07,
                2.699578096393206e-07,
                2.3823688159291947e-07,
                2.6995784182140636e-07,
                1.6373772528704005e-07,
                3.466325797888292e-07,
                2.1024334103505245e-07,
                8.315284241560147e-07
            ],
            [
                3.4663274507713016e-07,
                3.4663253846718004e-07,
                5.04347528446051e-07,
                3.466327037539638e-07,
                1.8553907971855875e-07,
                3.0590237279032884e-07,
                1.8553907971855875e-07,
                7.734423152941018e-08,
                3.0590215399183813e-07,
                2.1024336609843824e-07
            ],
            [
                6.023576347299818e-08,
                4.691162124067829e-08,
                1.444980209564556e-07,
                9.931187406410953e-08,
                1.6373766672973748e-07,
                7.734424996967756e-08,
                1.6373774480605869e-07,
                6.023574911170301e-08,
                7.734424996967756e-08,
                9.931195693628605e-08
            ],
            [
                5.715004470313855e-07,
                1.0677028700363782e-06,
                9.4224425692559e-07,
                1.7603440527286572e-06,
                1.0677024881980089e-06,
                1.0677028700363782e-06,
                1.994730197090463e-06,
                1.2098658277451275e-06,
                8.315283250371857e-07,
                2.260325106237323e-06
            ],
            [
                3.4663249714451116e-07,
                3.0590222692437275e-07,
                2.699578096393206e-07,
                3.9278615344178325e-07,
                5.715003789033962e-07,
                3.05902190458764e-07,
                5.043472879525233e-07,
                3.4663266243308805e-07,
                1.6373764721072816e-07,
                3.059021175247079e-07
            ]
        ]
    },
    {
        "q_id": "9517_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.7603434231833873e-06,
                0.9999942280799796,
                0.00023050666077090176,
                9.422444815792981e-07,
                6.475950298011458e-07,
                0.9999724643024204,
                5.715003107755449e-07,
                1.8553914607267268e-07,
                0.9999996310113721,
                2.699577452775239e-07
            ],
            [
                0.9999990577554065,
                0.9999995818811275,
                0.9999942280779097,
                2.3823693839325527e-07,
                0.9999980052707552,
                1.994729721518893e-06,
                0.9999974387171812,
                0.999975699762193,
                4.785096206076165e-06,
                9.422442569315887e-07
            ],
            [
                0.9999989322972577,
                2.5612828213818346e-06,
                0.9999975938982366,
                0.9999989322971307,
                0.9999987901340288,
                7.338207180898968e-07,
                8.939693107288474e-06,
                5.1442238195844654e-05,
                0.9999997463980427,
                0.9999978766212855
            ],
            [
                6.475950298021765e-07,
                1.4449805540763184e-07,
                2.382369667929001e-07,
                1.444979692800516e-07,
                0.9999898700090297,
                6.1441767993788005e-06,
                8.315284241665078e-07,
                3.927862470905692e-07,
                1.2751902768612997e-07,
                1.4449798650569826e-07
            ],
            [
                3.120190393794438e-05,
                1.2098656835252174e-06,
                7.889261645427538e-06,
                1.5534973842076057e-06,
                2.5612834320563895e-06,
                3.2887502415767434e-06,
                4.22283545819819e-06,
                1.2098659719757836e-06,
                2.90231094723893e-06,
                4.222832437798974e-06
            ],
            [
                0.9999989322966214,
                4.450848927658745e-07,
                2.1024336609874897e-07,
                1.637377057680051e-07,
                0.9999960330155063,
                2.699576809143613e-07,
                0.9999982396563681,
                4.450848927658745e-07,
                0.9999978766210325,
                1.275190732904469e-07
            ],
            [
                6.962257079775324e-06,
                5.4222209089700225e-06,
                2.2603242978778778e-06,
                0.9999982396561584,
                5.715005832872586e-07,
                0.9999982396565789,
                0.9999964991443374,
                0.99999963101146,
                0.9999991684719732,
                3.4663266243308805e-07
            ],
            [
                0.9999989969857935,
                0.9999984465020616,
                1.2098659719757836e-06,
                1.2751899728311609e-07,
                0.9999991684722704,
                0.9999975938968036,
                1.3709568799919866e-06,
                5.422217030747413e-06,
                0.9999930377454284,
                0.9999991684718741
            ],
            [
                0.9999997617630333,
                0.9999997300423191,
                0.9999992661791945,
                0.9999997617630333,
                0.9999987901346056,
                0.9999987901346055,
                0.9999994956527724,
                6.825598028392069e-08,
                0.9999982396574172,
                0.9999991684718735
            ],
            [
                4.222834954801051e-06,
                6.475945666063607e-07,
                1.7603438428800754e-06,
                6.475946438055299e-07,
                1.0677026154619133e-06,
                5.715003789046955e-07,
                7.338210680021253e-07,
                4.450852641737424e-07,
                6.962253760024999e-06,
                1.8553910183607374e-07
            ],
            [
                3.059022269254856e-07,
                3.927860597945825e-07,
                1.1253526937697666e-07,
                1.275190580890061e-07,
                1.2751902768612997e-07,
                4.450850519403407e-07,
                6.023577783447482e-08,
                1.4449798650569826e-07,
                0.99998987000782,
                1.4449800373118268e-07
            ],
            [
                0.9999969105044496,
                0.9998601779444952,
                0.00010889690933730302,
                8.481101106463892e-05,
                1.3709568799919866e-06,
                2.430024942462891e-05,
                0.9999724643122737,
                0.9999741325629106,
                3.288749457469787e-06,
                1.0129988564974359e-05
            ],
            [
                2.5612812947508257e-06,
                9.422447062270609e-07,
                8.315283250394546e-07,
                0.9997965729625861,
                1.3709572068522336e-06,
                7.338210680002898e-07,
                0.9999921107336655,
                1.3709567165579959e-06,
                4.450849988811838e-07,
                2.260324836787226e-06
            ],
            [
                0.9999667857973237,
                2.1024334103581732e-07,
                0.9999982396563688,
                0.9999981261241709,
                0.9999916019279783,
                0.9999957771670641,
                7.734415776836702e-08,
                0.9999916019269732,
                0.9999969105040821,
                2.6995790618469934e-07
            ],
            [
                2.902312331170226e-06,
                4.222832437798974e-06,
                3.726639284144195e-06,
                1.1478772231086046e-05,
                5.043475885696228e-07,
                2.260324567337161e-06,
                5.715004470313855e-07,
                1.5534983101602148e-06,
                7.338212429582604e-07,
                4.4508494582405734e-07
            ],
            [
                1.3709567165579959e-06,
                3.7266392840781026e-06,
                0.9999898700041993,
                2.1024339116168358e-07,
                0.9999869928684474,
                4.450849988811838e-07,
                1.0677026154730804e-06,
                1.2098656835224664e-06,
                9.422449308716635e-07,
                5.715003107755449e-07
            ],
            [
                NaN,
                0.999997739674895,
                3.4663274507713016e-07,
                1.1253525596174225e-07,
                1.370957860576702e-06,
                4.450850519409479e-07,
                4.450852111155216e-07,
                1.855391681906175e-07,
                0.9999955048189609,
                0.9999599362983845
            ],
            [
                2.3823699519225038e-07,
                2.102434412875379e-07,
                1.0677032518814388e-06,
                2.6995784182140636e-07,
                2.3823688159291947e-07,
                1.6373772528581146e-07,
                4.450848927650143e-07,
                3.05902190458764e-07,
                5.422220909009474e-06,
                2.1024326584639497e-07
            ],
            [
                2.1024334103581732e-07,
                NaN,
                0.9999938558246716,
                0.9999810748517849,
                1.1478770862882149e-05,
                0.999978555046489,
                5.315781803390236e-08,
                0.9999938558239392,
                0.9999999006881377,
                0.9999949062962141
            ],
            [
                2.6995777745711594e-07,
                9.422444815792981e-07,
                1.9947292459347367e-06,
                1.9947297215125433e-06,
                2.1024336609843824e-07,
                3.466327450765785e-07,
                8.315283250394546e-07,
                1.6373762769138607e-07,
                7.338212429582604e-07,
                1.3709570434219446e-06
            ],
            [
                7.338209805200689e-07,
                3.726638839878908e-06,
                1.0677029973219343e-06,
                1.9947301970972664e-06,
                0.9999910603069019,
                1.067703124601679e-06,
                NaN,
                2.382368815932174e-07,
                0.999569442920003,
                1.0677024882009222e-06
            ],
            [
                0.999999391640891,
                8.939698435560267e-06,
                9.422447062294175e-07,
                0.9999992188514836,
                5.315787506612373e-08,
                7.338212429582604e-07,
                0.9999989322968762,
                8.7642558095602e-08,
                3.9278605979534166e-07,
                6.144176066901277e-06
            ],
            [
                2.1024339116168358e-07,
                0.9999983463104157,
                6.475946438055299e-07,
                0.9999852610215523,
                0.9999972735290815,
                6.962257079889302e-06,
                0.9999934595620015,
                0.9999955048200333,
                4.2228319344021954e-06,
                0.9999964991464225
            ],
            [
                8.481108183851022e-05,
                6.475945666051092e-07,
                7.338211554801876e-07,
                5.04347287955046e-07,
                0.00037998448691587246,
                5.144221366623174e-05,
                4.0063696969564425e-05,
                1.3709572068522336e-06,
                2.90231094723893e-06,
                7.338208055664991e-07
            ],
            [
                0.9999998144609645,
                0.9999992661787573,
                0.999999631011592,
                1.1253509497883659e-07,
                0.9999984465016905,
                0.9999996072136126,
                0.9999992188514835,
                0.9999995549149484,
                0.9999996310115039,
                0.999999746398073
            ],
            [
                1.4738983729535602e-05,
                2.902312677150514e-06,
                0.9999960330155133,
                4.785094494811783e-06,
                0.9999952149043722,
                0.9999771720032017,
                3.059022269250683e-07,
                1.7603430034867993e-06,
                1.760342793638743e-06,
                8.315279285351409e-07
            ],
            [
                1.7603440527286572e-06,
                3.927863407379485e-07,
                8.939696304311336e-06,
                8.315284241650899e-07,
                7.338209805240734e-07,
                3.72663883989755e-06,
                2.699578740032504e-07,
                7.889263526409699e-06,
                7.338207180898968e-07,
                5.715002426486762e-07
            ],
            [
                2.10243290909724e-07,
                2.6995774527718623e-07,
                6.023577783447482e-08,
                0.9999969105066581,
                0.9999980052702797,
                0.9999955048189613,
                0.9999599363078904,
                9.931185038635267e-08,
                2.102434162245973e-07,
                2.382369951932796e-07
            ],
            [
                1.0677024882009222e-06,
                6.962253760024999e-06,
                1.0677027427600627e-06,
                4.006368264282944e-05,
                1.7603440527286572e-06,
                5.422218969895357e-06,
                1.4738983729535602e-05,
                1.3709568799919866e-06,
                1.30071315662049e-05,
                0.9999485577743099
            ],
            [
                0.017986206935351235,
                0.9999993106387903,
                0.9999756997535176,
                5.715003789046955e-07,
                0.9999646437577925,
                0.9999964991468399,
                6.962257909842961e-06,
                0.9999974387177901,
                1.760342793638743e-06,
                0.9999898700054063
            ],
            [
                0.9999995818813271,
                0.9999987901338854,
                5.422217030781934e-06,
                0.9999967112521153,
                0.9999994631251244,
                0.9999994284996898,
                0.9999916019289776,
                0.9999995549150015,
                2.4300249425247723e-05,
                0.9999985406237801
            ],
            [
                NaN,
                1.1478764021029928e-05,
                NaN,
                1.7603440527334603e-06,
                5.715003789046955e-07,
                8.315284241665078e-07,
                2.2603242978943238e-06,
                0.9999339478243222,
                2.3823688159291947e-07,
                1.7603425837903113e-06
            ],
            [
                0.9999987121049384,
                0.9999967112501521,
                0.9999993106387906,
                0.9999998724809572,
                0.9999995549150013,
                0.9999986290426306,
                0.999999495652592,
                0.9999952149055094,
                0.9999934595643382,
                0.9999993106387903
            ],
            [
                4.4508510499849186e-07,
                0.0002305067706362583,
                2.382368247924618e-07,
                3.059023727894942e-07,
                7.338208055664991e-07,
                1.3007123813382511e-05,
                2.3823688159291947e-07,
                7.338211554783522e-07,
                5.715005832853093e-07,
                1.9947299593078385e-06
            ],
            [
                2.2603253756956754e-06,
                1.1253512180925583e-07,
                2.4300237838535383e-05,
                9.422450432014836e-07,
                7.889266347786918e-06,
                0.9999339478634945,
                1.5534977545886537e-06,
                2.6995768091383957e-07,
                0.9999957771675655,
                1.0677024882009222e-06
            ],
            [
                NaN,
                NaN,
                3.2887502415767434e-06,
                1.0129994602895546e-05,
                7.889263526409699e-06,
                7.338208930460318e-07,
                9.422443692574719e-07,
                NaN,
                2.561282210740037e-06,
                4.222832437798974e-06
            ],
            [
                4.539786865090791e-05,
                0.9999942280799786,
                3.288749065423109e-06,
                5.04347468323289e-07,
                1.7603438428800754e-06,
                4.222832941193893e-06,
                1.6701425827133152e-05,
                7.338207180898968e-07,
                0.9999861539938415,
                NaN
            ],
            [
                5.043476486915964e-07,
                1.0677026154806063e-06,
                4.450849988811838e-07,
                5.71500719545698e-07,
                7.338209805200689e-07,
                3.7266410611296085e-06,
                9.422450432014836e-07,
                1.0677029973219343e-06,
                1.5534981249697903e-06,
                1.3709567165579959e-06
            ],
            [
                4.139934092760465e-08,
                3.927862470899887e-07,
                3.466325797896173e-07,
                1.3709572068522336e-06,
                2.699577774585891e-07,
                2.699577774589574e-07,
                7.734414854823498e-08,
                2.902312677150514e-06,
                6.023572038912295e-08,
                1.2751899728311609e-07
            ],
            [
                3.059022269250683e-07,
                2.3823690999290963e-07,
                2.1024336609843824e-07,
                4.450848927650143e-07,
                3.927863407379485e-07,
                5.04347528446051e-07,
                2.382369667929001e-07,
                2.1024339116134898e-07,
                0.999996033012195,
                4.139941495546278e-08
            ],
            [
                0.9999982396574175,
                0.9999960330150349,
                0.9999967112513312,
                1.7603430034867993e-06,
                3.72663883989755e-06,
                1.3709568799823232e-06,
                4.785092783519724e-06,
                0.9999885212332577,
                0.9999822214439529,
                0.9999877809269246
            ],
            [
                6.475947210012481e-07,
                1.067702870039777e-06,
                6.962257079832313e-06,
                4.785092783519724e-06,
                8.315280276607289e-07,
                1.3709573702778664e-06,
                4.450851580555361e-07,
                3.4663253846718004e-07,
                5.04347468318358e-07,
                8.315281267882195e-07
            ],
            [
                3.288747889284851e-06,
                1.0677031245953668e-06,
                2.7535704231043113e-05,
                1.0677024882009222e-06,
                0.001926734726906348,
                9.931200429212718e-08,
                3.927860597945825e-07,
                3.726639728370556e-06,
                1.444979692800516e-07,
                1.012999098021058e-05
            ],
            [
                8.315283250371857e-07,
                1.5534975693869924e-06,
                3.288749457469787e-06,
                8.939695238634211e-06,
                1.9947292459347367e-06,
                7.484624512911504e-05,
                2.5612819054028872e-06,
                7.889261645427538e-06,
                1.994730434879465e-06,
                2.561281600086738e-06
            ],
            [
                0.9999952149055163,
                3.726638839878908e-06,
                0.9999938558232218,
                1.994730672668496e-06,
                1.7603432133296774e-06,
                3.726639728370556e-06,
                6.144176066901277e-06,
                4.450852111148132e-07,
                1.012999218752948e-05,
                1.0677026154806063e-06
            ],
            [
                7.33821330437595e-07,
                6.825606978822427e-08,
                8.315279285370317e-07,
                1.637376862489725e-07,
                6.475950298021765e-07,
                0.9999852610197967,
                0.0002959572061151019,
                0.9999724643024294,
                0.9999978766222976,
                0.9999151889492061
            ],
            [
                8.315282259138311e-07,
                7.338210680021253e-07,
                3.059021175247079e-07,
                2.3823688159237777e-07,
                NaN,
                5.043472278322555e-07,
                3.466327037548308e-07,
                1.637377057673536e-07,
                2.699577774585891e-07,
                5.715003789046955e-07
            ],
            [
                1.6701427818034747e-05,
                3.5356238069902345e-05,
                8.939700567004841e-06,
                4.2228329411708495e-06,
                1.209865539295696e-06,
                1.5534975693933505e-06,
                2.5612825160562587e-06,
                2.561283432035425e-06,
                2.561281905376098e-06,
                1.209865539295696e-06
            ],
            [
                5.043474683220276e-07,
                2.3823688159291947e-07,
                NaN,
                3.466326211113502e-07,
                3.059022998581767e-07,
                6.144177531811707e-06,
                NaN,
                1.27519088491875e-07,
                8.939700567094277e-06,
                4.450850519403407e-07
            ],
            [
                0.999997273529406,
                0.9999970976890545,
                0.9999952149066488,
                0.999983298578174,
                0.999997593896515,
                0.999998863436561,
                1.3709576971463352e-06,
                0.9999988634361544,
                0.9999988634366963,
                0.9999974387165694
            ],
            [
                0.9999991148429644,
                0.9999974387180982,
                5.3157900413760374e-08,
                0.9999987121052456,
                0.9999989322973852,
                0.9999994956527122,
                0.9999993524053564,
                0.9999989969855535,
                0.9999988634364253,
                0.9999994631247404
            ],
            [
                1.0677032518814388e-06,
                0.999997593897949,
                0.9999921107374198,
                0.999997739675973,
                0.9999983463100208,
                3.120192625482384e-05,
                9.422450432014836e-07,
                2.753568453792444e-05,
                0.9999687980998433,
                1.855391239544352e-07
            ],
            [
                3.726638839833152e-06,
                2.5612828213690224e-06,
                1.8925143729575624e-05,
                1.1478764020727177e-05,
                1.7603434231705793e-06,
                2.5612825160271407e-06,
                0.00048785706351821414,
                3.535625071602016e-05,
                1.892514598551715e-05,
                2.1444943302181958e-05
            ],
            [
                1.3709578605729614e-06,
                0.9999978766215384,
                0.9999916019259856,
                0.9999992661791949,
                0.999999730042094,
                0.9999962733593855,
                0.9999967112493685,
                0.9999916019249738,
                0.9999977396762437,
                0.999998126124394
            ],
            [
                6.9622595696935874e-06,
                7.889261645427538e-06,
                1.7603425837903113e-06,
                3.4663274507713016e-07,
                6.962256249885085e-06,
                5.04347468323289e-07,
                4.450852111155216e-07,
                1.5534983101602148e-06,
                1.3709575337078829e-06,
                3.927862002663297e-07
            ],
            [
                2.3823682479292225e-07,
                1.6373774480605869e-07,
                2.6995777745711594e-07,
                1.4449795205472734e-07,
                2.1024336609843824e-07,
                0.999978555046489,
                1.1253524254650944e-07,
                1.0677032518814388e-06,
                0.9999646437367106,
                0.9999869928653476
            ],
            [
                0.9999942280772278,
                2.9023126771227976e-06,
                3.288747889178668e-06,
                0.9999977396762426,
                0.9999945777810407,
                0.9999960330155104,
                0.9999916019249806,
                0.9999916019279792,
                0.9999877809284249,
                0.9999916019259839
            ],
            [
                0.9999885212359978,
                5.71500719545698e-07,
                3.05902336324494e-07,
                0.9999975938976617,
                0.9999997126314126,
                1.2098659719788098e-06,
                6.962253760024999e-06,
                8.939697369980456e-06,
                7.338208930460318e-07,
                7.338210680021253e-07
            ],
            [
                9.422442569315887e-07,
                6.475949526020042e-07,
                1.209865827752005e-06,
                1.7603425837855082e-06,
                0.9980732657508307,
                1.8553916819032217e-07,
                6.47595107001401e-07,
                9.422448185534261e-07,
                8.315282259151545e-07,
                2.699578740032504e-07
            ],
            [
                1.2098659719788098e-06,
                4.2228319344021954e-06,
                3.466327037548308e-07,
                3.4663274507713016e-07,
                5.715003789046955e-07,
                1.3709567165617364e-06,
                1.3709576971463352e-06,
                1.3709576971425944e-06,
                1.9947304348862686e-06,
                9.422449308716635e-07
            ],
            [
                4.450851049991497e-07,
                1.8553914607267268e-07,
                0.9999987901347499,
                1.4449807263312446e-07,
                8.315277302857965e-07,
                4.450852111148132e-07,
                4.450848927658745e-07,
                3.059022998576899e-07,
                0.999998790134173,
                2.561282210740037e-06
            ],
            [
                7.338208055664991e-07,
                5.043475885674441e-07,
                4.450848927650143e-07,
                1.0677029973158649e-06,
                5.715007195447234e-07,
                6.475951069985296e-07,
                7.338213304363436e-07,
                0.9999964991451714,
                8.315278294097538e-07,
                2.6995784182140636e-07
            ],
            [
                3.466327037553825e-07,
                1.760342793638743e-06,
                3.288749065423109e-06,
                3.05902263391829e-07,
                1.1253522913127183e-07,
                1.9947304348862686e-06,
                1.5534984953510149e-06,
                6.023569166654288e-08,
                1.855391239547094e-07,
                2.2603242978871282e-06
            ],
            [
                9.422448185510695e-07,
                NaN,
                1.9947297215125433e-06,
                1.855391681906175e-07,
                2.9023119851781017e-06,
                1.2098659719788098e-06,
                5.04347468323289e-07,
                3.466327037553825e-07,
                3.12019225345861e-05,
                6.144176066901277e-06
            ],
            [
                2.1024336609843824e-07,
                1.8553907971855875e-07,
                0.9999970976883625,
                2.699576809143613e-07,
                4.450852111155216e-07,
                2.6995784182140636e-07,
                3.0590237279085045e-07,
                1.444980209564556e-07,
                1.4449805540763184e-07,
                0.999998712105092
            ],
            [
                0.9997388096484766,
                3.4663249714612693e-07,
                5.043473480777865e-07,
                1.4738983729535602e-05,
                5.715003789046955e-07,
                3.9278605979534166e-07,
                5.043472879540142e-07,
                2.5612831267202583e-06,
                1.0677033791612137e-06,
                4.785092783519724e-06
            ],
            [
                3.927862002663297e-07,
                3.0590237279085045e-07,
                2.3823690999323465e-07,
                2.2603253756956754e-06,
                2.699578740032504e-07,
                3.0590237279085045e-07,
                3.05902263391829e-07,
                1.8553919030858602e-07,
                0.9999957771660539,
                0.9999985406241274
            ],
            [
                5.422220262599396e-06,
                3.72664061681327e-06,
                1.760342793638743e-06,
                0.0003353501911629164,
                0.9999921107383732,
                0.9997388096947052,
                7.338208055664991e-07,
                3.726637951387472e-06,
                7.889263526266196e-06,
                3.927862002663297e-07
            ],
            [
                2.3823693839290317e-07,
                NaN,
                0.9998204720593383,
                3.9278629391427843e-07,
                3.288749457469787e-06,
                3.0590237279085045e-07,
                0.9999942280792922,
                0.9999546021152963,
                0.9999706884616105,
                7.338208930460318e-07
            ],
            [
                5.043475885696228e-07,
                8.315284241665078e-07,
                0.9999964991451715,
                8.764253720001207e-08,
                1.0677029973219343e-06,
                6.475947210046347e-07,
                3.059022998581767e-07,
                2.382368815932174e-07,
                5.715006514176113e-07,
                3.466327037553825e-07
            ],
            [
                7.338208055664991e-07,
                3.927863407379485e-07,
                8.315284241650899e-07,
                7.889259764517575e-06,
                5.04347528446051e-07,
                1.5534979397790343e-06,
                8.315283250371857e-07,
                4.006369219393695e-05,
                6.962255419931625e-06,
                2.2603253756956754e-06
            ],
            [
                0.9999996533673376,
                0.9999997617631469,
                0.9999985406232578,
                0.9999997761971049,
                0.9999995549151075,
                0.9999996743687034,
                0.9999994956524118,
                0.9999997617630617,
                0.9999996310113279,
                1.4449805540763184e-07
            ],
            [
                1.2098656835224664e-06,
                1.5534975693933505e-06,
                1.3007130015488633e-05,
                5.4222209089700225e-06,
                1.1478770862735993e-05,
                1.5534979397677313e-06,
                5.71500515159253e-07,
                2.5612819054028872e-06,
                8.31528126775552e-07,
                8.315278294097538e-07
            ],
            [
                9.931186222523604e-08,
                1.670142980893658e-05,
                2.1024326584639497e-07,
                2.102433660979124e-07,
                2.3823688159291947e-07,
                2.2603240284371276e-06,
                2.3823696679230424e-07,
                1.6373764721072816e-07,
                8.764245361752286e-08,
                1.2751899728311609e-07
            ],
            [
                0.9999925887227872,
                1.300712536408621e-05,
                2.260324567337161e-06,
                3.9278610661902853e-07,
                1.0677029973219343e-06,
                6.475945666063607e-07,
                7.338208055680009e-07,
                1.473898900066424e-05,
                0.999998996986271,
                3.4663249714612693e-07
            ],
            [
                0.9999599363126715,
                0.9996646499713251,
                3.1201922535494165e-05,
                5.315787506612373e-08,
                5.422217677152175e-06,
                0.9999983463102172,
                1.4449800373118268e-07,
                0.9999972735297306,
                1.1253526937697666e-07,
                0.9999869928761992
            ],
            [
                0.9999995262093293,
                2.2603253756956754e-06,
                3.059022269250683e-07,
                0.9999960330150346,
                0.9999989969862709,
                0.9999997300422226,
                2.2603248367949354e-06,
                0.9999990577552941,
                0.9999898700102344,
                0.9999982396574172
            ],
            [
                0.9999885212332607,
                0.9999989322968762,
                0.9999975938965142,
                0.9999921107402563,
                0.9999945777823368,
                0.9999921107355442,
                0.9999987121044781,
                0.9999945777784498,
                7.338212429582604e-07,
                0.9999934595643518
            ],
            [
                5.043472278322555e-07,
                1.3709568799919866e-06,
                7.338212429582604e-07,
                4.4508510499849186e-07,
                1.444980209564556e-07,
                3.9278634073732336e-07,
                3.927863407379485e-07,
                4.450848927658745e-07,
                3.059023727894942e-07,
                5.715002426486762e-07
            ],
            [
                2.144495864059426e-05,
                6.475948754012522e-07,
                4.4508510499849186e-07,
                1.8925141473599938e-05,
                1.7603438428740716e-06,
                3.726641061085547e-06,
                7.338209805224048e-07,
                6.475947982002148e-07,
                3.466326211113502e-07,
                5.715002426475718e-07
            ],
            [
                0.999997097687326,
                1.2098661162056318e-06,
                0.9999980052707549,
                6.605216831803618e-05,
                0.9999985406241279,
                0.9999993106387906,
                0.9999960330126714,
                0.9999962733593877,
                0.9999974387184021,
                1.994729483723626e-06
            ],
            [
                8.315282259089153e-07,
                2.260325106237323e-06,
                2.3823702359290413e-07,
                2.902312677150514e-06,
                5.04347468323289e-07,
                8.315277302857965e-07,
                1.4738985486721259e-05,
                NaN,
                2.10243290909724e-07,
                9.422442569315887e-07
            ],
            [
                3.4663266243308805e-07,
                1.9947304348862686e-06,
                7.338211554783522e-07,
                NaN,
                4.4508494582405734e-07,
                1.067703124601679e-06,
                3.927862002663297e-07,
                4.785092783519724e-06,
                8.315281267861397e-07,
                5.043476486915964e-07
            ],
            [
                0.9999785550465105,
                3.2241881707148775e-08,
                1.2751902768612997e-07,
                4.4508515805735777e-07,
                1.0677027427624903e-06,
                1.6373772528704005e-07,
                3.466326624336003e-07,
                0.9999981261237243,
                4.4508515805735777e-07,
                3.726638839878908e-06
            ],
            [
                0.9999996072136594,
                0.9999993916410359,
                4.785096206076165e-06,
                1.0677027427624903e-06,
                0.9999996743686647,
                3.7266383956509585e-06,
                1.3709575337159875e-06,
                7.338212429594283e-07,
                5.71500719545698e-07,
                1.637377057680051e-07
            ],
            [
                2.102434162245973e-07,
                2.382368815932174e-07,
                0.9999724643089399,
                1.9947304348862686e-06,
                4.785093353940187e-06,
                1.8553907971879076e-07,
                5.715005832886879e-07,
                4.450850519403407e-07,
                3.4663274507713016e-07,
                5.715005832895975e-07
            ],
            [
                0.9999982396565775,
                0.9999998144608983,
                0.999997273529406,
                0.9999994284992807,
                0.9999957771675665,
                0.9999995818813767,
                0.9999993106390369,
                0.9999987901341726,
                0.9999985406237798,
                0.9999993916411085
            ],
            [
                1.4449800373118268e-07,
                3.059021175261338e-07,
                1.0677027427600627e-06,
                6.023572038912295e-08,
                2.5612831267202583e-06,
                1.3709576971463352e-06,
                3.059021175261338e-07,
                9.422449308774482e-07,
                2.2603245673443566e-06,
                1.8553914607267268e-07
            ],
            [
                6.825598842065202e-08,
                0.00013982210756291363,
                NaN,
                1.275190732904469e-07,
                1.1253522913127183e-07,
                7.734415776836702e-08,
                3.726639284144195e-06,
                0.9999904837471815,
                3.059022998581767e-07,
                5.715005832886879e-07
            ],
            [
                4.4508510499849186e-07,
                1.6373766672973748e-07,
                1.760342793638743e-06,
                0.9999687980923947,
                2.3823690999290963e-07,
                1.4449805540763184e-07,
                0.999993855825405,
                1.0677028700422047e-06,
                0.9999982396559487,
                0.999998996985434
            ],
            [
                3.7266383956509585e-06,
                8.315278294097538e-07,
                5.422220262636381e-06,
                0.9999983463098231,
                1.994729721518893e-06,
                0.9999980052695663,
                1.994729008145876e-06,
                7.734428685047173e-08,
                0.9999869928700016,
                0.9999785550541804
            ],
            [
                1.8553914607267268e-07,
                2.6995784182183607e-07,
                4.222833948008874e-06,
                3.927862002663297e-07,
                2.5612834320563895e-06,
                9.422442569334097e-07,
                3.059021175261338e-07,
                0.9999952149072184,
                2.561281600086738e-06,
                1.370957860576702e-06
            ],
            [
                6.475947210046347e-07,
                0.9999993916408187,
                0.9999998144609646,
                1.8553919030858602e-07,
                2.10243290909724e-07,
                0.9999998724809723,
                9.93120161310289e-08,
                0.999998996986271,
                2.3823682479292225e-07,
                0.999996910505558
            ],
            [
                NaN,
                0.9999687980886737,
                0.9998766054256153,
                NaN,
                0.9997388095711424,
                0.9999885212359884,
                0.9999964991439175,
                NaN,
                8.315279285370317e-07,
                5.715005832895975e-07
            ],
            [
                7.889261645427538e-06,
                6.475948754012522e-07,
                1.370957860576702e-06,
                8.315283250371857e-07,
                6.475945666051092e-07,
                1.1478768126057254e-05,
                2.9023133690980155e-06,
                3.466327863983311e-07,
                2.1444953527476883e-05,
                2.5612825160562587e-06
            ],
            [
                1.5534983101602148e-06,
                1.2098661162056318e-06,
                2.6995774527718623e-07,
                8.764242227418718e-08,
                1.994729483729522e-06,
                2.6995790618469934e-07,
                1.6373774480605869e-07,
                6.475946438055299e-07,
                3.9278634073732336e-07,
                5.71500719545698e-07
            ],
            [
                4.22283545819819e-06,
                NaN,
                NaN,
                2.2603234895372223e-06,
                2.2603253756956754e-06,
                6.605215256765022e-05,
                9.422445939054222e-07,
                0.9996646498400292,
                5.422220262636381e-06,
                2.2603248367949354e-06
            ],
            [
                9.422448185510695e-07,
                5.715005832886879e-07,
                3.4663249714612693e-07,
                5.043473480777865e-07,
                4.450848927658745e-07,
                5.715003789046955e-07,
                3.0590237279085045e-07,
                1.067703124601679e-06,
                1.855391239547094e-07,
                1.8553905760062447e-07
            ],
            [
                2.902312677137316e-06,
                8.764244316973974e-08,
                1.444980209564556e-07,
                9.422443692527585e-07,
                5.04347468323289e-07,
                0.9999623635667143,
                5.715003107715166e-07,
                1.4449798650551755e-07,
                6.9622595696935874e-06,
                2.699578740032504e-07
            ],
            [
                1.9947299593014888e-06,
                5.715003788993679e-07,
                1.760344052714248e-06,
                1.7603438428460541e-06,
                8.315284241597959e-07,
                1.5534981249697903e-06,
                6.962255419653012e-06,
                0.9999949062925761,
                1.4738987243478167e-05,
                0.9999960330136181
            ],
            [
                1.0677029973192638e-06,
                3.466325797896173e-07,
                6.475945666051092e-07,
                9.422447062294175e-07,
                6.475947982037486e-07,
                1.8553905760062447e-07,
                2.382368531929327e-07,
                4.4508510499849186e-07,
                2.1024339116168358e-07,
                3.0590237279032884e-07
            ],
            [
                2.260324836776948e-06,
                7.338209805200689e-07,
                7.484626297142789e-05,
                2.1444945858485726e-05,
                0.9999771720083277,
                0.9999706884476542,
                NaN,
                1.2098661161927025e-06,
                6.144174601935314e-06,
                1.1478770862589836e-05
            ],
            [
                4.450852641737424e-07,
                1.209865827752005e-06,
                2.902312331170226e-06,
                2.9023119851899796e-06,
                1.0677027427624903e-06,
                7.338207180898968e-07,
                1.2098656835252174e-06,
                2.561281600086738e-06,
                9.422445939054222e-07,
                3.288749849529972e-06
            ],
            [
                8.315277302841894e-07,
                6.962256249885085e-06,
                1.0129989772412744e-05,
                4.539787406217992e-05,
                0.9999987121041706,
                6.47595107001401e-07,
                1.6373774480605869e-07,
                4.4508510499849186e-07,
                5.315788140303327e-08,
                0.999999218851949
            ],
            [
                0.9999997617631753,
                0.9999989969856732,
                0.9999997897565839,
                0.9999962733620503,
                8.764253720001207e-08,
                0.9999992188519491,
                0.9999985406232574,
                0.9971990725815604,
                7.889264466725156e-06,
                2.9023116392097746e-06
            ],
            [
                0.999999554914736,
                0.9999996940977732,
                0.9999982396572076,
                0.9999995549150543,
                0.9999995549148952,
                0.9999993106389549,
                0.9999987901346057,
                0.999999730042094,
                0.9999687980812432,
                0.9999991684720718
            ],
            [
                1.5534979397790343e-06,
                6.144176799334096e-06,
                0.9999877809254893,
                2.2603240284371276e-06,
                3.288748673376478e-06,
                0.9999573525422935,
                6.475947210031623e-07,
                4.222832941193893e-06,
                2.9023119851781017e-06,
                1.5534984953552536e-06
            ],
            [
                0.9999978766217913,
                0.9999992661792823,
                0.9999986290431205,
                2.260325106237323e-06,
                0.9999904837517332,
                1.2098652508391807e-06,
                0.9999916019289735,
                2.1024334103581732e-07,
                0.9999339478555562,
                0.9999974387168746
            ],
            [
                4.006367786720367e-05,
                5.715003789046955e-07,
                0.9999995818814267,
                7.484624513510494e-05,
                0.999997273528432,
                1.2098659719788098e-06,
                7.889259764517575e-06,
                6.962257909842961e-06,
                5.043476486924565e-07,
                0.9999991684722704
            ],
            [
                0.9999925887174994,
                1.1478766757718129e-05,
                4.539788488687281e-05,
                9.610244939803353e-05,
                0.9999970976890578,
                0.0001584362736893196,
                NaN,
                0.999999114843176,
                2.9023109472244114e-06,
                8.315284241650899e-07
            ],
            [
                2.1024336609843824e-07,
                8.764254764780641e-08,
                8.315277302857965e-07,
                0.9999974387177901,
                2.1024331597262577e-07,
                1.6373772528704005e-07,
                0.9999646437367763,
                1.6373772528704005e-07,
                0.9999962733620504,
                2.382369951932796e-07
            ],
            [
                1.2098656835224664e-06,
                1.5534975693933505e-06,
                4.006370651557427e-05,
                0.0004878572379327933,
                0.9999993524052025,
                9.610241501774589e-05,
                7.338208930460318e-07,
                1.3709576971425944e-06,
                1.5534979397790343e-06,
                3.120191137659974e-05
            ],
            [
                0.9999990577557439,
                0.9999983463102178,
                0.9999987901340288,
                0.9999993524051248,
                0.9999995262095552,
                0.9999998362623529,
                0.9999969105040807,
                0.9999989322973849,
                0.9999992661787575,
                0.9999984465015057
            ],
            [
                6.475949526020042e-07,
                1.4738978458382043e-05,
                0.9999925887166301,
                6.1441724046434924e-06,
                0.9999916019309951,
                0.9999861539905233,
                5.715005832853093e-07,
                3.120190393794438e-05,
                3.7266397283908927e-06,
                1.994729008145876e-06
            ],
            [
                1.8553905760062447e-07,
                1.9947299593078385e-06,
                6.475946438055299e-07,
                4.450852111155216e-07,
                3.05902190458764e-07,
                1.637377448057981e-07,
                0.9999910603015771,
                3.927862470899887e-07,
                1.8925148242250705e-05,
                4.450850519403407e-07
            ],
            [
                0.9999756997535677,
                0.9999097195907166,
                8.315277302857965e-07,
                0.9999885212278115,
                0.9999942280793017,
                0.9999938558246724,
                0.9997694933819801,
                0.9999970976869809,
                6.962257079832313e-06,
                8.939693107288474e-06
            ],
            [
                0.9999998802069873,
                0.9999995549147359,
                0.9999994631251884,
                0.999999653367503,
                0.999999855502048,
                0.999997273530381,
                0.9999995262092163,
                0.9999996940976638,
                1.4449807263325588e-07,
                0.9999993524048932
            ],
            [
                1.0677027427569065e-06,
                0.9999724643025703,
                1.2098661162056318e-06,
                4.785093924362895e-06,
                0.9999339478557172,
                7.338212429537553e-07,
                0.9999869928762698,
                1.209865539295696e-06,
                9.422444815792981e-07,
                1.3709570434122812e-06
            ],
            [
                0.9999991148429646,
                0.9999969105055604,
                1.3709576971425944e-06,
                0.9999991684720719,
                0.9999997300421584,
                0.9999975938973762,
                0.9999972735290824,
                0.999997593897089,
                3.2887498495150166e-06,
                0.999999631011372
            ],
            [
                3.0590237279085045e-07,
                1.855391239544352e-07,
                3.927862939126708e-07,
                3.05902263391829e-07,
                1.275190276859705e-07,
                1.4449805540763184e-07,
                2.699577774585891e-07,
                1.1253525596174225e-07,
                2.1024326584582131e-07,
                9.931190958076104e-08
            ],
            [
                0.999996499144758,
                2.5612819054133693e-06,
                1.444980209564556e-07,
                7.338213304363436e-07,
                1.3007123813382511e-05,
                7.338212429582604e-07,
                1.0677029973192638e-06,
                8.315284241650899e-07,
                1.9947299593078385e-06,
                1.0677029973219343e-06
            ],
            [
                3.726639284144195e-06,
                1.0677027427624903e-06,
                2.561281294760143e-06,
                6.144177531811707e-06,
                1.2098656835136636e-06,
                1.637377057680051e-07,
                8.315281267882195e-07,
                0.9999921107364796,
                3.4663274507713016e-07,
                9.422445939054222e-07
            ],
            [
                1.370957860576702e-06,
                1.8925150497848527e-05,
                8.315278294097538e-07,
                2.9023119851781017e-06,
                1.9947297215125433e-06,
                3.7266410611296085e-06,
                4.222833444590791e-06,
                1.9947304348862686e-06,
                6.475945666063607e-07,
                2.2603234895372223e-06
            ],
            [
                6.144175334468545e-06,
                2.902311639183378e-06,
                6.962256249885085e-06,
                7.484621836619826e-05,
                2.4300237837960777e-05,
                4.785093353940187e-06,
                4.785096206076165e-06,
                1.6701423836262173e-05,
                7.889265407255982e-06,
                0.0002959570650765635
            ],
            [
                NaN,
                2.430024073523505e-05,
                NaN,
                1.4449798650569826e-07,
                NaN,
                0.9999810748517999,
                1.855390576008354e-07,
                3.05902263391829e-07,
                1.2098661162056318e-06,
                2.3823693839325527e-07
            ],
            [
                0.9999996072137064,
                0.9999998461826956,
                0.9999998555020481,
                NaN,
                0.9999993106387908,
                0.9999996743688587,
                0.999999855501962,
                0.9999992661791076,
                0.9999992188517632,
                0.999999554914736
            ],
            [
                0.9999832985841441,
                1.2098662604291696e-06,
                1.1253508156363576e-07,
                3.4663278639892215e-07,
                6.475947210046347e-07,
                1.2751902768612997e-07,
                0.9999852610145291,
                3.05902263391829e-07,
                1.1253506814842375e-07,
                4.139941002027314e-08
            ],
            [
                2.699578740032504e-07,
                6.825608606172863e-08,
                0.9999986290429571,
                2.699578096403948e-07,
                1.9947306726594253e-06,
                0.9999980052693281,
                0.9999038976196352,
                7.33821330437595e-07,
                3.0590237279085045e-07,
                0.9999993524053563
            ]
        ]
    },
    {
        "q_id": "9355_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999994631250603,
                0.999999495652592,
                0.9999996940976272,
                0.9999989969860317,
                0.9999998257021007,
                0.9999967112501533,
                0.9999993916409636,
                0.9999992661792823,
                0.999999607213753,
                0.999999495652652
            ],
            [
                0.999999872480942,
                0.9999996940976638,
                0.9999999317439384,
                0.9999998024947038,
                0.9999998024946095,
                0.9999998555019791,
                0.9999997463981334,
                0.9999997463980428,
                0.9999998257021006,
                0.9999999067051499
            ],
            [
                0.9999997300422226,
                0.9999991148426479,
                0.9999997126313098,
                0.9999999176674454,
                0.9999998461826222,
                0.9999993524051249,
                0.9999998942830358,
                0.9999982396561579,
                0.9999995549151075,
                0.9999990577555189
            ],
            [
                0.9999995549151074,
                0.9999998802069731,
                0.9999999358793714,
                0.9999998024947272,
                0.9999998724809723,
                0.9999999006881378,
                0.9999999656787406,
                0.9999998642567028,
                0.999999495652592,
                0.999999906705061
            ],
            [
                0.9999999226557869,
                0.9999995262096116,
                0.9999998144609646,
                0.9999998461826588,
                0.9999998024945624,
                0.9999998724809116,
                0.9999998461826037,
                0.9999997463980427,
                0.9999996310114598,
                0.9999999358794097
            ],
            [
                0.999999352405125,
                0.9999997897565588,
                0.9999995818810777,
                0.9999996310113279,
                0.9999993524052795,
                0.9999997463981938,
                0.9999996310115039,
                8.315277302819205e-07,
                0.9999992661790199,
                0.999999653367503
            ],
            [
                0.9999980052698044,
                0.9999993524054338,
                0.9999990577552943,
                0.9999996940977367,
                0.9999992661786699,
                0.9999992661786699,
                0.9999978766217915,
                0.9999993916406735,
                0.9999993106389549,
                0.999998712105092
            ],
            [
                0.9999999468421947,
                0.9999999397643154,
                0.9999999358793409,
                0.999999802494586,
                0.999999917667573,
                0.9999998257021214,
                0.9999998362622943,
                0.999999864256719,
                0.9999997761971583,
                0.9999997897565839
            ],
            [
                0.9999996072137999,
                0.9999974387174865,
                0.9999995262092728,
                0.999999168472171,
                0.9999969105044507,
                0.9999988634358837,
                0.9999993106389548,
                0.9999991684722702,
                0.9999996743686257,
                0.9999977396754343
            ],
            [
                0.9999999468421124,
                0.9999999317439465,
                0.999994906293181,
                0.9999998642566543,
                0.9999999006880668,
                0.9999997761970781,
                0.9999996310115039,
                0.9999991684718735,
                0.9999998874649185,
                0.99999992265575
            ],
            [
                0.9999978766210322,
                0.9999975938965142,
                0.9999991148427534,
                0.9999997126313441,
                0.9999994284997578,
                0.9999998024947038,
                0.9999997617631184,
                6.475946438022905e-07,
                0.9999998024945624,
                0.9999997897565588
            ],
            [
                0.9999997463980427,
                0.9999997126313098,
                0.9999996310116359,
                0.9999986290431204,
                0.9999991148429642,
                0.9999995262096117,
                0.9999997126315154,
                0.9999975938965142,
                0.9999993916408184,
                0.9999925887210216
            ],
            [
                0.9999969105051849,
                0.9999998642566704,
                0.9999991684719727,
                0.9999960330131427,
                0.9999970976876709,
                1.2098659719757836e-06,
                0.9999938558254029,
                0.9999962733616061,
                0.9999987901340284,
                0.9999993916410359
            ],
            [
                0.999999864256719,
                0.999999894282935,
                0.9999999656786956,
                0.9999998942830737,
                0.9999996533672137,
                0.9999998362623138,
                0.9999997761971582,
                0.9999997617630617,
                0.9999998024947272,
                0.9999999500628274
            ],
            [
                1.0677026154774503e-06,
                0.9999980052709943,
                0.9999986290431208,
                0.9999989322971307,
                0.999998863436426,
                5.715007195447234e-07,
                3.927862002641863e-07,
                0.999999266178845,
                5.71500378896509e-07,
                0.9999962733620525
            ],
            [
                0.9999996743688975,
                0.999999946842106,
                0.9999996743687422,
                0.999999946842106,
                0.9999998555019447,
                0.9999999176675436,
                0.9999999530883563,
                0.9999998724809267,
                0.9999996940978462,
                0.9999998802069302
            ],
            [
                0.9999997126313098,
                0.9999997617630333,
                0.9999999358793714,
                0.9999999006881377,
                0.9999997126314811,
                0.9999998874649184,
                0.9999998257021213,
                0.9999997897566341,
                0.9999997300421261,
                0.9999996940978826
            ],
            [
                0.999999953088362,
                0.9999999226558054,
                0.9999998642566543,
                0.9999993106389548,
                0.9999998555020309,
                0.999999864256719,
                1.0,
                0.9999999006880904,
                0.999999894282935,
                1.0
            ],
            [
                0.9999998362622747,
                0.999999855502048,
                0.9999998257020591,
                0.9999996940978462,
                0.9999998024946566,
                0.999998126124394,
                0.9999999067050387,
                0.9999999397642724,
                0.9999996533672965,
                0.9999994956526522
            ],
            [
                0.999999653367503,
                0.9999996940976273,
                0.9999996743687422,
                0.9999999397642868,
                0.9999998024947038,
                0.9999998144608762,
                0.9999999358793485,
                0.9999992661792824,
                0.9999998144608319,
                0.9999998555019619
            ],
            [
                0.9999991148427535,
                0.9999989969861514,
                0.9999986290426301,
                0.9999998802069159,
                0.9999987121044778,
                0.9999998874648648,
                0.9999999358793638,
                0.9999998874649051,
                0.9999999123574941,
                0.9999997463981333
            ],
            [
                0.9999998362623723,
                0.9999999611088858,
                0.9999999176674848,
                0.9999999067050721,
                0.9999999500628511,
                0.9999999468421187,
                0.999999935879425,
                0.9999997897567342,
                0.9999993916411811,
                0.9999997300421583
            ],
            [
                0.9999997617631752,
                0.9999999434137098,
                0.9999999176675142,
                0.9999998257021422,
                0.9999996940976638,
                0.9999998024945624,
                0.9999998874648917,
                0.9999997617630901,
                0.9999999176674553,
                0.9999989969859122
            ],
            [
                0.9999999530883563,
                0.9999996310115039,
                0.9999999500627798,
                0.9999997126313098,
                0.9999999500628453,
                0.9999925887219018,
                0.9999998942829729,
                0.9999994284992807,
                0.9999996072136126,
                0.9999997761970515
            ],
            [
                0.9999993916408912,
                0.9999995549150013,
                0.9999998362623528,
                0.9999999067050498,
                0.9999995818811275,
                0.9999998144608541,
                0.9999997897566841,
                0.9999998724809875,
                0.9999996743688975,
                0.9999991148428591
            ],
            [
                0.9999999273417922,
                0.9999999317439628,
                0.9999995818813269,
                0.9999999634651444,
                0.9999998642566866,
                0.9999997617631469,
                0.9999998555020481,
                0.9999995818811275,
                0.9999999123575151,
                0.9999999559305576
            ],
            [
                0.9999994284995531,
                0.9999996310114599,
                0.9999996533673791,
                0.9999921107402411,
                0.9999996940977367,
                0.9999995818811773,
                0.9999998024947272,
                0.9999998642567189,
                0.9999998257020798,
                0.9999997897567342
            ],
            [
                0.999999631011416,
                0.9999999559305681,
                0.9999995262093857,
                0.9999981261252882,
                0.999999802494633,
                0.9999997897566841,
                0.9999994631248683,
                0.9999952149043706,
                0.9999996940978096,
                0.9999988634357481
            ],
            [
                0.9999998874648246,
                0.9999998555020307,
                0.9999998024946095,
                0.9999995262092729,
                0.9999998461826222,
                0.9999997897565839,
                0.9999998024945624,
                0.9999998257022046,
                0.9999998724809268,
                0.9999991148433868
            ],
            [
                0.9999998802069587,
                0.9999999123574629,
                0.9999999006880668,
                0.9999999434137165,
                0.9999998642566219,
                0.9999998874647575,
                0.9999999468421567,
                0.9999999123575359,
                0.999999946842182,
                0.9999999559306312
            ],
            [
                0.9999997897567092,
                0.9999988634358835,
                0.9999998942830106,
                0.9999996310116358,
                0.9999998942830485,
                0.9999996940978462,
                0.9999996940976272,
                0.9999994956524115,
                0.9999999358793868,
                0.9999998461826956
            ],
            [
                0.9999995549151074,
                0.9999996533672137,
                0.9999998257021214,
                0.9999998024946095,
                0.9999996310113719,
                1.8553919030826963e-07,
                0.9999998362623138,
                0.9999997617631186,
                0.9999997126315496,
                0.9999996533672963
            ],
            [
                0.999999814460876,
                0.9999996072136593,
                0.9999996940977367,
                0.9999998555019963,
                0.9999996940978462,
                0.9999992188513903,
                0.9999991684717744,
                0.9999998024946801,
                0.9999998802069302,
                0.9999996533672136
            ],
            [
                0.9999969105059241,
                0.999997593897089,
                0.9999964991468425,
                0.9999989969855536,
                0.999999391640746,
                0.9999972735290816,
                2.3823690999290963e-07,
                0.9999978766220463,
                0.9999981261246178,
                0.9999970976880196
            ],
            [
                0.9999998942829477,
                0.9999996310114599,
                0.9999998874648782,
                0.9999997897567091,
                0.9999997300421904,
                0.9999996533672963,
                0.9999999434137637,
                0.9999998874648917,
                0.9999996533673791,
                0.9999999006881259
            ],
            [
                0.9999998144608098,
                0.9999995818811774,
                0.9999998555019275,
                0.9999998642566542,
                0.9999997761971315,
                0.9999999123575568,
                0.999999802494633,
                0.9999998144609424,
                0.9999990577552943,
                0.9999996940978461
            ],
            [
                0.9999993524054336,
                0.9999999634651661,
                0.9999992661792821,
                0.999999958600659,
                0.9999999067051054,
                0.999999789756634,
                0.9999995549148951,
                0.9999999006880195,
                0.9999996743686257,
                0.9999999559305576
            ],
            [
                0.9999997761970781,
                0.9999998642567028,
                1.0,
                1.553497384180408e-06,
                0.9999997300421584,
                0.9999999317439302,
                0.9999996533674617,
                0.9999998362623723,
                0.9999998257020591,
                0.9999998144608319
            ],
            [
                0.9999999530883508,
                0.999999894283061,
                0.9999994631249324,
                0.9999992188516698,
                0.9999998362623138,
                0.999999802494586,
                0.9999998642566704,
                0.9999999176675044,
                0.999999887464932,
                0.9999998802068873
            ],
            [
                0.999999814460876,
                0.9999996533674617,
                0.9999996533674202,
                0.999999802494586,
                0.9999997300421583,
                1.0,
                0.9999998555019274,
                0.9999996310115479,
                0.9999999226558054,
                0.9999997617631186
            ],
            [
                0.9999995549150544,
                0.9999996533672137,
                0.9999987121041712,
                0.9999997761971849,
                2.561281905390075e-06,
                0.999999939764258,
                0.9999999123575046,
                0.9999999358794174,
                0.9999998461826772,
                0.9999998874648246
            ],
            [
                0.9999861539888868,
                0.999998239656578,
                0.9999996940976273,
                0.9999994284996213,
                0.9999997897566089,
                0.9999999176675829,
                0.999999894282935,
                0.999999495652592,
                0.9999993916406736,
                0.999999931743979
            ],
            [
                0.9999996743688199,
                0.9999998724809571,
                0.9999999123575568,
                0.999999789756634,
                0.9999996940976638,
                0.9999997300421584,
                0.9999994284994852,
                0.9999999397642508,
                0.9999995262094986,
                0.9999998874649051
            ],
            [
                0.9999999226557316,
                0.9999999317440279,
                0.9999999226558515,
                0.9999038976201386,
                0.9999999468421883,
                0.9999998362623529,
                0.9999999226558146,
                0.9999997463981032,
                0.9999998461826588,
                0.9999999067051387
            ],
            [
                0.9999997300421903,
                0.9999997897567091,
                0.9999997463980427,
                0.9999999634651966,
                0.9999985406234316,
                0.9999972735300556,
                0.9999990577557434,
                0.9999993916406733,
                0.9999995549150543,
                0.9999997463981333
            ],
            [
                0.999999825702059,
                0.9999999273418355,
                0.9999998362623723,
                0.9999998257021214,
                0.9999997463982241,
                0.9999997463982241,
                0.9999998802069873,
                0.9999997300422226,
                0.9999998942829854,
                0.9999998874648782
            ],
            [
                0.9999993916410361,
                0.9999995549148951,
                0.9999999226558515,
                0.999999825702059,
                0.9999998461826222,
                0.999999943413757,
                0.9999998555019791,
                0.9999997126313098,
                0.9999998257020591,
                0.9999998257021006
            ],
            [
                0.9999999006880431,
                0.9999999123575881,
                0.9999999397643083,
                0.9999997126314469,
                0.9999999226558146,
                0.9999999226557776,
                0.9999996940978827,
                0.99999967436882,
                0.999999814460854,
                0.9999998802068873
            ],
            [
                0.9999997126315154,
                0.999999900688055,
                0.9999994956524717,
                0.9999998874648917,
                0.9999998802068873,
                0.9999996533673791,
                0.999999730042094,
                0.9999998802069587,
                0.9999998362622552,
                0.9999997300422226
            ],
            [
                0.9999994956527725,
                0.9999997761972116,
                0.9999996310115039,
                2.2603242978665707e-06,
                0.9999999468421376,
                1.553498495338299e-06,
                8.315278294038928e-07,
                2.26032402841657e-06,
                3.2887498494282754e-06,
                5.422217030614265e-06
            ],
            [
                0.9999999067050165,
                0.9999996533674617,
                0.9999999500628274,
                0.9999996533672963,
                0.9999999358793562,
                0.99999976176309,
                0.9999999358793714,
                0.9999997463980729,
                0.9999999656787039,
                2.144494330116777e-05
            ],
            [
                0.999998346310021,
                0.9999967112497612,
                0.9999904837505881,
                0.9999975938976633,
                0.9999999067050832,
                0.9999960330131432,
                0.9999969105066601,
                0.9999960330155101,
                0.9999852610180593,
                0.9999998362623528
            ],
            [
                0.9999999176675044,
                0.9999999468421439,
                0.9999998642566381,
                0.9999998362623138,
                0.9999998461826772,
                0.999999855502048,
                0.9999999397642724,
                3.2887502415438413e-06,
                0.9999987901337402,
                0.9999996940978095
            ],
            [
                0.9999998802069587,
                0.9999999123574838,
                0.9999998362623332,
                0.9999993524049707,
                0.9999996940978462,
                0.9999999273417923,
                0.9999998724809875,
                0.9999999397642796,
                0.9999998724808964,
                0.9999999123574942
            ],
            [
                0.9999986290431208,
                0.9999997300420939,
                2.9023112931873767e-06,
                0.9999995818813766,
                0.9999982396559484,
                0.9999989969857928,
                0.9999997126314468,
                0.9999955048189616,
                0.9999997463981032,
                0.9999992661791949
            ],
            [
                0.9999992188517631,
                0.9999990577555191,
                0.9999992661788448,
                0.9999987901344616,
                0.9999969105040846,
                0.9999987121044793,
                0.999999428499281,
                0.9999994284995534,
                0.999998712104632,
                0.9999957771650517
            ],
            [
                0.9999998461826589,
                0.9999998024947037,
                0.999999814460854,
                0.9999997617630049,
                0.9999994631248045,
                0.9999999317439383,
                0.9999998802069874,
                0.999999674368781,
                0.9999999067050832,
                0.9999996072137999
            ],
            [
                0.9999998802069731,
                0.9999997897565839,
                0.9999998642566543,
                1.9947292459265734e-06,
                0.9999998555020307,
                0.9999996533674204,
                2.561282210729555e-06,
                0.9999996072139404,
                0.9999998724809116,
                0.9999998642566866
            ],
            [
                0.9999987121041707,
                0.999999495652592,
                0.9999998461826956,
                4.450852111148132e-07,
                1.067703379154416e-06,
                0.9999999273417922,
                0.9999999397643154,
                0.9999997761970248,
                0.9999998724809875,
                0.9999925887219043
            ],
            [
                0.9999997463981939,
                0.9999997897565838,
                0.999999894283061,
                0.9999999067050943,
                0.9999999317439384,
                0.9999998942829981,
                0.9999999397643083,
                0.999999802494586,
                0.99999976176309,
                0.9999998024946095
            ],
            [
                0.9999785550465765,
                0.9999964991451735,
                5.715007195431641e-07,
                1.3007125363908762e-05,
                0.9999869928700342,
                0.9999983463100203,
                1.147877359926923e-05,
                0.9999962733598409,
                2.9023119851781017e-06,
                0.9999972735284333
            ],
            [
                0.9999885212346403,
                0.9999998874649185,
                0.9999990577552942,
                0.9999997761971048,
                0.9999999226557131,
                6.475947982022763e-07,
                0.9999997617631753,
                0.9999997300421583,
                0.9999999358794097,
                0.999999554914842
            ],
            [
                0.9999998555019274,
                0.9999998642566219,
                0.9999998724809571,
                0.9999998362623723,
                0.9999999397643083,
                0.9999999123575151,
                0.9999999656787365,
                0.9999998724809268,
                0.999999958600595,
                0.9999997761970248
            ],
            [
                0.999986992874666,
                0.9999964991443469,
                0.9999975938982407,
                5.715006514105942e-07,
                0.9999925887192563,
                0.9999957771645479,
                0.9999949062937897,
                0.9999984465016928,
                5.715005832872586e-07,
                5.043475284350422e-07
            ],
            [
                0.9999998362623529,
                0.9999998942830233,
                0.9999993106387902,
                0.9999996743686257,
                0.9999998461826222,
                0.9999997126313441,
                0.9999999176674454,
                0.9999999586006542,
                0.9999998724809267,
                0.9999999067051055
            ],
            [
                0.9999962733607173,
                0.999999855501979,
                0.9999994631247402,
                0.9999967112509365,
                0.9999974387180959,
                0.9999964991460056,
                0.9999646437619992,
                0.9999938558246729,
                0.9999987121052455,
                0.9999996310114599
            ],
            [
                0.9999990577550696,
                0.999999581881327,
                0.9999998874648514,
                0.9999996743686257,
                0.9999997761971849,
                0.9999998257020799,
                0.9999998724809116,
                0.9999994284997576,
                0.9999997300422226,
                0.9999996940976273
            ],
            [
                0.9999999397642222,
                0.9999999226557778,
                0.9999998362622357,
                0.9999998461826405,
                0.9999999317439058,
                0.9999998555019618,
                0.9999999067050721,
                0.9999999358794479,
                0.9999998874649051,
                0.9999998257021007
            ],
            [
                0.9999996940978826,
                5.715007195384861e-07,
                0.9999999006880076,
                0.9999869928684678,
                0.9999994284996213,
                0.9999995262093293,
                0.9999987121052457,
                0.999999789756659,
                0.9999993106387906,
                0.9999978766222982
            ],
            [
                0.9999994956527725,
                0.999999674368781,
                0.9999997761971049,
                0.999998446502061,
                0.9999992188516699,
                0.9999996533672965,
                0.9999994631251242,
                0.9999960330155054,
                0.9999993524049705,
                0.9999996533673378
            ],
            [
                0.9999996743688586,
                0.9999999500628036,
                0.9999998874648112,
                0.9999999273417923,
                0.9999999586006049,
                0.9999997761971849,
                0.9999999500628274,
                0.999999814460854,
                0.9999999434137636,
                0.9999999273417662
            ],
            [
                0.9999996743688586,
                0.9999995262095551,
                0.9999994631249323,
                0.9999994956523516,
                0.999999855501979,
                0.999999391641181,
                0.9999997126315496,
                0.9999986290424667,
                0.9999998802069445,
                0.9999996940976638
            ],
            [
                0.999998712104171,
                0.9999993916408185,
                0.9999892166903616,
                0.9999921107346007,
                0.999999761763147,
                0.9999995549149483,
                0.9999980052709926,
                0.9999999226557408,
                0.9999998874648782,
                0.999999581881277
            ],
            [
                0.9999997300420939,
                0.9999985406239541,
                0.999999900688043,
                0.9999998461826771,
                0.9999997617630901,
                0.9999994284993488,
                0.9999996310113721,
                0.999999864256719,
                0.9999998724809875,
                0.9999995549150013
            ],
            [
                0.999998005270042,
                0.9999999468421567,
                0.9999985406230839,
                0.9999999468421693,
                0.999999789756634,
                0.9999999176674552,
                0.999999872480942,
                0.9999998942829602,
                0.9999996743688586,
                0.9999997463981334
            ],
            [
                0.9999998802069873,
                0.9999998942829477,
                0.9999992188517628,
                0.9999999067051387,
                2.2603248367512505e-06,
                0.9999998802068873,
                1.994729721482609e-06,
                0.9999998642566704,
                0.9999996940978826,
                0.9999998257021007
            ],
            [
                0.9999998942829602,
                0.9999998802069159,
                0.9999999123575881,
                0.9999999123574733,
                1.0677031245990084e-06,
                0.9999999397642222,
                0.9999997300421262,
                0.9999999006881378,
                0.9999999226558515,
                0.9999999226558515
            ],
            [
                0.9999998144608098,
                0.9999994956527724,
                0.9999991684719726,
                0.9999996310113719,
                0.999999730042287,
                0.9999995549148422,
                0.9999996072136125,
                0.9999997463980124,
                0.9999996940977731,
                0.9999995262093293
            ],
            [
                0.9999997617629764,
                0.9999995262094987,
                0.9999988634358841,
                0.9999996072139403,
                0.9999993106391193,
                0.9999996533673791,
                0.9999994956523516,
                0.9999960330126726,
                0.999999855502048,
                0.9999992661787573
            ],
            [
                1.7603427936183298e-06,
                1.7603440527222532e-06,
                9.422445939002803e-07,
                1.2098653950606901e-06,
                6.475948754012522e-07,
                8.315278294038928e-07,
                1.760343003481596e-06,
                0.9999934595620203,
                3.2887490653872164e-06,
                1.553497754583709e-06
            ],
            [
                0.9999999397642293,
                0.9999995262094987,
                0.9999986290432844,
                0.999999802494633,
                0.9999998257021422,
                0.9999996940977367,
                0.9999996533672963,
                0.9999998144609424,
                0.9999989322971305,
                0.9999599363127705
            ],
            [
                0.9999999226558054,
                0.9999996743687422,
                0.99999994341373,
                0.9999996940976639,
                0.9999993916408185,
                0.9999998257020591,
                0.9999999358794327,
                0.999999730042287,
                0.9999999530883397,
                0.9999998362623138
            ],
            [
                0.999999958600659,
                0.9999998942829602,
                0.9999995818810777,
                0.999999789756684,
                0.9999999226558423,
                0.9999999123574732,
                0.9999998802069159,
                0.9999998461826405,
                0.9999999067050165,
                0.9999998642566704
            ],
            [
                0.9999999611088487,
                0.9999998461827139,
                0.9999999006881022,
                0.999999887464838,
                0.9999998942829981,
                0.9999998942829854,
                0.9999998802069444,
                0.9999999358793715,
                0.999999939764258,
                0.9999998874647575
            ],
            [
                0.9999999586006295,
                0.9999999434137098,
                0.9999999067050499,
                0.99999995860059,
                0.9999998257021422,
                0.9999999123575569,
                0.9999999273418962,
                0.9999999500628155,
                0.999999887464905,
                0.9999999226557684
            ],
            [
                0.999999825702059,
                0.999999814460876,
                0.9999988634364252,
                0.9999998362623528,
                0.9999995818811275,
                3.927861066170637e-07,
                0.999999631011416,
                0.9999997126314468,
                0.999999825702059,
                4.450852641717689e-07
            ],
            [
                0.9999993916407461,
                0.9999998874648917,
                0.999999927341827,
                0.9999998802068873,
                0.9999999317439221,
                0.9999998642566542,
                0.9999998802069017,
                0.9999995818813768,
                0.9999998362623723,
                0.9999998874648245
            ],
            [
                0.9999982396569989,
                0.9999960330131515,
                0.9999960330145675,
                0.9999982396559496,
                0.9999981261246192,
                0.9999967112493738,
                0.9999967112501613,
                0.999996711252116,
                3.726641061109272e-06,
                0.9999985406241283
            ],
            [
                0.9999999123574732,
                9.422450431912e-07,
                1.3709576971379186e-06,
                6.475948753965404e-07,
                0.999999943413757,
                8.939698435096828e-06,
                0.9999997761971582,
                0.9999994284993489,
                7.338209805200689e-07,
                6.475951069985296e-07
            ],
            [
                0.9999998257021837,
                0.9999999226558423,
                0.9999999500628513,
                0.9999999176674651,
                0.999999931743979,
                0.9999999500628155,
                0.9999999358793867,
                0.9999999530883844,
                0.9999999634651661,
                0.9999999468421376
            ],
            [
                0.9999998724810027,
                0.9999999176675142,
                0.9999999006880668,
                0.9999999358793792,
                0.9999998802068873,
                0.9999997300421261,
                0.9999998362622943,
                0.9999997761971583,
                0.9999999176675634,
                0.9999999123574523
            ],
            [
                0.9999999317440198,
                0.9999996743687034,
                0.9999999006880431,
                0.999999931743979,
                0.9999998724809267,
                0.9999997300422547,
                0.9999998024946566,
                0.9999996072137531,
                0.9999999067051388,
                0.9999997126315497
            ],
            [
                0.9999999397642078,
                0.9999996940976638,
                0.999999554914736,
                0.999999802494633,
                0.9999997617630616,
                0.9999996310115039,
                0.9999998461826405,
                0.9999989969857929,
                0.9999998024947037,
                0.9999998802068873
            ],
            [
                0.9999999677581528,
                0.9999999530884011,
                0.9999997761972116,
                0.9999999586005998,
                0.9999997126314811,
                1.0,
                0.9999998362623528,
                1.0,
                0.9999997897566841,
                0.9999999273418009
            ],
            [
                0.9999997300421583,
                0.9999999500628095,
                0.9999999067049831,
                0.9999997463982241,
                0.9999995549147891,
                0.9999999123575568,
                0.999999352405202,
                0.9999999748900271,
                0.9999999067050388,
                0.9999996940977002
            ],
            [
                0.9999997126314126,
                0.9999832985841517,
                0.9999996940976638,
                0.9999996743688975,
                0.9999997126313441,
                0.9999990577555189,
                0.9999991684717743,
                0.9999996743688975,
                0.9999981261252878,
                0.9999987901344611
            ],
            [
                0.999999554914736,
                0.9999998555020135,
                0.9999997126313098,
                0.9999997300423192,
                0.9999996310115918,
                0.999999900687972,
                0.9999997897566341,
                0.999999825702059,
                0.9999996940976273,
                0.9999998802069587
            ],
            [
                0.9999999273418355,
                0.9999998724809116,
                0.9999997761971582,
                0.9999998144609424,
                0.9999998024946566,
                0.9999999006881497,
                0.9999995549148952,
                0.9999991148431756,
                0.9999996940977002,
                0.9999983463098242
            ],
            [
                0.9999997300421904,
                0.9999998942829225,
                0.999999730042094,
                0.9999999123575986,
                0.9999996743687034,
                1.2098652508391807e-06,
                0.9999998257020798,
                0.9999997300421904,
                0.999999825702059,
                0.9999999317439383
            ],
            [
                0.9999999273418789,
                0.9999999317439628,
                0.9999996940978096,
                0.9999998461827139,
                0.9999994956527123,
                0.9999999500627916,
                0.9999996072137999,
                0.9999997300422226,
                0.999999931743979,
                0.9999998024946095
            ],
            [
                0.9999995818811773,
                0.9999983463098238,
                0.999999712631481,
                0.9999993106392014,
                0.9999995549147891,
                0.9999996940978096,
                0.9999980052698048,
                1.2098652508347793e-06,
                0.9999998555020481,
                0.9999996940977002
            ],
            [
                0.9999999226558515,
                0.9999999317439139,
                0.9999999434137165,
                0.9999997300421261,
                0.9999999067050276,
                0.9999999176675632,
                0.99999976176309,
                0.9999999317439139,
                0.9999998802069017,
                0.9999999176675143
            ],
            [
                0.9999967112509368,
                0.9999997463981636,
                0.9999998942830233,
                0.9999999273418356,
                0.9999998362622747,
                0.9999999176674356,
                0.9999988634364252,
                0.9999999273417663,
                0.9999999358793409,
                0.9999999176674454
            ],
            [
                0.9999991148433867,
                0.9999921107364868,
                0.9999942280806676,
                8.31527928532683e-07,
                0.9999994284993489,
                0.9999981261237241,
                0.9999983463100209,
                9.422448185435711e-07,
                0.9999987121052455,
                0.9999949062925761
            ],
            [
                0.9999997897567342,
                3.927862470840049e-07,
                0.999999554914736,
                0.999999581881327,
                0.9999997126314811,
                0.9999987121050921,
                0.9999995818811275,
                0.9999998555019619,
                0.9999996533675031,
                0.9999995818812273
            ],
            [
                0.9999997300421261,
                0.9999997463981637,
                0.999999814460854,
                0.9999999500628274,
                0.9999999123574524,
                0.9999997126313783,
                0.9999994284996214,
                0.9999990577549571,
                0.9999997617630333,
                0.9999998724809875
            ],
            [
                0.9999994284996895,
                0.9999996940976638,
                0.9999993524050479,
                0.9999997300423191,
                0.9999996533672965,
                0.9999997761971582,
                0.9999996072137998,
                0.9999997617630901,
                0.9999997126315154,
                0.999999526209273
            ],
            [
                0.9999993106391194,
                0.9999994956524718,
                0.9999994284992809,
                0.999999906705072,
                0.9999993524051252,
                0.999999855501979,
                0.9999998942829729,
                0.9999995549150544,
                0.999999554914736,
                0.9999996743687423
            ],
            [
                0.9999999358793639,
                0.9999999273418269,
                9.422442569290178e-07,
                0.9999998802069444,
                0.999999581881277,
                0.9999989322972576,
                0.9999997897565588,
                0.9999996310113279,
                1.5534981249574276e-06,
                0.9999999434138042
            ],
            [
                0.9999996072137999,
                0.9999999586006049,
                0.999999631011328,
                0.9999997300421583,
                0.9999999434137435,
                0.9999999634652009,
                0.9999999273418096,
                0.999999927341775,
                0.9999999067050498,
                0.9999998461826406
            ],
            [
                0.9999997897567342,
                0.9999998257020798,
                0.9999996940978826,
                0.9999996072139403,
                0.9999999468421376,
                0.9999997761970781,
                0.9999995262096116,
                0.9999997126313098,
                0.9999998802069017,
                0.9999994956524116
            ],
            [
                0.9999996743687811,
                0.9999994284996214,
                0.9999996310116359,
                0.9999995262096117,
                0.9999998802069874,
                0.9999998724809723,
                0.9999974387168761,
                0.9999999176675632,
                0.999999631011548,
                0.9999995549151074
            ],
            [
                0.9999999317439059,
                0.9999998802069587,
                0.9999998802069017,
                0.9999998642567351,
                0.9999996743688199,
                0.9999998642567028,
                0.9999999358793562,
                0.9999998724809875,
                0.9999997761970781,
                0.9999999434137368
            ],
            [
                0.9999998024946566,
                0.9999996533673791,
                0.999999935879425,
                0.9999992188516698,
                0.9999999176674651,
                0.9999998257020799,
                0.9999998257021214,
                0.999999855502048,
                0.999999855501979,
                0.9999997126315154
            ],
            [
                0.9999985406232578,
                0.9999999559305524,
                0.9999998942830106,
                0.9999999500628334,
                0.9999999656786874,
                0.9999993916409635,
                0.9999999500628095,
                0.9999999273418788,
                0.9999999530883172,
                0.999999931743979
            ],
            [
                0.9999997463980124,
                0.9999997617631753,
                0.9999999434137907,
                0.9999999434137636,
                0.9999999006880195,
                0.9999998461826222,
                0.9999999226558423,
                0.9999999358793868,
                0.9999999067050054,
                0.9999999317440197
            ],
            [
                0.9999993524048935,
                0.9999999530883396,
                0.999999814460876,
                0.9999996940977002,
                0.9999990577557436,
                0.9999999273418615,
                0.9999998802069444,
                0.9999999468421756,
                0.9999998874647977,
                0.9999994631248683
            ],
            [
                0.9999999434137368,
                0.9999995549147892,
                0.9999998461826405,
                0.9999995549147361,
                0.9999998024946801,
                0.9999998024947273,
                0.9999999006880195,
                0.9999987121041711,
                0.9999998874648917,
                0.9999999226557684
            ],
            [
                0.9999999468421756,
                0.9999999358793639,
                0.9999999317440116,
                0.9999999067050831,
                0.9999999434137907,
                0.9999999317439383,
                0.9999998461826405,
                0.9999999067050165,
                0.9999999006879957,
                0.9999996310114598
            ],
            [
                0.9999998257021213,
                0.9999996743686257,
                0.9999999176674553,
                0.9999998257021837,
                0.9999998642566219,
                0.9999995262092163,
                0.9999997617630049,
                0.999999712631344,
                0.9999997463981938,
                0.9999997617630617
            ],
            [
                0.9999999176674357,
                0.9999997300421904,
                0.9999998724809572,
                0.9999999611089182,
                0.9999999067050054,
                0.9999999226557501,
                0.9999999468421503,
                0.999999887464744,
                0.9999998942829981,
                0.9999999006881142
            ],
            [
                0.999999730042287,
                0.9999999067049942,
                1.5534983101602148e-06,
                0.9999999273418009,
                0.9999996743687034,
                0.9999998257020798,
                0.9999996743687422,
                0.9999999226557316,
                0.9999998362623138,
                0.9999996310114599
            ],
            [
                0.9999998724809267,
                0.9999998257022046,
                0.9999997300421583,
                0.9999992188519492,
                0.9999999611088766,
                0.9999999123574836,
                0.999999526209273,
                0.9999998257021837,
                0.9999991148426479,
                0.9999999500628631
            ],
            [
                0.9999985406232578,
                0.9999999748899912,
                0.9999999273418788,
                0.9999996940977367,
                0.9999999317439872,
                0.9999997463981032,
                0.9999999226558515,
                0.999999631011592,
                0.9999999468421567,
                0.9999998555019274
            ],
            [
                0.9999996743687034,
                0.9999999226557778,
                0.999999887464838,
                0.999999894283061,
                0.9999999273418789,
                0.9999998257021837,
                0.9999997126313098,
                0.9999995262093293,
                0.9999998024945624,
                0.999999761763147
            ],
            [
                0.9999997897565587,
                0.9999998362623529,
                0.999999814460854,
                0.9999999500627739,
                0.9999998724809419,
                1.370957860567974e-06,
                0.9999998724809724,
                0.9999996743686645,
                0.9999999176674651,
                0.9999999317439221
            ],
            [
                0.9999974387171808,
                0.9999993524052794,
                0.999999428499349,
                1.760343423160973e-06,
                1.9947306726594253e-06,
                0.9999986290431205,
                0.9999981261252875,
                0.9999977396765125,
                0.9999991148433864,
                0.9999984465026168
            ],
            [
                0.9999994631251242,
                0.9999992188513906,
                0.9999994631249324,
                0.9999987121050937,
                0.9999978766222994,
                0.999993037744588,
                0.9999992188519492,
                0.9999985406236055,
                0.9999987901343174,
                0.9999985406239539
            ]
        ]
    },
    {
        "q_id": "9611_mmlu_physics",
        "cot_ids": [
            1,
            3,
            4,
            5,
            7,
            8,
            9,
            11,
            12,
            15,
            16,
            18,
            19,
            23,
            27,
            30,
            31,
            32,
            34,
            36,
            38,
            39,
            40,
            43,
            46,
            48,
            51,
            54,
            55,
            57,
            58,
            59,
            60,
            61,
            64,
            67,
            68,
            69,
            72,
            73,
            75,
            77,
            81,
            83,
            90,
            93,
            94,
            95,
            96,
            97,
            98,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            125,
            127
        ],
        "rewards": [
            [
                5.043476486915964e-07,
                1.3709573702778664e-06,
                5.043473480777865e-07,
                3.726637951387472e-06,
                5.715004470313855e-07,
                1.2098655392921197e-06,
                4.785094494783494e-06,
                3.726639284103523e-06,
                3.7266410611296085e-06,
                8.315284241650899e-07
            ],
            [
                5.043474683204221e-07,
                2.5612831266946347e-06,
                9.422444815765128e-07,
                5.04347468323289e-07,
                1.7603434231777837e-06,
                1.2098658277451275e-06,
                1.2098652508391807e-06,
                3.288748673360027e-06,
                1.2098655392871682e-06,
                4.450852111148132e-07
            ],
            [
                1.3709572068478697e-06,
                2.561283126679493e-06,
                1.3709570434122812e-06,
                1.7603436330179102e-06,
                9.422449308716635e-07,
                3.288750241500471e-06,
                1.9947297215043796e-06,
                3.288748281295496e-06,
                8.315280276546789e-07,
                2.2603242978778778e-06
            ],
            [
                1.7603425837903113e-06,
                1.5534973842076057e-06,
                1.9947301970972664e-06,
                1.7603438428800754e-06,
                9.422450432014836e-07,
                4.4508515805735777e-07,
                1.209866260432471e-06,
                9.422450432014836e-07,
                5.715006514176113e-07,
                6.475947982037486e-07
            ],
            [
                0.9999945777816839,
                6.962253759904688e-06,
                1.1253524254650944e-07,
                0.9999974387174873,
                2.2603251062450327e-06,
                2.5612828213934817e-06,
                1.9947304348862686e-06,
                9.422444815814404e-07,
                1.7603440527286572e-06,
                1.3709570434178922e-06
            ],
            [
                2.5612825160562587e-06,
                1.6701415872385704e-05,
                2.2603253756956754e-06,
                1.1478768126057254e-05,
                1.99473067264854e-06,
                8.315283250394546e-07,
                3.288748281329893e-06,
                5.715003107738556e-07,
                8.315283250394546e-07,
                2.260324836776948e-06
            ],
            [
                5.715005151606823e-07,
                2.1024326584639497e-07,
                3.4663266243111764e-07,
                3.466327037539638e-07,
                1.0677028700363782e-06,
                1.0677026154806063e-06,
                1.5534979397500702e-06,
                6.475945666051092e-07,
                4.4508505193932864e-07,
                8.315284241650899e-07
            ],
            [
                6.475947982037486e-07,
                1.5534973842076057e-06,
                3.0590237279085045e-07,
                6.475947982037486e-07,
                5.422217677152175e-06,
                7.338209805224048e-07,
                1.5534971990169383e-06,
                1.9947301970972664e-06,
                3.466326211113502e-07,
                2.69957906184239e-07
            ],
            [
                4.2228329411708495e-06,
                9.422448185534261e-07,
                4.450850519403407e-07,
                3.927862002663297e-07,
                4.4508526417298334e-07,
                8.31528424162821e-07,
                3.0590226339061185e-07,
                7.338208055664991e-07,
                2.3823696679327928e-07,
                2.2603253756874524e-06
            ],
            [
                9.422443692527585e-07,
                2.6995790618350237e-07,
                1.147877359926923e-05,
                2.5612828213690224e-06,
                6.475946438022905e-07,
                5.043472278312808e-07,
                8.31528126775552e-07,
                3.466327863983311e-07,
                7.338207180801359e-07,
                2.7535697664698622e-05
            ],
            [
                2.3823685319244518e-07,
                5.043476486924565e-07,
                4.450850519403407e-07,
                2.1024336609874897e-07,
                1.209866260432471e-06,
                2.382368531929327e-07,
                1.209865539295696e-06,
                1.4449802095666915e-07,
                1.209865539295696e-06,
                2.69957906184239e-07
            ],
            [
                2.260324567337161e-06,
                1.1253525596134564e-07,
                4.450850519403407e-07,
                3.7266397283908927e-06,
                1.7603438428800754e-06,
                5.043474081993875e-07,
                2.1024341622426268e-07,
                5.715003789033962e-07,
                3.46632497145457e-07,
                1.2098662604291696e-06
            ],
            [
                2.699576809143613e-07,
                1.9947304348862686e-06,
                1.637377448057981e-07,
                1.6373762769138607e-07,
                1.0677031245953668e-06,
                1.8553910183674878e-07,
                1.209865539295696e-06,
                6.47595107001401e-07,
                2.382369951932796e-07,
                1.6373776432509826e-07
            ],
            [
                3.2887502415438413e-06,
                1.5534971990126997e-06,
                5.715004470295662e-07,
                4.450852111135988e-07,
                9.422449308673789e-07,
                2.9023112932045342e-06,
                1.5534975693869924e-06,
                1.7603436330091044e-06,
                7.338207180801359e-07,
                6.144175334418252e-06
            ],
            [
                2.4300249425247723e-05,
                3.288749065406658e-06,
                8.315280276546789e-07,
                4.450848927637999e-07,
                7.338209805170655e-07,
                1.3709573702647743e-06,
                1.2098655392662613e-06,
                2.260323489490968e-06,
                1.0677024881887838e-06,
                1.5534975693979422e-06
            ],
            [
                5.043475885674441e-07,
                4.222834954778007e-06,
                5.043472879540142e-07,
                1.3709567165461505e-06,
                3.288749849477628e-06,
                1.7603430034655858e-06,
                1.2098653950692178e-06,
                2.5612834320470717e-06,
                8.315284241650899e-07,
                9.422448185534261e-07
            ],
            [
                4.785096776499213e-06,
                5.422217030707961e-06,
                3.2887506336086064e-06,
                6.962255419931625e-06,
                7.88926634755014e-06,
                2.260325106237323e-06,
                1.0677032518785256e-06,
                4.222833947960866e-06,
                2.5612825160562587e-06,
                7.889262585886274e-06
            ],
            [
                1.994730672675753e-06,
                2.2603237589676295e-06,
                8.315277302857965e-07,
                1.0677032518700286e-06,
                2.1024331597262577e-07,
                1.5534983101602148e-06,
                6.144172404587612e-06,
                6.475950297971703e-07,
                2.10243290909724e-07,
                4.222834954801051e-06
            ],
            [
                1.2098655392871682e-06,
                3.288747889284851e-06,
                4.785095635655362e-06,
                1.3709567165530083e-06,
                1.0677033791612137e-06,
                3.059023727894942e-07,
                5.715007195447234e-07,
                3.2887506336235617e-06,
                2.2603245673155757e-06,
                1.9947292459347367e-06
            ],
            [
                1.8925143729954285e-05,
                1.2098655392871682e-06,
                1.2098662604247682e-06,
                9.422444815765128e-07,
                1.2098655392811161e-06,
                2.561281905390075e-06,
                3.2887482813149375e-06,
                1.2098662604291696e-06,
                7.338212429537553e-07,
                4.222834451327159e-06
            ],
            [
                1.444979692800516e-07,
                1.6373776432509826e-07,
                7.338207180898968e-07,
                2.1024336609843824e-07,
                3.9278629391427843e-07,
                4.450848927658745e-07,
                2.1024326584582131e-07,
                2.1024336609843824e-07,
                2.10243290909724e-07,
                1.6373770576776313e-07
            ],
            [
                1.3709576971425944e-06,
                1.3007128464961824e-05,
                3.120190765625026e-05,
                2.260325106237323e-06,
                1.994729008145876e-06,
                1.0677032518578904e-06,
                3.7266401726173067e-06,
                1.5534981249697903e-06,
                1.3007126913820052e-05,
                4.222833444590791e-06
            ],
            [
                1.3709575337078829e-06,
                1.7603427936263351e-06,
                1.5534979397592542e-06,
                0.9999960330145675,
                0.9999945777803908,
                0.9999981261252889,
                0.999998790134174,
                1.0677027427600627e-06,
                0.999994228080667,
                2.2603251062450327e-06
            ],
            [
                9.93120161310289e-08,
                2.5612831267202583e-06,
                7.889261645427538e-06,
                5.715005832872586e-07,
                6.144176066901277e-06,
                6.475946438042047e-07,
                1.7603434231833873e-06,
                1.3709572068522336e-06,
                1.5534983101602148e-06,
                9.422448185534261e-07
            ],
            [
                9.422448185510695e-07,
                1.2751902768478173e-07,
                1.7603430034867993e-06,
                1.2098662604291696e-06,
                3.4663249714451116e-07,
                1.8553919030858602e-07,
                4.450849988811838e-07,
                1.5534983101602148e-06,
                1.0677024882009222e-06,
                1.8553903548231313e-07
            ],
            [
                0.9999996940978827,
                0.9999962733620603,
                1.760343423160973e-06,
                4.785092783519724e-06,
                0.9999985406234329,
                0.9999151889798835,
                0.9999985406232584,
                1.2098659719757836e-06,
                1.370957860576702e-06,
                1.8553910183674878e-07
            ],
            [
                9.422447062294175e-07,
                2.561281600086738e-06,
                5.715003788993679e-07,
                2.561281600086738e-06,
                1.7603425837903113e-06,
                3.927862002663297e-07,
                1.0677028700363782e-06,
                3.059022269250683e-07,
                3.927862002641863e-07,
                2.699578739984626e-07
            ],
            [
                3.927862470899887e-07,
                5.715003789033962e-07,
                9.422445939002803e-07,
                7.338208930460318e-07,
                1.0677026154774503e-06,
                3.466326211113502e-07,
                9.422448185478557e-07,
                4.450850519403407e-07,
                6.475949526020042e-07,
                3.0590215399183813e-07
            ],
            [
                2.9023116391675407e-06,
                3.2887502415438413e-06,
                0.00023050668694863803,
                3.0590237279032884e-07,
                8.315278294001114e-07,
                1.7603438428740716e-06,
                6.962253760024999e-06,
                0.0007096702894637353,
                1.4449795205429202e-07,
                6.475946438022905e-07
            ],
            [
                3.7266379512857925e-06,
                1.2098652508287273e-06,
                7.889262585441413e-06,
                1.0129994601872894e-05,
                1.2098661161927025e-06,
                1.4738981971813965e-05,
                6.144173137014406e-06,
                1.2098655392662613e-06,
                1.0129988564716393e-05,
                3.5356238073889594e-05
            ],
            [
                5.715005151606823e-07,
                5.043474081993875e-07,
                5.043475885674441e-07,
                3.927861066170637e-07,
                3.288750241561788e-06,
                2.9023119851781017e-06,
                1.994729008145876e-06,
                9.422445939032799e-07,
                1.0677027427471959e-06,
                5.715007195431641e-07
            ],
            [
                7.734418542875216e-08,
                1.855391239547094e-07,
                8.7642526752214e-08,
                1.637376862489725e-07,
                1.3709567165617364e-06,
                6.023578501513224e-08,
                7.734414854823498e-08,
                9.931202796993203e-08,
                1.27519088491875e-07,
                1.4738976701170414e-05
            ],
            [
                9.422442569315887e-07,
                4.006370171677219e-05,
                7.338207180864763e-07,
                0.9999988634357482,
                0.9999970976869793,
                4.450852641737424e-07,
                3.927863875616689e-07,
                0.9999955048200393,
                1.3709570434178922e-06,
                4.450849458200093e-07
            ],
            [
                4.785095635624897e-06,
                1.0129992187658463e-05,
                8.939697369882888e-06,
                1.3709572068422585e-06,
                9.422448185478557e-07,
                5.715005832886879e-07,
                3.927860597935108e-07,
                6.475947982037486e-07,
                2.5612822107167428e-06,
                9.422444815765128e-07
            ],
            [
                2.699576809143613e-07,
                2.102434412871794e-07,
                1.2751901248454963e-07,
                3.466327450765785e-07,
                3.927863875616689e-07,
                3.466325797900508e-07,
                8.7642526752214e-08,
                3.927863875616689e-07,
                3.05902336324494e-07,
                1.6373766672994222e-07
            ],
            [
                2.2603240284371276e-06,
                2.902311639183378e-06,
                8.7642558095602e-08,
                0.9999938558224811,
                2.561281600086738e-06,
                1.5534975693979422e-06,
                1.553497199007048e-06,
                1.0677029973158649e-06,
                1.0677032518814388e-06,
                0.9999938558239417
            ],
            [
                7.338208930460318e-07,
                3.927862470861484e-07,
                1.637377057680051e-07,
                3.466325797896173e-07,
                5.715003107755449e-07,
                7.338211554783522e-07,
                9.422445939054222e-07,
                6.475947982022763e-07,
                5.715004470313855e-07,
                4.006369173950397e-05
            ],
            [
                1.3007123813382511e-05,
                6.475947210012481e-07,
                1.2098653950551882e-06,
                1.9947304348595095e-06,
                5.71500515159253e-07,
                6.144177531767002e-06,
                1.0677026154730804e-06,
                1.99472900813862e-06,
                6.1441724046434924e-06,
                1.0677026154730804e-06
            ],
            [
                7.734421308914719e-08,
                3.466326624336003e-07,
                1.8553907971855875e-07,
                3.4663249714612693e-07,
                1.1253513522447425e-07,
                3.9278634073732336e-07,
                7.338208930460318e-07,
                3.059022998576899e-07,
                5.043476486915964e-07,
                2.10243290909724e-07
            ],
            [
                7.338207180864763e-07,
                3.2887482813149375e-06,
                2.5612812947508257e-06,
                7.338212429537553e-07,
                4.450851049941403e-07,
                1.3709567165530083e-06,
                5.422221555380179e-06,
                5.715005151574337e-07,
                5.422218969895357e-06,
                2.5612828213818346e-06
            ],
            [
                3.7266392840781026e-06,
                1.0129990979842057e-05,
                5.422217030614265e-06,
                4.2228334445370225e-06,
                1.3709578605729614e-06,
                4.785096205973894e-06,
                1.2098661161789477e-06,
                1.1478766757404937e-05,
                8.939693106873817e-06,
                4.785094494716039e-06
            ],
            [
                1.5534984953552536e-06,
                3.288748281329893e-06,
                4.450848927658745e-07,
                5.043476486924565e-07,
                2.9023116391978967e-06,
                3.7266406168827523e-06,
                5.4222176771176554e-06,
                1.8553919030858602e-07,
                3.9278629391427843e-07,
                1.3709576971463352e-06
            ],
            [
                5.043472278322555e-07,
                7.338207180864763e-07,
                9.422450431989127e-07,
                9.422450431989127e-07,
                1.2098652508424818e-06,
                5.043473480777865e-07,
                5.04347348075149e-07,
                1.0677032518814388e-06,
                2.699577774585891e-07,
                4.785095635624897e-06
            ],
            [
                1.275190276859705e-07,
                1.8553907971758842e-07,
                1.7603438428800754e-06,
                1.1253509497883659e-07,
                2.3823690999290963e-07,
                3.466327450765785e-07,
                4.450850519403407e-07,
                1.4449798650551755e-07,
                1.1253513522447425e-07,
                9.931185038635267e-08
            ],
            [
                2.5612828213818346e-06,
                1.5534979397740895e-06,
                1.2098659719716573e-06,
                2.260324028427877e-06,
                1.0677028700363782e-06,
                2.260324836787226e-06,
                1.8925143729575624e-05,
                1.3709576971425944e-06,
                3.726639728370556e-06,
                9.422448185435711e-07
            ],
            [
                5.422217030747413e-06,
                4.450849988811838e-07,
                5.715005832886879e-07,
                6.144173137126169e-06,
                8.315280276546789e-07,
                1.7603427936335396e-06,
                2.902312677137316e-06,
                1.5534975693933505e-06,
                1.994729008145876e-06,
                7.338210680021253e-07
            ],
            [
                3.466325384661554e-07,
                2.699579061812927e-07,
                8.315284241650899e-07,
                1.3709567165579959e-06,
                4.450848927658745e-07,
                1.5534981249397663e-06,
                5.715007195447234e-07,
                4.450851580555361e-07,
                7.338209805200689e-07,
                7.338211554783522e-07
            ],
            [
                3.466326624336003e-07,
                3.726639284144195e-06,
                0.9999852610128469,
                8.315277302857965e-07,
                2.2603234895289998e-06,
                3.927863407379485e-07,
                3.9278629391427843e-07,
                2.2603251062450327e-06,
                2.699578096403948e-07,
                7.338208055680009e-07
            ],
            [
                3.7266383956509585e-06,
                9.422448185510695e-07,
                4.450850519403407e-07,
                1.3709573702822306e-06,
                7.338210680021253e-07,
                0.007577241432440344,
                0.9999785550492455,
                3.0590219045914655e-07,
                1.9947292459347367e-06,
                1.5534977545886537e-06
            ],
            [
                3.0590226339061185e-07,
                9.422443692555439e-07,
                4.450852111135988e-07,
                4.4508494582314646e-07,
                1.7603432132624344e-06,
                3.46632497145457e-07,
                7.338208055613267e-07,
                5.04347528446051e-07,
                5.715003789033962e-07,
                1.3709567165617364e-06
            ],
            [
                1.994729483723626e-06,
                5.715003107689177e-07,
                1.209865539295696e-06,
                1.5534983101602148e-06,
                9.422450432014836e-07,
                4.450851580540182e-07,
                2.6995774527718623e-07,
                5.715003789017068e-07,
                9.422448185534261e-07,
                4.785093353787868e-06
            ],
            [
                2.5612819054028872e-06,
                2.382369667929001e-07,
                5.715003107767143e-07,
                5.715007195447234e-07,
                5.715002426486762e-07,
                1.994730197090463e-06,
                4.785095635624897e-06,
                NaN,
                3.927860597945825e-07,
                3.726637951367137e-06
            ],
            [
                7.338207180864763e-07,
                3.2887482812745586e-06,
                6.144176066901277e-06,
                3.535626336072768e-05,
                3.2887482812745586e-06,
                4.2228324377164004e-06,
                3.7266406168827523e-06,
                4.4508494582405734e-07,
                NaN,
                7.889266347715168e-06
            ],
            [
                5.422221555414699e-06,
                9.931190958076104e-08,
                1.209865827752005e-06,
                1.1253517547010071e-07,
                2.1024336609843824e-07,
                4.006369219393695e-05,
                2.3823690999290963e-07,
                4.450852111155216e-07,
                0.9999706884585127,
                2.382369667929001e-07
            ],
            [
                5.422218323399208e-06,
                1.2098655392662613e-06,
                8.764249540862797e-08,
                1.2098658277451275e-06,
                3.466325797896173e-07,
                1.2098655392921197e-06,
                9.422444815765128e-07,
                1.5534979397394734e-06,
                1.2751905808881762e-07,
                5.315780536011123e-08
            ],
            [
                1.4738985486265496e-05,
                2.902312331125353e-06,
                3.288748673319648e-06,
                8.481101106463892e-05,
                6.962256249821764e-06,
                1.4738980215111302e-05,
                7.889265407177056e-06,
                0.00012339454556667436,
                3.726641061085547e-06,
                2.5612825160271407e-06
            ],
            [
                4.450849988798682e-07,
                1.0677027427600627e-06,
                3.059022998576899e-07,
                1.7603434231777837e-06,
                5.043472278312808e-07,
                4.2228339479858295e-06,
                2.2603242978871282e-06,
                5.715003107767143e-07,
                6.962257079832313e-06,
                4.450851580540182e-07
            ],
            [
                2.561281600076256e-06,
                8.315283250371857e-07,
                9.422448185534261e-07,
                9.422445939032799e-07,
                2.102434412875379e-07,
                1.5534973842076057e-06,
                3.726639284125553e-06,
                1.3709575337125585e-06,
                8.315279285370317e-07,
                1.3709568799919866e-06
            ],
            [
                6.475948754012522e-07,
                7.338211554783522e-07,
                1.3709576971379186e-06,
                1.5534979397790343e-06,
                8.939700567004841e-06,
                8.315279285351409e-07,
                0.00017952790209545142,
                1.0677027427569065e-06,
                4.2228334445370225e-06,
                4.785095635592258e-06
            ],
            [
                3.2887490653872164e-06,
                2.260325375634003e-06,
                6.475949526003845e-07,
                1.9947301970813926e-06,
                1.7603427936183298e-06,
                4.222833444467892e-06,
                8.315279285351409e-07,
                8.93969950101825e-06,
                9.422444815814404e-07,
                7.889264466725156e-06
            ],
            [
                1.5534975693979422e-06,
                1.3007130015299356e-05,
                3.9278624708775595e-07,
                3.9278629391427843e-07,
                9.422450431989127e-07,
                1.5534975693979422e-06,
                6.962257909785973e-06,
                5.71500515159253e-07,
                9.422447062294175e-07,
                2.902312331170226e-06
            ],
            [
                2.260324836787226e-06,
                1.7603434231777837e-06,
                2.561282210729555e-06,
                9.422448185510695e-07,
                9.422450432014836e-07,
                4.222832941193893e-06,
                3.2887506336086064e-06,
                1.0677026154730804e-06,
                1.209866260432471e-06,
                1.5534975693979422e-06
            ],
            [
                5.422221555296344e-06,
                1.994730197071414e-06,
                4.222833947932061e-06,
                9.4224425692559e-07,
                1.0677029973192638e-06,
                3.726641061109272e-06,
                6.144173137126169e-06,
                8.315279285370317e-07,
                1.9947297215043796e-06,
                5.422218969661113e-06
            ],
            [
                9.931186222523604e-08,
                3.466326624336003e-07,
                5.04347468323289e-07,
                8.315280276607289e-07,
                3.9278605979534166e-07,
                1.6373776432509826e-07,
                1.6373768624837685e-07,
                2.3823688159291947e-07,
                3.4663274507713016e-07,
                5.04347468323289e-07
            ],
            [
                2.69957906184239e-07,
                3.466325797888292e-07,
                2.6995771309523475e-07,
                4.785095065232451e-06,
                2.260324567337161e-06,
                2.699577774585891e-07,
                5.043472879540142e-07,
                6.144172404738491e-06,
                4.450852111148132e-07,
                5.043474081993875e-07
            ],
            [
                2.10243290909724e-07,
                2.10243290909724e-07,
                2.3823688159237777e-07,
                5.043473480777865e-07,
                3.9278629391427843e-07,
                3.9278605979534166e-07,
                4.4508494582405734e-07,
                1.855391239544352e-07,
                3.059021175261338e-07,
                2.382369951932796e-07
            ],
            [
                1.3709576971425944e-06,
                6.144176066795103e-06,
                1.760344052714248e-06,
                4.785093924330255e-06,
                6.9622587393661365e-06,
                3.2887502415438413e-06,
                1.3709575337078829e-06,
                5.422217030614265e-06,
                2.5612825160096693e-06,
                6.144175334468545e-06
            ],
            [
                2.902312331170226e-06,
                2.561282516066741e-06,
                8.315279285351409e-07,
                1.2098659719757836e-06,
                9.422448185510695e-07,
                1.7603438428800754e-06,
                1.0677029973192638e-06,
                8.315281267861397e-07,
                1.0677029973192638e-06,
                1.3709576971242028e-06
            ],
            [
                3.05902263391829e-07,
                4.4508494582405734e-07,
                7.338210680021253e-07,
                2.699577774585891e-07,
                8.315282259138311e-07,
                8.315278294114555e-07,
                1.5534984953552536e-06,
                1.0677029973219343e-06,
                NaN,
                6.47595107001401e-07
            ],
            [
                1.855391239544352e-07,
                2.260325375650449e-06,
                2.3823682479181176e-07,
                1.1253514863968147e-07,
                7.338211554758494e-07,
                2.2603240284371276e-06,
                1.8553907971855875e-07,
                7.889265407255982e-06,
                1.1253514863968147e-07,
                1.1253525596174225e-07
            ],
            [
                3.7266401726359486e-06,
                9.422450432014836e-07,
                1.3709576971463352e-06,
                1.7603440527286572e-06,
                1.209865827752005e-06,
                2.5612812947508257e-06,
                8.315282259138311e-07,
                1.3709575337159875e-06,
                1.9947304348862686e-06,
                1.5534984953552536e-06
            ],
            [
                1.3709570434178922e-06,
                1.7603438428800754e-06,
                2.3823688159291947e-07,
                3.726639284125553e-06,
                5.715003789017068e-07,
                1.9947290081286418e-06,
                5.715006514105942e-07,
                1.9947304348862686e-06,
                1.5534973842076057e-06,
                6.475951069985296e-07
            ],
            [
                9.422444815814404e-07,
                1.209866260432471e-06,
                2.5612819054133693e-06,
                4.2228319344021954e-06,
                5.715003107767143e-07,
                3.466325797888292e-07,
                2.3823696679327928e-07,
                6.475951069932288e-07,
                1.3007130015677909e-05,
                1.3709568799760888e-06
            ],
            [
                8.315281267649641e-07,
                3.0590215399183813e-07,
                7.338209805090567e-07,
                1.5534971990126997e-06,
                4.450849988811838e-07,
                2.5612816000646084e-06,
                1.3709573702822306e-06,
                1.2098661161982042e-06,
                9.422445939002803e-07,
                4.450849988811838e-07
            ],
            [
                9.422448185478557e-07,
                NaN,
                1.8553907971855875e-07,
                6.475947982037486e-07,
                1.5534979397740895e-06,
                4.222833444590791e-06,
                1.3709567165579959e-06,
                4.222834451382849e-06,
                2.5612819054133693e-06,
                1.0677027427600627e-06
            ]
        ]
    },
    {
        "q_id": "9461_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            11,
            12,
            13,
            14,
            15,
            18,
            19,
            20,
            21,
            22,
            23,
            25,
            26,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            65,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            108,
            109,
            110,
            111,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                8.939693107288474e-06,
                1.3709568799879344e-06,
                NaN,
                9.931193325797878e-08,
                3.4663278639892215e-07,
                8.315277302857965e-07,
                2.10243290909724e-07,
                NaN,
                3.466326624336003e-07,
                2.902312677150514e-06
            ],
            [
                7.338210680002898e-07,
                2.1024334103505245e-07,
                1.6373764721072816e-07,
                1.2751904288710323e-07,
                8.315277302841894e-07,
                2.3823696679230424e-07,
                6.475950297993789e-07,
                2.6995771309523475e-07,
                1.6373762769138607e-07,
                5.715005832872586e-07
            ],
            [
                0.9999995262092728,
                0.9999997463982241,
                0.9999996940977732,
                0.9999996533673791,
                0.9999993106391194,
                0.9999996940976273,
                0.9999996072136593,
                0.9999986290424675,
                0.9999988634361551,
                0.9999997300422226
            ],
            [
                0.9999987121041726,
                3.2887506336086064e-06,
                1.5534975693979422e-06,
                7.338209805240734e-07,
                0.9999988634361555,
                0.9999983463108107,
                0.999998629042469,
                3.120190393794438e-05,
                0.999998540624303,
                0.9999485577938383
            ],
            [
                4.450851049959619e-07,
                3.288749849529972e-06,
                2.382369951932796e-07,
                4.450852111155216e-07,
                1.6373776432509826e-07,
                2.561283126728994e-06,
                7.734428685047173e-08,
                NaN,
                NaN,
                9.931189774187203e-08
            ],
            [
                0.9999949062968272,
                0.9999983463100228,
                0.9999975938973762,
                8.315279285370317e-07,
                0.9999706884621271,
                1.209865827752005e-06,
                0.9999989322972579,
                0.9999994284996898,
                0.9999967112513323,
                0.9999989969862713
            ],
            [
                NaN,
                8.315281267834927e-07,
                4.450849988811838e-07,
                5.715006514176113e-07,
                1.994730197090463e-06,
                8.315279285370317e-07,
                7.338208055664991e-07,
                1.2098662604291696e-06,
                8.315283250371857e-07,
                7.338208930460318e-07
            ],
            [
                3.927861534370498e-07,
                2.382369667929001e-07,
                5.043472879504592e-07,
                3.726638839806038e-06,
                1.8925157266089433e-05,
                1.9947306726594253e-06,
                7.889262585728421e-06,
                1.4738985486506781e-05,
                3.466327037512053e-07,
                NaN
            ],
            [
                2.902312677150514e-06,
                1.8553914607267268e-07,
                2.2603234895372223e-06,
                4.785094494783494e-06,
                3.927862470899887e-07,
                1.6373772528704005e-07,
                1.5534973842076057e-06,
                1.8925157266089433e-05,
                4.222833444590791e-06,
                2.6995774527718623e-07
            ],
            [
                1.7603425837855082e-06,
                NaN,
                3.466325797896173e-07,
                NaN,
                3.466325797888292e-07,
                NaN,
                6.962255419931625e-06,
                3.0590215399183813e-07,
                3.059022269250683e-07,
                4.450852641737424e-07
            ],
            [
                0.9999994956527726,
                0.9999994284994854,
                0.9999981261239484,
                0.9999987121043253,
                0.9999987121044795,
                0.999999114843282,
                0.9999981261237243,
                0.9999980052709936,
                0.9999724643188831,
                0.9999989322971323
            ],
            [
                0.9999993524048937,
                0.9999997463981939,
                0.9999999123575674,
                0.9999994284995533,
                0.9999990577556316,
                0.9999996743687034,
                0.9999904837483342,
                0.9999994631249965,
                0.999999730042094,
                0.9999998724809116
            ],
            [
                0.9999977396759758,
                0.9999993524048938,
                0.9999985406241295,
                0.9999993106386265,
                0.9999991684716757,
                0.9999810748563532,
                0.9999984465016916,
                0.9999983463106132,
                0.9999987901340298,
                0.9999985406232591
            ],
            [
                0.9999995818814267,
                0.9999994284992807,
                0.9999989969860322,
                0.9999989969859123,
                0.9999996310115479,
                0.9999984465016909,
                0.9999967112513296,
                0.9999980052709931,
                0.9999996310115918,
                0.9999991684721713
            ],
            [
                2.902312331170226e-06,
                2.260323758987159e-06,
                1.6373776432509826e-07,
                1.1478770862882149e-05,
                1.6701417863559525e-05,
                2.2603242978871282e-06,
                8.939700567094277e-06,
                0.0001795280091563771,
                1.5534977545886537e-06,
                9.422442569315887e-07
            ],
            [
                0.9999964991443404,
                0.999999554914842,
                0.9999992661791951,
                0.9999991684716757,
                0.9999989322973859,
                0.9999987901346064,
                NaN,
                0.999999761763147,
                0.9999981261243969,
                0.9999991148430705
            ],
            [
                0.9999986290426317,
                NaN,
                0.9999960330145656,
                0.9999962733607262,
                0.9999960330126738,
                0.9999975938982388,
                0.999998629042141,
                0.9999877809211278,
                1.0,
                0.999998346309628
            ],
            [
                8.315280276626197e-07,
                5.043472278322555e-07,
                3.466325797896173e-07,
                8.93969950132721e-06,
                1.9947292459347367e-06,
                2.699578740032504e-07,
                4.222834954801051e-06,
                8.315279285370317e-07,
                7.338209805240734e-07,
                4.450848927658745e-07
            ],
            [
                3.927863875616689e-07,
                NaN,
                6.962255419931625e-06,
                7.338209805240734e-07,
                2.7535700950274782e-05,
                2.2603253756956754e-06,
                2.561281294760143e-06,
                1.994729008145876e-06,
                NaN,
                3.53562422882756e-05
            ],
            [
                0.9999988634366969,
                0.9999985406234331,
                0.9999996940976639,
                0.9999986290423042,
                0.999999310639202,
                0.999999310638873,
                2.1024336609638268e-07,
                0.99999971263131,
                0.9999991148432815,
                9.422449308789479e-07
            ],
            [
                NaN,
                8.315279285351409e-07,
                6.475947982022763e-07,
                2.430024073523505e-05,
                2.5612834320470717e-06,
                1.2098652508424818e-06,
                6.144176066901277e-06,
                5.043474683220276e-07,
                3.4663274507713016e-07,
                5.71500515159253e-07
            ],
            [
                4.785093924362895e-06,
                1.2098653950692178e-06,
                1.0677024881887838e-06,
                1.3007133116542802e-05,
                6.475950297971703e-07,
                NaN,
                7.338210679979539e-07,
                1.3709572068272963e-06,
                1.209865539295696e-06,
                NaN
            ],
            [
                0.999999218851856,
                0.9999997126315154,
                0.9999994631249322,
                0.9999969105062925,
                0.9999989322966217,
                0.999998996986271,
                0.9999987901338846,
                0.9999952149072224,
                0.9999995549150543,
                0.9999987901344614
            ],
            [
                0.9999989322968761,
                0.9999989322967486,
                0.9999981261241712,
                0.9999994956525919,
                0.9999994956523517,
                0.9999996072138936,
                0.9999993916411086,
                0.999998932297385,
                0.9999996072136593,
                0.9999869928747058
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                0.9999910603047856,
                NaN,
                NaN,
                NaN,
                0.9999885212291697,
                NaN
            ],
            [
                7.338207180898968e-07,
                2.6995790618469934e-07,
                8.315281267882195e-07,
                2.699578096403948e-07,
                5.04347468323289e-07,
                1.6373776432509826e-07,
                2.699578096403948e-07,
                3.0590237279085045e-07,
                2.1024334103581732e-07,
                1.3709572068522336e-06
            ],
            [
                0.9999991684718738,
                0.9999964991447577,
                NaN,
                NaN,
                0.9999996743686645,
                NaN,
                0.9999977396757045,
                0.9999989322973857,
                0.9999992188512972,
                0.999994228082046
            ],
            [
                2.9023119851899796e-06,
                8.315277302857965e-07,
                7.338209805240734e-07,
                1.209866260432471e-06,
                2.2603251062450327e-06,
                1.0677026154806063e-06,
                1.9947299593078385e-06,
                1.9947299592933255e-06,
                4.2228339479858295e-06,
                1.5534971990169383e-06
            ],
            [
                0.9999994631248045,
                0.9999985406237806,
                0.999997876620781,
                0.9999988634364262,
                0.9999988634358838,
                NaN,
                0.9999995262093294,
                0.9999997617631471,
                8.315277302857965e-07,
                0.9999994284995531
            ],
            [
                5.043475885674441e-07,
                0.0001233945603033627,
                1.8553903548231313e-07,
                5.043473480777865e-07,
                1.2098653950692178e-06,
                1.27519073289925e-07,
                2.382368531929327e-07,
                2.382370235922541e-07,
                6.475949526003845e-07,
                NaN
            ],
            [
                0.9999981261246202,
                0.999998712104325,
                0.9999980052702836,
                0.9999998144608319,
                8.315278294114555e-07,
                NaN,
                0.999997438717792,
                0.9999934595627961,
                0.9999984465018764,
                0.9999991684720728
            ],
            [
                0.9999988634358842,
                0.9999969105055602,
                0.9999945777797501,
                0.9999949062968346,
                0.9999967112493711,
                2.5612812947077304e-06,
                0.9999970976876753,
                0.9999982396572114,
                0.9999930377429542,
                NaN
            ],
            [
                1.637377448057981e-07,
                5.715003107767143e-07,
                9.422450432014836e-07,
                0.9992903295781548,
                8.315278294114555e-07,
                2.6995790618350237e-07,
                2.6995774527718623e-07,
                2.1024341622297196e-07,
                4.450852111148132e-07,
                9.422443692574719e-07
            ],
            [
                0.9999969105059243,
                0.9999988634358844,
                1.2098656835252174e-06,
                0.9999989322968762,
                0.999999495652472,
                0.9999994284994853,
                0.9998911030401636,
                0.9999988634365619,
                0.9999994631248688,
                0.9999986290421409
            ],
            [
                1.6373768624837685e-07,
                1.2751901248391176e-07,
                2.6995790618350237e-07,
                9.931194509683815e-08,
                3.466327037548308e-07,
                2.1024341622426268e-07,
                2.10243290909724e-07,
                1.8553905760024476e-07,
                2.382368815916736e-07,
                3.9278629391427843e-07
            ],
            [
                2.2603251062450327e-06,
                2.2603245673443566e-06,
                9.422443692574719e-07,
                2.5612819054133693e-06,
                1.012998977264307e-05,
                8.76424013786396e-08,
                6.144176066943187e-06,
                1.5534984953552536e-06,
                5.043476486924565e-07,
                6.962258739796719e-06
            ],
            [
                1.3709575337159875e-06,
                1.5534971990169383e-06,
                4.222833948008874e-06,
                NaN,
                6.475945666063607e-07,
                2.2603242978943238e-06,
                8.315284241665078e-07,
                1.209865827752005e-06,
                1.209866260432471e-06,
                2.9023116392097746e-06
            ],
            [
                0.9999989969855535,
                0.9999485577622738,
                0.9999998642566543,
                0.9999987121046316,
                0.9999996533673376,
                0.9999994284994169,
                0.9999992661787573,
                0.9999997617630901,
                0.9999995549149482,
                0.9999985406237797
            ],
            [
                0.9999992188516701,
                0.9999991148427536,
                0.9999991148433871,
                0.9999993524049707,
                0.9999942280792928,
                0.9999995262092163,
                0.9999992661791951,
                0.9999990577551827,
                0.9999987121046326,
                0.9999989969860325
            ],
            [
                0.9999995549148423,
                0.9999996072136595,
                0.9999998362622358,
                0.9999994956524719,
                0.9999998874648514,
                0.9999967112497639,
                0.9999987121043249,
                9.422450432030903e-07,
                0.9999997617630617,
                0.9999996743687424
            ],
            [
                5.043475885657239e-07,
                1.3709570434178922e-06,
                7.889259764517575e-06,
                1.892515501014656e-05,
                4.222834954778007e-06,
                6.962259569750576e-06,
                1.99473067264854e-06,
                2.260325106237323e-06,
                5.715007195447234e-07,
                4.2228319344021954e-06
            ],
            [
                0.999994228080667,
                0.9999991684718745,
                0.9999994631251884,
                0.9999980052705193,
                0.9999989322970041,
                0.9999986290432862,
                0.9999993524052795,
                0.9999993106386263,
                0.9999992188514836,
                0.999997739674629
            ],
            [
                0.9999993916406735,
                NaN,
                0.9999987121047852,
                0.9999977396754359,
                0.9999949062950045,
                0.9999996940978096,
                0.9999998724809419,
                0.9999995818810778,
                0.999999776197105,
                0.9999996940978096
            ],
            [
                0.9999991684720729,
                0.9999992188519493,
                0.9999994631251884,
                0.9999980052707562,
                0.9999984465020626,
                0.9999993106392018,
                0.9999623635354433,
                0.9999987901340306,
                0.9999945777791278,
                0.9999964991439227
            ],
            [
                NaN,
                1.8553914607237736e-07,
                4.222833948008874e-06,
                5.043475885688201e-07,
                NaN,
                2.2603242978943238e-06,
                1.012999098021058e-05,
                0.9999980052693281,
                3.72663883989755e-06,
                3.2887494574832472e-06
            ],
            [
                0.9999992661791075,
                0.9999987121044791,
                0.9999984465022475,
                0.9999984465022472,
                NaN,
                0.9999991148427539,
                0.9999998555019963,
                0.9999998024946566,
                0.999999266179195,
                0.999999761763147
            ],
            [
                0.9999985406230844,
                0.9999904837483264,
                3.4663249714612693e-07,
                0.9999949062956104,
                NaN,
                1.0677032518814388e-06,
                2.561281294760143e-06,
                0.9999987121043253,
                0.9999988634357483,
                0.9999987901346057
            ],
            [
                1.0677024882009222e-06,
                3.9278634073625165e-07,
                6.144172404738491e-06,
                5.043472879540142e-07,
                3.288749849529972e-06,
                9.422445939054222e-07,
                3.927862470899887e-07,
                9.422442569315887e-07,
                3.0590215399246414e-07,
                1.0677024882009222e-06
            ],
            [
                0.9999983463100234,
                0.9999994956527124,
                0.9999991684717763,
                0.9999988634362914,
                0.9999987121049413,
                0.9999993106391197,
                0.9999987901347513,
                0.9999984465028046,
                0.9999993524052025,
                0.9999989322968773
            ],
            [
                2.902313023130843e-06,
                1.9947304348862686e-06,
                NaN,
                1.1478764021029928e-05,
                2.902312677137316e-06,
                3.2887506336235617e-06,
                6.475945666051092e-07,
                5.715006514176113e-07,
                1.3709575337159875e-06,
                7.889266347786918e-06
            ],
            [
                7.338210680021253e-07,
                6.962258739796719e-06,
                4.22283545819819e-06,
                NaN,
                4.222833444590791e-06,
                2.753569766795419e-05,
                8.315278294114555e-07,
                2.75356812556058e-05,
                1.8925157266089433e-05,
                1.4738987243692646e-05
            ],
            [
                0.9999987901338854,
                4.7850933539684755e-06,
                2.699578096403948e-07,
                0.9999991684722705,
                NaN,
                0.9999998461827139,
                0.9999997617631753,
                0.9999996743687034,
                0.9999989969856735,
                0.9999992188518564
            ],
            [
                1.2098653950606901e-06,
                1.5534975693869924e-06,
                1.3709572068179446e-06,
                2.561281905376098e-06,
                1.5534983101301911e-06,
                2.561282210701601e-06,
                1.3709578605542582e-06,
                1.0677027427569065e-06,
                1.7603436329714805e-06,
                1.9947290080343035e-06
            ],
            [
                0.9999982396561583,
                0.9999985406230844,
                3.466325797900508e-07,
                0.999999391640746,
                0.9999987901343176,
                7.338208930460318e-07,
                0.9999994956525321,
                0.9999988634362905,
                0.9999985406234325,
                0.9999987121052457
            ],
            [
                5.715005151606823e-07,
                5.715005151606823e-07,
                1.0677029973192638e-06,
                3.059022269250683e-07,
                4.785093353909723e-06,
                6.144176799283803e-06,
                3.059021175261338e-07,
                2.2603253756874524e-06,
                3.4663278639892215e-07,
                1.3709576971242028e-06
            ],
            [
                0.999999554914736,
                0.9999992188518559,
                0.999998790134606,
                0.9999995549148951,
                0.999998932296749,
                0.9999996940976638,
                0.999997593897666,
                0.9999993916408186,
                0.9999993106387083,
                0.9999991684718736
            ],
            [
                8.939697369980456e-06,
                NaN,
                2.260324836776948e-06,
                1.5534979397790343e-06,
                3.466326624336003e-07,
                1.5534983101478522e-06,
                1.0129993395336818e-05,
                7.338210680021253e-07,
                3.05902263391829e-07,
                5.715002426486762e-07
            ],
            [
                8.939693107288474e-06,
                3.059022998576899e-07,
                5.715005832886879e-07,
                2.699577774585891e-07,
                6.475949526020042e-07,
                2.9023112932177327e-06,
                2.102434162245973e-07,
                3.9278610661902853e-07,
                5.715005832886879e-07,
                4.785094494811783e-06
            ],
            [
                0.9999984465018767,
                0.9999987901346066,
                0.9999988634365616,
                4.4508515805735777e-07,
                0.9999993916410362,
                0.9999991684722702,
                0.9999987901340298,
                0.999999168472072,
                0.9999993524052795,
                0.9999970976869834
            ],
            [
                1.9947292459406333e-06,
                9.931198061405701e-08,
                7.338212429582604e-07,
                3.466326624336003e-07,
                6.144176066943187e-06,
                1.3007123813559956e-05,
                2.1024344128660572e-07,
                NaN,
                NaN,
                1.1253526937656726e-07
            ],
            [
                0.9999989322973865,
                0.9999985406241283,
                0.9999974387168757,
                0.9999974387187107,
                0.9999972735297329,
                0.9999993916408912,
                0.9999974387171848,
                0.9999955048184399,
                0.9999962733598364,
                0.9999975938968041
            ],
            [
                4.785093353940187e-06,
                8.315278294097538e-07,
                2.2603242978871282e-06,
                3.2887482813149375e-06,
                2.382368247924618e-07,
                1.760343003481596e-06,
                5.04347528446051e-07,
                8.315283250371857e-07,
                1.5534983101602148e-06,
                NaN
            ],
            [
                0.9999984465015059,
                0.9999985406232591,
                0.9999972735294095,
                0.999999168472072,
                0.999957352527139,
                0.9999989969861516,
                0.9999997761971848,
                0.9999975938965167,
                0.9999972735284356,
                0.9999974387180983
            ],
            [
                3.0590237279085045e-07,
                3.466327037539638e-07,
                7.338208930460318e-07,
                5.715002426475718e-07,
                3.466325797896173e-07,
                3.927862002663297e-07,
                3.9278634073625165e-07,
                3.4663266243111764e-07,
                4.006367786720367e-05,
                9.422447062294175e-07
            ],
            [
                1.2751899728311609e-07,
                1.8553916819032217e-07,
                9.422445939054222e-07,
                4.450849458218309e-07,
                1.8553919030858602e-07,
                1.0677029973192638e-06,
                1.6373774480605869e-07,
                1.855391239544352e-07,
                3.9278610661822475e-07,
                NaN
            ],
            [
                NaN,
                5.422221555380179e-06,
                3.466327037548308e-07,
                4.4508515805735777e-07,
                NaN,
                2.2603251062450327e-06,
                NaN,
                NaN,
                3.927862002663297e-07,
                1.5534981249736758e-06
            ],
            [
                7.338208930460318e-07,
                4.4508515805735777e-07,
                NaN,
                NaN,
                5.043475885696228e-07,
                8.315279285370317e-07,
                2.5612819054133693e-06,
                NaN,
                NaN,
                NaN
            ],
            [
                1.760343003481596e-06,
                1.2098662604291696e-06,
                3.726638395611981e-06,
                1.7603440527222532e-06,
                1.0677027427600627e-06,
                2.902311639183378e-06,
                9.422445939032799e-07,
                5.422218969858371e-06,
                3.2887478892683997e-06,
                1.553497384196656e-06
            ],
            [
                0.9999981261243962,
                0.9999993916408911,
                7.338207180898968e-07,
                0.9999978766210351,
                0.9999990577556312,
                0.999997739675437,
                0.9999989322968765,
                0.9999996533674205,
                0.9999988634358842,
                0.9999991684717745
            ],
            [
                1.892514147435727e-05,
                0.9999989322970033,
                1.3007130015677909e-05,
                0.9999934595596827,
                6.1441767993788005e-06,
                NaN,
                7.338207180898968e-07,
                8.315278294114555e-07,
                2.2603248367949354e-06,
                1.2098656835252174e-06
            ],
            [
                NaN,
                1.0677026154806063e-06,
                NaN,
                8.315281267861397e-07,
                9.422449308716635e-07,
                1.760343213335281e-06,
                1.2098659719716573e-06,
                NaN,
                1.3709568799919866e-06,
                1.7603440527286572e-06
            ],
            [
                8.315278293899016e-07,
                4.785094494750855e-06,
                1.994729483630195e-06,
                1.9947299592570416e-06,
                1.2098653950480359e-06,
                1.0677026154730804e-06,
                1.2098662604247682e-06,
                5.715003107655392e-07,
                5.715007195410849e-07,
                2.260325375634003e-06
            ],
            [
                2.753569110256289e-05,
                1.994729008151319e-06,
                5.043476486924565e-07,
                5.829124470847917e-05,
                NaN,
                NaN,
                1.5534983101644536e-06,
                0.00015843623590271617,
                7.338207180898968e-07,
                NaN
            ],
            [
                0.9999992661789324,
                0.9999992661792825,
                0.9999997126313441,
                0.9999987901343182,
                0.9999996072136595,
                0.9999989322975125,
                0.999999789756659,
                0.9999983463098239,
                0.9999995818811774,
                0.9999996940978461
            ],
            [
                0.9999967112497625,
                0.9999998024946332,
                0.9999984465026167,
                0.9999991684715767,
                0.9999998874648515,
                0.999998629042794,
                0.9999992188516699,
                0.99999926617867,
                0.9999989969857936,
                NaN
            ],
            [
                0.9999985406234343,
                0.9999987121047866,
                0.9999992661791077,
                0.999998346310614,
                8.939700567004841e-06,
                0.999996273359396,
                0.9999991148429659,
                0.9999989322966234,
                0.9999988634358853,
                0.9999988634364269
            ],
            [
                7.338207180898968e-07,
                NaN,
                6.47595107001401e-07,
                3.4663262111182307e-07,
                1.3007134667436886e-05,
                NaN,
                1.4449807263312446e-07,
                3.0590219045914655e-07,
                4.785095635655362e-06,
                NaN
            ],
            [
                2.561282516066741e-06,
                1.2098658277451275e-06,
                1.6373776432509826e-07,
                1.637377448057981e-07,
                1.7603438428740716e-06,
                1.3709568799823232e-06,
                NaN,
                1.2098662604291696e-06,
                1.9947304348862686e-06,
                2.2603242978778778e-06
            ],
            [
                0.9999930377462821,
                0.9999987121046325,
                0.9999982396563705,
                0.9999984465024326,
                0.9999991148433879,
                0.9999996072138468,
                0.9999989969861519,
                0.999998790134319,
                0.9999982396559498,
                0.9999990577555194
            ],
            [
                0.9999985406230862,
                NaN,
                0.999996910506293,
                0.9999822214505384,
                0.9999999006880904,
                0.9999993916410362,
                0.9999952149055152,
                0.9999996072136128,
                0.9999771719975249,
                0.999996033015516
            ],
            [
                1.2098656835252174e-06,
                5.043474683204221e-07,
                4.450850519403407e-07,
                5.04347468323289e-07,
                3.927862002663297e-07,
                2.561281294760143e-06,
                9.422443692574719e-07,
                2.4300237838535383e-05,
                5.043472278322555e-07,
                5.043476486924565e-07
            ],
            [
                0.9999998257022045,
                2.2603242978943238e-06,
                0.9999992188516696,
                0.9999983463098243,
                0.9999996940978462,
                0.9999980052707559,
                0.9999982396559496,
                8.315282259151545e-07,
                0.9999991684721711,
                0.9999987901341734
            ],
            [
                1.6373776432509826e-07,
                6.475945666063607e-07,
                1.2098661162056318e-06,
                8.764244316973974e-08,
                1.6373764721072816e-07,
                7.338207180898968e-07,
                NaN,
                NaN,
                6.144176799166453e-06,
                6.475950298021765e-07
            ],
            [
                1.1253526937656726e-07,
                0.9999957771650522,
                0.9999969105059294,
                0.9999938558254116,
                0.9999989969856735,
                0.999997097687326,
                0.9999991148432815,
                0.9999997463981637,
                0.9999992188519493,
                0.9999996310113279
            ],
            [
                NaN,
                2.1024339116168358e-07,
                NaN,
                1.8553907971879076e-07,
                NaN,
                3.0590219045914655e-07,
                4.450848927658745e-07,
                NaN,
                5.043476486915964e-07,
                1.5534971990169383e-06
            ],
            [
                0.9999985406243025,
                NaN,
                0.9999997463980731,
                0.9999987901338855,
                0.9999955048184324,
                0.9999987901341731,
                0.9999869928731443,
                0.9999938558276141,
                0.9999981261246186,
                0.9999203269730822
            ],
            [
                1.7603425837903113e-06,
                5.04347468323289e-07,
                6.962257079889302e-06,
                1.0677026154827912e-06,
                9.422445939054222e-07,
                7.33821330437595e-07,
                3.7266410611465547e-06,
                9.422449308789479e-07,
                4.785095635655362e-06,
                5.422217677152175e-06
            ],
            [
                1.8925145985895816e-05,
                1.3007125363908762e-05,
                7.484626297142789e-05,
                0.9999960330140983,
                8.481104139717231e-05,
                1.6701423836262173e-05,
                0.0009110512455811098,
                NaN,
                4.006371129615879e-05,
                8.939698435657833e-06
            ],
            [
                0.999998863436426,
                0.9999993106386261,
                0.9999972735297316,
                0.9999962733598318,
                0.9999964991460071,
                0.999999674368781,
                0.9999987121047851,
                0.9999983463104156,
                0.9999877809240075,
                0.9999993106388728
            ],
            [
                0.999998863436019,
                0.9999987121050926,
                0.9999925887174903,
                0.9999960330150365,
                0.9999991684721714,
                0.9999991684716755,
                0.9999996940978462,
                0.9999987121041718,
                0.9999955048194994,
                0.9999991148429647
            ],
            [
                0.9999771720002699,
                NaN,
                2.260324028427877e-06,
                NaN,
                0.9999960330150418,
                0.9999982396569992,
                0.9999843104466282,
                0.9999994631249964,
                0.9999952149060884,
                0.9999995262094422
            ],
            [
                1.370957860576702e-06,
                8.939698435657833e-06,
                4.222833947960866e-06,
                3.05902190458764e-07,
                3.466327037553825e-07,
                1.7603440527334603e-06,
                1.8925155009767892e-05,
                NaN,
                4.222834451382849e-06,
                3.726639728370556e-06
            ],
            [
                0.9999987901347505,
                0.99999812612462,
                0.9999993524050477,
                6.605212107986466e-05,
                0.999948557774415,
                0.9999994956525321,
                0.9999910603016141,
                0.9999990577550699,
                0.9999985406234333,
                0.9999962733598418
            ],
            [
                5.715004470243685e-07,
                9.422448185510695e-07,
                2.902311639183378e-06,
                2.5612812947508257e-06,
                1.3007134667259441e-05,
                3.288748281329893e-06,
                5.422217677152175e-06,
                4.785094494783494e-06,
                2.9023112932177327e-06,
                4.450851580555361e-07
            ],
            [
                0.9999756997564421,
                0.9999994284996895,
                0.9999984465028021,
                0.9999987901343173,
                0.9999993916411812,
                0.9999980052693295,
                0.9999995549147891,
                NaN,
                0.999994577782977,
                0.9999989969856732
            ],
            [
                2.260324028427877e-06,
                0.9999960330140881,
                NaN,
                0.9999996072136127,
                8.315283250371857e-07,
                0.9999151889799576,
                7.889259764445822e-06,
                1.5534971989907999e-06,
                0.9999986290429579,
                1.5534979397740895e-06
            ],
            [
                0.9999955048168288,
                0.9999991148432814,
                0.9999989322968762,
                0.9999983463106143,
                0.9999969105062976,
                0.9999989322968775,
                NaN,
                NaN,
                0.9999969105048233,
                NaN
            ],
            [
                6.475950298021765e-07,
                NaN,
                1.0677027427624903e-06,
                8.315279285370317e-07,
                5.422221555414699e-06,
                0.9999038975431964,
                1.8553910183674878e-07,
                NaN,
                NaN,
                2.9023116392097746e-06
            ],
            [
                0.9999339478792945,
                0.9999995549150015,
                0.9999977396759737,
                0.9999957771655555,
                0.9999997761971849,
                0.9999967112497623,
                2.1024331597262577e-07,
                0.9999992188519494,
                0.9999938558254139,
                0.9999991684721714
            ],
            [
                7.338207180898968e-07,
                1.855391681906175e-07,
                2.6995790618469934e-07,
                3.2887502415767434e-06,
                1.4449802095666915e-07,
                2.102434162245973e-07,
                2.2603242978871282e-06,
                2.699577774585891e-07,
                6.475947982037486e-07,
                6.475945666063607e-07
            ],
            [
                2.2603237589676295e-06,
                1.3709570434178922e-06,
                5.043476486902204e-07,
                1.2098659719757836e-06,
                1.5534975693933505e-06,
                1.2098652508347793e-06,
                3.059022269250683e-07,
                3.9278615344178325e-07,
                0.999998790134461,
                6.475947982022763e-07
            ],
            [
                1.2098652508424818e-06,
                1.994729483723626e-06,
                4.785096776499213e-06,
                6.475947982037486e-07,
                1.2098661162056318e-06,
                7.88926070489716e-06,
                1.2098653950692178e-06,
                4.222831934379152e-06,
                3.288747889284851e-06,
                3.059022998576899e-07
            ],
            [
                5.715003107767143e-07,
                NaN,
                4.450852641737424e-07,
                5.043474683220276e-07,
                NaN,
                3.059022998576899e-07,
                NaN,
                2.2603248367949354e-06,
                9.93118503859575e-08,
                3.05902263391829e-07
            ],
            [
                0.9999998257021422,
                0.9999994284995533,
                0.9999996743688976,
                0.9999996743688975,
                0.9999994631247402,
                NaN,
                0.9999989969856734,
                0.9999983463104154,
                0.9999986290426311,
                9.610244939803353e-05
            ],
            [
                8.939694172957213e-06,
                2.260323758987159e-06,
                8.315284241665078e-07,
                8.315278294114555e-07,
                6.475945666063607e-07,
                6.475946438055299e-07,
                3.466325797888292e-07,
                4.450852641737424e-07,
                3.288749065423109e-06,
                1.8553919030858602e-07
            ],
            [
                2.1024326584639497e-07,
                1.9947292459347367e-06,
                0.9999938558224885,
                NaN,
                2.6995771309523475e-07,
                1.9947304348862686e-06,
                8.939700567004841e-06,
                2.2603234895289998e-06,
                8.315281267882195e-07,
                0.9999785550542449
            ],
            [
                3.120191137659974e-05,
                0.9999974387171829,
                0.999997876622046,
                0.999999352405048,
                0.9999949062931953,
                0.9999910603058544,
                0.9999869928763022,
                0.9999977396754359,
                0.9999916019289848,
                0.9999986290432847
            ],
            [
                8.764242227380856e-08,
                1.2751910369310194e-07,
                3.059022998581767e-07,
                NaN,
                3.4663253846718004e-07,
                1.6373766672973748e-07,
                1.1253524254615121e-07,
                2.3823696679327928e-07,
                4.222832437798974e-06,
                1.2751910369275402e-07
            ],
            [
                2.382370235922541e-07,
                1.6373774480605869e-07,
                NaN,
                1.855391239539711e-07,
                1.4449802095666915e-07,
                4.4508499888275247e-07,
                3.05902263391829e-07,
                2.3823702359290413e-07,
                7.338208055680009e-07,
                3.9278629391427843e-07
            ],
            [
                5.715006514176113e-07,
                0.9999296881590813,
                3.9278629391427843e-07,
                NaN,
                9.422443692574719e-07,
                2.561281600086738e-06,
                3.72663883989755e-06,
                3.120190765829341e-05,
                NaN,
                1.370957860576702e-06
            ],
            [
                0.9999989969859125,
                0.9999988634365607,
                0.9999993916411087,
                0.9999995549151073,
                0.9999988634361542,
                0.9999992661791074,
                0.9999885212277781,
                0.9999983463108105,
                0.9999998144609203,
                8.315282259151545e-07
            ],
            [
                6.023573475041126e-08,
                0.9999667858170859,
                1.370957860576702e-06,
                3.726637951387472e-06,
                0.9999996743687422,
                1.3709572068522336e-06,
                7.338211554758494e-07,
                0.9999985406239539,
                1.9947304348862686e-06,
                0.9999987901337405
            ],
            [
                NaN,
                0.9999991148429648,
                0.9999972735307099,
                0.9999984465018777,
                0.9999993916408185,
                0.999999694097664,
                0.9999485577685727,
                NaN,
                0.9999974387177939,
                0.9999983463102182
            ],
            [
                5.71500719545698e-07,
                2.2603248367949354e-06,
                8.315284241665078e-07,
                1.3709572068553509e-06,
                1.7603425837903113e-06,
                7.33821330437595e-07,
                3.0590219045914655e-07,
                3.288749065423109e-06,
                1.9947299593078385e-06,
                1.9947292459406333e-06
            ],
            [
                1.8925150497848527e-05,
                1.2098658277451275e-06,
                1.994730434879465e-06,
                1.2098655392871682e-06,
                3.927862470899887e-07,
                1.7603425837855082e-06,
                1.7603430034743913e-06,
                1.2098656835224664e-06,
                1.8925148241872038e-05,
                5.043472879540142e-07
            ]
        ]
    },
    {
        "q_id": "9507_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            18,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            64,
            65,
            66,
            67,
            68,
            69,
            71,
            72,
            73,
            74,
            75,
            76,
            78,
            79,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            90,
            91,
            92,
            93,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                5.04347287955046e-07,
                7.338208930460318e-07,
                5.043475885696228e-07,
                2.902313023130843e-06,
                6.144177531811707e-06,
                6.475949526020042e-07,
                0.999996711250154,
                5.043475885696228e-07,
                1.1478764021029928e-05,
                1.7603430034867993e-06
            ],
            [
                0.00026119040327709245,
                9.610242648063708e-05,
                1.4738989000422955e-05,
                8.939697369980456e-06,
                4.2228319344021954e-06,
                1.670141786325573e-05,
                3.120190021759579e-05,
                1.0129993395336818e-05,
                6.605215256765022e-05,
                4.785095635655362e-06
            ],
            [
                0.9999964991439189,
                0.9999969105044486,
                0.9999962733616083,
                1.5534983101602148e-06,
                NaN,
                0.9999985406234319,
                0.9999983463098238,
                0.9999974387184012,
                0.9999785550491092,
                0.9999986290429571
            ],
            [
                0.9999996072138935,
                0.9999992661792825,
                NaN,
                0.9999999434138042,
                0.9999998461826037,
                0.9999997463981334,
                5.043476486915964e-07,
                0.999999789756684,
                0.9999999273418616,
                0.9999999006880905
            ],
            [
                5.715003107767143e-07,
                0.9999975938968025,
                0.999997097688364,
                0.9999974387184013,
                0.9999972735300573,
                0.999998932297385,
                0.9999984465028019,
                0.9999983463106118,
                0.9999994956527121,
                0.9999992188512972
            ],
            [
                1.3709568799919866e-06,
                3.927862002663297e-07,
                3.059022269254856e-07,
                3.05902263391829e-07,
                3.466326624336003e-07,
                2.902313023130843e-06,
                3.9278620026686556e-07,
                8.315278294114555e-07,
                2.1024336609874897e-07,
                5.715006514176113e-07
            ],
            [
                2.561282821402217e-06,
                8.315280276626197e-07,
                6.475945666063607e-07,
                2.3823693839325527e-07,
                1.994729483729522e-06,
                4.4508515805735777e-07,
                9.93120161310289e-08,
                2.9023119851899796e-06,
                7.338207180898968e-07,
                7.338212429594283e-07
            ],
            [
                0.9999972735284319,
                0.999997876622298,
                0.999995777166558,
                0.9999982396572071,
                0.9999977396759734,
                0.9999955048162812,
                0.9999952149066503,
                0.9999977396762432,
                0.9999978766212857,
                0.999998446502617
            ],
            [
                1.30071315662049e-05,
                4.785096206076165e-06,
                1.067703124601679e-06,
                8.31528325040778e-07,
                0.9998204719502661,
                3.7266401726359486e-06,
                3.726639284125553e-06,
                2.561281600086738e-06,
                4.785093353940187e-06,
                3.7266401726173067e-06
            ],
            [
                9.422444815814404e-07,
                0.999983298582182,
                8.315279285351409e-07,
                2.699576809143613e-07,
                6.475950298021765e-07,
                9.422450432014836e-07,
                3.05902336324494e-07,
                1.9947299593078385e-06,
                NaN,
                8.76424013786396e-08
            ],
            [
                6.475949526020042e-07,
                8.315278294038928e-07,
                2.3823696679327928e-07,
                3.927862470899887e-07,
                6.475950297906914e-07,
                5.043473480777865e-07,
                8.315283250394546e-07,
                9.422445939002803e-07,
                6.475947982022763e-07,
                5.04347468323289e-07
            ],
            [
                1.2098661162056318e-06,
                1.760343213335281e-06,
                1.1478769494542698e-05,
                4.22283545819819e-06,
                1.0677026154827912e-06,
                0.9999989969857924,
                1.892515049819277e-05,
                0.00043055714365133354,
                3.224184327183648e-08,
                3.288747889284851e-06
            ],
            [
                2.1444953527944967e-05,
                1.2098656835224664e-06,
                5.715006514176113e-07,
                1.0677027427624903e-06,
                3.288749065423109e-06,
                6.475946438055299e-07,
                7.338207180898968e-07,
                9.422447062294175e-07,
                1.2098661162056318e-06,
                5.04347287955046e-07
            ],
            [
                1.370957860567974e-06,
                2.1024341622426268e-07,
                3.9278634073732336e-07,
                3.927863875584984e-07,
                4.2228339479858295e-06,
                1.0677026154774503e-06,
                9.422448185534261e-07,
                6.475947982037486e-07,
                3.059022998581767e-07,
                1.8553905760062447e-07
            ],
            [
                0.9999978766222999,
                0.999999114842754,
                0.9999997463980428,
                0.9999974387184035,
                0.9999975938985239,
                0.9999989322970045,
                0.9999982396574191,
                0.9999992188518562,
                0.9999991684722705,
                0.9999993106387907
            ],
            [
                4.450850519403407e-07,
                1.2098656835224664e-06,
                1.3709575337078829e-06,
                1.3709568799919866e-06,
                1.9947297215125433e-06,
                1.9947304348862686e-06,
                1.99472900813862e-06,
                9.422443692555439e-07,
                4.2228339479858295e-06,
                1.994730672668496e-06
            ],
            [
                3.4663278639892215e-07,
                9.422444815814404e-07,
                1.275190580884987e-07,
                2.6995784182183607e-07,
                1.5534971990169383e-06,
                3.9278610661902853e-07,
                1.5534981249736758e-06,
                2.5612834320563895e-06,
                1.1253524254615121e-07,
                1.5534971990126997e-06
            ],
            [
                1.4449798650476187e-07,
                1.275190884913241e-07,
                3.653482951291499e-08,
                8.764249540862797e-08,
                9.931198061405701e-08,
                1.1253526937697666e-07,
                7.734414854792722e-08,
                1.275190276853036e-07,
                9.93120161306789e-08,
                4.691162683297406e-08
            ],
            [
                7.734416698849138e-08,
                2.6995774527577444e-07,
                2.10243290909963e-07,
                2.1024334103352274e-07,
                1.6373776432509826e-07,
                1.2098659719757836e-06,
                3.4663278639892215e-07,
                2.1024336609874897e-07,
                5.043472879525233e-07,
                3.466327037553825e-07
            ],
            [
                8.939700567004841e-06,
                0.9999573525126194,
                1.9947304348703948e-06,
                0.999968798074136,
                0.999970688472486,
                1.1478770862589836e-05,
                0.999978555047048,
                0.9999756997684558,
                0.9999785550570695,
                0.9999599362995694
            ],
            [
                2.382368247924618e-07,
                1.1253513522391131e-07,
                2.1024341622368903e-07,
                1.6373766672821107e-07,
                5.043475885696228e-07,
                5.315780535989972e-08,
                2.3823685319244518e-07,
                1.855391681898159e-07,
                1.6373768624837685e-07,
                1.8553916819032217e-07
            ],
            [
                1.012999218776902e-05,
                0.9999982396574183,
                4.4508510499849186e-07,
                1.0677026154806063e-06,
                9.931195693628605e-08,
                5.715007195431641e-07,
                1.2098659719788098e-06,
                1.0677026154806063e-06,
                3.9278634073732336e-07,
                5.715005151606823e-07
            ],
            [
                4.450848927637999e-07,
                4.450851580540182e-07,
                4.450852111135988e-07,
                8.315283250371857e-07,
                4.450849458218309e-07,
                5.043474683204221e-07,
                5.043475885674441e-07,
                7.338209805224048e-07,
                1.2098661161927025e-06,
                2.1024326584639497e-07
            ],
            [
                9.931187406410953e-08,
                9.931186222523604e-08,
                3.466326624336003e-07,
                7.734414854823498e-08,
                9.422445939054222e-07,
                2.699578740032504e-07,
                7.889259764517575e-06,
                1.0677027427624903e-06,
                5.71500515161527e-07,
                4.222834451403972e-06
            ],
            [
                1.0677029973219343e-06,
                2.699576809143613e-07,
                2.699578740032504e-07,
                5.04347287955046e-07,
                5.715002426486762e-07,
                1.0677032518814388e-06,
                1.275190884913241e-07,
                2.3823693839325527e-07,
                1.5534971990169383e-06,
                7.73441946488886e-08
            ],
            [
                0.9999955048189596,
                1.2098662604126641e-06,
                0.999998239656578,
                2.260325106237323e-06,
                0.9999991148433864,
                0.9999970976876719,
                1.1253508156363576e-07,
                0.9999945777790953,
                0.9999997617629764,
                0.9999995262094987
            ],
            [
                0.9999996940977731,
                0.999999825702059,
                0.9999997761971048,
                0.9999996533673376,
                0.9999975938982357,
                0.9999995818813767,
                0.9999994631250603,
                0.9999998362623723,
                0.9999998555019618,
                0.9999984465015059
            ],
            [
                9.422445939002803e-07,
                1.855391239547094e-07,
                9.422447062240614e-07,
                1.5534981249291695e-06,
                4.450849988811838e-07,
                0.9999832985821784,
                1.370957860567974e-06,
                9.422444815765128e-07,
                6.475951069961737e-07,
                1.5534975693488444e-06
            ],
            [
                2.10243290909963e-07,
                1.6373764721072816e-07,
                7.734426841017797e-08,
                3.059021175261338e-07,
                0.9999991684718734,
                5.315784971839039e-08,
                4.139934092760465e-08,
                3.653485128944664e-08,
                3.05902263391829e-07,
                1.275189972832538e-07
            ],
            [
                0.9999962733593882,
                0.9999972735287569,
                0.9999938558224792,
                0.9999916019289817,
                0.9999910603069186,
                5.315780536011123e-08,
                0.9999985406234319,
                0.999998005269329,
                0.9999972735294079,
                0.9999771719975122
            ],
            [
                1.7603436329978976e-06,
                1.0677026154806063e-06,
                4.785094494750855e-06,
                8.315281267861397e-07,
                1.0677029973192638e-06,
                4.785094494750855e-06,
                1.5534971990126997e-06,
                5.715003107767143e-07,
                1.2098653950656417e-06,
                9.422442569315887e-07
            ],
            [
                1.2098658277451275e-06,
                2.2603234895053587e-06,
                9.422447062094932e-07,
                1.3709578605617394e-06,
                4.785094494783494e-06,
                2.2603251061849014e-06,
                1.9947304348703948e-06,
                8.315284241597959e-07,
                1.0677026154730804e-06,
                1.0677032518748838e-06
            ],
            [
                0.9999993106387904,
                0.9999980052700421,
                0.9999999067051388,
                0.9999989322973851,
                0.9999998642566866,
                0.9999991684716754,
                0.9999998024946566,
                0.9999998642566866,
                0.9999998024946566,
                0.9999998024946095
            ],
            [
                0.9999984465015062,
                0.9999952149055148,
                3.2887506336086064e-06,
                0.9999938558224772,
                0.9999975938973771,
                0.999998126124172,
                3.927862470899887e-07,
                3.05902190458764e-07,
                0.9999974387168766,
                0.9999970976873266
            ],
            [
                1.3709568799919866e-06,
                5.715002426475718e-07,
                1.067703124601679e-06,
                1.4449798650551755e-07,
                1.0677026154806063e-06,
                4.785093924389007e-06,
                1.7603440527046419e-06,
                2.2603248367656408e-06,
                1.3709568799919866e-06,
                1.0677032518814388e-06
            ],
            [
                4.4508494582405734e-07,
                3.4663249714325014e-07,
                1.2751904288710323e-07,
                7.338213304316717e-07,
                3.466327863961242e-07,
                8.315279285370317e-07,
                5.043474081993875e-07,
                7.338213304316717e-07,
                5.04347528446051e-07,
                5.715002426460124e-07
            ],
            [
                1.8553919030858602e-07,
                1.2751901248454963e-07,
                1.6373776432509826e-07,
                8.764247451307293e-08,
                1.4449798650551755e-07,
                3.05902336324494e-07,
                1.855391239547094e-07,
                2.6995784182183607e-07,
                3.466326624336003e-07,
                1.6373762769138607e-07
            ],
            [
                0.9999904837494645,
                0.9999995549149484,
                0.999997739674896,
                0.9999989322975129,
                0.9999995549150013,
                0.9999998724809875,
                0.9999996072137062,
                0.9999995262093859,
                0.9999969105048184,
                0.9999997463981031
            ],
            [
                1.8553905760062447e-07,
                3.05902117523595e-07,
                2.1024336609843824e-07,
                8.7642516304188e-08,
                8.764242227380856e-08,
                3.466325797888292e-07,
                7.734428685019034e-08,
                1.637377057673536e-07,
                1.1253525596055243e-07,
                3.9278610661902853e-07
            ],
            [
                NaN,
                1.7603432132912532e-06,
                4.450848927658745e-07,
                1.9947290081286418e-06,
                9.422444815765128e-07,
                1.4449798650551755e-07,
                6.475950298011458e-07,
                1.7603436330091044e-06,
                1.3709567165087443e-06,
                NaN
            ],
            [
                6.825606165129312e-08,
                8.764249540862797e-08,
                6.825598028364134e-08,
                7.73441946488886e-08,
                4.691162124067829e-08,
                4.139939521459479e-08,
                6.023571320847322e-08,
                7.734423152941018e-08,
                7.734424996967756e-08,
                7.338212429582604e-07
            ],
            [
                8.764244316973974e-08,
                4.691164920214251e-08,
                8.764245361752286e-08,
                6.825606165129312e-08,
                6.825606165129312e-08,
                4.6911638017556955e-08,
                4.691162683297406e-08,
                6.825608606148807e-08,
                9.931195693628605e-08,
                6.825602910433871e-08
            ],
            [
                6.825600469412533e-08,
                0.9999998874647977,
                1.1253509497883659e-07,
                6.023576347299818e-08,
                0.999999887464905,
                5.715003789046955e-07,
                0.9999991684721711,
                5.043472278322555e-07,
                1.637377057680051e-07,
                0.9999993106386261
            ],
            [
                4.785096776499213e-06,
                1.012999218776902e-05,
                1.2098656835224664e-06,
                6.9622587397397306e-06,
                8.315281267649641e-07,
                1.3709575337078829e-06,
                4.4508505193386385e-07,
                7.338208930421943e-07,
                0.9999984465018761,
                2.260324028427877e-06
            ],
            [
                0.999999114842648,
                0.9999989969862711,
                0.9999988634362901,
                0.9999996743686257,
                0.9999984465024317,
                0.9999997126315153,
                0.9999997463980125,
                0.9999975938968007,
                0.9999992661791075,
                0.9999987121041711
            ],
            [
                0.9999984465020608,
                0.9999983463096267,
                0.9999962733607202,
                0.9999417087139718,
                0.9999955048189634,
                7.338209805240734e-07,
                0.9999964991451715,
                0.9999964991451716,
                0.9999977396754344,
                0.999970688454597
            ],
            [
                0.9999964991439233,
                5.715003107767143e-07,
                1.8925141473599938e-05,
                7.734418542875216e-08,
                4.450848927658745e-07,
                2.1024331597262577e-07,
                2.102434162245973e-07,
                3.2887506336086064e-06,
                1.2751899728311609e-07,
                8.315283250371857e-07
            ],
            [
                8.764244316973974e-08,
                2.7535697667202906e-05,
                6.825602910433871e-08,
                0.9999998555019275,
                9.931195693628605e-08,
                7.73441946488886e-08,
                7.338212429562581e-07,
                1.553498495338299e-06,
                7.734423152941018e-08,
                1.1253520230052635e-07
            ],
            [
                6.962255419931625e-06,
                1.4449807263312446e-07,
                1.067703124601679e-06,
                5.715003788993679e-07,
                6.825609419848033e-08,
                2.3823693839325527e-07,
                1.2098656835252174e-06,
                3.9278605979534166e-07,
                1.6373776432509826e-07,
                1.370957860576702e-06
            ],
            [
                1.2098661162056318e-06,
                4.222834954801051e-06,
                3.05902263391829e-07,
                3.7266397283908927e-06,
                6.475945666063607e-07,
                1.3709568799919866e-06,
                5.715006514176113e-07,
                1.5534971990169383e-06,
                8.315278294114555e-07,
                5.829124470847917e-05
            ],
            [
                5.715006514176113e-07,
                3.927863407379485e-07,
                2.699578096403948e-07,
                2.6995784182183607e-07,
                2.699577774585891e-07,
                1.637376862489725e-07,
                3.466327037553825e-07,
                8.764242227418718e-08,
                1.6373772528704005e-07,
                9.422445939032799e-07
            ],
            [
                3.9278605979534166e-07,
                2.2603253756956754e-06,
                1.5534975693979422e-06,
                9.931195693628605e-08,
                2.6995774527718623e-07,
                7.338207180838067e-07,
                8.315281267882195e-07,
                8.315278294072958e-07,
                2.1024336609874897e-07,
                3.9278634073732336e-07
            ],
            [
                9.422449308774482e-07,
                1.6373774480605869e-07,
                1.7603438428848787e-06,
                6.475945666063607e-07,
                1.1253506814842375e-07,
                7.338208930460318e-07,
                2.1024331597262577e-07,
                1.0677028700422047e-06,
                2.382370235933104e-07,
                2.699578096403948e-07
            ],
            [
                0.9999991148426479,
                0.9999993916409639,
                0.9999982396574175,
                0.9999984465026167,
                0.9999989969859124,
                0.9999984465026177,
                0.9999992661791947,
                0.9999964991451711,
                0.999999887464744,
                0.9999983463100209
            ],
            [
                6.475946438055299e-07,
                6.962259569750576e-06,
                8.939696304311336e-06,
                1.9947299592933255e-06,
                6.475947210046347e-07,
                1.5534971990126997e-06,
                5.043475885696228e-07,
                8.315282259089153e-07,
                7.889263526266196e-06,
                1.0677028700320085e-06
            ],
            [
                5.043476486915964e-07,
                0.9999987901341748,
                0.9999962733620593,
                0.9999978766217933,
                0.9999974387187095,
                0.9999967112509444,
                0.9999969105048195,
                0.999993037740452,
                0.9999983463110075,
                0.9999974387168785
            ],
            [
                9.931198061405701e-08,
                6.825597214718257e-08,
                5.315787506612373e-08,
                6.825597214718257e-08,
                7.734423152941018e-08,
                1.275190732904469e-07,
                2.10243290909724e-07,
                1.444979692800516e-07,
                3.466326624336003e-07,
                1.275190732904469e-07
            ],
            [
                0.9999945777784656,
                7.338210680021253e-07,
                0.9999977396765143,
                5.715005832886879e-07,
                0.9999969105066633,
                9.422443692555439e-07,
                3.466327037539638e-07,
                6.475950298011458e-07,
                0.9999955048200352,
                4.450849988811838e-07
            ],
            [
                1.1253516205489029e-07,
                1.0677024881980089e-06,
                4.450849458218309e-07,
                3.466325797888292e-07,
                2.382369383923073e-07,
                3.46632497145457e-07,
                3.927860597945825e-07,
                4.450849988798682e-07,
                1.8553916819032217e-07,
                6.475949526003845e-07
            ],
            [
                1.637377057680051e-07,
                2.1024339116134898e-07,
                7.73441946488886e-08,
                9.931188590255539e-08,
                1.855391239539711e-07,
                8.764245361708445e-08,
                6.023574911170301e-08,
                3.653479467066246e-08,
                1.125352291309328e-07,
                6.825609419823202e-08
            ],
            [
                0.9999987901347499,
                0.9999998362623334,
                0.9999998642567351,
                0.9999996743686645,
                0.9999983463110063,
                0.9999998642566704,
                0.9999989969862709,
                0.9999996533672963,
                0.9999999123574836,
                0.9999998461826956
            ],
            [
                9.931185038635267e-08,
                2.561283126728994e-06,
                1.8553914607267268e-07,
                3.9278629391427843e-07,
                4.4508515805735777e-07,
                NaN,
                8.315277302857965e-07,
                1.6701427818034747e-05,
                8.315284241665078e-07,
                1.1478770862882149e-05
            ],
            [
                3.059022998576899e-07,
                8.315278294114555e-07,
                1.275190124842887e-07,
                3.9278610661822475e-07,
                1.4449805540700758e-07,
                1.6373774480479287e-07,
                4.785093353909723e-06,
                9.931190958026426e-08,
                6.825598028392069e-08,
                NaN
            ],
            [
                6.47595107001401e-07,
                3.927863875616689e-07,
                2.1024334103581732e-07,
                5.04347528446051e-07,
                5.043475284468537e-07,
                5.04347287955046e-07,
                3.927862002654366e-07,
                5.715006514176113e-07,
                5.715004470295662e-07,
                1.0677029973192638e-06
            ],
            [
                4.222832941193893e-06,
                1.855391239544352e-07,
                NaN,
                2.3823702359290413e-07,
                2.260324836776948e-06,
                6.962256249821764e-06,
                6.144172404738491e-06,
                1.8553916819032217e-07,
                2.3823699519143784e-07,
                1.5534973842076057e-06
            ],
            [
                6.825600469412533e-08,
                0.9999993106391192,
                0.9999987901347499,
                0.9999980052693296,
                0.9999995549147891,
                0.999999391641036,
                0.999999310638626,
                0.9999975938973749,
                0.9999982396572072,
                0.9999989322970033
            ],
            [
                8.315277302857965e-07,
                1.0677033791612137e-06,
                3.05902336324494e-07,
                1.8553910183674878e-07,
                3.927863407379485e-07,
                3.726639284144195e-06,
                1.7603425837903113e-06,
                2.5612819054133693e-06,
                8.315279285370317e-07,
                7.338209805240734e-07
            ],
            [
                5.043472278322555e-07,
                2.1024339116168358e-07,
                1.855391239547094e-07,
                5.715006514176113e-07,
                5.04347287955046e-07,
                1.994729721518893e-06,
                2.1024339116168358e-07,
                6.475946438055299e-07,
                1.5534973842076057e-06,
                7.338213304363436e-07
            ],
            [
                4.450852111155216e-07,
                0.9999987121044781,
                1.8553916819032217e-07,
                5.04347648686092e-07,
                0.9999843104522015,
                9.931202796957073e-08,
                6.023571320847322e-08,
                9.422448185534261e-07,
                1.5534975693979422e-06,
                1.6373770576776313e-07
            ],
            [
                2.2603234895372223e-06,
                1.8553919030858602e-07,
                NaN,
                NaN,
                3.0590226339061185e-07,
                1.8553919030858602e-07,
                5.715002426486762e-07,
                6.475946438022905e-07,
                NaN,
                2.3823693839290317e-07
            ],
            [
                0.9999985406230837,
                0.9999988634361543,
                0.9999996743687034,
                0.9999982396567874,
                0.9999957771655513,
                0.999998446502061,
                0.999999802494633,
                0.9999974387174857,
                0.999998540623258,
                0.9999986290431205
            ],
            [
                1.275190580884987e-07,
                1.855391018347238e-07,
                NaN,
                9.931201612997889e-08,
                5.04347408197782e-07,
                8.764240137829087e-08,
                2.3823682479292225e-07,
                1.1253513522391131e-07,
                1.6373762769138607e-07,
                9.931198061405701e-08
            ],
            [
                0.9999975938968009,
                1.9947299593014888e-06,
                3.466327450756327e-07,
                1.2098653950656417e-06,
                0.9999992661791954,
                0.9999983463102186,
                0.9999995818812769,
                1.0677024881980089e-06,
                9.931202796957073e-08,
                0.9999952149066511
            ],
            [
                0.999998863436019,
                0.9999984465020612,
                0.9999990577555188,
                0.9999995262096116,
                0.9999997897567341,
                0.9999987121050922,
                0.9999994631250603,
                0.9999991684719726,
                0.999998629042957,
                0.9999955048173534
            ],
            [
                4.450852111155216e-07,
                1.8553907971855875e-07,
                2.2603245673443566e-06,
                9.931189774187203e-08,
                1.3709576971463352e-06,
                9.931195693628605e-08,
                6.47595107001401e-07,
                2.6995784182183607e-07,
                7.33821330437595e-07,
                1.8553919030858602e-07
            ],
            [
                1.0677029973192638e-06,
                1.1253512180925583e-07,
                6.475951070002966e-07,
                6.825597214718257e-08,
                0.999999554914789,
                6.023578501491997e-08,
                6.825608606148807e-08,
                1.370957860567974e-06,
                1.2751908849088918e-07,
                2.6995784182140636e-07
            ],
            [
                1.209865827752005e-06,
                NaN,
                2.2603248367949354e-06,
                2.902312677150514e-06,
                NaN,
                9.422442569334097e-07,
                8.315280276626197e-07,
                7.338207180898968e-07,
                2.2603245673443566e-06,
                5.043472278322555e-07
            ],
            [
                0.9999984465026202,
                0.9999994956525318,
                0.9999945777829765,
                0.9999967112513304,
                0.9999977396757056,
                0.9999945777829782,
                0.9999945777823311,
                0.9999970976876728,
                0.9999970976890573,
                0.9999964991468424
            ],
            [
                3.653479902594117e-08,
                1.8553903548287212e-07,
                2.2603234895372223e-06,
                2.902312331170226e-06,
                2.1024326584702836e-07,
                NaN,
                2.10243290909963e-07,
                3.466325797900508e-07,
                1.1253525596174225e-07,
                9.422447062294175e-07
            ],
            [
                4.450849458200093e-07,
                5.715004470313855e-07,
                1.7603430034867993e-06,
                1.3709576971425944e-06,
                8.315279285351409e-07,
                2.2603253756956754e-06,
                1.4449798650551755e-07,
                4.4508515805735777e-07,
                1.8553905760062447e-07,
                5.715003789046955e-07
            ],
            [
                4.4508515805735777e-07,
                1.1253506814842375e-07,
                2.382368815932174e-07,
                5.71500719545698e-07,
                3.05902263391829e-07,
                1.5534983101644536e-06,
                2.1024334103581732e-07,
                1.3709576971463352e-06,
                4.4508499888275247e-07,
                1.2098656835252174e-06
            ],
            [
                1.444979692800516e-07,
                1.0677028700363782e-06,
                7.338211554758494e-07,
                6.475951069932288e-07,
                1.9947301970587145e-06,
                1.0677033791495609e-06,
                2.561282515988704e-06,
                1.760343213322473e-06,
                6.023573475041126e-08,
                7.338208930443633e-07
            ],
            [
                9.422449308335287e-07,
                2.382369383923073e-07,
                1.8553919030708836e-07,
                7.338208055664991e-07,
                9.422448185510695e-07,
                2.102434412875379e-07,
                1.0677033791291683e-06,
                1.6373774480605869e-07,
                5.043472278322555e-07,
                2.3823702359138736e-07
            ],
            [
                8.31528424162821e-07,
                1.553497199007048e-06,
                3.2887478892504536e-06,
                2.561282516042282e-06,
                1.5534984953510149e-06,
                1.0677026154730804e-06,
                3.2887502415438413e-06,
                1.5534983101478522e-06,
                1.370957860567974e-06,
                1.2098661161927025e-06
            ],
            [
                2.1024326584639497e-07,
                1.5534979397790343e-06,
                3.466326211113502e-07,
                7.484625405027093e-05,
                0.9999904837460543,
                1.6373770576776313e-07,
                9.422448185534261e-07,
                4.222833444590791e-06,
                1.8553916819032217e-07,
                1.2751910369310194e-07
            ],
            [
                1.275190580890061e-07,
                1.5534983101644536e-06,
                7.338208055680009e-07,
                1.275190732904469e-07,
                3.9278629391427843e-07,
                9.422443692574719e-07,
                8.315277302857965e-07,
                5.715002426486762e-07,
                2.3823696679327928e-07,
                1.067703124601679e-06
            ],
            [
                2.6995784182183607e-07,
                6.962254589978262e-06,
                6.475947210046347e-07,
                1.5534983101644536e-06,
                1.1478770862882149e-05,
                2.3823693839325527e-07,
                3.2887506336235617e-06,
                3.6534833868287154e-08,
                2.2603242978943238e-06,
                2.382369951932796e-07
            ],
            [
                0.9999993106389546,
                0.9999995262094987,
                0.9999962733589438,
                0.9999960330121993,
                0.9999984465018763,
                0.9999980052693298,
                0.9999989969861518,
                0.9999978766212868,
                0.9999970976876742,
                0.9999992661786701
            ],
            [
                6.475950298011458e-07,
                5.043476486915964e-07,
                2.699577774585891e-07,
                3.927863407379485e-07,
                2.3823688159291947e-07,
                2.102433660979124e-07,
                1.27519088491875e-07,
                1.7603434231833873e-06,
                3.05902190458764e-07,
                9.422445939054222e-07
            ],
            [
                1.637377057680051e-07,
                4.222832941193893e-06,
                NaN,
                1.370957860576702e-06,
                2.2603234895372223e-06,
                8.315282259138311e-07,
                1.5534971990169383e-06,
                2.561281600086738e-06,
                2.260323758987159e-06,
                4.785096206076165e-06
            ],
            [
                1.6373774480535133e-07,
                3.059022998581767e-07,
                9.931187406410953e-08,
                1.275190580890061e-07,
                6.47595107001401e-07,
                7.338212429594283e-07,
                5.04347287955046e-07,
                3.466325797900508e-07,
                1.1253526937656726e-07,
                2.3823690999323465e-07
            ],
            [
                1.4738976701411704e-05,
                1.670142980893658e-05,
                NaN,
                1.0129989772532511e-05,
                2.9023116391978967e-06,
                4.0063696969564425e-05,
                2.7535691101761522e-05,
                1.7603427936263351e-06,
                1.2098662604291696e-06,
                3.535625914621054e-05
            ],
            [
                9.422445938917108e-07,
                7.338208930443633e-07,
                3.05902263391829e-07,
                1.8553916819032217e-07,
                4.450852111148132e-07,
                1.855391681898159e-07,
                3.927860597945825e-07,
                5.8291258607931044e-05,
                0.999993855823207,
                2.102433410343832e-07
            ],
            [
                5.043475284468537e-07,
                6.475947210046347e-07,
                3.059022998581767e-07,
                5.422220909041528e-06,
                1.2098656835252174e-06,
                1.5534981249736758e-06,
                0.9999982396572079,
                0.9999982396565797,
                0.9999962733602765,
                1.5534984953552536e-06
            ],
            [
                7.338209805240734e-07,
                9.422447062294175e-07,
                5.043474082005342e-07,
                2.2603240284371276e-06,
                4.785093353940187e-06,
                5.04347408197782e-07,
                5.043473480777865e-07,
                5.422220262636381e-06,
                2.5612831267086116e-06,
                2.2603234895176927e-06
            ],
            [
                1.6373776432509826e-07,
                1.0677032518814388e-06,
                1.1253514863909295e-07,
                6.475946438055299e-07,
                3.4663266243308805e-07,
                1.8553916819032217e-07,
                2.1024331597262577e-07,
                1.8553905760062447e-07,
                2.3823702359290413e-07,
                8.315282259138311e-07
            ],
            [
                8.315277302857965e-07,
                1.0677028700422047e-06,
                2.382369951932796e-07,
                1.5534983101644536e-06,
                1.275190428875671e-07,
                7.338212429594283e-07,
                2.382368815932174e-07,
                2.9023119851899796e-06,
                1.7603430034867993e-06,
                1.5534984953552536e-06
            ],
            [
                0.9999993916410361,
                0.9999822214397333,
                0.9999977396754351,
                7.734424996967756e-08,
                0.9999977396751649,
                0.9999945777797453,
                5.315784971839039e-08,
                0.9999989322975124,
                0.9999981261246184,
                1.1253521571574156e-07
            ],
            [
                0.9999993106386259,
                0.9999982396574177,
                0.9999991684718739,
                0.9999993106390369,
                0.9999988634358834,
                0.9999991148428591,
                0.9999983463108102,
                0.9999994956526522,
                0.9999986290432847,
                0.9999989322967489
            ],
            [
                0.9999983463100209,
                0.9999996310116359,
                0.9999977396751648,
                0.999997593897663,
                0.9999995549149483,
                0.9999983463108102,
                0.9999972735290811,
                5.315786239218605e-08,
                0.9999869928653624,
                7.73441946488886e-08
            ],
            [
                2.1024334103581732e-07,
                3.927862002663297e-07,
                3.466327037553825e-07,
                6.023571320847322e-08,
                9.931202796957073e-08,
                1.5534979397740895e-06,
                0.9999417087069759,
                1.1253525596174225e-07,
                1.2751901248454963e-07,
                9.931188590255539e-08
            ],
            [
                0.999999554914736,
                0.9999997761970781,
                0.9999999123575151,
                0.9999998257020799,
                0.9999989969859123,
                0.9999998362622747,
                0.9999997617630617,
                0.9999997617631753,
                0.9999980052705173,
                0.9999999123574524
            ],
            [
                2.6995774527718623e-07,
                2.699578740032504e-07,
                1.4449805540740185e-07,
                5.043475284468537e-07,
                2.6995784182183607e-07,
                2.382370235933104e-07,
                3.05902190458764e-07,
                1.3709576971463352e-06,
                1.4449803818215767e-07,
                5.043473480777865e-07
            ],
            [
                2.3823702359138736e-07,
                2.10243290909724e-07,
                6.475945666009864e-07,
                5.715004470243685e-07,
                1.1253521571574156e-07,
                6.47594952595231e-07,
                1.760344052714248e-06,
                2.3823702359138736e-07,
                8.315284241597959e-07,
                5.043476486915964e-07
            ],
            [
                1.1253506814842375e-07,
                2.1024334103581732e-07,
                6.1441746020359e-06,
                3.224185864592658e-08,
                5.315781803390236e-08,
                8.764242227418718e-08,
                5.3157887739943563e-08,
                6.825600469412533e-08,
                8.76424013786396e-08,
                2.6995790618469934e-07
            ],
            [
                3.726637951387472e-06,
                1.7603438428800754e-06,
                8.315283250371857e-07,
                1.2098661162023305e-06,
                4.4508505193932864e-07,
                8.315279285351409e-07,
                8.315284241650899e-07,
                7.338211554801876e-07,
                2.9023123311583482e-06,
                2.561282516066741e-06
            ],
            [
                3.0590237279085045e-07,
                8.315280276626197e-07,
                1.8553910183674878e-07,
                2.3823688159291947e-07,
                1.6373766672973748e-07,
                3.927862470899887e-07,
                1.2751905808881762e-07,
                NaN,
                1.1253512180925583e-07,
                6.962256249885085e-06
            ],
            [
                1.0677024882029858e-06,
                6.475946438055299e-07,
                NaN,
                4.22283545819819e-06,
                1.209865539298447e-06,
                9.422450432030903e-07,
                7.338212429594283e-07,
                2.102434412875379e-07,
                6.47595107001401e-07,
                2.699577774589574e-07
            ],
            [
                7.734424996967756e-08,
                1.2751902768478173e-07,
                1.6373766672973748e-07,
                9.931186222482958e-08,
                9.93120161306789e-08,
                1.1253517547010071e-07,
                1.855391681898159e-07,
                1.2751905808881762e-07,
                1.2751905808881762e-07,
                1.5534973842076057e-06
            ],
            [
                7.734415776805048e-08,
                1.6373772528704005e-07,
                1.4449798650551755e-07,
                5.3157837044597743e-08,
                7.734424996967756e-08,
                9.422450431954847e-07,
                1.6373764721072816e-07,
                1.2751901248454963e-07,
                4.691162683297406e-08,
                6.825598842065202e-08
            ],
            [
                3.46632497145457e-07,
                2.1024334103505245e-07,
                8.315279285351409e-07,
                1.209865539295696e-06,
                2.1024341622426268e-07,
                3.466326211113502e-07,
                3.0590237279085045e-07,
                7.338210680021253e-07,
                2.1024326584639497e-07,
                1.855391681898159e-07
            ],
            [
                1.444980209564556e-07,
                1.4449803818107344e-07,
                6.825602910433871e-08,
                6.825606165129312e-08,
                9.931187406410953e-08,
                3.653485128944664e-08,
                1.4449798650417048e-07,
                1.1253521571574156e-07,
                1.444980209564556e-07,
                3.0590237279085045e-07
            ],
            [
                8.764254764780641e-08,
                1.6373770576776313e-07,
                7.338212429582604e-07,
                2.75356878194421e-05,
                4.4508515805735777e-07,
                5.315786239218605e-08,
                3.9278605979534166e-07,
                2.382369951932796e-07,
                1.553498124964492e-06,
                0.9999984465020613
            ],
            [
                1.3709570434219446e-06,
                1.994729008145876e-06,
                9.422449308716635e-07,
                1.5534975693601474e-06,
                1.2098659719757836e-06,
                1.5534971990126997e-06,
                NaN,
                6.475947210046347e-07,
                4.785093353940187e-06,
                1.209865683500459e-06
            ],
            [
                8.764244316973974e-08,
                8.764247451307293e-08,
                7.73441946488886e-08,
                4.139936066832438e-08,
                1.637377448057981e-07,
                9.931192141912081e-08,
                5.3157830707696514e-08,
                6.825604537781398e-08,
                6.825601283086733e-08,
                7.73442776303243e-08
            ]
        ]
    },
    {
        "q_id": "9676_mmlu_physics",
        "cot_ids": [
            0,
            1,
            3,
            4,
            5,
            6,
            7,
            8,
            11,
            12,
            14,
            15,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            32,
            33,
            34,
            35,
            36,
            38,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            76,
            77,
            78,
            79,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                8.315282259138311e-07,
                3.726639728370556e-06,
                1.5534979397740895e-06,
                4.785093924330255e-06,
                8.939693107288474e-06,
                1.209865539295696e-06,
                NaN,
                3.7266410611296085e-06,
                3.466326211113502e-07,
                1.4738980215352592e-05
            ],
            [
                1.0129993395217047e-05,
                5.4222170304318e-06,
                5.715007195410849e-07,
                NaN,
                NaN,
                1.012999460251781e-05,
                8.939700566435704e-06,
                5.4222176771176554e-06,
                5.8291293323071325e-05,
                6.962253759904688e-06
            ],
            [
                2.7535697667202906e-05,
                1.7603440527286572e-06,
                4.785095635592258e-06,
                8.315279285351409e-07,
                1.1478768126057254e-05,
                1.1478768126057254e-05,
                2.5612831266946347e-06,
                1.0677028700320085e-06,
                2.561281600076256e-06,
                1.3007133116542802e-05
            ],
            [
                1.0677033791437343e-06,
                1.3007130015488633e-05,
                7.889261645427538e-06,
                7.338209805200689e-07,
                1.760344052714248e-06,
                1.3007126914435202e-05,
                9.422450431989127e-07,
                6.9622595696935874e-06,
                6.475947210031623e-07,
                1.1478772231086046e-05
            ],
            [
                1.2098656835224664e-06,
                NaN,
                2.9023112931873767e-06,
                6.475949525981759e-07,
                9.422450431989127e-07,
                9.422449308774482e-07,
                3.46632497145457e-07,
                1.5534975693869924e-06,
                4.5397857828200684e-05,
                2.9023119851635836e-06
            ],
            [
                NaN,
                1.4738978458382043e-05,
                1.0129989772412744e-05,
                1.9947304348862686e-06,
                2.902313369111213e-06,
                4.450852111148132e-07,
                2.5612825160562587e-06,
                7.338208930391909e-07,
                3.288748281329893e-06,
                3.0590215399183813e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                7.338210680021253e-07,
                NaN,
                NaN,
                NaN,
                NaN
            ],
            [
                1.0129987357407137e-05,
                7.338209805200689e-07,
                1.8553907971758842e-07,
                1.994729008145876e-06,
                2.7535694384882703e-05,
                1.0677024881980089e-06,
                1.0677032518785256e-06,
                5.422217030747413e-06,
                1.2098656835224664e-06,
                3.288749065423109e-06
            ],
            [
                2.7535700948722127e-05,
                2.2603240284371276e-06,
                2.90231233114251e-06,
                7.3382080556433e-07,
                6.605217618626244e-05,
                7.338211554783522e-07,
                NaN,
                NaN,
                6.475947210012481e-07,
                3.120191509592808e-05
            ],
            [
                4.2228324377740105e-06,
                2.144495864059426e-05,
                1.2098662604291696e-06,
                5.422219616228845e-06,
                4.450852111135988e-07,
                6.475947210012481e-07,
                7.734423152941018e-08,
                6.475945666051092e-07,
                6.9622537599680095e-06,
                1.0677032518785256e-06
            ],
            [
                6.144176799283803e-06,
                5.422217030747413e-06,
                2.260324836776948e-06,
                7.889259764359722e-06,
                1.1478770862735993e-05,
                1.9947297215043796e-06,
                3.726641061085547e-06,
                2.5612819054028872e-06,
                4.222831934379152e-06,
                4.222834954753043e-06
            ],
            [
                NaN,
                NaN,
                2.382370235922541e-07,
                2.5612831267202583e-06,
                6.475948754012522e-07,
                5.043474683220276e-07,
                1.9947304348862686e-06,
                1.3709570434178922e-06,
                4.450848927650143e-07,
                3.726638839878908e-06
            ],
            [
                1.2098656835224664e-06,
                6.1441724046434924e-06,
                6.144173869603344e-06,
                3.288749065423109e-06,
                4.222834451382849e-06,
                2.561282516042282e-06,
                1.7603427936183298e-06,
                1.0129995810463632e-05,
                1.994729483705484e-06,
                3.7266383955882547e-06
            ],
            [
                1.2098653950656417e-06,
                4.222834451382849e-06,
                1.7603434231705793e-06,
                5.829126555256903e-05,
                1.7603432133296774e-06,
                1.9947299593014888e-06,
                2.4300237837960777e-05,
                3.7266406168827523e-06,
                7.338213304363436e-07,
                8.315278294114555e-07
            ],
            [
                1.1478766757718129e-05,
                2.561281294760143e-06,
                NaN,
                4.222833444590791e-06,
                3.7266383955882547e-06,
                NaN,
                3.288750633545794e-06,
                3.288749457469787e-06,
                1.3709573702722555e-06,
                1.5534971990126997e-06
            ],
            [
                5.715002426460124e-07,
                9.422443692574719e-07,
                1.9947292459347367e-06,
                2.9023119851781017e-06,
                4.4508510499849186e-07,
                7.889264466868659e-06,
                NaN,
                2.9023133690980155e-06,
                3.9278634073625165e-07,
                5.422219616228845e-06
            ],
            [
                NaN,
                NaN,
                4.222833444590791e-06,
                1.6701421845057263e-05,
                6.475946438055299e-07,
                1.5534977545886537e-06,
                1.067703124601679e-06,
                2.2603237589779086e-06,
                2.2603242978871282e-06,
                1.5534975693979422e-06
            ],
            [
                1.0677027427600627e-06,
                3.12019225345861e-05,
                4.222832941193893e-06,
                5.422219616228845e-06,
                1.7603438428800754e-06,
                4.2228329411708495e-06,
                1.7603427936335396e-06,
                3.726638395634011e-06,
                3.927862939126708e-07,
                7.338211554783522e-07
            ],
            [
                1.0677024882009222e-06,
                4.2228319344021954e-06,
                3.288748673376478e-06,
                5.422217677152175e-06,
                7.338213304316717e-07,
                1.892515501014656e-05,
                NaN,
                NaN,
                1.1478768126057254e-05,
                1.3709570434178922e-06
            ],
            [
                5.422219616265831e-06,
                0.0001233945749933723,
                7.889259764359722e-06,
                1.5534983101549167e-06,
                1.3007128464961824e-05,
                1.7603427936263351e-06,
                3.1201900218617364e-05,
                0.00013982202420767366,
                2.260324836787226e-06,
                2.561282516066741e-06
            ],
            [
                4.222832437798974e-06,
                4.450852111148132e-07,
                5.043474081993875e-07,
                8.315281267861397e-07,
                2.5612825160562587e-06,
                1.3709567165617364e-06,
                3.9278638756099906e-07,
                1.067702870039777e-06,
                4.450849988811838e-07,
                3.0590237279032884e-07
            ],
            [
                1.670142980893658e-05,
                1.3709573702722555e-06,
                8.315280276607289e-07,
                7.484622728735096e-05,
                1.1478766757561534e-05,
                1.0677028700266676e-06,
                2.5612825160271407e-06,
                2.1444940745839484e-05,
                7.338210680021253e-07,
                3.535625914235192e-05
            ],
            [
                5.715007195447234e-07,
                8.315278294072958e-07,
                6.605215257197525e-05,
                NaN,
                8.315283250371857e-07,
                NaN,
                1.2098653950656417e-06,
                1.7603436330259153e-06,
                8.939698435657833e-06,
                1.3709567165530083e-06
            ],
            [
                NaN,
                NaN,
                2.561281600086738e-06,
                5.715004470313855e-07,
                1.3709570434178922e-06,
                1.553497754583709e-06,
                0.00013982209088087594,
                2.260324028427877e-06,
                4.222833947932061e-06,
                2.1024326584639497e-07
            ],
            [
                7.338212429582604e-07,
                NaN,
                NaN,
                1.3709573702822306e-06,
                NaN,
                1.760344052714248e-06,
                NaN,
                2.5612812947508257e-06,
                NaN,
                NaN
            ],
            [
                1.994729245917502e-06,
                1.7603432133136672e-06,
                1.5534983101393749e-06,
                1.9947304348595095e-06,
                1.99472924590571e-06,
                1.0129987357407137e-05,
                4.2228329411708495e-06,
                7.338212429504183e-07,
                3.4663249714451116e-07,
                1.9947290081177566e-06
            ],
            [
                6.475947210031623e-07,
                2.5612828213934817e-06,
                5.043472879525233e-07,
                2.2603251062450327e-06,
                8.315279285351409e-07,
                2.2603251062450327e-06,
                1.670141786325573e-05,
                2.382368531929327e-07,
                5.71500515159253e-07,
                2.1024341622297196e-07
            ],
            [
                8.315283250371857e-07,
                5.715005832853093e-07,
                3.120190021759579e-05,
                1.4738983729535602e-05,
                1.2098661161927025e-06,
                9.422444815628016e-07,
                2.5612831267086116e-06,
                2.430023783734196e-05,
                1.1478772231086046e-05,
                2.5612812947508257e-06
            ],
            [
                1.1478770862882149e-05,
                1.760343003481596e-06,
                2.902312677137316e-06,
                3.927862470899887e-07,
                2.5612828213934817e-06,
                8.93969950132721e-06,
                5.715005151574337e-07,
                1.1478764021029928e-05,
                NaN,
                1.3007126914612648e-05
            ],
            [
                7.338212429582604e-07,
                9.422450431989127e-07,
                1.0677029973192638e-06,
                7.338211554783522e-07,
                3.53562422882756e-05,
                3.1201922535494165e-05,
                NaN,
                4.4508510499849186e-07,
                6.475947210012481e-07,
                1.5534981249697903e-06
            ],
            [
                4.4508526417014975e-07,
                8.939694172420599e-06,
                3.288748281220719e-06,
                8.939696304213768e-06,
                NaN,
                NaN,
                1.892515049571424e-05,
                1.0129988564716393e-05,
                3.726638839806038e-06,
                4.785093353787868e-06
            ],
            [
                1.4738983729053029e-05,
                4.785093353940187e-06,
                1.7603430034867993e-06,
                4.785096776468749e-06,
                3.2887498495150166e-06,
                2.9023119851635836e-06,
                NaN,
                1.9947292459347367e-06,
                6.962257909785973e-06,
                1.5534984953298217e-06
            ],
            [
                9.422447062202052e-07,
                1.0129990979842057e-05,
                6.475945666009864e-07,
                1.4738976701411704e-05,
                2.902312677104321e-06,
                1.3709572068478697e-06,
                2.430023204460668e-05,
                4.785096206013061e-06,
                1.147877359926923e-05,
                8.315278294072958e-07
            ],
            [
                3.466325797896173e-07,
                1.2751904288739315e-07,
                2.69957906184239e-07,
                1.8553903548231313e-07,
                3.466327450765785e-07,
                3.46632497145457e-07,
                3.466327037548308e-07,
                3.466327037548308e-07,
                1.0129995810463632e-05,
                3.059022998581767e-07
            ],
            [
                3.7266406168624155e-06,
                1.0129993394959082e-05,
                8.939695238333382e-06,
                6.962253759904688e-06,
                1.8925143729162536e-05,
                0.0001584362925203847,
                2.430024073399743e-05,
                1.670142980893658e-05,
                1.6701427817730953e-05,
                5.422220908925639e-06
            ],
            [
                9.422448185534261e-07,
                1.012999098021058e-05,
                1.5534981249496567e-06,
                9.422444815765128e-07,
                NaN,
                NaN,
                NaN,
                6.475951069855719e-07,
                NaN,
                1.2098659719757836e-06
            ],
            [
                3.466327863983311e-07,
                NaN,
                6.1441746020359e-06,
                2.69957906184239e-07,
                8.315281267882195e-07,
                3.0590226339061185e-07,
                NaN,
                NaN,
                3.9278605979534166e-07,
                3.927863875616689e-07
            ],
            [
                5.715007195447234e-07,
                3.0590237279085045e-07,
                6.144175334468545e-06,
                4.785092783519724e-06,
                8.315279285351409e-07,
                3.927860597945825e-07,
                5.715004470313855e-07,
                7.338209805224048e-07,
                1.5534975693979422e-06,
                3.726638395634011e-06
            ],
            [
                5.043473480777865e-07,
                7.338211554783522e-07,
                2.9023126771227976e-06,
                1.3709568799919866e-06,
                1.7603440527286572e-06,
                1.067702870039777e-06,
                5.715006514151423e-07,
                NaN,
                4.222831934379152e-06,
                1.4738981972564636e-05
            ],
            [
                NaN,
                1.1478766757718129e-05,
                2.699578418198104e-07,
                NaN,
                9.422449308673789e-07,
                NaN,
                NaN,
                9.422443692527585e-07,
                2.902313023130843e-06,
                6.475947210012481e-07
            ],
            [
                1.7603440527222532e-06,
                2.4300252319959737e-05,
                7.338207180864763e-07,
                5.715003788993679e-07,
                6.1441731370702875e-06,
                3.466325384661554e-07,
                4.2228324377740105e-06,
                7.338211554783522e-07,
                1.9947294837154625e-06,
                1.2098662604247682e-06
            ],
            [
                2.1024336609843824e-07,
                1.0677029973158649e-06,
                5.715004470313855e-07,
                5.71500719545698e-07,
                2.1024341622368903e-07,
                6.475945666051092e-07,
                1.2098661162056318e-06,
                5.715007195447234e-07,
                1.444980209564556e-07,
                4.450849988811838e-07
            ],
            [
                1.2098659719757836e-06,
                1.7603427936263351e-06,
                3.288749065406658e-06,
                1.0129993394959082e-05,
                3.2887494574518405e-06,
                4.222834954778007e-06,
                2.9023119851781017e-06,
                8.31527928532683e-07,
                1.9947297215043796e-06,
                1.1478766757718129e-05
            ],
            [
                NaN,
                NaN,
                5.4222215552470286e-06,
                1.3709572068522336e-06,
                4.78509278348926e-06,
                1.5534984953453635e-06,
                1.994729008105057e-06,
                5.422218969818919e-06,
                3.288749457469787e-06,
                4.2228334445370225e-06
            ],
            [
                3.92786293909545e-07,
                4.222832437747125e-06,
                1.4738976701411704e-05,
                1.55349775456958e-06,
                2.5612834320214477e-06,
                4.785096776468749e-06,
                3.2887486733420804e-06,
                1.3709568799823232e-06,
                1.3007126914245925e-05,
                1.2098656835076114e-06
            ],
            [
                6.962255419728997e-06,
                6.144176799166453e-06,
                7.338208055664991e-07,
                3.7266406168624155e-06,
                1.3709575337078829e-06,
                9.422450431989127e-07,
                2.144494585801764e-05,
                2.561281905376098e-06,
                1.1478768125577027e-05,
                4.222834451382849e-06
            ],
            [
                1.7603440527046419e-06,
                4.450851049890802e-07,
                2.6995780963588326e-07,
                NaN,
                1.067702615468225e-06,
                1.2098656835136636e-06,
                6.962256249821764e-06,
                1.0129992187400498e-05,
                3.288747889229516e-06,
                6.475949525981759e-07
            ],
            [
                5.04347528446051e-07,
                1.0677029973192638e-06,
                8.939697369980456e-06,
                2.902312677150514e-06,
                2.9023119851781017e-06,
                6.144175334468545e-06,
                4.450851580555361e-07,
                5.715007195447234e-07,
                5.043472278322555e-07,
                2.2603234895372223e-06
            ],
            [
                1.2098655392811161e-06,
                7.338212429537553e-07,
                1.5534983101602148e-06,
                1.5534984953453635e-06,
                1.0129993395088066e-05,
                9.422444815765128e-07,
                2.9023112932045342e-06,
                4.2228324377740105e-06,
                3.288747889229516e-06,
                2.260324836776948e-06
            ],
            [
                8.315281267882195e-07,
                1.0677028700422047e-06,
                8.939695238634211e-06,
                2.260324028427877e-06,
                6.962259569750576e-06,
                NaN,
                1.7603432133296774e-06,
                7.889266347786918e-06,
                4.0063696969564425e-05,
                2.2603242978871282e-06
            ],
            [
                5.043472879540142e-07,
                1.8553903548231313e-07,
                NaN,
                1.3007126914435202e-05,
                NaN,
                4.222833947960866e-06,
                2.561282210740037e-06,
                1.2098656835224664e-06,
                7.889265407255982e-06,
                9.931198061405701e-08
            ],
            [
                3.288749457432399e-06,
                1.2098662604192665e-06,
                2.260324836776948e-06,
                1.553497199007048e-06,
                1.7603434231705793e-06,
                6.475947209985977e-07,
                5.715006514105942e-07,
                3.059022269250683e-07,
                7.338208055579897e-07,
                1.8925150497848527e-05
            ],
            [
                1.5534975693933505e-06,
                1.147877359957198e-05,
                2.5612828213818346e-06,
                7.338208930391909e-07,
                3.288749457469787e-06,
                4.4508510499737865e-07,
                4.785093353940187e-06,
                1.7603434231777837e-06,
                9.422447062270609e-07,
                1.0677026154806063e-06
            ],
            [
                4.006371129615879e-05,
                NaN,
                1.1478773599425825e-05,
                1.670142383595838e-05,
                9.422448185478557e-07,
                8.315281267834927e-07,
                1.0677024881980089e-06,
                1.5534981249574276e-06,
                6.60521289442408e-05,
                NaN
            ],
            [
                1.8553903548231313e-07,
                4.450851049941403e-07,
                1.0677032518785256e-06,
                8.939697369980456e-06,
                2.1024341622426268e-07,
                2.2603234895372223e-06,
                8.315281267834927e-07,
                8.315277302841894e-07,
                2.2603242978871282e-06,
                1.0677028700363782e-06
            ],
            [
                1.0677028700422047e-06,
                3.2887506336086064e-06,
                7.33821330437595e-07,
                NaN,
                4.785095635624897e-06,
                1.9947301970972664e-06,
                NaN,
                7.889263526345123e-06,
                9.422447062270609e-07,
                3.466327450756327e-07
            ],
            [
                NaN,
                0.9999646437493439,
                0.9999957771655502,
                0.9997388097232875,
                0.9999978766205255,
                0.9999921107355392,
                0.9999485577925582,
                0.9999955048168195,
                0.9999990577550696,
                0.9999930377404336
            ],
            [
                6.144172404693786e-06,
                3.288749457432399e-06,
                1.994730197071414e-06,
                1.0677028700320085e-06,
                6.144173869502757e-06,
                5.715007195447234e-07,
                4.2228334445370225e-06,
                1.0129987356541108e-05,
                2.561281600049467e-06,
                NaN
            ],
            [
                8.315283250371857e-07,
                1.300712691403299e-05,
                1.670141587208191e-05,
                1.1478772230929451e-05,
                1.2098661161982042e-06,
                3.726638839878908e-06,
                1.2098658277451275e-06,
                1.7603427936335396e-06,
                1.7603434231777837e-06,
                1.7603434231777837e-06
            ],
            [
                4.222835458117536e-06,
                3.2887502415243994e-06,
                2.9023116391675407e-06,
                9.422445939002803e-07,
                2.902311639183378e-06,
                1.1478772230929451e-05,
                6.144177531767002e-06,
                1.1478764020727177e-05,
                1.5534981249574276e-06,
                9.422445939032799e-07
            ],
            [
                5.422217030707961e-06,
                6.475949526003845e-07,
                NaN,
                NaN,
                5.829126555256903e-05,
                3.535624650150453e-05,
                6.144176799283803e-06,
                2.3823690999160957e-07,
                4.222833947960866e-06,
                3.535626336072768e-05
            ],
            [
                2.260325106237323e-06,
                6.475951069985296e-07,
                1.6373774480535133e-07,
                3.288750241561788e-06,
                3.535625071602016e-05,
                1.0677029973158649e-06,
                3.059023727894942e-07,
                NaN,
                4.785094494783494e-06,
                3.466326211113502e-07
            ],
            [
                1.8925143728749452e-05,
                NaN,
                5.715003107767143e-07,
                1.067703379154416e-06,
                9.422449308673789e-07,
                1.7603434231833873e-06,
                1.209865539295696e-06,
                8.939694172867777e-06,
                6.475951069961737e-07,
                NaN
            ],
            [
                1.5534981249496567e-06,
                1.7603425837606927e-06,
                1.994729721469003e-06,
                8.315283250260307e-07,
                1.300712846477255e-05,
                4.785092783454444e-06,
                2.5612828213690224e-06,
                2.2603242978665707e-06,
                1.0677031245905116e-06,
                2.2603242978213447e-06
            ],
            [
                NaN,
                1.147877359926923e-05,
                0.9999646437409403,
                6.144175334468545e-06,
                0.9999869928715508,
                2.1444940745371397e-05,
                8.93969950132721e-06,
                1.0129990980100021e-05,
                6.144173137126169e-06,
                0.9999724642991498
            ],
            [
                1.9947304348595095e-06,
                NaN,
                4.785095635592258e-06,
                2.2603242978665707e-06,
                4.4508505193791187e-07,
                NaN,
                0.00020342707066267436,
                1.209865539274514e-06,
                5.715003107755449e-07,
                3.288748281295496e-06
            ],
            [
                5.043475885657239e-07,
                5.144221979793211e-05,
                2.102433660979124e-07,
                5.043475885657239e-07,
                9.422448185478557e-07,
                1.1478768126057254e-05,
                NaN,
                2.3823702359138736e-07,
                1.7603436330179102e-06,
                6.9622587397397306e-06
            ],
            [
                2.9023119851899796e-06,
                3.059023363221292e-07,
                1.7603440527222532e-06,
                NaN,
                7.338208055664991e-07,
                6.475949525981759e-07,
                1.2098656835224664e-06,
                3.927863875584984e-07,
                1.5534971990126997e-06,
                6.475949525981759e-07
            ],
            [
                2.2603242978778778e-06,
                3.288750241561788e-06,
                7.338209805224048e-07,
                1.0677026154806063e-06,
                NaN,
                9.422448185478557e-07,
                NaN,
                1.3709568799919866e-06,
                9.422444815765128e-07,
                NaN
            ],
            [
                5.4222176771176554e-06,
                6.144176799283803e-06,
                3.726641061027928e-06,
                1.5534981249574276e-06,
                NaN,
                3.288748673319648e-06,
                NaN,
                1.147876812574406e-05,
                3.726639728370556e-06,
                NaN
            ],
            [
                NaN,
                7.889259764445822e-06,
                3.466327037539638e-07,
                4.785095635624897e-06,
                6.144173137126169e-06,
                1.760343633031919e-06,
                3.927862470899887e-07,
                8.315283250371857e-07,
                8.315281267861397e-07,
                2.382369383923073e-07
            ],
            [
                4.006369219393695e-05,
                4.785093353940187e-06,
                6.1441746020359e-06,
                6.144172404693786e-06,
                NaN,
                8.315284241597959e-07,
                5.422217030747413e-06,
                1.30071315662049e-05,
                6.144175334418252e-06,
                NaN
            ],
            [
                8.939694172867777e-06,
                1.760344052714248e-06,
                2.260324028427877e-06,
                7.88926446679691e-06,
                9.4224425692559e-07,
                1.3709567165386693e-06,
                5.422219616228845e-06,
                3.726638839878908e-06,
                2.5612831267202583e-06,
                3.288749457432399e-06
            ],
            [
                1.637377448057981e-07,
                1.855391239544352e-07,
                1.4449798650551755e-07,
                1.855391239544352e-07,
                1.1253516205489029e-07,
                2.1024329090781183e-07,
                1.6373774480535133e-07,
                1.2751901248391176e-07,
                2.102434412875379e-07,
                9.93120161306789e-08
            ],
            [
                4.785094494783494e-06,
                2.260324028427877e-06,
                6.962255419868303e-06,
                1.3709567165579959e-06,
                1.7603425837702984e-06,
                NaN,
                1.994729245917502e-06,
                4.450851580540182e-07,
                1.670141587174774e-05,
                3.9278634073625165e-07
            ],
            [
                NaN,
                1.0129988564974359e-05,
                3.288749457469787e-06,
                NaN,
                2.5612819054133693e-06,
                1.1478768126057254e-05,
                1.3709573702722555e-06,
                2.6995771309523475e-07,
                NaN,
                2.2603242978871282e-06
            ],
            [
                7.889265407090955e-06,
                5.715003107738556e-07,
                3.726638839878908e-06,
                1.994729483694599e-06,
                4.2228334445658276e-06,
                1.0129995810463632e-05,
                3.288749457469787e-06,
                NaN,
                0.00012339463375701896,
                NaN
            ],
            [
                3.059023727894942e-07,
                3.7266410611296085e-06,
                1.8925148241872038e-05,
                NaN,
                8.315282259138311e-07,
                5.829126554917624e-05,
                1.670142980893658e-05,
                3.9278634073732336e-07,
                5.043475885674441e-07,
                4.222833444590791e-06
            ],
            [
                1.2098659719757836e-06,
                5.422220909009474e-06,
                0.0001088969222801779,
                3.2887502415438413e-06,
                5.422218969818919e-06,
                2.260324567337161e-06,
                2.902313023130843e-06,
                8.939697369980456e-06,
                8.315277302819205e-07,
                3.9278634073098236e-07
            ],
            [
                4.785096206013061e-06,
                8.939697369671496e-06,
                0.0017007221519163664,
                2.430024942462891e-05,
                8.315281267800897e-07,
                8.939693107093343e-06,
                1.067703379154416e-06,
                1.99472900813862e-06,
                3.2887486733420804e-06,
                1.2098655392871682e-06
            ],
            [
                NaN,
                7.889266347636241e-06,
                4.785095635624897e-06,
                NaN,
                1.3007131566015624e-05,
                8.939696304311336e-06,
                NaN,
                1.147877359957198e-05,
                1.30071315662049e-05,
                1.3007130015677909e-05
            ],
            [
                1.7603436330179102e-06,
                1.0677027427600627e-06,
                9.4224425692559e-07,
                1.3709576971316842e-06,
                2.2603251062013478e-06,
                2.4300232043369055e-05,
                1.147877359926923e-05,
                2.2603242978665707e-06,
                2.9023119851635836e-06,
                1.760343423160973e-06
            ],
            [
                2.2603242978213447e-06,
                6.475950298011458e-07,
                1.760342793583908e-06,
                1.2098656835224664e-06,
                1.5534971990126997e-06,
                7.338208055664991e-07,
                2.75356812513986e-05,
                8.315277302841894e-07,
                4.4508510499849186e-07,
                8.939696304311336e-06
            ],
            [
                9.422442569315887e-07,
                5.4222183234485234e-06,
                2.561281905376098e-06,
                2.260325375664839e-06,
                1.7603432133296774e-06,
                1.0677032518748838e-06,
                5.043475885674441e-07,
                9.422443692489024e-07,
                4.222834451355964e-06,
                7.889263526266196e-06
            ],
            [
                2.4300240731964193e-05,
                2.902313023101807e-06,
                3.288747889229516e-06,
                NaN,
                0.00013982204085104992,
                1.670141587141357e-05,
                8.939700567004841e-06,
                1.553498124964492e-06,
                0.00033535011038718945,
                7.88926352599354e-06
            ],
            [
                7.88926446679691e-06,
                7.889263526345123e-06,
                6.962257079775324e-06,
                NaN,
                1.994729008145876e-06,
                6.475946437996402e-07,
                4.222833444590791e-06,
                6.144176799334096e-06,
                5.04347528446051e-07,
                5.043474081993875e-07
            ],
            [
                1.3709567165530083e-06,
                4.222834954778007e-06,
                4.785096206013061e-06,
                5.422218323487975e-06,
                2.9023112931688987e-06,
                3.726641061085547e-06,
                2.9023119851781017e-06,
                2.260325375664839e-06,
                1.9947290081286418e-06,
                4.222835458117536e-06
            ],
            [
                1.6701429808632785e-05,
                6.9622587396067566e-06,
                4.785093924362895e-06,
                4.785095635592258e-06,
                1.9947297215125433e-06,
                3.288748673360027e-06,
                1.0677029973158649e-06,
                1.1478764021029928e-05,
                3.726638839878908e-06,
                4.785092783519724e-06
            ],
            [
                1.7603438428740716e-06,
                3.288749457469787e-06,
                3.288749457432399e-06,
                2.5612828213818346e-06,
                2.9023116391978967e-06,
                1.9947304348703948e-06,
                4.785095635624897e-06,
                2.9023112932045342e-06,
                6.475949526003845e-07,
                1.7603425837702984e-06
            ],
            [
                1.8925148239290237e-05,
                5.04347528446051e-07,
                6.475951069985296e-07,
                1.7603432133296774e-06,
                9.42244256915735e-07,
                NaN,
                2.260324028427877e-06,
                1.3007128464961824e-05,
                6.475951069985296e-07,
                5.422220262505697e-06
            ],
            [
                9.931189774140912e-08,
                2.1024334103505245e-07,
                4.450848927637999e-07,
                NaN,
                2.561281600086738e-06,
                9.931189774187203e-08,
                1.1253509497883659e-07,
                1.27519088491875e-07,
                1.275190276853036e-07,
                7.734415776836702e-08
            ],
            [
                2.5612831267202583e-06,
                2.561282210701601e-06,
                7.338213304316717e-07,
                8.481108183110588e-05,
                2.2603242978665707e-06,
                2.1444953527476883e-05,
                1.0677031245905116e-06,
                1.0677032518748838e-06,
                1.5534981249397663e-06,
                9.422444815726566e-07
            ],
            [
                8.315279285370317e-07,
                4.450852641656969e-07,
                1.8553910183674878e-07,
                8.315279285370317e-07,
                5.04347287955046e-07,
                5.043472278322555e-07,
                9.422445939054222e-07,
                1.3709567165617364e-06,
                9.931190958076104e-08,
                1.9947299593078385e-06
            ],
            [
                NaN,
                2.7535697667202906e-05,
                1.7603425837702984e-06,
                9.4224425692559e-07,
                2.9023126771227976e-06,
                1.0129993395336818e-05,
                3.2887478892683997e-06,
                6.144174601991196e-06,
                7.889263526180094e-06,
                3.726638395611981e-06
            ],
            [
                7.88926446679691e-06,
                2.5612816000145246e-06,
                2.902312677104321e-06,
                1.760343003481596e-06,
                1.0677028700363782e-06,
                2.5612834320214477e-06,
                1.2098655392811161e-06,
                4.2228324377740105e-06,
                3.7266379513434106e-06,
                2.561283126679493e-06
            ],
            [
                NaN,
                8.93969950132721e-06,
                1.0129988564716393e-05,
                5.715005151606823e-07,
                NaN,
                NaN,
                1.7603434231833873e-06,
                5.422219616265831e-06,
                NaN,
                2.561281294760143e-06
            ],
            [
                1.892514598551715e-05,
                4.222831934379152e-06,
                3.5356267573959116e-05,
                3.7266397283231055e-06,
                9.422450431860582e-07,
                9.422442569208767e-07,
                4.222833947932061e-06,
                1.994729008145876e-06,
                2.6995774527577444e-07,
                9.422443692489024e-07
            ],
            [
                0.999996711250154,
                0.9999972735284306,
                0.9999898700102401,
                0.9999989969855544,
                0.9997040429766347,
                0.9999938558232032,
                0.9999981261237246,
                0.9999546021260649,
                0.9999957771655507,
                0.9999885212305138
            ],
            [
                NaN,
                8.481106161413668e-05,
                1.1478773598914277e-05,
                5.82912516531155e-05,
                1.0129993394959082e-05,
                2.430023783601594e-05,
                2.1444943302181958e-05,
                1.8925145985895816e-05,
                4.222831934321543e-06,
                5.422219616085833e-06
            ],
            [
                5.043475885674441e-07,
                1.7603432133296774e-06,
                5.04347468318358e-07,
                1.2098661161927025e-06,
                9.4224425692559e-07,
                1.5534984953453635e-06,
                1.0677033791437343e-06,
                1.7603432133136672e-06,
                7.338209805170655e-07,
                5.71500651413193e-07
            ],
            [
                8.315281267882195e-07,
                9.422444815765128e-07,
                3.726639284144195e-06,
                1.2098652508424818e-06,
                4.4508494582405734e-07,
                8.93969950132721e-06,
                1.5534975693792215e-06,
                1.5534975693707442e-06,
                1.3007131566015624e-05,
                1.209865539295696e-06
            ],
            [
                2.430024942462891e-05,
                4.539788488059714e-05,
                1.3007123813193233e-05,
                1.4738989000181669e-05,
                6.144176066672166e-06,
                3.1201907657271834e-05,
                0.0001233945308156245,
                1.892514598551715e-05,
                1.1478765389222573e-05,
                7.484620943960125e-05
            ],
            [
                4.222833444590791e-06,
                5.71500651413193e-07,
                2.902310947208574e-06,
                5.422218969895357e-06,
                7.889259764445822e-06,
                1.4738983729535602e-05,
                5.043472879540142e-07,
                5.1442201405453086e-05,
                2.260324836787226e-06,
                4.5397852414783676e-05
            ],
            [
                3.726638395611981e-06,
                7.889266347715168e-06,
                2.5612812946681295e-06,
                5.829126554196652e-05,
                1.553498310118888e-06,
                8.939696304116203e-06,
                6.144177531767002e-06,
                2.430024942462891e-05,
                1.3007125363908762e-05,
                1.7603438428740716e-06
            ],
            [
                NaN,
                5.715005151606823e-07,
                9.422444815814404e-07,
                3.288749065423109e-06,
                1.2098661162056318e-06,
                6.144173137126169e-06,
                1.2098659719788098e-06,
                7.889266347715168e-06,
                1.5534981249697903e-06,
                6.47595107001401e-07
            ],
            [
                4.450848927621807e-07,
                6.962254589914941e-06,
                2.561281294760143e-06,
                NaN,
                NaN,
                3.726639284144195e-06,
                NaN,
                4.785096206047877e-06,
                NaN,
                7.338209805200689e-07
            ],
            [
                9.422447062270609e-07,
                1.0677031245953668e-06,
                7.338209805224048e-07,
                5.04347287955046e-07,
                7.338213304363436e-07,
                6.475948754012522e-07,
                1.2098658277451275e-06,
                7.338209805200689e-07,
                1.0677027427600627e-06,
                5.715003789046955e-07
            ],
            [
                2.561282210740037e-06,
                1.5534979397740895e-06,
                1.4449800373065699e-07,
                3.059022998558814e-07,
                1.0677026154774503e-06,
                NaN,
                2.2603234895176927e-06,
                NaN,
                1.8553919030858602e-07,
                3.466326211113502e-07
            ],
            [
                5.715003789017068e-07,
                1.9947304348862686e-06,
                6.605212107121456e-05,
                NaN,
                4.450851580555361e-07,
                8.315284241597959e-07,
                7.338212429537553e-07,
                NaN,
                7.889260704732132e-06,
                1.3709572068522336e-06
            ],
            [
                1.067703379154416e-06,
                NaN,
                7.338209805224048e-07,
                7.338211554783522e-07,
                NaN,
                NaN,
                9.422450431989127e-07,
                2.260325375677174e-06,
                NaN,
                NaN
            ],
            [
                2.2603234895289998e-06,
                3.72664061681327e-06,
                8.939696304116203e-06,
                1.5534981249574276e-06,
                4.785095065132354e-06,
                4.785096776468749e-06,
                NaN,
                7.338208055664991e-07,
                2.1444950970626095e-05,
                1.5534981249697903e-06
            ]
        ]
    },
    {
        "q_id": "10332_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            98,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127,
            25,
            32,
            96,
            97,
            102
        ],
        "rewards": [
            [
                0.9999998802069587,
                0.9999998555019618,
                0.9999967112493681,
                0.9999998257021214,
                0.9999996743688975,
                0.9999999434137098,
                0.9999998724809419,
                0.9999997463980427,
                0.9999995818810776,
                0.9999998724809268
            ],
            [
                0.99999994341373,
                0.9999999358794096,
                0.99999976176309,
                0.999999653367255,
                0.9999997300420939,
                0.9999994956527122,
                0.9999998874649051,
                1.0,
                0.99999994341373,
                0.9999999677581375
            ],
            [
                0.9999998144609645,
                0.9999995818810776,
                0.9999998874647709,
                0.9999991148431754,
                0.999999802494586,
                0.9999996743688975,
                0.9999993106388725,
                0.9999998362622357,
                0.9999993106387904,
                0.9999998874647307
            ],
            [
                0.9999998942830358,
                0.9999997617630333,
                0.9999999226557593,
                0.9999999559306049,
                0.999999825702059,
                0.9999987121041711,
                0.9999998802068873,
                0.9999999226557225,
                0.999999946842182,
                0.9999996072136595
            ],
            [
                0.9999999468421187,
                0.9999999715466426,
                0.9999997617631753,
                0.9999997463981333,
                1.0,
                0.9999999715466493,
                0.9999999656787243,
                0.9999999715466257,
                0.9999998802069444,
                1.0
            ],
            [
                0.9999999176675436,
                0.9999999434137098,
                0.999999961108909,
                0.9999999778405029,
                0.9999998802069302,
                0.9999999634651618,
                0.9999998555019446,
                0.9999999067050832,
                0.9999998942830358,
                0.9999992661791072
            ],
            [
                0.9999999611088487,
                0.9999999176674552,
                0.9999999715466392,
                0.999999967758149,
                0.9999999634651923,
                0.999999931743971,
                0.9999998642567351,
                0.999999917667475,
                0.9999998642566542,
                0.9999999732705315
            ],
            [
                0.9999999611088904,
                0.9999999397642582,
                0.9999998942830233,
                0.999999967758122,
                0.9999999611088812,
                0.9999994631247403,
                0.9999999715466696,
                0.9999999715466696,
                0.9999999715466765,
                0.9999999715466528
            ],
            [
                0.999999631011592,
                0.9999999273418962,
                0.9999998461826222,
                0.9999999559305732,
                0.9999999791830714,
                0.9999999273418615,
                0.999999607213753,
                0.9999999778404975,
                0.999999894282935,
                0.9999997300421904
            ],
            [
                1.0,
                0.9999999530883675,
                0.9999997761972116,
                0.9999998461826222,
                0.9999994284996212,
                0.9999999677581067,
                1.0,
                0.9999998362623334,
                0.9999998461826956,
                0.9999997300422547
            ],
            [
                0.9999998724809116,
                0.9999998724810027,
                0.999999310639119,
                0.9999996940977367,
                0.9999999586006443,
                0.9999997463981334,
                0.9999993106392013,
                0.9999997897567091,
                0.9999998461826589,
                0.9999996310116358
            ],
            [
                2.9023112932177327e-06,
                3.05902190458764e-07,
                0.000123394633832426,
                8.315282259138311e-07,
                0.9999987901341726,
                0.9999938558232025,
                6.475947982037486e-07,
                0.9999994284995531,
                0.9999972735287553,
                2.2603237589779086e-06
            ],
            [
                0.9999994631251243,
                1.3709570434178922e-06,
                1.209865539295696e-06,
                0.9999999273418442,
                0.9999982396574172,
                0.9999997463981031,
                0.9999998555019275,
                1.4449798650551755e-07,
                2.3823688159291947e-07,
                1.6373774480605869e-07
            ],
            [
                0.9999964991464262,
                0.9999996533674204,
                0.9999999006881259,
                0.9999994956524717,
                0.999996499145588,
                0.999998996985434,
                0.9999992661792821,
                0.9999994956526522,
                0.9999998362623138,
                0.9999999123575255
            ],
            [
                0.9999997463981636,
                0.9999998802069587,
                0.9999999530883787,
                0.999999554914736,
                0.999999887464838,
                0.99999994341373,
                0.9999998942830737,
                0.9999999500627976,
                0.9999997126313783,
                0.999999814460876
            ],
            [
                0.9999999123575151,
                0.9999996533673376,
                0.9999999006880905,
                0.9999999468421124,
                0.9999999500628214,
                0.9999998942829351,
                0.9999998724809723,
                0.9999998024945624,
                0.9999998555020481,
                0.9999994631251242
            ],
            [
                0.9999910603058351,
                0.9999967112497599,
                0.9999983463098232,
                0.9999996743688974,
                0.9999998461826037,
                0.9999997463982241,
                5.4222176771176554e-06,
                0.9999999434138109,
                0.9999992188516695,
                0.9999980052709924
            ],
            [
                0.9999996310115479,
                0.9999999067050499,
                0.9999999123575672,
                0.9999998942830106,
                0.9999999067049942,
                0.9999998362622943,
                0.9999999006881378,
                0.9999998802069587,
                0.9999999067050832,
                0.9999995818812272
            ],
            [
                0.9999999530883898,
                0.9999999226558238,
                0.9999998802069587,
                0.9999995262092163,
                0.9999999611089043,
                0.9999995549148951,
                0.9999998874647843,
                0.9999999358794021,
                1.9947306726358406e-06,
                0.9999999434137098
            ],
            [
                0.9999999273418355,
                0.9999998461827139,
                0.9999998874649318,
                0.9999999358793333,
                0.999999581881277,
                0.9999998942829225,
                0.9999999358793562,
                0.9999998802069017,
                0.9999996072136593,
                0.9999999358793715
            ],
            [
                0.9999999656787325,
                0.9999999611088626,
                0.999999946842163,
                0.999999974889988,
                0.9999999611088487,
                0.9999999715466663,
                0.9999999677581453,
                0.9999996310113278,
                1.0,
                0.9999997897567091
            ],
            [
                0.999999946842106,
                0.9999999611088858,
                0.9999998642566704,
                0.9999999586006592,
                0.9999999559306259,
                0.9999998362622358,
                0.9999999358793485,
                0.9999999715466663,
                1.0,
                0.9999999634651748
            ],
            [
                0.9999999176675338,
                0.9999997300421583,
                0.9999999317439058,
                0.9999997300422548,
                0.9999998555019447,
                0.9999999067050832,
                0.9999999468421883,
                0.9999997463981938,
                0.999999631011328,
                0.9999999468421756
            ],
            [
                0.999999965678708,
                0.9999997897565839,
                0.999999894283061,
                0.9999996743686257,
                0.9999999226558423,
                0.999999912357442,
                0.9999987901337404,
                0.9999999559305996,
                0.9999995818813766,
                0.9999998724809875
            ],
            [
                0.9999999500627738,
                0.9999997897567091,
                0.9999999067051388,
                0.9999999468421756,
                0.9999999530883955,
                0.9999996743688586,
                0.9999998144608097,
                0.9999999559306206,
                0.9999999176675338,
                0.9999999634651966
            ],
            [
                1.0,
                0.9999999317439546,
                0.9999999176674552,
                0.9999998144608319,
                0.9999999273418182,
                0.9999999634651836,
                0.9999999358793868,
                0.9999992661791947,
                0.9999995262093293,
                0.9999999226557131
            ],
            [
                0.9999999611089043,
                0.9999999697115406,
                0.9999999006880786,
                0.9999999715466426,
                0.9999999634651618,
                0.999999802494586,
                0.9999999273418183,
                0.999999974889994,
                0.9999998257022045,
                0.9999998802069302
            ],
            [
                0.9999999358794479,
                0.9999999764113296,
                0.9999998724810027,
                0.9999998802069587,
                0.9999995818814266,
                1.0,
                0.9999998024946566,
                1.0,
                0.9999999358793639,
                1.0
            ],
            [
                0.9999999468421186,
                0.9999999317440197,
                0.9999998642566704,
                0.9999998942829098,
                0.9999998874647843,
                0.9999999317439953,
                0.9999999176674848,
                0.9999998555019446,
                0.9999999358794097,
                0.9999998724809723
            ],
            [
                0.9999997897565588,
                0.9999999434137435,
                0.9999997897565838,
                0.9999997300422226,
                0.9999998257020799,
                0.9999999586006096,
                0.9999998942830358,
                0.9999999586006442,
                0.9999999006881259,
                1.0
            ],
            [
                0.9999999067050721,
                0.9999999273418961,
                0.999999922655833,
                1.0,
                0.9999999397642724,
                0.999999674368781,
                0.9999999067050831,
                0.9999998874647977,
                0.9999987121043242,
                0.9999998642566866
            ],
            [
                0.9999997463980125,
                0.9999998461826222,
                0.9999998642566219,
                0.9999998555019446,
                0.9999997463980729,
                0.999999887464811,
                0.9999996072137999,
                0.9999987901338843,
                0.9999998802069159,
                0.9999998802069017
            ],
            [
                0.9999993916406734,
                5.043475284430694e-07,
                1.0,
                5.043474081993875e-07,
                0.9999997617630049,
                0.9999999176674848,
                0.9999984465028016,
                7.338207180864763e-07,
                4.222834451382849e-06,
                2.3823690999160957e-07
            ],
            [
                0.9999999634651662,
                0.9999999273418875,
                0.9999999500627976,
                0.9999999273418182,
                0.9999999715466594,
                0.9999998362622552,
                0.9999997463980729,
                0.9999998802069302,
                0.9999999500628274,
                0.999999864256719
            ],
            [
                0.9999998024947038,
                0.9999999468421377,
                0.9999997463982241,
                0.9999999358794173,
                1.0,
                0.9999999176674946,
                0.999999961108909,
                0.9999999273418616,
                0.9999999530883285,
                0.9999997897566841
            ],
            [
                1.0,
                0.9999999434137232,
                0.9999999067051276,
                0.9999999697115407,
                0.9999997463980729,
                0.9999998555020307,
                0.9999996072137999,
                0.9999999530883732,
                0.9999999123575568,
                0.9999999559305838
            ],
            [
                0.9999995262092163,
                0.999999802494633,
                0.9999995262094987,
                0.9999998461827321,
                0.9999998257021837,
                0.9999997126313097,
                1.0,
                0.9999997126313783,
                0.9999999123575046,
                0.9999998724809115
            ],
            [
                5.043474082012222e-07,
                0.9999996310114159,
                0.9999991684719729,
                0.9999999611089183,
                0.9999982396565775,
                2.1024339116168358e-07,
                4.4508515805735777e-07,
                5.043475885696228e-07,
                4.450850519409479e-07,
                2.6995784182183607e-07
            ],
            [
                0.9999999317439546,
                0.9999999656787202,
                0.9999999656786792,
                0.9999999006881497,
                0.9999998642566219,
                0.9999999586006344,
                0.9999999317439384,
                0.9999999006880312,
                0.9999999530883283,
                0.9999999434137502
            ],
            [
                0.9999999358793792,
                0.9999997126313783,
                0.9999999317440035,
                0.9999999176675535,
                0.9999999067049831,
                0.9999999468421883,
                0.999999931743914,
                0.9999997126314468,
                0.9999997463981032,
                0.9999998642566381
            ],
            [
                0.9999989969854337,
                0.9999992188517627,
                0.9999993524053563,
                0.9999982396565777,
                0.9999991684720716,
                8.315280276607289e-07,
                0.9999997761970515,
                0.9999981261246174,
                7.338209805224048e-07,
                0.9999993524050476
            ],
            [
                0.9999999397642939,
                0.999998996985912,
                0.9999999500628095,
                0.9999996310114598,
                0.9999993916408184,
                0.9999992188516695,
                0.9999999634652009,
                0.9999998942829602,
                0.9999998942829098,
                0.9999999434137232
            ],
            [
                1.9947297215043796e-06,
                0.999999631011372,
                2.260324836776948e-06,
                2.561282210590951e-06,
                1.2098655392662613e-06,
                0.9999934595620028,
                3.535623806720131e-05,
                0.9999998724810027,
                1.5534977545243671e-06,
                5.043472278299047e-07
            ],
            [
                0.9999930377404334,
                0.9999985406236054,
                0.9999942280772225,
                2.1024331597262577e-07,
                3.927862002663297e-07,
                7.734424996967756e-08,
                0.9999998942830611,
                0.9999980052707548,
                3.059022269250683e-07,
                3.4663278639892215e-07
            ],
            [
                0.9999998555019618,
                0.9999991148431755,
                0.999999428499485,
                0.9999994631251241,
                0.9999981261241703,
                0.9999984465026162,
                0.999999057755294,
                0.9999998724809419,
                0.9999984465028016,
                0.9999993916406733
            ],
            [
                0.9999999791831037,
                0.9999999764113268,
                0.9999999748899941,
                0.9999999226557776,
                0.9999999176675731,
                1.0,
                0.9999999226557408,
                0.9999999123574836,
                0.9999999500628333,
                0.9999999634651879
            ],
            [
                1.0,
                0.9999999634651487,
                0.9999999715466595,
                0.9999999397642366,
                0.9999999067051276,
                0.9999999748899912,
                0.9999998802068873,
                0.9999999697115949,
                0.9999999677581183,
                0.9999999611088904
            ],
            [
                0.9999999434137097,
                0.9999999123574942,
                0.999999391641036,
                0.9999999397642724,
                0.9999995818813269,
                0.9999996310116358,
                0.9999999611088627,
                0.9999999006880668,
                0.9999999656787243,
                1.0
            ],
            [
                0.9999998874647574,
                0.9999999778405002,
                1.0,
                0.9999999634651923,
                1.0,
                0.9999999697115696,
                0.9999999586005949,
                0.99999997489,
                0.9999999791830912,
                0.9999999397642222
            ],
            [
                0.9999998461826956,
                0.9999995262095551,
                0.9999998461826956,
                0.9999999176675043,
                0.9999996940978826,
                0.9999998362622747,
                0.999999554914842,
                0.999999825702163,
                0.9999997761970248,
                0.9999998942830611
            ],
            [
                0.9999992661787575,
                0.9999995549149483,
                0.9999998362623138,
                0.9999999317439872,
                0.999999814460854,
                0.9999999434137435,
                0.999999900688055,
                0.9999999006880786,
                0.9999999226558423,
                0.9999999006880549
            ],
            [
                0.9999998942829602,
                0.9999997897567342,
                0.9999996743686645,
                0.9999997617631184,
                0.9999999434137772,
                0.9999982396567875,
                0.9999998942830233,
                0.9999994631249324,
                0.9999996743687422,
                0.9999998802069731
            ],
            [
                0.9999998362623334,
                0.9999999677581144,
                0.9999999791830739,
                0.9999999677581298,
                0.9999999697115515,
                0.9999999559306311,
                0.9999999732705411,
                0.999999946842163,
                0.999999917667524,
                0.999999814460854
            ],
            [
                0.9999996743687034,
                0.9999998362623723,
                0.9999999611088719,
                0.9999999358794479,
                0.9999996743688585,
                0.9999999006881496,
                0.9999999732705411,
                0.9999999559305786,
                0.9999989969859121,
                0.999999961108858
            ],
            [
                0.9999998874648245,
                0.9999999715466765,
                0.9999997300421261,
                0.9999999715466731,
                0.9999999123575672,
                0.9999987901340284,
                0.9999999397642365,
                0.9999991148428589,
                0.9999999500627976,
                0.999999969711555
            ],
            [
                0.999999712631344,
                0.9999999006880549,
                0.9999986290431208,
                0.9999987121044779,
                0.9999998024946095,
                0.9999980052695666,
                0.9999999273418961,
                0.9999998144609645,
                0.9999998024946095,
                0.9999998461826222
            ],
            [
                0.9999989322966211,
                0.9999997761970781,
                0.9999994284996212,
                0.9999999559305732,
                0.9999999317439384,
                0.9999995549150013,
                0.9999996310114159,
                0.9999998024946566,
                0.9999998724808964,
                0.9999995262093292
            ],
            [
                1.994729008145876e-06,
                1.3709578605729614e-06,
                2.382369951932796e-07,
                1.444979692797559e-07,
                0.9999998874648246,
                0.9999975938979487,
                0.9999989969856731,
                1.3709573702822306e-06,
                2.6995774527718623e-07,
                0.9999998257021006
            ],
            [
                0.999999872480942,
                0.9999999006880076,
                0.9999998555019962,
                0.9999998257021421,
                0.999999814460876,
                0.9999998642567351,
                0.9999995262093857,
                0.9999999067050943,
                0.9999983463098231,
                0.9999998802069873
            ],
            [
                0.9999999434138109,
                0.9999999530883789,
                0.9999999176675436,
                0.9999998144608098,
                0.9999997617630048,
                0.9999999397643011,
                0.9999999273418355,
                0.9999999634651661,
                0.9999999530883676,
                0.9999999611088998
            ],
            [
                0.9999996072137998,
                0.9999995818811275,
                0.9999999226558146,
                0.9999998024946801,
                0.9999999586005851,
                0.9999995262094422,
                0.9999996743687422,
                0.9999992661790197,
                0.9999999434137232,
                0.9999999006880076
            ],
            [
                0.999998005270042,
                0.9999999067050164,
                0.9999998724809115,
                0.9999999468421122,
                0.9999998942829854,
                0.9999996310115918,
                0.9999998942829477,
                0.9999999317439954,
                0.9999998362622943,
                0.9999999468421187
            ],
            [
                0.9999991148427533,
                0.999999653367503,
                0.9999988634364252,
                0.9999997463980427,
                0.9999978766210325,
                0.9999989322972576,
                0.9999993916406734,
                0.9999996072137999,
                0.9999984465020606,
                0.9999970976876704
            ],
            [
                0.9999998144609645,
                0.9999999006881259,
                0.9999998724809572,
                0.9999998555019963,
                0.999999894283061,
                0.9999997126313098,
                0.9999999317440278,
                0.9999999397642365,
                0.9999998257021628,
                0.9999999226557593
            ],
            [
                0.9999999397642222,
                0.9999999358793867,
                0.9999999397642939,
                0.9999997463981939,
                0.9999998555019446,
                0.9999998642566704,
                0.9999999358793944,
                0.9999999358794327,
                0.9999999317439872,
                0.9999999397642437
            ],
            [
                0.9999999586006344,
                0.9999999827421558,
                0.9999999226557408,
                0.9999999732705475,
                1.0,
                0.9999998642566381,
                1.0,
                0.9999999273418442,
                0.999999935879425,
                0.999999943413784
            ],
            [
                0.9999998024946566,
                0.9999999226558515,
                0.9999999634651878,
                0.9999998942829477,
                0.9999997897565838,
                0.9999999611088766,
                0.9999998724809723,
                0.9999999273418096,
                0.9999991684715764,
                1.0
            ],
            [
                0.9999998724810027,
                0.9999998461826956,
                0.9999984465024312,
                0.9999998024947273,
                0.9999995818811275,
                0.9999994284992807,
                0.9999992661788447,
                0.9999989322972577,
                0.9999987121050918,
                0.9999993106387903
            ],
            [
                1.2098659719601033e-06,
                8.939697369882888e-06,
                5.422218969769604e-06,
                0.9999997300422226,
                0.9999999273417922,
                0.9999999586006245,
                0.9999996310115038,
                0.9999999500628571,
                0.9999994631248041,
                0.9999999358794402
            ],
            [
                1.0,
                0.9999996533673376,
                0.999999802494633,
                0.9999999634651487,
                0.9999998461827139,
                0.9999993916411084,
                0.9999999677581528,
                0.9999999067051499,
                0.9999999067050276,
                0.9999998362623723
            ],
            [
                0.9999998724809419,
                0.9999999500627916,
                0.9999999358793944,
                0.9999999586006048,
                0.9999998942829729,
                0.9999999732705602,
                0.9999998942829728,
                0.9999997897567342,
                0.9999994284995531,
                0.9999999317439221
            ],
            [
                0.9999995262096116,
                0.9999998724809419,
                0.9999998461826038,
                0.9999999358794021,
                0.9999998362622748,
                0.9999998555019447,
                0.9999998555019446,
                0.9999998257021422,
                0.9999998874648917,
                0.9999998555019619
            ],
            [
                0.9999998144608983,
                0.9999988634365611,
                0.9999999123574523,
                0.999999927341853,
                0.9999999434137434,
                0.9999998874648112,
                0.9999999317440278,
                0.9999998257021006,
                0.9999984465026169,
                0.9999999358794021
            ],
            [
                0.999998629042957,
                0.9999998024947037,
                0.9999988634361542,
                0.9999996940977731,
                0.9999998724809267,
                0.9999997300421904,
                0.9999994956527123,
                0.999999352405279,
                0.999999310638626,
                0.9999999397643154
            ],
            [
                0.9999997897565839,
                0.9999992661790199,
                0.9999999273417662,
                0.9999999226557317,
                0.9999999006880195,
                0.9999998461826405,
                0.9999993106388727,
                0.9999999397642437,
                0.9999999273418443,
                0.9999998461827322
            ],
            [
                0.9999997463980729,
                2.902311293147782e-06,
                0.9999972735300552,
                0.9999991148426477,
                0.00010889694827288516,
                0.9999994631248682,
                1.0677028699955933e-06,
                2.561282515988704e-06,
                1.8925157265332104e-05,
                0.9999996310113719
            ],
            [
                0.9999996310115479,
                0.9999999226558238,
                0.9999998802069016,
                0.9999999123575359,
                0.9999998724809419,
                0.9999999226557224,
                0.9999997126315497,
                0.9999999586005949,
                0.9999999611088766,
                0.9999999176674652
            ],
            [
                0.9999999123574942,
                0.9999998724809875,
                0.999999894282935,
                0.9999998257022045,
                0.999999814460854,
                0.9999998555019791,
                0.9999999067050832,
                0.9999999226557408,
                0.9999999006881497,
                0.9999999067051499
            ],
            [
                0.9999999468420996,
                0.9999999559305628,
                0.9999999317439221,
                0.9999999468421122,
                0.9999997761970248,
                0.9999999273418356,
                0.9999997126314811,
                0.999999946842163,
                0.9999998724809115,
                0.9999998461826405
            ],
            [
                0.9999999611088812,
                0.9999999559306102,
                0.9999998555020307,
                0.9999998461826222,
                0.9999998642566704,
                0.9999987121047849,
                0.9999999226557592,
                0.9999999273418269,
                0.9999999434137165,
                0.9999998362622943
            ],
            [
                0.9999999530883675,
                0.9999999176674946,
                0.9999999006881142,
                0.9999999273417662,
                0.9999999397643156,
                0.9999999273418442,
                0.9999999176675142,
                0.9999999067049943,
                0.9999998024947272,
                0.9999999434138043
            ],
            [
                0.9999999559305522,
                0.9999998024945624,
                0.9999999500628631,
                1.0,
                0.9999997300421261,
                0.9999999611089183,
                0.9999977396754332,
                0.9999977396762416,
                0.9999999317440198,
                0.9999998874647709
            ],
            [
                1.300712846477255e-05,
                2.3823696679230424e-07,
                0.9999974387174855,
                4.450851580540182e-07,
                0.9999969105062896,
                1.8553907971758842e-07,
                3.927862470861484e-07,
                1.3709578605542582e-06,
                4.450849458200093e-07,
                6.475951069985296e-07
            ],
            [
                0.9999998802069731,
                0.9999998024946095,
                0.9999999468421756,
                0.9999998024947037,
                0.9999997300422869,
                0.999999939764215,
                0.9999998942830485,
                0.9999999434138042,
                0.9999999067051388,
                0.9999981261250637
            ],
            [
                0.9999996310114159,
                0.9999999656786915,
                0.9999997463981636,
                0.9999999559305891,
                0.9999999006881141,
                0.9999999634651879,
                0.9999997761971848,
                0.9999999791830937,
                0.9999999317439465,
                0.9999999697115912
            ],
            [
                0.9999985406236054,
                0.9999991684716752,
                0.9999970976866319,
                0.9999999468421947,
                0.9999999273417749,
                0.9999982396572068,
                0.9999977396748948,
                0.9999991148432809,
                0.9999978766207788,
                0.9999999226557317
            ],
            [
                0.9999999559306102,
                0.9999999434137232,
                0.9999999397642508,
                0.9999996533674617,
                0.9999974387171794,
                0.999999554914842,
                0.9999998874647977,
                0.9999999317439628,
                0.9999999500628215,
                0.9999999397642437
            ],
            [
                1.0,
                0.9999999123575255,
                0.9999978766212855,
                0.9999993524050476,
                0.9999991684716751,
                0.9999999559305575,
                0.9999997761971048,
                1.3709570434122812e-06,
                0.9999997617630332,
                0.9999993916408184
            ],
            [
                0.9999999397643011,
                0.9999999123575255,
                0.9999999468421313,
                1.0,
                0.9999999006880076,
                0.9999998942829981,
                0.9999999176674553,
                0.9999998642567028,
                0.9999999273417836,
                0.9999997617631469
            ],
            [
                0.9999999067051499,
                0.9999998257021422,
                1.0,
                0.9999998942829729,
                0.9999997761970515,
                0.9999999067051276,
                0.9999999656787121,
                0.9999999677581413,
                0.9999999500628393,
                0.9999999634651618
            ],
            [
                0.9999999500628571,
                0.9999999317440279,
                0.999999814460876,
                0.9999999273418528,
                0.9999998555020135,
                0.9999996072136594,
                0.9999998257021837,
                0.9999999123575464,
                0.9999998802069587,
                0.99999967436882
            ],
            [
                5.422220909009474e-06,
                0.9999997463980125,
                8.31527928532683e-07,
                0.9999998642566542,
                0.9999999123575569,
                0.999999814460854,
                2.5612812947508257e-06,
                0.9999989969857926,
                0.9999999397642151,
                3.059022998576899e-07
            ],
            [
                0.9999998257022045,
                0.9999999358794249,
                0.9999999697115948,
                0.9999999358793639,
                0.999998712105092,
                0.9999998555019618,
                0.9999994631248041,
                0.9999998144608983,
                0.9999998802069873,
                0.9999997617631468
            ],
            [
                0.9999989322970031,
                0.9999987901340288,
                0.9999991684715762,
                0.9999989322968759,
                0.999999554914842,
                0.9999997761971582,
                0.9999993916411811,
                0.9999998555019619,
                0.9999995262096117,
                0.9999998024946802
            ],
            [
                0.999999922655833,
                0.9999998461826588,
                0.9999999656786793,
                0.999999168471576,
                0.9999999123575464,
                0.9999999611088487,
                0.9999999748899941,
                0.9999999226558054,
                0.9999999176675338,
                0.9999996940976638
            ],
            [
                0.9999998461827322,
                0.9999999500628393,
                0.9999999067050165,
                0.9999993524054337,
                0.999999939764258,
                0.9999998802069444,
                0.9999998802069873,
                0.9999999273418269,
                0.9999998024946566,
                0.9999995818811773
            ],
            [
                0.9999999006880668,
                0.9999999656787407,
                0.9999999816291512,
                1.0,
                0.9999999865595854,
                0.9999999697115876,
                1.0,
                0.9999999559305838,
                1.0,
                0.999999963465201
            ],
            [
                0.9999999123574628,
                0.9999999397642365,
                0.999999814460876,
                0.9999997463980124,
                1.0,
                0.9999995549150013,
                0.9999998642566381,
                0.999998629043284,
                0.999999802494633,
                0.9999991684721707
            ],
            [
                0.9999998461826038,
                0.9999997617630616,
                0.9999999358794402,
                0.9999999500628155,
                0.999999931743979,
                0.9999999611089136,
                0.9999999176674356,
                0.999999802494633,
                0.9999999123575778,
                0.9999995262094986
            ],
            [
                0.9999998362623723,
                0.9999999067051165,
                0.9999998724809723,
                0.9999999397642078,
                0.9999999226558329,
                0.999999730042287,
                0.9999999226557961,
                0.9999986290421404,
                0.9999999468421756,
                0.9999996533674617
            ],
            [
                0.9999999697115732,
                0.9999999530883955,
                0.9999999559306049,
                0.9999999317439708,
                0.9999999697115876,
                0.9999999715466765,
                0.9999999530883732,
                0.9999999067051388,
                0.9999999748899852,
                0.9999999677581336
            ],
            [
                0.9999997761971048,
                0.9999999123574628,
                0.9999996940978826,
                0.9999994284994169,
                0.9999988634362896,
                0.9999994956527123,
                0.9999996743687809,
                0.9999998461826406,
                0.9999999559306154,
                0.9999999358794479
            ],
            [
                0.9999991148432811,
                1.7603438428740716e-06,
                0.9999995818813767,
                8.31527928532683e-07,
                1.9947306726594253e-06,
                0.9999989969855535,
                1.553498124964492e-06,
                0.9999921107355408,
                9.422448185478557e-07,
                8.315277302788957e-07
            ],
            [
                0.9999987121041708,
                0.999998932297003,
                0.9999995818810776,
                0.9999969105059217,
                0.999999927341827,
                0.9999999067050721,
                0.9999992188518558,
                0.9999999123575359,
                0.9999999500628274,
                0.999999730042287
            ],
            [
                2.382369667929001e-07,
                3.466326211113502e-07,
                0.9999983463098235,
                3.927862470899887e-07,
                0.9999998461827322,
                7.734421308914719e-08,
                0.999983298578203,
                2.6995787400282076e-07,
                1.1253512180925583e-07,
                0.9999982396569974
            ],
            [
                0.9999998461826038,
                0.9999997761971315,
                0.999999114843281,
                0.9999988634358833,
                0.9999997126313098,
                0.9999999006880905,
                0.9999992661787572,
                0.9999997463981334,
                0.999999428499485,
                0.9999997617631753
            ],
            [
                0.999999931743971,
                0.9999999226558054,
                0.9999998724809116,
                0.9999999500628571,
                0.9999999123575672,
                0.9999998362622943,
                0.9999998874649051,
                0.9999999006880904,
                0.9999998802068873,
                0.9999999500627916
            ],
            [
                0.9999999434138042,
                0.9999998942829351,
                0.9999999634651836,
                0.9999998942829855,
                0.9999999778405266,
                1.0,
                0.9999999067051165,
                0.9999998555019619,
                0.9999999634651662,
                0.9999999530883285
            ],
            [
                0.9999998257021422,
                0.9999998874648782,
                0.9999998555019619,
                0.9999998257022045,
                0.9999999397642436,
                0.9999999176675632,
                0.9999993106387906,
                0.9999999559305524,
                0.9999999586006146,
                0.999999825702059
            ],
            [
                0.999999730042287,
                1.0,
                0.9999999226557501,
                0.9999999634651836,
                0.9999999500628036,
                0.9999994284996212,
                0.9999998642567189,
                0.9999999634652009,
                1.0,
                0.9999998144609203
            ],
            [
                0.9999999611088487,
                0.9999999468421122,
                0.9999999559306259,
                0.9999999656787202,
                0.9999999611088487,
                0.9999998257021213,
                0.9999999397642079,
                1.0,
                0.9999998802069159,
                0.9999999434137974
            ],
            [
                0.9999997126313097,
                0.9999996310116358,
                0.9999999067050388,
                0.9999996743686645,
                0.999999802494586,
                0.9999998024947272,
                0.9999992661789322,
                0.9999999176674946,
                0.9999999530883956,
                0.9999996533673791
            ],
            [
                0.9999999176674651,
                0.9999993916411812,
                4.691162124067829e-08,
                0.9999999067051277,
                0.9999993106387083,
                1.637377057673536e-07,
                0.9999999176675535,
                8.764249540862797e-08,
                0.9999995262094987,
                4.00637112929524e-05
            ],
            [
                0.999999825702163,
                0.999999974890027,
                0.9999998024946566,
                1.0,
                1.0,
                0.9999999176675338,
                0.9999999732705316,
                1.0,
                0.9999998802069302,
                1.0
            ],
            [
                0.9999998802069017,
                0.9999996072136594,
                0.9999995818812272,
                0.9999988634364253,
                0.999999943413757,
                0.999999825702163,
                0.9999999006881497,
                0.999999814460854,
                0.9999998555019963,
                0.999999887464771
            ],
            [
                0.9999999559306205,
                1.0,
                0.9999999697115696,
                0.999998005269804,
                0.9999998024945624,
                0.9999999530883285,
                0.9999998362623528,
                0.9999994956526521,
                0.9999999468421503,
                0.999999971546629
            ],
            [
                0.9999974387184009,
                0.9999980052695655,
                3.05902190458764e-07,
                3.927862002663297e-07,
                5.04347528446051e-07,
                0.9999992188519491,
                5.715005151606823e-07,
                8.764242227418718e-08,
                2.1024336609843824e-07,
                5.715003789033962e-07
            ],
            [
                0.999999977840508,
                0.9999998362622552,
                0.9999999677581528,
                0.9999999067050164,
                0.9999999715466765,
                0.9999996940977002,
                0.9999999397642079,
                0.9999999067050387,
                0.9999999500628453,
                1.0
            ],
            [
                0.9999999273417662,
                0.9999996940978826,
                0.9999992188513903,
                0.9999998724809723,
                0.9999999067051277,
                0.9999997126315154,
                0.9999998942828973,
                0.9999996743688975,
                0.9999999358793715,
                0.9999996743686645
            ],
            [
                0.9999998942829981,
                0.9999999468421565,
                0.999999746398073,
                0.9999999123575568,
                0.9999998802069159,
                0.9999998942830611,
                0.9999999226557317,
                0.9999999397642868,
                0.9999999358794021,
                0.9999998802069587
            ],
            [
                0.9999998642567189,
                0.9999999273418789,
                0.9999997463982241,
                0.9999999530883843,
                0.999999607213753,
                0.9999999586006196,
                0.9999997463980427,
                0.9999998144608983,
                0.9999999067051277,
                0.9999999530883563
            ],
            [
                0.9999999123575987,
                0.9999999006880905,
                0.9999999123575359,
                0.999999746398073,
                0.9999998874647977,
                0.9999990577550696,
                0.9999999226557592,
                0.9999997126315153,
                0.9999974387184006,
                0.9999999530883283
            ],
            [
                3.2887502415243994e-06,
                0.9999993524050477,
                0.9999977396746254,
                9.93120161306789e-08,
                1.7603440527222532e-06,
                1.2098662604291696e-06,
                0.9999972735300559,
                5.715004470313855e-07,
                7.3382080556433e-07,
                2.6995768091310296e-07
            ],
            [
                1.6373764721039308e-07,
                1.1253516205489029e-07,
                3.466326211105621e-07,
                2.1024344128584085e-07,
                2.1024339116134898e-07,
                1.0677029973158649e-06,
                1.4449798650476187e-07,
                9.93118503859575e-08,
                1.855391239539711e-07,
                2.3823696679230424e-07
            ],
            [
                0.9999998802069731,
                1.9947290080343035e-06,
                1.0677028700203557e-06,
                0.999998239656787,
                0.9999982396561578,
                0.9999999006880785,
                1.209865827740176e-06,
                6.144177531767002e-06,
                9.422449308673789e-07,
                0.9999988634361543
            ],
            [
                1.855391239547094e-07,
                7.734416698849138e-08,
                4.691159887151251e-08,
                1.27519088491875e-07,
                2.10243290909724e-07,
                1.6373776432509826e-07,
                1.275191036933194e-07,
                3.9278620026686556e-07,
                2.3823690999290963e-07,
                5.4222176771176554e-06
            ],
            [
                0.9999998942830485,
                0.9999998724809267,
                0.9999997897565838,
                0.9999996743687034,
                0.9999998802069017,
                0.9999998874647441,
                0.9999997897566841,
                0.9999999067049831,
                0.9999995818813269,
                0.9999998257020798
            ],
            [
                0.9999999273418788,
                0.999999887464811,
                0.9999995549151074,
                0.9999999397642436,
                0.9999999273418788,
                0.9999999778405239,
                0.9999999634652054,
                0.9999999500627976,
                0.9999999530883955,
                0.9999999226557592
            ]
        ]
    },
    {
        "q_id": "10128_mmlu_physics",
        "cot_ids": [
            0,
            2,
            4,
            6,
            7,
            9,
            10,
            11,
            13,
            14,
            15,
            17,
            19,
            22,
            25,
            27,
            28,
            32,
            33,
            35,
            39,
            40,
            44,
            46,
            47,
            48,
            50,
            53,
            54,
            60,
            61,
            69,
            70,
            72,
            73,
            75,
            76,
            78,
            80,
            82,
            83,
            84,
            85,
            86,
            88,
            89,
            90,
            91,
            92,
            94,
            95,
            96,
            98,
            100,
            102,
            104,
            105,
            106,
            107,
            110,
            111,
            112,
            113,
            114,
            115,
            117,
            120,
            121,
            122,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.3709570433979422e-06,
                1.7603440527046419e-06,
                1.1478773599425825e-05,
                4.450849988780466e-07,
                1.760343423160973e-06,
                5.715005832886879e-07,
                9.42244818532859e-07,
                1.55349775456958e-06,
                1.9947304348862686e-06,
                7.338212429464139e-07
            ],
            [
                6.962259569630266e-06,
                3.288749065423109e-06,
                2.9023133690980155e-06,
                1.7603440527222532e-06,
                5.422220262599396e-06,
                2.2603240284371276e-06,
                1.0129987357407137e-05,
                NaN,
                3.2887498495150166e-06,
                7.889266347636241e-06
            ],
            [
                2.9023112932045342e-06,
                1.760343003481596e-06,
                4.2228329411708495e-06,
                1.147877359957198e-05,
                1.7603425837791042e-06,
                5.1442195268327955e-05,
                1.0129988564716393e-05,
                7.889263526266196e-06,
                4.222832437639588e-06,
                4.222835458117536e-06
            ],
            [
                5.422220262599396e-06,
                5.422217030747413e-06,
                1.5534971989258068e-06,
                5.422217030747413e-06,
                4.4508505193791187e-07,
                5.04347348075149e-07,
                6.475951069985296e-07,
                5.71500719531729e-07,
                NaN,
                NaN
            ],
            [
                6.962256249885085e-06,
                3.7266401726359486e-06,
                5.04347468323289e-07,
                1.3709568799823232e-06,
                4.785094494783494e-06,
                7.889263526345123e-06,
                1.7603430034867993e-06,
                1.0129988564845378e-05,
                1.3709576971425944e-06,
                6.475951069985296e-07
            ],
            [
                8.315279285149107e-07,
                5.829127250060064e-05,
                6.475948754012522e-07,
                1.3709568799823232e-06,
                6.475947982002148e-07,
                1.553498124964492e-06,
                1.2098659719757836e-06,
                8.315283250371857e-07,
                3.927862002641863e-07,
                1.5534983101602148e-06
            ],
            [
                8.315283250371857e-07,
                2.5612828213934817e-06,
                4.222832437798974e-06,
                5.715007195447234e-07,
                2.5612819054133693e-06,
                1.3709576971463352e-06,
                2.9023130227124616e-06,
                1.3709572068522336e-06,
                1.0677032518578904e-06,
                2.3823682479181176e-07
            ],
            [
                2.902313023063532e-06,
                7.889259764359722e-06,
                6.475950297768503e-07,
                6.144172404587612e-06,
                NaN,
                4.222832437747125e-06,
                1.6701417862648148e-05,
                8.939697369785323e-06,
                4.78509563535725e-06,
                4.785092783371756e-06
            ],
            [
                4.785096776468749e-06,
                1.3709575337125585e-06,
                2.5612822107167428e-06,
                5.422219616265831e-06,
                1.994730672668496e-06,
                1.1478770862735993e-05,
                1.3709578605617394e-06,
                2.2603234895289998e-06,
                2.5612822106654943e-06,
                1.9947294837154625e-06
            ],
            [
                2.9023119851781017e-06,
                1.8553910183607374e-07,
                7.338212429582604e-07,
                1.067702870039777e-06,
                2.902310947208574e-06,
                2.6995790618350237e-07,
                1.994730434879465e-06,
                4.450850519403407e-07,
                3.927862002663297e-07,
                4.450849458218309e-07
            ],
            [
                5.715003789033962e-07,
                2.5612812947077304e-06,
                7.338209805224048e-07,
                1.3007126913820052e-05,
                2.3823682478975334e-07,
                1.6373774480479287e-07,
                6.475951069896949e-07,
                1.2098658277451275e-06,
                4.4508510499849186e-07,
                2.1444945858485726e-05
            ],
            [
                7.889262585728421e-06,
                1.3007133116542802e-05,
                8.315280276626197e-07,
                2.561282516066741e-06,
                1.0129989772532511e-05,
                2.9023116391978967e-06,
                1.5534983101602148e-06,
                7.889262585886274e-06,
                2.9023119851781017e-06,
                NaN
            ],
            [
                1.30071315662049e-05,
                3.2887478892683997e-06,
                1.7603430034867993e-06,
                6.144174601991196e-06,
                4.222833947960866e-06,
                1.2098656835224664e-06,
                1.012999460278499e-05,
                6.144173869603344e-06,
                1.5534973842030142e-06,
                7.338212429582604e-07
            ],
            [
                3.120190393260949e-05,
                2.9023133690188264e-06,
                NaN,
                8.939698435226916e-06,
                2.561281905376098e-06,
                NaN,
                1.3709576971242028e-06,
                5.82912516391202e-05,
                1.9947306726213275e-06,
                2.561281600049467e-06
            ],
            [
                4.78509563555309e-06,
                4.222832941034507e-06,
                5.04347528440776e-07,
                3.726637951367137e-06,
                NaN,
                3.535625914363812e-05,
                1.7603430034743913e-06,
                4.222831934352267e-06,
                1.5534975693933505e-06,
                4.222832941142044e-06
            ],
            [
                1.4738980215352592e-05,
                1.7603425837791042e-06,
                1.1478764020727177e-05,
                7.88926446679691e-06,
                4.785094494750855e-06,
                0.99992515373869,
                5.422220262636381e-06,
                4.450852111135988e-07,
                2.4300237837960777e-05,
                1.6701419853852583e-05
            ],
            [
                7.889266347636241e-06,
                6.475945666051092e-07,
                5.043473480777865e-07,
                3.7266397283908927e-06,
                5.715002426475718e-07,
                4.450850519403407e-07,
                8.939695238439078e-06,
                7.338208055664991e-07,
                2.1024341622368903e-07,
                3.927862002654366e-07
            ],
            [
                1.5534975693707442e-06,
                6.144177531660828e-06,
                3.2887494574518405e-06,
                8.939698435454571e-06,
                1.0677024882009222e-06,
                3.726641061109272e-06,
                2.430025232128576e-05,
                7.889263526266196e-06,
                2.7535691100960147e-05,
                1.3007123812980299e-05
            ],
            [
                1.0677024882009222e-06,
                3.466326211113502e-07,
                5.043474081993875e-07,
                8.315279285370317e-07,
                3.059022998576899e-07,
                1.9947297215125433e-06,
                5.715002426475718e-07,
                3.0590226339061185e-07,
                1.8553903548231313e-07,
                3.059021175247079e-07
            ],
            [
                1.0129993395088066e-05,
                3.288749849498565e-06,
                4.450851580555361e-07,
                2.561282210729555e-06,
                1.8925152752586028e-05,
                1.0129993395088066e-05,
                4.222831934352267e-06,
                3.288749457469787e-06,
                4.2228334445370225e-06,
                5.422218323487975e-06
            ],
            [
                NaN,
                5.422218323399208e-06,
                2.9023119851635836e-06,
                4.785096205973894e-06,
                2.5612819054028872e-06,
                1.8925152753790864e-05,
                5.4222202624563834e-06,
                6.144174601991196e-06,
                1.3709576971425944e-06,
                4.2228334445370225e-06
            ],
            [
                3.05902336324494e-07,
                5.043472879540142e-07,
                2.260324028404236e-06,
                1.8553916819032217e-07,
                2.69957906184239e-07,
                1.275190884913241e-07,
                3.0590215399183813e-07,
                3.927862939113312e-07,
                8.315280276626197e-07,
                2.1024331597262577e-07
            ],
            [
                1.6701425826191394e-05,
                NaN,
                2.9023130231176453e-06,
                2.2603234895176927e-06,
                2.260325375664839e-06,
                2.56128159999123e-06,
                2.9023126771227976e-06,
                4.222831934321543e-06,
                NaN,
                3.726641061027928e-06
            ],
            [
                1.760343003481596e-06,
                NaN,
                5.04347287955046e-07,
                1.0129993395336818e-05,
                3.726638395634011e-06,
                7.338208055680009e-07,
                1.7603438428740716e-06,
                8.315281267861397e-07,
                6.475950298011458e-07,
                1.3709573702822306e-06
            ],
            [
                4.785096776468749e-06,
                6.962256249885085e-06,
                9.422443692330485e-07,
                NaN,
                1.5534979397740895e-06,
                3.535625914363812e-05,
                1.7603440527286572e-06,
                1.99473067264854e-06,
                3.2887506336086064e-06,
                5.422217030707961e-06
            ],
            [
                1.5534979397740895e-06,
                NaN,
                5.043475885696228e-07,
                5.829126555256903e-05,
                NaN,
                NaN,
                2.561282210729555e-06,
                6.144176066795103e-06,
                NaN,
                1.4738976701411704e-05
            ],
            [
                3.7266388398585725e-06,
                1.2098659719757836e-06,
                1.7603430034743913e-06,
                3.2887494574518405e-06,
                NaN,
                2.2603242978377903e-06,
                1.0677028700363782e-06,
                8.939700566907275e-06,
                1.3709572068422585e-06,
                2.5612816000646084e-06
            ],
            [
                9.42244930862237e-07,
                7.338211554783522e-07,
                3.288749849477628e-06,
                3.726641061027928e-06,
                NaN,
                1.2098662604291696e-06,
                4.2228329411708495e-06,
                7.889266347715168e-06,
                1.7603432132912532e-06,
                1.3709572068522336e-06
            ],
            [
                5.422217030707961e-06,
                1.892515049702235e-05,
                1.2098655392871682e-06,
                3.2887482812745586e-06,
                1.3007131566015624e-05,
                2.5612819054028872e-06,
                3.288750241561788e-06,
                NaN,
                8.939697369882888e-06,
                1.5534979397740895e-06
            ],
            [
                1.0677024881980089e-06,
                4.222833947960866e-06,
                1.7603425837702984e-06,
                4.785093924362895e-06,
                4.222832941193893e-06,
                2.2603245673279107e-06,
                1.7603427936335396e-06,
                2.753569110256289e-05,
                1.760343003481596e-06,
                4.785095065204162e-06
            ],
            [
                7.889266347715168e-06,
                6.144173137126169e-06,
                NaN,
                2.561282516066741e-06,
                3.726639284144195e-06,
                1.2098656835224664e-06,
                3.7266406168624155e-06,
                2.561281294760143e-06,
                4.222832941193893e-06,
                NaN
            ],
            [
                2.6995784182140636e-07,
                4.222832437677995e-06,
                1.7603425837791042e-06,
                9.422442569290178e-07,
                3.288749457432399e-06,
                2.9023133690980155e-06,
                1.9947294837154625e-06,
                1.0129995809763438e-05,
                4.539789029401802e-05,
                6.475947210031623e-07
            ],
            [
                5.043472879525233e-07,
                5.422217030747413e-06,
                5.043476486902204e-07,
                1.7603430034439723e-06,
                4.222834451327159e-06,
                4.222832941142044e-06,
                4.2228329411708495e-06,
                1.2098653950606901e-06,
                3.7266388398585725e-06,
                3.2887486733420804e-06
            ],
            [
                1.0677033791437343e-06,
                6.962257909501028e-06,
                9.422445939032799e-07,
                1.3709572068522336e-06,
                6.475947982037486e-07,
                1.9947304348862686e-06,
                4.22283545808297e-06,
                1.3709578605455302e-06,
                1.300712846477255e-05,
                1.0677028700363782e-06
            ],
            [
                2.5612831267086116e-06,
                1.3709570434178922e-06,
                7.338208055536515e-07,
                9.422443692489024e-07,
                4.222835458175145e-06,
                1.7603438428460541e-06,
                6.962254589914941e-06,
                1.9947304348703948e-06,
                3.9278624708775595e-07,
                2.5612812947380135e-06
            ],
            [
                6.9622587397397306e-06,
                8.31528424162821e-07,
                2.5612819054028872e-06,
                2.9023112932045342e-06,
                1.3709568799823232e-06,
                1.7603427936263351e-06,
                1.5534981249574276e-06,
                1.4738980214843206e-05,
                1.3007123812767362e-05,
                7.338209805224048e-07
            ],
            [
                8.315277302747361e-07,
                1.3709567165461505e-06,
                1.6701417862648148e-05,
                2.561281905376098e-06,
                1.1478766757404937e-05,
                1.3709578605617394e-06,
                1.5534979397592542e-06,
                5.715003788993679e-07,
                9.422448185478557e-07,
                8.939694172420599e-06
            ],
            [
                3.7266410611296085e-06,
                3.2887494574518405e-06,
                2.9023116391675407e-06,
                2.4300246525983375e-05,
                1.6701423836262173e-05,
                4.222833444467892e-06,
                2.5612816000646084e-06,
                2.430023783667895e-05,
                2.1444945858485726e-05,
                6.475947210012481e-07
            ],
            [
                5.043472879540142e-07,
                2.9023133690980155e-06,
                4.4508510499737865e-07,
                1.3709572068522336e-06,
                1.5534971990169383e-06,
                2.2603242978871282e-06,
                4.222832941193893e-06,
                0.9999981261241716,
                1.3709567165579959e-06,
                6.144173869603344e-06
            ],
            [
                3.4663249714325014e-07,
                5.043472879540142e-07,
                9.422450431954847e-07,
                3.72664061681327e-06,
                1.2098659719716573e-06,
                8.315278294072958e-07,
                3.726639284125553e-06,
                5.715007195431641e-07,
                6.475945666033422e-07,
                1.3709567165530083e-06
            ],
            [
                6.144172404520556e-06,
                2.5612825160562587e-06,
                2.9023109471689794e-06,
                3.7266401725681614e-06,
                4.22283545808297e-06,
                5.422218969818919e-06,
                7.338208055579897e-07,
                7.88926352599354e-06,
                1.994730672668496e-06,
                3.2887494574518405e-06
            ],
            [
                NaN,
                2.9023112932045342e-06,
                2.90231094723893e-06,
                3.288747889229516e-06,
                2.9023109472244114e-06,
                4.7850933538313875e-06,
                7.889259764445822e-06,
                1.012999460278499e-05,
                1.4738985486265496e-05,
                1.8925143728749452e-05
            ],
            [
                1.3709573702722555e-06,
                6.14417533430649e-06,
                5.715003789033962e-07,
                5.043474081993875e-07,
                3.4663249714612693e-07,
                8.315279285351409e-07,
                2.260325375664839e-06,
                7.889261645355786e-06,
                8.315279285351409e-07,
                9.422447062202052e-07
            ],
            [
                5.8291251656508296e-05,
                1.2098659719757836e-06,
                2.9023133690821773e-06,
                4.785094494750855e-06,
                1.2098661162023305e-06,
                6.144176066795103e-06,
                1.0129990980100021e-05,
                2.5612828213818346e-06,
                1.3709570434178922e-06,
                2.9023130230846496e-06
            ],
            [
                6.962259569484628e-06,
                4.78509392429544e-06,
                2.902312677104321e-06,
                4.785095065093186e-06,
                1.994729008105057e-06,
                3.726641061027928e-06,
                6.962254589781966e-06,
                NaN,
                5.422218969818919e-06,
                6.144176799166453e-06
            ],
            [
                5.829128640005915e-05,
                1.5534983101478522e-06,
                1.7603430034743913e-06,
                7.88926634755014e-06,
                1.7603436330091044e-06,
                1.6373772528424783e-07,
                4.450849458200093e-07,
                0.9994472212625499,
                1.7603432133136672e-06,
                1.3709578605455302e-06
            ],
            [
                7.338213304363436e-07,
                4.785095635592258e-06,
                7.338209805224048e-07,
                1.9947301970972664e-06,
                1.0677027427569065e-06,
                4.222831934379152e-06,
                2.90231233114251e-06,
                1.3709572068522336e-06,
                7.338209805200689e-07,
                2.75356845363217e-05
            ],
            [
                9.422448185510695e-07,
                7.338211554783522e-07,
                7.338212429537553e-07,
                3.2887498495150166e-06,
                9.422443692574719e-07,
                3.535625071602016e-05,
                NaN,
                9.422444815792981e-07,
                1.0129994602656007e-05,
                8.939693107190907e-06
            ],
            [
                1.067703379154416e-06,
                NaN,
                5.715004470243685e-07,
                3.9278605979208185e-07,
                4.450849988758202e-07,
                5.04347348070562e-07,
                1.2098662604291696e-06,
                1.0677027427471959e-06,
                3.0590215398829087e-07,
                8.315284241560147e-07
            ],
            [
                7.484623619706945e-05,
                4.222834954687752e-06,
                3.726641061027928e-06,
                2.902312677084523e-06,
                1.9947304348595095e-06,
                1.3007126914245925e-05,
                3.288747889229516e-06,
                4.222833444506298e-06,
                6.1441724044534996e-06,
                2.902312677137316e-06
            ],
            [
                1.3709576971425944e-06,
                1.370957860576702e-06,
                1.3709575337078829e-06,
                2.260324567337161e-06,
                9.422448185510695e-07,
                1.7603430034867993e-06,
                NaN,
                NaN,
                5.715007195447234e-07,
                1.0129990980100021e-05
            ],
            [
                4.785096206013061e-06,
                3.2887482813149375e-06,
                1.067702615468225e-06,
                2.2603242978871282e-06,
                2.5612825160562587e-06,
                7.338209805200689e-07,
                3.726639284125553e-06,
                1.5534975693869924e-06,
                3.927862939126708e-07,
                2.5612822107167428e-06
            ],
            [
                8.315279285351409e-07,
                1.0677027427525368e-06,
                8.315281267800897e-07,
                8.315277302747361e-07,
                1.3709568799760888e-06,
                2.5612825160096693e-06,
                1.0677032518748838e-06,
                2.5612812947380135e-06,
                2.5612822107167428e-06,
                NaN
            ],
            [
                2.5612815999679353e-06,
                7.889261645269683e-06,
                NaN,
                3.726639728348526e-06,
                6.962259569630266e-06,
                3.726638839878908e-06,
                2.9023126771227976e-06,
                9.422442569208767e-07,
                7.338207180864763e-07,
                0.0001584361792089968
            ],
            [
                5.043476486833397e-07,
                4.222833947820683e-06,
                2.1024331597262577e-07,
                1.0677024882009222e-06,
                1.8553910183674878e-07,
                8.315283250371857e-07,
                2.90231094723893e-06,
                3.927860597935108e-07,
                NaN,
                1.9947292459265734e-06
            ],
            [
                4.785095635624897e-06,
                NaN,
                5.8291244705086375e-05,
                3.726638839878908e-06,
                4.78509278348926e-06,
                1.0677028700266676e-06,
                1.7603438428800754e-06,
                1.0677033791583005e-06,
                1.0129988564974359e-05,
                1.4738988999940381e-05
            ],
            [
                2.1444940744864302e-05,
                5.4222209089700225e-06,
                1.3007125363908762e-05,
                1.2098659719716573e-06,
                2.7535697664698622e-05,
                4.2228329411708495e-06,
                8.93969630388855e-06,
                4.222834451327159e-06,
                6.962257079705671e-06,
                5.422217677078203e-06
            ],
            [
                5.715005151606823e-07,
                1.0677027427569065e-06,
                7.889262585728421e-06,
                7.338207180898968e-07,
                5.043472879540142e-07,
                1.1478764021029928e-05,
                6.144173869603344e-06,
                1.3007133115903994e-05,
                2.5612812947508257e-06,
                1.3709575336947905e-06
            ],
            [
                1.012999218752948e-05,
                6.962259569630266e-06,
                3.7266379513434106e-06,
                1.1478769494250387e-05,
                2.5612831266608576e-06,
                2.5612825160271407e-06,
                5.422218969818919e-06,
                NaN,
                NaN,
                2.561281600049467e-06
            ],
            [
                9.422445939032799e-07,
                1.067702870039777e-06,
                2.9023133690188264e-06,
                1.7603427936335396e-06,
                1.3709576971425944e-06,
                1.553498495338299e-06,
                2.144494841482881e-05,
                2.5612812947508257e-06,
                1.0677029973192638e-06,
                8.939700566289352e-06
            ],
            [
                1.5534981249574276e-06,
                3.5356267573959116e-05,
                1.9947299593014888e-06,
                1.6701429808632785e-05,
                4.539785782605375e-05,
                2.260325375664839e-06,
                2.26032402841657e-06,
                3.288749849477628e-06,
                2.4300232042706045e-05,
                1.3709572068422585e-06
            ],
            [
                5.715005832853093e-07,
                5.04347528446051e-07,
                1.5534979397740895e-06,
                5.04347528446051e-07,
                1.855391681906175e-07,
                1.2098656835224664e-06,
                2.382369667929001e-07,
                5.715007195447234e-07,
                1.2098652508347793e-06,
                1.4449805540700758e-07
            ],
            [
                NaN,
                3.927862002641863e-07,
                1.9947297215043796e-06,
                2.2603240284371276e-06,
                7.889265407327733e-06,
                7.889266347636241e-06,
                1.3709567165617364e-06,
                NaN,
                1.0129988564974359e-05,
                5.422219616184461e-06
            ],
            [
                6.144173136885882e-06,
                4.2228334445370225e-06,
                7.338208055664991e-07,
                1.3007134667070165e-05,
                2.2603242978665707e-06,
                1.1478765389222573e-05,
                2.260323758987159e-06,
                8.315281267882195e-07,
                NaN,
                1.9947297215043796e-06
            ],
            [
                2.4300243631272052e-05,
                1.0129989771288745e-05,
                1.1478765389368729e-05,
                4.222833947960866e-06,
                6.962256249821764e-06,
                7.338210679979539e-07,
                6.962254589914941e-06,
                6.475950298011458e-07,
                4.785093924362895e-06,
                3.288749457409966e-06
            ],
            [
                5.4222209089700225e-06,
                2.7535694384081332e-05,
                1.0129995810076682e-05,
                2.561282516042282e-06,
                NaN,
                5.422220262599396e-06,
                3.7266388398585725e-06,
                4.785092783415276e-06,
                4.222832437747125e-06,
                3.288749457432399e-06
            ],
            [
                6.962257079832313e-06,
                1.4738983729535602e-05,
                1.0677033791612137e-06,
                2.561282210740037e-06,
                1.994729008145876e-06,
                1.0677027427600627e-06,
                3.4663249714612693e-07,
                3.466327037512053e-07,
                2.1024331597262577e-07,
                1.0677024881980089e-06
            ],
            [
                6.962254589617333e-06,
                5.422217676866151e-06,
                1.0677027427525368e-06,
                6.962257909722651e-06,
                1.147876402018431e-05,
                5.8291244705086375e-05,
                6.144173869312763e-06,
                6.1441760667392215e-06,
                2.902311293147782e-06,
                6.144173137014406e-06
            ],
            [
                3.288749457469787e-06,
                1.9947299593014888e-06,
                1.7603434231705793e-06,
                7.338211554783522e-07,
                1.0129993395336818e-05,
                1.3709575337078829e-06,
                4.78509392429544e-06,
                9.422445939032799e-07,
                9.422443692527585e-07,
                1.209865683518615e-06
            ],
            [
                3.535625914363812e-05,
                2.4300237837960777e-05,
                5.422217030614265e-06,
                2.902311639183378e-06,
                7.889261645427538e-06,
                6.144173137126169e-06,
                4.222832941142044e-06,
                1.1478772230929451e-05,
                2.9023126771227976e-06,
                9.610238066473817e-05
            ],
            [
                8.315281267861397e-07,
                1.3709568799879344e-06,
                1.7603434231777837e-06,
                8.315281267834927e-07,
                9.422450431989127e-07,
                9.422450431860582e-07,
                2.2603242978871282e-06,
                1.3709576971379186e-06,
                8.315281267861397e-07,
                5.715007195431641e-07
            ],
            [
                2.5612834320470717e-06,
                1.0677032518700286e-06,
                1.0677031245905116e-06,
                4.222834451355964e-06,
                9.422443692446175e-07,
                2.2603242978665707e-06,
                2.561282516066741e-06,
                1.3709575337016483e-06,
                1.7603438428740716e-06,
                1.5534981249574276e-06
            ],
            [
                1.5534981249397663e-06,
                1.012998735687278e-05,
                5.422220262555012e-06,
                8.315283250260307e-07,
                1.370956716529941e-06,
                6.144173136952939e-06,
                4.222833444467892e-06,
                4.785096205830278e-06,
                1.7603427936263351e-06,
                7.889265407255982e-06
            ]
        ]
    },
    {
        "q_id": "10308_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            22,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999988634365623,
                0.9999982396565805,
                0.9999974387168786,
                0.999997593896518,
                0.9999987901344631,
                0.9999992661792836,
                0.9999978766215432,
                0.9999990577552953,
                0.9999989322968779,
                0.9999989969861534
            ],
            [
                0.9999987901338863,
                0.999999218851484,
                0.9999989969856734,
                0.9999995262095551,
                0.9999981261252894,
                0.9999981261243959,
                0.9999990577557438,
                0.9999992661789323,
                0.9999984465022481,
                0.9999957771665643
            ],
            [
                0.9999992188516702,
                0.9999986290431223,
                0.9999975938982377,
                0.9999986290432864,
                0.9999989969856745,
                0.9999984465026189,
                0.9999992661792829,
                0.999998540623956,
                0.999997273528758,
                0.9999945777823344
            ],
            [
                0.9999977396765157,
                0.999998126124172,
                0.9999987121046323,
                0.9999988634362914,
                3.535626757125808e-05,
                0.9999980052698069,
                0.9999991148432813,
                0.9999989969862713,
                0.999999266178758,
                0.9999989322971311
            ],
            [
                7.338213304363436e-07,
                3.46632497145457e-07,
                2.1024341622426268e-07,
                2.699577774585891e-07,
                1.3709572068522336e-06,
                2.6995784182140636e-07,
                2.102434412875379e-07,
                5.715003107767143e-07,
                3.466327037553825e-07,
                1.637377448057981e-07
            ],
            [
                8.315283250371857e-07,
                8.315277302841894e-07,
                2.3823682479292225e-07,
                NaN,
                3.05902336324494e-07,
                0.9999861539939094,
                1.5534979397790343e-06,
                5.71500515159253e-07,
                2.3823693839325527e-07,
                1.855391681906175e-07
            ],
            [
                3.466325797896173e-07,
                1.7603440527286572e-06,
                4.450850519403407e-07,
                3.466327863983311e-07,
                3.927862470899887e-07,
                5.715003789046955e-07,
                6.475951069985296e-07,
                1.2098662604247682e-06,
                4.785095065204162e-06,
                4.450848927650143e-07
            ],
            [
                6.475945666051092e-07,
                3.0590237279032884e-07,
                9.422444815765128e-07,
                2.260325106237323e-06,
                5.715005151606823e-07,
                3.288750241561788e-06,
                7.338208055664991e-07,
                9.422445939032799e-07,
                1.0677027427600627e-06,
                5.715003107715166e-07
            ],
            [
                3.0590215399183813e-07,
                3.05902190458764e-07,
                4.450848927658745e-07,
                1.5534977545886537e-06,
                2.382369667929001e-07,
                3.059022998576899e-07,
                1.855391239544352e-07,
                2.382368531929327e-07,
                1.8553916819032217e-07,
                4.78509278348926e-06
            ],
            [
                3.4663266242969896e-07,
                3.059021175247079e-07,
                4.450849988811838e-07,
                6.475945666033422e-07,
                5.04347348075149e-07,
                3.059023727894942e-07,
                3.0590237278532086e-07,
                5.043472278280699e-07,
                3.927862002606139e-07,
                7.889265407327733e-06
            ],
            [
                0.9999997463981033,
                0.9999994956525922,
                0.9999995262094991,
                0.9999992188516704,
                0.9999994631247405,
                0.9999993916409635,
                0.9999993106387083,
                0.9999996533672553,
                0.9999996940978826,
                0.9999997617630901
            ],
            [
                1.3709573702822306e-06,
                2.902312677137316e-06,
                1.7603425837855082e-06,
                5.715007195431641e-07,
                4.2228339479858295e-06,
                2.2603242978871282e-06,
                3.7266410611296085e-06,
                5.715006514151423e-07,
                8.939696304213768e-06,
                3.12019150949065e-05
            ],
            [
                5.715006514176113e-07,
                4.450852111155216e-07,
                7.338208930460318e-07,
                2.1024334103581732e-07,
                3.059021175261338e-07,
                1.6373764721072816e-07,
                1.0677032518814388e-06,
                7.338210680021253e-07,
                1.855391681906175e-07,
                1.2751905808881762e-07
            ],
            [
                7.338208055664991e-07,
                3.466326211113502e-07,
                4.450852111135988e-07,
                1.8553916819032217e-07,
                3.9278615344178325e-07,
                5.043472879540142e-07,
                5.043472879540142e-07,
                2.382370235922541e-07,
                3.9278634073732336e-07,
                3.466327037539638e-07
            ],
            [
                2.2603242978665707e-06,
                9.422448185510695e-07,
                0.9999964991468686,
                5.043474081993875e-07,
                2.6995768091310296e-07,
                3.927860597935108e-07,
                1.0677029973192638e-06,
                1.0677024882009222e-06,
                5.715007195431641e-07,
                6.144176066850984e-06
            ],
            [
                0.9999997761970515,
                0.9999994956527725,
                0.9999997463980125,
                0.999998629042304,
                0.9999997761971583,
                0.9999997897566592,
                0.9999994631249323,
                0.9999997463981637,
                0.9999998024945626,
                0.9999993916410361
            ],
            [
                6.962256249885085e-06,
                1.7603432133296774e-06,
                1.8925145985895816e-05,
                8.315279285351409e-07,
                1.0129993395336818e-05,
                4.785093924362895e-06,
                5.043472879540142e-07,
                1.7603427936335396e-06,
                3.288750241561788e-06,
                1.9947292459347367e-06
            ],
            [
                2.9023119851781017e-06,
                1.0677026154806063e-06,
                1.5534971990126997e-06,
                9.422450432014836e-07,
                1.7603425837855082e-06,
                1.3709573702822306e-06,
                7.338207180864763e-07,
                9.422442569315887e-07,
                6.475945666051092e-07,
                1.7603427936335396e-06
            ],
            [
                0.9999972735297352,
                0.9999974387174919,
                0.9999989969856742,
                0.9999993916408194,
                0.9999983463110094,
                0.999998346311009,
                0.9999982396574187,
                0.999997273528433,
                0.9999987121049397,
                0.9999960330145656
            ],
            [
                7.338208055664991e-07,
                1.4449798650551755e-07,
                2.1024336609843824e-07,
                1.2098656835224664e-06,
                2.102434162245973e-07,
                5.715005832886879e-07,
                1.0677029973192638e-06,
                3.927863875616689e-07,
                8.315281267882195e-07,
                1.8553919030826963e-07
            ],
            [
                0.9999987901337419,
                0.9999978766207807,
                0.9999975938979518,
                0.9999949062950204,
                0.9999977396748989,
                0.9999985406243034,
                0.9999972735290878,
                0.9999942280772485,
                0.999996711252116,
                0.9999986290424705
            ],
            [
                1.209865539295696e-06,
                4.785095635624897e-06,
                1.5534979397740895e-06,
                5.715005151574337e-07,
                1.9947297215125433e-06,
                1.5534981249697903e-06,
                1.7603432133296774e-06,
                9.422449308748773e-07,
                2.260324028427877e-06,
                8.315281267834927e-07
            ],
            [
                2.90231094723893e-06,
                5.715005151606823e-07,
                3.726637951387472e-06,
                5.715005151606823e-07,
                4.2228339479858295e-06,
                7.338210680021253e-07,
                8.315284241650899e-07,
                7.338209805240734e-07,
                5.715005832886879e-07,
                7.338212429582604e-07
            ],
            [
                0.9999996310114599,
                0.999999712631481,
                0.9999994631251243,
                0.9999998362622747,
                0.9999996743686645,
                0.9999997463980428,
                0.9999998257021422,
                0.9999996743688586,
                0.999999631011372,
                0.9999998555019963
            ],
            [
                0.99999963101146,
                0.9999995818812274,
                0.9999990577555197,
                0.9999986290421405,
                0.9999994284994855,
                0.9999991684721712,
                0.9999985406230857,
                0.9999977396748975,
                0.9999987901343176,
                0.9999995549150545
            ],
            [
                0.9999997761971582,
                0.99999976176309,
                0.9999998024947273,
                0.9999994284992807,
                0.9999997761971582,
                0.9999993106387906,
                0.9999990577549578,
                0.9999997300421261,
                0.999999730042094,
                0.9999997126314811
            ],
            [
                0.9999969105051943,
                0.9999993916408914,
                0.9999987901338862,
                0.9999952149043824,
                0.9999977396759745,
                0.9999962733611706,
                0.999998629042958,
                0.9999964991447584,
                0.9999993106387909,
                0.9999987121047886
            ],
            [
                3.466326211113502e-07,
                4.785092783519724e-06,
                1.3709573702822306e-06,
                3.7266410611296085e-06,
                3.466327037548308e-07,
                9.422448185534261e-07,
                2.6995774527718623e-07,
                1.6373764721072816e-07,
                4.450850519403407e-07,
                2.6995784182183607e-07
            ],
            [
                0.9999993916411811,
                0.9999996940976273,
                0.999999825702059,
                0.9999972735284316,
                0.9999978766205262,
                0.9999993916408909,
                0.9999997761971315,
                0.9999993106387082,
                0.9999998144608541,
                0.9999990577551817
            ],
            [
                0.9999994284996216,
                0.9999991148430702,
                0.9999985406230849,
                0.999999391640819,
                0.9999991148427548,
                0.9999962733593972,
                0.9999986290432851,
                0.9999986290421405,
                0.9999987901344624,
                0.9999989969856731
            ],
            [
                0.9999938558232172,
                0.9999969105040872,
                0.999995214903804,
                0.9999910603005271,
                0.9999957771660668,
                0.9999955048200497,
                0.99999490629683,
                0.9999910603026695,
                0.9999945777823508,
                0.9999938558232254
            ],
            [
                7.338208055664991e-07,
                3.9278634073732336e-07,
                6.475946438042047e-07,
                6.475945666051092e-07,
                3.927863407379485e-07,
                1.5534983101602148e-06,
                4.450852641737424e-07,
                1.067703379154416e-06,
                5.715003788993679e-07,
                5.04347408197782e-07
            ],
            [
                0.9999989322970049,
                0.9999987901338869,
                0.9999964991439229,
                0.9999989969861519,
                0.9999977396765143,
                0.9999962733593912,
                0.9999975938982398,
                0.999996910504452,
                0.9999996533674205,
                0.9999986290432854
            ],
            [
                2.2603253756956754e-06,
                2.7535694384882703e-05,
                1.5534973842030142e-06,
                1.3709576971425944e-06,
                2.382370235933104e-07,
                4.4508510499849186e-07,
                2.9023116391978967e-06,
                2.6995784182140636e-07,
                1.553497754583709e-06,
                1.4738981972323349e-05
            ],
            [
                0.999999428499758,
                0.9999990577556321,
                0.9999980052709977,
                0.9999977396765148,
                0.9999987121049393,
                0.9999969105066653,
                0.9999982396567888,
                0.9999989969859141,
                0.999998629042795,
                0.9999991684715768
            ],
            [
                1.6373776432509826e-07,
                2.1024331597262577e-07,
                2.5612825160562587e-06,
                3.927862470899887e-07,
                2.1024331597262577e-07,
                0.0003353501912702401,
                2.1024336609843824e-07,
                3.9278634073732336e-07,
                2.1024331597262577e-07,
                7.338208055664991e-07
            ],
            [
                2.2603234895372223e-06,
                0.9999975938965165,
                3.7266397283908927e-06,
                3.059021175261338e-07,
                4.4508510499737865e-07,
                9.422448185510695e-07,
                6.144176066901277e-06,
                0.9999987901343184,
                1.3709575337125585e-06,
                1.5534979397790343e-06
            ],
            [
                1.2098658277451275e-06,
                4.785096776394765e-06,
                7.889264465986113e-06,
                NaN,
                1.0677026154806063e-06,
                6.962254589781966e-06,
                2.9023130231176453e-06,
                3.2887482813149375e-06,
                3.726639728370556e-06,
                2.9023119851781017e-06
            ],
            [
                0.9999992188514839,
                0.9999996743688587,
                0.9999996072136128,
                0.999999581881377,
                0.9999989969860323,
                0.9999996940977003,
                0.9999993524052025,
                0.9999997761970782,
                0.9999991148432815,
                0.9999992661789326
            ],
            [
                0.9999999067050165,
                0.9999998942829602,
                0.9999987121047851,
                0.9999998555019618,
                0.9999998802069445,
                0.9999998724809723,
                0.9999998642566381,
                0.9999998642567189,
                0.9999998802069017,
                0.9999998555019619
            ],
            [
                0.9999916019269979,
                0.9999934595643486,
                0.9999925887228049,
                0.9999925887201645,
                0.9999983463102218,
                0.9999957771675735,
                0.9999981261250712,
                0.9999952149066667,
                0.9999975938970967,
                0.9999969105059361
            ],
            [
                0.999998126124619,
                0.9999996940978462,
                0.9999989969854344,
                0.9999995549148423,
                0.9999987121047856,
                0.9999992188519492,
                0.9999996072138467,
                0.9999942280806683,
                0.9999993106388729,
                0.9999995549148952
            ],
            [
                1.0677032518785256e-06,
                6.962257909785973e-06,
                1.9947299593014888e-06,
                4.222834954778007e-06,
                5.04347528446051e-07,
                7.338212429582604e-07,
                1.7603432133296774e-06,
                9.422443692555439e-07,
                1.7603440527286572e-06,
                7.338212429582604e-07
            ],
            [
                1.3709567165579959e-06,
                8.315284241650899e-07,
                1.7603436330259153e-06,
                1.3709568799879344e-06,
                1.3709572068522336e-06,
                1.0677028700363782e-06,
                2.5612828213934817e-06,
                2.9023133690980155e-06,
                9.422445939032799e-07,
                8.939700567004841e-06
            ],
            [
                0.9999962733607204,
                0.9999984465024339,
                0.9999993106388729,
                0.9999981261243974,
                0.999998346310614,
                0.9999991684722708,
                0.999996273359392,
                0.9999996533672966,
                0.9999993524048941,
                0.9999978766223001
            ],
            [
                1.637376862489725e-07,
                4.539785241676547e-05,
                5.4222176771176554e-06,
                4.450852641737424e-07,
                6.475947210046347e-07,
                2.1024339116168358e-07,
                1.670142980920999e-05,
                1.6373774480605869e-07,
                1.5534971990169383e-06,
                1.8925141473978602e-05
            ],
            [
                6.962257909722651e-06,
                2.5612812947077304e-06,
                7.88926164518358e-06,
                8.939697369882888e-06,
                0.00026119021642442364,
                1.4738978458140753e-05,
                3.7266401725935817e-06,
                1.4738983729053029e-05,
                9.610243791626202e-05,
                8.481107169392881e-05
            ],
            [
                0.9999991148428606,
                0.9999984465016946,
                0.9999982396561637,
                0.9999988634358857,
                0.999999057755183,
                0.9999974387184066,
                0.9999978766220502,
                0.9999984465028039,
                0.9999984465016956,
                0.9999995549147892
            ],
            [
                0.9999996940977732,
                0.9999990577555194,
                0.9999981261237263,
                0.9999988634362906,
                0.9999989322972589,
                0.9999994284996216,
                0.9999993916406738,
                0.9999952149060972,
                0.9999996743686647,
                0.9999989969854358
            ],
            [
                0.9999993916406735,
                0.9999987121052474,
                0.9999984465015073,
                0.9999960330136213,
                0.9999992661789328,
                0.9999978766223023,
                0.9999989322971325,
                0.9999990577550705,
                0.9999989322966228,
                0.999998126123726
            ],
            [
                0.9999972735287587,
                3.1201911375578156e-05,
                0.999997593897663,
                0.9999984465028031,
                0.9999987901340297,
                0.9999984465022462,
                0.9999843104465559,
                0.9999989969862726,
                0.9999986290427958,
                0.9999991148428595
            ],
            [
                3.288750241561788e-06,
                8.939695238536645e-06,
                1.7603440527222532e-06,
                1.5534971990126997e-06,
                2.260324836787226e-06,
                2.9023116391978967e-06,
                1.3007131566015624e-05,
                2.5612828213818346e-06,
                0.0002034270464616072,
                8.939695238536645e-06
            ],
            [
                4.785096776499213e-06,
                1.2098652508424818e-06,
                1.3709570434219446e-06,
                5.04347287955046e-07,
                1.892515501014656e-05,
                3.7266397283908927e-06,
                3.0590237279032884e-07,
                9.422442569315887e-07,
                3.7266397283908927e-06,
                3.7266406168827523e-06
            ],
            [
                1.0677032518785256e-06,
                6.475945666051092e-07,
                5.043474081993875e-07,
                8.315284241597959e-07,
                1.5534979397790343e-06,
                1.5534979397740895e-06,
                2.5612834320470717e-06,
                9.422450431989127e-07,
                7.338208055664991e-07,
                8.315281267861397e-07
            ],
            [
                8.939693107190907e-06,
                4.785093924330255e-06,
                1.99472900813862e-06,
                9.422448185510695e-07,
                2.9023126771227976e-06,
                1.8925152753790864e-05,
                3.726638839878908e-06,
                8.315281267861397e-07,
                1.3709570434178922e-06,
                8.315279285351409e-07
            ],
            [
                0.9999983463104173,
                0.9999991148430702,
                0.999999391640674,
                0.9999995549149484,
                0.9999989969862714,
                0.9999995262096119,
                0.9999974387187097,
                0.9999987121046325,
                0.9999984465018766,
                0.9999992661786702
            ],
            [
                1.4449798650551755e-07,
                4.450852111148132e-07,
                1.7603434231833873e-06,
                3.4663262110945863e-07,
                1.1253518888531272e-07,
                3.05902190458764e-07,
                3.466326624322211e-07,
                3.0590215399183813e-07,
                2.144494841482881e-05,
                2.561281905390075e-06
            ],
            [
                4.222834954778007e-06,
                2.1444953527944967e-05,
                2.699578096393206e-07,
                2.9023116391477434e-06,
                4.785092783519724e-06,
                7.338211554783522e-07,
                1.4738987243236881e-05,
                4.78509392429544e-06,
                1.5534975693933505e-06,
                2.7535691101761522e-05
            ],
            [
                3.2887478892504536e-06,
                5.715003107755449e-07,
                3.726641061109272e-06,
                3.0590215399183813e-07,
                3.288749065406658e-06,
                4.222834954778007e-06,
                4.785093353909723e-06,
                1.8925157265710765e-05,
                4.785093353909723e-06,
                1.670142383595838e-05
            ],
            [
                1.3007123813193233e-05,
                1.3709573702822306e-06,
                1.4738976701411704e-05,
                3.927862002663297e-07,
                1.4449798650551755e-07,
                3.4663266243308805e-07,
                3.059021175261338e-07,
                1.7603425837855082e-06,
                2.699578740032504e-07,
                6.475947982037486e-07
            ],
            [
                4.2228339479858295e-06,
                5.715006514151423e-07,
                1.209866260432471e-06,
                9.422449308774482e-07,
                9.422447062270609e-07,
                2.6995774527718623e-07,
                7.338210680021253e-07,
                8.315284241650899e-07,
                5.715002426475718e-07,
                3.466327450765785e-07
            ],
            [
                0.9999991684716757,
                0.999997739675168,
                0.99999926617902,
                0.9999989322972588,
                0.9999988634362911,
                0.9999992661790201,
                0.9999987121043266,
                0.9999977396754357,
                0.9999989322975127,
                0.9999981261243955
            ],
            [
                1.7603440527286572e-06,
                0.9999975938982377,
                1.3709568799919866e-06,
                5.829124470169357e-05,
                1.8925152753790864e-05,
                6.475949526020042e-07,
                3.7266410611296085e-06,
                0.9999977396751658,
                0.9999972735284333,
                1.5534973842030142e-06
            ],
            [
                0.999996499144339,
                0.999999168472271,
                0.9999962733611653,
                0.9999967112505523,
                0.9999978766212879,
                0.9999988634358838,
                0.9999992188517629,
                0.9999983463106127,
                0.9999978766223016,
                0.9999955048173664
            ],
            [
                0.9999987121043266,
                0.9999977396754366,
                0.9999938558224845,
                0.999996499146845,
                0.9999984465018764,
                0.9999988634362906,
                0.9999987901341736,
                0.9999984465015068,
                0.9999957771670641,
                0.9999988634357491
            ],
            [
                1.0129994602895546e-05,
                1.30071315662049e-05,
                4.2228319344021954e-06,
                5.422217677152175e-06,
                0.000179528009125033,
                6.144175334468545e-06,
                1.3709573702822306e-06,
                1.0677026154806063e-06,
                0.9999921107336603,
                8.481101107142626e-05
            ],
            [
                0.999999607213847,
                0.9999983463096278,
                0.999999057755632,
                0.9999987901338847,
                0.9999967112501534,
                0.9999995549149484,
                0.9999983463106124,
                0.9999987121046318,
                0.9999987121047852,
                0.999998239657209
            ],
            [
                0.999999761763147,
                0.9999997463981939,
                0.9999994631251242,
                0.9999997897567092,
                0.9999995262092728,
                0.9999992661792823,
                0.9999998642567351,
                0.9999997300422228,
                0.9999997617630049,
                0.999999802494586
            ],
            [
                1.0677024881980089e-06,
                3.7266401726359486e-06,
                3.927862002663297e-07,
                9.422442569315887e-07,
                6.475945666051092e-07,
                6.9622587397397306e-06,
                2.260324567337161e-06,
                1.0677029973192638e-06,
                4.785092783519724e-06,
                1.3709568799919866e-06
            ],
            [
                0.9999910602994905,
                0.999998005270045,
                0.9999980052707582,
                0.999993855822487,
                0.999994228082059,
                0.9999964991451833,
                0.9999972735294116,
                0.9999960330136249,
                0.9999970976890601,
                0.9999967112493771
            ],
            [
                0.9999974387184055,
                0.9999989322970039,
                0.9999964991455961,
                0.9999978766207827,
                0.9999990577554072,
                0.9999988634366971,
                0.9999969105062947,
                0.9999991684718743,
                0.9999993524054338,
                0.9999981261252912
            ],
            [
                0.9999993524051248,
                0.9999991684716754,
                0.9999992188512974,
                0.9999987901346058,
                0.9999978766212866,
                0.9999992661789323,
                0.9999990577557437,
                0.9999991684717747,
                0.999998629043121,
                0.9999994631247402
            ],
            [
                0.999999218851484,
                0.9999989322966234,
                0.9999994284996901,
                0.9999986290424685,
                0.9999985406241293,
                0.9999984465022476,
                0.999999463124869,
                0.9999967112509422,
                0.9999991684719745,
                0.9999975938965165
            ],
            [
                1.4449805540740185e-07,
                1.2751910369310194e-07,
                1.6373764721072816e-07,
                3.927860597945825e-07,
                7.338207180884785e-07,
                8.315280276607289e-07,
                3.059022269250683e-07,
                3.2887506336086064e-06,
                1.8553907971813685e-07,
                2.69957906184239e-07
            ],
            [
                2.699578740032504e-07,
                0.9999983463096287,
                0.9999977396751667,
                NaN,
                0.000804086057081396,
                2.6995790618469934e-07,
                3.9278610661902853e-07,
                1.2751901248454963e-07,
                5.715003789046955e-07,
                9.422442569315887e-07
            ],
            [
                4.785095635592258e-06,
                4.222834451355964e-06,
                6.962256249885085e-06,
                6.962256249821764e-06,
                2.561281905390075e-06,
                0.00010889692232771249,
                2.9023133690980155e-06,
                1.8925143729954285e-05,
                6.144176799283803e-06,
                2.9023126771227976e-06
            ],
            [
                0.9999955048168224,
                0.9999921107355595,
                0.9999977396759813,
                1.637376862489725e-07,
                5.715002426486762e-07,
                0.9999925887192554,
                0.9999771719950477,
                0.9999984465016923,
                4.785096776499213e-06,
                0.9998313472651751
            ],
            [
                4.539786865090791e-05,
                0.9999984465018776,
                0.9999930377429522,
                0.9999987121052474,
                0.9999955048162916,
                0.9999938558232181,
                0.9999984465024339,
                0.9999921107336718,
                0.9999949062938008,
                0.9999955048189676
            ],
            [
                1.4449800373065699e-07,
                2.382370235933104e-07,
                2.382368531929327e-07,
                8.315277302841894e-07,
                5.715005832886879e-07,
                8.764247451307293e-08,
                5.715006514167015e-07,
                1.6373764721072816e-07,
                2.3823690999290963e-07,
                5.04347528446051e-07
            ],
            [
                0.9999983463106134,
                0.9999989969859127,
                0.9999991684715772,
                0.999999730042287,
                0.9999987121044789,
                0.9999989322971312,
                0.9999988634358835,
                0.9999994631247406,
                0.9999991148430702,
                0.9999993916409636
            ],
            [
                1.1253517547010071e-07,
                1.0677029973192638e-06,
                1.8553916819032217e-07,
                2.902312677137316e-06,
                1.4738976701652988e-05,
                3.288749457469787e-06,
                0.9999930377454253,
                5.715005832886879e-07,
                1.553498124964492e-06,
                4.4508510499849186e-07
            ],
            [
                0.9999962733620548,
                0.9999417087559026,
                1.1478769494250387e-05,
                NaN,
                1.0129993395336818e-05,
                0.9998766054708684,
                2.753568782024347e-05,
                1.9947297215125433e-06,
                NaN,
                6.962256249885085e-06
            ],
            [
                5.715003789046955e-07,
                7.484620943960125e-05,
                0.00010889694827288516,
                5.1442232055908106e-05,
                1.9947292459347367e-06,
                2.561281600086738e-06,
                9.422447062294175e-07,
                1.0677029973219343e-06,
                4.785092783519724e-06,
                5.715003107767143e-07
            ],
            [
                1.3709575337125585e-06,
                2.6995784182140636e-07,
                9.422448185534261e-07,
                5.715007195447234e-07,
                1.7603425837855082e-06,
                4.2228334445658276e-06,
                9.422443692555439e-07,
                7.338210680021253e-07,
                1.3709572068522336e-06,
                3.46632497145457e-07
            ],
            [
                3.9278610661902853e-07,
                3.466325797888292e-07,
                5.715002426475718e-07,
                4.450849988811838e-07,
                3.466326211113502e-07,
                5.715007195431641e-07,
                8.315281267882195e-07,
                4.4508526417298334e-07,
                2.561282210729555e-06,
                6.475947982037486e-07
            ],
            [
                0.9999981261252906,
                0.9999991684717754,
                0.9999975938976657,
                0.9999977396746291,
                0.9999983463104177,
                0.9999962733593946,
                0.9999967112505517,
                0.9999984465022487,
                0.9999993916410368,
                0.999999114843071
            ],
            [
                1.8553907971855875e-07,
                5.043473480777865e-07,
                1.2098659719788098e-06,
                3.05902190458764e-07,
                9.422448185534261e-07,
                1.6373762769138607e-07,
                2.902313023130843e-06,
                3.466327450765785e-07,
                1.2098658277489788e-06,
                3.9278610661902853e-07
            ],
            [
                1.209865827752005e-06,
                2.5612834320563895e-06,
                5.715006514176113e-07,
                3.7266397283908927e-06,
                6.144172404738491e-06,
                4.2228319344021954e-06,
                6.144173137126169e-06,
                1.300712536408621e-05,
                2.4300237838535383e-05,
                5.422220909009474e-06
            ],
            [
                0.9999975938982366,
                0.9999977396762434,
                0.999998346309825,
                0.9999984465015066,
                0.9999996072136595,
                0.9999986290421405,
                0.9999992661791075,
                0.9999988634360198,
                0.9999989322966214,
                0.9999995818811278
            ],
            [
                0.9999949062937972,
                0.9999949062968343,
                0.9999988634361563,
                0.9999981261248452,
                0.999998629042796,
                0.9999993106389549,
                0.9999990577549576,
                0.9999985406237831,
                0.999992588717524,
                0.9999985406230854
            ],
            [
                0.999997438717796,
                0.9999993916411092,
                0.9999998024946567,
                0.9999997617631754,
                0.9999993106387094,
                0.9999994284993494,
                0.9999994631250607,
                0.9999985406241305,
                0.9999984465016932,
                0.9999983463096278
            ],
            [
                1.0677027427525368e-06,
                9.422444815765128e-07,
                9.422450431860582e-07,
                2.2603234895289998e-06,
                3.059022998569248e-07,
                2.2603234895176927e-06,
                1.7603432133296774e-06,
                1.7603440527286572e-06,
                2.9023119851781017e-06,
                1.994730434879465e-06
            ],
            [
                1.8553910183607374e-07,
                2.1024336609843824e-07,
                2.3823702359290413e-07,
                2.699578740032504e-07,
                2.3823690999290963e-07,
                2.3823690999290963e-07,
                2.382369667929001e-07,
                3.9278605979534166e-07,
                1.855391239544352e-07,
                7.33821330437595e-07
            ],
            [
                1.8553905760062447e-07,
                1.3709576971463352e-06,
                7.338212429582604e-07,
                9.422442569315887e-07,
                6.475947210046347e-07,
                3.05902190458764e-07,
                3.4663249714612693e-07,
                5.422221555380179e-06,
                3.7266383956509585e-06,
                5.043476486915964e-07
            ],
            [
                0.9999990577557436,
                0.9999981261248418,
                2.3823696679327928e-07,
                0.9999972735297313,
                5.043476486924565e-07,
                0.999999712631344,
                0.9999992188519492,
                5.715002426486762e-07,
                0.9999974387184036,
                0.9999995262093858
            ],
            [
                1.2098652508424818e-06,
                9.422449308774482e-07,
                2.382368531929327e-07,
                5.043473480777865e-07,
                7.338210680021253e-07,
                1.3709575337078829e-06,
                5.715003107755449e-07,
                1.3709568799919866e-06,
                1.3709568799919866e-06,
                8.764249540862797e-08
            ],
            [
                0.9999992661786706,
                0.9999977396754355,
                0.9999974387177921,
                0.9999994284996898,
                0.9999990577555197,
                5.422220909009474e-06,
                0.999999266178845,
                0.999998629042631,
                0.9999996743687811,
                0.9999994631251249
            ],
            [
                0.9999984465016958,
                0.9999945777797501,
                0.9999986290423052,
                2.561282210740037e-06,
                0.999997739675978,
                0.9999975938970901,
                0.999997593896806,
                0.9999975938965187,
                0.9999987121049407,
                0.9999992661788448
            ],
            [
                0.9999977396762451,
                0.9999993106390371,
                0.9999970976876745,
                0.9999993524053568,
                0.9999991148426488,
                0.9999960330150407,
                0.9999987121043267,
                0.9999974387171834,
                0.9999989969854349,
                0.9999991148429657
            ],
            [
                5.043476486915964e-07,
                1.0677029973192638e-06,
                1.209865539295696e-06,
                2.382369667929001e-07,
                1.3709568799919866e-06,
                4.450852111148132e-07,
                7.889263526345123e-06,
                2.69957906184239e-07,
                2.382368247924618e-07,
                5.043476486915964e-07
            ],
            [
                0.9999996533674205,
                0.9999989322971308,
                2.5612819054028872e-06,
                0.9999994956526526,
                0.999999391640746,
                0.9999986290426317,
                0.999999352405048,
                0.9999989969854346,
                0.9999986290426315,
                0.9999993524052023
            ],
            [
                0.9999982396559489,
                4.785095635624897e-06,
                1.3709575337016483e-06,
                5.4222183234485234e-06,
                1.9947306726594253e-06,
                1.994730434879465e-06,
                2.2603242978871282e-06,
                2.2603251062270446e-06,
                5.715004470295662e-07,
                1.3709570434178922e-06
            ],
            [
                0.9999985406232593,
                0.9999977396748971,
                0.9999981261237253,
                0.9999983463100222,
                0.9999969105044524,
                0.9999921107336698,
                0.9999985406239548,
                0.9999970976883655,
                0.9999980052695675,
                0.9999985406239548
            ],
            [
                0.9999995818812775,
                0.999999057755408,
                0.9999983463106143,
                0.9999972735300623,
                0.9999993524051255,
                0.9999995262093296,
                0.9999994956527731,
                0.9999992661792827,
                0.9999982396559505,
                0.9999967112513336
            ],
            [
                0.9999339478324273,
                3.726639284125553e-06,
                7.338207180864763e-07,
                2.430024073461624e-05,
                0.00013982209088087594,
                0.999998346309627,
                2.260324567337161e-06,
                1.2098658277451275e-06,
                4.785094494750855e-06,
                1.0129989772412744e-05
            ],
            [
                1.0677026154806063e-06,
                3.466326211105621e-07,
                3.05902226923399e-07,
                6.475948754012522e-07,
                2.1024334103505245e-07,
                3.466327037539638e-07,
                3.466326211105621e-07,
                3.059021175247079e-07,
                1.8553916819032217e-07,
                5.71500515159253e-07
            ],
            [
                0.9999982396559514,
                0.999997593898239,
                0.9999986290432855,
                0.9999994631250606,
                0.9999991684719729,
                0.9999995262092165,
                0.9999981261243972,
                0.9999974387180991,
                0.9999996940977004,
                0.9999991684720727
            ],
            [
                1.7603440527222532e-06,
                6.475948754012522e-07,
                9.422448185510695e-07,
                6.475951069985296e-07,
                3.927860597945825e-07,
                4.450848927650143e-07,
                3.9278638755992735e-07,
                1.370957860567974e-06,
                3.0590237279032884e-07,
                1.5534975693933505e-06
            ],
            [
                0.9999984465026204,
                0.9999982396570033,
                0.9999969105066728,
                0.999997438716579,
                0.999998712104327,
                0.9999974387181148,
                0.9999972735290935,
                0.9999964991468506,
                0.999999218851764,
                0.9999916019240246
            ],
            [
                6.475949526020042e-07,
                5.715003789046955e-07,
                4.222832437798974e-06,
                1.5534971990126997e-06,
                1.3709572068522336e-06,
                5.043473480777865e-07,
                7.889264466725156e-06,
                3.2887502415438413e-06,
                1.0677027427600627e-06,
                1.7603434231833873e-06
            ],
            [
                0.9999993916409639,
                0.9999980052702818,
                0.9999995262094427,
                0.9999994956524121,
                0.9999994631249967,
                0.9999992188513909,
                0.9999991684721714,
                0.9999989969860327,
                0.9999993524050481,
                0.9999974387171824
            ],
            [
                0.9999978766217944,
                0.9999992188518563,
                0.9999980052709943,
                0.9999986290424682,
                0.9999995549151076,
                0.9999987901341736,
                0.9999991148432816,
                0.9999995549149484,
                0.9999995549150545,
                0.9999987901343176
            ],
            [
                0.9999978766223026,
                0.9999993916407462,
                0.9999982396572082,
                0.9999984465015066,
                0.9999904837460779,
                0.9999987901341743,
                0.9999992188512977,
                0.9999957771670681,
                0.9999974387165721,
                0.9999957771655592
            ],
            [
                0.9999964991451769,
                0.9999972735303877,
                0.9999987121044795,
                0.9999986290431229,
                0.9999995818810777,
                0.9999990577552949,
                0.9999945777810398,
                0.9999980052705199,
                0.9999972735300577,
                0.9999988634360211
            ],
            [
                0.9999997617630617,
                0.9999998144609424,
                0.9999997897567343,
                0.9999998461827322,
                0.9999990577555191,
                0.9999992188515766,
                0.9999997300422226,
                0.9999997897567342,
                0.9999997897566841,
                0.9999960330140882
            ]
        ]
    },
    {
        "q_id": "10058_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                0.9999998642566704,
                0.9999997126313783,
                0.9999982396572071,
                0.9999997463980729,
                0.9999998724809419,
                0.9999989322972574,
                0.9999992188518559,
                0.9999997463980427,
                0.9999992661786697,
                0.9999998257022045
            ],
            [
                8.315280276626197e-07,
                0.9999981261252874,
                3.9278634073098236e-07,
                0.9999546021152204,
                0.9999969105059221,
                0.9999975938976613,
                0.9999982396574167,
                1.0129994602895546e-05,
                0.9999990577554064,
                0.9999975938979483
            ],
            [
                5.715005151606823e-07,
                8.315280276626197e-07,
                5.715002426486762e-07,
                0.9999972735303801,
                1.067703124601679e-06,
                4.450848927658745e-07,
                1.6373774480605869e-07,
                4.450852641737424e-07,
                0.9999997897565588,
                0.999999428499485
            ],
            [
                0.9999996533673376,
                0.9999988634358833,
                4.450851580540182e-07,
                6.475950297971703e-07,
                0.9999985406243014,
                5.04347348075149e-07,
                3.726641061027928e-06,
                0.9999984465026164,
                7.338210679979539e-07,
                2.2603237589676295e-06
            ],
            [
                0.9999997463980125,
                0.99999926617867,
                0.9999989322972577,
                0.9999991684721709,
                0.9999998874648648,
                3.927861066170637e-07,
                0.9999991684717745,
                0.9999989322971303,
                0.9999921107402446,
                0.9999974387177905
            ],
            [
                0.9999993916411085,
                0.9999952149072185,
                0.9999756997592878,
                0.9999982396572068,
                0.9999998144608983,
                0.9999987121050917,
                0.9999930377412655,
                0.9999832985801581,
                0.9999967112493677,
                0.9999998461826954
            ],
            [
                0.9999993524051247,
                2.2603245673155757e-06,
                0.9999978766212851,
                0.9999974387174843,
                3.2887506335906595e-06,
                0.9999972735297303,
                0.9999993524053563,
                0.9999985406234313,
                3.4663249714325014e-07,
                3.927861066170637e-07
            ],
            [
                0.9999996533674615,
                0.9999972735300554,
                0.999997097688708,
                2.102434412871794e-07,
                1.370957860576702e-06,
                0.9999986290424668,
                3.9278629391427843e-07,
                0.9999869928715429,
                5.04347287955046e-07,
                0.9999997617631753
            ],
            [
                0.9999987121046313,
                7.3382080556433e-07,
                2.753569766560016e-05,
                0.9999992188513904,
                0.9999985406243014,
                2.2603245673279107e-06,
                0.99999671125172,
                0.9999998802069302,
                0.9999955048189608,
                1.1253506814842375e-07
            ],
            [
                0.9999996940977367,
                0.9999995549150543,
                0.9999999067051499,
                0.9999988634362896,
                0.9999998257021214,
                0.9999994956523515,
                0.9999990577557434,
                0.999997876622298,
                0.9999985406232573,
                0.9999996940976638
            ],
            [
                0.9999981261250639,
                3.0590237279085045e-07,
                0.9999998362622552,
                0.9999938558275995,
                0.999999218851949,
                0.9999997897567091,
                0.9999999176675338,
                0.9999995818810776,
                0.9999993106389546,
                0.9999967112501514
            ],
            [
                0.9999997617630049,
                0.9999998362622747,
                0.9999993106387082,
                0.9999997300423191,
                0.9999998942829098,
                0.9999998461826588,
                0.9999998802069731,
                0.9999995262094986,
                0.9999987901346054,
                0.9999996533674204
            ],
            [
                0.9999978766217917,
                0.9999910603005062,
                0.9999785550414021,
                3.0590237279085045e-07,
                0.9999975938973746,
                2.699577774585891e-07,
                0.999999218851949,
                3.9278610661902853e-07,
                0.9999996310116358,
                0.9999930377445877
            ],
            [
                2.5612831267202583e-06,
                0.9999986290423034,
                0.9999974387177905,
                0.9999992188517628,
                3.05902226923399e-07,
                0.9999949062962138,
                0.9999978766205262,
                0.9999993106390369,
                0.9999994631249323,
                0.9999921107345964
            ],
            [
                6.825597214718257e-08,
                3.288747889284851e-06,
                6.962259569750576e-06,
                1.6701415872659116e-05,
                2.102434412875379e-07,
                0.9999981261248408,
                0.9999980052693282,
                2.561281294760143e-06,
                0.9999996072137062,
                3.288747889284851e-06
            ],
            [
                0.9999997300423191,
                5.043474683156057e-07,
                5.715005151606823e-07,
                2.1024334103352274e-07,
                0.9999996310116359,
                0.9999646437493439,
                0.9999975938970878,
                0.9999999067050721,
                0.9999992188514834,
                8.315277302841894e-07
            ],
            [
                0.9999994956526522,
                0.9999997897567091,
                0.9999996940978096,
                0.9999992661790198,
                0.9999975938979481,
                1.637376862489725e-07,
                2.9023112932177327e-06,
                0.9999997761972116,
                4.450848927658745e-07,
                9.422448185510695e-07
            ],
            [
                7.338209805170655e-07,
                0.9999921107336583,
                1.6373768624837685e-07,
                5.715006514176113e-07,
                7.338207180864763e-07,
                5.04347468323289e-07,
                2.5612819054133693e-06,
                3.927862939126708e-07,
                6.475950297971703e-07,
                1.637376862489725e-07
            ],
            [
                1.4449795205429202e-07,
                1.275191036933194e-07,
                0.9999988634365606,
                2.902312677137316e-06,
                1.1253512180925583e-07,
                1.275190276859705e-07,
                2.1024334103581732e-07,
                1.855391681906175e-07,
                1.6373766672973748e-07,
                1.8553914607267268e-07
            ],
            [
                9.422447062270609e-07,
                6.475947210012481e-07,
                1.125351083940518e-07,
                8.315279285370317e-07,
                0.9999995262092728,
                1.8553914607267268e-07,
                3.9278610661902853e-07,
                0.9999999434138043,
                0.9999999358793485,
                0.9999977396757029
            ],
            [
                0.9999998942829854,
                0.9999993916407459,
                0.9999981261243938,
                0.999999352405202,
                0.9999999273418443,
                0.9999998362623723,
                0.9999998362622943,
                0.9999981261241705,
                0.9999995262096116,
                0.9999996072137531
            ],
            [
                2.5612834320563895e-06,
                0.9999967112517203,
                9.422444815814404e-07,
                0.9999952149049391,
                1.067703124601679e-06,
                0.9999991148433864,
                0.9999997897565587,
                0.9999987901340284,
                1.99472900813862e-06,
                0.9999898700054077
            ],
            [
                0.9999994631247403,
                0.9999985406239537,
                0.9999996310115918,
                0.999986992876196,
                0.9999996533673376,
                2.3823696679230424e-07,
                0.9999910603047658,
                0.9999991684720717,
                0.999996910504817,
                0.999999114843281
            ],
            [
                0.999999631011416,
                0.999999730042094,
                0.9999998144609203,
                1.2751901248454963e-07,
                2.561281294760143e-06,
                0.9999998461826588,
                0.9999998257021006,
                0.9999997463980124,
                1.1253509497883659e-07,
                1.209865539295696e-06
            ],
            [
                0.999999168471576,
                0.9999952149055075,
                0.9999993524048932,
                0.9999998144608319,
                0.9999995818810775,
                0.9999885212264098,
                0.9999988634364251,
                0.9999997761971849,
                0.9999990577554062,
                0.9999992188513902
            ],
            [
                0.9999989322967485,
                0.999995777165048,
                0.99999211074024,
                0.9999996072137999,
                0.9999993524052793,
                0.9999969105051849,
                0.9999997463981032,
                0.9999975938982353,
                0.9999994631249963,
                0.9999938558224708
            ],
            [
                0.9999930377429249,
                0.9999969105059221,
                3.466327450756327e-07,
                0.9999997761971315,
                1.8553914607267268e-07,
                0.9999989322973849,
                0.9999969105051858,
                0.9999964991460052,
                7.338212429562581e-07,
                0.9999997617630333
            ],
            [
                0.999987780924003,
                0.9999970976887076,
                0.999998446502061,
                0.999989870011438,
                0.9999997126315496,
                0.9999996940977003,
                0.9999997300421261,
                0.9999916019249726,
                0.9999997761971582,
                0.9999997300420939
            ],
            [
                5.715006514167015e-07,
                1.5534984953510149e-06,
                0.9999987901338843,
                5.043476486915964e-07,
                1.8553914607267268e-07,
                3.9278605979534166e-07,
                0.999998239656578,
                4.450852111148132e-07,
                4.4508510499849186e-07,
                1.8553905760024476e-07
            ],
            [
                4.22283545819819e-06,
                0.9999989969857926,
                0.9999992661791071,
                0.9999990577549572,
                3.466327450756327e-07,
                0.9999995262092728,
                5.715007195447234e-07,
                6.475946438055299e-07,
                0.9999992188517627,
                0.9999987901340285
            ],
            [
                0.9999998362623723,
                0.9999998642567028,
                0.9999962733616059,
                0.9999999434137232,
                0.9999993916411085,
                1.5534984953552536e-06,
                0.9999977396762418,
                1.9947292459406333e-06,
                0.9999997617630617,
                0.999999855501979
            ],
            [
                0.9999974387165685,
                0.9999975938979482,
                0.9999969105044482,
                0.999999554914842,
                0.9999998555020135,
                0.9999987121046314,
                0.9999989322967483,
                0.9999997761971315,
                0.9999998461826405,
                0.9999993106387903
            ],
            [
                0.9999999226557869,
                0.9999952149032266,
                0.9999990577554064,
                0.9999974387180959,
                0.9999986290421402,
                0.9999998024945624,
                0.9999930377429266,
                7.338208055664991e-07,
                0.999997273528756,
                0.9999934595643389
            ],
            [
                0.9999998874647441,
                0.9999995262094986,
                0.9999996533672963,
                0.9999998724808964,
                1.3709575337159875e-06,
                7.889265407327733e-06,
                0.9999938558261322,
                1.0,
                0.999999872480942,
                3.9278629391427843e-07
            ],
            [
                0.9999994956524718,
                0.9999999397642294,
                0.9999998257020799,
                0.9999998024947037,
                0.999999057755294,
                0.9999996072138466,
                0.9999994284994169,
                0.999999674368781,
                0.999999310638626,
                0.9999997300423191
            ],
            [
                0.9999997617630617,
                0.9999989322967484,
                0.9999993916407459,
                0.9999996072136126,
                0.9999993524048932,
                0.999998932297003,
                0.9999999500628036,
                0.9999974387174853,
                0.9999996072137531,
                0.9999996940978096
            ],
            [
                3.059021539909339e-07,
                3.92786293909545e-07,
                5.04347287955046e-07,
                2.1024336609874897e-07,
                2.3823696679230424e-07,
                3.466327450765785e-07,
                3.4663249714612693e-07,
                7.338210679979539e-07,
                1.5534973842030142e-06,
                3.9278634073732336e-07
            ],
            [
                0.999999802494633,
                0.9999995818813269,
                0.9999998024946095,
                0.9999996743688975,
                0.9999993524053564,
                0.9999997126315153,
                0.9999996533672963,
                0.9999996072138936,
                0.9999997300422226,
                0.9999984465018759
            ],
            [
                0.9999992661791072,
                4.691160446380562e-08,
                2.5612834320563895e-06,
                1.5534984953552536e-06,
                4.691167157146029e-08,
                5.715003107767143e-07,
                3.7266383956509585e-06,
                8.315278294114555e-07,
                9.93120161310289e-08,
                6.475950298021765e-07
            ],
            [
                0.9999993916409634,
                0.9999949062956077,
                0.9999987901343171,
                0.9999992188517627,
                0.9999983463096261,
                0.999999789756659,
                0.9999960330145603,
                0.9999988634362897,
                3.4663253846316044e-07,
                0.9999997126314468
            ],
            [
                0.9999997126313097,
                0.9999996533673376,
                0.9999993916407459,
                0.9999996072136125,
                0.999996711250936,
                0.999999746398073,
                0.9999972735300551,
                0.99999976176309,
                0.9999980052693281,
                0.999999946842106
            ],
            [
                0.9999985406241275,
                0.9999992188513903,
                0.9999910603005034,
                3.05902336324494e-07,
                1.760343003481596e-06,
                0.9999991148426476,
                4.450850519403407e-07,
                0.9999996743688199,
                5.71500719545698e-07,
                1.0677027427600627e-06
            ],
            [
                0.9999995818812272,
                0.999999730042287,
                0.9999999500627976,
                0.9999996533673376,
                0.9999993106386259,
                0.9999975938979481,
                0.9999997761971315,
                0.9999997300422226,
                0.9999984465020608,
                0.9999995549150013
            ],
            [
                6.144175334468545e-06,
                0.9999957771660547,
                0.999997739675164,
                0.9999997761970781,
                0.9999998724809419,
                0.9999998642566704,
                0.9999987901346054,
                0.9999993106388725,
                0.999999607213753,
                0.9999998802069731
            ],
            [
                7.338208930460318e-07,
                1.0677026154827912e-06,
                3.4663274507713016e-07,
                0.9999898700102348,
                1.7603430034867993e-06,
                5.715005832886879e-07,
                2.561281600086738e-06,
                6.475947210012481e-07,
                0.9999999500628036,
                3.288748281329893e-06
            ],
            [
                0.9999952149043672,
                0.9999992661791947,
                0.9999952149055068,
                0.9999687980998476,
                0.999997438716569,
                0.999989870010236,
                0.9999970976890543,
                5.715006514105942e-07,
                0.9999994631250603,
                0.999999168471576
            ],
            [
                0.9999995549149482,
                0.9999992188516696,
                0.9999916019239682,
                3.9278634073732336e-07,
                0.9999974387168746,
                0.9999952149049381,
                0.9999998362622552,
                1.6373762769138607e-07,
                0.9999938558239349,
                1.8553905760024476e-07
            ],
            [
                0.9999996940977002,
                0.9999921107392997,
                4.4508494582405734e-07,
                3.7266401726359486e-06,
                2.1024339116168358e-07,
                3.927863875616689e-07,
                2.699578096403948e-07,
                0.9999984465026164,
                1.2751908849167202e-07,
                0.9999980052707552
            ],
            [
                7.338207180864763e-07,
                2.699578096403948e-07,
                3.0590215398829087e-07,
                5.315788140303327e-08,
                5.71500515159253e-07,
                2.102433660979124e-07,
                4.450849988758202e-07,
                4.450850519403407e-07,
                2.561283126728994e-06,
                1.2098658277335738e-06
            ],
            [
                0.9999998642566381,
                0.9999995262092728,
                0.9999995549149482,
                0.9999998802069731,
                0.9999996310113719,
                0.9999997126314811,
                0.9999989969859122,
                0.9999997126314811,
                0.9999999500628572,
                0.9999999317439953
            ],
            [
                0.9999987121044777,
                0.999994228078597,
                3.4663249714325014e-07,
                0.9999974387180957,
                0.9999994956524116,
                3.9278605979534166e-07,
                0.9999992188515765,
                7.338209805224048e-07,
                1.9947306726594253e-06,
                3.4663266243111764e-07
            ],
            [
                0.9999998461826771,
                0.999998712104785,
                0.9999994956524116,
                0.9999998257021007,
                0.999999730042287,
                0.9999997463981939,
                0.999999114843281,
                0.9999986290427936,
                0.999999653367255,
                0.9999997617630901
            ],
            [
                0.999998446502246,
                0.9999993106388727,
                0.9999992661790198,
                0.9999994284996894,
                0.9999989969862709,
                0.9999991148426477,
                0.9999957771670615,
                0.9999981261248404,
                0.999998346311006,
                0.9999996072138935
            ],
            [
                0.9999974387168747,
                0.9999988634362897,
                0.9999996072138936,
                0.9999957771675635,
                0.9999978766210327,
                1.1253513522447425e-07,
                1.8553907971855875e-07,
                NaN,
                4.450852641737424e-07,
                0.9999987901340286
            ],
            [
                6.475945666063607e-07,
                1.7603438428800754e-06,
                1.7603430034867993e-06,
                1.5534979397829198e-06,
                3.466326624336003e-07,
                8.315278294114555e-07,
                2.9023119851899796e-06,
                8.315281267882195e-07,
                7.338208930460318e-07,
                2.699578740032504e-07
            ],
            [
                0.9999999123575778,
                0.9999992188517629,
                0.9999996743688975,
                0.9999986290429571,
                0.9999998642566219,
                0.9999978766212854,
                0.9999999559305681,
                1.0,
                0.9999999006880431,
                1.0
            ],
            [
                0.999989870011442,
                6.47595107001401e-07,
                1.0677026154827912e-06,
                7.338208055536515e-07,
                3.288749849529972e-06,
                7.338209805240734e-07,
                3.466327037553825e-07,
                8.315282259009745e-07,
                8.315277302747361e-07,
                5.715004470243685e-07
            ],
            [
                0.9999998257021214,
                0.9999987901346054,
                0.9999980052709928,
                0.9999987901338842,
                0.9999995262095552,
                0.9999995818814266,
                0.9999997463980125,
                0.9999996072137531,
                0.9999998461826589,
                0.9999995262093293
            ],
            [
                4.450849988758202e-07,
                2.561281600076256e-06,
                0.9999942280799775,
                0.9999960330155053,
                1.7603425837702984e-06,
                1.0677028700422047e-06,
                2.260323758987159e-06,
                0.9999921107383591,
                0.9999986290423032,
                0.9999930377454158
            ],
            [
                1.275190580890061e-07,
                6.475947982002148e-07,
                8.764244316973974e-08,
                4.139941495546278e-08,
                0.9999999123575464,
                8.7642558095602e-08,
                1.4449803818215767e-07,
                4.139936066832438e-08,
                1.8553907971855875e-07,
                4.691167716359673e-08
            ],
            [
                2.6995784182140636e-07,
                1.444979692800516e-07,
                2.699576809143613e-07,
                0.9999938558261342,
                1.444980209564556e-07,
                6.475948753991907e-07,
                1.8553905760024476e-07,
                2.382370235933104e-07,
                0.9999985406239535,
                0.99999879013374
            ],
            [
                1.5534975693792215e-06,
                1.2098662604192665e-06,
                3.927862002663297e-07,
                6.475947981904966e-07,
                2.6995768091310296e-07,
                0.9999998942829477,
                5.04347287955046e-07,
                1.2098656835136636e-06,
                0.9999970976880167,
                1.444979692797559e-07
            ],
            [
                5.043472879481655e-07,
                3.927862470861484e-07,
                4.450849988758202e-07,
                0.9999975938965142,
                6.47594643788744e-07,
                0.9999994284996895,
                0.9999724642991075,
                3.927862470861484e-07,
                9.42244818532859e-07,
                0.9999964991451699
            ],
            [
                0.9999994284993488,
                2.902312331170226e-06,
                0.9999885212359875,
                8.315278294114555e-07,
                5.043474683220276e-07,
                0.999999554914736,
                0.9999988634358832,
                0.9999957771655497,
                0.9999151889792159,
                8.315281267882195e-07
            ],
            [
                0.999996910504817,
                0.9999964991464215,
                0.9999991684716754,
                0.9999038976083772,
                0.9999949062968229,
                0.9999964991460054,
                0.9999921107402409,
                0.9999952149066477,
                0.999993037741266,
                0.9999997126313097
            ],
            [
                0.9999990577555189,
                0.9999997126315496,
                5.715006514176113e-07,
                0.9999991148431753,
                8.315282259009745e-07,
                0.9999989969854339,
                0.9999989322968758,
                0.9999992661790197,
                0.9999997897567342,
                0.9999995549150543
            ],
            [
                0.9999997897565839,
                0.9999992661787572,
                0.9999998257021837,
                0.999999168472171,
                0.9999955048162817,
                0.9999996533673376,
                0.9999986290423034,
                9.931202796993203e-08,
                0.9999992661791947,
                0.9999997126314126
            ],
            [
                2.1024326584639497e-07,
                5.715004470295662e-07,
                9.422448185435711e-07,
                1.5534983101478522e-06,
                1.0677033791583005e-06,
                1.7603438428564603e-06,
                0.9999990577549571,
                3.9278634073732336e-07,
                3.4663249714325014e-07,
                0.9999987121043241
            ],
            [
                0.9999999067051499,
                6.47595107001401e-07,
                0.9999993106390369,
                0.9999999434137571,
                0.9999930377404328,
                0.9999999530883172,
                0.9999974387165684,
                0.9999985406237795,
                0.9999885212318809,
                0.9999952149032261
            ],
            [
                0.9999998024946801,
                0.9999993106387903,
                0.999999631011416,
                0.999994577780388,
                0.9999998642567351,
                0.9999998362622747,
                0.9999991684717744,
                0.999999887464771,
                0.999999607213753,
                0.9999991148427534
            ],
            [
                0.9999999123575255,
                0.9999999123575778,
                0.9999999397642221,
                0.9999995262092728,
                0.9999998461827322,
                0.9999998874647441,
                0.9999998362623332,
                0.9999999837877829,
                1.0,
                0.9999995549150543
            ],
            [
                0.9999998461827322,
                0.9999991148433865,
                6.475946438055299e-07,
                0.9999869928653483,
                0.9999952149066492,
                0.9999985406239537,
                0.9999991148433864,
                0.999997438718401,
                0.9999952149072185,
                0.9999987121049384
            ],
            [
                0.9999977396765112,
                0.9999977396757028,
                0.9999986290426305,
                0.9999980052700415,
                0.9999992188514834,
                0.9999991148428587,
                0.9999989322967485,
                0.9999962733616061,
                0.9999990577554064,
                0.9999987121046312
            ],
            [
                4.450851580540182e-07,
                1.8553914607267268e-07,
                0.9999998461826222,
                2.561281294760143e-06,
                0.9999997617629764,
                2.2603248367949354e-06,
                3.0590226338838606e-07,
                1.994730672675753e-06,
                3.0590237279085045e-07,
                7.338210679979539e-07
            ],
            [
                0.9999687980886605,
                0.9999970976887074,
                3.466325384678894e-07,
                2.6995784182183607e-07,
                0.999991060304768,
                0.9999984465015053,
                0.9999978766205255,
                0.9999992188519489,
                0.9999251537728793,
                0.9999756997505892
            ],
            [
                0.9999998461826771,
                0.9999996743687033,
                0.9999999317439465,
                0.9999997300423192,
                0.9999999226558515,
                0.9999999006880076,
                0.9999957771655507,
                0.9999991684718734,
                0.9999995262093292,
                0.999999887464744
            ],
            [
                0.9999997897567091,
                0.9999999468421059,
                0.9999989322968758,
                0.9999991148426478,
                0.9999960330121969,
                0.9999995549148951,
                0.9999998257021006,
                0.9999998642566866,
                0.9999996310116358,
                0.999999712631481
            ],
            [
                0.999999391641036,
                0.9999967112509358,
                0.9999934595596596,
                1.0677026154730804e-06,
                5.715003788993679e-07,
                0.9999993916411812,
                4.4508489275752546e-07,
                0.9999921107336578,
                0.9999994631251883,
                0.9999984465024312
            ],
            [
                3.927860597945825e-07,
                0.9999987901337399,
                2.1024339116082313e-07,
                8.315278294038928e-07,
                4.450851580540182e-07,
                0.9999998724810027,
                3.466327450756327e-07,
                0.9999989322971303,
                2.260325375650449e-06,
                1.5534979397592542e-06
            ],
            [
                0.9999995262095551,
                0.9999983463100203,
                0.9999997463981636,
                0.9999998555020307,
                0.9999987901347497,
                0.999999391641036,
                0.9999987121049384,
                0.9999993524048932,
                1.0,
                0.9999970976890544
            ],
            [
                0.9999998362623724,
                0.9999998642566866,
                0.9999994631247403,
                0.9999995262094987,
                0.9999974387177902,
                0.9999987901338843,
                0.9999994956527122,
                0.9999991148430699,
                0.9999983463098232,
                0.9999994956524717
            ],
            [
                3.9278634073625165e-07,
                0.9999983463098232,
                0.9999995262095552,
                0.9999989322967484,
                0.9999994631247402,
                0.999983298582147,
                0.999991060304768,
                0.9999998461826588,
                0.9999982396567874,
                0.9999921107364772
            ],
            [
                0.9999989322973851,
                0.9999995818811773,
                0.9999925887210183,
                0.9999969105051848,
                0.9999910603037028,
                0.9999992661791948,
                0.9999978766222978,
                0.9999990577550696,
                0.9999991148431754,
                0.9999995549148951
            ],
            [
                4.4508494582405734e-07,
                5.04347348075149e-07,
                0.999999114843281,
                0.9999996940978461,
                5.71500719545698e-07,
                0.9999987121044778,
                0.9999810748562891,
                1.6373772528704005e-07,
                0.9999994956523515,
                0.9999930377445836
            ],
            [
                0.9999998362622358,
                0.9999996310114599,
                2.382370235933104e-07,
                0.9999998555020307,
                3.0590226339137693e-07,
                5.043472278322555e-07,
                2.10243290909724e-07,
                2.1024339116168358e-07,
                0.9999995262092163,
                2.3823702359290413e-07
            ],
            [
                5.715003107738556e-07,
                0.9999785550592731,
                4.222832941142044e-06,
                7.338208055536515e-07,
                5.715004470243685e-07,
                7.338211554783522e-07,
                1.2098662604247682e-06,
                1.7603434231705793e-06,
                0.9999925887219018,
                0.9997965729341676
            ],
            [
                4.450849988798682e-07,
                0.9999967112505435,
                3.05902336324494e-07,
                0.9999852610180423,
                0.9999921107383588,
                2.9023123311055552e-06,
                2.2603251062450327e-06,
                1.5534971990169383e-06,
                6.475948753991907e-07,
                5.04347528440776e-07
            ],
            [
                0.9999980052700418,
                0.9999990577556311,
                0.9999998724809115,
                0.9999994284996213,
                0.9999981261252878,
                0.9999985406243015,
                0.9999992188514834,
                0.9999994631248682,
                0.9999987901338842,
                0.999984310446563
            ],
            [
                2.902312331170226e-06,
                9.42244256915735e-07,
                0.9999990577554063,
                9.422443692574719e-07,
                4.006371129615879e-05,
                0.9999983463096261,
                3.288747889284851e-06,
                1.2098661162056318e-06,
                1.9947304348862686e-06,
                0.9999945777829717
            ],
            [
                0.9999997761972116,
                0.9999999067050054,
                0.999998346309626,
                0.999999906705072,
                0.9999988634360187,
                0.9999977396765113,
                0.9999998257021837,
                0.9999996072138936,
                0.9999991684718734,
                0.9999987901344609
            ],
            [
                6.475947982037486e-07,
                0.9999997761970515,
                0.9999999123574419,
                0.9999995262092728,
                6.144175334468545e-06,
                1.994729721518893e-06,
                8.31527928532683e-07,
                2.2603242978871282e-06,
                9.422443692555439e-07,
                0.9999999358793409
            ],
            [
                0.9999998874648246,
                1.855391239544352e-07,
                0.9999999317439302,
                0.9999985406241275,
                0.9999955048184245,
                0.9999997463982241,
                0.9999910603047667,
                0.9999646437577823,
                2.2603253756956754e-06,
                1.6373772528704005e-07
            ],
            [
                5.043475885696228e-07,
                7.338208055680009e-07,
                3.9278605979208185e-07,
                1.2098652508424818e-06,
                1.760343003481596e-06,
                7.338213304283347e-07,
                9.42244930862237e-07,
                5.043474683204221e-07,
                6.475950297942253e-07,
                9.422447062202052e-07
            ],
            [
                1.0677027427624903e-06,
                9.422442569334097e-07,
                3.9278624708775595e-07,
                2.3823690999323465e-07,
                7.338210679979539e-07,
                1.0677027427624903e-06,
                1.2098658277451275e-06,
                1.0129994602895546e-05,
                2.6995784182183607e-07,
                1.444980726324838e-07
            ],
            [
                3.0590215399183813e-07,
                3.0590237279085045e-07,
                0.9999988634364253,
                0.9999993106392012,
                1.6373774480605869e-07,
                0.9999983463110059,
                1.8553919030776337e-07,
                0.9999985406232577,
                3.466327037553825e-07,
                0.9999991684719727
            ],
            [
                0.9999997126315496,
                0.9999998642566381,
                0.9999998362623332,
                3.9278610661902853e-07,
                0.999999310639037,
                0.9999998642566219,
                0.9998204720132834,
                3.927861066170637e-07,
                0.9999996940976273,
                0.9999997761971849
            ],
            [
                0.9999989322975121,
                0.9999995262095552,
                0.9999988634357478,
                1.4738980215111302e-05,
                0.9999997463980125,
                0.9999970976866325,
                0.9999957771650467,
                0.9999756997621945,
                0.9999995549151074,
                9.422445939002803e-07
            ],
            [
                1.3709572068272963e-06,
                3.9278624708775595e-07,
                8.315279285251204e-07,
                0.9999989969856731,
                0.9999987901347493,
                3.7266401725935817e-06,
                0.9999995818811773,
                0.9999964991451703,
                0.9999993916411085,
                0.9999993106387904
            ],
            [
                4.4508515805199415e-07,
                4.450849458200093e-07,
                2.5612812947077304e-06,
                7.338213304316717e-07,
                7.3382080556433e-07,
                0.999998996985673,
                0.9999998802069731,
                0.999999922655833,
                4.4508515805199415e-07,
                3.4663274506893337e-07
            ],
            [
                0.9999985406234315,
                0.9999991684721709,
                0.9999994956527121,
                0.9999910603047643,
                0.9999869928699935,
                0.99999862904263,
                0.9999994284996212,
                1.5534984953510149e-06,
                0.9999999358793485,
                0.9999869928653375
            ],
            [
                0.9999960330126697,
                1.855391239539711e-07,
                1.0677026154774503e-06,
                0.999999310639119,
                5.715002426460124e-07,
                2.6995774527657245e-07,
                1.209865683518615e-06,
                0.9999960330121964,
                1.3709573702822306e-06,
                0.9999970976880167
            ],
            [
                2.382369383923073e-07,
                1.855391239547094e-07,
                9.422447062294175e-07,
                6.47595107001401e-07,
                6.475947210046347e-07,
                3.726637951387472e-06,
                4.450852641737424e-07,
                2.382369383923073e-07,
                3.466325797900508e-07,
                2.1024339116168358e-07
            ],
            [
                0.9999977396746254,
                0.9999417087346094,
                0.9999998362623138,
                0.9999998555019447,
                3.466325384661554e-07,
                0.9999982396561575,
                0.9999995549149482,
                4.450850519403407e-07,
                0.999995214907218,
                0.9999994956525919
            ],
            [
                0.9999996072138935,
                0.999999943413811,
                0.9999989969861512,
                0.9999997897565588,
                9.422442569290178e-07,
                0.9999974387184015,
                0.9999997617630049,
                0.9999996743687422,
                0.9999998802069302,
                3.059023363231725e-07
            ],
            [
                3.653485564473625e-08,
                0.9999995262095551,
                7.734428685047173e-08,
                2.8453323536912213e-08,
                4.691168275606451e-08,
                1.6373766672973748e-07,
                1.444980726324838e-07,
                6.023568448589658e-08,
                6.475945666033422e-07,
                1.1253506814842375e-07
            ],
            [
                7.338211554688417e-07,
                5.043472879504592e-07,
                7.338213304316717e-07,
                6.475950297971703e-07,
                0.9999987901344615,
                1.2098662604192665e-06,
                3.4663253846316044e-07,
                4.450849458200093e-07,
                0.9999810748517781,
                1.0677026154774503e-06
            ],
            [
                0.9999998555019963,
                0.9999998724810027,
                0.9999996743686257,
                0.9999998802069731,
                0.9999998724809419,
                0.999999894283061,
                0.9999998144609424,
                0.9999998942829602,
                0.9999999559306154,
                0.9999998874649318
            ],
            [
                0.9999989322973851,
                0.9999989969854345,
                0.9999972735297313,
                0.9999960330136155,
                0.9999957771680682,
                0.9999980052693282,
                0.9999997897565589,
                0.9999982396559483,
                0.999999266179195,
                0.9999989969861515
            ],
            [
                1.2098659719441482e-06,
                1.0677027427471959e-06,
                5.71500515151976e-07,
                6.475947209918244e-07,
                6.475950297942253e-07,
                0.9999990577555189,
                1.0677024881829577e-06,
                5.71500515151976e-07,
                5.715006514105942e-07,
                9.422443692330485e-07
            ],
            [
                0.9999997761970781,
                0.9999997463981636,
                0.9999998874649051,
                0.9999998802069017,
                0.9999987121041706,
                0.9999987121044779,
                0.9999999530883174,
                0.9999997300421583,
                0.9999996310114599,
                0.9999996743686644
            ],
            [
                0.999997097688016,
                0.9999996072136593,
                0.9999995818813766,
                0.9999997897565839,
                0.9999930377404361,
                0.9999995262092727,
                0.999999814460854,
                0.9999998144609424,
                0.9999997761971049,
                0.9999993524054336
            ],
            [
                0.999999802494586,
                0.9999998874648514,
                0.9999998874648515,
                0.9999998144608983,
                0.9999970976890538,
                0.999999864256719,
                0.9999998555019446,
                0.9999992661788447,
                0.9999989322971305,
                0.9999996743688586
            ],
            [
                0.9999993916409635,
                0.9999990577555188,
                0.9999978766215386,
                0.9999999006881142,
                0.9999978766220451,
                2.5612825160271407e-06,
                0.9999957771645435,
                3.05902263389638e-07,
                0.9999994956523515,
                0.9999998724809267
            ],
            [
                8.315277302788957e-07,
                0.9999898700041968,
                1.4449807263312446e-07,
                1.275190428875671e-07,
                2.6995768091310296e-07,
                3.9278634073625165e-07,
                2.6995784182140636e-07,
                0.9999967112521118,
                1.275190580884987e-07,
                0.9999869928715429
            ],
            [
                0.9999990577549571,
                0.9999991148429643,
                0.9999986290423033,
                0.9999994956524115,
                0.999999495652652,
                0.9999991684718734,
                0.9999990577557434,
                0.9999996940977002,
                0.9999993916409635,
                0.9999987121047847
            ],
            [
                0.9999938558232027,
                0.9999993524049704,
                7.338213304316717e-07,
                1.5534971989992774e-06,
                6.144175334468545e-06,
                0.999998346309626,
                7.338208055680009e-07,
                5.715005832895975e-07,
                2.902312331170226e-06,
                1.994729721518893e-06
            ],
            [
                0.9999987121052453,
                0.9999993916409635,
                0.999996711250936,
                0.9999995818813767,
                0.9999995818810777,
                0.9999986290429571,
                0.9999997300421581,
                0.9999980052707549,
                0.9999994631247402,
                0.9999970976866319
            ],
            [
                2.2603248367949354e-06,
                0.9999960330131412,
                0.9999993524048932,
                0.9999987901341728,
                0.9999981261241706,
                0.9999852610198073,
                0.9999982396563677,
                0.9999952149037967,
                0.9999724643187786,
                NaN
            ],
            [
                6.475949525919915e-07,
                2.699578740032504e-07,
                5.715004470313855e-07,
                3.9278605979208185e-07,
                2.699578418172324e-07,
                8.315284241665078e-07,
                2.3823690999063455e-07,
                1.8553919030776337e-07,
                5.04347528440776e-07,
                0.9999994631251242
            ],
            [
                0.9999981261241707,
                0.9999992188516698,
                0.9999996533673376,
                2.3823682479292225e-07,
                0.9999982396572077,
                0.9999999006880785,
                0.9999987901341728,
                0.9999997300422225,
                3.466325384661554e-07,
                0.9999994631248041
            ],
            [
                0.9999810748585477,
                4.4508494582405734e-07,
                0.9999996533672963,
                3.9278624708775595e-07,
                3.466327863983311e-07,
                0.9999997617631186,
                0.999999168472171,
                0.9999994956525919,
                0.9999997617631184,
                0.9999997617629764
            ],
            [
                0.9999992188517628,
                0.9999988634366963,
                0.9999996310115479,
                7.889259764517575e-06,
                0.9999921107346014,
                0.9999977396751646,
                0.9999998257021213,
                0.9999995818810776,
                2.6995774527657245e-07,
                0.9999964991451701
            ],
            [
                9.422447062270609e-07,
                1.444979692797559e-07,
                7.338211554758494e-07,
                5.043476486902204e-07,
                0.9999989969860317,
                1.067703379154416e-06,
                0.9999995818813269,
                2.6995784182183607e-07,
                1.3709572068522336e-06,
                1.637376862489725e-07
            ],
            [
                4.139940508508409e-08,
                1.8553905760024476e-07,
                3.653485564473625e-08,
                8.764254764780641e-08,
                6.825609419848033e-08,
                6.023569166654288e-08,
                6.825597214718257e-08,
                2.69957906184239e-07,
                1.2751902768612997e-07,
                2.260324028404236e-06
            ],
            [
                0.9999977396754337,
                0.999999495652592,
                0.9999970976873244,
                5.71500651413193e-07,
                0.9999957771645444,
                6.144173869558639e-06,
                0.999994228079975,
                1.3709572068478697e-06,
                0.9999969105040797,
                0.9999997300421261
            ],
            [
                0.9999993524052792,
                2.561281294760143e-06,
                0.9999990577551816,
                0.9999910603047647,
                0.9999885212332492,
                1.2098653950656417e-06,
                0.9999724643089247,
                0.999998346309823,
                0.9999999500627976,
                0.9999996533673791
            ],
            [
                5.04347528440776e-07,
                3.0590237278838124e-07,
                2.6995771309210433e-07,
                3.05902226923399e-07,
                2.699577774560111e-07,
                3.4663266243111764e-07,
                2.6995790618252024e-07,
                5.043472879504592e-07,
                3.059021175247079e-07,
                0.9999996940976636
            ],
            [
                0.9999986290421399,
                2.5612834320563895e-06,
                5.043475885688201e-07,
                0.9999996533673791,
                0.9999986290429571,
                0.9999964991451709,
                0.9999998024945624,
                0.9999990577551817,
                0.9999599362887508,
                0.9999898700102356
            ]
        ]
    },
    {
        "q_id": "9649_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            5,
            6,
            7,
            8,
            9,
            10,
            12,
            13,
            14,
            16,
            17,
            18,
            20,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            33,
            34,
            36,
            37,
            38,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            51,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            62,
            63,
            64,
            65,
            66,
            67,
            69,
            70,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            82,
            83,
            85,
            87,
            94,
            97,
            98,
            100,
            103,
            104,
            105,
            106,
            107,
            109,
            111,
            112,
            113,
            114,
            117,
            118,
            119,
            120,
            123,
            124,
            125
        ],
        "rewards": [
            [
                1.760343003481596e-06,
                8.315283250371857e-07,
                1.9947301970813926e-06,
                3.2887478892683997e-06,
                1.5534983101478522e-06,
                4.222833947960866e-06,
                2.2603245673279107e-06,
                5.422217030707961e-06,
                8.315281267861397e-07,
                1.760343213322473e-06
            ],
            [
                1.0677027427600627e-06,
                7.338212429582604e-07,
                6.475947982022763e-07,
                0.9999977396759743,
                0.9999985406237806,
                4.450851580555361e-07,
                0.9999982396572088,
                8.315278294072958e-07,
                0.9999967112493703,
                8.315284241597959e-07
            ],
            [
                1.9947299593014888e-06,
                1.2098655392921197e-06,
                6.475947210046347e-07,
                NaN,
                1.2098656835224664e-06,
                6.475950298011458e-07,
                1.2098661162056318e-06,
                4.222834954778007e-06,
                7.338210680021253e-07,
                8.315277302788957e-07
            ],
            [
                8.315277302857965e-07,
                4.4508515805735777e-07,
                1.209865827752005e-06,
                1.7603440527334603e-06,
                1.0677028700422047e-06,
                5.144221366623174e-05,
                3.466325384678894e-07,
                8.315284241665078e-07,
                4.785093924389007e-06,
                2.9023119851899796e-06
            ],
            [
                2.9023133690637e-06,
                1.4738976701170414e-05,
                6.144173869502757e-06,
                1.0129987357287368e-05,
                3.120190021657421e-05,
                5.422218969818919e-06,
                1.670141786325573e-05,
                3.288750241500471e-06,
                1.0129995810463632e-05,
                1.6701421844753466e-05
            ],
            [
                2.5612816000646084e-06,
                3.2887490653872164e-06,
                1.370957860567974e-06,
                4.78509392429544e-06,
                1.2098661162023305e-06,
                3.288748281295496e-06,
                6.1441746020359e-06,
                1.9947294837154625e-06,
                1.5534983101301911e-06,
                5.422221555340727e-06
            ],
            [
                3.927862939126708e-07,
                1.3709567165530083e-06,
                4.4508526417014975e-07,
                6.475945666033422e-07,
                6.475947210012481e-07,
                7.338213304363436e-07,
                1.3709567165579959e-06,
                3.4663274507713016e-07,
                2.2603240284371276e-06,
                1.2098655392871682e-06
            ],
            [
                3.05902190458764e-07,
                2.102434412875379e-07,
                1.1253525596174225e-07,
                9.422444815814404e-07,
                2.3823702359290413e-07,
                2.1024336609874897e-07,
                4.450852111148132e-07,
                1.275190276859705e-07,
                8.764245361752286e-08,
                1.6373774480605869e-07
            ],
            [
                0.9999972735294165,
                0.9999977396762484,
                0.9999955048195127,
                0.9999832985703938,
                0.9999945777804476,
                0.9999981261250698,
                0.9999957771650689,
                0.9999980052710037,
                0.9999949062931985,
                0.9999993106392024
            ],
            [
                3.2887490653408545e-06,
                2.561282210701601e-06,
                1.7603438428460541e-06,
                1.3709570434122812e-06,
                4.2228329411708495e-06,
                2.9023119851266288e-06,
                1.2098658277489788e-06,
                1.209865827740176e-06,
                2.561283432005142e-06,
                2.2603251060985603e-06
            ],
            [
                NaN,
                5.422220909009474e-06,
                6.962257079832313e-06,
                6.962257079832313e-06,
                2.4300249425247723e-05,
                5.4222176771176554e-06,
                3.535625071730638e-05,
                4.539786323732447e-05,
                6.144174601991196e-06,
                5.4222183235249605e-06
            ],
            [
                4.006369219233375e-05,
                6.475949526020042e-07,
                1.3709570434178922e-06,
                6.144175334418252e-06,
                1.994729008145876e-06,
                2.6995771309210433e-07,
                3.726638395611981e-06,
                5.4222209089700225e-06,
                1.7603440527286572e-06,
                2.5612822107167428e-06
            ],
            [
                3.46632497145457e-07,
                NaN,
                1.5534981249697903e-06,
                1.5534975693933505e-06,
                9.422447062294175e-07,
                2.561281600076256e-06,
                5.4222176771176554e-06,
                NaN,
                7.338213304363436e-07,
                4.2228349547223175e-06
            ],
            [
                3.726638839833152e-06,
                1.6701421844753466e-05,
                4.2228324377740105e-06,
                4.2228329411708495e-06,
                2.26032402841657e-06,
                2.561281905390075e-06,
                5.4222183234485234e-06,
                1.9947292459347367e-06,
                9.422448185435711e-07,
                1.7603436330259153e-06
            ],
            [
                3.726638395527247e-06,
                3.466327037539638e-07,
                1.553497754577351e-06,
                9.422448185534261e-07,
                5.04347468323289e-07,
                3.288749457469787e-06,
                3.288748673319648e-06,
                2.2603234895289998e-06,
                3.726639728370556e-06,
                3.288750633569722e-06
            ],
            [
                2.561282821352716e-06,
                3.9278634073625165e-07,
                8.939699501229642e-06,
                4.785092783415276e-06,
                3.726638395611981e-06,
                1.1478772230929451e-05,
                3.7266379513162962e-06,
                2.3823682479292225e-07,
                1.7603430034743913e-06,
                3.9278615344267634e-07
            ],
            [
                1.0677027427624903e-06,
                1.0677033791583005e-06,
                1.0677024881941248e-06,
                2.5612828213934817e-06,
                2.561281600086738e-06,
                NaN,
                9.422448185510695e-07,
                2.902311639183378e-06,
                3.4663266242969896e-07,
                9.422443692555439e-07
            ],
            [
                4.4508510499849186e-07,
                0.00020342707062123925,
                3.4663249714612693e-07,
                6.1441731370702875e-06,
                9.422449308774482e-07,
                1.2098656835136636e-06,
                3.9278615344178325e-07,
                5.715003107715166e-07,
                5.715003107755449e-07,
                5.043476486924565e-07
            ],
            [
                1.1478770861859053e-05,
                1.0129988564716393e-05,
                1.300713466685723e-05,
                9.610242648063708e-05,
                7.889266347636241e-06,
                2.144495608378187e-05,
                3.7266397282926013e-06,
                2.260324297853209e-06,
                8.939695238333382e-06,
                4.222832941142044e-06
            ],
            [
                2.902313023101807e-06,
                2.6995777745711594e-07,
                1.0677027427471959e-06,
                4.450852111148132e-07,
                5.043472879504592e-07,
                4.450848927650143e-07,
                1.553497384180408e-06,
                7.338208055579897e-07,
                9.422443692555439e-07,
                4.222834451355964e-06
            ],
            [
                NaN,
                4.4508494582405734e-07,
                1.370957860576702e-06,
                1.9947299593078385e-06,
                3.9278610661902853e-07,
                9.422448185534261e-07,
                1.7603430034867993e-06,
                5.715006514176113e-07,
                2.902312677150514e-06,
                3.7266397283908927e-06
            ],
            [
                3.7266397283908927e-06,
                1.5534971990169383e-06,
                1.7603430034867993e-06,
                4.450852641737424e-07,
                1.5534971990169383e-06,
                3.9278610661902853e-07,
                1.2098653950692178e-06,
                1.6373766672973748e-07,
                3.288749457469787e-06,
                3.4663249714612693e-07
            ],
            [
                5.043474683240344e-07,
                3.288749065423109e-06,
                1.209866260432471e-06,
                6.47595107001401e-07,
                1.9947297215043796e-06,
                3.288748281329893e-06,
                4.78509278348926e-06,
                4.785096206076165e-06,
                1.9947301970813926e-06,
                2.5612834320214477e-06
            ],
            [
                3.05902117523595e-07,
                9.422443692574719e-07,
                2.2603240284371276e-06,
                9.422442569315887e-07,
                5.04347468323289e-07,
                9.422448185534261e-07,
                5.043476486915964e-07,
                1.0677024881980089e-06,
                2.2603240284371276e-06,
                2.6995784182140636e-07
            ],
            [
                4.785096776499213e-06,
                3.4663249714325014e-07,
                2.2603251062450327e-06,
                4.785095635655362e-06,
                3.535624228698939e-05,
                1.444979692797559e-07,
                1.2751899728311609e-07,
                5.4222183235249605e-06,
                3.927861066170637e-07,
                1.2751904288739315e-07
            ],
            [
                2.9023112931688987e-06,
                2.2603251062147097e-06,
                1.4738976700366126e-05,
                2.902312677150514e-06,
                4.4508526417298334e-07,
                2.9023130230846496e-06,
                2.561281905376098e-06,
                2.260325375677174e-06,
                2.260324028351814e-06,
                3.726641061085547e-06
            ],
            [
                8.315278294001114e-07,
                8.31528424151477e-07,
                1.3709572068272963e-06,
                3.9278634073732336e-07,
                1.994730434798734e-06,
                2.2603242978778778e-06,
                2.9023133690980155e-06,
                6.144173868670137e-06,
                1.7603436330179102e-06,
                2.2603234895176927e-06
            ],
            [
                2.1024329090929374e-07,
                2.3823682479181176e-07,
                1.6373766672821107e-07,
                2.2603253756874524e-06,
                3.059021175255426e-07,
                7.734423152941018e-08,
                2.6995784182140636e-07,
                3.9278634073732336e-07,
                2.3823682479181176e-07,
                3.059023363231725e-07
            ],
            [
                8.315278294072958e-07,
                1.9947301970813926e-06,
                2.9023119851635836e-06,
                5.715003789033962e-07,
                1.5534971990126997e-06,
                5.043474081957179e-07,
                1.2098653950551882e-06,
                2.9023116391477434e-06,
                2.260324028404236e-06,
                6.475947209918244e-07
            ],
            [
                1.2098661162056318e-06,
                1.5534983101644536e-06,
                3.4663274507713016e-07,
                5.71500719545698e-07,
                3.466325384678894e-07,
                6.144176799334096e-06,
                5.043475885696228e-07,
                6.47595107001401e-07,
                5.422218969720291e-06,
                3.9278610661902853e-07
            ],
            [
                3.927862002663297e-07,
                5.715002426475718e-07,
                5.1442225927013303e-05,
                NaN,
                1.3709576971463352e-06,
                3.726639728370556e-06,
                2.90231094723893e-06,
                4.450848927658745e-07,
                1.9947292459347367e-06,
                1.2098653950692178e-06
            ],
            [
                1.2098656835076114e-06,
                1.3709575337078829e-06,
                1.2098653950692178e-06,
                6.475947210012481e-07,
                8.315277302841894e-07,
                1.7603430034743913e-06,
                2.561282821209454e-06,
                1.9947294837154625e-06,
                1.5534984953453635e-06,
                3.4663274507713016e-07
            ],
            [
                2.6995774527718623e-07,
                2.2603248367512505e-06,
                3.466325384661554e-07,
                2.6995784182073116e-07,
                5.422219616265831e-06,
                1.209865827752005e-06,
                6.475945666063607e-07,
                3.466326624322211e-07,
                2.2603242978213447e-06,
                6.962255419804982e-06
            ],
            [
                3.9278605979534166e-07,
                1.9947304348862686e-06,
                1.209866260432471e-06,
                2.2603251062450327e-06,
                2.5612834320470717e-06,
                2.5612828213934817e-06,
                9.422444815814404e-07,
                3.9278605979534166e-07,
                4.4508494582405734e-07,
                1.9947301970972664e-06
            ],
            [
                4.4508510499849186e-07,
                8.76424013786396e-08,
                3.288749457409966e-06,
                2.6995784182073116e-07,
                4.450852111148132e-07,
                8.764254764749753e-08,
                1.637376862489725e-07,
                1.1253514863909295e-07,
                1.3709576971425944e-06,
                1.067702870039777e-06
            ],
            [
                NaN,
                8.315281267882195e-07,
                3.0590237279085045e-07,
                3.7266397283908927e-06,
                5.422218969895357e-06,
                3.05902336324494e-07,
                6.475951070002966e-07,
                1.760343213335281e-06,
                1.4738985486721259e-05,
                1.209865827752005e-06
            ],
            [
                2.1024339116168358e-07,
                7.338209805240734e-07,
                7.338212429582604e-07,
                3.288749065423109e-06,
                2.699576809143613e-07,
                3.927863875616689e-07,
                5.715003789046955e-07,
                3.05902336324494e-07,
                1.8553907971879076e-07,
                5.71500719545698e-07
            ],
            [
                0.9999986290426319,
                0.999996273361618,
                2.902313369111213e-06,
                0.9999934595643737,
                0.9999982396572097,
                4.222834451327159e-06,
                0.999998446502247,
                0.9999991684719732,
                0.9999798543116455,
                0.9999930377404613
            ],
            [
                1.0677029973192638e-06,
                1.3709570434178922e-06,
                1.994729721436347e-06,
                4.4508510499849186e-07,
                9.422450431954847e-07,
                4.450848927650143e-07,
                1.0677031245953668e-06,
                6.475951070002966e-07,
                6.475950298011458e-07,
                4.222832941193893e-06
            ],
            [
                1.209865539274514e-06,
                3.0590215399183813e-07,
                1.2098662604247682e-06,
                5.715005832872586e-07,
                5.043475284430694e-07,
                6.475949525981759e-07,
                2.1024329090867228e-07,
                2.2603242978871282e-06,
                6.475948754012522e-07,
                1.7603430034311638e-06
            ],
            [
                1.855391239539711e-07,
                1.1253510839355284e-07,
                5.715007195447234e-07,
                1.275190124842887e-07,
                2.699576809143613e-07,
                1.994729483705484e-06,
                1.855391239544352e-07,
                1.6373774480479287e-07,
                1.637377448057981e-07,
                4.450848927650143e-07
            ],
            [
                5.043472278280699e-07,
                3.92786340734912e-07,
                9.422447062202052e-07,
                3.9278634073625165e-07,
                7.338213304316717e-07,
                2.382368247909451e-07,
                9.422445938861406e-07,
                6.475945666009864e-07,
                4.450852111135988e-07,
                5.715003107738556e-07
            ],
            [
                7.3382080556433e-07,
                3.9278624708775595e-07,
                6.144174601991196e-06,
                9.422450431989127e-07,
                1.5534971990169383e-06,
                1.6701427817427163e-05,
                1.7603425837791042e-06,
                9.422442569290178e-07,
                1.994729483723626e-06,
                5.04347408197782e-07
            ],
            [
                3.288750633488963e-06,
                7.889263526345123e-06,
                3.7266392839425286e-06,
                1.1478769492893215e-05,
                2.5612812947380135e-06,
                4.222834451292594e-06,
                1.994729008145876e-06,
                3.7266379512857925e-06,
                4.222833947897496e-06,
                1.3709578605729614e-06
            ],
            [
                5.715002426460124e-07,
                1.7603427936183298e-06,
                1.2098652508347793e-06,
                4.4508494582314646e-07,
                1.855391239544352e-07,
                1.8553907971758842e-07,
                3.4663249714451116e-07,
                3.0590237279032884e-07,
                1.5534971989992774e-06,
                2.2603251062270446e-06
            ],
            [
                3.4663262110803996e-07,
                3.2887494574518405e-06,
                2.2603240283888175e-06,
                3.2887478892683997e-06,
                8.315279285351409e-07,
                2.2603234895176927e-06,
                1.3709567165530083e-06,
                7.889263526266196e-06,
                6.475945666051092e-07,
                6.47594566597747e-07
            ],
            [
                1.0129993395088066e-05,
                1.553497199007048e-06,
                1.3709568799879344e-06,
                4.450852641717689e-07,
                6.962253759670401e-06,
                1.5534973842076057e-06,
                2.75356878194421e-05,
                8.315282259089153e-07,
                5.715006514176113e-07,
                3.9278615344267634e-07
            ],
            [
                3.288749849477628e-06,
                3.2887502415438413e-06,
                1.2098656835076114e-06,
                4.785094494019719e-06,
                3.726639284103523e-06,
                1.9947292459347367e-06,
                1.5534973842076057e-06,
                3.726639284103523e-06,
                2.902312677137316e-06,
                6.475947981975644e-07
            ],
            [
                8.31527928532683e-07,
                6.962253760024999e-06,
                6.475947982037486e-07,
                3.4663266243308805e-07,
                2.382370235933104e-07,
                3.288749457469787e-06,
                2.3823685319174098e-07,
                2.5612819054133693e-06,
                1.5534971990126997e-06,
                9.422445939054222e-07
            ],
            [
                7.338208055664991e-07,
                1.0677029973192638e-06,
                3.288750241561788e-06,
                2.9023112931688987e-06,
                1.5534981249291695e-06,
                1.5534979397677313e-06,
                2.3823685319244518e-07,
                1.0129992187658463e-05,
                7.889265407255982e-06,
                4.785093924330255e-06
            ],
            [
                3.466327037539638e-07,
                9.422449308748773e-07,
                1.7603436330179102e-06,
                3.726641061085547e-06,
                9.422444815765128e-07,
                4.4508505193791187e-07,
                1.2098662604192665e-06,
                1.7603425837855082e-06,
                2.561282210729555e-06,
                9.422450431860582e-07
            ],
            [
                1.012999581021488e-05,
                2.7535704231043113e-05,
                2.5612828213690224e-06,
                1.067702742726318e-06,
                1.7603438428460541e-06,
                7.338209805090567e-07,
                1.5534971989696065e-06,
                1.7603438428460541e-06,
                3.726638395611981e-06,
                1.9947301970451086e-06
            ],
            [
                2.5612812947240366e-06,
                1.7603430034655858e-06,
                1.9947304348332037e-06,
                3.059022998576899e-07,
                1.8925145985895816e-05,
                8.31528424151477e-07,
                2.5612834320214477e-06,
                1.012999460278499e-05,
                5.422218969818919e-06,
                4.785096776499213e-06
            ],
            [
                7.338210680002898e-07,
                1.2098655392871682e-06,
                1.7603436330259153e-06,
                2.5612816000646084e-06,
                1.7603436330179102e-06,
                2.9023116391675407e-06,
                2.561283432035425e-06,
                1.7603425837855082e-06,
                NaN,
                1.9947299593014888e-06
            ],
            [
                2.4300243630653244e-05,
                1.55349775456958e-06,
                3.288749849498565e-06,
                2.260325375634003e-06,
                3.2887498494282754e-06,
                2.2603237589542675e-06,
                5.422221555340727e-06,
                2.260324567302214e-06,
                6.962253759752719e-06,
                3.726640172503764e-06
            ],
            [
                5.422220908876325e-06,
                2.902313023101807e-06,
                8.315284241560147e-07,
                5.4222209089700225e-06,
                2.260324028372372e-06,
                5.04347528440776e-07,
                1.2098656835076114e-06,
                2.561281600049467e-06,
                9.422447062202052e-07,
                8.31528424146183e-07
            ],
            [
                3.4663262111182307e-07,
                1.2098656835252174e-06,
                2.3823696679327928e-07,
                9.422442569315887e-07,
                3.4663278639892215e-07,
                3.9278605979534166e-07,
                5.043475885696228e-07,
                NaN,
                1.0677028700422047e-06,
                3.4663249714612693e-07
            ],
            [
                3.4663266243111764e-07,
                7.338208055664991e-07,
                6.475947210046347e-07,
                8.315279285370317e-07,
                9.4224425692559e-07,
                4.450849988798682e-07,
                5.715006514151423e-07,
                1.3709567165530083e-06,
                4.450852111148132e-07,
                3.466326211113502e-07
            ],
            [
                3.0590237279085045e-07,
                5.715007195447234e-07,
                2.1024341622426268e-07,
                7.338211554783522e-07,
                4.222834954607099e-06,
                3.466325797896173e-07,
                5.715004470295662e-07,
                2.6995784182140636e-07,
                5.715003107767143e-07,
                1.7603430034867993e-06
            ],
            [
                1.7603438428800754e-06,
                1.5534984953510149e-06,
                1.5534977545886537e-06,
                1.0677032518814388e-06,
                4.785094494783494e-06,
                3.7266410611296085e-06,
                8.315280276626197e-07,
                1.1478768126057254e-05,
                5.715003789017068e-07,
                6.962254589978262e-06
            ],
            [
                6.825604537781398e-08,
                4.139941002027314e-08,
                1.725781328907039e-08,
                5.04347287955046e-07,
                4.691162683297406e-08,
                2.5110005893648856e-08,
                6.023569884718319e-08,
                1.4449800373118268e-07,
                7.338208930460318e-07,
                3.6534807736504303e-08
            ],
            [
                1.3709573702647743e-06,
                4.785095065204162e-06,
                1.7603425837702984e-06,
                7.338207180864763e-07,
                4.450849458200093e-07,
                7.338209805200689e-07,
                9.422444815765128e-07,
                2.2603237589676295e-06,
                1.994730197090463e-06,
                NaN
            ],
            [
                3.288749457432399e-06,
                3.7266410611296085e-06,
                8.315278294038928e-07,
                4.222834451355964e-06,
                1.7603425837855082e-06,
                1.5534979397394734e-06,
                NaN,
                4.22283394786293e-06,
                1.9947301970587145e-06,
                1.9947297215043796e-06
            ],
            [
                1.7603440527046419e-06,
                8.315278294001114e-07,
                6.962255419728997e-06,
                8.315280276456036e-07,
                1.1478768125911099e-05,
                5.715003107655392e-07,
                2.902311985079115e-06,
                1.0677029972993568e-06,
                7.338211554688417e-07,
                1.7603436329978976e-06
            ],
            [
                6.962255419931625e-06,
                6.144173137126169e-06,
                3.9278605979011705e-07,
                1.855391681891831e-07,
                2.2603251062270446e-06,
                9.931189774187203e-08,
                5.422220262599396e-06,
                NaN,
                5.71500651413193e-07,
                3.059022998569248e-07
            ],
            [
                1.7603427936079236e-06,
                3.726639284103523e-06,
                2.2603237589779086e-06,
                2.26032402841657e-06,
                4.006368741510365e-05,
                5.422217030614265e-06,
                9.422443692555439e-07,
                2.9023116391675407e-06,
                7.484626297142789e-05,
                1.9947292459265734e-06
            ],
            [
                0.9999975938985254,
                0.999999114842965,
                0.999995504817909,
                0.9999996533672963,
                0.9999995549147892,
                0.9997694931815859,
                0.9999843104465936,
                0.9999994956526524,
                0.9999995262096121,
                0.9999998144608098
            ],
            [
                3.9278634073732336e-07,
                2.902312677150514e-06,
                1.209865827752005e-06,
                1.9947304348862686e-06,
                2.902312677104321e-06,
                5.043476486924565e-07,
                1.3709567165617364e-06,
                6.962255419931625e-06,
                4.785095635624897e-06,
                9.422445939054222e-07
            ],
            [
                4.450849458218309e-07,
                1.3007134667070165e-05,
                2.2603234895176927e-06,
                3.726640172503764e-06,
                1.7603440527222532e-06,
                5.422218323399208e-06,
                1.5534981249496567e-06,
                3.2887490653408545e-06,
                6.962257079832313e-06,
                1.0129989772274546e-05
            ],
            [
                1.3709567165579959e-06,
                3.059023727894942e-07,
                6.9622537599680095e-06,
                3.288748281295496e-06,
                4.2228334445370225e-06,
                3.2887486733420804e-06,
                5.422217030747413e-06,
                3.7266401726359486e-06,
                2.2603242978871282e-06,
                4.2228349547223175e-06
            ],
            [
                8.939700566143004e-06,
                3.120191881321371e-05,
                2.2603251060985603e-06,
                4.78509563546605e-06,
                4.4508515805199415e-07,
                1.2098662604192665e-06,
                6.962253759581752e-06,
                3.288747889178668e-06,
                1.0677031245783732e-06,
                1.553498495308628e-06
            ],
            [
                4.4508526417298334e-07,
                1.9947299592570416e-06,
                1.6701427817730953e-05,
                9.422448185534261e-07,
                5.04347528446051e-07,
                1.0677033791612137e-06,
                0.9999986290429584,
                4.450852111148132e-07,
                3.726639728348526e-06,
                1.9947292459265734e-06
            ],
            [
                5.043476486924565e-07,
                4.222833947960866e-06,
                4.785092783454444e-06,
                1.067703124601679e-06,
                1.7603430034867993e-06,
                5.715004470326849e-07,
                3.726639728370556e-06,
                1.6701415872385704e-05,
                4.785092783519724e-06,
                4.785093353940187e-06
            ],
            [
                8.315278294114555e-07,
                8.939695238634211e-06,
                3.7266397283908927e-06,
                7.338209805224048e-07,
                1.5534983101602148e-06,
                1.760343633031919e-06,
                1.760342793638743e-06,
                NaN,
                4.222835458175145e-06,
                5.422220262636381e-06
            ],
            [
                3.059022998576899e-07,
                9.422447062270609e-07,
                3.466327863983311e-07,
                5.04347287955046e-07,
                1.3709567165579959e-06,
                9.422450432014836e-07,
                8.315278294097538e-07,
                2.2603240284371276e-06,
                5.043472278312808e-07,
                3.466326624322211e-07
            ],
            [
                1.2098656835136636e-06,
                5.422218323399208e-06,
                9.422445939032799e-07,
                7.484626286742124e-05,
                1.2098661161927025e-06,
                2.9023116391477434e-06,
                1.2098656835224664e-06,
                1.2098653950656417e-06,
                1.3007123813193233e-05,
                1.760344052714248e-06
            ],
            [
                5.422220909009474e-06,
                8.315284241650899e-07,
                3.7266383955611403e-06,
                1.5534971990126997e-06,
                3.2887498495150166e-06,
                2.2603240284371276e-06,
                3.288748673360027e-06,
                1.2098661162056318e-06,
                1.067703124601679e-06,
                1.3709572068522336e-06
            ],
            [
                2.3823688159237777e-07,
                2.3823688159291947e-07,
                3.4663266243308805e-07,
                1.7603425837903113e-06,
                2.6995784182073116e-07,
                2.6995774527718623e-07,
                1.0677029973219343e-06,
                2.3823693839290317e-07,
                1.444979692800516e-07,
                8.315282259138311e-07
            ],
            [
                2.2603253756874524e-06,
                2.9023126771227976e-06,
                9.422449308748773e-07,
                3.9278615344178325e-07,
                2.69957906184239e-07,
                3.9278634073625165e-07,
                3.726641061109272e-06,
                5.715003788993679e-07,
                8.315277302788957e-07,
                3.927860597945825e-07
            ],
            [
                3.2887490653408545e-06,
                3.288748673319648e-06,
                4.785096776394765e-06,
                2.9023109471689794e-06,
                7.889259764445822e-06,
                1.0129989772412744e-05,
                1.7603432133136672e-06,
                1.7603432132784448e-06,
                1.1478765389222573e-05,
                3.726639728348526e-06
            ],
            [
                1.2098653950656417e-06,
                1.2098662604291696e-06,
                8.315284241597959e-07,
                3.927862939126708e-07,
                2.9023133690637e-06,
                8.939693107288474e-06,
                9.422448185510695e-07,
                1.370957860576702e-06,
                2.5612828213934817e-06,
                5.043472879525233e-07
            ],
            [
                1.3709578605729614e-06,
                2.902313023130843e-06,
                3.92786340734912e-07,
                2.10243290909724e-07,
                3.059022998558814e-07,
                3.4663270375278157e-07,
                2.382368531929327e-07,
                1.209866260432471e-06,
                6.475948753991907e-07,
                2.561283432035425e-06
            ],
            [
                4.785095065204162e-06,
                5.715003107755449e-07,
                2.260325106237323e-06,
                6.475945666051092e-07,
                2.9023119851635836e-06,
                3.9278605979208185e-07,
                4.785095065171522e-06,
                7.338212429582604e-07,
                2.2603245673279107e-06,
                3.7266406168827523e-06
            ],
            [
                2.6995790618252024e-07,
                4.4508505193386385e-07,
                5.715002426460124e-07,
                1.0677024881829577e-06,
                3.05902190458764e-07,
                1.5534979397790343e-06,
                2.561281905376098e-06,
                2.3823685319244518e-07,
                1.0677031245783732e-06,
                6.475951069985296e-07
            ],
            [
                9.422444815726566e-07,
                1.7603440527046419e-06,
                NaN,
                2.561282516042282e-06,
                1.0677031245990084e-06,
                3.7266410611296085e-06,
                2.561282210729555e-06,
                4.785093924362895e-06,
                2.7535704232595768e-05,
                2.9023116392097746e-06
            ],
            [
                0.9999945777829804,
                1.5534975693601474e-06,
                NaN,
                0.9999516743397816,
                0.9999962733598385,
                1.7603438428460541e-06,
                0.9999938558225193,
                0.999994228077257,
                4.006370174344354e-05,
                0.9999892166917537
            ],
            [
                8.315282259051341e-07,
                4.785095065204162e-06,
                2.3823688159291947e-07,
                6.9622595696935874e-06,
                5.715002426475718e-07,
                1.300712381094558e-05,
                1.8925141473599938e-05,
                4.222832941142044e-06,
                6.962254589851619e-06,
                7.889264466725156e-06
            ]
        ]
    },
    {
        "q_id": "9240_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            39,
            40,
            41,
            42,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            115,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                5.715005832886879e-07,
                1.0677028700422047e-06,
                2.1024334103581732e-07,
                5.715003789033962e-07,
                NaN,
                3.4663278639892215e-07,
                2.6995784182140636e-07,
                2.382369951932796e-07,
                1.6373766672973748e-07,
                3.927863407379485e-07
            ],
            [
                0.9999981261248414,
                9.422443692555439e-07,
                1.5534983101644536e-06,
                7.33821330437595e-07,
                5.043475885696228e-07,
                4.785095635655362e-06,
                1.6373764721072816e-07,
                5.4222176771176554e-06,
                7.889266347786918e-06,
                0.9999798542996431
            ],
            [
                1.637377057680051e-07,
                0.9999957771645479,
                3.466325797896173e-07,
                1.1253524254650944e-07,
                0.9999981261243946,
                0.9999994631248043,
                0.9999989322973851,
                5.043472879540142e-07,
                0.9999987121049387,
                3.0590237279085045e-07
            ],
            [
                9.422448185534261e-07,
                2.6995790618350237e-07,
                4.450850519403407e-07,
                2.1024341622297196e-07,
                2.6995790618350237e-07,
                1.3709576971463352e-06,
                2.3823699519225038e-07,
                1.8553903548231313e-07,
                3.059023727894942e-07,
                4.4508510499849186e-07
            ],
            [
                3.4663253846718004e-07,
                6.023574911170301e-08,
                8.939699501229642e-06,
                1.6373770576776313e-07,
                2.6995784182140636e-07,
                9.93120161310289e-08,
                9.931193325852072e-08,
                1.2751907329024393e-07,
                5.315784971839039e-08,
                1.4449798650476187e-07
            ],
            [
                1.0677024881980089e-06,
                1.760343423160973e-06,
                2.6995774527718623e-07,
                1.855391239544352e-07,
                6.475947210046347e-07,
                1.5534979397740895e-06,
                1.7603425837606927e-06,
                1.0677024881980089e-06,
                6.475945666051092e-07,
                1.6373766672973748e-07
            ],
            [
                1.0677029973158649e-06,
                1.444979692800516e-07,
                1.2098656835224664e-06,
                1.2098652508424818e-06,
                3.927862470899887e-07,
                1.6373764721072816e-07,
                7.3382080556433e-07,
                7.338213304363436e-07,
                9.931189774187203e-08,
                3.927862002663297e-07
            ],
            [
                1.6373770576776313e-07,
                1.8553907971855875e-07,
                2.3823693839325527e-07,
                1.6373776432509826e-07,
                1.4449807263287805e-07,
                3.059021904580685e-07,
                5.715007195384861e-07,
                6.475949526020042e-07,
                5.043476486915964e-07,
                5.715003789033962e-07
            ],
            [
                0.9999990577557439,
                0.9999997617630049,
                8.76424013786396e-08,
                0.9999997761970782,
                0.9999975938973773,
                3.224186633297071e-08,
                6.825604537781398e-08,
                2.3823682479292225e-07,
                0.9999992188514837,
                6.825601283086733e-08
            ],
            [
                5.422221555380179e-06,
                9.422449308716635e-07,
                1.7603430034867993e-06,
                1.7603427936263351e-06,
                4.450852641737424e-07,
                8.315283250371857e-07,
                5.422220262599396e-06,
                7.484620944504663e-05,
                1.5534975693979422e-06,
                1.553497754577351e-06
            ],
            [
                1.0677032518814388e-06,
                1.0677029973219343e-06,
                4.222833444590791e-06,
                2.5612819054133693e-06,
                1.5534984953453635e-06,
                9.422445939032799e-07,
                1.1478772231232203e-05,
                3.927863407379485e-07,
                5.043474683240344e-07,
                4.785093353940187e-06
            ],
            [
                1.275190732904469e-07,
                8.764244316973974e-08,
                1.275190732904469e-07,
                9.931189774187203e-08,
                NaN,
                7.338207180884785e-07,
                1.1253509497883659e-07,
                1.444980209564556e-07,
                6.825600469412533e-08,
                1.8553916819032217e-07
            ],
            [
                5.715004470295662e-07,
                3.7266410611296085e-06,
                2.902312677060767e-06,
                3.2887502415438413e-06,
                4.450848927650143e-07,
                8.315283250371857e-07,
                5.715003789033962e-07,
                3.466327037539638e-07,
                4.785093353874907e-06,
                7.338209805200689e-07
            ],
            [
                1.8553903548231313e-07,
                1.8553905760062447e-07,
                1.6373776432509826e-07,
                9.931185038635267e-08,
                2.9023112932177327e-06,
                9.422450431989127e-07,
                8.939694172867777e-06,
                6.023573475041126e-08,
                7.734416698849138e-08,
                1.637376862489725e-07
            ],
            [
                1.7603440527222532e-06,
                5.4222183234485234e-06,
                1.4449798650551755e-07,
                1.0677027427600627e-06,
                2.1024339116082313e-07,
                1.0677032518785256e-06,
                5.04347528446051e-07,
                3.0590215398968196e-07,
                9.422450431989127e-07,
                3.927862939126708e-07
            ],
            [
                5.3157837044597743e-08,
                NaN,
                6.023568448589658e-08,
                NaN,
                8.764242227418718e-08,
                NaN,
                4.450850519403407e-07,
                9.931190958076104e-08,
                7.734418542875216e-08,
                7.734416698849138e-08
            ],
            [
                2.6995790618469934e-07,
                1.637377057680051e-07,
                8.315277302788957e-07,
                8.315282259138311e-07,
                1.0677032518814388e-06,
                8.315282259138311e-07,
                1.9947301970972664e-06,
                9.422442569315887e-07,
                3.4663249714612693e-07,
                1.2098661162056318e-06
            ],
            [
                2.902312331170226e-06,
                1.994729721518893e-06,
                9.422447062294175e-07,
                0.9999970976873256,
                2.561283126728994e-06,
                3.466327037553825e-07,
                1.2098659719788098e-06,
                3.05902263391829e-07,
                0.9999646437410037,
                9.422443692574719e-07
            ],
            [
                2.5612834320563895e-06,
                1.8925157266089433e-05,
                0.00020342692526097766,
                1.2098656835224664e-06,
                NaN,
                1.0677031245990084e-06,
                1.4738985486506781e-05,
                5.715007195410849e-07,
                2.9023112932177327e-06,
                1.0677028700320085e-06
            ],
            [
                1.8553905760062447e-07,
                2.3823690999323465e-07,
                3.05902190458764e-07,
                7.734418542875216e-08,
                6.475947982037486e-07,
                1.2751905808881762e-07,
                8.764245361752286e-08,
                2.10243290909724e-07,
                1.275190580890061e-07,
                1.8553910183674878e-07
            ],
            [
                4.4508510499849186e-07,
                3.927862470905692e-07,
                1.5534971990169383e-06,
                3.059021539909339e-07,
                5.04347287955046e-07,
                1.1253509497883659e-07,
                3.9278610661902853e-07,
                1.855391681906175e-07,
                8.764245361752286e-08,
                9.931190958076104e-08
            ],
            [
                0.999997739675166,
                0.9999964991439216,
                1.2751899728286965e-07,
                0.9999992188514835,
                0.9999989322975128,
                0.9999980052702802,
                7.734423152941018e-08,
                0.9999986290432846,
                0.9999984465024329,
                0.9999967112501551
            ],
            [
                1.4449803818215767e-07,
                2.102434412875379e-07,
                1.6373766672973748e-07,
                1.2098658277489788e-06,
                8.315284241650899e-07,
                1.275190580890061e-07,
                5.04347468323289e-07,
                5.715003107767143e-07,
                3.059022998581767e-07,
                5.715003789046955e-07
            ],
            [
                3.466325797896173e-07,
                6.475950298011458e-07,
                3.466327863983311e-07,
                5.422218969895357e-06,
                1.2098662604291696e-06,
                1.2098659719757836e-06,
                1.7603438428800754e-06,
                8.315283250371857e-07,
                2.102434412875379e-07,
                1.4449803818215767e-07
            ],
            [
                1.0677027427600627e-06,
                1.8553907971855875e-07,
                7.338213304363436e-07,
                4.785095065232451e-06,
                3.288749457469787e-06,
                1.5534975693979422e-06,
                1.3709567165617364e-06,
                2.2603242978871282e-06,
                1.3709573702856596e-06,
                3.288750241561788e-06
            ],
            [
                1.6373762769138607e-07,
                2.5612812947508257e-06,
                1.275190124846946e-07,
                3.059021175261338e-07,
                7.338208055664991e-07,
                2.382368531929327e-07,
                3.927862939126708e-07,
                3.927862939126708e-07,
                3.4663274507098256e-07,
                3.927862470905692e-07
            ],
            [
                4.2228334445658276e-06,
                3.7266406168827523e-06,
                1.2098662604247682e-06,
                1.1478766757718129e-05,
                NaN,
                2.5612816000646084e-06,
                8.93969950132721e-06,
                8.939696304116203e-06,
                0.00010889693531733128,
                1.3007125363908762e-05
            ],
            [
                4.785092783519724e-06,
                4.450850519403407e-07,
                3.726637951387472e-06,
                3.288748673360027e-06,
                1.2098652508347793e-06,
                NaN,
                1.9947301970972664e-06,
                NaN,
                1.3709572068522336e-06,
                1.7603427936263351e-06
            ],
            [
                1.8553905760062447e-07,
                2.6995784182140636e-07,
                7.338208930460318e-07,
                1.8553903548231313e-07,
                9.931190958076104e-08,
                8.315281267882195e-07,
                1.3709572068522336e-06,
                3.466327037553825e-07,
                2.3823696679327928e-07,
                7.338208055664991e-07
            ],
            [
                1.6373766672888118e-07,
                5.04347468318358e-07,
                1.7603438428740716e-06,
                6.475950297971703e-07,
                4.4508526417298334e-07,
                4.222834954778007e-06,
                1.0677026154806063e-06,
                1.0677031245990084e-06,
                1.2098662604291696e-06,
                1.8925155009767892e-05
            ],
            [
                6.475945666051092e-07,
                9.422450431989127e-07,
                2.69957906184239e-07,
                1.760342793638743e-06,
                3.0590226339061185e-07,
                3.288750241561788e-06,
                7.338209805224048e-07,
                9.931193325852072e-08,
                1.760343423160973e-06,
                8.315279285351409e-07
            ],
            [
                6.023569884718319e-08,
                1.1253518888531272e-07,
                0.9999975938965162,
                0.999994906295618,
                1.1253518888531272e-07,
                1.4449805540740185e-07,
                6.023572038912295e-08,
                6.023571320847322e-08,
                9.931190958076104e-08,
                6.023574911170301e-08
            ],
            [
                7.889263526345123e-06,
                1.7603438428740716e-06,
                1.067703251864202e-06,
                6.475949526020042e-07,
                1.0677024882009222e-06,
                3.7266401726359486e-06,
                1.4738980215352592e-05,
                2.5612819054133693e-06,
                2.9023112932177327e-06,
                3.288749849498565e-06
            ],
            [
                0.9999972735287628,
                2.6995784182183607e-07,
                8.315280276626197e-07,
                0.999994577778472,
                0.9999869928715752,
                0.9999955048189803,
                1.5534975693979422e-06,
                0.9999921107365107,
                0.9999741325631464,
                6.475947210046347e-07
            ],
            [
                7.73442776303243e-08,
                1.1253518888531272e-07,
                8.764241182641775e-08,
                1.4449807263325588e-07,
                1.6373766672973748e-07,
                1.4449805540763184e-07,
                5.04347528446051e-07,
                2.2603248367949354e-06,
                1.4449800373118268e-07,
                7.734416698849138e-08
            ],
            [
                0.9999898700102391,
                0.9999980052702813,
                0.9999960330150345,
                0.999997273529406,
                3.72663883989755e-06,
                7.338209805240734e-07,
                1.855391239539711e-07,
                0.9999930377462478,
                NaN,
                0.9999952149049387
            ],
            [
                8.315277302857965e-07,
                3.9278629391427843e-07,
                2.5612819054133693e-06,
                NaN,
                1.0677029973219343e-06,
                6.47595107001401e-07,
                1.855391681906175e-07,
                1.0677032518814388e-06,
                NaN,
                4.4508526417298334e-07
            ],
            [
                3.059022269250683e-07,
                1.1253512180925583e-07,
                6.023569884718319e-08,
                5.043476486915964e-07,
                2.3823688159291947e-07,
                1.9947301970972664e-06,
                1.444979692800516e-07,
                2.1024326584639497e-07,
                1.4449798650551755e-07,
                1.2751905808881762e-07
            ],
            [
                5.04347287955046e-07,
                7.734416698849138e-08,
                1.0,
                8.764245361752286e-08,
                2.5612819054028872e-06,
                0.9999997617629766,
                0.9999984465016915,
                0.999997438717792,
                5.3157837044597743e-08,
                4.691161005609407e-08
            ],
            [
                3.0590237279085045e-07,
                5.315781803390236e-08,
                9.93120161310289e-08,
                0.999993855827603,
                9.422443692574719e-07,
                0.9999986290423037,
                0.999996273358942,
                3.4663262111182307e-07,
                3.0590219045914655e-07,
                0.9999970976883629
            ],
            [
                5.715006514167015e-07,
                5.715003107755449e-07,
                3.46632497145457e-07,
                8.315281267800897e-07,
                2.3823685319244518e-07,
                7.889261645427538e-06,
                6.475949526020042e-07,
                2.2603242978871282e-06,
                8.315279285351409e-07,
                3.466327450756327e-07
            ],
            [
                6.475947210046347e-07,
                1.7603432133296774e-06,
                1.5534983101602148e-06,
                6.144175334468545e-06,
                2.2603253756956754e-06,
                2.6995774527718623e-07,
                1.9947292459347367e-06,
                5.422221555380179e-06,
                6.475945666051092e-07,
                2.1024339116168358e-07
            ],
            [
                NaN,
                1.0677024881829577e-06,
                4.450849988811838e-07,
                1.0677028700363782e-06,
                4.4508526417014975e-07,
                9.422444815765128e-07,
                1.7603425837702984e-06,
                9.422448185388577e-07,
                1.473898900066424e-05,
                7.338212429537553e-07
            ],
            [
                1.9947297215125433e-06,
                5.043474082012222e-07,
                7.338208930460318e-07,
                2.6995774527718623e-07,
                2.699576809143613e-07,
                8.764244316973974e-08,
                2.699576809143613e-07,
                9.931189774187203e-08,
                1.6373762769187936e-07,
                1.855391239544352e-07
            ],
            [
                3.0590219045914655e-07,
                7.889259764517575e-06,
                1.5534979397829198e-06,
                NaN,
                6.475950298021765e-07,
                3.0590215399281185e-07,
                NaN,
                5.3157811697009444e-08,
                NaN,
                7.338211554813555e-07
            ],
            [
                1.4449805540763184e-07,
                6.475946438022905e-07,
                8.764253720001207e-08,
                1.4449805540763184e-07,
                2.1024336609874897e-07,
                8.76424013786396e-08,
                6.023568448589658e-08,
                5.04347528446051e-07,
                2.1024334103581732e-07,
                NaN
            ],
            [
                8.764247451307293e-08,
                3.46632497145457e-07,
                2.10243290909724e-07,
                1.4449798650551755e-07,
                1.1253512180925583e-07,
                7.734423152941018e-08,
                9.931187406410953e-08,
                1.8553919030776337e-07,
                3.9278634073732336e-07,
                2.1024341622426268e-07
            ],
            [
                5.043472278322555e-07,
                0.9999983463096269,
                1.4449798650551755e-07,
                5.715006514167015e-07,
                5.043475885696228e-07,
                1.5534979397790343e-06,
                6.475948754028718e-07,
                3.059022998569248e-07,
                3.4663278639892215e-07,
                5.715006514167015e-07
            ],
            [
                1.6373770576776313e-07,
                2.10243290909724e-07,
                8.315277302841894e-07,
                1.8553919030858602e-07,
                2.1444950970119003e-05,
                6.475945666033422e-07,
                1.27519088491875e-07,
                1.4738987242968784e-05,
                2.10243290909724e-07,
                5.422218969858371e-06
            ],
            [
                9.931187406410953e-08,
                6.825601283086733e-08,
                1.1253516205489029e-07,
                6.023573475041126e-08,
                1.1253516205489029e-07,
                1.637377448057981e-07,
                1.4449798650551755e-07,
                5.3157837044597743e-08,
                2.1024344128660572e-07,
                1.4449805540740185e-07
            ],
            [
                8.764244316973974e-08,
                1.3709572068522336e-06,
                2.699577774585891e-07,
                9.931186222523604e-08,
                2.1024341622426268e-07,
                5.043473480777865e-07,
                1.1253509497883659e-07,
                5.422219616228845e-06,
                5.04347468323289e-07,
                1.1253518888531272e-07
            ],
            [
                0.9999910603047819,
                3.059022269250683e-07,
                0.9999998257021422,
                1.5534975693979422e-06,
                2.1024331597262577e-07,
                7.338212429582604e-07,
                0.9999996072138935,
                0.9999869928700058,
                0.9999970976880191,
                1.8553910183674878e-07
            ],
            [
                6.475945666051092e-07,
                9.422450432014836e-07,
                1.2098661162056318e-06,
                1.2098653950656417e-06,
                NaN,
                3.466326211113502e-07,
                1.1253509497883659e-07,
                9.422450432014836e-07,
                1.6373764721072816e-07,
                NaN
            ],
            [
                3.4663274507713016e-07,
                5.715006514176113e-07,
                NaN,
                1.0677028700422047e-06,
                4.691160446380562e-08,
                4.4508515805735777e-07,
                3.9278605979534166e-07,
                5.04347468323289e-07,
                1.1253525596174225e-07,
                1.8553905760062447e-07
            ],
            [
                3.288750241561788e-06,
                1.0129995810463632e-05,
                1.6373770576776313e-07,
                1.9947299593014888e-06,
                1.637377448057981e-07,
                2.561283432035425e-06,
                NaN,
                1.6373766672973748e-07,
                6.475947210031623e-07,
                6.144172404587612e-06
            ],
            [
                4.139941495546278e-08,
                6.023578501513224e-08,
                5.315789407685159e-08,
                6.825598842065202e-08,
                2.8453371023563735e-08,
                7.734425919002834e-08,
                6.023572038912295e-08,
                9.422444815726566e-07,
                8.7642558095602e-08,
                3.653479031538012e-08
            ],
            [
                1.2098653950692178e-06,
                0.9999964991460067,
                7.734416698849138e-08,
                1.8553903548231313e-07,
                4.450848927650143e-07,
                6.825609419848033e-08,
                2.1024331597288867e-07,
                5.715002426486762e-07,
                3.927862470899887e-07,
                8.764254764780641e-08
            ],
            [
                2.2603248367949354e-06,
                5.422217677152175e-06,
                4.785092783519724e-06,
                4.53978632394714e-05,
                1.5534981249697903e-06,
                1.9947299593078385e-06,
                1.7603432133296774e-06,
                6.1441746020359e-06,
                1.5534975693933505e-06,
                2.1444950971601277e-05
            ],
            [
                2.902312677137316e-06,
                2.561282210740037e-06,
                NaN,
                5.4222183235249605e-06,
                2.1024331597262577e-07,
                9.422443692555439e-07,
                5.043476486924565e-07,
                1.5534975693933505e-06,
                3.927860597945825e-07,
                5.715002426486762e-07
            ],
            [
                2.1024334103581732e-07,
                2.699576809143613e-07,
                6.023579219579052e-08,
                NaN,
                NaN,
                NaN,
                7.338210680021253e-07,
                1.147877359957198e-05,
                3.726639284144195e-06,
                1.0677032518814388e-06
            ],
            [
                2.102434412875379e-07,
                0.9999938558276013,
                4.450852641737424e-07,
                0.9999987901347496,
                6.475950298021765e-07,
                1.209865827752005e-06,
                1.012998977264307e-05,
                5.715006514176113e-07,
                7.73442776303243e-08,
                2.6995784182183607e-07
            ],
            [
                0.9999996533673791,
                3.2241847115356483e-08,
                6.825598842065202e-08,
                0.9999995549148952,
                0.9999989969861517,
                0.999993037745427,
                0.9999994631251242,
                0.999999894283061,
                0.9999997463981334,
                7.734415776836702e-08
            ],
            [
                3.9278610661902853e-07,
                1.2751908849167202e-07,
                7.734416698849138e-08,
                2.260324028427877e-06,
                1.1253521571574156e-07,
                2.7535680059658692e-05,
                6.825601283086733e-08,
                1.8553916819032217e-07,
                1.2098662604291696e-06,
                6.962258739796719e-06
            ],
            [
                1.2751907329024393e-07,
                1.2751899728311609e-07,
                2.699576809143613e-07,
                3.9278605979534166e-07,
                2.3823682479181176e-07,
                2.6995768091310296e-07,
                2.102434412871794e-07,
                3.059022998569248e-07,
                5.04347348075149e-07,
                2.1024341622426268e-07
            ],
            [
                4.4508510499849186e-07,
                5.043474082005342e-07,
                4.691160446380562e-08,
                4.691161005609407e-08,
                5.315781803390236e-08,
                1.444980209564556e-07,
                1.2098659719757836e-06,
                6.023572038912295e-08,
                1.2751902768612997e-07,
                5.043473480777865e-07
            ],
            [
                4.22283545819819e-06,
                2.1024326584639497e-07,
                1.067703124601679e-06,
                4.785095065232451e-06,
                4.785096206076165e-06,
                2.2603242978871282e-06,
                4.4508510499849186e-07,
                5.715005151606823e-07,
                3.0590237279085045e-07,
                1.5534981249697903e-06
            ],
            [
                3.466326624336003e-07,
                5.715005832886879e-07,
                8.939694172957213e-06,
                7.338209805240734e-07,
                1.760342793638743e-06,
                7.338209805240734e-07,
                0.999996033013143,
                4.22283545819819e-06,
                3.7266397283908927e-06,
                1.444980209564556e-07
            ],
            [
                6.1441767993788005e-06,
                4.78509278348926e-06,
                2.561281294760143e-06,
                1.067703124601679e-06,
                2.260323758987159e-06,
                2.753568453792444e-05,
                1.2098661162056318e-06,
                1.760342793638743e-06,
                2.3823693839290317e-07,
                2.2603242978943238e-06
            ],
            [
                4.2228339479858295e-06,
                9.422443692574719e-07,
                1.2751902768612997e-07,
                5.043473480777865e-07,
                1.5534983101644536e-06,
                0.9999964991439194,
                1.209865539298447e-06,
                2.90231233114251e-06,
                0.9999982396565777,
                0.9999978766205276
            ],
            [
                1.0677033791495609e-06,
                9.422445939032799e-07,
                9.931193325852072e-08,
                1.2098658277451275e-06,
                8.315278294072958e-07,
                1.444980209564556e-07,
                1.27519088491875e-07,
                7.889260704818233e-06,
                1.2751907329024393e-07,
                1.7603436330179102e-06
            ],
            [
                2.1024339116168358e-07,
                1.2751902768612997e-07,
                1.6373774480605869e-07,
                0.9999999067050276,
                0.99999921885167,
                1.637376862489725e-07,
                0.9999997761971315,
                2.102434162245973e-07,
                1.1253512180925583e-07,
                2.1024336609874897e-07
            ],
            [
                2.699578740032504e-07,
                2.3823685319320354e-07,
                3.466325797896173e-07,
                1.4449798650569826e-07,
                1.4449798650569826e-07,
                5.043472278322555e-07,
                1.4738976701652988e-05,
                6.475948754012522e-07,
                5.422218323487975e-06,
                1.1478769494542698e-05
            ],
            [
                1.637377057680051e-07,
                3.9278629391427843e-07,
                3.466325797900508e-07,
                1.2751899728286965e-07,
                5.04347287955046e-07,
                1.1253508156363576e-07,
                9.931186222482958e-08,
                3.4663257978465195e-07,
                9.422445939032799e-07,
                5.715003107755449e-07
            ],
            [
                2.2603242978871282e-06,
                1.892515501014656e-05,
                5.71500719545698e-07,
                1.0677027427600627e-06,
                1.5534975693933505e-06,
                5.043475885696228e-07,
                3.05902336324494e-07,
                5.829128640005915e-05,
                8.315278294114555e-07,
                2.699576809143613e-07
            ],
            [
                8.315277302857965e-07,
                2.561282210740037e-06,
                1.5534984953510149e-06,
                8.939699501416646e-06,
                2.3823693839325527e-07,
                1.855391239544352e-07,
                3.2887506336235617e-06,
                1.5534973842076057e-06,
                4.450850519403407e-07,
                7.338209805240734e-07
            ],
            [
                3.726638839878908e-06,
                7.338211554801876e-07,
                0.9999969105055584,
                0.9999877809254648,
                1.8553919030776337e-07,
                0.9999945777797455,
                2.6995771309523475e-07,
                NaN,
                2.3823688159291947e-07,
                3.0590237279032884e-07
            ],
            [
                1.3709568799879344e-06,
                6.144176799099397e-06,
                2.3823682479292225e-07,
                3.653479467066246e-08,
                6.825597214718257e-08,
                7.338212429582604e-07,
                2.102434412875379e-07,
                1.6373774480605869e-07,
                1.6373768624837685e-07,
                2.3823702359290413e-07
            ],
            [
                1.3709576971463352e-06,
                9.422443692555439e-07,
                6.023579219579052e-08,
                6.475947210046347e-07,
                8.764247451307293e-08,
                NaN,
                7.338209805224048e-07,
                2.699577130957872e-07,
                NaN,
                2.215950249040774e-08
            ],
            [
                8.315279285370317e-07,
                2.699576809143613e-07,
                3.4663262111182307e-07,
                6.475950298021765e-07,
                3.927863407379485e-07,
                4.139940508508409e-08,
                1.3709576971463352e-06,
                NaN,
                3.653484693415755e-08,
                8.315277302819205e-07
            ],
            [
                5.715003107715166e-07,
                3.4663253846718004e-07,
                2.5612812947380135e-06,
                1.6373770576776313e-07,
                2.3823693839290317e-07,
                3.466325797888292e-07,
                2.382370235933104e-07,
                1.0677027427600627e-06,
                1.0129987357407137e-05,
                3.466327037539638e-07
            ],
            [
                3.224189323773857e-08,
                NaN,
                8.764241182641775e-08,
                6.023571320847322e-08,
                4.139939521459479e-08,
                3.653479031538012e-08,
                9.931196877517082e-08,
                5.3157811697009444e-08,
                1.1253521571574156e-07,
                6.825600469412533e-08
            ],
            [
                3.726639728348526e-06,
                1.7603438428800754e-06,
                1.0677028700266676e-06,
                5.71500515159253e-07,
                9.422443692555439e-07,
                9.422448185510695e-07,
                5.043472879540142e-07,
                1.994729483705484e-06,
                2.6995768091310296e-07,
                6.475945666033422e-07
            ],
            [
                4.691168275606451e-08,
                NaN,
                9.422449308716635e-07,
                1.6373766672994222e-07,
                3.05902336324494e-07,
                0.9999975938970875,
                1.2751902768612997e-07,
                6.962257079832313e-06,
                3.224188555067886e-08,
                7.73442776303243e-08
            ],
            [
                1.3709567165579959e-06,
                3.05902190458764e-07,
                9.931186222523604e-08,
                5.715007195447234e-07,
                4.4508510499849186e-07,
                8.315281267882195e-07,
                5.043476486915964e-07,
                1.067702870039777e-06,
                1.3709572068422585e-06,
                2.102434162245973e-07
            ],
            [
                9.931195693628605e-08,
                1.8553905760024476e-07,
                1.637377448057981e-07,
                3.059021175255426e-07,
                1.2098659719757836e-06,
                2.1024334103581732e-07,
                3.9278615344267634e-07,
                1.5534979397790343e-06,
                8.764245361752286e-08,
                2.1024334103553052e-07
            ],
            [
                5.04347528446051e-07,
                4.4508499888219586e-07,
                1.012999218776902e-05,
                3.927862002663297e-07,
                1.067703124601679e-06,
                9.931200429212718e-08,
                1.2098662604291696e-06,
                0.999999730042287,
                5.043472278312808e-07,
                8.764242227418718e-08
            ],
            [
                1.0129995810343862e-05,
                5.043476486902204e-07,
                1.2751901248454963e-07,
                0.9999994631248683,
                0.9999998024946801,
                0.9999978766217934,
                0.9999974387168757,
                0.9999972735290815,
                3.653485128944664e-08,
                6.023573475041126e-08
            ],
            [
                8.315279285370317e-07,
                5.715005151606823e-07,
                0.9999997300422871,
                1.4449805540763184e-07,
                9.422443692574719e-07,
                2.102434162245973e-07,
                1.209865827752005e-06,
                6.47595107001401e-07,
                6.475946438055299e-07,
                3.05902336324494e-07
            ],
            [
                2.102433410343832e-07,
                0.9999934595620041,
                0.9999998144609425,
                0.9999995818812272,
                0.9999938558224767,
                0.999999802494633,
                4.4508526417298334e-07,
                0.9999988634361546,
                0.9999916019309835,
                0.9999999176674456
            ],
            [
                1.209865539295696e-06,
                6.023569884718319e-08,
                8.315281267861397e-07,
                3.927863407379485e-07,
                3.4663249714612693e-07,
                8.315281267882195e-07,
                3.059021904580685e-07,
                6.825597214718257e-08,
                2.10243290909724e-07,
                7.734416698849138e-08
            ],
            [
                6.47595107001401e-07,
                2.4300237837960777e-05,
                1.0677027427600627e-06,
                5.043475284468537e-07,
                0.9999810748607565,
                1.6373776432509826e-07,
                8.939697369980456e-06,
                1.9947304348862686e-06,
                6.47595107001401e-07,
                1.994729721518893e-06
            ],
            [
                1.3709576971463352e-06,
                5.71500719545698e-07,
                4.785095065232451e-06,
                0.9999984465020624,
                2.561282210740037e-06,
                7.338208055680009e-07,
                1.670142383595838e-05,
                6.475947210046347e-07,
                9.422444815814404e-07,
                3.059022998581767e-07
            ],
            [
                1.6373764721072816e-07,
                1.6373764721091427e-07,
                5.043474683240344e-07,
                2.3823690999323465e-07,
                2.10243290909963e-07,
                5.715002426475718e-07,
                4.4508499888275247e-07,
                1.855391681906175e-07,
                1.4449800373118268e-07,
                3.9278629391427843e-07
            ],
            [
                9.422444815765128e-07,
                3.2887482813149375e-06,
                1.8553916819032217e-07,
                1.0677032518785256e-06,
                1.9947292459347367e-06,
                1.8553903548231313e-07,
                1.0677029973192638e-06,
                NaN,
                1.3709573702822306e-06,
                2.2603253756956754e-06
            ],
            [
                1.27519088491875e-07,
                6.825600469412533e-08,
                8.764244316973974e-08,
                5.715003107767143e-07,
                1.4449800373118268e-07,
                9.931189774187203e-08,
                7.734423152941018e-08,
                9.931202796993203e-08,
                9.931186222523604e-08,
                6.023571320847322e-08
            ],
            [
                2.699577774585891e-07,
                1.7603434231705793e-06,
                3.059022998576899e-07,
                5.043473480777865e-07,
                1.6373768624837685e-07,
                NaN,
                7.338212429582604e-07,
                2.1024331597152624e-07,
                5.715007195447234e-07,
                7.338210680021253e-07
            ],
            [
                4.222831934321543e-06,
                1.0677026154730804e-06,
                3.466327037539638e-07,
                1.7603425837903113e-06,
                1.2098652508424818e-06,
                1.5534984953453635e-06,
                3.4663253846718004e-07,
                5.715002426439334e-07,
                5.043473480766399e-07,
                5.71500651413193e-07
            ],
            [
                4.450848927650143e-07,
                1.855391681898159e-07,
                9.422444815792981e-07,
                3.927862470899887e-07,
                9.931198061405701e-08,
                5.043475885674441e-07,
                8.315278294114555e-07,
                6.475949526020042e-07,
                2.6995771309523475e-07,
                1.8553916819032217e-07
            ],
            [
                8.315281267834927e-07,
                1.2098658277451275e-06,
                1.7603430034655858e-06,
                5.043472879540142e-07,
                2.9023126771227976e-06,
                3.4663257978638593e-07,
                1.760343213322473e-06,
                1.2098662604247682e-06,
                1.5534973842030142e-06,
                5.043472278280699e-07
            ],
            [
                0.9999988634362903,
                1.275190428875671e-07,
                4.450848927658745e-07,
                6.82560779249779e-08,
                9.422443692574719e-07,
                1.6373766672973748e-07,
                5.715003789046955e-07,
                8.315279285370317e-07,
                3.224186633297071e-08,
                3.927863407379485e-07
            ],
            [
                1.5534975693979422e-06,
                6.475950298011458e-07,
                1.3709568799919866e-06,
                0.9999832985821908,
                1.9947301970972664e-06,
                2.2603253756956754e-06,
                1.6373766672994222e-07,
                0.9999991148427534,
                9.931202796993203e-08,
                1.1253526937697666e-07
            ],
            [
                3.05902117523595e-07,
                3.288747889284851e-06,
                5.715004470272272e-07,
                2.2603237589779086e-06,
                4.785095635655362e-06,
                3.466327037548308e-07,
                NaN,
                9.422445939054222e-07,
                2.5612828213934817e-06,
                7.338209805240734e-07
            ],
            [
                1.1253516205489029e-07,
                1.2751902768612997e-07,
                3.4663278639892215e-07,
                1.6373770576776313e-07,
                1.8553907971855875e-07,
                5.715004470295662e-07,
                2.10243290909724e-07,
                1.637377448057981e-07,
                NaN,
                1.1253512180925583e-07
            ],
            [
                2.6995784182140636e-07,
                3.059022998576899e-07,
                2.102434412875379e-07,
                0.9999988634362909,
                6.475950298011458e-07,
                3.059021904580685e-07,
                2.6995784182140636e-07,
                3.466327037539638e-07,
                0.9999985406234323,
                6.475946438055299e-07
            ],
            [
                3.466325797896173e-07,
                6.962257909785973e-06,
                3.05902336324494e-07,
                6.1441731370702875e-06,
                3.059022998576899e-07,
                3.4663266243308805e-07,
                4.450852111155216e-07,
                1.8553919030858602e-07,
                9.931187406410953e-08,
                1.8553905760062447e-07
            ],
            [
                1.3709573702822306e-06,
                5.422218969858371e-06,
                5.043473480777865e-07,
                2.3823702359290413e-07,
                6.475949526020042e-07,
                6.475947210046347e-07,
                4.4508499888219586e-07,
                5.715003107767143e-07,
                1.0677024881941248e-06,
                5.04347528446051e-07
            ],
            [
                1.1253516205489029e-07,
                9.931189774187203e-08,
                5.715003107755449e-07,
                1.1253513522447425e-07,
                5.422220909009474e-06,
                8.764249540862797e-08,
                1.2751905808881762e-07,
                3.927862002663297e-07,
                2.10243290909724e-07,
                8.764242227418718e-08
            ],
            [
                0.9999996940977732,
                1.1253513522447425e-07,
                7.734416698849138e-08,
                4.450851580566494e-07,
                0.9999997761971315,
                0.9999980052695674,
                0.9999994956527122,
                0.9999997126313441,
                6.475948754028718e-07,
                0.9999964991439203
            ],
            [
                5.043473480766399e-07,
                1.7603440527286572e-06,
                1.6373764721072816e-07,
                8.315280276626197e-07,
                1.994729721518893e-06,
                1.637377448057981e-07,
                1.5534975693979422e-06,
                1.9947301970972664e-06,
                7.889265407090955e-06,
                7.338208930460318e-07
            ],
            [
                8.764247451307293e-08,
                1.637377057673536e-07,
                5.315787506598473e-08,
                6.023569884718319e-08,
                2.845337441546675e-08,
                4.4508494582405734e-07,
                3.927863407379485e-07,
                6.023569884692295e-08,
                1.8553916819032217e-07,
                1.2751899728286965e-07
            ],
            [
                4.785092783519724e-06,
                1.209865539295696e-06,
                9.422448185510695e-07,
                1.3709572068522336e-06,
                5.422218323487975e-06,
                1.9947304348862686e-06,
                1.9947292459347367e-06,
                6.475947982037486e-07,
                2.561281600086738e-06,
                1.9947299593078385e-06
            ],
            [
                1.3709567165579959e-06,
                2.2603242978871282e-06,
                1.2098652508287273e-06,
                1.5534979397677313e-06,
                1.6373770576776313e-07,
                1.76034300345598e-06,
                1.0677032518748838e-06,
                1.209865683518615e-06,
                5.715003789046955e-07,
                1.0677029972920738e-06
            ],
            [
                4.691162124067829e-08,
                8.764247451307293e-08,
                9.931202796993203e-08,
                8.764242227418718e-08,
                3.0590237279032884e-07,
                0.9999974387184021,
                2.902313023130843e-06,
                0.9999990577552942,
                1.5534973842076057e-06,
                1.275190276859705e-07
            ],
            [
                3.466326624336003e-07,
                3.0590226339061185e-07,
                6.475951069985296e-07,
                3.927862939126708e-07,
                8.315284241650899e-07,
                5.715003107755449e-07,
                7.3382080556433e-07,
                3.0590215399183813e-07,
                3.4663278639738526e-07,
                1.4449805540740185e-07
            ],
            [
                6.475950298011458e-07,
                5.043472278322555e-07,
                1.5534973842076057e-06,
                1.1253525596174225e-07,
                1.9947299593078385e-06,
                2.6995790618469934e-07,
                1.275190124846946e-07,
                8.315282259138311e-07,
                2.1024334103581732e-07,
                5.715004470326849e-07
            ],
            [
                2.699578096403948e-07,
                7.734416698849138e-08,
                NaN,
                4.1399365603508136e-08,
                7.338208930460318e-07,
                1.9555694692738946e-08,
                8.764245361752286e-08,
                1.2751899728311609e-07,
                5.715005151606823e-07,
                2.3823682479292225e-07
            ]
        ]
    },
    {
        "q_id": "10024_mmlu_physics",
        "cot_ids": [
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            33,
            34,
            35,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            74,
            75,
            76,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                0.999996499146841,
                0.9999982396569981,
                0.9999987121041709,
                2.1444948415296896e-05,
                5.043476486924565e-07,
                1.0,
                0.9999993524054337,
                1.8925145985104064e-05,
                0.9999925887183693,
                0.9999910602994412
            ],
            [
                0.9999994956524118,
                0.9999989322973851,
                0.9999994631249324,
                1.9947306726594253e-06,
                0.999999495652532,
                0.9999995818813768,
                0.9999994956524717,
                0.9999997463981032,
                0.9999930377420976,
                0.9999999006879958
            ],
            [
                1.0677028700363782e-06,
                2.902310947190096e-06,
                5.422217030614265e-06,
                2.5612828213690224e-06,
                7.338212429537553e-07,
                3.2887490652810324e-06,
                2.561281905390075e-06,
                5.422221555069497e-06,
                1.3709572068422585e-06,
                1.3007126913583456e-05
            ],
            [
                4.4508515805735777e-07,
                8.315283250371857e-07,
                1.5534983101602148e-06,
                1.0129987357407137e-05,
                2.6995790618350237e-07,
                1.3709572068522336e-06,
                5.043472879540142e-07,
                1.994730672675753e-06,
                2.1024331597262577e-07,
                2.6995771309523475e-07
            ],
            [
                0.9999996940978826,
                8.315281267882195e-07,
                0.999999922655833,
                0.9999995262096116,
                0.9999995262095553,
                8.939694172867777e-06,
                0.9999993106387906,
                3.0590237279032884e-07,
                0.9999822214545363,
                3.927863407379485e-07
            ],
            [
                8.315283250371857e-07,
                3.0590215399183813e-07,
                1.0677024881980089e-06,
                8.315280276626197e-07,
                3.927862002663297e-07,
                5.715005151606823e-07,
                3.466326211113502e-07,
                1.7603434231833873e-06,
                5.715002426475718e-07,
                3.059021175261338e-07
            ],
            [
                1.5534975693933505e-06,
                6.475947982002148e-07,
                3.7266392840781026e-06,
                2.2603234895176927e-06,
                2.5612828213690224e-06,
                8.939696304213768e-06,
                2.2603242978665707e-06,
                5.715003788993679e-07,
                6.475950297942253e-07,
                6.475947210012481e-07
            ],
            [
                0.9999993524048932,
                NaN,
                4.2228339479858295e-06,
                0.9999994631249961,
                0.999999114843281,
                0.9999993524054337,
                0.9999994956523516,
                0.9999997761970515,
                0.9999993106390369,
                0.9999930377412694
            ],
            [
                0.9999921107393018,
                0.9999952149072185,
                0.9999991148427534,
                2.9023123311583482e-06,
                0.9999952149066489,
                0.9999969105066593,
                0.9999972735297307,
                0.9999910603005041,
                0.9999756997506082,
                0.9999921107336572
            ],
            [
                5.043473480777865e-07,
                1.9947301970972664e-06,
                1.0677029973219343e-06,
                3.466327037553825e-07,
                5.043476486924565e-07,
                NaN,
                3.059022998581767e-07,
                7.338207180898968e-07,
                1.275190124846946e-07,
                9.422444815814404e-07
            ],
            [
                3.2887502415767434e-06,
                1.0677027427624903e-06,
                7.338207180898968e-07,
                1.7603430034867993e-06,
                NaN,
                8.939696304311336e-06,
                5.043472278322555e-07,
                1.760343213335281e-06,
                8.939700567094277e-06,
                1.855391239547094e-07
            ],
            [
                0.9998204721018356,
                1.994729721482609e-06,
                0.9998601779445542,
                1.147876675686207e-05,
                2.561281600049467e-06,
                1.5534983101393749e-06,
                1.067702615468225e-06,
                0.9996646498269846,
                3.726638395611981e-06,
                3.726639728262097e-06
            ],
            [
                6.475946438055299e-07,
                2.6995790618469934e-07,
                2.3823702359290413e-07,
                1.855391239547094e-07,
                2.1024339116168358e-07,
                1.4449807263312446e-07,
                2.102434412875379e-07,
                2.102434412875379e-07,
                1.8553919030858602e-07,
                2.69957906184239e-07
            ],
            [
                8.315278293899016e-07,
                1.2098658277082653e-06,
                2.9023119851635836e-06,
                2.2603242978665707e-06,
                1.5534979397740895e-06,
                5.715006514151423e-07,
                8.315278293899016e-07,
                6.962257909785973e-06,
                9.422450431860582e-07,
                1.2098653950656417e-06
            ],
            [
                3.05902190458764e-07,
                1.9947301970972664e-06,
                6.475947210046347e-07,
                2.9023119851781017e-06,
                6.475947982037486e-07,
                2.1024334103505245e-07,
                3.9278634073732336e-07,
                2.260323758987159e-06,
                0.9999992661788447,
                9.422442569315887e-07
            ],
            [
                1.444979692800516e-07,
                0.9999998461826588,
                1.7603434231833873e-06,
                0.9999938558224725,
                NaN,
                0.9999998724809116,
                0.9999892166916532,
                0.9999756997477486,
                NaN,
                NaN
            ],
            [
                0.999999391640891,
                4.450849988811838e-07,
                3.927862939126708e-07,
                1.6373770576776313e-07,
                0.9999987901343174,
                1.994730434879465e-06,
                0.9999994956527725,
                0.9999981261246176,
                5.715007195447234e-07,
                1.3007125363908762e-05
            ],
            [
                1.3709573702566696e-06,
                9.422445939032799e-07,
                1.209865827740176e-06,
                1.994729483694599e-06,
                6.475948754012522e-07,
                7.3382080556433e-07,
                1.209865827740176e-06,
                NaN,
                5.715005832872586e-07,
                9.422447062030659e-07
            ],
            [
                4.4508494582405734e-07,
                1.0677029973192638e-06,
                0.9999996533674617,
                0.9999991684718735,
                0.9999987121043243,
                0.9999985406234317,
                0.999999631011592,
                0.9999997300421583,
                0.999999631011416,
                0.9999975938979495
            ],
            [
                3.2887506335906595e-06,
                0.9999962733616088,
                2.3823696679230424e-07,
                5.715003789033962e-07,
                1.2098659719757836e-06,
                9.422448185478557e-07,
                2.3823685318968256e-07,
                0.9999964991455885,
                1.6373766672888118e-07,
                2.3823685319244518e-07
            ],
            [
                6.475951069985296e-07,
                5.715007195447234e-07,
                1.0677028700363782e-06,
                3.4663249714451116e-07,
                7.338210680021253e-07,
                6.475945666051092e-07,
                3.466325797896173e-07,
                4.450850519403407e-07,
                1.3709576971425944e-06,
                6.475946438022905e-07
            ],
            [
                NaN,
                8.315278294114555e-07,
                0.0,
                1.994729483729522e-06,
                2.9023119851899796e-06,
                1.3007130015299356e-05,
                1.5534971990169383e-06,
                5.043475885696228e-07,
                NaN,
                NaN
            ],
            [
                8.939693107288474e-06,
                1.0129987357407137e-05,
                1.6701423836262173e-05,
                8.315282259138311e-07,
                2.1024331597262577e-07,
                5.715003789046955e-07,
                5.04347287955046e-07,
                1.2098659719788098e-06,
                5.043473480777865e-07,
                3.059022269250683e-07
            ],
            [
                1.3709567165530083e-06,
                3.466327037548308e-07,
                7.338211554783522e-07,
                2.9023123311055552e-06,
                1.9947297215043796e-06,
                6.475945666033422e-07,
                2.2603242978007868e-06,
                9.422448185510695e-07,
                4.450849988811838e-07,
                1.5534973841895917e-06
            ],
            [
                5.043473480777865e-07,
                2.102434162245973e-07,
                4.222834451327159e-06,
                5.422217030747413e-06,
                1.7603438428740716e-06,
                2.902311639183378e-06,
                3.059021175255426e-07,
                2.902313023101807e-06,
                1.0677031245905116e-06,
                2.102434412871794e-07
            ],
            [
                3.288749457469787e-06,
                3.05902226923399e-07,
                2.102434412871794e-07,
                8.939700567004841e-06,
                2.260325106237323e-06,
                5.715005832886879e-07,
                1.1478772230929451e-05,
                1.5534975693933505e-06,
                3.059022998581767e-07,
                5.043474683204221e-07
            ],
            [
                6.475951069985296e-07,
                1.0677031245905116e-06,
                3.927861066170637e-07,
                3.05902263389638e-07,
                3.0590215398829087e-07,
                4.785093353940187e-06,
                4.450852111100568e-07,
                2.9023109472244114e-06,
                3.9278624708775595e-07,
                6.962253759904688e-06
            ],
            [
                0.9999998802069445,
                0.9999996072137999,
                0.9999994956524116,
                0.9999990577550696,
                0.999999631011372,
                0.9999992661787577,
                0.999992588719254,
                0.9999989322967487,
                0.9999994284993489,
                0.999512142899981
            ],
            [
                6.475945666063607e-07,
                4.450850519403407e-07,
                2.699577774585891e-07,
                0.9999949062943951,
                8.315279285370317e-07,
                2.1024331597262577e-07,
                1.6373762769138607e-07,
                8.315284241650899e-07,
                6.475945666051092e-07,
                3.927862002663297e-07
            ],
            [
                5.04347528446051e-07,
                3.466325797896173e-07,
                1.125352291309328e-07,
                8.315280276626197e-07,
                5.043474081993875e-07,
                1.7603427936335396e-06,
                2.102434412875379e-07,
                1.1253506814842375e-07,
                5.715005832886879e-07,
                1.8553905760062447e-07
            ],
            [
                5.043472278280699e-07,
                8.315283250371857e-07,
                5.043472879540142e-07,
                3.466327863961242e-07,
                4.450851580555361e-07,
                2.6995774527577444e-07,
                3.4663253846316044e-07,
                1.0677026154730804e-06,
                1.5534983101549167e-06,
                2.1024329090867228e-07
            ],
            [
                1.0677031245905116e-06,
                5.715004470295662e-07,
                1.9947292459347367e-06,
                7.338211554783522e-07,
                1.3709567165579959e-06,
                5.043474683204221e-07,
                3.7266401726359486e-06,
                5.04347528440776e-07,
                1.5534971990126997e-06,
                1.3709576971379186e-06
            ],
            [
                3.4663262110945863e-07,
                4.450849458218309e-07,
                7.338208055579897e-07,
                5.715005832827105e-07,
                1.7603425837702984e-06,
                3.9278610661366994e-07,
                3.466327863961242e-07,
                3.927862002641863e-07,
                5.715003107715166e-07,
                4.4508505193791187e-07
            ],
            [
                1.1253518888531272e-07,
                6.475947982037486e-07,
                2.2603234895372223e-06,
                1.994730197090463e-06,
                3.726640616748873e-06,
                2.699576809143613e-07,
                NaN,
                2.2603248367949354e-06,
                NaN,
                3.9278615344178325e-07
            ],
            [
                3.05902336324494e-07,
                1.8553914607267268e-07,
                1.8553919030858602e-07,
                2.1024336609874897e-07,
                1.4449805540763184e-07,
                2.3823693839325527e-07,
                3.466325797896173e-07,
                9.422448185534261e-07,
                2.6995790618469934e-07,
                2.3823696679327928e-07
            ],
            [
                3.46632497145457e-07,
                8.315280276626197e-07,
                3.0590237279085045e-07,
                3.927862002663297e-07,
                3.927862470899887e-07,
                8.315281267882195e-07,
                1.209866260432471e-06,
                3.927863407379485e-07,
                6.475947210046347e-07,
                1.5534973842076057e-06
            ],
            [
                5.04347287955046e-07,
                3.288748281329893e-06,
                1.0677026154806063e-06,
                NaN,
                7.889262585886274e-06,
                2.10243290909724e-07,
                5.715006514176113e-07,
                9.422447062294175e-07,
                5.043473480777865e-07,
                NaN
            ],
            [
                5.043475885696228e-07,
                7.338209805240734e-07,
                2.382368815932174e-07,
                8.315281267800897e-07,
                5.715002426486762e-07,
                1.5534983101478522e-06,
                3.927863407379485e-07,
                1.5534983101549167e-06,
                1.1478769494542698e-05,
                2.102434412875379e-07
            ],
            [
                2.6995774527718623e-07,
                3.059022998576899e-07,
                1.6373762769138607e-07,
                2.6995771309523475e-07,
                2.9023119851781017e-06,
                3.0590237279032884e-07,
                0.9999885212264173,
                1.760343213335281e-06,
                1.6373770576776313e-07,
                1.9947292459347367e-06
            ],
            [
                5.043472278322555e-07,
                6.475945666063607e-07,
                1.0677026154806063e-06,
                6.475947982037486e-07,
                4.450852641737424e-07,
                1.0677027427624903e-06,
                5.04347528446051e-07,
                1.9947301970972664e-06,
                5.04347468323289e-07,
                5.04347528446051e-07
            ],
            [
                5.715003107767143e-07,
                6.475947210046347e-07,
                7.338207180898968e-07,
                NaN,
                1.6373776432509826e-07,
                1.7603430034867993e-06,
                3.9278629391427843e-07,
                3.4663278639892215e-07,
                1.8553919030858602e-07,
                3.466327037553825e-07
            ],
            [
                6.475947982037486e-07,
                2.5612828213934817e-06,
                2.9023119851899796e-06,
                5.04347468323289e-07,
                1.5534981249697903e-06,
                5.043475284468537e-07,
                3.466325797896173e-07,
                2.102434412875379e-07,
                5.043472879540142e-07,
                1.067702870039777e-06
            ],
            [
                NaN,
                2.9023116392097746e-06,
                3.466327450765785e-07,
                2.5612834320563895e-06,
                5.043473480777865e-07,
                3.927862939126708e-07,
                1.637376276909393e-07,
                2.9023119851899796e-06,
                5.715003107755449e-07,
                1.2751908849167202e-07
            ],
            [
                6.475947210046347e-07,
                6.475950297971703e-07,
                4.450848927650143e-07,
                4.450852111135988e-07,
                6.475945666051092e-07,
                1.7603436330259153e-06,
                1.5534971990126997e-06,
                6.144177531767002e-06,
                1.2098659719757836e-06,
                5.4222183235249605e-06
            ],
            [
                3.46632497145457e-07,
                8.315277302747361e-07,
                7.338213304343413e-07,
                NaN,
                3.927862470890063e-07,
                8.315277302841894e-07,
                1.3709567165617364e-06,
                5.715004470295662e-07,
                3.05902190458764e-07,
                5.715003107755449e-07
            ],
            [
                0.9999962733607184,
                1.9947292459347367e-06,
                0.9999985406232578,
                0.9999989969860319,
                0.9999962733616085,
                0.9999985406241273,
                0.9999877809283763,
                0.999997273530707,
                0.999998346310218,
                0.9999981261239481
            ],
            [
                5.043474081993875e-07,
                8.315278294097538e-07,
                2.9023133690980155e-06,
                1.9947306726594253e-06,
                5.715004470313855e-07,
                7.338210679979539e-07,
                8.315283250371857e-07,
                3.466324971415162e-07,
                8.315283250371857e-07,
                1.7603425837855082e-06
            ],
            [
                1.5534971990126997e-06,
                5.715005832886879e-07,
                0.9999991148426478,
                0.9999983463110071,
                0.9999990577549576,
                NaN,
                0.9999999067050165,
                0.9999955048200337,
                0.9999986290424682,
                0.9999910603058397
            ],
            [
                6.475945666063607e-07,
                1.9947299593078385e-06,
                6.47595107001401e-07,
                4.450852111155216e-07,
                2.699578096403948e-07,
                6.475946438055299e-07,
                3.059021175261338e-07,
                1.0677029973219343e-06,
                9.422442569290178e-07,
                1.855391239547094e-07
            ],
            [
                2.2603234895176927e-06,
                2.561283126728994e-06,
                4.2228339479858295e-06,
                3.4663262111182307e-07,
                3.4663262110945863e-07,
                NaN,
                2.2603242978871282e-06,
                3.059021904559123e-07,
                1.760343423160973e-06,
                NaN
            ],
            [
                1.2098662604247682e-06,
                7.338212429582604e-07,
                1.300713466685723e-05,
                2.5612825160562587e-06,
                3.7266410611296085e-06,
                4.222834451355964e-06,
                1.99472900813862e-06,
                2.561281600086738e-06,
                7.338212429582604e-07,
                1.994729483723626e-06
            ],
            [
                0.9999984465015062,
                0.9999992661789324,
                0.9999980052709931,
                3.726638839878908e-06,
                0.9999982396567884,
                4.4508505193932864e-07,
                5.715005151606823e-07,
                5.043474683204221e-07,
                0.9999972735284328,
                1.7603434231777837e-06
            ],
            [
                0.999986992865365,
                6.475946437996402e-07,
                7.338209805224048e-07,
                5.715005832853093e-07,
                2.5612831267086116e-06,
                8.315283250371857e-07,
                2.382368815916736e-07,
                1.7603436330259153e-06,
                3.288750241561788e-06,
                5.715003107715166e-07
            ],
            [
                3.927862939126708e-07,
                2.6995771309523475e-07,
                1.8553916819032217e-07,
                7.338207180864763e-07,
                4.4508510499849186e-07,
                2.6995790618252024e-07,
                3.4663266243308805e-07,
                9.422448185478557e-07,
                2.3823690999290963e-07,
                4.4508526417298334e-07
            ],
            [
                3.4663262110945863e-07,
                5.715006514105942e-07,
                1.6701429808632785e-05,
                5.043472879525233e-07,
                4.450848927621807e-07,
                3.927862470861484e-07,
                3.466327037539638e-07,
                6.144176066850984e-06,
                4.0063706519072155e-05,
                2.1024331597066579e-07
            ],
            [
                3.4663274507713016e-07,
                2.2603245673155757e-06,
                4.4508494582405734e-07,
                1.3709575337125585e-06,
                7.338209805240734e-07,
                1.2098659719788098e-06,
                1.855391239547094e-07,
                1.4449798650569826e-07,
                2.561281905376098e-06,
                1.300713311614059e-05
            ],
            [
                7.338208930391909e-07,
                9.422445938964242e-07,
                6.475947210012481e-07,
                5.043475885674441e-07,
                1.7603436330179102e-06,
                1.3709578605617394e-06,
                8.939700566801578e-06,
                1.1478772230407462e-05,
                6.144177531599359e-06,
                2.902312331125353e-06
            ],
            [
                0.9999982396572072,
                NaN,
                0.9999987901346054,
                0.9999993106391193,
                0.9978172836018145,
                0.9999981261241704,
                0.9999987121041712,
                0.9999992661787573,
                7.338208055664991e-07,
                0.9999996072136594
            ],
            [
                2.1024331597152624e-07,
                1.0677026154774503e-06,
                5.043475284430694e-07,
                2.9023112932177327e-06,
                2.260325106237323e-06,
                1.209865539295696e-06,
                3.4663249714325014e-07,
                1.1478769494542698e-05,
                3.927861066170637e-07,
                1.99472900813862e-06
            ],
            [
                7.338208930391909e-07,
                6.962254589781966e-06,
                7.889261645090304e-06,
                2.260325106237323e-06,
                1.0677028700363782e-06,
                1.4738976700366126e-05,
                3.927860597945825e-07,
                1.1478770861859053e-05,
                1.300712846411008e-05,
                2.5612831266946347e-06
            ],
            [
                1.5534984953453635e-06,
                5.4222202624563834e-06,
                7.889261645427538e-06,
                5.043472879525233e-07,
                7.889261645427538e-06,
                5.043472879540142e-07,
                1.3007126914435202e-05,
                1.994730197090463e-06,
                7.338211554783522e-07,
                5.422218323231539e-06
            ],
            [
                5.422221555340727e-06,
                6.605213675960068e-05,
                1.7603427936263351e-06,
                2.260324567337161e-06,
                5.422217677078203e-06,
                1.9947299593014888e-06,
                9.422449308673789e-07,
                3.288748673360027e-06,
                4.785094494783494e-06,
                4.785096776468749e-06
            ],
            [
                9.931195693628605e-08,
                2.69957906184239e-07,
                3.9278634073732336e-07,
                2.1024326584639497e-07,
                2.3823685319244518e-07,
                1.4449800373065699e-07,
                3.059023727894942e-07,
                2.1024334103505245e-07,
                1.2751899728286965e-07,
                1.4449805540740185e-07
            ],
            [
                6.962254589851619e-06,
                0.9999810748427593,
                0.9992903295540065,
                1.5534975693979422e-06,
                1.760343003481596e-06,
                2.561282210740037e-06,
                6.962257909785973e-06,
                2.382369383923073e-07,
                5.422218969858371e-06,
                5.04347468323289e-07
            ],
            [
                3.059022998581767e-07,
                2.3823693838429036e-07,
                9.931201612997889e-08,
                2.382368247909451e-07,
                1.3574334580531584e-07,
                2.699579061798195e-07,
                2.3823682478975334e-07,
                1.6373774480404828e-07,
                2.382368531929327e-07,
                3.927861534370498e-07
            ],
            [
                0.9999977396757042,
                0.9999984465016907,
                0.9999987901341734,
                0.9999997463981334,
                0.9999985406237797,
                0.9999992188515767,
                0.9999989322973852,
                0.9999992188516698,
                0.9999994284994851,
                0.9999984465028019
            ],
            [
                1.0677024882009222e-06,
                0.9999724643024294,
                0.9999904837449227,
                0.9999916019239732,
                3.05902190458764e-07,
                1.3709576971425944e-06,
                0.9999978766210329,
                2.5612831267202583e-06,
                1.1478765389222573e-05,
                1.209865539295696e-06
            ],
            [
                0.9999993106389546,
                0.9999998874647977,
                0.9999997897566841,
                0.9999995262094987,
                0.9999993916411812,
                0.9999998724808964,
                0.9999998461826037,
                0.9999988634365607,
                0.9999998724808964,
                0.9999989969860318
            ],
            [
                0.9999995262096119,
                0.9999995818811773,
                0.9999995262093295,
                0.9999992661792824,
                0.9999992661787576,
                0.9999988634357482,
                0.9999993106390372,
                0.999999802494633,
                0.9999994631250604,
                0.9999989322970033
            ],
            [
                NaN,
                5.715007195447234e-07,
                9.422448185510695e-07,
                1.0677029973192638e-06,
                1.3709568799919866e-06,
                NaN,
                9.422445939054222e-07,
                1.2098656835224664e-06,
                6.475947210031623e-07,
                2.5612834320470717e-06
            ],
            [
                1.7603434231777837e-06,
                5.715003107755449e-07,
                1.5534981249496567e-06,
                5.422221555340727e-06,
                1.7603436330259153e-06,
                3.288750241561788e-06,
                9.4224425692559e-07,
                2.3823685319174098e-07,
                1.2098653950656417e-06,
                4.450848927637999e-07
            ],
            [
                NaN,
                NaN,
                2.902312677150514e-06,
                1.5534975693933505e-06,
                0.9997694931772062,
                1.2098652508424818e-06,
                6.60521446989462e-05,
                3.288748673376478e-06,
                1.0677033791612137e-06,
                8.315284241650899e-07
            ],
            [
                0.999996033012198,
                0.9999972735297322,
                0.9999985406243019,
                4.4508494582405734e-07,
                3.927863407379485e-07,
                0.9999949062950021,
                7.338212429582604e-07,
                0.9999998144608098,
                6.475945666063607e-07,
                0.9999756997593403
            ],
            [
                5.04347468323289e-07,
                5.043474081993875e-07,
                9.422448185534261e-07,
                3.927862939126708e-07,
                3.9278610661822475e-07,
                1.0677031245953668e-06,
                8.764249540862797e-08,
                4.4508494582405734e-07,
                7.338210680021253e-07,
                1.4449807263312446e-07
            ],
            [
                1.4449800373118268e-07,
                NaN,
                3.9278629391427843e-07,
                3.466327037553825e-07,
                1.855390576008354e-07,
                1.4449800373118268e-07,
                1.994729721518893e-06,
                7.338207180898968e-07,
                7.338207180898968e-07,
                3.726639284144195e-06
            ],
            [
                1.3709576971425944e-06,
                1.9947299592824403e-06,
                1.5534975693792215e-06,
                3.4663249714612693e-07,
                7.338208055664991e-07,
                1.8553916819032217e-07,
                3.288749849498565e-06,
                2.3823702359290413e-07,
                8.315280276626197e-07,
                3.7266397283231055e-06
            ],
            [
                5.715002426486762e-07,
                2.902312677104321e-06,
                4.450852111148132e-07,
                2.90231233114251e-06,
                5.715005832886879e-07,
                3.927860597945825e-07,
                2.561283431986506e-06,
                8.315284241650899e-07,
                6.475945666051092e-07,
                2.3823696679230424e-07
            ],
            [
                1.855391239544352e-07,
                1.99472924590571e-06,
                2.1024329090867228e-07,
                1.0677031245990084e-06,
                1.4449798650417048e-07,
                2.2603242978871282e-06,
                2.1024334103505245e-07,
                3.9278605979208185e-07,
                2.699578096393206e-07,
                7.338212429582604e-07
            ],
            [
                1.3007123813193233e-05,
                1.5534979397740895e-06,
                8.315282259009745e-07,
                8.315281267834927e-07,
                3.059021904571643e-07,
                3.4663249714325014e-07,
                6.962254589978262e-06,
                7.338212429582604e-07,
                1.0677032518814388e-06,
                6.475947209985977e-07
            ],
            [
                0.99999905775507,
                0.9999992188519491,
                0.9999938558254053,
                0.9999993916407462,
                0.9999978766205263,
                0.999999631011328,
                0.999999428499417,
                0.999999310638955,
                0.999999730042255,
                0.9999996072138467
            ],
            [
                1.0677027427600627e-06,
                2.382368531929327e-07,
                2.260323758987159e-06,
                3.288749457469787e-06,
                2.561281294760143e-06,
                3.7266397283908927e-06,
                6.475948754012522e-07,
                1.8925141473978602e-05,
                1.0129994602895546e-05,
                1.3709572068522336e-06
            ],
            [
                3.9278615344178325e-07,
                3.059021175261338e-07,
                2.5612828213934817e-06,
                8.315277302841894e-07,
                3.288748281295496e-06,
                2.2603234895053587e-06,
                NaN,
                NaN,
                3.927862002663297e-07,
                2.561281905390075e-06
            ],
            [
                3.05902190458764e-07,
                8.315281267882195e-07,
                1.0677032518814388e-06,
                2.5612816000646084e-06,
                6.962254589978262e-06,
                5.715007195431641e-07,
                2.102433159721477e-07,
                NaN,
                1.0677032518814388e-06,
                3.927862939126708e-07
            ],
            [
                1.3007130015677909e-05,
                0.9999986290423045,
                7.338213304363436e-07,
                3.2887502415767434e-06,
                0.9999981261241706,
                1.4738983729535602e-05,
                4.785093353940187e-06,
                0.9999989969857929,
                4.450851580555361e-07,
                0.9999982396574175
            ],
            [
                4.450849988780466e-07,
                1.3709576971425944e-06,
                4.450852111148132e-07,
                0.9999687980813213,
                3.059021904559123e-07,
                6.962259569313662e-06,
                6.962259569313662e-06,
                6.475949525981759e-07,
                2.699578096393206e-07,
                3.466327863961242e-07
            ],
            [
                3.0590237279085045e-07,
                2.1024336609874897e-07,
                8.315281267882195e-07,
                7.338212429582604e-07,
                6.475946438055299e-07,
                4.4508494582405734e-07,
                2.1024339116168358e-07,
                5.71500719545698e-07,
                3.05902336324494e-07,
                5.715002426486762e-07
            ],
            [
                4.222834954778007e-06,
                8.315277302747361e-07,
                1.8553905759893702e-07,
                3.466327037472645e-07,
                6.475946437928669e-07,
                3.466327037472645e-07,
                6.475945665900901e-07,
                7.338207180661203e-07,
                6.475950297942253e-07,
                9.422443692446175e-07
            ],
            [
                1.6373762769138607e-07,
                1.8553916819032217e-07,
                1.6373762769138607e-07,
                1.8553910183607374e-07,
                1.637377448057981e-07,
                2.699577774585891e-07,
                2.6995771309523475e-07,
                1.8553903548231313e-07,
                2.102433660979124e-07,
                8.315277302841894e-07
            ],
            [
                1.3709572068522336e-06,
                4.450850519403407e-07,
                NaN,
                8.939693107190907e-06,
                1.2098652508424818e-06,
                6.475950298011458e-07,
                3.4663278639892215e-07,
                2.1024334103505245e-07,
                9.422442569315887e-07,
                3.927862470899887e-07
            ],
            [
                5.71500515159253e-07,
                5.715006514105942e-07,
                5.715003789046955e-07,
                1.3709576971242028e-06,
                3.927861066170637e-07,
                7.338207180864763e-07,
                4.450849458200093e-07,
                7.338212429582604e-07,
                1.3709567165579959e-06,
                7.3382080556433e-07
            ],
            [
                3.466325384678894e-07,
                2.699576809143613e-07,
                9.422444815814404e-07,
                2.1024331597262577e-07,
                2.3823682479181176e-07,
                2.699578096403948e-07,
                2.699576809143613e-07,
                NaN,
                2.10243290909724e-07,
                6.475947982037486e-07
            ],
            [
                3.4663253846718004e-07,
                2.9023112932177327e-06,
                7.338210679909462e-07,
                6.47594952595231e-07,
                1.5534979397740895e-06,
                3.4663278639738526e-07,
                4.222832437747125e-06,
                7.338212429504183e-07,
                8.31528126775552e-07,
                1.994729245917502e-06
            ],
            [
                0.9999993106387904,
                0.9999993524054338,
                0.9999994284994851,
                0.9999987901338844,
                0.9999997761972116,
                0.999999653367255,
                0.9999989969855538,
                0.9999994631248044,
                0.999998996986032,
                0.9999987121044782
            ],
            [
                0.9999993106387084,
                0.9999995549148952,
                0.9999985406232579,
                0.9999970976866333,
                0.9999995262094422,
                0.9999989969856734,
                0.9999988634361543,
                0.9999987901341729,
                0.9999986290423039,
                0.9999970976887086
            ],
            [
                0.9999984465020608,
                0.9999989322972578,
                0.9999996072137062,
                0.9999997300422548,
                0.9999993524050477,
                0.999999789756634,
                0.9999994956527123,
                0.9999992188513905,
                0.9999993524054337,
                0.9999989322970034
            ],
            [
                9.422450431989127e-07,
                4.450849988798682e-07,
                3.9278615344178325e-07,
                3.9278615344178325e-07,
                2.699578096393206e-07,
                6.475950298011458e-07,
                2.3823685319244518e-07,
                2.1024341622297196e-07,
                4.450848927650143e-07,
                3.059023727894942e-07
            ],
            [
                1.3709567165579959e-06,
                3.288748673376478e-06,
                9.422447062270609e-07,
                1.2098653950656417e-06,
                2.5612822106841303e-06,
                5.043475885674441e-07,
                6.475949525981759e-07,
                7.338209805133949e-07,
                1.0677026154730804e-06,
                1.0677028700363782e-06
            ],
            [
                9.422445939002803e-07,
                0.9999988634361547,
                0.9999987901346056,
                1.067703379154416e-06,
                2.699578418185828e-07,
                2.9023130230846496e-06,
                0.9999975938982364,
                0.9999898700054043,
                0.9999992661786699,
                0.9999995818813766
            ],
            [
                0.9999994631247405,
                6.962257909842961e-06,
                0.9999994956527725,
                0.9999992188517632,
                0.9999989969857929,
                0.9999987121043248,
                0.9999995262096121,
                0.9999990577554069,
                0.9999984465020616,
                0.9999981261237254
            ],
            [
                1.0677028700266676e-06,
                8.315282259051341e-07,
                3.927862470899887e-07,
                4.78509563546605e-06,
                1.1478764020883773e-05,
                1.0129995810343862e-05,
                NaN,
                2.902310947190096e-06,
                3.726639728262097e-06,
                8.939693107093343e-06
            ],
            [
                1.2098661162023305e-06,
                8.315281267800897e-07,
                1.760343213335281e-06,
                1.7603434231833873e-06,
                6.475945666033422e-07,
                1.553497199007048e-06,
                3.059022269250683e-07,
                1.99473067264854e-06,
                7.338211554783522e-07,
                1.7603440527222532e-06
            ],
            [
                0.9999996940976638,
                0.999999825702163,
                0.9999998144609425,
                0.999999746398073,
                0.9999998461826406,
                0.999999310638626,
                0.9999998724809571,
                0.9999999397642867,
                0.9999999273418269,
                0.9999997617631753
            ],
            [
                NaN,
                1.2098659719757836e-06,
                8.315279285370317e-07,
                NaN,
                4.785094494783494e-06,
                1.4738976701170414e-05,
                NaN,
                NaN,
                4.222834954801051e-06,
                8.939696304311336e-06
            ],
            [
                2.2603242978778778e-06,
                2.38237023590304e-07,
                2.2603248367656408e-06,
                1.2098659719524008e-06,
                8.93970056668775e-06,
                6.475949525919915e-07,
                3.4663266242575825e-07,
                3.466324971415162e-07,
                2.382370235922541e-07,
                3.059023727869902e-07
            ],
            [
                8.315277302841894e-07,
                8.315281267861397e-07,
                1.5534971990126997e-06,
                5.043476486915964e-07,
                6.475948754012522e-07,
                5.04347528446051e-07,
                3.4663249714612693e-07,
                8.315278294097538e-07,
                5.043472879540142e-07,
                7.338212429582604e-07
            ],
            [
                3.059022269250683e-07,
                3.059022998569248e-07,
                1.0677032518785256e-06,
                4.450852111135988e-07,
                NaN,
                8.315277302841894e-07,
                1.3709570434122812e-06,
                3.288747889284851e-06,
                3.46632497145457e-07,
                1.855391681898159e-07
            ],
            [
                5.422218969858371e-06,
                1.3709568799919866e-06,
                5.043472879540142e-07,
                0.9399133443558415,
                3.9278615344178325e-07,
                3.9278610661822475e-07,
                7.338210680021253e-07,
                1.3709576971425944e-06,
                1.8925145985895816e-05,
                NaN
            ],
            [
                2.382369951932796e-07,
                1.6373766672973748e-07,
                5.04347468323289e-07,
                3.927863407379485e-07,
                1.8553907971855875e-07,
                1.4449802095609418e-07,
                2.382369667929001e-07,
                3.466326211113502e-07,
                3.0590237279085045e-07,
                1.444979692800516e-07
            ],
            [
                1.7603434231705793e-06,
                4.4508526417014975e-07,
                1.7603425837791042e-06,
                2.9023112931688987e-06,
                1.5534984953453635e-06,
                1.7603438428660665e-06,
                4.4508526417014975e-07,
                5.715006514151423e-07,
                2.260325375664839e-06,
                1.2098658277451275e-06
            ],
            [
                1.9947299593078385e-06,
                1.2751899728286965e-07,
                1.067703124601679e-06,
                4.450850519403407e-07,
                9.422443692574719e-07,
                1.0677028700422047e-06,
                3.2887502415767434e-06,
                2.2603240284371276e-06,
                2.2603253756956754e-06,
                2.1024339116168358e-07
            ],
            [
                0.9999988634361544,
                0.9999995262093858,
                0.9999998144609646,
                0.9999994631248043,
                0.9999993524053565,
                0.9999997300420939,
                0.9999995549150013,
                0.9999967112521129,
                0.9999993524052793,
                0.9999993916408185
            ],
            [
                2.6995774527718623e-07,
                3.059022998576899e-07,
                1.6373772528704005e-07,
                5.715003107767143e-07,
                5.715005151606823e-07,
                4.450848927658745e-07,
                5.043476486924565e-07,
                3.05902336324494e-07,
                2.3823693839325527e-07,
                1.8553905760062447e-07
            ],
            [
                2.2603234895289998e-06,
                2.2603237589676295e-06,
                6.144173869446876e-06,
                4.222834954753043e-06,
                1.994729483705484e-06,
                2.9023116391675407e-06,
                7.338212429504183e-07,
                5.422217677078203e-06,
                3.726641061085547e-06,
                9.422448185435711e-07
            ]
        ]
    },
    {
        "q_id": "9541_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.0,
                0.9999999358793944,
                0.9999999176674945,
                0.9999999434137571,
                0.9999999317439873,
                0.9999998461826588,
                1.0,
                0.9999999468420996,
                0.9999999317439872,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999999656786874,
                0.999999946842182,
                1.0,
                1.0,
                0.9999999468421122,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999998642566704,
                0.9999996533674617,
                0.9999999317439708,
                0.9999998144609646,
                0.9999997300422548,
                0.9999998362622552,
                0.9999999006880431,
                0.9999999530883675,
                1.0,
                0.9999998724809268
            ],
            [
                1.0,
                0.9999998724809875,
                0.9999999273418528,
                1.0,
                0.9999999586006344,
                0.9999999397643083,
                0.9999995818812272,
                0.9999999500628036,
                0.9999999176674848,
                0.9999998802069445
            ],
            [
                0.9999999559306312,
                0.9999999677581375,
                0.9999999468421883,
                0.999999961108909,
                1.0,
                1.0,
                1.0,
                0.9999999123575674,
                0.9999999634651531,
                1.0
            ],
            [
                0.9999996743688199,
                0.9999999468421756,
                0.9999998024947273,
                0.9999991148427534,
                0.9999998362623334,
                0.999999864256719,
                0.999999814460854,
                0.9999994631249324,
                0.9999999006880668,
                0.9999998802068873
            ],
            [
                1.0,
                0.9999999530883787,
                1.0,
                1.0,
                0.9999998555019618,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999995549148951
            ],
            [
                1.0,
                0.9999999358794479,
                0.9999999500628513,
                1.0,
                1.0,
                1.0,
                0.99999994341373,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                0.9999999123575881,
                0.9999998642566866,
                1.0,
                0.9999999358794096,
                0.9999999358794174,
                0.999999953088362,
                1.0,
                1.0,
                0.9999999006880195
            ],
            [
                1.0,
                0.999999946842163,
                1.0,
                1.0,
                0.999999931743979,
                0.9999998802069444,
                0.9999999317439058,
                1.0,
                0.9999999358793714,
                0.9999999530883787
            ],
            [
                0.9999998257021837,
                0.9999997761971315,
                0.9999999434137301,
                0.9999998874647575,
                0.9999998362623334,
                0.9999999123575046,
                0.9999998802069159,
                0.9999998144609424,
                0.9999998555019274,
                0.9999998724809723
            ],
            [
                1.0,
                0.999999825702163,
                0.9999998942829477,
                0.9999999273418442,
                0.9999997897567092,
                0.9999999067050498,
                0.9999999434137907,
                1.0,
                0.9999999006881142,
                0.9999999067050832
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                0.999999946842163,
                0.9999999317439627,
                0.9999998257021422,
                0.9999999656786874,
                1.0,
                1.0
            ],
            [
                0.9999999273418355,
                0.999998790133741,
                0.9999999123574836,
                0.9999998724808963,
                0.9999998642566219,
                0.9999999317439302,
                0.9999999273418009,
                0.9999998874647709,
                0.9999998942830358,
                0.999999946842163
            ],
            [
                1.0,
                0.9999999500628155,
                0.9999999358794326,
                0.9999999317439465,
                0.9999994631248043,
                0.9999999677581606,
                0.9999999611088766,
                0.9999999634651704,
                0.9999999500628155,
                0.9999994631249324
            ],
            [
                1.0,
                1.0,
                0.9999999358793485,
                0.9999998257021422,
                0.9999999656786956,
                0.9999992661790198,
                0.9999998942830485,
                0.9999992188515765,
                0.9999998642566866,
                0.9999998802069159
            ],
            [
                6.825609419848033e-08,
                1.444980209564556e-07,
                6.825608606172863e-08,
                2.3823685319244518e-07,
                9.931202796993203e-08,
                6.825604537781398e-08,
                1.1253524254650944e-07,
                6.825609419848033e-08,
                2.69957906184239e-07,
                1.275190428875671e-07
            ],
            [
                1.0,
                0.9999999067051499,
                0.9999999634651835,
                1.0,
                0.999999887464838,
                1.0,
                1.0,
                0.9999999226557225,
                0.9999999317439221,
                0.9999999123575151
            ],
            [
                1.0,
                0.9999999634651444,
                0.99999995308839,
                0.9999997897567342,
                1.0,
                0.999999927341853,
                1.0,
                0.999999961108858,
                0.9999999468421884,
                1.0
            ],
            [
                1.0,
                1.0,
                0.999999946842182,
                1.0,
                1.0,
                0.9999998642566381,
                0.9999999500628453,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999997897567091,
                0.9999998461826589,
                1.0,
                1.0,
                0.9999998461826956,
                1.0,
                0.9999997897566841,
                0.9999996743688199,
                0.9999999226557961,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999273418788,
                0.9999999397642796,
                1.0,
                0.9999999358794021,
                0.9999999468421693,
                1.0
            ],
            [
                0.999999939764294,
                1.0,
                0.999999825702059,
                0.9999999067050943,
                0.9999999226557778,
                0.9999996533672137,
                0.9999998942829476,
                0.9999999226557961,
                0.9999998642566542,
                0.9999996743686645
            ],
            [
                0.9999999273418182,
                0.9999998461826589,
                0.9999998802069302,
                0.9999998642567353,
                0.9999982396561592,
                0.9999998724809875,
                0.9999999434138043,
                0.9999999530883228,
                0.9999999434138109,
                3.059022998581767e-07
            ],
            [
                0.9999999656787039,
                1.0,
                1.0,
                0.999999927341853,
                1.0,
                1.0,
                1.0,
                0.9999999677581567,
                0.9999999273417662,
                1.0
            ],
            [
                1.6701419853518415e-05,
                1.4738978458140753e-05,
                0.9999995549147891,
                1.7603438428740716e-06,
                6.1441746020359e-06,
                1.6701419853852583e-05,
                3.2887478892055875e-06,
                1.012998977213635e-05,
                8.939700567004841e-06,
                4.222832941142044e-06
            ],
            [
                0.9999998362622553,
                0.9999998724809571,
                0.9999999434137368,
                0.9999998724809268,
                1.0,
                0.9999999358793867,
                0.9999999468421946,
                0.9999999226558054,
                0.9999921107336626,
                1.0
            ],
            [
                1.5534975693933505e-06,
                1.7603438428740716e-06,
                7.889262585814522e-06,
                0.9999985406239552,
                1.9947297215125433e-06,
                7.889263526345123e-06,
                7.889266347715168e-06,
                0.9999975938973775,
                1.0129989772274546e-05,
                8.939695238439078e-06
            ],
            [
                0.9999999611088812,
                1.0,
                1.0,
                0.9999999434137435,
                0.9999999434137975,
                1.0,
                0.9999999123574942,
                1.0,
                0.9999999176674651,
                1.0
            ],
            [
                0.9999995549147892,
                0.9999998724808964,
                0.9999996072138468,
                0.9999997761970782,
                0.999999864256622,
                0.999999730042287,
                0.9999997617631186,
                0.9999993106392018,
                0.9999999006880076,
                0.9999991684718738
            ],
            [
                0.9999999358793638,
                1.0,
                0.9999998802069731,
                0.9999999358794402,
                1.0,
                0.9999999317439302,
                0.9999999468421313,
                0.999999900687984,
                1.0,
                1.0
            ],
            [
                0.9999999006881378,
                0.9999999500627798,
                0.9999999176674553,
                0.9999996533672137,
                1.0,
                0.9999997463980125,
                0.9999999500627798,
                0.9999997897566592,
                0.9999999123575464,
                0.9999998362623334
            ],
            [
                1.0,
                0.9999999273418528,
                0.9999999006880786,
                0.9999999634651878,
                1.0,
                1.0,
                0.9999999067049942,
                0.9999999611088858,
                0.999999581881277,
                1.0
            ],
            [
                0.9999998144608319,
                0.9999999273418096,
                0.9999997617630049,
                0.9999999273418183,
                0.999999927341801,
                0.9999998724809116,
                0.9999997126314469,
                0.9999999273418442,
                1.0,
                0.9999999123574419
            ],
            [
                1.0,
                1.0,
                0.9999997897565838,
                1.0,
                0.9999999397643083,
                0.9999999123574942,
                0.9999999434137975,
                0.9999999273418962,
                1.0,
                0.999999927341853
            ],
            [
                0.9999999732705507,
                1.0,
                0.9999999611089043,
                1.0,
                0.9999999530883452,
                1.0,
                0.9999999317439302,
                0.9999999273417836,
                0.9999999273418095,
                0.9999999123574629
            ],
            [
                0.9999999176674946,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999998642566704,
                0.9999999317439384,
                0.9999998144609425,
                0.9999999006879957
            ],
            [
                0.9999998942829224,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999586005851,
                1.0,
                0.9999999317439221,
                0.9999999176675829,
                0.999999931743979
            ],
            [
                0.9999999006880905,
                0.999997097688364,
                0.9999996310115921,
                0.999998540623258,
                1.0,
                1.0,
                0.9999999067051054,
                0.9999999317439059,
                0.9999999397642508,
                0.9999998461826222
            ],
            [
                0.9999999273418182,
                0.9999998942830862,
                0.9999999468421122,
                1.0,
                0.9999999123575255,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999998257021422,
                0.999999946842125,
                1.0,
                0.9999999634651617,
                1.0,
                0.999999931743971,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999176675436,
                0.9999999226558146,
                0.9999999358794097,
                1.0,
                0.9999997617630617,
                0.9999998802068873,
                0.9999996533674617,
                0.9999999468421883,
                1.0,
                0.9999999067050943
            ],
            [
                1.0,
                1.0,
                0.9999999226557962,
                0.9999999500627976,
                1.0,
                1.0,
                0.9999998874647977,
                0.9999998642566866,
                1.0,
                0.999999931743979
            ],
            [
                0.9999999006880076,
                1.0,
                0.9999998642567351,
                0.9999999358794174,
                1.0,
                0.9999997617630901,
                0.9999999586006295,
                1.0,
                0.9999999559306259,
                0.9999996940977002
            ],
            [
                1.0,
                0.9999999468421567,
                1.0,
                1.0,
                1.0,
                1.0,
                0.999999864256719,
                0.9999999559306154,
                1.0,
                1.0
            ],
            [
                0.9999999397642151,
                0.9999999176675437,
                1.0,
                1.0,
                0.9999998724809724,
                1.0,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999176675436,
                0.9999999317439546,
                0.9999998362622943,
                0.9999997617631469,
                0.9999999358794174,
                1.0,
                0.9999996310115039,
                1.0,
                0.9999999176675239,
                1.0
            ],
            [
                0.9999998362622552,
                1.0,
                0.9999999732705347,
                0.9999998362622358,
                0.9999999611088904,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999677581028
            ],
            [
                0.9999998257021837,
                0.9999998724809419,
                0.9999998874648515,
                0.9999999559305733,
                0.9999999500628036,
                0.9999999500627917,
                0.9999998257020799,
                0.9999998942829099,
                0.9999999317439708,
                0.9999998362623724
            ],
            [
                0.999999939764258,
                0.999999946842182,
                0.9999997126313783,
                1.0,
                0.9999999397642796,
                1.0,
                0.9999999123574732,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999530883452,
                0.9999998257021422,
                0.9999996533672963,
                5.422219616184461e-06,
                0.999999495652592,
                0.999999872480942,
                3.7266401726359486e-06,
                0.9999993524049705,
                0.9999993524051248,
                0.9999999067050387
            ],
            [
                0.9999999715466289,
                1.0,
                1.0,
                0.9999999656786833,
                0.9999999468421313,
                0.9999999634651531,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999998144608762,
                1.0,
                0.999999894282998,
                0.9999993524052794,
                0.9999998942830359,
                1.0,
                0.9999994631251883,
                0.9999999176675829
            ],
            [
                0.9999995818813768,
                0.9999991148429646,
                0.9999998461826405,
                0.9999999067050943,
                0.9999997761970782,
                0.9999999123575569,
                0.9999998802069017,
                0.9999998942830863,
                0.9999984465022468,
                0.9999999530883228
            ],
            [
                1.0,
                1.0,
                0.9999999176675437,
                1.0,
                1.0,
                1.0,
                0.999999974890009,
                1.0,
                1.0,
                0.9999999176675535
            ],
            [
                1.0,
                1.0,
                0.9999999067050387,
                0.9999999067051165,
                0.9999999226557409,
                0.9999998555019446,
                0.9999998024946332,
                0.9999998362622943,
                0.9999999123574629,
                0.9999999067050165
            ],
            [
                0.9999999611089183,
                0.9999990577557434,
                0.9999997126314125,
                0.9999998724809116,
                NaN,
                1.0,
                0.9999998874648917,
                0.9999998802069016,
                0.9999997126313441,
                0.9999999530883174
            ],
            [
                0.9999999176675535,
                0.9999998555019274,
                0.9999998942830359,
                0.9999997897565588,
                0.9999998362622553,
                0.9999999559306049,
                0.9999998362623139,
                0.999999917667524,
                0.9999998642566381,
                0.9999998642567028
            ],
            [
                0.9999999656787284,
                1.0,
                0.9999998874647843,
                1.0,
                1.0,
                1.0,
                0.9999999358793867,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999994284994851,
                0.9999997463981032,
                3.9278605979534166e-07,
                5.715005151606823e-07,
                4.1399390279513406e-08,
                2.699577452775239e-07,
                1.6373776432509826e-07,
                0.9999998362623137,
                6.475949525981759e-07,
                0.9999997761971315
            ],
            [
                1.0,
                1.0,
                0.9999999611088904,
                1.0,
                0.9999999764113381,
                0.9999999468421947,
                1.0,
                1.0,
                NaN,
                1.0
            ],
            [
                0.9999998555020136,
                1.0,
                0.9999999317439954,
                1.0,
                0.9999999500628393,
                0.999999900687984,
                0.9999999273418876,
                1.0,
                0.9999998942829225,
                1.0
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999434137368,
                1.0,
                0.9999999273418183,
                0.9999999067051276,
                1.0,
                0.9999999358793714,
                0.999999846182604
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999998555019274,
                1.0,
                0.9999999656787407,
                0.9999999317439708,
                0.9999999226558238,
                0.9999999586006146,
                0.9999999559305524
            ],
            [
                1.760342793638743e-06,
                6.475945666063607e-07,
                1.0,
                3.466325384682834e-07,
                0.00033535015120922363,
                0.9999993524052794,
                4.4508494582405734e-07,
                1.444980381819277e-07,
                1.637377057680051e-07,
                5.043475885696228e-07
            ],
            [
                0.9999998942830737,
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999500628274,
                0.9999998874649184,
                1.0,
                0.9999995262092165,
                0.9999999634651748
            ],
            [
                0.999999961108858,
                1.0,
                0.9999999764113577,
                0.9999998802069444,
                0.9999999273418789,
                0.9999999500627917,
                0.9999999611088534,
                0.9999997126313784,
                0.9999999559306206,
                0.9999998555020135
            ],
            [
                1.0677024882009222e-06,
                0.9999996940978096,
                0.999998346309628,
                0.9999998362623334,
                0.9999998257021838,
                0.9999995262093293,
                0.9999998724809723,
                0.9999999067051388,
                0.9999832985841705,
                3.9278605979534166e-07
            ],
            [
                0.9999996940977731,
                0.9999999226557408,
                0.9999999586006492,
                0.9999999397642653,
                0.9999997617631753,
                1.0,
                1.0,
                1.0,
                0.9999999500628334,
                0.9999999273418096
            ],
            [
                0.9999999123574732,
                0.999999802494633,
                0.9999999226557776,
                0.9999999358794479,
                0.9999999176674651,
                0.9999998802069873,
                0.9999996940978096,
                0.9999998874648112,
                0.9999998642566219,
                0.9999998724808963
            ],
            [
                0.9999999434137907,
                0.9999998555020135,
                1.0,
                1.0,
                1.0,
                0.9999999358793715,
                1.0,
                0.9999999500627917,
                1.0,
                0.9999999226557684
            ],
            [
                1.0,
                0.9999991684716755,
                5.422221555340727e-06,
                1.0,
                1.0,
                0.9999999530883452,
                1.0,
                0.9999999715466629,
                1.0,
                0.9999984465015059
            ],
            [
                0.9999999397642365,
                0.9999999468421503,
                0.9999997126313784,
                0.9999998802069445,
                0.9999998024946567,
                0.9999997761971849,
                0.9999998802069445,
                0.9999999434137571,
                0.9999998942830485,
                0.9999998555019447
            ],
            [
                0.9999998257021214,
                0.9999999530883732,
                0.9999999123575359,
                0.9999997463981637,
                0.9999997126314126,
                0.9999998724809724,
                0.9999999611088766,
                0.9999998257020798,
                0.9999999317439546,
                0.9999999434137974
            ],
            [
                0.9999999123575881,
                1.0,
                1.0,
                0.9999999273418009,
                1.0,
                1.0,
                0.9999999176675239,
                0.9999999226557962,
                1.0,
                0.9999999226557961
            ],
            [
                4.785092783519724e-06,
                3.726638839878908e-06,
                2.2603234895372223e-06,
                2.9023119851781017e-06,
                1.6701429808632785e-05,
                1.370957860576702e-06,
                7.338207180884785e-07,
                5.043473480766399e-07,
                7.889266347786918e-06,
                6.144176799334096e-06
            ],
            [
                0.9999998555020135,
                0.9999999611088951,
                0.999999927341853,
                0.999999958600595,
                0.9999999530883787,
                1.0,
                1.0,
                0.999999931743979,
                0.9999999611089182,
                0.9999999677581529
            ],
            [
                0.9999997761970515,
                0.9999989322966216,
                1.0,
                1.0,
                0.999998712104171,
                0.9999999123575046,
                1.0,
                1.0,
                0.9999992188513905,
                0.9999999656786956
            ],
            [
                1.0,
                0.9999999586005999,
                0.9999999559306049,
                0.9999999006881497,
                0.9999999397642293,
                0.9999998724809571,
                0.9999989322967489,
                0.9999995818814266,
                0.9999999397642796,
                0.9999991148433868
            ],
            [
                0.9999999611088812,
                0.9999997897566841,
                1.0,
                0.9999999358793867,
                0.9999999317439547,
                1.0,
                0.9999999273418702,
                0.9999999434137098,
                0.9999999358793562,
                0.9999998555019619
            ],
            [
                0.9999999500628572,
                0.999999057755182,
                1.0,
                0.9999999176675142,
                1.0,
                0.9999999226557131,
                1.0,
                0.9999999697115624,
                1.0,
                1.0
            ],
            [
                0.9999999530883787,
                0.9999999176675436,
                0.9999999176675338,
                1.0,
                0.9999999434137637,
                0.9999999317439873,
                0.9999998461826771,
                0.9999999500627857,
                0.9999999273418876,
                0.9999999317440116
            ],
            [
                1.0,
                1.0,
                0.9999999634651966,
                0.9999999006879721,
                1.0,
                1.0,
                0.9999999273418355,
                0.9999999067051165,
                1.0,
                0.9999999586006146
            ],
            [
                7.734414854823498e-08,
                0.9999993524050478,
                0.9999997761970516,
                0.999999927341775,
                0.9999998144609645,
                0.9999998257022045,
                1.0,
                0.9999998144609203,
                1.0,
                0.9999986290429576
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999999677581528,
                1.0,
                1.0,
                0.9999999611088672,
                1.0,
                1.0
            ],
            [
                0.9999999468421377,
                0.9999999006880904,
                1.0,
                0.9999999468421439,
                1.0,
                0.9999999434137705,
                1.0,
                0.9999997761971049,
                0.9999999434137097,
                1.0
            ],
            [
                1.0,
                1.0,
                0.9999999317439383,
                1.0,
                0.9999999226557316,
                0.999999939764215,
                0.9999999434137503,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999273418096,
                0.9999999273418096,
                0.9999999067050276,
                0.9999999530883174,
                1.0,
                0.9999999559306312,
                1.0,
                1.0,
                0.9999999358793485,
                1.0
            ],
            [
                1.0,
                0.9999998362623723,
                0.999999961108909,
                0.9999999317440035,
                0.999999900688055,
                1.0,
                0.9999998942829854,
                0.9999999468421186,
                0.9999998555019963,
                1.0
            ],
            [
                3.726637951367137e-06,
                1.473898372822193e-05,
                4.222832941193893e-06,
                2.144494841482881e-05,
                6.1441731370702875e-06,
                2.561282821352716e-06,
                6.962257079832313e-06,
                1.1478773599425825e-05,
                2.7535691101761522e-05,
                3.288748281329893e-06
            ],
            [
                0.999999943413757,
                1.0,
                0.9999999317439954,
                0.9999999634651705,
                0.999999887464744,
                1.0,
                0.999999958600659,
                0.9999999586006146,
                0.9999999804443217,
                1.0
            ],
            [
                0.9999999123575255,
                0.9999999530883452,
                0.9999997617631753,
                0.9999999530883676,
                0.9999999273418615,
                0.9999999358793639,
                0.9999999273418962,
                1.0,
                1.0,
                0.9999998257021422
            ],
            [
                0.9999999559305943,
                1.0,
                0.999999931743914,
                0.9999996072138467,
                1.0,
                1.0,
                1.0,
                0.9999998942829854,
                1.0,
                1.0
            ],
            [
                0.9999999559305681,
                0.999999894282998,
                0.9999996072136126,
                0.9999998942830358,
                1.0,
                0.999999894283061,
                0.9999998724809723,
                0.999999943413811,
                0.9999998942829225,
                0.9999997761970248
            ],
            [
                0.9999999559306206,
                0.9999999468420996,
                1.0,
                1.0,
                1.0,
                0.9999999500627857,
                1.0,
                1.0,
                0.9999999067050832,
                1.0
            ],
            [
                0.9999997463981032,
                0.9999999067050054,
                0.9999999067049831,
                0.9999998461826222,
                0.9999996743686257,
                0.9999997300421262,
                5.315787506612373e-08,
                0.9999989969854346,
                0.9999964991447554,
                0.9999998144608983
            ],
            [
                0.9999964991468413,
                0.9999999634651835,
                0.9999952149049439,
                0.9999999559305733,
                1.0,
                0.9999991684719727,
                0.9999970976866334,
                0.9999998642567351,
                0.9999999226558146,
                0.9999975938985225
            ],
            [
                1.4738978458140753e-05,
                1.0129988564974359e-05,
                3.2887498494551953e-06,
                0.999999802494633,
                3.120191509172827e-05,
                2.2603253756874524e-06,
                0.9999991684719728,
                1.6701417862648148e-05,
                8.315280276626197e-07,
                0.0004878571217604719
            ],
            [
                0.9999999586006542,
                1.0,
                0.9999999434137772,
                1.0,
                0.9999999397642293,
                0.9999999559305733,
                1.0,
                0.9999999317439058,
                0.9999999358793409,
                0.9999999176674848
            ],
            [
                0.9999999358793409,
                0.999999894283061,
                1.0,
                1.0,
                0.999999789756609,
                0.9999998802069017,
                1.0,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999999500628036,
                0.999999789756609,
                0.9999997126313441,
                0.9999998555019447,
                0.9999999468421946,
                0.9999998874647307,
                0.9999998024946566,
                0.9999999226557685,
                0.9999998257021422,
                0.9999999006879721
            ],
            [
                0.9999997761970248,
                0.9999992188517629,
                0.999999825702163,
                0.9999999067050276,
                0.999999864256719,
                0.9999997126313441,
                0.9999999273418876,
                0.9999995262093858,
                0.9999955048178925,
                4.450851580566494e-07
            ],
            [
                0.999998996985434,
                0.9999980052702803,
                0.9999997761970515,
                0.9999998257020591,
                0.9999998642566381,
                0.9999999586006146,
                0.9999992188515767,
                0.9999998461827139,
                0.9999997126315497,
                0.999997739676512
            ],
            [
                0.9999999067050054,
                6.47595107001401e-07,
                4.450850519409479e-07,
                3.466327037553825e-07,
                2.902311639183378e-06,
                0.999999931743979,
                0.9999999273417922,
                1.553498124964492e-06,
                0.9999999358793715,
                8.315278294114555e-07
            ],
            [
                0.9999999067051166,
                0.9999996310115918,
                1.0,
                1.0,
                0.9999999530883843,
                1.0,
                1.0,
                0.9999999715466324,
                0.9999999634651618,
                1.0
            ],
            [
                0.9999992188512972,
                1.0,
                0.9999996533673378,
                0.9999960330155081,
                0.9999994631251883,
                1.2751902768612997e-07,
                0.9999994631249962,
                0.9999993106386261,
                0.99999976176309,
                0.9999992188514836
            ],
            [
                0.9999999434137704,
                4.69116603868534e-08,
                1.0,
                4.1399390279513406e-08,
                1.0,
                1.0,
                1.0,
                0.9999998461826037,
                1.0,
                1.0
            ],
            [
                0.9999999176674357,
                1.0,
                1.0,
                0.9999998724809268,
                0.9999993524050477,
                1.0,
                0.9999998461826954,
                0.9999999559305787,
                0.9999999358794174,
                0.9999999176675731
            ],
            [
                0.9999997897566089,
                0.99999976176309,
                0.9999998362623332,
                0.9999999226557408,
                0.9999998802069302,
                0.9999997761971583,
                0.9999998362623528,
                0.9999995549151074,
                0.9999998642566704,
                0.9999997897567342
            ],
            [
                0.9999999500627916,
                0.9999998802069159,
                1.0,
                0.999997273530706,
                0.9999996072136594,
                0.9999987901346056,
                0.9999999586006344,
                0.9999996940978098,
                0.9999999226557778,
                0.9999999123575568
            ],
            [
                0.9999996743686257,
                0.9999993916411086,
                0.9999999176675437,
                0.9999998874647844,
                0.9999998942830485,
                0.9999999317439303,
                0.9999999358793333,
                0.9999998024946801,
                0.9999999586006245,
                0.9999999273417922
            ],
            [
                0.9999999226557962,
                1.0,
                0.9999999500627857,
                1.0,
                0.9999997761971849,
                1.0,
                1.0,
                0.9999999067050165,
                1.0,
                0.9999999586006245
            ],
            [
                0.9999999226557593,
                0.9999993524052022,
                0.9999992188517628,
                0.9999993524054338,
                0.9999998024945624,
                0.9999990577557437,
                0.9999997300423192,
                0.9999990577552943,
                0.9999995549148951,
                0.9999994956524718
            ],
            [
                1.0,
                1.0,
                1.0,
                0.9999999226557225,
                1.0,
                0.9999999634652054,
                1.0,
                1.0,
                1.0,
                0.9999996310113279
            ],
            [
                0.9999999732705347,
                1.0,
                0.9999998874648245,
                1.0,
                0.9999999067050165,
                1.0,
                0.9999999611089182,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999998724809723,
                0.9999994631250603,
                1.855391681906175e-07,
                0.9999999006881259,
                4.222835458175145e-06,
                0.9999988634357478,
                1.6373776432509826e-07,
                0.9999861539905195,
                1.7603425837791042e-06,
                1.760343213335281e-06
            ],
            [
                1.4449807263312446e-07,
                3.466327037553825e-07,
                6.023571320847322e-08,
                1.1253508156363576e-07,
                2.3823688159291947e-07,
                7.73442776303243e-08,
                8.764244316973974e-08,
                9.931185038635267e-08,
                1.6373774480605869e-07,
                1.8553905760062447e-07
            ],
            [
                0.9999999006880786,
                0.9999999176675632,
                0.9999999123575986,
                1.0,
                1.0,
                0.9999999732705411,
                1.0,
                1.0,
                1.0,
                0.9999998802069302
            ],
            [
                0.9999998874648246,
                0.9999999317440197,
                0.9999995549151075,
                0.9999998461826223,
                0.9999999176675044,
                0.999999880206916,
                0.9999998024946095,
                0.9999999123574733,
                0.9999999358793485,
                0.9999999317439384
            ],
            [
                0.9999999500627976,
                0.999999974889994,
                0.9999999656786833,
                0.9999999468421122,
                0.9999999732705379,
                0.9999999530883787,
                1.0,
                1.0,
                0.9999999397642508,
                0.9999999067049943
            ],
            [
                0.999999900687984,
                0.999999931743914,
                0.9999998461826589,
                0.9999999358793332,
                0.9999999006880786,
                0.9999998642566866,
                0.9999997300423192,
                0.999999872480942,
                0.9999996940976639,
                0.9999999067051166
            ],
            [
                1.0,
                1.0,
                1.0,
                0.999999961108909,
                1.0,
                1.0,
                0.9999999358793332,
                1.0,
                0.9999996940978826,
                1.0
            ],
            [
                0.9999997126314469,
                0.9999997126314811,
                0.9999998257020798,
                0.9999997617630617,
                0.9999994631249962,
                0.9999998024946095,
                0.9999999176675437,
                0.9999983463106118,
                0.9999998724809267,
                0.9999994284995531
            ],
            [
                0.9999998802069587,
                0.999999931743971,
                0.9999999067051055,
                1.0,
                0.9999997761971315,
                0.9999999500627976,
                0.9999998257021006,
                0.9999999123575256,
                0.9999999067050498,
                0.9999999358793867
            ],
            [
                0.9999999317440116,
                0.9999999273417922,
                0.999999864256719,
                0.9999999067050388,
                0.9999999358793867,
                0.9999998724810027,
                1.0,
                0.9999999634652097,
                0.9999994284992807,
                0.9999999123575046
            ],
            [
                0.9999998461826588,
                1.0,
                0.9999999123575882,
                0.9999998144608762,
                0.9999995818812771,
                1.0,
                0.9999999317439221,
                0.9999999358793485,
                0.9999998362623335,
                0.9999999317439953
            ],
            [
                1.0,
                1.0,
                1.0,
                1.0,
                0.9999991148433867,
                0.9999999123574942,
                1.0,
                1.0,
                1.0,
                0.9999999317440279
            ],
            [
                0.9999999006880904,
                0.9999999634651923,
                0.999999946842125,
                1.0,
                0.9999999434137907,
                1.0,
                0.9999999468421124,
                1.0,
                1.0,
                1.0
            ]
        ]
    },
    {
        "q_id": "9790_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            9,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            49,
            50,
            51,
            52,
            53,
            54,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            101,
            102,
            103,
            105,
            106,
            107,
            109,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            124,
            125,
            127
        ],
        "rewards": [
            [
                0.9999980052702814,
                0.9999986290421411,
                9.422445939032799e-07,
                0.9999987121050962,
                0.9999949062962428,
                0.9999977396765162,
                0.9999977396759773,
                5.422219616265831e-06,
                0.9999981261248432,
                0.999997739675707
            ],
            [
                3.9278610661902853e-07,
                2.902313023130843e-06,
                5.043472278322555e-07,
                NaN,
                2.3823690999323465e-07,
                1.9947304348862686e-06,
                NaN,
                6.96225873967641e-06,
                NaN,
                1.994730434879465e-06
            ],
            [
                1.6373774480605869e-07,
                1.209865827752005e-06,
                1.760342793638743e-06,
                5.715002426486762e-07,
                2.6995784182183607e-07,
                3.05902336324494e-07,
                5.04347468323289e-07,
                3.927862002663297e-07,
                5.422220262599396e-06,
                2.6995784182183607e-07
            ],
            [
                4.4508494582314646e-07,
                NaN,
                NaN,
                4.450852641737424e-07,
                1.0677029973192638e-06,
                NaN,
                NaN,
                NaN,
                2.260325106237323e-06,
                NaN
            ],
            [
                1.0677033791495609e-06,
                1.3007126913583456e-05,
                3.7266392840781026e-06,
                4.785094494576774e-06,
                8.315281267861397e-07,
                NaN,
                5.422217030707961e-06,
                5.715007195431641e-07,
                1.0677029973056687e-06,
                1.0677029973158649e-06
            ],
            [
                4.785096776394765e-06,
                6.475947981975644e-07,
                1.2098662604192665e-06,
                5.71500651413193e-07,
                NaN,
                7.338212429562581e-07,
                2.5612812947508257e-06,
                3.059021175247079e-07,
                6.475950298011458e-07,
                1.3709570434178922e-06
            ],
            [
                3.059022998581767e-07,
                1.855391239544352e-07,
                1.7603438428848787e-06,
                3.05902190458764e-07,
                2.902312677150514e-06,
                2.9023116391978967e-06,
                1.0677027427624903e-06,
                1.2098652508347793e-06,
                1.5534979397790343e-06,
                1.760342793638743e-06
            ],
            [
                9.422445939032799e-07,
                1.6373766672888118e-07,
                3.927860597935108e-07,
                2.3823682479181176e-07,
                1.855391681891831e-07,
                3.0590226339061185e-07,
                1.5534981249397663e-06,
                5.043472879504592e-07,
                3.9278605979208185e-07,
                1.0677027427525368e-06
            ],
            [
                0.9999989969857935,
                0.9999843104503394,
                0.9999985406234329,
                NaN,
                0.00010889687041282619,
                0.9999989969854347,
                3.927860597935108e-07,
                0.9999952149072339,
                NaN,
                0.9999993524052794
            ],
            [
                1.7603425837903113e-06,
                1.0129987357517693e-05,
                9.422448185510695e-07,
                5.043476486902204e-07,
                4.450852111120808e-07,
                3.466327450756327e-07,
                1.7603438428800754e-06,
                3.288748281329893e-06,
                3.05902190458764e-07,
                5.715003788993679e-07
            ],
            [
                NaN,
                0.9999843104429548,
                4.450852111155216e-07,
                NaN,
                6.962256249885085e-06,
                NaN,
                2.902313023130843e-06,
                2.9023119851781017e-06,
                4.2228339479858295e-06,
                NaN
            ],
            [
                3.72663883989755e-06,
                2.2603242978871282e-06,
                7.338208055680009e-07,
                NaN,
                NaN,
                2.5612834320563895e-06,
                8.315277302857965e-07,
                7.338211554813555e-07,
                NaN,
                9.422450432030903e-07
            ],
            [
                2.1024334103581732e-07,
                5.043474683240344e-07,
                5.715003789046955e-07,
                3.466325797900508e-07,
                1.637377057680051e-07,
                1.27519088491875e-07,
                2.699578096393206e-07,
                NaN,
                NaN,
                3.466325797888292e-07
            ],
            [
                1.9947304348862686e-06,
                8.315279285370317e-07,
                NaN,
                NaN,
                NaN,
                1.2098662604291696e-06,
                1.067703379154416e-06,
                7.889261645427538e-06,
                1.2098652508424818e-06,
                5.715003789046955e-07
            ],
            [
                1.9947306726594253e-06,
                NaN,
                NaN,
                6.962253759904688e-06,
                7.338211554783522e-07,
                NaN,
                1.7603425837855082e-06,
                2.5612812947508257e-06,
                4.785092783454444e-06,
                3.7266392840781026e-06
            ],
            [
                4.222834954778007e-06,
                1.7603425837494853e-06,
                1.9947292459347367e-06,
                9.422442569097361e-07,
                7.889266347786918e-06,
                1.5534971990126997e-06,
                3.726639728370556e-06,
                1.209865539295696e-06,
                4.785092783454444e-06,
                2.902312677137316e-06
            ],
            [
                NaN,
                1.6373776432509826e-07,
                NaN,
                8.764242227418718e-08,
                2.3823688159291947e-07,
                9.931185038635267e-08,
                NaN,
                NaN,
                1.1253525596174225e-07,
                2.102434412875379e-07
            ],
            [
                2.1024339116168358e-07,
                NaN,
                1.0677032518814388e-06,
                8.315281267882195e-07,
                3.7266410611296085e-06,
                NaN,
                5.043476486915964e-07,
                1.1478770862735993e-05,
                9.422448185510695e-07,
                3.9278605979534166e-07
            ],
            [
                4.450851580555361e-07,
                9.422442569315887e-07,
                1.209866260432471e-06,
                NaN,
                6.475951069985296e-07,
                1.0677033791583005e-06,
                2.2603240284371276e-06,
                NaN,
                3.2887506336235617e-06,
                2.2603242978871282e-06
            ],
            [
                7.338212429594283e-07,
                3.466327863983311e-07,
                5.71500515161527e-07,
                2.699577452775239e-07,
                5.04347468323289e-07,
                8.31528325040778e-07,
                2.1024334103581732e-07,
                1.855391239539711e-07,
                1.760343633031919e-06,
                4.4508494582405734e-07
            ],
            [
                8.315278294114555e-07,
                1.4449798650551755e-07,
                NaN,
                NaN,
                2.102434412875379e-07,
                5.715003789046955e-07,
                3.9278629391427843e-07,
                8.315284241665078e-07,
                9.422448185510695e-07,
                1.4449805540763184e-07
            ],
            [
                1.3709572068272963e-06,
                1.3709567165530083e-06,
                1.0677032518785256e-06,
                7.338213304316717e-07,
                4.450849458200093e-07,
                NaN,
                1.2098652508347793e-06,
                NaN,
                8.315278294001114e-07,
                9.422448185435711e-07
            ],
            [
                1.3709567165617364e-06,
                9.422442569334097e-07,
                1.5534984953552536e-06,
                4.450850519403407e-07,
                NaN,
                NaN,
                NaN,
                9.422442569315887e-07,
                1.5534971990126997e-06,
                1.5534984953552536e-06
            ],
            [
                1.4449802095609418e-07,
                4.450850519403407e-07,
                4.450851580555361e-07,
                1.8553905759969634e-07,
                3.927860597945825e-07,
                5.715006514040971e-07,
                1.6373768624837685e-07,
                1.2751901248391176e-07,
                1.4449805540700758e-07,
                1.6373764720990908e-07
            ],
            [
                1.2098662604291696e-06,
                8.315284241650899e-07,
                1.3709576971425944e-06,
                2.9023112931688987e-06,
                5.043472278322555e-07,
                3.7266406168827523e-06,
                4.450848927658745e-07,
                1.0677027427600627e-06,
                NaN,
                8.315283250371857e-07
            ],
            [
                NaN,
                2.561281600086738e-06,
                1.9947292459347367e-06,
                2.2603240284371276e-06,
                5.715003107767143e-07,
                8.315284241665078e-07,
                1.760343633031919e-06,
                4.2228339479858295e-06,
                2.5612834320470717e-06,
                NaN
            ],
            [
                1.0677032518814388e-06,
                0.9999991148430701,
                1.0677024882009222e-06,
                2.2603242978871282e-06,
                3.2887502415767434e-06,
                9.422443692574719e-07,
                6.47594952603035e-07,
                7.338210680021253e-07,
                6.475950298011458e-07,
                1.0677027427624903e-06
            ],
            [
                NaN,
                1.7603436330179102e-06,
                1.3709567165579959e-06,
                3.927862470899887e-07,
                NaN,
                8.315281267834927e-07,
                NaN,
                3.7266410611296085e-06,
                NaN,
                NaN
            ],
            [
                6.475947982037486e-07,
                1.7603430034867993e-06,
                1.2098653950656417e-06,
                4.4508494582405734e-07,
                1.6373766672994222e-07,
                2.1024334103581732e-07,
                9.422443692574719e-07,
                2.6995771309523475e-07,
                3.466326624336003e-07,
                6.475945666063607e-07
            ],
            [
                3.4663274507713016e-07,
                1.0677032518814388e-06,
                2.6995774527718623e-07,
                6.9622537599680095e-06,
                NaN,
                0.9999810748587095,
                2.902311639183378e-06,
                5.04347528446051e-07,
                1.3709572068522336e-06,
                NaN
            ],
            [
                1.6373768624837685e-07,
                2.1024334103505245e-07,
                8.315284241560147e-07,
                2.3823690999160957e-07,
                3.059021175247079e-07,
                1.444980209564556e-07,
                2.382369383923073e-07,
                6.475947982002148e-07,
                3.059021904559123e-07,
                2.1024341622368903e-07
            ],
            [
                2.90231094723893e-06,
                NaN,
                2.1024341622426268e-07,
                3.7266401726359486e-06,
                4.450849988811838e-07,
                1.209865539295696e-06,
                3.05902190458764e-07,
                8.315282259089153e-07,
                NaN,
                5.715005151606823e-07
            ],
            [
                1.1253520230052635e-07,
                3.7266383956509585e-06,
                1.553497199007048e-06,
                2.3823688159291947e-07,
                7.338207180898968e-07,
                2.2603248367949354e-06,
                9.422449308716635e-07,
                5.715003107767143e-07,
                1.8925157265332104e-05,
                1.3007133116542802e-05
            ],
            [
                4.4508510499737865e-07,
                6.475949525919915e-07,
                5.715006514105942e-07,
                7.338209805224048e-07,
                3.059023727894942e-07,
                5.715004470295662e-07,
                5.715005832853093e-07,
                1.067702742726318e-06,
                3.92786293909545e-07,
                7.338210679909462e-07
            ],
            [
                NaN,
                5.043472879540142e-07,
                2.561281294760143e-06,
                8.31528325040778e-07,
                1.760343633036322e-06,
                NaN,
                2.3823702359290413e-07,
                8.315284241665078e-07,
                0.9999756997535292,
                2.6995790618469934e-07
            ],
            [
                2.69957906184239e-07,
                3.466327863983311e-07,
                3.4663253846718004e-07,
                3.927862939126708e-07,
                2.6995790618350237e-07,
                3.059021175247079e-07,
                3.05902226923399e-07,
                3.4663262110945863e-07,
                2.1024336609843824e-07,
                1.855391239539711e-07
            ],
            [
                1.30071315662049e-05,
                1.5534979397790343e-06,
                NaN,
                NaN,
                8.315278294072958e-07,
                NaN,
                3.466326211105621e-07,
                2.9023116392097746e-06,
                8.315281267861397e-07,
                NaN
            ],
            [
                1.3709572068522336e-06,
                NaN,
                5.715005832872586e-07,
                NaN,
                NaN,
                3.288750241561788e-06,
                1.5534971990126997e-06,
                9.422450432014836e-07,
                6.475949526020042e-07,
                NaN
            ],
            [
                1.8553907971758842e-07,
                3.7266383956509585e-06,
                6.475945666063607e-07,
                1.0677027427624903e-06,
                3.466326624336003e-07,
                2.561281600086738e-06,
                1.3709572068553509e-06,
                8.939696304311336e-06,
                1.760344052693435e-06,
                NaN
            ],
            [
                6.475946438055299e-07,
                5.043475885696228e-07,
                1.3709576971463352e-06,
                6.475947210046347e-07,
                1.3709575337159875e-06,
                2.90231094723893e-06,
                3.05902336324494e-07,
                5.715003789046955e-07,
                2.102434412875379e-07,
                9.931202796993203e-08
            ],
            [
                NaN,
                NaN,
                1.0677029973192638e-06,
                NaN,
                NaN,
                8.315284241650899e-07,
                8.315279285351409e-07,
                NaN,
                NaN,
                9.422444815814404e-07
            ],
            [
                NaN,
                1.2751902768612997e-07,
                2.3823690999323465e-07,
                NaN,
                1.4449803818215767e-07,
                2.382369667929001e-07,
                NaN,
                1.0677028700422047e-06,
                1.8553916819032217e-07,
                8.315278294114555e-07
            ],
            [
                NaN,
                7.338213304363436e-07,
                NaN,
                1.6373766672973748e-07,
                5.715006514176113e-07,
                2.5612831267202583e-06,
                2.5612828213934817e-06,
                NaN,
                1.2098659719788098e-06,
                NaN
            ],
            [
                1.760343633031919e-06,
                3.9278634073732336e-07,
                1.994729008145876e-06,
                1.9947297215125433e-06,
                2.3823693839290317e-07,
                2.699577774585891e-07,
                6.475947981975644e-07,
                NaN,
                NaN,
                NaN
            ],
            [
                5.043474683156057e-07,
                3.726639728262097e-06,
                1.994729721436347e-06,
                7.889261645427538e-06,
                2.9023109471689794e-06,
                2.902311985079115e-06,
                4.450849458218309e-07,
                2.902313023130843e-06,
                1.0677026154619133e-06,
                1.760343213335281e-06
            ],
            [
                7.338209805224048e-07,
                NaN,
                1.3709568799823232e-06,
                NaN,
                2.260324567337161e-06,
                1.0677031245990084e-06,
                NaN,
                1.2098652508347793e-06,
                3.2887502415438413e-06,
                NaN
            ],
            [
                2.699577774585891e-07,
                1.5534975693933505e-06,
                1.5534975693979422e-06,
                9.422442569315887e-07,
                1.3709570434178922e-06,
                5.715006514105942e-07,
                3.288749457469787e-06,
                2.382368531929327e-07,
                6.962257079775324e-06,
                NaN
            ],
            [
                2.902312677137316e-06,
                NaN,
                1.2098656835076114e-06,
                NaN,
                3.7266392840781026e-06,
                NaN,
                NaN,
                NaN,
                5.715007195447234e-07,
                NaN
            ],
            [
                1.5534983101644536e-06,
                8.315277302857965e-07,
                5.043472278322555e-07,
                6.475945666051092e-07,
                NaN,
                5.043474683240344e-07,
                1.2098656835252174e-06,
                8.315284241665078e-07,
                4.785093924389007e-06,
                4.450849988798682e-07
            ],
            [
                0.0004305569894503386,
                1.3709567165617364e-06,
                4.0063696967815485e-05,
                NaN,
                1.0677026154806063e-06,
                3.466326211113502e-07,
                3.4663274507713016e-07,
                2.902312677150514e-06,
                1.7603440527286572e-06,
                1.2098659719716573e-06
            ],
            [
                1.5534973842076057e-06,
                2.1024339116082313e-07,
                3.7266397283908927e-06,
                8.315277302857965e-07,
                1.0677028700422047e-06,
                1.9947292459347367e-06,
                1.994729008145876e-06,
                3.05902336324494e-07,
                9.422443692574719e-07,
                5.715003789046955e-07
            ],
            [
                6.475948754028718e-07,
                1.9947297215125433e-06,
                5.04347468323289e-07,
                3.288749457469787e-06,
                5.715006514176113e-07,
                3.05902336324494e-07,
                2.561281600086738e-06,
                1.7603434231777837e-06,
                3.927863407379485e-07,
                4.450848927658745e-07
            ],
            [
                2.10243290909724e-07,
                6.475947210031623e-07,
                1.9947292459347367e-06,
                3.927862002663297e-07,
                6.475950298011458e-07,
                NaN,
                1.209865539295696e-06,
                1.5534971990169383e-06,
                1.8553905760062447e-07,
                5.715004470295662e-07
            ],
            [
                NaN,
                NaN,
                1.4738980213985297e-05,
                2.4300246526646385e-05,
                7.338208055664991e-07,
                2.260325106237323e-06,
                1.2098662604291696e-06,
                NaN,
                9.422442569315887e-07,
                4.785096776468749e-06
            ],
            [
                1.3709567165530083e-06,
                1.3709573702722555e-06,
                2.561282516066741e-06,
                1.7603440527286572e-06,
                3.7266406168624155e-06,
                8.939699501229642e-06,
                1.3709568799679844e-06,
                1.9947299592933255e-06,
                1.9947299592570416e-06,
                1.7603430034439723e-06
            ],
            [
                1.7603440527286572e-06,
                8.315284241650899e-07,
                1.3709575337078829e-06,
                5.043474683204221e-07,
                9.422447062270609e-07,
                5.715003107755449e-07,
                1.209865827740176e-06,
                7.338207180864763e-07,
                1.3709567165530083e-06,
                1.7603427936335396e-06
            ],
            [
                7.889266347786918e-06,
                1.0677024882009222e-06,
                4.222832941193893e-06,
                NaN,
                4.2228329411708495e-06,
                1.5534983101602148e-06,
                5.715003789046955e-07,
                4.4508499888219586e-07,
                1.994729008145876e-06,
                1.7603434231777837e-06
            ],
            [
                2.5612812947508257e-06,
                4.785096206076165e-06,
                5.715005151574337e-07,
                7.338210680021253e-07,
                1.2098653950551882e-06,
                1.2098662604291696e-06,
                6.475947982002148e-07,
                5.715005832886879e-07,
                3.9278634073732336e-07,
                1.5534983101602148e-06
            ],
            [
                7.338210680021253e-07,
                1.8553916819032217e-07,
                3.9278610661902853e-07,
                NaN,
                NaN,
                3.4663266243308805e-07,
                8.315277302788957e-07,
                7.338210680002898e-07,
                4.222835458175145e-06,
                NaN
            ],
            [
                NaN,
                5.043474683240344e-07,
                NaN,
                NaN,
                1.5534971990169383e-06,
                4.4508510499737865e-07,
                NaN,
                5.043475885696228e-07,
                1.553497384196656e-06,
                6.475950298011458e-07
            ],
            [
                NaN,
                1.275190428875671e-07,
                3.927863875616689e-07,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                NaN,
                3.05902263391829e-07
            ],
            [
                NaN,
                1.7603440527286572e-06,
                3.46632497145457e-07,
                8.315279285351409e-07,
                5.043474082012222e-07,
                1.2098652508424818e-06,
                NaN,
                6.475950298011458e-07,
                0.999997593897951,
                NaN
            ],
            [
                1.0677024882009222e-06,
                0.999998005269567,
                5.04347468323289e-07,
                0.9999987901343176,
                NaN,
                1.9947292459347367e-06,
                4.450850519403407e-07,
                8.315277302841894e-07,
                NaN,
                3.9278634073732336e-07
            ],
            [
                3.466327037539638e-07,
                5.043472278280699e-07,
                2.3823685319244518e-07,
                3.9278605979534166e-07,
                1.6373776432509826e-07,
                4.450849458218309e-07,
                2.1024334103505245e-07,
                2.6995790618350237e-07,
                8.315284241560147e-07,
                1.8553903548231313e-07
            ],
            [
                0.9999985406234323,
                1.5534975693979422e-06,
                1.3709568799919866e-06,
                9.422444815814404e-07,
                NaN,
                1.0129993395336818e-05,
                9.422443692574719e-07,
                9.422445939054222e-07,
                1.2098662604192665e-06,
                NaN
            ],
            [
                1.067702615468225e-06,
                3.4663262110803996e-07,
                6.962256249821764e-06,
                1.0677031245905116e-06,
                9.422449308716635e-07,
                5.043472278280699e-07,
                1.147876949310201e-05,
                7.338213304316717e-07,
                4.450848927650143e-07,
                1.3709576971425944e-06
            ],
            [
                1.2098652508424818e-06,
                6.962258739796719e-06,
                5.422217030781934e-06,
                1.1478768126057254e-05,
                NaN,
                5.715005832886879e-07,
                2.5612812947508257e-06,
                3.7266406168827523e-06,
                1.3709568799919866e-06,
                1.9947301970972664e-06
            ],
            [
                3.927862470905692e-07,
                1.7603425837903113e-06,
                8.315277302857965e-07,
                NaN,
                9.422449308774482e-07,
                1.7603425837903113e-06,
                3.927863407379485e-07,
                4.450851049991497e-07,
                NaN,
                6.475947210031623e-07
            ],
            [
                9.422448185534261e-07,
                1.5534975693933505e-06,
                2.1024341622426268e-07,
                3.726639284144195e-06,
                8.315281267882195e-07,
                1.5534979397790343e-06,
                2.382368531929327e-07,
                NaN,
                0.9999938558224866,
                7.338207180898968e-07
            ],
            [
                1.0677027427624903e-06,
                2.2603234895289998e-06,
                2.561283432035425e-06,
                2.2603234895176927e-06,
                1.3709575337159875e-06,
                5.71500515159253e-07,
                1.760344052714248e-06,
                1.0129993394959082e-05,
                8.315283250394546e-07,
                7.338213304363436e-07
            ],
            [
                9.422444815765128e-07,
                1.0677027427569065e-06,
                8.315282259117513e-07,
                3.535625071602016e-05,
                8.939693107093343e-06,
                1.0677032518785256e-06,
                9.422442569315887e-07,
                1.2098659719716573e-06,
                1.99472900813862e-06,
                1.2098659719601033e-06
            ],
            [
                2.753568453792444e-05,
                5.043472278322555e-07,
                0.9999904837460964,
                NaN,
                1.3709573702822306e-06,
                NaN,
                1.7603427936335396e-06,
                4.2228339479858295e-06,
                6.475945666063607e-07,
                1.7603438428740716e-06
            ],
            [
                2.5612812947508257e-06,
                1.2098652508424818e-06,
                NaN,
                2.2603242978871282e-06,
                NaN,
                1.2098653950656417e-06,
                6.475947982037486e-07,
                1.9947292459347367e-06,
                7.338209805224048e-07,
                1.370957860576702e-06
            ],
            [
                3.9278605979534166e-07,
                7.338208930460318e-07,
                0.9999904837460621,
                3.288748281329893e-06,
                0.9999962733589483,
                1.7603425837903113e-06,
                5.422220262636381e-06,
                9.931195693628605e-08,
                2.382369667929001e-07,
                1.3709572068522336e-06
            ],
            [
                1.9947297215125433e-06,
                1.994730197090463e-06,
                9.422444815792981e-07,
                4.2228334445658276e-06,
                1.8925148241493373e-05,
                1.2098659719757836e-06,
                7.88926634755014e-06,
                1.553497754583709e-06,
                1.2098659719757836e-06,
                1.8925145985895816e-05
            ],
            [
                1.2098656835076114e-06,
                1.7603436330179102e-06,
                5.422220262636381e-06,
                1.3709575336947905e-06,
                4.222835458117536e-06,
                4.222834954778007e-06,
                2.2603253756956754e-06,
                7.338209805170655e-07,
                9.422450431860582e-07,
                1.994729721482609e-06
            ],
            [
                NaN,
                NaN,
                0.9999892166916676,
                NaN,
                NaN,
                NaN,
                2.699577130957872e-07,
                5.043472278322555e-07,
                2.699576809143613e-07,
                NaN
            ],
            [
                2.144495864106235e-05,
                1.3007123813193233e-05,
                1.3709572068553509e-06,
                1.553498124964492e-06,
                7.889265407327733e-06,
                5.715005832895975e-07,
                NaN,
                1.209865827752005e-06,
                7.338208055680009e-07,
                NaN
            ],
            [
                7.734423152941018e-08,
                0.9999987121041712,
                5.715004470334646e-07,
                3.466325797900508e-07,
                0.9999996533672963,
                1.855391239547094e-07,
                9.422444815814404e-07,
                0.9999991684716754,
                0.9999985406241276,
                1.994729008151319e-06
            ],
            [
                2.2603242978871282e-06,
                2.3823688159291947e-07,
                3.059022998576899e-07,
                2.3823699519290042e-07,
                1.8553910183607374e-07,
                5.043476486915964e-07,
                3.9278615344178325e-07,
                4.450849988811838e-07,
                NaN,
                4.450852111155216e-07
            ],
            [
                1.2098661162056318e-06,
                4.785096776499213e-06,
                NaN,
                NaN,
                NaN,
                9.422442569315887e-07,
                1.760343213335281e-06,
                5.715006514176113e-07,
                1.5534975693869924e-06,
                1.5534973842076057e-06
            ],
            [
                2.561281600086738e-06,
                6.475946438055299e-07,
                1.0677027427624903e-06,
                3.9278605979534166e-07,
                6.475950298021765e-07,
                1.7603425837903113e-06,
                1.275190124846946e-07,
                5.715006514176113e-07,
                3.466325384661554e-07,
                1.5534984953552536e-06
            ],
            [
                7.338209805200689e-07,
                5.715005832886879e-07,
                2.699578096373564e-07,
                1.370957860576702e-06,
                1.2098659719757836e-06,
                5.715003107715166e-07,
                4.4508515805199415e-07,
                2.3823685318968256e-07,
                1.0677029972993568e-06,
                5.715002426460124e-07
            ],
            [
                7.338208055664991e-07,
                6.475947210046347e-07,
                3.288749457432399e-06,
                1.2098653950656417e-06,
                3.9278605979534166e-07,
                0.9999667857934511,
                1.0,
                2.699577774585891e-07,
                8.315277302841894e-07,
                NaN
            ],
            [
                1.0677032518700286e-06,
                1.2098659719716573e-06,
                7.338210679979539e-07,
                1.3709575337125585e-06,
                4.785095065204162e-06,
                1.4738983727900215e-05,
                5.043476486902204e-07,
                1.3709567165530083e-06,
                1.3709567165530083e-06,
                7.338208055664991e-07
            ],
            [
                2.902311639183378e-06,
                6.475951069932288e-07,
                NaN,
                6.475950297971703e-07,
                1.2098656835076114e-06,
                3.9278624708775595e-07,
                9.422450431989127e-07,
                1.3709573702722555e-06,
                8.315277302747361e-07,
                5.043472278227948e-07
            ],
            [
                NaN,
                1.3709568799919866e-06,
                NaN,
                3.2887502415767434e-06,
                NaN,
                1.760342793638743e-06,
                1.7603427936263351e-06,
                5.043474683204221e-07,
                3.2887478892683997e-06,
                NaN
            ],
            [
                9.422444815814404e-07,
                NaN,
                8.315284241650899e-07,
                8.939693107190907e-06,
                1.2098662604247682e-06,
                6.144172404738491e-06,
                8.315277302857965e-07,
                7.338208055680009e-07,
                1.7603434231833873e-06,
                1.3709572068522336e-06
            ],
            [
                3.0590226339137693e-07,
                1.2098659719757836e-06,
                6.1441746020359e-06,
                2.2603245673443566e-06,
                8.315279285351409e-07,
                3.927862470899887e-07,
                5.71500719545698e-07,
                1.7603438428800754e-06,
                5.71500719545698e-07,
                2.9023119851781017e-06
            ],
            [
                1.9947304348703948e-06,
                8.939699501132077e-06,
                1.3007130015677909e-05,
                1.209865539295696e-06,
                NaN,
                NaN,
                4.785095635655362e-06,
                1.7603430034867993e-06,
                NaN,
                NaN
            ],
            [
                NaN,
                1.3709570434178922e-06,
                NaN,
                NaN,
                5.715007195431641e-07,
                5.715003107755449e-07,
                NaN,
                5.043472879525233e-07,
                6.9622595696935874e-06,
                5.715007195431641e-07
            ],
            [
                2.9023109472494878e-06,
                2.1444950971601277e-05,
                1.5534975693979422e-06,
                7.889261645427538e-06,
                0.9999995818813768,
                NaN,
                3.120191137762131e-05,
                6.962258739796719e-06,
                2.144495608424996e-05,
                8.315277302841894e-07
            ],
            [
                3.466325384661554e-07,
                NaN,
                3.466326211113502e-07,
                2.1024329090929374e-07,
                1.6373772528677946e-07,
                2.69957906184239e-07,
                5.04347528440776e-07,
                NaN,
                2.6995784182140636e-07,
                3.9278615344178325e-07
            ],
            [
                2.382369667929001e-07,
                3.059022269250683e-07,
                9.422450432014836e-07,
                1.5534973842076057e-06,
                5.043474081993875e-07,
                1.5534984953510149e-06,
                5.043472278312808e-07,
                3.4663266243308805e-07,
                3.059021175255426e-07,
                1.760343003481596e-06
            ],
            [
                4.4508515805735777e-07,
                8.31527928532683e-07,
                1.3709567165617364e-06,
                1.994729721518893e-06,
                1.209866260432471e-06,
                7.338211554783522e-07,
                3.466325384661554e-07,
                NaN,
                1.9947304348862686e-06,
                6.9622587397397306e-06
            ],
            [
                1.8553907971758842e-07,
                4.450851580540182e-07,
                NaN,
                2.382369667892166e-07,
                1.6373766672821107e-07,
                8.315279285149107e-07,
                NaN,
                2.1024334103352274e-07,
                1.0677032518785256e-06,
                4.450851580540182e-07
            ],
            [
                5.043475885696228e-07,
                3.05902226923399e-07,
                1.637377057680051e-07,
                3.466326624336003e-07,
                NaN,
                NaN,
                1.209866260432471e-06,
                2.1024334103581732e-07,
                1.3709573702856596e-06,
                7.338208055664991e-07
            ],
            [
                1.2751902768612997e-07,
                2.6995771309523475e-07,
                2.699578740032504e-07,
                1.6373772528704005e-07,
                3.05902190458764e-07,
                3.466326624336003e-07,
                5.04347528446051e-07,
                2.1024336609843824e-07,
                2.699576809143613e-07,
                2.1024331597262577e-07
            ],
            [
                NaN,
                NaN,
                NaN,
                1.5534975693933505e-06,
                2.9023123311583482e-06,
                1.2098662604247682e-06,
                2.2603253756874524e-06,
                9.422445939032799e-07,
                1.994730434879465e-06,
                1.7603427936263351e-06
            ],
            [
                NaN,
                1.0677027427569065e-06,
                3.288748281329893e-06,
                4.222835458175145e-06,
                1.9947299593014888e-06,
                1.0677024881980089e-06,
                5.422220262599396e-06,
                5.422217030747413e-06,
                1.0677024881980089e-06,
                NaN
            ],
            [
                6.475945666063607e-07,
                NaN,
                2.699577774585891e-07,
                1.892515049819277e-05,
                8.939693107288474e-06,
                6.962257909842961e-06,
                2.5612819054133693e-06,
                1.9947292459347367e-06,
                1.5534971990169383e-06,
                NaN
            ],
            [
                7.338208930460318e-07,
                1.1253526937697666e-07,
                5.043476486924565e-07,
                5.043472278322555e-07,
                2.3823690999323465e-07,
                7.338209805240734e-07,
                6.475945666063607e-07,
                2.382369951932796e-07,
                2.6995790618469934e-07,
                3.05902336324494e-07
            ],
            [
                3.466326624336003e-07,
                5.715004470334646e-07,
                2.6995784182183607e-07,
                5.043476486924565e-07,
                0.9999982396563688,
                6.47595107001401e-07,
                8.315279285370317e-07,
                7.338207180898968e-07,
                3.9278610661902853e-07,
                1.7603425837903113e-06
            ],
            [
                6.962254589978262e-06,
                7.338208930443633e-07,
                1.760343003481596e-06,
                NaN,
                NaN,
                2.1024341622426268e-07,
                1.760343633031919e-06,
                1.760343213335281e-06,
                2.902312677150514e-06,
                0.00048785723458357865
            ],
            [
                4.222835458148261e-06,
                2.2603237589676295e-06,
                1.0677029973056687e-06,
                2.2603237589779086e-06,
                9.422444815814404e-07,
                6.475947209985977e-07,
                3.726637951387472e-06,
                4.0063701745046735e-05,
                1.3709568799760888e-06,
                NaN
            ],
            [
                9.422443692555439e-07,
                2.3823688159291947e-07,
                6.475947982037486e-07,
                5.715003789033962e-07,
                6.475946438055299e-07,
                1.7603425837903113e-06,
                2.1024339116168358e-07,
                9.422448185510695e-07,
                3.46632497145457e-07,
                6.475949526020042e-07
            ],
            [
                9.422449308748773e-07,
                1.7603434231833873e-06,
                5.715003789046955e-07,
                4.222835458175145e-06,
                1.7603440527334603e-06,
                NaN,
                2.90231094723893e-06,
                NaN,
                6.475947982037486e-07,
                3.726638839878908e-06
            ],
            [
                1.760343423160973e-06,
                1.7603440527046419e-06,
                NaN,
                1.5534973841895917e-06,
                8.315281267800897e-07,
                1.760344052714248e-06,
                1.3709568799679844e-06,
                9.422445939054222e-07,
                1.994730197071414e-06,
                1.0677032518748838e-06
            ],
            [
                1.9947304348703948e-06,
                1.1478765389222573e-05,
                1.012998977108606e-05,
                6.144176066672166e-06,
                NaN,
                1.0129992187253088e-05,
                2.9023112931688987e-06,
                1.3709575336860625e-06,
                2.2603248367173307e-06,
                3.288750241500471e-06
            ],
            [
                1.5534983101644536e-06,
                NaN,
                5.043476486915964e-07,
                NaN,
                6.475945666051092e-07,
                9.422448185510695e-07,
                1.5534977545886537e-06,
                6.475947210031623e-07,
                5.04347348075149e-07,
                NaN
            ]
        ]
    },
    {
        "q_id": "9186_mmlu_physics",
        "cot_ids": [
            0,
            1,
            3,
            4,
            6,
            8,
            11,
            13,
            14,
            15,
            18,
            19,
            20,
            22,
            23,
            24,
            25,
            27,
            28,
            30,
            31,
            32,
            33,
            34,
            36,
            37,
            39,
            40,
            41,
            44,
            47,
            49,
            51,
            52,
            55,
            57,
            59,
            60,
            61,
            65,
            67,
            68,
            69,
            70,
            74,
            76,
            77,
            80,
            81,
            84,
            86,
            87,
            89,
            90,
            93,
            96,
            97,
            98,
            99,
            103,
            104,
            106,
            108,
            109,
            111,
            113,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                NaN,
                8.315283250394546e-07,
                1.5534971990169383e-06,
                1.7603438428800754e-06,
                2.6995790618469934e-07,
                2.102434412875379e-07,
                3.9278610661902853e-07,
                5.715005151606823e-07,
                NaN,
                5.043472879540142e-07
            ],
            [
                NaN,
                2.2603253756956754e-06,
                2.561281600076256e-06,
                NaN,
                NaN,
                NaN,
                2.7535704231844484e-05,
                NaN,
                5.422218323399208e-06,
                NaN
            ],
            [
                1.2098653950692178e-06,
                2.699577774585891e-07,
                3.288747889284851e-06,
                6.962257909785973e-06,
                2.2603234895289998e-06,
                1.4449805540763184e-07,
                1.4449800373065699e-07,
                2.902313023130843e-06,
                NaN,
                1.5534975693979422e-06
            ],
            [
                3.4663278639892215e-07,
                1.9947304348862686e-06,
                1.3709575337125585e-06,
                7.338208055680009e-07,
                2.6995784182140636e-07,
                2.1024326584639497e-07,
                1.5534977545886537e-06,
                7.338207180864763e-07,
                NaN,
                5.715003788993679e-07
            ],
            [
                1.209865683518615e-06,
                4.4508505193791187e-07,
                1.553498124964492e-06,
                6.475950297942253e-07,
                1.8925150497848527e-05,
                4.450848927650143e-07,
                NaN,
                9.422450431860582e-07,
                3.466327863961242e-07,
                2.2603240284371276e-06
            ],
            [
                8.315281267861397e-07,
                NaN,
                5.4222183235249605e-06,
                2.260323758987159e-06,
                7.338212429582604e-07,
                1.2098661162056318e-06,
                NaN,
                5.4222183235249605e-06,
                1.5534975693979422e-06,
                2.102434412875379e-07
            ],
            [
                2.9023126771227976e-06,
                1.6701415872385704e-05,
                6.962257909785973e-06,
                3.927860597945825e-07,
                1.5534979397740895e-06,
                1.2098659719757836e-06,
                1.3709572068522336e-06,
                1.9947292459347367e-06,
                1.0677026154806063e-06,
                5.422218323487975e-06
            ],
            [
                1.209865539295696e-06,
                4.691162683297406e-08,
                1.1253521571574156e-07,
                1.275190428875671e-07,
                3.653481209178873e-08,
                7.734423152941018e-08,
                6.023569166654288e-08,
                8.7642558095602e-08,
                1.3007125363293615e-05,
                8.7642516304188e-08
            ],
            [
                1.0129989772412744e-05,
                4.450848927650143e-07,
                0.00029595702964256804,
                NaN,
                1.3709572068522336e-06,
                NaN,
                1.7603438428660665e-06,
                1.5534984953298217e-06,
                1.4738987243478167e-05,
                1.7603430034655858e-06
            ],
            [
                2.3823690998803445e-07,
                1.7603434231777837e-06,
                2.5612825160562587e-06,
                1.7603440527286572e-06,
                3.288748673376478e-06,
                5.715003789017068e-07,
                8.315279285351409e-07,
                2.9023119851781017e-06,
                1.3007123813193233e-05,
                8.31527928532683e-07
            ],
            [
                3.288749065406658e-06,
                6.475946437928669e-07,
                1.553497754577351e-06,
                1.5534977545886537e-06,
                7.338209805224048e-07,
                1.2098653950480359e-06,
                1.5534973841895917e-06,
                2.5612825160096693e-06,
                7.338212429367364e-07,
                1.5534984953453635e-06
            ],
            [
                4.450851049941403e-07,
                6.475946437996402e-07,
                3.726637951387472e-06,
                NaN,
                1.067703251864202e-06,
                9.422450431954847e-07,
                NaN,
                1.5534984953453635e-06,
                8.315281267800897e-07,
                NaN
            ],
            [
                NaN,
                3.927860597945825e-07,
                2.561282516066741e-06,
                8.315284241650899e-07,
                5.043473480777865e-07,
                6.47594566597747e-07,
                6.475950297993789e-07,
                7.338208930460318e-07,
                9.422443692555439e-07,
                7.338207180838067e-07
            ],
            [
                2.902313023039776e-06,
                8.31527928532683e-07,
                1.7603436330259153e-06,
                3.0590226338282174e-07,
                1.6373768624837685e-07,
                8.315279285351409e-07,
                3.288749457383046e-06,
                1.994730434778778e-06,
                3.466327863983311e-07,
                8.31528424162821e-07
            ],
            [
                1.0677027427525368e-06,
                2.561283431888668e-06,
                1.3709576971242028e-06,
                5.715005151574337e-07,
                2.5612825160562587e-06,
                NaN,
                NaN,
                2.382369951932796e-07,
                NaN,
                4.78509563546605e-06
            ],
            [
                5.715005832886879e-07,
                1.2751901248454963e-07,
                3.05902190458764e-07,
                1.209865827740176e-06,
                2.3823696679327928e-07,
                6.475945666063607e-07,
                3.9278629391427843e-07,
                1.3709567165617364e-06,
                1.5534977545886537e-06,
                NaN
            ],
            [
                4.222834451382849e-06,
                2.102432658440048e-07,
                0.00010889689634689507,
                8.939695238536645e-06,
                5.4222176771176554e-06,
                1.7603438428460541e-06,
                1.5534984953510149e-06,
                1.8553919030776337e-07,
                4.785092783519724e-06,
                9.422445939054222e-07
            ],
            [
                NaN,
                5.715007195447234e-07,
                1.637377057680051e-07,
                2.6995790618469934e-07,
                4.450849458218309e-07,
                2.10243290909724e-07,
                4.4508515805735777e-07,
                1.4449800373065699e-07,
                6.825609419848033e-08,
                4.450848927658745e-07
            ],
            [
                NaN,
                2.382369951932796e-07,
                NaN,
                6.475951069985296e-07,
                5.043475885696228e-07,
                9.4224425692559e-07,
                2.102433660979124e-07,
                NaN,
                0.9999724643026503,
                1.0677029973219343e-06
            ],
            [
                1.2098662604247682e-06,
                6.475951069985296e-07,
                5.1442225927013303e-05,
                7.3382080556433e-07,
                2.561281600049467e-06,
                4.450849988811838e-07,
                2.3823699519143784e-07,
                2.5612816000646084e-06,
                7.338208055536515e-07,
                1.0677027427525368e-06
            ],
            [
                NaN,
                5.715003789046955e-07,
                1.0677026154806063e-06,
                4.539787405573911e-05,
                NaN,
                1.0677028700422047e-06,
                2.1024341622426268e-07,
                1.209865539295696e-06,
                2.3823702359290413e-07,
                NaN
            ],
            [
                1.7603440527286572e-06,
                7.338207180864763e-07,
                4.785093353940187e-06,
                3.288750241561788e-06,
                2.9023112932177327e-06,
                1.209865539295696e-06,
                5.043472879540142e-07,
                1.5534971990126997e-06,
                9.422444815765128e-07,
                2.699578096393206e-07
            ],
            [
                2.5612822107167428e-06,
                NaN,
                1.8925157265332104e-05,
                1.2098658277451275e-06,
                6.475946437996402e-07,
                8.315281267834927e-07,
                8.315284241650899e-07,
                5.04347468318358e-07,
                8.315284241401329e-07,
                2.9023109472244114e-06
            ],
            [
                1.0677027427624903e-06,
                NaN,
                1.5534979397740895e-06,
                2.382368815916736e-07,
                8.315281267882195e-07,
                6.475945666063607e-07,
                1.4449805540763184e-07,
                3.9278624708775595e-07,
                2.561281294760143e-06,
                6.475947210031623e-07
            ],
            [
                1.1478768126057254e-05,
                9.422448185510695e-07,
                1.5534971990126997e-06,
                9.422448185534261e-07,
                1.3709567165579959e-06,
                5.715005832853093e-07,
                1.7603440527286572e-06,
                3.927862939126708e-07,
                6.475945666051092e-07,
                1.994729483723626e-06
            ],
            [
                1.553497754577351e-06,
                NaN,
                NaN,
                NaN,
                2.902311985146426e-06,
                8.315284241650899e-07,
                6.47594566597747e-07,
                7.338209805224048e-07,
                4.450848927621807e-07,
                4.785096776468749e-06
            ],
            [
                1.9947299593078385e-06,
                3.288750241561788e-06,
                9.422442569208767e-07,
                3.9278615344178325e-07,
                3.2887506335906595e-06,
                1.7603440527286572e-06,
                1.5534971990126997e-06,
                3.7266410611296085e-06,
                5.715003789017068e-07,
                6.962257079553702e-06
            ],
            [
                4.450850519403407e-07,
                2.102433410343832e-07,
                3.059022998576899e-07,
                5.043473480777865e-07,
                2.1024329090867228e-07,
                7.734421308914719e-08,
                2.6995774527718623e-07,
                2.382368247924618e-07,
                7.73441946488886e-08,
                5.315780536011123e-08
            ],
            [
                3.4663249714325014e-07,
                4.450852111135988e-07,
                5.043476486902204e-07,
                6.475951070002966e-07,
                5.715002426460124e-07,
                5.715004470295662e-07,
                9.422448185510695e-07,
                1.0677032518814388e-06,
                3.4663266243308805e-07,
                3.927862002654366e-07
            ],
            [
                5.71500515159253e-07,
                3.0590215398968196e-07,
                2.561281600086738e-06,
                NaN,
                2.6995784182073116e-07,
                1.6373776432481905e-07,
                1.4449800373065699e-07,
                3.466326211113502e-07,
                1.8553916819032217e-07,
                9.931190958076104e-08
            ],
            [
                3.0590237279085045e-07,
                1.8553910183674878e-07,
                NaN,
                2.561282210740037e-06,
                3.726638395634011e-06,
                1.2098652508424818e-06,
                6.962255419931625e-06,
                1.0677032518814388e-06,
                2.561282516066741e-06,
                NaN
            ],
            [
                1.3709573702822306e-06,
                NaN,
                2.902312331170226e-06,
                1.994730197090463e-06,
                4.785096776499213e-06,
                3.4663253846718004e-07,
                0.00012339454553615247,
                2.1024336609843824e-07,
                2.561282210740037e-06,
                9.422443692574719e-07
            ],
            [
                5.043476486915964e-07,
                NaN,
                1.7603425837606927e-06,
                2.2603253756874524e-06,
                NaN,
                1.2098658277451275e-06,
                1.209865827752005e-06,
                1.209865827740176e-06,
                9.422447062294175e-07,
                8.315283250371857e-07
            ],
            [
                1.9947297215125433e-06,
                3.927863875616689e-07,
                2.102434162245973e-07,
                4.4508510499849186e-07,
                7.338210680021253e-07,
                NaN,
                3.059022998576899e-07,
                2.699576809143613e-07,
                4.4508510499849186e-07,
                1.0129988565084915e-05
            ],
            [
                2.3823682479181176e-07,
                7.338212429562581e-07,
                1.2098658277489788e-06,
                6.962255419931625e-06,
                1.670141587208191e-05,
                1.3709567165579959e-06,
                5.422219616265831e-06,
                7.338207180801359e-07,
                1.0677024882009222e-06,
                3.288749457383046e-06
            ],
            [
                1.2098659719757836e-06,
                3.0590215399183813e-07,
                1.3709578605617394e-06,
                3.466327863983311e-07,
                1.5534971990169383e-06,
                2.430024073461624e-05,
                2.260325106237323e-06,
                1.2098662604291696e-06,
                1.7603440527286572e-06,
                3.288748673376478e-06
            ],
            [
                2.7535694384882703e-05,
                1.0129992186202796e-05,
                4.785093924330255e-06,
                8.315280276546789e-07,
                5.715003107715166e-07,
                1.7603434231833873e-06,
                2.5612828213352452e-06,
                3.4663274507713016e-07,
                6.475947982002148e-07,
                7.338212429420757e-07
            ],
            [
                7.889259764445822e-06,
                1.994730434879465e-06,
                5.715005151550947e-07,
                9.422443692330485e-07,
                4.222832437798974e-06,
                1.5534975693979422e-06,
                9.610240358212368e-05,
                3.726639728370556e-06,
                2.5612828213818346e-06,
                1.9947299593014888e-06
            ],
            [
                8.315280276626197e-07,
                2.9023116390421582e-06,
                2.2603248367173307e-06,
                2.561283431942246e-06,
                1.7603427935967163e-06,
                4.4508505193791187e-07,
                1.067702870039777e-06,
                9.422448185388577e-07,
                6.605214469462115e-05,
                2.1024336609874897e-07
            ],
            [
                1.7603425837702984e-06,
                2.69957906184239e-07,
                6.475946438055299e-07,
                2.2603237589542675e-06,
                8.315282259009745e-07,
                NaN,
                1.670142980893658e-05,
                NaN,
                1.3709567165530083e-06,
                2.5612819054028872e-06
            ],
            [
                3.466326211113502e-07,
                2.382370235922541e-07,
                2.699578096393206e-07,
                1.6373774480479287e-07,
                4.450852641717689e-07,
                2.6995784182140636e-07,
                2.699577452733192e-07,
                3.4663274507713016e-07,
                6.144173137170873e-06,
                7.338208930460318e-07
            ],
            [
                1.1253526937697666e-07,
                8.764247451307293e-08,
                1.99472900813862e-06,
                9.422443692574719e-07,
                5.043475885696228e-07,
                2.902312677150514e-06,
                9.931190958076104e-08,
                7.338210680021253e-07,
                9.931190958076104e-08,
                2.699577774589574e-07
            ],
            [
                3.466327863983311e-07,
                5.043474081993875e-07,
                8.315278294114555e-07,
                3.466326624336003e-07,
                1.2098652508424818e-06,
                1.2098662604247682e-06,
                2.3823685319244518e-07,
                1.3709567165617364e-06,
                2.382369383923073e-07,
                2.382370235933104e-07
            ],
            [
                3.05902190458764e-07,
                1.7603430034867993e-06,
                2.1024326584639497e-07,
                3.927860597935108e-07,
                2.69957906184239e-07,
                1.8553916819032217e-07,
                8.315278294114555e-07,
                2.3823702359138736e-07,
                3.0590237279085045e-07,
                1.0677029973192638e-06
            ],
            [
                1.2751902768612997e-07,
                1.6373764721072816e-07,
                2.5612834320470717e-06,
                1.1253508156363576e-07,
                1.855391681906175e-07,
                1.637377448057981e-07,
                2.3823696679327928e-07,
                1.8553910183674878e-07,
                5.04347528446051e-07,
                9.422448185478557e-07
            ],
            [
                2.9023116391675407e-06,
                3.726640172503764e-06,
                3.726641061058432e-06,
                NaN,
                2.5612812947508257e-06,
                4.450850519403407e-07,
                5.422218969384951e-06,
                2.2603237589676295e-06,
                7.338211554783522e-07,
                1.0677026154730804e-06
            ],
            [
                1.3709567165530083e-06,
                NaN,
                2.5612828213934817e-06,
                1.994729008145876e-06,
                5.715005151606823e-07,
                2.90231094723893e-06,
                2.5612819054028872e-06,
                3.927862002663297e-07,
                9.422445939032799e-07,
                5.04347528446051e-07
            ],
            [
                4.222835457906302e-06,
                4.785096776394765e-06,
                7.338209805200689e-07,
                2.2603251061458426e-06,
                5.715004470272272e-07,
                NaN,
                6.47594566597747e-07,
                3.2887478892504536e-06,
                1.0129992187400498e-05,
                2.26032402841657e-06
            ],
            [
                2.1024329090781183e-07,
                3.0590215398829087e-07,
                4.450852641656969e-07,
                1.6373764720990908e-07,
                6.475951069932288e-07,
                1.1253518888464745e-07,
                1.6373772528581146e-07,
                1.1253520229983549e-07,
                2.1024341622368903e-07,
                1.6373772528581146e-07
            ],
            [
                8.315278294038928e-07,
                8.315277302841894e-07,
                1.0677028700363782e-06,
                2.1024334103505245e-07,
                1.5534983101602148e-06,
                NaN,
                3.7266406168624155e-06,
                9.422448185478557e-07,
                1.637377448057981e-07,
                1.0677029973192638e-06
            ],
            [
                6.144173137126169e-06,
                3.726639284125553e-06,
                3.288747889284851e-06,
                6.475947210046347e-07,
                NaN,
                2.5612828213934817e-06,
                1.5534971990126997e-06,
                0.9999977396751667,
                NaN,
                NaN
            ],
            [
                1.3709576970824327e-06,
                1.2098655392871682e-06,
                1.209865827740176e-06,
                1.2098652508424818e-06,
                1.9947301970451086e-06,
                7.338210679949506e-07,
                2.902311639183378e-06,
                6.144172404693786e-06,
                1.2098658277451275e-06,
                6.475951069985296e-07
            ],
            [
                4.450852111155216e-07,
                5.043472278227948e-07,
                7.338210679979539e-07,
                2.6995768091310296e-07,
                6.475947981975644e-07,
                6.475948753930064e-07,
                1.3709573702647743e-06,
                1.7603440527286572e-06,
                7.338208930391909e-07,
                6.475947210012481e-07
            ],
            [
                NaN,
                3.9278624708775595e-07,
                NaN,
                6.825606165129312e-08,
                1.2751908849088918e-07,
                2.1024336609874897e-07,
                3.466325797896173e-07,
                9.422448185534261e-07,
                2.2603253756956754e-06,
                NaN
            ],
            [
                2.2603248367512505e-06,
                1.7603427936263351e-06,
                6.475951069985296e-07,
                1.3709572068422585e-06,
                6.475949525981759e-07,
                3.535624228313077e-05,
                5.715005151550947e-07,
                8.315280276626197e-07,
                1.067703251864202e-06,
                1.4738980215352592e-05
            ],
            [
                1.5534975693707442e-06,
                2.260325375664839e-06,
                1.3709572068354007e-06,
                2.561282210729555e-06,
                3.4663253846718004e-07,
                0.9999822214503336,
                2.2603234895372223e-06,
                2.5612819054028872e-06,
                3.9278615344178325e-07,
                2.6995771309523475e-07
            ],
            [
                6.962256249885085e-06,
                9.422450432014836e-07,
                4.222832941193893e-06,
                5.043476486924565e-07,
                2.9023109472244114e-06,
                5.715005832827105e-07,
                6.475950298011458e-07,
                5.715007195447234e-07,
                6.475951069985296e-07,
                1.8553903548231313e-07
            ],
            [
                2.5612828213818346e-06,
                1.7603430034867993e-06,
                5.422221555380179e-06,
                NaN,
                1.994729483705484e-06,
                2.9023112932045342e-06,
                1.9947297215043796e-06,
                1.5534973841895917e-06,
                3.288749065423109e-06,
                9.422442569334097e-07
            ],
            [
                1.4449803818215767e-07,
                1.3709573702566696e-06,
                7.734414854823498e-08,
                NaN,
                2.5612831267202583e-06,
                1.9947301970106386e-06,
                4.450852641656969e-07,
                2.382368531929327e-07,
                1.5534971989696065e-06,
                1.855391681906175e-07
            ],
            [
                0.9999885212360063,
                1.5534975693979422e-06,
                0.9999967112497615,
                7.734426841017797e-08,
                3.059023363231725e-07,
                NaN,
                1.4449798650417048e-07,
                NaN,
                0.9999977396765126,
                3.726639284144195e-06
            ],
            [
                3.726638839878908e-06,
                1.2098659719788098e-06,
                5.715003107767143e-07,
                3.466325384678894e-07,
                3.2887478892683997e-06,
                3.466325797896173e-07,
                NaN,
                8.315282259138311e-07,
                NaN,
                5.422221555380179e-06
            ],
            [
                3.466325797896173e-07,
                5.043474081993875e-07,
                9.422448185388577e-07,
                5.715003789046955e-07,
                1.5534979397677313e-06,
                1.3709575336654889e-06,
                2.2603248367512505e-06,
                3.9278634073732336e-07,
                5.715005151606823e-07,
                1.209865827752005e-06
            ],
            [
                2.2603251062270446e-06,
                5.715005832886879e-07,
                5.715006514105942e-07,
                5.043474081993875e-07,
                NaN,
                2.5612812947508257e-06,
                3.46632497145457e-07,
                5.422219616265831e-06,
                2.6995784182073116e-07,
                NaN
            ],
            [
                5.715005832886879e-07,
                1.8553905760062447e-07,
                2.382370235933104e-07,
                1.8553919030858602e-07,
                1.4449805540740185e-07,
                1.7603427936335396e-06,
                1.994730197090463e-06,
                2.382370235933104e-07,
                1.3709578605729614e-06,
                7.338208055664991e-07
            ],
            [
                1.2751902768612997e-07,
                1.7603427936335396e-06,
                2.6995784182183607e-07,
                NaN,
                6.023572038912295e-08,
                3.05902263391829e-07,
                1.444980209564556e-07,
                1.2098656835224664e-06,
                7.338208930460318e-07,
                1.855391681906175e-07
            ],
            [
                8.315277302649045e-07,
                1.3709572068422585e-06,
                3.927860597935108e-07,
                2.1024341622368903e-07,
                5.043472278280699e-07,
                3.927863875584984e-07,
                8.315281267882195e-07,
                2.5612819054028872e-06,
                7.338209805133949e-07,
                2.4300243631272052e-05
            ],
            [
                4.4508494582405734e-07,
                0.9999869928716173,
                0.9999972735287601,
                3.288749849477628e-06,
                8.315278294072958e-07,
                NaN,
                5.422220908876325e-06,
                0.9999952149055227,
                1.0129995810343862e-05,
                0.9999978766223003
            ],
            [
                2.5612812947380135e-06,
                1.7603425837855082e-06,
                NaN,
                4.222832941193893e-06,
                3.4663262110945863e-07,
                3.059023363231725e-07,
                4.006371129776199e-05,
                1.3709568799679844e-06,
                1.2098659719757836e-06,
                1.5534971990126997e-06
            ],
            [
                7.338211554783522e-07,
                1.3709572068522336e-06,
                NaN,
                7.889262585886274e-06,
                1.0129989772412744e-05,
                NaN,
                NaN,
                7.889265407255982e-06,
                2.102434412875379e-07,
                3.9278615344178325e-07
            ],
            [
                4.450849988811838e-07,
                3.466325797896173e-07,
                0.9999646437621025,
                0.9999986290421402,
                7.338209805224048e-07,
                0.9999988634364257,
                0.9999974387165714,
                NaN,
                0.9999934595596709,
                0.999996033013621
            ],
            [
                5.422220262636381e-06,
                4.785093353940187e-06,
                1.209866260432471e-06,
                2.2603242978871282e-06,
                NaN,
                5.422218969463855e-06,
                1.1253506814842375e-07,
                5.422219616085833e-06,
                NaN,
                2.902312677150514e-06
            ],
            [
                5.043475885674441e-07,
                3.4663249714451116e-07,
                7.338211554688417e-07,
                8.315277302788957e-07,
                3.9278634073625165e-07,
                1.370957860567974e-06,
                5.715003788993679e-07,
                5.715003788993679e-07,
                5.715002426301592e-07,
                6.475949526020042e-07
            ],
            [
                1.4449798650551755e-07,
                NaN,
                4.139938534423022e-08,
                1.444980209564556e-07,
                1.1253516205489029e-07,
                1.8553919030858602e-07,
                NaN,
                1.6373772528704005e-07,
                NaN,
                7.734418542875216e-08
            ],
            [
                8.93970056668775e-06,
                2.902312677137316e-06,
                1.3007123812317831e-05,
                NaN,
                8.315283250394546e-07,
                2.3823702359290413e-07,
                1.3709576971425944e-06,
                3.2887506336086064e-06,
                1.7603434231777837e-06,
                1.994730434879465e-06
            ],
            [
                5.043472278299047e-07,
                3.466326211113502e-07,
                3.927862002663297e-07,
                2.902312677137316e-06,
                2.5612831267202583e-06,
                NaN,
                2.561282210729555e-06,
                3.0590215399183813e-07,
                2.4300252321904572e-05,
                7.889262585886274e-06
            ],
            [
                1.2098658277264215e-06,
                2.9023112931873767e-06,
                2.561282210701601e-06,
                6.144172404380855e-06,
                1.300712846477255e-05,
                2.260325375634003e-06,
                2.260324028404236e-06,
                2.260323758939877e-06,
                4.2228344511197656e-06,
                1.9947297214544894e-06
            ]
        ]
    },
    {
        "q_id": "9495_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            4,
            5,
            6,
            8,
            9,
            10,
            11,
            12,
            13,
            15,
            16,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            35,
            36,
            39,
            40,
            41,
            42,
            43,
            45,
            46,
            47,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            61,
            62,
            63,
            65,
            67,
            68,
            69,
            70,
            72,
            73,
            74,
            76,
            77,
            78,
            80,
            81,
            82,
            83,
            85,
            86,
            88,
            91,
            92,
            94,
            95,
            97,
            99,
            100,
            101,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            119,
            120,
            123,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.4449795205429202e-07,
                5.043472879540142e-07,
                4.450848927637999e-07,
                6.475951069985296e-07,
                5.715002426475718e-07,
                5.043472879540142e-07,
                5.715005832886879e-07,
                1.8553903548231313e-07,
                3.4663278639738526e-07,
                3.466327863961242e-07
            ],
            [
                3.288747889284851e-06,
                1.1478769494542698e-05,
                3.2887502415767434e-06,
                1.5534979397790343e-06,
                3.726639284144195e-06,
                1.994729008145876e-06,
                2.561282516066741e-06,
                1.2098661162056318e-06,
                4.785094494811783e-06,
                1.7603425837855082e-06
            ],
            [
                3.05902336324494e-07,
                8.315284241665078e-07,
                1.1253526937697666e-07,
                1.7603425837903113e-06,
                5.715006514176113e-07,
                4.4508515805735777e-07,
                5.715002426486762e-07,
                3.9278629391427843e-07,
                2.902312331170226e-06,
                5.043472278322555e-07
            ],
            [
                1.0677028700422047e-06,
                9.422443692574719e-07,
                6.47594952603035e-07,
                1.209865827752005e-06,
                0.9999993916409636,
                0.9999991684715762,
                0.9999991684721713,
                0.9999991148431756,
                0.9999994284996895,
                6.475946438055299e-07
            ],
            [
                0.9999999226557593,
                5.715003788993679e-07,
                9.93120161306789e-08,
                0.9999998555019274,
                4.450851580566494e-07,
                8.764252675194995e-08,
                5.715002426460124e-07,
                2.699577774579753e-07,
                1.067703251864202e-06,
                0.999999943413784
            ],
            [
                1.2098661162056318e-06,
                3.05902336324494e-07,
                3.4663274507713016e-07,
                8.315282259138311e-07,
                3.059022998581767e-07,
                7.338208055680009e-07,
                6.47595107001401e-07,
                3.2887506336235617e-06,
                1.0677032518814388e-06,
                2.2603245673443566e-06
            ],
            [
                0.9999995549148951,
                0.9999993106387903,
                0.9999997897565839,
                0.9999996072138466,
                0.9999988634366966,
                0.999999674368781,
                0.9999980052698045,
                1.209865827752005e-06,
                0.9999994631250603,
                0.9999996072138
            ],
            [
                1.0677027427624903e-06,
                3.4663262111182307e-07,
                NaN,
                6.47594952603035e-07,
                4.4508515805735777e-07,
                1.209866260432471e-06,
                4.785092783519724e-06,
                4.450848927658745e-07,
                1.444979692800516e-07,
                3.9278629391427843e-07
            ],
            [
                3.05902263391829e-07,
                5.043474683240344e-07,
                4.450852641737424e-07,
                1.6373772528704005e-07,
                4.4508515805735777e-07,
                5.715005832895975e-07,
                4.450852111155216e-07,
                2.3823690999323465e-07,
                1.994729008151319e-06,
                1.2098656835252174e-06
            ],
            [
                7.734418542839164e-08,
                1.1253524254650944e-07,
                4.222832437798974e-06,
                1.6373774480605869e-07,
                2.1024341622426268e-07,
                3.288749065406658e-06,
                7.889265407327733e-06,
                9.422444815814404e-07,
                9.93120161310289e-08,
                9.93120161306789e-08
            ],
            [
                7.338207180898968e-07,
                1.1253522913127183e-07,
                NaN,
                1.994729483729522e-06,
                6.47595107001401e-07,
                1.1253513522447425e-07,
                7.734416698849138e-08,
                1.1253508156363576e-07,
                3.9278610661902853e-07,
                6.475950298021765e-07
            ],
            [
                2.3823693839325527e-07,
                3.0590237279085045e-07,
                6.962256249885085e-06,
                1.6373762769138607e-07,
                1.4449803818156628e-07,
                1.27519073289925e-07,
                1.6373762769138607e-07,
                1.2751910369310194e-07,
                7.338208930460318e-07,
                1.855391681898159e-07
            ],
            [
                0.9999980052698044,
                6.023571320847322e-08,
                0.9999999500628571,
                7.73442776300517e-08,
                7.734415776836702e-08,
                4.1399375473868e-08,
                0.9999998362622747,
                4.139934092760465e-08,
                0.9999996310114159,
                0.999999961108909
            ],
            [
                3.9278605979534166e-07,
                2.382368531929327e-07,
                2.6995774527718623e-07,
                3.466327037553825e-07,
                6.47595107001401e-07,
                2.10243290909724e-07,
                1.637377448057981e-07,
                1.637377057680051e-07,
                3.9278610661902853e-07,
                6.475947210046347e-07
            ],
            [
                1.2098652508424818e-06,
                6.9622579096593295e-06,
                3.288749849498565e-06,
                1.2098653950606901e-06,
                2.2603245673155757e-06,
                2.260324836787226e-06,
                2.9023112932177327e-06,
                2.561282210740037e-06,
                4.785092783519724e-06,
                7.889266347715168e-06
            ],
            [
                6.475947982037486e-07,
                5.04347287955046e-07,
                8.764245361752286e-08,
                6.825604537781398e-08,
                1.5534977545886537e-06,
                3.927862470899887e-07,
                2.561282210740037e-06,
                1.27519088491875e-07,
                1.2751899728311609e-07,
                3.059021175261338e-07
            ],
            [
                2.1024334103581732e-07,
                3.927863875616689e-07,
                8.764241182641775e-08,
                1.8553914607267268e-07,
                4.450852111155216e-07,
                2.699576809143613e-07,
                2.699577774585891e-07,
                1.855391681906175e-07,
                2.699578740032504e-07,
                2.102434412875379e-07
            ],
            [
                3.0590215399183813e-07,
                2.6995784182140636e-07,
                6.023576347299818e-08,
                1.209865539295696e-06,
                2.382369383923073e-07,
                9.422442569315887e-07,
                3.9278605979534166e-07,
                2.3823702359290413e-07,
                8.31527928532683e-07,
                1.2751908849167202e-07
            ],
            [
                0.9999993106388728,
                0.9999994284996214,
                0.9999995262094423,
                0.9999998942830233,
                0.9999995818811773,
                0.9999999067050387,
                0.9999998802069159,
                0.9999995818812771,
                0.999999802494586,
                0.9999999006881496
            ],
            [
                NaN,
                2.699577774585891e-07,
                5.715003107767143e-07,
                6.475951070002966e-07,
                4.450849988811838e-07,
                2.5612819054133693e-06,
                9.93120161310289e-08,
                8.31527928532683e-07,
                2.561281600086738e-06,
                6.475947210046347e-07
            ],
            [
                3.288749849529972e-06,
                1.0677024882029858e-06,
                8.481108184529756e-05,
                4.450851049991497e-07,
                0.9999996533672963,
                NaN,
                1.994729008151319e-06,
                3.9278629391427843e-07,
                3.9278620026686556e-07,
                0.9999996743686645
            ],
            [
                9.422444815814404e-07,
                4.22283545819819e-06,
                1.2098659719788098e-06,
                2.5612828213934817e-06,
                6.962258739796719e-06,
                6.475950298011458e-07,
                1.2098659719757836e-06,
                5.043473480777865e-07,
                1.3007130015677909e-05,
                3.927862002663297e-07
            ],
            [
                0.99999994341373,
                0.9999994631251883,
                0.9999999226557316,
                1.0,
                0.9999995549147891,
                0.9999996940978826,
                0.9999999530883898,
                1.0,
                0.9999998724810027,
                0.9999996533672136
            ],
            [
                7.338208930443633e-07,
                1.0677031245990084e-06,
                1.0677033791583005e-06,
                NaN,
                5.043474081993875e-07,
                1.370957860576702e-06,
                5.043476486915964e-07,
                2.6995774527577444e-07,
                1.994730197090463e-06,
                1.3709573702822306e-06
            ],
            [
                7.734428685047173e-08,
                3.6534838223576766e-08,
                1.0,
                2.699577130960941e-07,
                3.224186633297071e-08,
                3.224186633297071e-08,
                0.9999999226557684,
                5.71500719545698e-07,
                5.3157811697009444e-08,
                9.931193325852072e-08
            ],
            [
                0.9999977396759752,
                0.9999942280806711,
                0.9999996940976275,
                NaN,
                0.9999992188514837,
                0.9999991684716759,
                3.288748281329893e-06,
                NaN,
                0.999998446502618,
                8.315277302841894e-07
            ],
            [
                2.382368815932174e-07,
                9.93120161310289e-08,
                3.466325797900508e-07,
                9.931200429212718e-08,
                9.931199245322124e-08,
                9.93119806143167e-08,
                2.3823690999323465e-07,
                1.4449807263325588e-07,
                3.4663262111182307e-07,
                6.47594875403829e-07
            ],
            [
                3.288749849529972e-06,
                2.561281600086738e-06,
                8.315278294114555e-07,
                2.6995790618469934e-07,
                1.4738985486721259e-05,
                3.4663249714612693e-07,
                9.422447062294175e-07,
                3.2887506336235617e-06,
                9.422442569334097e-07,
                6.962259569750576e-06
            ],
            [
                2.9023116391675407e-06,
                1.3709572068354007e-06,
                6.475946437996402e-07,
                1.0677029973056687e-06,
                2.561283432035425e-06,
                5.043475885688201e-07,
                9.422445938917108e-07,
                1.3709575337159875e-06,
                NaN,
                6.962258739796719e-06
            ],
            [
                3.9278629391427843e-07,
                2.1024334103581732e-07,
                3.9278620026686556e-07,
                5.043474082012222e-07,
                1.1253520230052635e-07,
                3.2887494574832472e-06,
                6.47594952603035e-07,
                1.8553903548287212e-07,
                1.4449805540740185e-07,
                1.1253525596134564e-07
            ],
            [
                4.4508499888275247e-07,
                3.4663262111182307e-07,
                3.4663278639892215e-07,
                1.8553916819032217e-07,
                1.8553916819032217e-07,
                0.999999653367503,
                5.71500515161527e-07,
                1.4449795205429202e-07,
                5.04347468323289e-07,
                4.785093924389007e-06
            ],
            [
                1.8553914607267268e-07,
                1.1253526937697666e-07,
                8.764245361752286e-08,
                2.699577774585891e-07,
                3.0590237279085045e-07,
                1.6373776432509826e-07,
                1.6373772528704005e-07,
                1.4449798650551755e-07,
                1.8553914607267268e-07,
                8.764245361752286e-08
            ],
            [
                0.9999993916406734,
                1.4738987243478167e-05,
                1.7603430034867993e-06,
                1.209865827752005e-06,
                5.043475885696228e-07,
                NaN,
                0.9999910603058397,
                6.962258739796719e-06,
                3.9278610661902853e-07,
                3.466327037553825e-07
            ],
            [
                3.927862470905692e-07,
                NaN,
                0.9999485577864872,
                5.043474683240344e-07,
                0.9999998942830485,
                1.209865539298447e-06,
                0.9999995262092163,
                2.1024334103581732e-07,
                0.9999997761971315,
                2.2603251062450327e-06
            ],
            [
                0.9999955048194992,
                2.1024341622426268e-07,
                0.9999989322972577,
                0.9999983463102179,
                0.9999983463102179,
                2.3823690999323465e-07,
                1.0677031245710902e-06,
                2.1024326584639497e-07,
                0.9999942280786015,
                0.999999653367379
            ],
            [
                2.699578096403948e-07,
                9.422445939054222e-07,
                3.466326211113502e-07,
                4.450852641737424e-07,
                0.0009110510303688655,
                3.4663262111182307e-07,
                5.422217677152175e-06,
                3.466326624336003e-07,
                1.2098661162056318e-06,
                1.2751902768612997e-07
            ],
            [
                7.338207180898968e-07,
                3.927863407379485e-07,
                7.33821330437595e-07,
                3.9278605979534166e-07,
                5.715006514176113e-07,
                2.561281600086738e-06,
                1.7603438428848787e-06,
                6.962255419931625e-06,
                5.04347468323289e-07,
                2.382368815932174e-07
            ],
            [
                0.9999997897566091,
                1.0677028700422047e-06,
                2.102434412875379e-07,
                0.9999987121043247,
                0.9999989322971317,
                8.315280276626197e-07,
                7.734415776836702e-08,
                8.764247451307293e-08,
                7.734423152941018e-08,
                2.1024336609874897e-07
            ],
            [
                3.927862002663297e-07,
                2.699576809143613e-07,
                1.275190124846946e-07,
                2.699578740032504e-07,
                3.9278610661902853e-07,
                4.785096776499213e-06,
                5.043475284468537e-07,
                2.3823688159291947e-07,
                3.9278629391427843e-07,
                5.043474081993875e-07
            ],
            [
                9.93120161310289e-08,
                3.466327037553825e-07,
                4.4508499888275247e-07,
                1.275190124846946e-07,
                NaN,
                0.999999730042287,
                5.71500515161527e-07,
                3.466325384682834e-07,
                3.9278620026686556e-07,
                1.275190124846946e-07
            ],
            [
                0.9999999176675534,
                0.9999999434137502,
                4.691162124067829e-08,
                4.691164920214251e-08,
                0.999999922655833,
                1.1253520230052635e-07,
                2.6995774527718623e-07,
                0.9999999397642365,
                4.139934092760465e-08,
                0.9999999611088627
            ],
            [
                0.9999945777829804,
                1.9947304348862686e-06,
                0.999999428499349,
                0.9999667857926144,
                0.9999970976866358,
                NaN,
                0.9999925887192601,
                0.9999986290427946,
                8.939700567094277e-06,
                NaN
            ],
            [
                2.6995790618350237e-07,
                4.450852641737424e-07,
                5.04347287955046e-07,
                1.0677027427624903e-06,
                6.475947982037486e-07,
                5.715003107767143e-07,
                1.4449796927932878e-07,
                2.102433660979124e-07,
                1.4449798650476187e-07,
                1.5534973842076057e-06
            ],
            [
                3.05902336324494e-07,
                1.637377057680051e-07,
                9.931199245322124e-08,
                3.0590215399183813e-07,
                7.734416698849138e-08,
                4.691161005609407e-08,
                2.1024336609874897e-07,
                3.927862002663297e-07,
                5.3157900413760374e-08,
                6.023568448589658e-08
            ],
            [
                9.931195693628605e-08,
                7.33821330437595e-07,
                3.927863407379485e-07,
                1.7603438428848787e-06,
                3.4663278639892215e-07,
                2.2603248367949354e-06,
                1.0677027427624903e-06,
                9.422443692574719e-07,
                7.338212429594283e-07,
                8.481108183851022e-05
            ],
            [
                4.4508515805735777e-07,
                4.450848927658745e-07,
                3.4663274507713016e-07,
                2.561281294760143e-06,
                3.466326624336003e-07,
                3.059022998576899e-07,
                7.33821330437595e-07,
                2.1024336609874897e-07,
                2.10243290909724e-07,
                NaN
            ],
            [
                4.6911638017556955e-08,
                1.444980209564556e-07,
                2.5109990926882483e-08,
                1.2751910369275402e-07,
                1.275189972832538e-07,
                1.9555685367819447e-08,
                6.825600469412533e-08,
                1.1253525596174225e-07,
                8.764254764780641e-08,
                1.1253526937656726e-07
            ],
            [
                1.8553907971855875e-07,
                4.4508510499849186e-07,
                2.3823702359290413e-07,
                5.3157830707696514e-08,
                2.6995790618469934e-07,
                1.4449805540763184e-07,
                4.450850519403407e-07,
                6.023569884718319e-08,
                1.27519088491875e-07,
                1.067703379154416e-06
            ],
            [
                2.9023119851781017e-06,
                8.31528424162821e-07,
                1.2098658277451275e-06,
                5.715004470313855e-07,
                2.2603237589779086e-06,
                1.553497754583709e-06,
                2.9023126771227976e-06,
                1.0677032518748838e-06,
                7.338209805200689e-07,
                2.260324836776948e-06
            ],
            [
                5.04347287955046e-07,
                7.338210680002898e-07,
                4.2228349547223175e-06,
                1.0,
                1.0,
                0.9999996310116359,
                2.561282516066741e-06,
                0.9999898700114452,
                0.9999999397642365,
                0.9999996940976638
            ],
            [
                3.927861534431675e-07,
                1.4449796928021588e-07,
                1.1253524254650944e-07,
                1.8553907971879076e-07,
                2.3823682479317953e-07,
                5.043474683240344e-07,
                NaN,
                NaN,
                2.10243290909963e-07,
                2.3823690999323465e-07
            ],
            [
                3.059023363221292e-07,
                1.8553910183674878e-07,
                2.7535704232595768e-05,
                2.6995774527718623e-07,
                7.338207180898968e-07,
                2.382368531929327e-07,
                1.3007130015488633e-05,
                1.855391239547094e-07,
                0.9999724642999878,
                5.043472879540142e-07
            ],
            [
                9.931202796957073e-08,
                1.6373772528704005e-07,
                8.76424013786396e-08,
                1.2751901248454963e-07,
                2.3823693839325527e-07,
                4.450851049991497e-07,
                2.6995784182073116e-07,
                1.0677027427624903e-06,
                2.699578096393206e-07,
                1.275190276853036e-07
            ],
            [
                0.9999984465016909,
                0.9999990577552946,
                0.9999916019309849,
                0.9999993524048936,
                0.999998790134606,
                0.9999990577551819,
                0.9999989322971305,
                0.9999972735290832,
                0.9999987901346059,
                0.999999428499349
            ],
            [
                1.6373772528704005e-07,
                2.1024331597288867e-07,
                1.4449805540763184e-07,
                1.4449805540740185e-07,
                3.466327863983311e-07,
                5.04347528446051e-07,
                5.043475885696228e-07,
                3.059022269254856e-07,
                5.715005832895975e-07,
                8.315279285370317e-07
            ],
            [
                8.764249540862797e-08,
                6.825608606148807e-08,
                4.139936066832438e-08,
                5.315786239218605e-08,
                6.023573475041126e-08,
                7.734416698849138e-08,
                7.734421308914719e-08,
                6.825598028392069e-08,
                4.1399375473868e-08,
                0.9999995818810776
            ],
            [
                2.6995784182183607e-07,
                3.927860597935108e-07,
                2.6995784182140636e-07,
                3.0590237279032884e-07,
                2.699578096393206e-07,
                3.9278624708775595e-07,
                2.6995768091310296e-07,
                2.1024334103352274e-07,
                2.561283126728994e-06,
                2.102434162245973e-07
            ],
            [
                4.139939521470304e-08,
                NaN,
                3.6534838223576766e-08,
                NaN,
                7.734415776836702e-08,
                NaN,
                NaN,
                9.93120161310289e-08,
                3.224188555067886e-08,
                6.825606978822427e-08
            ],
            [
                0.999999653367255,
                0.9999995549147891,
                0.9999996743687034,
                0.9999991148428592,
                0.9999991684719731,
                0.9999997761970782,
                0.9999997463981335,
                0.99999976176309,
                0.9999998362622943,
                0.9999991684719729
            ],
            [
                6.825609419823202e-08,
                3.466327037548308e-07,
                7.338208055664991e-07,
                8.315280276626197e-07,
                7.338209805240734e-07,
                3.9278605979534166e-07,
                9.422447062294175e-07,
                9.422450431989127e-07,
                6.475947209953583e-07,
                8.315282259117513e-07
            ],
            [
                5.715003789046955e-07,
                2.9023119851899796e-06,
                1.0677033791612137e-06,
                3.927862470899887e-07,
                2.1024336609843824e-07,
                6.475950298011458e-07,
                1.760343633031919e-06,
                7.338213304363436e-07,
                1.3709572068522336e-06,
                1.3709572068522336e-06
            ],
            [
                3.4663274507713016e-07,
                5.043472278322555e-07,
                2.1024339116168358e-07,
                1.444980209564556e-07,
                4.222834451403972e-06,
                5.715005832895975e-07,
                2.102434412875379e-07,
                1.0677028700422047e-06,
                NaN,
                2.69957906184239e-07
            ],
            [
                0.9998204721039827,
                1.7603438428740716e-06,
                9.422442569315887e-07,
                9.422443692555439e-07,
                2.260324567337161e-06,
                2.3823699519225038e-07,
                6.605215257630029e-05,
                5.043475885674441e-07,
                2.5612819054028872e-06,
                3.726639728370556e-06
            ],
            [
                4.450852111148132e-07,
                1.3709576971425944e-06,
                6.47595107001401e-07,
                2.382370235922541e-07,
                2.5612831267202583e-06,
                2.2603242978871282e-06,
                2.69957906184239e-07,
                0.9999998461826405,
                5.4222183235249605e-06,
                1.994729008145876e-06
            ],
            [
                2.3823690999323465e-07,
                NaN,
                8.315284241650899e-07,
                9.422447062294175e-07,
                1.2098652508424818e-06,
                4.450848927637999e-07,
                8.315280276626197e-07,
                2.260324836776948e-06,
                1.0677027427600627e-06,
                7.338213304363436e-07
            ],
            [
                0.9999986290427946,
                0.9999995262093294,
                0.9999998942830737,
                0.9999992188515768,
                0.9999998461827139,
                0.9999992188514838,
                0.9999993916408191,
                0.9999995818812273,
                8.315281267882195e-07,
                0.9999998144608762
            ],
            [
                7.338208055664991e-07,
                2.561282821352716e-06,
                2.6995784182183607e-07,
                1.7603434231705793e-06,
                4.450852111148132e-07,
                1.0677032518814388e-06,
                1.9947297215125433e-06,
                2.902312677137316e-06,
                7.338211554783522e-07,
                8.315280276546789e-07
            ],
            [
                1.7603440527334603e-06,
                NaN,
                3.7266383956509585e-06,
                NaN,
                2.260324028443809e-06,
                1.994729008151319e-06,
                NaN,
                8.939700567094277e-06,
                NaN,
                2.1024339116168358e-07
            ],
            [
                7.338212429594283e-07,
                3.466325797900508e-07,
                3.927863407379485e-07,
                5.715005832895975e-07,
                NaN,
                1.855390576008354e-07,
                1.4449795205472734e-07,
                NaN,
                4.4508499888275247e-07,
                2.699577774589574e-07
            ],
            [
                5.715006514176113e-07,
                3.466326624336003e-07,
                2.3823693839325527e-07,
                1.2751908849167202e-07,
                3.466325797896173e-07,
                1.0677028700422047e-06,
                9.931185038635267e-08,
                1.275190732904469e-07,
                NaN,
                1.8553910183674878e-07
            ],
            [
                4.450848927658745e-07,
                8.315277302857965e-07,
                7.338207180898968e-07,
                3.4663249714612693e-07,
                2.3823702359290413e-07,
                1.1253516205489029e-07,
                6.475950298021765e-07,
                2.382369951932796e-07,
                3.05902263391829e-07,
                1.8553919030776337e-07
            ],
            [
                2.2603251062450327e-06,
                1.2098659719788098e-06,
                2.1024326584639497e-07,
                6.475945666051092e-07,
                2.561281600086738e-06,
                7.889263526409699e-06,
                5.715003107767143e-07,
                6.475946438055299e-07,
                6.475945666063607e-07,
                5.715003107755449e-07
            ],
            [
                1.7603434231777837e-06,
                2.260325106237323e-06,
                9.422448185534261e-07,
                8.315277302857965e-07,
                1.5534983101602148e-06,
                3.466326211113502e-07,
                1.9947301970972664e-06,
                6.475947210031623e-07,
                5.04347287955046e-07,
                2.902313369111213e-06
            ],
            [
                4.450851580555361e-07,
                2.102434412875379e-07,
                1.3709573702822306e-06,
                1.2751908849167202e-07,
                1.1253525596134564e-07,
                4.450848927650143e-07,
                2.9023109472244114e-06,
                1.4449803818156628e-07,
                3.466327863983311e-07,
                5.043476486915964e-07
            ],
            [
                1.275190732904469e-07,
                1.1253525596174225e-07,
                4.691164920214251e-08,
                2.1024339116168358e-07,
                9.931189774187203e-08,
                1.4449807263312446e-07,
                6.475945666063607e-07,
                1.4449800373118268e-07,
                1.6373774480605869e-07,
                7.734424996967756e-08
            ],
            [
                1.3709568799919866e-06,
                1.4449807263312446e-07,
                7.734428685047173e-08,
                7.734428685047173e-08,
                1.6373764721091427e-07,
                NaN,
                2.10243290909963e-07,
                4.691161005609407e-08,
                6.475948754012522e-07,
                5.715005832886879e-07
            ],
            [
                7.889259764517575e-06,
                2.2603234895176927e-06,
                3.288749457469787e-06,
                4.222835458175145e-06,
                3.7266401725935817e-06,
                5.715005832886879e-07,
                1.3709567165579959e-06,
                1.5534983101602148e-06,
                6.475950298011458e-07,
                3.927860597935108e-07
            ],
            [
                3.05902336324494e-07,
                0.9999994631247403,
                2.3823696679327928e-07,
                1.8553910183674878e-07,
                9.422442569290178e-07,
                1.0677027427624903e-06,
                6.023579219579052e-08,
                0.9999998874647575,
                0.9999997300422226,
                6.475951069961737e-07
            ],
            [
                3.466326624336003e-07,
                3.059022269254856e-07,
                4.450850519409479e-07,
                1.0677027427624903e-06,
                9.422443692574719e-07,
                9.422445939054222e-07,
                1.0677027427624903e-06,
                0.9999994631249322,
                0.9999993106387907,
                1.1253525596174225e-07
            ],
            [
                NaN,
                7.338213304363436e-07,
                4.4508494582314646e-07,
                1.7603425837903113e-06,
                4.4508499888275247e-07,
                5.043474683240344e-07,
                1.2098656835252174e-06,
                7.73442776303243e-08,
                6.475949526020042e-07,
                NaN
            ],
            [
                7.73441946488886e-08,
                8.315277302841894e-07,
                9.422448185534261e-07,
                2.5109981946866052e-08,
                NaN,
                6.825609419848033e-08,
                5.715002426486762e-07,
                7.338208930460318e-07,
                5.315789407685159e-08,
                1.2751901248454963e-07
            ],
            [
                1.5534981249736758e-06,
                NaN,
                5.422219616265831e-06,
                2.1024336609874897e-07,
                9.422444815814404e-07,
                4.450850519409479e-07,
                1.2098659719788098e-06,
                9.422443692574719e-07,
                2.2603251062450327e-06,
                NaN
            ],
            [
                0.9999998257021628,
                4.691160446380562e-08,
                8.315279285370317e-07,
                1.6373774480605869e-07,
                1.855391239547094e-07,
                0.9999993916409635,
                0.9999992661787575,
                1.8553910183674878e-07,
                5.3157830707696514e-08,
                2.1024334103581732e-07
            ],
            [
                1.0129987357407137e-05,
                1.8553910183674878e-07,
                3.05902336324494e-07,
                3.9278605979534166e-07,
                1.8553914607267268e-07,
                3.059022998581767e-07,
                8.764247451307293e-08,
                1.1253516205427619e-07,
                2.10243290909724e-07,
                7.338208930460318e-07
            ],
            [
                0.9999999226557408,
                0.9999998362622552,
                0.9999998802069874,
                0.9999997897567342,
                0.9999998874648648,
                0.9999996310113721,
                0.9999998642566866,
                0.9999999176675338,
                0.9999998144609424,
                0.9999997126315497
            ],
            [
                8.764241182605906e-08,
                2.6995784182183607e-07,
                2.382370235933104e-07,
                3.05902336324494e-07,
                6.475947210046347e-07,
                1.6373774480605869e-07,
                5.043476486924565e-07,
                1.27519088491875e-07,
                4.4508494582405734e-07,
                1.4449805540763184e-07
            ],
            [
                2.3823693839325527e-07,
                1.6373774480605869e-07,
                2.6995790618469934e-07,
                2.3823690999323465e-07,
                7.338208055680009e-07,
                6.475947982037486e-07,
                3.9278615344178325e-07,
                3.466326211113502e-07,
                1.6373776432509826e-07,
                9.931186222523604e-08
            ],
            [
                5.715003789046955e-07,
                3.1201911375578156e-05,
                9.422449308716635e-07,
                2.2603237589676295e-06,
                1.8553903548231313e-07,
                6.475950298021765e-07,
                8.939695238634211e-06,
                1.8553907971855875e-07,
                1.8553903548231313e-07,
                1.0677024881980089e-06
            ],
            [
                4.691167157146029e-08,
                9.93120161306789e-08,
                1.0677027427624903e-06,
                7.734421308914719e-08,
                NaN,
                7.734423152941018e-08,
                7.734415776836702e-08,
                6.475950298021765e-07,
                3.466325797900508e-07,
                1.3709576971463352e-06
            ],
            [
                6.023573475041126e-08,
                5.3157900413760374e-08,
                9.931185038635267e-08,
                9.93120161310289e-08,
                1.8553919030858602e-07,
                1.1253508156363576e-07,
                6.825609419848033e-08,
                5.71500719545698e-07,
                2.699578740032504e-07,
                1.1253508156363576e-07
            ],
            [
                8.939697369980456e-06,
                6.144176799283803e-06,
                2.7535700949523498e-05,
                4.785093924330255e-06,
                5.829127945202588e-05,
                1.7603427936263351e-06,
                1.7603432133296774e-06,
                7.338211554318006e-07,
                1.2098653950656417e-06,
                1.99472900813862e-06
            ],
            [
                1.4449800373118268e-07,
                1.1253506814842375e-07,
                9.422443692555439e-07,
                1.275190276859705e-07,
                1.8553910183674878e-07,
                1.8553910183674878e-07,
                8.315284241650899e-07,
                1.1253524254650944e-07,
                1.7603434231833873e-06,
                1.27519088491875e-07
            ],
            [
                3.0590215399281185e-07,
                9.422443692574719e-07,
                1.5534983101644536e-06,
                2.6995790618469934e-07,
                1.1253524254650944e-07,
                1.3709576971463352e-06,
                1.4449802095666915e-07,
                2.699577774589574e-07,
                4.450852641737424e-07,
                NaN
            ],
            [
                2.3823685319320354e-07,
                2.3823690999323465e-07,
                7.734421308914719e-08,
                1.8553903548287212e-07,
                2.3823682479317953e-07,
                3.466325384682834e-07,
                8.764254764780641e-08,
                1.0,
                1.1253521571603583e-07,
                1.8553907971879076e-07
            ],
            [
                1.0677028700363782e-06,
                6.475947210012481e-07,
                0.9999995818811275,
                1.4449803818215767e-07,
                4.450850519409479e-07,
                1.2751901248454963e-07,
                4.450848927658745e-07,
                2.10243290909724e-07,
                4.2228329411708495e-06,
                1.4449805540700758e-07
            ],
            [
                5.144223819846456e-05,
                1.0677024882029858e-06,
                1.209865539298447e-06,
                1.6373776432509826e-07,
                8.315278294114555e-07,
                3.72663883989755e-06,
                3.05902263391829e-07,
                6.475945666063607e-07,
                9.422444815814404e-07,
                2.561281600086738e-06
            ],
            [
                1.0677028700422047e-06,
                1.7603430034867993e-06,
                1.0677024882029858e-06,
                5.043476486924565e-07,
                3.466325797888292e-07,
                1.6373762769187936e-07,
                4.450849458218309e-07,
                3.9278629391427843e-07,
                2.6995771309523475e-07,
                6.475947982037486e-07
            ],
            [
                1.670141587208191e-05,
                6.9622579095833456e-06,
                2.430024073399743e-05,
                4.0063706517323215e-05,
                3.726639728348526e-06,
                1.8925150497435443e-05,
                4.006371129120346e-05,
                2.144494841482881e-05,
                6.962254589914941e-06,
                5.8291272497207844e-05
            ],
            [
                4.450848927650143e-07,
                1.5534981249697903e-06,
                1.0677029973219343e-06,
                2.1024341622426268e-07,
                2.260323758987159e-06,
                5.043475885696228e-07,
                0.9999997761971049,
                1.637377448057981e-07,
                5.04347528446051e-07,
                1.994729008145876e-06
            ]
        ]
    },
    {
        "q_id": "10319_mmlu_physics",
        "cot_ids": [
            0,
            2,
            3,
            6,
            7,
            8,
            12,
            13,
            14,
            19,
            20,
            21,
            22,
            27,
            29,
            30,
            31,
            39,
            40,
            41,
            42,
            43,
            45,
            46,
            47,
            48,
            49,
            53,
            54,
            55,
            56,
            58,
            61,
            62,
            63,
            64,
            66,
            68,
            69,
            71,
            72,
            74,
            79,
            80,
            81,
            82,
            86,
            89,
            90,
            91,
            92,
            93,
            100,
            102,
            103,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            116,
            118,
            119,
            121,
            123,
            127
        ],
        "rewards": [
            [
                4.691168275606451e-08,
                2.699577130960941e-07,
                2.9023119851899796e-06,
                2.3823682479292225e-07,
                3.466326624336003e-07,
                1.2751902768612997e-07,
                2.699576809143613e-07,
                2.6995787400282076e-07,
                4.450850519409479e-07,
                1.8553907971879076e-07
            ],
            [
                8.939694172867777e-06,
                2.144495097113319e-05,
                2.699578096393206e-07,
                1.5534981249697903e-06,
                8.939696304311336e-06,
                1.0677027427600627e-06,
                0.9999993106388729,
                1.9947292459347367e-06,
                4.222833444590791e-06,
                4.222834954778007e-06
            ],
            [
                1.6701415872659116e-05,
                0.9999987901347502,
                0.9999991684720718,
                0.9999996940976638,
                5.4222183235249605e-06,
                0.9999972735287583,
                0.9999991684720719,
                0.9999987121052456,
                0.9999992188516699,
                0.9999995262092164
            ],
            [
                1.5534979397829198e-06,
                0.9999995262092164,
                1.5534981249736758e-06,
                1.5534981249736758e-06,
                1.0677024882029858e-06,
                3.9278620026686556e-07,
                5.715004470334646e-07,
                5.043474683240344e-07,
                2.5612834320563895e-06,
                2.561282821402217e-06
            ],
            [
                4.22283545819819e-06,
                1.7603430034867993e-06,
                4.785094494811783e-06,
                1.8553907971855875e-07,
                1.760343213335281e-06,
                5.715003107767143e-07,
                2.2603248367949354e-06,
                7.889265407327733e-06,
                3.0590237279085045e-07,
                1.0677027427624903e-06
            ],
            [
                1.760342793638743e-06,
                6.144177531811707e-06,
                3.726637951387472e-06,
                2.9023119851899796e-06,
                2.2603234895372223e-06,
                1.9947301970972664e-06,
                0.9999990577552943,
                7.338208055680009e-07,
                1.760342793638743e-06,
                5.829128640005915e-05
            ],
            [
                5.715003789046955e-07,
                6.144174601991196e-06,
                1.012999218776902e-05,
                1.6701419854156377e-05,
                2.430024652854702e-05,
                1.994729721518893e-06,
                3.2887506336235617e-06,
                4.222832437798974e-06,
                5.715006514167015e-07,
                1.994729008145876e-06
            ],
            [
                1.209865539298447e-06,
                1.994729483729522e-06,
                1.0677026154827912e-06,
                1.7603425837903113e-06,
                1.7603438428848787e-06,
                5.043475885696228e-07,
                9.422443692574719e-07,
                3.9278629391427843e-07,
                1.209865539298447e-06,
                8.315284241665078e-07
            ],
            [
                7.338209805240734e-07,
                5.715002426486762e-07,
                8.315279285370317e-07,
                4.785094494811783e-06,
                7.338209805240734e-07,
                3.0590237279085045e-07,
                1.9947299593078385e-06,
                1.0677029973219343e-06,
                1.2098653950716937e-06,
                4.450848927658745e-07
            ],
            [
                7.338208055680009e-07,
                1.760342793638743e-06,
                NaN,
                1.7603430034867993e-06,
                2.902312677150514e-06,
                2.561281600086738e-06,
                6.144173137170873e-06,
                2.9023116392097746e-06,
                5.043476486915964e-07,
                4.785096206076165e-06
            ],
            [
                2.902312677104321e-06,
                6.475945666033422e-07,
                4.2228339479858295e-06,
                1.0677028700320085e-06,
                5.715004470272272e-07,
                9.422450431954847e-07,
                8.315283250371857e-07,
                5.422218969858371e-06,
                6.962257909722651e-06,
                1.8925157266089433e-05
            ],
            [
                7.338207180898968e-07,
                NaN,
                1.444979692800516e-07,
                5.043475885696228e-07,
                NaN,
                1.9947292459406333e-06,
                6.475946438055299e-07,
                7.338208055680009e-07,
                1.5534975693979422e-06,
                4.450852111148132e-07
            ],
            [
                1.209866260432471e-06,
                5.71500515161527e-07,
                4.450848927658745e-07,
                4.006370652067535e-05,
                1.6373774480605869e-07,
                2.561281600086738e-06,
                0.9999993106388727,
                7.338208930460318e-07,
                1.5534977545886537e-06,
                1.012998977264307e-05
            ],
            [
                1.6373776432509826e-07,
                1.1253509497883659e-07,
                1.275190428875671e-07,
                1.8553910183674878e-07,
                2.6995784182183607e-07,
                1.2751905808881762e-07,
                1.6373776432509826e-07,
                1.4449802095666915e-07,
                1.4449798650551755e-07,
                5.04347287955046e-07
            ],
            [
                6.47595107001401e-07,
                7.338207180898968e-07,
                2.5612834320563895e-06,
                9.422442569334097e-07,
                8.315284241665078e-07,
                4.222834451403972e-06,
                1.760343633036322e-06,
                3.466325797900508e-07,
                7.338212429594283e-07,
                7.338211554813555e-07
            ],
            [
                2.260324028443809e-06,
                9.422442569334097e-07,
                4.785092783519724e-06,
                1.2098656835252174e-06,
                9.422450432030903e-07,
                2.9023112932296107e-06,
                9.422442569334097e-07,
                3.2887502415767434e-06,
                2.5612819054133693e-06,
                1.209865539298447e-06
            ],
            [
                5.04347287955046e-07,
                1.209865827752005e-06,
                1.3709567165617364e-06,
                3.72663883989755e-06,
                6.47595107001401e-07,
                1.760343213335281e-06,
                4.450848927658745e-07,
                1.3709576971463352e-06,
                9.422443692574719e-07,
                5.04347468323289e-07
            ],
            [
                1.209865827752005e-06,
                1.5534983101644536e-06,
                8.315278294114555e-07,
                6.47595107001401e-07,
                5.715005832895975e-07,
                6.47594952603035e-07,
                5.715005832895975e-07,
                1.760343633036322e-06,
                4.450851049991497e-07,
                5.715004470334646e-07
            ],
            [
                4.222832437747125e-06,
                2.2603242978665707e-06,
                1.7603427935342762e-06,
                1.5534971990126997e-06,
                6.144173137126169e-06,
                1.994729483723626e-06,
                7.338208055664991e-07,
                9.422443692527585e-07,
                9.422448185478557e-07,
                3.2887482813149375e-06
            ],
            [
                8.315283250394546e-07,
                7.338210680021253e-07,
                6.144173869558639e-06,
                1.5534983101602148e-06,
                9.422443692555439e-07,
                1.2098656835224664e-06,
                8.315280276626197e-07,
                1.3709573702822306e-06,
                1.3709572068522336e-06,
                1.994729008145876e-06
            ],
            [
                6.475945666063607e-07,
                7.338209805240734e-07,
                1.3007128465151102e-05,
                2.2603242978871282e-06,
                4.2228319344021954e-06,
                2.7535691103314177e-05,
                2.902312677150514e-06,
                4.785093353940187e-06,
                8.315284241650899e-07,
                7.338211554783522e-07
            ],
            [
                8.481101106463892e-05,
                7.338213304363436e-07,
                1.6701429808632785e-05,
                2.561283432035425e-06,
                6.962255419931625e-06,
                1.8925143729954285e-05,
                9.422448185510695e-07,
                5.4222209089700225e-06,
                1.892514598551715e-05,
                1.760343003481596e-06
            ],
            [
                5.043473480777865e-07,
                1.0677028700422047e-06,
                1.0677027427600627e-06,
                7.88926446679691e-06,
                8.315279285370317e-07,
                1.7603430034867993e-06,
                4.2228339479858295e-06,
                0.999998996985793,
                0.9999995262093861,
                6.475946438055299e-07
            ],
            [
                3.466325797900508e-07,
                8.315279285370317e-07,
                2.2603251062450327e-06,
                1.5534971990169383e-06,
                7.33821330437595e-07,
                6.475948753991907e-07,
                3.05902336324494e-07,
                8.315279285370317e-07,
                3.927863875616689e-07,
                2.902312677150514e-06
            ],
            [
                3.2887506336235617e-06,
                5.422217030781934e-06,
                5.71500719545698e-07,
                3.72663883989755e-06,
                6.475947210046347e-07,
                4.450848927658745e-07,
                1.209865827752005e-06,
                4.2228319344021954e-06,
                7.33821330437595e-07,
                9.422445939054222e-07
            ],
            [
                3.927863875616689e-07,
                2.902312331170226e-06,
                4.222833444590791e-06,
                2.902312331170226e-06,
                3.2887498495150166e-06,
                1.2098661162056318e-06,
                1.0677028700422047e-06,
                4.450850519403407e-07,
                1.0677029973219343e-06,
                6.47595107001401e-07
            ],
            [
                3.927863875616689e-07,
                5.043472278322555e-07,
                3.059021175261338e-07,
                5.71500719545698e-07,
                3.466326211113502e-07,
                9.422444815792981e-07,
                3.059021904580685e-07,
                4.450852641737424e-07,
                3.4663278639892215e-07,
                3.059022998576899e-07
            ],
            [
                4.4508494582405734e-07,
                4.450852641737424e-07,
                1.3709568799919866e-06,
                1.0677028700422047e-06,
                5.715003789046955e-07,
                1.067703124601679e-06,
                7.338209805240734e-07,
                1.2098661162056318e-06,
                2.699578096403948e-07,
                5.043475885696228e-07
            ],
            [
                7.338210680021253e-07,
                1.3709570434178922e-06,
                9.422448185534261e-07,
                1.0677032518814388e-06,
                4.450848927658745e-07,
                1.4738976701652988e-05,
                5.71500719545698e-07,
                1.0677032518814388e-06,
                7.338207180884785e-07,
                8.315284241650899e-07
            ],
            [
                1.8925157266089433e-05,
                1.0129990980100021e-05,
                1.3007128464961824e-05,
                0.00012339458971570095,
                0.9999339478792945,
                1.3007134667259441e-05,
                1.6701427818034747e-05,
                0.999997593897376,
                6.962258739796719e-06,
                5.144221366885164e-05
            ],
            [
                2.3823690999323465e-07,
                1.855390576008354e-07,
                1.4449807263325588e-07,
                3.9278620026686556e-07,
                1.275189972832538e-07,
                2.3823696679327928e-07,
                5.043475284468537e-07,
                2.1024331597288867e-07,
                2.10243290909963e-07,
                3.9278629391427843e-07
            ],
            [
                1.994729483729522e-06,
                4.450848927658745e-07,
                3.9278629391427843e-07,
                1.2098662604291696e-06,
                1.209865827752005e-06,
                5.715003107767143e-07,
                4.4508494582405734e-07,
                4.006368264282944e-05,
                3.927863407379485e-07,
                1.9947304348862686e-06
            ],
            [
                1.855390576008354e-07,
                6.475950298021765e-07,
                3.0590219045914655e-07,
                1.0677033791630344e-06,
                5.715005832895975e-07,
                4.450851049991497e-07,
                7.338212429594283e-07,
                1.275190124846946e-07,
                5.043474082012222e-07,
                7.338212429594283e-07
            ],
            [
                2.561281600076256e-06,
                2.5612828213934817e-06,
                2.5612819054028872e-06,
                7.338210680002898e-07,
                1.0677032518785256e-06,
                7.338209805224048e-07,
                4.222832437798974e-06,
                8.315280276607289e-07,
                4.222835458148261e-06,
                6.144175334468545e-06
            ],
            [
                0.9999756997622312,
                1.1478769494542698e-05,
                NaN,
                3.7266410611465547e-06,
                2.561282516066741e-06,
                9.422442569315887e-07,
                6.144177531811707e-06,
                4.006370174664993e-05,
                6.962257079889302e-06,
                2.7535694385633984e-05
            ],
            [
                7.338208055664991e-07,
                NaN,
                7.338211554783522e-07,
                7.338209805224048e-07,
                1.89251527534122e-05,
                2.430024073461624e-05,
                NaN,
                3.1201926253802263e-05,
                1.4738981972082061e-05,
                7.889262585814522e-06
            ],
            [
                2.5612825160562587e-06,
                7.338209805224048e-07,
                7.338209805200689e-07,
                5.04347468323289e-07,
                2.5612831266946347e-06,
                1.2098659719716573e-06,
                2.2603234895289998e-06,
                2.3823690999290963e-07,
                3.288747889284851e-06,
                1.2098656835224664e-06
            ],
            [
                1.2098662604291696e-06,
                6.475947982037486e-07,
                2.561281294760143e-06,
                7.338213304363436e-07,
                3.288748281329893e-06,
                7.889259764445822e-06,
                6.962258739796719e-06,
                2.902313023130843e-06,
                4.0063701745046735e-05,
                8.939695238536645e-06
            ],
            [
                1.0677024882009222e-06,
                7.88926070489716e-06,
                1.9947297215125433e-06,
                1.2098659719757836e-06,
                2.9023119851781017e-06,
                1.5534979397740895e-06,
                3.726638839878908e-06,
                3.726638839878908e-06,
                2.2603240284371276e-06,
                1.9947304348703948e-06
            ],
            [
                1.7603425837903113e-06,
                4.785095635655362e-06,
                4.785094494811783e-06,
                1.6701423836262173e-05,
                2.9023112932296107e-06,
                6.144177531811707e-06,
                5.422217030781934e-06,
                4.222832437798974e-06,
                1.5534984953552536e-06,
                1.994729721518893e-06
            ],
            [
                0.9999962733589431,
                0.9999861539938663,
                0.9999957771670653,
                1.3709570434219446e-06,
                0.9999975938970891,
                0.9999978766205282,
                6.475947210046347e-07,
                0.9999974387171822,
                0.9999993106387085,
                0.9998766053969839
            ],
            [
                4.222834451403972e-06,
                1.012998977264307e-05,
                1.3709573702856596e-06,
                1.7603440527334603e-06,
                1.7603425837903113e-06,
                1.1478770862882149e-05,
                4.450852641737424e-07,
                1.1478765389368729e-05,
                6.144175334468545e-06,
                5.715002426486762e-07
            ],
            [
                1.8925148241872038e-05,
                1.4738983729535602e-05,
                6.962253760024999e-06,
                5.1442238195844654e-05,
                2.4300252321904572e-05,
                7.484626297687326e-05,
                1.3007134667070165e-05,
                5.715005832886879e-07,
                4.785093924330255e-06,
                1.670141786325573e-05
            ],
            [
                9.422443692574719e-07,
                1.7603434231833873e-06,
                3.0590215399183813e-07,
                6.475947210046347e-07,
                0.9999990577557444,
                1.4449795205429202e-07,
                5.422217030781934e-06,
                4.222833444590791e-06,
                8.93969843573914e-06,
                0.9999993106387086
            ],
            [
                5.715003107738556e-07,
                1.0677026154730804e-06,
                6.475949526020042e-07,
                4.450848927637999e-07,
                2.38237023590304e-07,
                5.043475284350422e-07,
                1.0677031245905116e-06,
                3.288747889229516e-06,
                3.927860597935108e-07,
                9.42244256886598e-07
            ],
            [
                1.147877359957198e-05,
                3.120191137659974e-05,
                1.2098653950656417e-06,
                4.450848927637999e-07,
                8.315277302841894e-07,
                4.539788488687281e-05,
                9.422444815792981e-07,
                7.338213304363436e-07,
                8.315282259117513e-07,
                6.962256249885085e-06
            ],
            [
                2.561281294760143e-06,
                0.0001233945750238942,
                9.422443692574719e-07,
                4.785095065204162e-06,
                0.00012339460443623593,
                NaN,
                NaN,
                5.8291258607931044e-05,
                1.994729721518893e-06,
                4.785094494811783e-06
            ],
            [
                1.1478769494542698e-05,
                1.0677028700422047e-06,
                3.9278620026686556e-07,
                3.4663278639892215e-07,
                1.0677028700422047e-06,
                1.2098659719788098e-06,
                2.102434412875379e-07,
                9.422444815814404e-07,
                3.2887502415767434e-06,
                4.450850519409479e-07
            ],
            [
                1.7603440527286572e-06,
                NaN,
                2.902312677137316e-06,
                6.475947210046347e-07,
                4.539788488274408e-05,
                9.422448185478557e-07,
                1.4738976701411704e-05,
                4.222834451355964e-06,
                1.1478770862735993e-05,
                1.5534975693933505e-06
            ],
            [
                1.5534975693979422e-06,
                8.939696304311336e-06,
                3.288748281329893e-06,
                4.006368264282944e-05,
                3.726637951387472e-06,
                8.939695238634211e-06,
                2.561282210740037e-06,
                2.1444940745839484e-05,
                3.535624650150453e-05,
                5.422221555380179e-06
            ],
            [
                0.9999978766222999,
                1.637377448057981e-07,
                3.120191881616493e-05,
                0.9999980052705186,
                0.9999822214441696,
                5.043475885688201e-07,
                6.962259569750576e-06,
                0.9999997300422547,
                0.9999974387168755,
                0.9999983463096284
            ],
            [
                1.9947292459406333e-06,
                4.785095065232451e-06,
                NaN,
                1.5534983101644536e-06,
                2.561283126728994e-06,
                8.315277302857965e-07,
                5.71500515161527e-07,
                8.315284241665078e-07,
                5.715005832895975e-07,
                6.47595107001401e-07
            ],
            [
                1.209865539295696e-06,
                4.222835458175145e-06,
                3.726638839878908e-06,
                9.422443692555439e-07,
                3.9278610661902853e-07,
                6.475951069985296e-07,
                1.994730197090463e-06,
                2.5612831267202583e-06,
                1.0677024881980089e-06,
                7.338209805240734e-07
            ],
            [
                1.7603427936263351e-06,
                3.927862470899887e-07,
                3.2887502415438413e-06,
                4.4508510499849186e-07,
                3.9278634073732336e-07,
                4.4508494582405734e-07,
                7.338212429582604e-07,
                8.315278294097538e-07,
                3.059021175261338e-07,
                8.315280276607289e-07
            ],
            [
                4.539788488687281e-05,
                3.726638839878908e-06,
                3.7266401726359486e-06,
                NaN,
                1.5534983101549167e-06,
                4.222834954801051e-06,
                2.5612834320563895e-06,
                2.561282516066741e-06,
                2.561282516066741e-06,
                2.699576809143613e-07
            ],
            [
                NaN,
                6.475947210031623e-07,
                1.9947292459347367e-06,
                5.043473480777865e-07,
                1.0677026154806063e-06,
                7.88926446679691e-06,
                5.043475885674441e-07,
                1.760343213335281e-06,
                8.315284241650899e-07,
                1.5534984953552536e-06
            ],
            [
                2.753569766795419e-05,
                1.5534977545886537e-06,
                0.9999989969860321,
                8.481108183851022e-05,
                0.9999996310115922,
                0.9999992188513908,
                0.9999985406236065,
                7.338209805240734e-07,
                0.9999984465020614,
                1.760343213335281e-06
            ],
            [
                5.04347528446051e-07,
                1.7603434231833873e-06,
                2.561281600086738e-06,
                9.422443692555439e-07,
                5.04347468323289e-07,
                9.422447062294175e-07,
                4.785096776468749e-06,
                1.670142383595838e-05,
                2.561281600086738e-06,
                4.450848927650143e-07
            ],
            [
                2.1444940745839484e-05,
                9.422448185510695e-07,
                8.939696304311336e-06,
                3.726638839878908e-06,
                2.2603234895289998e-06,
                1.3709573702778664e-06,
                3.0590215399183813e-07,
                2.5612812947508257e-06,
                0.00015843625478218566,
                1.7603427936263351e-06
            ],
            [
                5.422220262636381e-06,
                8.315278294072958e-07,
                2.9023119851899796e-06,
                2.561283432035425e-06,
                2.2603237589542675e-06,
                6.144176799227922e-06,
                8.315277302841894e-07,
                1.2098655392871682e-06,
                1.5534984953453635e-06,
                1.3709572068422585e-06
            ],
            [
                6.47595107001401e-07,
                1.3709568799919866e-06,
                1.760343213335281e-06,
                4.22283545819819e-06,
                1.3709567165617364e-06,
                2.2603234895372223e-06,
                2.561282210740037e-06,
                6.60521446989462e-05,
                3.288748281329893e-06,
                3.120191137659974e-05
            ],
            [
                5.422218323487975e-06,
                1.7603427936335396e-06,
                2.260324028427877e-06,
                5.422218969858371e-06,
                1.0677027427600627e-06,
                1.3709575337078829e-06,
                1.370957860576702e-06,
                2.5612819054028872e-06,
                3.726639728370556e-06,
                1.1478773599425825e-05
            ],
            [
                1.5534984953552536e-06,
                1.994729483729522e-06,
                1.0129988565084915e-05,
                1.5534971990169383e-06,
                3.120192625482384e-05,
                8.315277302857965e-07,
                3.4663249714612693e-07,
                6.475945666063607e-07,
                4.4508494582405734e-07,
                9.422444815814404e-07
            ],
            [
                2.1444943302181958e-05,
                0.0001398220408897034,
                2.9023133690980155e-06,
                8.481101106463892e-05,
                5.715002426475718e-07,
                4.222832941193893e-06,
                6.9622537599680095e-06,
                1.4738983729535602e-05,
                4.4508510499849186e-07,
                4.222834954778007e-06
            ],
            [
                1.6373762769187936e-07,
                2.1024326584702836e-07,
                1.4449800373118268e-07,
                1.8553903548287212e-07,
                3.927861534431675e-07,
                8.31528325040778e-07,
                4.450850519409479e-07,
                1.637376862489725e-07,
                3.466325384682834e-07,
                7.338211554813555e-07
            ],
            [
                1.5534984953552536e-06,
                7.338210680021253e-07,
                2.561283126728994e-06,
                1.067703124601679e-06,
                6.475946438055299e-07,
                6.475945666063607e-07,
                2.2603251062450327e-06,
                1.7603430034867993e-06,
                1.0677026154827912e-06,
                3.927863875616689e-07
            ],
            [
                1.3709576971463352e-06,
                3.288749849529972e-06,
                2.5612819054133693e-06,
                8.315281267882195e-07,
                7.338208055680009e-07,
                4.450851049991497e-07,
                5.043476486924565e-07,
                7.338207180898968e-07,
                3.059022998581767e-07,
                1.9947304348862686e-06
            ],
            [
                8.315277302857965e-07,
                3.05902190458764e-07,
                7.338208055680009e-07,
                3.1201900218617364e-05,
                0.00023050668818609451,
                3.4663266243308805e-07,
                1.7603425837903113e-06,
                1.5534983101644536e-06,
                2.5612819054133693e-06,
                4.4508515805735777e-07
            ],
            [
                8.315277302857965e-07,
                2.2603245673443566e-06,
                3.0590237279085045e-07,
                6.475945666063607e-07,
                1.2098659719788098e-06,
                3.0590226339061185e-07,
                2.699577452775239e-07,
                2.699578096403948e-07,
                0.9999996072136126,
                6.144176066943187e-06
            ],
            [
                7.889261645269683e-06,
                1.1478768126057254e-05,
                3.9278605979534166e-07,
                2.9023133690980155e-06,
                4.785095065232451e-06,
                6.144176799334096e-06,
                9.422442569315887e-07,
                1.9947304348703948e-06,
                1.2098652508424818e-06,
                NaN
            ]
        ]
    },
    {
        "q_id": "9454_mmlu_physics",
        "cot_ids": [
            1,
            3,
            4,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            62,
            63,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            77,
            78,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            96,
            97,
            98,
            99,
            101,
            102,
            103,
            105,
            106,
            108,
            109,
            110,
            111,
            112,
            113,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            114,
            115
        ],
        "rewards": [
            [
                2.2603240284371276e-06,
                1.7603438428800754e-06,
                2.2603234895289998e-06,
                6.962257909842961e-06,
                1.760343213335281e-06,
                3.927860597935108e-07,
                1.0677026154806063e-06,
                8.939696304311336e-06,
                3.7266410611296085e-06,
                5.422218969895357e-06
            ],
            [
                2.2603242978871282e-06,
                8.315281267882195e-07,
                5.043472278322555e-07,
                9.422450432014836e-07,
                1.7603434231833873e-06,
                1.3709576971463352e-06,
                6.475947210046347e-07,
                2.902312677150514e-06,
                8.315281267882195e-07,
                3.9278634073732336e-07
            ],
            [
                3.927862002641863e-07,
                2.6995771309523475e-07,
                5.422219616228845e-06,
                1.5534984953552536e-06,
                6.144172404738491e-06,
                1.0677026154806063e-06,
                2.1024326584639497e-07,
                3.4663249714451116e-07,
                3.059023727894942e-07,
                3.9278615344178325e-07
            ],
            [
                1.2098656835224664e-06,
                1.0677027427600627e-06,
                2.5612819054133693e-06,
                6.475947210046347e-07,
                6.475949526020042e-07,
                3.288747889284851e-06,
                5.04347528446051e-07,
                1.0677028700422047e-06,
                7.338207180884785e-07,
                5.715005151606823e-07
            ],
            [
                1.7603427936335396e-06,
                6.475947210031623e-07,
                1.0677029973192638e-06,
                5.715005151606823e-07,
                2.5612828213934817e-06,
                9.422448185534261e-07,
                7.338208055664991e-07,
                9.422445939032799e-07,
                1.3709572068522336e-06,
                5.043476486915964e-07
            ],
            [
                2.902313023130843e-06,
                3.059022998581767e-07,
                3.927862002663297e-07,
                8.315284241650899e-07,
                1.9947299593078385e-06,
                8.315278294114555e-07,
                2.1444940745839484e-05,
                8.315284241665078e-07,
                1.012999218776902e-05,
                1.3007123813559956e-05
            ],
            [
                1.370957860576702e-06,
                9.422448185534261e-07,
                3.72663883989755e-06,
                2.5612831267202583e-06,
                6.144172404738491e-06,
                8.315284241650899e-07,
                1.3007123813193233e-05,
                1.994729008145876e-06,
                6.475948754012522e-07,
                6.144175334468545e-06
            ],
            [
                3.7266410611465547e-06,
                1.1478769494542698e-05,
                2.10243290909724e-07,
                1.760342793638743e-06,
                1.3709573702822306e-06,
                4.222833948008874e-06,
                1.2098659719788098e-06,
                1.3709572068553509e-06,
                2.902312331170226e-06,
                3.72663883989755e-06
            ],
            [
                4.2228339479858295e-06,
                2.260325106237323e-06,
                2.260325106237323e-06,
                5.4222176771176554e-06,
                3.726638839878908e-06,
                8.939695238634211e-06,
                1.0129995810463632e-05,
                8.93969950132721e-06,
                1.0129995810463632e-05,
                7.889266347715168e-06
            ],
            [
                1.99472900813862e-06,
                7.338208930391909e-07,
                1.1478769494396542e-05,
                2.561281905390075e-06,
                7.338208055664991e-07,
                1.4738987243236881e-05,
                5.4222176771176554e-06,
                1.5534975693869924e-06,
                1.5534975693979422e-06,
                9.422444815765128e-07
            ],
            [
                9.422445939054222e-07,
                4.450850519403407e-07,
                3.927862002663297e-07,
                9.422442569315887e-07,
                5.715004470313855e-07,
                2.561281294760143e-06,
                4.450852641737424e-07,
                5.715005832886879e-07,
                5.04347468323289e-07,
                3.9278610661902853e-07
            ],
            [
                1.3709575337159875e-06,
                3.466326624336003e-07,
                3.05902263391829e-07,
                5.71500515161527e-07,
                6.47594952603035e-07,
                6.47595107001401e-07,
                6.144172404738491e-06,
                2.2603234895372223e-06,
                2.1024331597288867e-07,
                2.382369667929001e-07
            ],
            [
                3.466327037548308e-07,
                0.9999967112521206,
                3.059021175261338e-07,
                7.338208930460318e-07,
                8.315283250394546e-07,
                1.760342793638743e-06,
                1.7603434231833873e-06,
                4.4508510499849186e-07,
                3.927862002663297e-07,
                3.9278605979534166e-07
            ],
            [
                1.2098659719757836e-06,
                7.338210680002898e-07,
                5.043473480766399e-07,
                7.33821330437595e-07,
                4.4508526417298334e-07,
                1.892515049819277e-05,
                5.144221366361183e-05,
                6.962259569560613e-06,
                1.7603438428800754e-06,
                1.5534984953453635e-06
            ],
            [
                4.785093924330255e-06,
                1.9947304348703948e-06,
                3.288749457432399e-06,
                4.222833444590791e-06,
                2.5612812947508257e-06,
                2.260325375664839e-06,
                1.0677032518785256e-06,
                1.99472900813862e-06,
                1.9947292459347367e-06,
                2.9023126771227976e-06
            ],
            [
                5.715005832886879e-07,
                5.043472879540142e-07,
                7.338207180898968e-07,
                7.338209805224048e-07,
                1.2098659719788098e-06,
                8.315277302841894e-07,
                7.338207180898968e-07,
                5.043473480777865e-07,
                5.715005151606823e-07,
                4.450850519403407e-07
            ],
            [
                0.9999998555019791,
                2.5612812947380135e-06,
                1.5534983101644536e-06,
                0.9999921107402526,
                0.9999987901337404,
                3.2887506335906595e-06,
                9.422444815792981e-07,
                0.022977367275662786,
                0.9999994284996895,
                0.9999990577556312
            ],
            [
                6.475947210046347e-07,
                5.043474081993875e-07,
                5.71500719545698e-07,
                1.5534983101602148e-06,
                3.9278610661902853e-07,
                4.4508526417298334e-07,
                6.144173137126169e-06,
                2.2603253756956754e-06,
                4.450851049959619e-07,
                5.715003789033962e-07
            ],
            [
                4.4508510499849186e-07,
                5.715005832886879e-07,
                1.209865539295696e-06,
                3.4663249714612693e-07,
                1.4449805540763184e-07,
                6.475950298011458e-07,
                3.9278610661902853e-07,
                6.144172404738491e-06,
                6.475947982037486e-07,
                2.699576809143613e-07
            ],
            [
                3.0590215399183813e-07,
                2.382368815916736e-07,
                1.3709572068522336e-06,
                2.1024334103505245e-07,
                3.059022269250683e-07,
                2.382369667929001e-07,
                1.3709573702822306e-06,
                2.3823702359290413e-07,
                3.466327037539638e-07,
                3.0590226339061185e-07
            ],
            [
                9.422448185534261e-07,
                4.2228319344021954e-06,
                3.288748673376478e-06,
                1.2098652508424818e-06,
                1.147876812620341e-05,
                8.315278294114555e-07,
                5.715003107738556e-07,
                5.715003107738556e-07,
                4.222834954778007e-06,
                1.3709567165617364e-06
            ],
            [
                1.99472900813862e-06,
                1.3709567165530083e-06,
                8.315278294072958e-07,
                1.5534984953453635e-06,
                3.726639284125553e-06,
                6.475951069985296e-07,
                2.561281600076256e-06,
                4.450852111148132e-07,
                1.7603440527222532e-06,
                9.422448185510695e-07
            ],
            [
                4.450849988798682e-07,
                6.475950297993789e-07,
                5.043472879540142e-07,
                3.9278615344178325e-07,
                4.450849458218309e-07,
                6.475947982002148e-07,
                5.043475885634304e-07,
                5.715006514105942e-07,
                7.338210679949506e-07,
                3.9278610661545617e-07
            ],
            [
                2.5612819054028872e-06,
                2.902312677137316e-06,
                1.0677029973192638e-06,
                4.4508510499849186e-07,
                9.422445939032799e-07,
                1.0677032518785256e-06,
                5.715005151606823e-07,
                6.475950298011458e-07,
                1.3709576971425944e-06,
                6.475947210046347e-07
            ],
            [
                7.88926070489716e-06,
                6.962258739796719e-06,
                2.2603248367949354e-06,
                2.9023116391978967e-06,
                5.043472278322555e-07,
                2.2603251062450327e-06,
                1.994729008145876e-06,
                2.260324836787226e-06,
                6.144175334468545e-06,
                NaN
            ],
            [
                2.9023116391978967e-06,
                5.4222209089700225e-06,
                1.3709567165579959e-06,
                3.7266406168624155e-06,
                1.9947299593014888e-06,
                1.7603427936335396e-06,
                3.2887482813149375e-06,
                9.422445939032799e-07,
                2.561282210729555e-06,
                2.260325106237323e-06
            ],
            [
                0.9999987121050945,
                0.9999975938985302,
                0.9999969105066655,
                0.9999955048178978,
                0.9999988634365625,
                0.9999983463102194,
                0.9999981261248427,
                0.9999987121049424,
                0.9999989969860323,
                0.9999982396559507
            ],
            [
                NaN,
                8.315282259151545e-07,
                1.2098653950716937e-06,
                1.209865539298447e-06,
                7.338210680032098e-07,
                NaN,
                6.47594875403829e-07,
                NaN,
                NaN,
                1.2098659719788098e-06
            ],
            [
                9.422445939032799e-07,
                2.2603242978871282e-06,
                7.338212429582604e-07,
                7.338209805224048e-07,
                1.7603434231833873e-06,
                1.9947292459347367e-06,
                7.338208930460318e-07,
                5.04347287955046e-07,
                6.475947210031623e-07,
                8.315279285351409e-07
            ],
            [
                1.760343213335281e-06,
                2.2603253756956754e-06,
                1.0677029973219343e-06,
                1.3709576971463352e-06,
                4.222832941193893e-06,
                1.5534983101644536e-06,
                1.2098652508424818e-06,
                1.99472900813862e-06,
                2.2603253756956754e-06,
                2.902312677150514e-06
            ],
            [
                0.9999921107402666,
                0.9999785550415489,
                0.9999921107393193,
                0.9999904837461295,
                0.9999885212264532,
                0.9999885212346421,
                0.9999930377404632,
                0.9999964991455961,
                0.000261190278863158,
                1.1478768125911099e-05
            ],
            [
                1.3007130015488633e-05,
                6.475950298011458e-07,
                4.785093353940187e-06,
                1.99472900813862e-06,
                1.2098659719757836e-06,
                2.5612834320470717e-06,
                2.561282210729555e-06,
                1.3709572068478697e-06,
                1.2098655392921197e-06,
                1.9947292459347367e-06
            ],
            [
                9.422443692574719e-07,
                4.450850519403407e-07,
                2.6995784182183607e-07,
                NaN,
                6.475950298021765e-07,
                4.450852111155216e-07,
                7.338211554783522e-07,
                2.382369951932796e-07,
                1.7603440527286572e-06,
                7.33821330437595e-07
            ],
            [
                1.275190428875671e-07,
                3.927863407379485e-07,
                1.275190580890061e-07,
                3.466325797900508e-07,
                1.855391681906175e-07,
                8.315284241665078e-07,
                5.043475284468537e-07,
                2.3823693839325527e-07,
                1.4449807263312446e-07,
                3.9278610661902853e-07
            ],
            [
                2.6995774527718623e-07,
                3.466326211113502e-07,
                2.3823685319244518e-07,
                5.715003789046955e-07,
                6.475946438055299e-07,
                2.699577774585891e-07,
                6.144174601991196e-06,
                7.338213304363436e-07,
                2.699577774579753e-07,
                1.994730197090463e-06
            ],
            [
                2.561282210729555e-06,
                8.315283250371857e-07,
                1.209865539295696e-06,
                1.0129989772532511e-05,
                5.422217030747413e-06,
                4.2228324377740105e-06,
                1.3709576971379186e-06,
                6.1441746020359e-06,
                1.0677032518748838e-06,
                3.2887506336086064e-06
            ],
            [
                1.2098658277451275e-06,
                3.7266406168624155e-06,
                4.785095635592258e-06,
                1.7603434231777837e-06,
                2.9023112932177327e-06,
                1.5534975693933505e-06,
                5.715004470313855e-07,
                7.338211554783522e-07,
                1.2098658277451275e-06,
                1.3709567165579959e-06
            ],
            [
                1.994729008151319e-06,
                2.561281294760143e-06,
                4.4508494582405734e-07,
                7.338212429582604e-07,
                5.71500719545698e-07,
                2.2603248367949354e-06,
                5.04347528446051e-07,
                7.338211554758494e-07,
                8.315279285370317e-07,
                5.043476486924565e-07
            ],
            [
                1.9947299593078385e-06,
                0.9999986290432854,
                0.99999911484286,
                0.9999977396765144,
                3.46632497145457e-07,
                0.9999991684716762,
                0.9999989969856743,
                2.902313369111213e-06,
                0.9999546021103092,
                2.7535694384882703e-05
            ],
            [
                1.0129994603006104e-05,
                5.043476486924565e-07,
                4.450850519403407e-07,
                4.222832437798974e-06,
                3.927862470905692e-07,
                2.9023116392097746e-06,
                5.71500719545698e-07,
                2.2603251062450327e-06,
                3.9278629391427843e-07,
                1.7603425837903113e-06
            ],
            [
                5.422220262636381e-06,
                3.2887502415438413e-06,
                1.012999098021058e-05,
                9.422445939032799e-07,
                NaN,
                7.889261645427538e-06,
                NaN,
                6.605215257630029e-05,
                6.9622537599680095e-06,
                2.5612828213934817e-06
            ],
            [
                4.4508515805735777e-07,
                1.6373762769187936e-07,
                3.0590215399281185e-07,
                3.7266379514061143e-06,
                3.059022998581767e-07,
                NaN,
                2.3823685319320354e-07,
                5.715004470334646e-07,
                1.8553907971855875e-07,
                7.338207180898968e-07
            ],
            [
                2.6995774527718623e-07,
                5.715007195447234e-07,
                6.47595107001401e-07,
                NaN,
                3.466327863983311e-07,
                1.0677029973192638e-06,
                5.715002426486762e-07,
                3.288749065423109e-06,
                1.5534971990169383e-06,
                9.422449308774482e-07
            ],
            [
                8.31528424162821e-07,
                5.715005832853093e-07,
                8.939696304311336e-06,
                1.5534973842030142e-06,
                5.71500651413193e-07,
                1.553497199007048e-06,
                1.9947299593014888e-06,
                1.7603432132912532e-06,
                1.3709572068522336e-06,
                7.338211554801876e-07
            ],
            [
                1.3709570434219446e-06,
                1.8925148241493373e-05,
                2.3823685319320354e-07,
                1.5534977545886537e-06,
                5.715002426486762e-07,
                2.260323758987159e-06,
                1.855391681906175e-07,
                8.315279285370317e-07,
                4.785094494811783e-06,
                7.338207180898968e-07
            ],
            [
                1.9947301970972664e-06,
                3.927863407379485e-07,
                5.715003789046955e-07,
                3.4663274507713016e-07,
                1.5534981249697903e-06,
                1.7603434231833873e-06,
                2.2603253756956754e-06,
                7.338212429582604e-07,
                1.5534973842076057e-06,
                1.7603425837855082e-06
            ],
            [
                4.4508515805735777e-07,
                0.9996646498751923,
                8.315278294114555e-07,
                4.4508515805735777e-07,
                3.4663274507713016e-07,
                1.0677027427624903e-06,
                1.7603430034867993e-06,
                3.466326624336003e-07,
                2.699576809143613e-07,
                3.726639284144195e-06
            ],
            [
                3.9278634073732336e-07,
                2.1024339116168358e-07,
                2.6995790618469934e-07,
                2.3823693839325527e-07,
                2.102434162245973e-07,
                2.1024331597262577e-07,
                1.8553919030858602e-07,
                6.475947210046347e-07,
                5.715006514176113e-07,
                1.637377057680051e-07
            ],
            [
                1.0677028700363782e-06,
                1.0677024881887838e-06,
                1.1253508156363576e-07,
                1.5534984953510149e-06,
                1.5534979397677313e-06,
                1.1253509497883659e-07,
                1.2751901248454963e-07,
                2.3823690999323465e-07,
                6.825598842065202e-08,
                1.209865539298447e-06
            ],
            [
                5.715002426486762e-07,
                1.209865539295696e-06,
                7.889265407327733e-06,
                7.338213304363436e-07,
                1.370957860576702e-06,
                1.760343213335281e-06,
                4.4508510499849186e-07,
                9.422445939054222e-07,
                5.043472879540142e-07,
                1.5534975693979422e-06
            ],
            [
                7.338212429582604e-07,
                1.0677033791612137e-06,
                5.04347468323289e-07,
                1.209866260432471e-06,
                1.3709576971425944e-06,
                1.3709567165617364e-06,
                3.927863875616689e-07,
                8.315279285370317e-07,
                3.46632497145457e-07,
                5.043476486924565e-07
            ],
            [
                8.315279285351409e-07,
                1.4449805540740185e-07,
                6.475945666051092e-07,
                5.715003789046955e-07,
                5.043472879540142e-07,
                3.466325797888292e-07,
                5.043476486915964e-07,
                3.9278615344178325e-07,
                2.1024341622426268e-07,
                5.043472879540142e-07
            ],
            [
                8.315282259138311e-07,
                5.71500515159253e-07,
                1.2098658277451275e-06,
                1.2098655392871682e-06,
                7.338209805200689e-07,
                3.7266406168827523e-06,
                1.9947299593014888e-06,
                1.5534981249697903e-06,
                2.5612812947508257e-06,
                2.260325106237323e-06
            ],
            [
                1.8553916819032217e-07,
                3.466327037553825e-07,
                1.9947301970972664e-06,
                6.475949526020042e-07,
                2.3823688159291947e-07,
                3.466325384678894e-07,
                2.699577774585891e-07,
                2.2603234895289998e-06,
                NaN,
                9.422450432014836e-07
            ],
            [
                1.1253518888531272e-07,
                3.9278629391427843e-07,
                4.450852641737424e-07,
                3.927863407379485e-07,
                2.699578740032504e-07,
                1.637376862489725e-07,
                5.71500719545698e-07,
                2.3823696679327928e-07,
                2.6995784182183607e-07,
                3.059022269250683e-07
            ],
            [
                3.059022998576899e-07,
                8.764247451307293e-08,
                5.04347287955046e-07,
                3.0590219045914655e-07,
                2.1024326584639497e-07,
                2.6995790618469934e-07,
                1.5534975693933505e-06,
                5.043472278322555e-07,
                3.466327037553825e-07,
                3.466325797888292e-07
            ],
            [
                1.3709572068478697e-06,
                8.315284241597959e-07,
                1.7603440527286572e-06,
                5.04347528446051e-07,
                6.475947210031623e-07,
                8.315281267861397e-07,
                1.5534971990126997e-06,
                6.475947210031623e-07,
                6.475951069985296e-07,
                2.699577774585891e-07
            ],
            [
                1.3709567165617364e-06,
                9.422442569315887e-07,
                1.994730672675753e-06,
                4.4508510499849186e-07,
                8.315280276626197e-07,
                6.475949525981759e-07,
                5.043476486924565e-07,
                3.2887502415767434e-06,
                9.422449308748773e-07,
                9.422442569315887e-07
            ],
            [
                5.715005151606823e-07,
                2.902312677150514e-06,
                2.2603234895372223e-06,
                1.7603430034867993e-06,
                3.2887494574832472e-06,
                8.315282259138311e-07,
                1.0677028700422047e-06,
                7.338208055680009e-07,
                6.475947210046347e-07,
                2.902313369111213e-06
            ],
            [
                1.2098659719757836e-06,
                1.5534975693933505e-06,
                7.338208930443633e-07,
                1.2098659719757836e-06,
                2.5612812947380135e-06,
                7.889264466868659e-06,
                4.222833444590791e-06,
                6.475950298011458e-07,
                1.0677026154806063e-06,
                2.2603253756956754e-06
            ],
            [
                5.043472879540142e-07,
                5.422220262636381e-06,
                9.4224425692559e-07,
                8.939693107093343e-06,
                5.715005832827105e-07,
                6.144173137126169e-06,
                3.2887506336086064e-06,
                6.962257079775324e-06,
                3.2887506336086064e-06,
                8.315281267861397e-07
            ],
            [
                1.994729008145876e-06,
                9.422448185510695e-07,
                1.8925157265710765e-05,
                1.2098662604291696e-06,
                2.9023123311583482e-06,
                2.902312677137316e-06,
                1.994729008145876e-06,
                1.3709576971425944e-06,
                6.475945666051092e-07,
                8.315279285351409e-07
            ],
            [
                5.043474081993875e-07,
                3.9278634073732336e-07,
                5.043472879525233e-07,
                5.715003107755449e-07,
                8.315280276546789e-07,
                2.2603234895289998e-06,
                1.2098659719757836e-06,
                3.466325797888292e-07,
                1.5534973842076057e-06,
                3.466326624322211e-07
            ],
            [
                8.315279285370317e-07,
                3.059022269250683e-07,
                1.6373766672973748e-07,
                6.475948754012522e-07,
                3.927862939126708e-07,
                1.553498124964492e-06,
                2.69957906184239e-07,
                4.450852111148132e-07,
                1.855391460719133e-07,
                2.69957906184239e-07
            ],
            [
                9.931187406410953e-08,
                0.9999942280799817,
                2.5612831266608576e-06,
                4.450850519409479e-07,
                5.043475284468537e-07,
                5.043475885696228e-07,
                9.422445938917108e-07,
                3.2887498495150166e-06,
                0.9999972735284338,
                5.715004470326849e-07
            ],
            [
                0.9999980052700418,
                0.9999972735303839,
                5.422217030781934e-06,
                0.9999996072138467,
                0.9999990577554068,
                0.9999989322967499,
                0.9999898700042344,
                0.9999981261246192,
                0.9999987121046325,
                0.9999994631249324
            ],
            [
                8.315277302841894e-07,
                3.05902336324494e-07,
                3.9278629391427843e-07,
                3.927862470899887e-07,
                5.715005151606823e-07,
                7.338208055680009e-07,
                1.370957860576702e-06,
                1.8553916819032217e-07,
                1.9947292459347367e-06,
                2.2603251062450327e-06
            ],
            [
                2.6995790618469934e-07,
                2.382368531929327e-07,
                9.422442569334097e-07,
                3.059021175261338e-07,
                3.4663274507713016e-07,
                6.475950298021765e-07,
                7.338213304363436e-07,
                1.8553905760062447e-07,
                8.315278294114555e-07,
                3.927863407379485e-07
            ],
            [
                4.222834954801051e-06,
                5.715007195447234e-07,
                1.012999218776902e-05,
                1.0677029973219343e-06,
                4.4508494582405734e-07,
                1.0677027427624903e-06,
                5.715006514176113e-07,
                8.939695238634211e-06,
                1.0677033791612137e-06,
                5.422217677152175e-06
            ],
            [
                2.902312677150514e-06,
                4.450852111148132e-07,
                1.7603430034867993e-06,
                8.315279285370317e-07,
                1.067703124601679e-06,
                4.4508494582405734e-07,
                5.043476486915964e-07,
                3.4663249714612693e-07,
                9.422443692555439e-07,
                2.699577774585891e-07
            ],
            [
                5.715002426486762e-07,
                1.5534975693933505e-06,
                2.9023133690821773e-06,
                7.338207180898968e-07,
                3.72663883989755e-06,
                9.422443692574719e-07,
                1.553498495338299e-06,
                1.5534984953453635e-06,
                3.466326211113502e-07,
                4.450852111155216e-07
            ],
            [
                9.422442569315887e-07,
                6.1441746020359e-06,
                NaN,
                2.561281294760143e-06,
                NaN,
                0.16451646904109266,
                1.892515501014656e-05,
                1.5534973842076057e-06,
                9.422449308774482e-07,
                8.939696304311336e-06
            ],
            [
                1.6701419854156377e-05,
                1.012999218776902e-05,
                1.2098653950656417e-06,
                0.00013982212420629982,
                7.889259764517575e-06,
                1.5534971990126997e-06,
                1.1478769494396542e-05,
                1.1478764021029928e-05,
                9.422448185510695e-07,
                2.5612834320470717e-06
            ],
            [
                6.475946438055299e-07,
                1.0677033791612137e-06,
                3.7266406168624155e-06,
                7.88926446679691e-06,
                7.889265407255982e-06,
                6.1441746020359e-06,
                1.8925157266089433e-05,
                1.1478772231232203e-05,
                5.422218969895357e-06,
                1.5534984953510149e-06
            ],
            [
                0.9999996743688199,
                0.9999998362622944,
                0.9999997897566341,
                0.9999981261243959,
                0.00023050671528605768,
                0.9999970976866338,
                0.9999991148426479,
                0.9999994631248683,
                0.9999960330121975,
                0.9999991684721715
            ],
            [
                4.450852641737424e-07,
                1.0677027427624903e-06,
                1.209865539295696e-06,
                1.2098652508424818e-06,
                7.338212429594283e-07,
                NaN,
                3.9278634073732336e-07,
                2.3823690999323465e-07,
                6.47595107001401e-07,
                1.5534971990169383e-06
            ],
            [
                9.422444815814404e-07,
                1.9947304348703948e-06,
                9.422444815765128e-07,
                1.012998977264307e-05,
                1.3709573702822306e-06,
                1.9947304348703948e-06,
                1.7603438428740716e-06,
                1.370957860576702e-06,
                3.288749065406658e-06,
                2.5612819054028872e-06
            ],
            [
                6.962253760024999e-06,
                4.222834954801051e-06,
                1.5534971990169383e-06,
                1.5534979397829198e-06,
                6.475945666051092e-07,
                3.2887506336235617e-06,
                5.715002426486762e-07,
                3.726639284144195e-06,
                1.473898900066424e-05,
                2.9023116392097746e-06
            ],
            [
                6.962257079832313e-06,
                NaN,
                9.422442569315887e-07,
                1.2098653950692178e-06,
                6.962258739796719e-06,
                5.422217030707961e-06,
                1.5534983101602148e-06,
                4.785094494811783e-06,
                6.144173869603344e-06,
                4.2228334445370225e-06
            ],
            [
                0.9999998642566543,
                0.99999963101146,
                1.3709570434178922e-06,
                0.9999989969854343,
                0.999999653367503,
                1.2098659719788098e-06,
                1.7603438428800754e-06,
                8.481105142266346e-05,
                0.9999998144609424,
                0.9999997617630901
            ],
            [
                5.715007195447234e-07,
                6.144173137170873e-06,
                6.144173869603344e-06,
                7.338212429582604e-07,
                2.561281600086738e-06,
                2.102433159721477e-07,
                8.315284241650899e-07,
                9.422443692574719e-07,
                1.2098652508424818e-06,
                9.422448185534261e-07
            ],
            [
                5.043476486915964e-07,
                1.0677032518785256e-06,
                9.422450432014836e-07,
                9.422450432014836e-07,
                1.994730672668496e-06,
                1.0677032518785256e-06,
                5.422220909009474e-06,
                1.994729245917502e-06,
                7.88926446679691e-06,
                1.0677032518785256e-06
            ],
            [
                6.475949526020042e-07,
                5.04347468323289e-07,
                3.9278610661902853e-07,
                8.315284241650899e-07,
                7.338213304363436e-07,
                7.338208055664991e-07,
                3.927860597945825e-07,
                7.338210680021253e-07,
                6.475946438055299e-07,
                7.338208055664991e-07
            ],
            [
                7.338210680021253e-07,
                1.2098659719788098e-06,
                7.338212429582604e-07,
                2.6995774527718623e-07,
                1.6373776432509826e-07,
                5.71500515161527e-07,
                3.466326624336003e-07,
                2.699578740032504e-07,
                2.699576809143613e-07,
                4.450852111155216e-07
            ],
            [
                1.8553910183674878e-07,
                2.3823690999323465e-07,
                8.31528325040778e-07,
                3.9278629391427843e-07,
                5.715003789046955e-07,
                1.6373774480605869e-07,
                7.734415776836702e-08,
                3.7266397283908927e-06,
                5.043476486924565e-07,
                9.422445939054222e-07
            ],
            [
                0.9999999123575568,
                4.785093353940187e-06,
                1.7603438428740716e-06,
                0.000709670383827381,
                6.962257909842961e-06,
                0.9999999317439302,
                1.3709578605729614e-06,
                0.9999992661791075,
                1.7603434231833873e-06,
                1.7603438428740716e-06
            ],
            [
                0.9999984465024359,
                0.9999984465018772,
                2.2603240284371276e-06,
                8.315278294072958e-07,
                0.9999962733611709,
                0.999977172002915,
                5.715003789033962e-07,
                8.315283250371857e-07,
                0.9999667858054339,
                5.043473480766399e-07
            ],
            [
                5.043472879525233e-07,
                4.450849988811838e-07,
                9.422444815814404e-07,
                8.315283250394546e-07,
                3.9278634073732336e-07,
                2.6995784182073116e-07,
                1.209865683518615e-06,
                7.338210680021253e-07,
                1.0677032518814388e-06,
                1.444980209564556e-07
            ],
            [
                1.0677031245990084e-06,
                5.71500515159253e-07,
                6.962254589851619e-06,
                5.043473480777865e-07,
                2.3823685319244518e-07,
                3.927860597945825e-07,
                5.715002426460124e-07,
                4.4508510499849186e-07,
                3.4663249714451116e-07,
                3.0590237279032884e-07
            ],
            [
                8.315281267861397e-07,
                4.4508494582405734e-07,
                3.927862002663297e-07,
                4.450850519403407e-07,
                4.4508494582405734e-07,
                1.5534971990126997e-06,
                5.04347287955046e-07,
                1.2098652508424818e-06,
                3.4663266243308805e-07,
                1.3709576971463352e-06
            ],
            [
                2.260324836787226e-06,
                1.3007126914435202e-05,
                2.9023126771227976e-06,
                4.222833444590791e-06,
                1.892515501014656e-05,
                4.006368264282944e-05,
                4.222834954778007e-06,
                2.260325106237323e-06,
                3.7266410611296085e-06,
                1.5534983101602148e-06
            ],
            [
                3.4663249714612693e-07,
                3.05902263391829e-07,
                5.043473480777865e-07,
                1.444980209564556e-07,
                5.715003107767143e-07,
                2.3823696679327928e-07,
                6.475945666063607e-07,
                2.102434162245973e-07,
                9.422443692574719e-07,
                5.71500515161527e-07
            ],
            [
                1.067703124601679e-06,
                3.927862002654366e-07,
                NaN,
                1.637376862489725e-07,
                7.889259764517575e-06,
                4.450852111155216e-07,
                2.1024339116168358e-07,
                3.72663883989755e-06,
                3.288749457469787e-06,
                2.902313023130843e-06
            ],
            [
                0.9999987901340288,
                1.2098653950656417e-06,
                6.475949526020042e-07,
                0.9999925887219054,
                1.0677026154806063e-06,
                0.9999974387174871,
                2.69957906184239e-07,
                0.9999992188515767,
                7.338213304363436e-07,
                5.715006514167015e-07
            ],
            [
                4.006368264282944e-05,
                1.3709567165579959e-06,
                8.315279285351409e-07,
                4.450849988811838e-07,
                3.7266406168827523e-06,
                8.939693107190907e-06,
                8.315284241650899e-07,
                3.927860597945825e-07,
                8.315277302841894e-07,
                3.726639728348526e-06
            ],
            [
                8.315284241650899e-07,
                5.715007195431641e-07,
                3.927861066170637e-07,
                3.2887506336235617e-06,
                8.315282259089153e-07,
                1.0677033791612137e-06,
                5.715003789046955e-07,
                6.475947982037486e-07,
                1.99472900813862e-06,
                3.46632497145457e-07
            ],
            [
                1.637377448057981e-07,
                5.715003107767143e-07,
                3.9278605979534166e-07,
                2.382370235933104e-07,
                2.1024331597262577e-07,
                8.315284241650899e-07,
                6.475950298011458e-07,
                2.382369951932796e-07,
                4.450850519403407e-07,
                1.8553916819032217e-07
            ],
            [
                3.535626757653154e-05,
                1.7603440527286572e-06,
                1.994730434879465e-06,
                1.9947292459347367e-06,
                7.889261645427538e-06,
                4.222834954778007e-06,
                1.9947292459347367e-06,
                1.067703124601679e-06,
                3.726637951387472e-06,
                6.962256249885085e-06
            ],
            [
                4.450848927658745e-07,
                2.2603248367949354e-06,
                1.7603434231833873e-06,
                3.927862470899887e-07,
                1.7603425837903113e-06,
                1.3709576971425944e-06,
                2.3823702359290413e-07,
                8.315284241665078e-07,
                1.0677033791612137e-06,
                1.7603425837903113e-06
            ],
            [
                9.931185038635267e-08,
                6.023573475041126e-08,
                1.760343213335281e-06,
                8.315277302841894e-07,
                9.931187406410953e-08,
                6.825602910433871e-08,
                1.1253512180925583e-07,
                1.3709576971463352e-06,
                1.1253524254650944e-07,
                5.315786239218605e-08
            ],
            [
                1.4449805540763184e-07,
                1.4449798650551755e-07,
                3.05902336324494e-07,
                1.275191036933194e-07,
                8.764247451307293e-08,
                6.825608606172863e-08,
                4.1399365603508136e-08,
                8.764242227418718e-08,
                1.6373772528704005e-07,
                1.275190276859705e-07
            ],
            [
                4.785093353909723e-06,
                1.5534983101478522e-06,
                1.3709575337078829e-06,
                1.3709567165530083e-06,
                2.561281600076256e-06,
                2.5612825160271407e-06,
                3.726641061027928e-06,
                1.9947299593014888e-06,
                3.2887478892055875e-06,
                3.288750241561788e-06
            ],
            [
                1.670141587208191e-05,
                1.9947306726358406e-06,
                2.382370235933104e-07,
                7.889266347715168e-06,
                9.422442569315887e-07,
                1.553498310118888e-06,
                2.3823682479292225e-07,
                2.561281905390075e-06,
                5.04347528446051e-07,
                1.1478769494250387e-05
            ],
            [
                1.3709567165617364e-06,
                4.450852111148132e-07,
                7.338208055664991e-07,
                1.0677032518785256e-06,
                6.475948754028718e-07,
                1.7603440527286572e-06,
                6.475945666051092e-07,
                2.3823685319244518e-07,
                8.315278294072958e-07,
                9.422448185510695e-07
            ],
            [
                0.9999972735297333,
                0.9999623635643912,
                0.9999978766217931,
                0.9999975938982371,
                0.9999843104466526,
                0.9999972735290837,
                0.9999981261250661,
                0.9999964991460089,
                0.9999981261237253,
                0.9999962733589466
            ],
            [
                2.5612828213934817e-06,
                1.892515501014656e-05,
                6.962259569750576e-06,
                6.475951070002966e-07,
                1.7603438428800754e-06,
                6.475947210046347e-07,
                7.889260704968913e-06,
                2.561282210740037e-06,
                1.2098659719788098e-06,
                6.962257909842961e-06
            ],
            [
                1.7603425837855082e-06,
                2.260323758987159e-06,
                2.260324836776948e-06,
                1.209865539295696e-06,
                4.450850519403407e-07,
                7.338213304363436e-07,
                1.5534981249697903e-06,
                8.315281267882195e-07,
                1.209865539295696e-06,
                7.338213304363436e-07
            ],
            [
                3.726638395634011e-06,
                3.726641061109272e-06,
                5.422218323487975e-06,
                9.422448185510695e-07,
                3.535626757524533e-05,
                7.338213304316717e-07,
                2.561283432035425e-06,
                6.144173137126169e-06,
                4.785093353940187e-06,
                1.9947299592933255e-06
            ],
            [
                8.315279285351409e-07,
                5.043475885674441e-07,
                4.450852111148132e-07,
                7.338212429582604e-07,
                6.475949526020042e-07,
                7.338213304363436e-07,
                4.450851580555361e-07,
                4.2228329411708495e-06,
                8.315281267861397e-07,
                2.260324567337161e-06
            ],
            [
                3.9278624708775595e-07,
                5.043474683204221e-07,
                2.753568782024347e-05,
                1.3007128465151102e-05,
                2.3823688159291947e-07,
                1.4738980215593877e-05,
                1.7603427936263351e-06,
                3.927862002641863e-07,
                1.994729008145876e-06,
                9.422443692555439e-07
            ],
            [
                5.715004470313855e-07,
                7.338208055664991e-07,
                8.315279285351409e-07,
                5.04347468323289e-07,
                2.5612812947508257e-06,
                5.043474081993875e-07,
                1.0677027427569065e-06,
                7.338213304363436e-07,
                5.715003789046955e-07,
                3.0590237279032884e-07
            ],
            [
                4.450850519403407e-07,
                4.450852111148132e-07,
                4.450852111135988e-07,
                1.4449795205472734e-07,
                3.466327450765785e-07,
                7.338211554783522e-07,
                3.9278634073098236e-07,
                5.043474683204221e-07,
                6.475950298011458e-07,
                4.450848927650143e-07
            ]
        ]
    },
    {
        "q_id": "9290_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            48,
            49,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            92,
            93,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            106,
            107,
            108,
            109,
            111,
            112,
            113,
            114,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.7603430034743913e-06,
                5.715006514151423e-07,
                0.9999987121046316,
                1.0677028700363782e-06,
                2.9023133690980155e-06,
                2.5612816000646084e-06,
                1.2098656835076114e-06,
                0.9999910603058397,
                1.5534981249697903e-06,
                3.05902190458764e-07
            ],
            [
                0.9999997463981638,
                0.9999998024945861,
                0.9999995262094991,
                0.9999998024946566,
                0.9999997463981335,
                0.9999997897566341,
                0.9999995262093296,
                0.9999998024946332,
                0.9999998362623529,
                0.9999996533673792
            ],
            [
                0.9999999006880194,
                0.9999994956525321,
                0.9999996743688201,
                0.9999998461826406,
                0.999999653367214,
                0.9999997897566842,
                0.999999168471577,
                0.9999997300420941,
                0.9999996533672553,
                0.9999998144608319
            ],
            [
                0.9999998642566866,
                0.9999977396759736,
                0.999999917667524,
                0.9999999123575359,
                0.999999872480942,
                0.9999996743687422,
                1.4449803818107344e-07,
                0.9999984465018763,
                0.9999998257021837,
                0.9999997126315497
            ],
            [
                0.9999998024946096,
                0.999999802494586,
                0.9999998144608098,
                0.9999994956527126,
                0.9999996940978098,
                0.9999992188513904,
                0.9999996072138936,
                0.9999996072136595,
                0.9999980052705173,
                1.0
            ],
            [
                0.9999994631249324,
                0.999999789756659,
                0.9999980052693297,
                0.999999814460854,
                0.9999981261237243,
                0.9999998942830106,
                0.9999995818812273,
                0.9999997897567342,
                0.9999998555020309,
                0.9999997300421904
            ],
            [
                1.0677032518814388e-06,
                1.6373766672973748e-07,
                9.931189774187203e-08,
                8.764254764749753e-08,
                1.4449805540740185e-07,
                8.764242227418718e-08,
                9.93120161306789e-08,
                2.102434412871794e-07,
                1.3709572068478697e-06,
                9.931198061405701e-08
            ],
            [
                2.9023133690980155e-06,
                1.2098662604247682e-06,
                3.2887498494551953e-06,
                2.2603251061849014e-06,
                2.9023119851266288e-06,
                5.422220262555012e-06,
                8.315280276626197e-07,
                1.7603432133136672e-06,
                2.561283432005142e-06,
                3.726639728348526e-06
            ],
            [
                0.9999999358793868,
                0.9999998362623139,
                1.0,
                0.9999999500628513,
                0.9999999559305839,
                0.9999999176675829,
                0.9999925887166069,
                0.9999999611088904,
                0.9999993106390371,
                0.9999996743688976
            ],
            [
                0.9999999067050832,
                0.9999995262094423,
                0.9999998257021423,
                1.0,
                1.0,
                0.9999999317439546,
                1.0,
                0.9999999176675437,
                0.9999998802069874,
                0.9999990577555193
            ],
            [
                0.9989677689636053,
                1.0129995810343862e-05,
                2.902313023130843e-06,
                2.9023112932177327e-06,
                1.3709570434178922e-06,
                4.2228339479858295e-06,
                0.9998911030522912,
                0.9999724643155202,
                2.1444940745371397e-05,
                0.0017007221685192513
            ],
            [
                0.9999998942829981,
                0.9999967112497654,
                0.9999996940978098,
                0.999997438717794,
                0.9999999067050831,
                0.9999991148431759,
                0.9999997897565589,
                0.9999997300422228,
                0.9999997761972117,
                0.9999972735307071
            ],
            [
                3.288747889229516e-06,
                1.1478768125577027e-05,
                4.785096205973894e-06,
                1.9947292459265734e-06,
                5.715006514105942e-07,
                3.120191137126484e-05,
                1.670142383495587e-05,
                1.3709576971316842e-06,
                1.8925155008528632e-05,
                9.422448185435711e-07
            ],
            [
                0.9999998024946095,
                0.9999992188512974,
                0.999999825702059,
                0.9999996743688976,
                0.9999997897565588,
                0.9999997463981033,
                0.9999998874647843,
                0.9999983463096274,
                0.9999995818811275,
                0.999999776197105
            ],
            [
                0.9999998802068875,
                0.9999991148426485,
                0.9999991148432815,
                0.9999998555019447,
                0.999997438718097,
                0.9999999067051277,
                0.9999999123574523,
                0.9999998802069302,
                0.9999997897565588,
                0.9999994284994171
            ],
            [
                0.9999379494902051,
                0.9999999273418962,
                0.999999631011592,
                0.999999776197025,
                0.9999785550516154,
                0.9999981261237241,
                0.9999978766220463,
                0.9999998802069445,
                0.9999999067050387,
                0.9999988634358836
            ],
            [
                0.9999996940977003,
                0.9999994631249325,
                0.9999998642566705,
                0.9999998874649185,
                0.9999996743687422,
                0.9999999006880668,
                0.9999996940977368,
                0.999999761763147,
                0.9999999176674553,
                0.99999854062378
            ],
            [
                6.475950297971703e-07,
                1.8553914607267268e-07,
                0.9999998024947037,
                5.04347287955046e-07,
                0.9999962733589428,
                1.8553910183607374e-07,
                1.2098653950606901e-06,
                4.450851580566494e-07,
                4.450852111120808e-07,
                0.9999938558246741
            ],
            [
                1.300712536408621e-05,
                6.144173137170873e-06,
                4.785092783519724e-06,
                2.2603242978871282e-06,
                4.222832941193893e-06,
                4.785096776468749e-06,
                1.4738980215352592e-05,
                1.760342793638743e-06,
                8.93969950132721e-06,
                2.902313023130843e-06
            ],
            [
                0.9999998874648782,
                0.9999999226557316,
                0.9999999006880312,
                0.9999997300423193,
                0.9999988634365614,
                0.9999999006879721,
                0.9999964991455894,
                0.9999996940978098,
                0.9999991148427536,
                0.9999995549151076
            ],
            [
                0.999997739675435,
                0.9999925887219058,
                1.5534983101644536e-06,
                0.9999952149043718,
                8.939693107190907e-06,
                0.9999989322968763,
                0.999997593897949,
                0.9999975938976645,
                NaN,
                0.9999995549147892
            ],
            [
                5.715004470272272e-07,
                2.9023126771227976e-06,
                0.9999417087139584,
                1.2098659719757836e-06,
                3.059021904571643e-07,
                0.9999861539921645,
                3.726639728348526e-06,
                0.9999417087347529,
                1.2098662604291696e-06,
                0.9999038976199652
            ],
            [
                1.6373762769138607e-07,
                6.475946438042047e-07,
                3.0590237279032884e-07,
                3.059022998576899e-07,
                2.6995774527657245e-07,
                3.059022998576899e-07,
                3.9278634073732336e-07,
                1.2751899728286965e-07,
                7.734423152941018e-08,
                9.931193325852072e-08
            ],
            [
                0.9999994956525321,
                0.9999998144608762,
                0.9999989322968763,
                0.9999998642567028,
                0.999999917667573,
                0.9999999317439628,
                0.9999999123574419,
                0.999999631011592,
                0.9999998874647441,
                0.999999310638955
            ],
            [
                2.6995784182140636e-07,
                6.825608606172863e-08,
                1.8553907971855875e-07,
                5.043475885674441e-07,
                2.699577774585891e-07,
                1.8553919030776337e-07,
                1.4449802095609418e-07,
                6.825602910433871e-08,
                8.764244316973974e-08,
                2.3823688159237777e-07
            ],
            [
                0.9999785550414502,
                0.9999996743686259,
                0.9999925887166001,
                0.9999916019289876,
                0.9999975938970881,
                0.9999998802068873,
                0.9999861539921808,
                0.9999938558224803,
                0.9999916019299746,
                0.9999916019299779
            ],
            [
                0.9999997617631753,
                0.999999939764251,
                0.9999999176674848,
                0.9999997897565588,
                0.9999999123575777,
                0.9999999123575255,
                1.0,
                0.9999999176675829,
                0.9999998942829729,
                0.9999997300421262
            ],
            [
                0.9999998874649184,
                0.9999998724809723,
                0.9999999176675044,
                0.9999997126314126,
                0.999999864256719,
                1.0,
                0.9999997300420941,
                0.9999960330155087,
                0.9999998362623724,
                0.999999730042287
            ],
            [
                0.9999997463980427,
                0.9999998724809115,
                0.9999998874648649,
                0.9999978766222994,
                0.9999994284996213,
                0.9999998362623334,
                0.9999925887201547,
                0.9999998461827139,
                0.9999996072136595,
                0.9999999226558424
            ],
            [
                0.9999998144608319,
                1.0,
                0.9999999317439221,
                1.0,
                0.999999776197105,
                0.9999996743686259,
                0.9999998362622358,
                0.9999998024947273,
                0.9999999123575882,
                0.9999995262096119
            ],
            [
                1.3709576971242028e-06,
                1.7603438428740716e-06,
                1.6701415872385704e-05,
                2.5612834320214477e-06,
                2.6995774527718623e-07,
                2.5612828213690224e-06,
                3.2887490653872164e-06,
                1.7603436330179102e-06,
                8.315281267800897e-07,
                4.785094494750855e-06
            ],
            [
                9.931187406368048e-08,
                2.5612831267202583e-06,
                0.9999989969862711,
                0.9999957771650495,
                0.9999970976880174,
                0.99999834631081,
                0.9999998642566705,
                0.9999962733620529,
                0.999999846182604,
                0.9999977396754348
            ],
            [
                0.9999999397642437,
                0.9999999468421059,
                0.9999969105040822,
                0.9999999559306206,
                0.9999999067050277,
                0.9999999434137773,
                0.9999999468421756,
                1.0,
                1.0,
                1.0
            ],
            [
                0.9999996310116359,
                0.9999998555019619,
                0.9999998874647307,
                0.9999998362623139,
                0.9999997126313441,
                0.9999998874647977,
                0.9999997300421583,
                0.9999998144609425,
                0.9999996072136595,
                0.999999789756584
            ],
            [
                0.9999999317439954,
                0.9999998724809723,
                0.9999999358794479,
                1.0,
                0.9999999006879721,
                0.9999999226557408,
                0.9999998802069731,
                0.9999998461826956,
                0.9999999176674945,
                0.9999998724809875
            ],
            [
                3.7266401726173067e-06,
                2.5612828213690224e-06,
                1.9947290081286418e-06,
                0.9999985406236066,
                1.5534984953453635e-06,
                3.2887490653872164e-06,
                8.31528424162821e-07,
                5.715004470272272e-07,
                2.5612831266946347e-06,
                4.2228324377740105e-06
            ],
            [
                0.9999985406234321,
                0.9999996072139403,
                0.9999994631248684,
                0.9999998144609203,
                0.9999972735290821,
                0.9999995549150015,
                0.9999999317439628,
                0.9999994284994851,
                0.9999999317440279,
                0.9999998724809572
            ],
            [
                2.9023112932177327e-06,
                1.855391681906175e-07,
                1.5534984953552536e-06,
                6.962259569750576e-06,
                3.288747889284851e-06,
                3.4663274507713016e-07,
                1.760343213335281e-06,
                1.8925150497848527e-05,
                3.7266410611296085e-06,
                1.7603434231833873e-06
            ],
            [
                0.9999997761970248,
                0.9999999500628394,
                0.9999999226558423,
                0.9999999677581606,
                0.9999998874649051,
                0.9999999123575674,
                1.0,
                0.9999996310116359,
                0.9999999358794021,
                0.999999789756659
            ],
            [
                0.9999785550414078,
                2.382369667929001e-07,
                0.9999957771665617,
                1.4449798650476187e-07,
                3.9278610661822475e-07,
                0.999987780922541,
                5.715003789033962e-07,
                8.7642516304188e-08,
                3.059022998576899e-07,
                9.931192141912081e-08
            ],
            [
                0.9999993916408912,
                0.9999997126313441,
                0.9999998555019274,
                0.9999993916406738,
                0.999999730042094,
                0.9999996940977003,
                0.999999825702059,
                0.9999996533674202,
                0.9999998642566381,
                0.9999997897567091
            ],
            [
                5.715005832886879e-07,
                4.2228319344021954e-06,
                5.04347468323289e-07,
                6.475947210046347e-07,
                2.260324567337161e-06,
                2.2603253756956754e-06,
                7.338210680021253e-07,
                7.338208055680009e-07,
                7.338209805224048e-07,
                2.3823688159291947e-07
            ],
            [
                0.9999969105055561,
                0.9999997897567091,
                0.9999998461826956,
                0.999999825702059,
                0.999999526209273,
                0.9999997463981637,
                0.9999993916408911,
                0.9999993916406738,
                0.9999998555020309,
                0.999999761763005
            ],
            [
                0.999998996986152,
                0.9999999317439221,
                0.9999982396569977,
                0.9999996743687812,
                0.9999981261248415,
                0.9999999500627857,
                0.9999984465020617,
                0.9999995549148424,
                0.9999999358794326,
                0.9999955048162829
            ],
            [
                0.9999996072136129,
                0.9999955048173627,
                0.9999952149043779,
                0.9999993916411092,
                0.9999992188515772,
                0.9999996533674206,
                0.9999975938965181,
                0.9999991148433872,
                0.999998712104786,
                0.9999993106392018
            ],
            [
                0.9999999226557225,
                0.9999999123574733,
                0.9999999468421503,
                0.9999998461827322,
                0.9999985406236066,
                0.9999992661791951,
                0.9999987121043253,
                0.9999996743688586,
                0.9999998874649185,
                0.9999992661791076
            ],
            [
                2.4300234941261454e-05,
                6.475946438055299e-07,
                2.9023119851781017e-06,
                3.9278610661902853e-07,
                2.3823693839290317e-07,
                4.450850519403407e-07,
                1.6373774480605869e-07,
                1.0677026154806063e-06,
                3.7266410611296085e-06,
                5.043472879540142e-07
            ],
            [
                0.9999998724809267,
                0.9999993916411812,
                0.999999057755519,
                0.9999996072136595,
                0.9999999226557778,
                0.9999999176674848,
                0.9999997617630334,
                0.9999985406230842,
                0.9999999434138043,
                0.9999998461826038
            ],
            [
                0.9999960330150349,
                2.2603253756956754e-06,
                1.6701427818034747e-05,
                0.9999942280806661,
                1.067703124601679e-06,
                5.1442238195844654e-05,
                7.338207180864763e-07,
                0.9999756997680205,
                0.9999984465024319,
                6.825600469412533e-08
            ],
            [
                0.9999978766210333,
                0.9999998144608983,
                0.9999997761970781,
                0.999999814460876,
                0.9999999634651923,
                0.9999999468421883,
                1.0,
                0.9999998555020307,
                0.9999999434137975,
                0.999999495652592
            ],
            [
                0.9999999468421946,
                0.9999998642566705,
                0.9999997761971582,
                0.9999999559306206,
                1.0,
                0.9999999530883228,
                1.0,
                0.9999998362622747,
                0.9999999358793638,
                1.0
            ],
            [
                0.9999960330140888,
                0.9999974387168786,
                0.9999949062950025,
                0.999999931743971,
                0.9999969105066606,
                0.9999898700078361,
                0.9999974387174875,
                0.9999949062950062,
                0.9999992661792826,
                0.9998766054706261
            ],
            [
                0.9999996533673378,
                0.9999993916408187,
                0.9999998461826038,
                0.9999998461826772,
                0.9999998362622552,
                0.9999998802068873,
                0.9999998724809875,
                1.0,
                0.9999997463981334,
                0.9999996533674617
            ],
            [
                3.927862002606139e-07,
                9.422444815765128e-07,
                1.0677028700363782e-06,
                0.9999869928762173,
                0.9999921107402423,
                1.637376862471855e-07,
                8.315277302788957e-07,
                5.715006514151423e-07,
                0.9997040428324447,
                0.9990889486830523
            ],
            [
                0.9999999273418616,
                0.9999996533674207,
                0.9999993106391198,
                0.9999985406230849,
                0.9999992661791949,
                0.9999996533675032,
                0.9999996940976641,
                0.9999998144608319,
                1.0,
                0.9999993916408915
            ],
            [
                0.9999972735284339,
                0.9999980052693302,
                0.9999957771665674,
                0.9999938558246834,
                0.9999975938985265,
                0.9999989322972583,
                0.9999994956526523,
                0.9999995818811276,
                0.9999986290427948,
                0.9999996533674205
            ],
            [
                0.9999982396565789,
                0.999999900688055,
                0.9999994956526524,
                0.9999925887183827,
                0.9999999468421312,
                0.9999993106386265,
                0.9999989969860321,
                0.9999957771665597,
                0.9999984465028036,
                0.9999798542996211
            ],
            [
                3.059022998581767e-07,
                0.9999999226558146,
                0.9999999176674357,
                0.9999989322975126,
                0.999999581881327,
                0.9999934595627804,
                0.9999999067050832,
                0.9999957771655547,
                0.9999885212319097,
                0.9999990577552943
            ],
            [
                0.9999998362623529,
                0.9999998874647844,
                0.999999825702163,
                0.9999998642566381,
                0.9999998555020307,
                0.9999994631249323,
                0.9999955048178923,
                0.9999999006880431,
                0.9999997761971849,
                0.9999998642566705
            ],
            [
                0.9999998555019791,
                1.0,
                0.9999995549148953,
                0.9999987901340294,
                0.9999975938982363,
                0.9999999273418183,
                0.9999771720110718,
                0.9999970976876715,
                0.9999987121046314,
                0.999999428499349
            ],
            [
                0.9999967112493688,
                0.9999969105048191,
                0.9999967112509391,
                0.9999978766220469,
                0.9999997761971315,
                0.9999998257022045,
                0.9999994631251887,
                0.9999998257021007,
                0.9999998024946802,
                0.9999998461827322
            ],
            [
                6.962255419868303e-06,
                1.444980726324838e-07,
                2.2603240284371276e-06,
                2.7535694384081332e-05,
                6.9622595696935874e-06,
                3.9278638756099906e-07,
                6.144176799334096e-06,
                1.3709567165579959e-06,
                7.889262585886274e-06,
                1.3709570434178922e-06
            ],
            [
                0.9999998802069017,
                0.9999998642566219,
                0.9999998144608099,
                0.9999978766217921,
                0.9999999123575151,
                0.9999999067050388,
                0.9999997617630618,
                0.9999987121043244,
                0.9999599363079457,
                0.9999980052700418
            ],
            [
                0.9999988634362903,
                0.9999996743686648,
                0.999998932296622,
                0.9999996743688199,
                0.9999996743686645,
                0.999999946842144,
                0.9999995549147359,
                0.9999997761972117,
                0.999999495652532,
                0.9999987121043247
            ],
            [
                0.9999981261237247,
                0.9999997126313099,
                0.9999997897566342,
                0.9999975938965158,
                0.9999996310115481,
                0.9999984465018767,
                0.9999997126315497,
                0.9999998362622943,
                0.9999992661789323,
                0.9999996940977004
            ],
            [
                7.734421308914719e-08,
                0.9999938558239528,
                0.9999916019259827,
                0.9999861539938292,
                0.9999885212291673,
                0.9999997761971048,
                1.4449805540740185e-07,
                0.9999987901343173,
                0.999996910504085,
                0.9999995262093857
            ],
            [
                1.0,
                0.9999999176675436,
                0.9999998257020591,
                0.999999894282935,
                0.999998863435748,
                0.9999999226557501,
                0.9999999358793867,
                1.0,
                0.9999999123575672,
                0.9999991148433869
            ],
            [
                5.715007195447234e-07,
                4.450848927650143e-07,
                3.9278634073625165e-07,
                7.338211554783522e-07,
                6.475947209985977e-07,
                5.043472879540142e-07,
                5.043472879504592e-07,
                5.715007195384861e-07,
                1.8553916819032217e-07,
                3.927862002641863e-07
            ],
            [
                0.9999996072136594,
                0.9999996072138935,
                0.9999998024947272,
                0.9999999468421756,
                0.9999999006881259,
                0.999999428499417,
                0.9999998642567351,
                0.9999999273417923,
                0.999999917667524,
                0.9999996072138937
            ],
            [
                0.9999999176675829,
                0.9999998642567353,
                0.999996711251724,
                0.999999653367255,
                0.9999997126315155,
                1.0,
                0.9999981261248413,
                0.9999982396572075,
                0.9999997617630335,
                0.9999998257021837
            ],
            [
                0.9999999226557869,
                0.999999872480942,
                0.9999984465015064,
                0.9999996072136128,
                0.9999998724808964,
                0.9999998461826222,
                0.9999999226558146,
                0.999999746398194,
                0.9999997897566592,
                0.9999998555020136
            ],
            [
                0.9999998024946801,
                1.0,
                0.9999999434137705,
                0.9999999006880904,
                0.9999999397643083,
                0.9999998874649051,
                0.9999999176675338,
                0.9999999226557131,
                0.9999999586006246,
                0.9999999123575464
            ],
            [
                0.99995460214249,
                0.9999987121046313,
                0.9999984465015055,
                0.999999825702163,
                0.9999996940978462,
                0.999999814460876,
                0.9999995262093292,
                0.9999991684722701,
                0.9999996310115039,
                0.9999980052702799
            ],
            [
                0.9999983463110068,
                0.9999978766222988,
                0.9999997463981637,
                0.9999999067049831,
                0.9999995818812273,
                0.9999972735287564,
                0.9999985406234321,
                0.9999995818814267,
                0.9999942280806707,
                0.9999998257021837
            ],
            [
                0.9999996533672137,
                0.9999999358793867,
                0.9999996072137063,
                0.9999999500627976,
                0.9999991148429648,
                0.9999998257022045,
                0.9999998144608762,
                0.9999998257021007,
                0.9999998874648649,
                0.999999495652412
            ],
            [
                0.9999998724809572,
                0.9999997897566592,
                0.9999998724808964,
                0.9999996533675031,
                0.9999998724810027,
                0.9999996940978096,
                0.9999998642566866,
                0.9999997300423192,
                0.9999988634366963,
                0.9999992188512973
            ],
            [
                1.1478766757049986e-05,
                3.288749849477628e-06,
                4.785095635655362e-06,
                5.043474081993875e-07,
                1.3709572068522336e-06,
                8.315281267834927e-07,
                5.043476486915964e-07,
                4.2228324375973415e-06,
                3.4663274507713016e-07,
                6.475945666063607e-07
            ],
            [
                4.222833947932061e-06,
                1.89251527534122e-05,
                1.1478770862589836e-05,
                6.9622595696935874e-06,
                0.9999921107393026,
                1.0677029973192638e-06,
                1.3709573702822306e-06,
                0.9999980052695663,
                1.6701427818034747e-05,
                0.9999921107364774
            ],
            [
                2.561281600086738e-06,
                5.4222183235249605e-06,
                2.90231094723893e-06,
                3.288748281329893e-06,
                8.315278294097538e-07,
                4.4508505193791187e-07,
                2.5612828213818346e-06,
                3.726638839878908e-06,
                NaN,
                1.3709573702822306e-06
            ],
            [
                6.47595107001401e-07,
                6.144172404738491e-06,
                2.3823682479292225e-07,
                3.1201922535494165e-05,
                9.931186222523604e-08,
                1.6701419854156377e-05,
                5.422221555414699e-06,
                6.962254589978262e-06,
                5.422218969895357e-06,
                7.88926446679691e-06
            ],
            [
                1.0,
                0.9999998642567028,
                0.9999999317439221,
                1.0,
                0.9999998461826223,
                0.9999957771670622,
                0.9999972735294068,
                0.9999996072137064,
                0.9999999317440279,
                2.5612812947508257e-06
            ],
            [
                0.9999998362623334,
                0.9999998024945624,
                1.0,
                0.9999995262092731,
                0.9999989969854343,
                0.9999998642566866,
                1.0,
                0.9999998724809875,
                1.0,
                0.9999998362623334
            ],
            [
                0.9999998555020135,
                0.9999997463980126,
                0.9999997761971582,
                0.9999960330155147,
                0.9999974387174895,
                0.9999998802069588,
                0.9999964991439231,
                0.9999934595635661,
                0.9999998555019791,
                0.9999998802068873
            ],
            [
                1.2098653950656417e-06,
                2.260324567337161e-06,
                8.315283250371857e-07,
                1.7603434231777837e-06,
                3.2887498495150166e-06,
                1.7603425837855082e-06,
                3.2887498495150166e-06,
                7.338209805224048e-07,
                4.222834954687752e-06,
                4.785095635624897e-06
            ],
            [
                0.9999993106386261,
                0.9999998724809267,
                0.999999746398073,
                0.9999999397642725,
                0.9999998874648515,
                0.9999999397642365,
                0.9999986290426306,
                4.222831934379152e-06,
                0.9999998362622357,
                0.9999992188515765
            ],
            [
                0.9999998257020799,
                1.0,
                0.9999999273418443,
                1.0,
                0.9999998724809724,
                1.0,
                0.9999997126315153,
                0.9999997897565589,
                0.9999999226558238,
                0.999999922655833
            ],
            [
                0.9999985406230841,
                0.9999999176675142,
                0.9999987901337404,
                0.9999998461826588,
                0.9999998942830485,
                0.9999985406239539,
                0.9999997897566592,
                0.9999998724809115,
                0.9999989322968764,
                0.9999998802069445
            ],
            [
                0.9999998362622553,
                0.9999998874648782,
                0.9999997617630333,
                0.9999945777823344,
                0.9999998257021007,
                0.9999998724809115,
                0.9999996072136126,
                0.9999999176674749,
                0.9999999067050499,
                0.9999417087141839
            ],
            [
                0.9999998724810027,
                0.9999999468421377,
                0.9999998144608763,
                0.9999998874647843,
                0.9999998802069302,
                0.9999999067050387,
                0.9999998461826223,
                0.9999999317439465,
                0.9999999434137166,
                0.9999998144608099
            ],
            [
                8.31527928532683e-07,
                4.785095635592258e-06,
                1.3709572068422585e-06,
                7.338210680002898e-07,
                2.5612834320470717e-06,
                5.715005151550947e-07,
                3.7266379513162962e-06,
                3.059023363221292e-07,
                1.9947301970813926e-06,
                6.47594798194325e-07
            ],
            [
                0.9999992661789324,
                1.0,
                2.3823690999160957e-07,
                0.9999987901340285,
                0.999997593897949,
                0.9999945777797438,
                0.9999756997564381,
                0.999999927341853,
                0.9999599362935554,
                0.9999993106388725
            ],
            [
                0.9999996940978462,
                0.9999987121046318,
                0.9999991684719729,
                0.9999998724809723,
                0.9999910603015767,
                0.9999981261237247,
                0.9999998144608762,
                0.9999997300421263,
                0.999998790134606,
                0.9999999176675829
            ],
            [
                0.9999997126314126,
                0.999999922655833,
                0.9999998642566866,
                0.9999993916408191,
                0.9999997761971049,
                0.9999999123575987,
                0.9999999123575882,
                0.9999998942829351,
                0.9999985406241285,
                0.9999991684715768
            ],
            [
                0.9999994631251885,
                0.9999998024947273,
                0.9999998802069874,
                0.9999955048189639,
                0.9999995262093294,
                0.9999999176674945,
                0.9999998555019274,
                0.9999999317439546,
                0.9999998257021007,
                0.9999998642567353
            ],
            [
                0.9999991684722702,
                0.9999998642567028,
                0.9999997617630051,
                0.9999998362623529,
                0.9999996940978464,
                0.9999995818812774,
                0.999999776197025,
                0.9999999067050054,
                0.9999998144608983,
                0.9999997617630619
            ],
            [
                0.9999995262093293,
                1.0,
                1.0,
                0.9999999273418789,
                0.9999998874648246,
                0.9999999586006147,
                0.9999998874648648,
                0.9999999176675239,
                0.999999906705072,
                1.0
            ],
            [
                1.0,
                0.9999999434137503,
                0.9999999468421122,
                0.9999999317439221,
                1.0,
                0.9999999434138043,
                0.9999998642566704,
                0.9999999397642939,
                0.9999999397642294,
                0.9999992661792821
            ],
            [
                0.9999997897566091,
                1.0,
                0.9999999006880668,
                0.999999917667573,
                0.999999266178845,
                0.9999999358794402,
                0.9999998942829225,
                0.9999998942830863,
                0.9999998461826588,
                0.9999998724809419
            ],
            [
                0.9999994956525922,
                0.9999999226558146,
                0.9999992188514837,
                0.9999999468421124,
                0.9999997617631187,
                0.9999998362623529,
                0.9999994631249326,
                0.9999934595620076,
                0.9999998257022045,
                0.9999998874648514
            ],
            [
                0.9999869928762029,
                2.9023112932045342e-06,
                0.9999995549148951,
                0.9999977396757042,
                0.9999706884685804,
                0.9999960330145617,
                0.9999997761971849,
                0.9999969105062931,
                0.999998239656368,
                0.999998126124171
            ],
            [
                0.9999992661790201,
                0.999997273529409,
                0.9999999397642868,
                0.9999985406243023,
                5.04347528446051e-07,
                0.9999993916411812,
                0.9999994284994171,
                0.9999991684721711,
                0.9999987901338855,
                0.9999957771660609
            ],
            [
                0.9999998942829099,
                0.9999998461827139,
                0.9999999006881024,
                0.9999998724808964,
                1.0,
                1.0,
                0.9999996072137063,
                1.0,
                0.9999996940978463,
                1.0
            ],
            [
                4.539787947345257e-05,
                0.9999898700102492,
                0.9999980052693305,
                0.9999992661786706,
                0.999989216687793,
                0.9999938558268693,
                0.9999724643057548,
                3.288750633569722e-06,
                7.889265407090955e-06,
                0.9999938558239427
            ],
            [
                0.9999998802068873,
                0.9999998461827139,
                0.9999999226557408,
                0.9999998802069731,
                0.9999998802069587,
                0.9999997897566341,
                0.9999999006880668,
                0.9999999123574629,
                0.9999998642566704,
                0.9999997897566841
            ],
            [
                0.9999997761971317,
                0.9999994956526523,
                0.9999992661789326,
                0.9999997126313442,
                0.9999998802068873,
                0.999999894282998,
                0.9999998144609203,
                0.9999999226558424,
                0.9999996072136128,
                0.9999982396563681
            ],
            [
                0.9999998724809115,
                0.9999998642567353,
                0.9999997126313441,
                0.999999802494633,
                0.9999986290421409,
                0.999998932296749,
                0.9999992661786702,
                0.9999998257021213,
                0.9999996533673379,
                0.9999998724809723
            ],
            [
                0.9999998642567028,
                0.9999998144608762,
                0.9999997761970247,
                0.9999998461826222,
                0.9999994631247404,
                0.9999997897566341,
                0.999998446502432,
                0.9999998362622358,
                0.9999998024947273,
                0.9999998024947273
            ],
            [
                0.9999997897567092,
                0.9999998461826956,
                0.999999846182714,
                0.9999996940978462,
                0.9999996743687034,
                0.9999997463982241,
                0.9999978766210356,
                0.999999761763147,
                0.999998712105093,
                0.9999997300422228
            ],
            [
                0.9999998942829602,
                0.9999942280806655,
                0.9999998555019447,
                0.9999998724810027,
                0.9999991148432812,
                0.9999998461827323,
                0.9999996072136594,
                0.9999997761971849,
                0.9999997897565838,
                0.9999999176675338
            ],
            [
                0.9999997126314469,
                0.9999997463981335,
                0.9999999123575465,
                0.9999999006880549,
                1.0,
                0.9999970976876736,
                0.9999999067050498,
                0.9999999273418616,
                0.9999996940977368,
                0.9999996072138
            ],
            [
                0.9999998642566866,
                0.9999991148430699,
                0.9999997897565588,
                0.9999985406234317,
                0.9999998802069587,
                0.9999991684720717,
                0.9999998144609424,
                0.9999916019279849,
                0.9999981261252883,
                1.209866260432471e-06
            ],
            [
                0.9999998257021838,
                0.9999999226558515,
                0.9999999006881259,
                0.9999998942830863,
                0.9999997463981939,
                0.9999997463981032,
                0.9999998024945626,
                0.9999251537374746,
                0.9999999067051165,
                0.9999997463980125
            ],
            [
                0.9999998144609205,
                0.9999998555019274,
                1.0,
                0.9999989969856742,
                0.9999998144609646,
                0.9999991684722703,
                0.999998996985793,
                0.9999998257021215,
                0.9999983463100208,
                0.9999998555019274
            ],
            [
                0.9999986290423047,
                0.9999983463110077,
                0.9999977396765131,
                0.9999996533672552,
                0.9999991148428595,
                0.9999999226557962,
                0.9999990577557439,
                0.9999983463096274,
                0.9999987901341734,
                0.9999996743688976
            ],
            [
                0.9999995818810777,
                0.9999999500628393,
                0.9999999123574629,
                0.9999999500628334,
                1.0,
                0.9999998724809268,
                0.9999992188515767,
                1.0,
                0.999999887464932,
                0.9999999226558516
            ],
            [
                5.04347468323289e-07,
                3.4663249714612693e-07,
                4.450852111148132e-07,
                6.475950298011458e-07,
                5.043472879540142e-07,
                1.6373764721072816e-07,
                7.338210680002898e-07,
                9.422450432014836e-07,
                2.3823702359290413e-07,
                1.0677027427600627e-06
            ],
            [
                3.2887502415438413e-06,
                0.9999994956525321,
                1.3709568799879344e-06,
                1.209865683518615e-06,
                0.9999995262092166,
                1.0129993395217047e-05,
                1.5534984953453635e-06,
                0.9999977396762438,
                0.9999985406239549,
                0.9999997300421585
            ]
        ]
    },
    {
        "q_id": "9524_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            10,
            11,
            12,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            30,
            31,
            32,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            43,
            44,
            45,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            62,
            64,
            65,
            66,
            67,
            68,
            70,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            98,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126
        ],
        "rewards": [
            [
                5.715003789046955e-07,
                1.0677027427569065e-06,
                3.0590237279085045e-07,
                9.422444815814404e-07,
                1.5534981249697903e-06,
                1.209865827740176e-06,
                7.338213304363436e-07,
                NaN,
                9.422442569315887e-07,
                4.785092783519724e-06
            ],
            [
                2.260323758987159e-06,
                1.9947297215125433e-06,
                3.9278605979534166e-07,
                6.475947210046347e-07,
                1.0129993395336818e-05,
                2.2603248367949354e-06,
                3.7266401726173067e-06,
                NaN,
                1.0677027427600627e-06,
                1.0677029973192638e-06
            ],
            [
                5.422218969818919e-06,
                1.7603427936263351e-06,
                3.726641061027928e-06,
                1.1478768126057254e-05,
                1.553498124964492e-06,
                3.2887502415438413e-06,
                6.962255419804982e-06,
                1.7603427936263351e-06,
                1.8925152753790864e-05,
                3.7266379513434106e-06
            ],
            [
                1.3709568799760888e-06,
                2.2603242978778778e-06,
                2.9023133690821773e-06,
                1.5534975693792215e-06,
                4.785095065171522e-06,
                4.222833444467892e-06,
                NaN,
                4.22283545819819e-06,
                2.2603234895176927e-06,
                NaN
            ],
            [
                1.0677028700363782e-06,
                3.059021175261338e-07,
                4.450852641737424e-07,
                1.553497384196656e-06,
                3.726637951387472e-06,
                6.475951069961737e-07,
                1.3709575337016483e-06,
                1.994729483705484e-06,
                1.0677028700422047e-06,
                3.059022269250683e-07
            ],
            [
                2.902312331125353e-06,
                NaN,
                1.7603440527046419e-06,
                4.222832437747125e-06,
                1.2098662604126641e-06,
                1.0129989772532511e-05,
                1.7603432133032607e-06,
                1.5534983101393749e-06,
                5.422219616265831e-06,
                1.0677032518748838e-06
            ],
            [
                4.222834954778007e-06,
                9.422443692489024e-07,
                1.9947292459265734e-06,
                2.260324567337161e-06,
                2.699578418172324e-07,
                4.450851580540182e-07,
                7.338213304316717e-07,
                2.902310947208574e-06,
                4.78509278348926e-06,
                5.422217030707961e-06
            ],
            [
                2.2603234895289998e-06,
                2.260325106237323e-06,
                4.450852111148132e-07,
                3.4663249714451116e-07,
                6.144176066795103e-06,
                2.1024326584639497e-07,
                3.2887494574518405e-06,
                1.5534975693933505e-06,
                3.72663883989755e-06,
                3.726639284125553e-06
            ],
            [
                1.0677027427569065e-06,
                1.7603440527286572e-06,
                0.9999980052693321,
                6.962256249758443e-06,
                2.561283432035425e-06,
                6.1441746020359e-06,
                4.785096206047877e-06,
                3.2887490653647836e-06,
                4.785094494750855e-06,
                3.288749457432399e-06
            ],
            [
                6.475945666051092e-07,
                1.2098656835136636e-06,
                1.994729721518893e-06,
                1.6373764721039308e-07,
                3.0590237279032884e-07,
                1.370957860576702e-06,
                7.889266346603015e-06,
                6.475947210046347e-07,
                5.715005151485975e-07,
                5.043474081993875e-07
            ],
            [
                5.4222176771176554e-06,
                1.6701419854156377e-05,
                3.726637951387472e-06,
                1.8925143729954285e-05,
                3.466325797888292e-07,
                5.715003789017068e-07,
                1.0129989772532511e-05,
                3.466327450765785e-07,
                3.927862002641863e-07,
                2.2603234895289998e-06
            ],
            [
                1.9947297215125433e-06,
                2.2603234895289998e-06,
                9.422442569290178e-07,
                2.2603237589779086e-06,
                1.760343213322473e-06,
                3.927862470899887e-07,
                1.3709575337078829e-06,
                1.9947306726594253e-06,
                1.553498124964492e-06,
                4.450851580566494e-07
            ],
            [
                3.2887478892055875e-06,
                8.315281267882195e-07,
                2.5612828213818346e-06,
                2.5612819054133693e-06,
                1.2098658277082653e-06,
                3.2887482813149375e-06,
                2.5612819053166966e-06,
                6.962258739271155e-06,
                2.26032402841657e-06,
                1.2098653950480359e-06
            ],
            [
                2.2603253756956754e-06,
                1.5534975693979422e-06,
                2.382368531929327e-07,
                5.422218969818919e-06,
                8.315280276607289e-07,
                2.902313023130843e-06,
                1.5534981249697903e-06,
                6.144173869558639e-06,
                2.260324567337161e-06,
                2.260324567337161e-06
            ],
            [
                3.288747889284851e-06,
                6.47595107001401e-07,
                NaN,
                1.0129995810463632e-05,
                1.4738981972564636e-05,
                6.1441746020359e-06,
                7.889265407327733e-06,
                NaN,
                4.222832941193893e-06,
                5.715003789046955e-07
            ],
            [
                1.8925150497848527e-05,
                5.715005151606823e-07,
                5.715004470326849e-07,
                3.0590237279085045e-07,
                NaN,
                1.0677033791437343e-06,
                4.4508505193791187e-07,
                8.315280276626197e-07,
                4.4508515805199415e-07,
                3.927860597945825e-07
            ],
            [
                6.475945666051092e-07,
                6.475948754012522e-07,
                1.0677029973192638e-06,
                5.715004470313855e-07,
                NaN,
                9.422442569208767e-07,
                3.726638839878908e-06,
                9.4224425692559e-07,
                NaN,
                1.3709567165530083e-06
            ],
            [
                4.222833947960866e-06,
                4.78509563546605e-06,
                7.889260704818233e-06,
                6.1441746018123775e-06,
                2.5612816000646084e-06,
                3.726641061027928e-06,
                3.2887486733420804e-06,
                6.144175334468545e-06,
                NaN,
                2.2603240284371276e-06
            ],
            [
                1.3709575337159875e-06,
                2.382370235933104e-07,
                2.382370235933104e-07,
                1.2098659719788098e-06,
                1.444980209564556e-07,
                1.2751899728286965e-07,
                1.1253513522447425e-07,
                NaN,
                1.6373766672973748e-07,
                1.444979692800516e-07
            ],
            [
                8.315281267861397e-07,
                5.422218969895357e-06,
                7.889262585886274e-06,
                6.9622587397397306e-06,
                4.785096206047877e-06,
                8.315282259117513e-07,
                2.2603234895372223e-06,
                3.726638395634011e-06,
                8.315279285351409e-07,
                1.2098659719788098e-06
            ],
            [
                5.715007195447234e-07,
                4.450852111135988e-07,
                2.3823690999290963e-07,
                3.466327450765785e-07,
                1.275190276859705e-07,
                6.475947209985977e-07,
                3.9278634073732336e-07,
                2.382369667929001e-07,
                1.1253512180925583e-07,
                3.0590226339061185e-07
            ],
            [
                3.288748673265808e-06,
                5.4222183235249605e-06,
                7.88926446679691e-06,
                1.8925148242250705e-05,
                6.962256249885085e-06,
                1.6701427818034747e-05,
                7.484624512911504e-05,
                4.2228324377740105e-06,
                NaN,
                1.0677029973192638e-06
            ],
            [
                3.2887498494551953e-06,
                9.422450432014836e-07,
                5.043472278312808e-07,
                2.9023109472244114e-06,
                3.288749457469787e-06,
                6.475948754012522e-07,
                3.9278634073732336e-07,
                6.475948754012522e-07,
                9.422445939032799e-07,
                2.2603245673155757e-06
            ],
            [
                3.4663253846718004e-07,
                3.53562422882756e-05,
                4.450849988798682e-07,
                5.043474081993875e-07,
                5.715005151606823e-07,
                2.3823685319244518e-07,
                6.962256249885085e-06,
                5.715005832886879e-07,
                2.699577774585891e-07,
                7.338207180898968e-07
            ],
            [
                2.260324836776948e-06,
                1.7603427936263351e-06,
                1.0677026154774503e-06,
                1.8925145985104064e-05,
                5.422219616228845e-06,
                2.561281905390075e-06,
                1.2098658277451275e-06,
                1.5534984953453635e-06,
                4.2228334445658276e-06,
                5.422220262555012e-06
            ],
            [
                1.6701427818034747e-05,
                7.338212429582604e-07,
                7.338207180898968e-07,
                2.5612828213934817e-06,
                1.209865250822125e-06,
                NaN,
                2.4300243631890864e-05,
                5.422217030707961e-06,
                1.5534983101602148e-06,
                3.288748281329893e-06
            ],
            [
                3.4663274507713016e-07,
                7.338211554783522e-07,
                1.0677028700422047e-06,
                1.760343003481596e-06,
                7.338207180898968e-07,
                NaN,
                8.93969950132721e-06,
                4.539789029616496e-05,
                3.05902190458764e-07,
                1.760343633031919e-06
            ],
            [
                6.475949526020042e-07,
                7.338209805224048e-07,
                9.422443692555439e-07,
                5.71500719545698e-07,
                2.10243290909724e-07,
                1.8553916819032217e-07,
                NaN,
                8.315277302857965e-07,
                6.475947210031623e-07,
                9.422445939054222e-07
            ],
            [
                2.561281600086738e-06,
                1.9947301970972664e-06,
                1.7603430034867993e-06,
                6.475945666051092e-07,
                1.067703124601679e-06,
                1.760342793638743e-06,
                8.315279285370317e-07,
                1.3709568799919866e-06,
                1.5534977545886537e-06,
                1.0677028700422047e-06
            ],
            [
                6.144173869558639e-06,
                1.8925155009767892e-05,
                3.535625914621054e-05,
                1.2098656835076114e-06,
                NaN,
                NaN,
                1.760344052714248e-06,
                1.9947297214544894e-06,
                9.422448185478557e-07,
                4.785096206047877e-06
            ],
            [
                6.962256249821764e-06,
                1.4738980215352592e-05,
                2.561282516066741e-06,
                1.9947301970813926e-06,
                NaN,
                1.994730672675753e-06,
                2.144495608424996e-05,
                2.9023133690980155e-06,
                8.315278294072958e-07,
                1.0677026154806063e-06
            ],
            [
                1.1478764020560142e-05,
                0.00017952794484876747,
                4.78509563555309e-06,
                2.9023112932177327e-06,
                1.1478768125911099e-05,
                2.2603242978665707e-06,
                8.93969950101825e-06,
                3.2887498494282754e-06,
                2.1444958640087166e-05,
                4.22283545795623e-06
            ],
            [
                8.315278294114555e-07,
                0.9999981261243939,
                8.315277302841894e-07,
                1.5534984953552536e-06,
                1.2098661162023305e-06,
                3.2887502415767434e-06,
                0.9999949062968219,
                0.9999885212305227,
                9.422444815765128e-07,
                NaN
            ],
            [
                5.043472278299047e-07,
                1.067702870039777e-06,
                1.473898900066424e-05,
                1.0677033791612137e-06,
                4.22283545819819e-06,
                7.33821330437595e-07,
                1.7603425837855082e-06,
                NaN,
                NaN,
                1.5534984953552536e-06
            ],
            [
                1.370957860567974e-06,
                1.2751910369275402e-07,
                1.275190276853036e-07,
                1.6373772528704005e-07,
                3.05902226923399e-07,
                1.1253513522447425e-07,
                3.4663253846316044e-07,
                1.0677028700363782e-06,
                1.8553916819032217e-07,
                2.6995784182073116e-07
            ],
            [
                3.2887502415767434e-06,
                5.422218969858371e-06,
                1.4738983729535602e-05,
                1.9947292459265734e-06,
                6.962259568889411e-06,
                5.422218323487975e-06,
                6.144176799283803e-06,
                NaN,
                2.2603251062270446e-06,
                NaN
            ],
            [
                1.067703124601679e-06,
                4.0063701745046735e-05,
                NaN,
                6.475947982037486e-07,
                NaN,
                4.006369219233375e-05,
                9.422450432014836e-07,
                1.3007126914612648e-05,
                1.3709572068522336e-06,
                2.2603245673443566e-06
            ],
            [
                4.785095635624897e-06,
                3.2887502415438413e-06,
                6.962257909785973e-06,
                3.2887494574518405e-06,
                4.222833947932061e-06,
                2.5612828213934817e-06,
                2.902313023063532e-06,
                2.2603234895053587e-06,
                4.222832941142044e-06,
                7.889263526266196e-06
            ],
            [
                7.338210680021253e-07,
                8.315281267882195e-07,
                4.450850519403407e-07,
                NaN,
                3.927862470899887e-07,
                NaN,
                8.315282259117513e-07,
                1.3709570434054234e-06,
                1.5534983101602148e-06,
                1.9947290081286418e-06
            ],
            [
                4.450852641737424e-07,
                6.475947982037486e-07,
                2.6995784182140636e-07,
                NaN,
                1.209865539274514e-06,
                8.315277302841894e-07,
                2.1024326584639497e-07,
                2.561281600086738e-06,
                2.6995784182073116e-07,
                3.927863875616689e-07
            ],
            [
                4.785093924251918e-06,
                1.5534975693792215e-06,
                2.260324567337161e-06,
                6.144175334468545e-06,
                1.994730197090463e-06,
                3.288748673319648e-06,
                1.067702615468225e-06,
                6.9622579096593295e-06,
                1.147877359957198e-05,
                8.31528126775552e-07
            ],
            [
                2.561282516042282e-06,
                4.785094494783494e-06,
                2.5612825160562587e-06,
                1.994729483694599e-06,
                2.902312331170226e-06,
                5.04347348070562e-07,
                4.785093353909723e-06,
                2.9023119851781017e-06,
                8.315279285351409e-07,
                2.260324567337161e-06
            ],
            [
                1.1478764021029928e-05,
                1.2098656835224664e-06,
                6.475951069985296e-07,
                NaN,
                2.561281600076256e-06,
                NaN,
                7.889259764517575e-06,
                2.561281600076256e-06,
                2.1444953527944967e-05,
                8.315278294072958e-07
            ],
            [
                5.04347408197782e-07,
                1.7603440527286572e-06,
                9.422450431954847e-07,
                1.7603425837855082e-06,
                1.0677029973192638e-06,
                1.2098652508391807e-06,
                1.994729008145876e-06,
                1.012999460278499e-05,
                2.2603253756874524e-06,
                3.535625914363812e-05
            ],
            [
                3.120190764966677e-05,
                NaN,
                6.962259569750576e-06,
                2.2603234895372223e-06,
                1.5534977545886537e-06,
                2.561281294760143e-06,
                5.422217030781934e-06,
                1.7603438428800754e-06,
                6.144173869603344e-06,
                NaN
            ],
            [
                7.338211554813555e-07,
                4.450852111155216e-07,
                1.5534971990169383e-06,
                5.043473480777865e-07,
                5.715006514176113e-07,
                1.0677033791495609e-06,
                4.450851049991497e-07,
                1.2098656835252174e-06,
                1.8553907971879076e-07,
                2.56128282131428e-06
            ],
            [
                8.315279285370317e-07,
                1.1478770862735993e-05,
                NaN,
                4.785093353940187e-06,
                4.785093353940187e-06,
                3.7266383955882547e-06,
                1.0677026154774503e-06,
                4.4508515805735777e-07,
                4.450849988811838e-07,
                4.222831934379152e-06
            ],
            [
                4.222834451382849e-06,
                1.4738989000422955e-05,
                1.1478770862735993e-05,
                5.04347348075149e-07,
                6.475945665900901e-07,
                6.475946438042047e-07,
                2.9023123311055552e-06,
                2.902310947208574e-06,
                6.475950298011458e-07,
                NaN
            ],
            [
                3.059022269250683e-07,
                1.0677024882009222e-06,
                3.4663278639892215e-07,
                1.637377448057981e-07,
                3.927863407379485e-07,
                1.2098656835224664e-06,
                2.699577774585891e-07,
                4.2228319344021954e-06,
                NaN,
                1.892515501014656e-05
            ],
            [
                1.6701415872385704e-05,
                3.7266401726173067e-06,
                1.1478772230762415e-05,
                2.2603237589676295e-06,
                1.9947292459347367e-06,
                NaN,
                1.0677024882009222e-06,
                7.889262585814522e-06,
                2.561281905390075e-06,
                1.3709578605617394e-06
            ],
            [
                5.043473480777865e-07,
                9.422445939054222e-07,
                3.288750241561788e-06,
                6.475945666033422e-07,
                3.466327037548308e-07,
                7.338207180864763e-07,
                9.422444815792981e-07,
                3.726639728224814e-06,
                1.9947290081286418e-06,
                6.475950298011458e-07
            ],
            [
                3.2887506336235617e-06,
                4.4508510499849186e-07,
                1.2098659719788098e-06,
                1.994729483729522e-06,
                1.5534975693601474e-06,
                2.2603242978778778e-06,
                NaN,
                2.5612819054028872e-06,
                5.715006514176113e-07,
                NaN
            ],
            [
                3.1201900218617364e-05,
                1.6701419854156377e-05,
                2.2603237589779086e-06,
                1.2098659719716573e-06,
                7.889263526345123e-06,
                1.760343423160973e-06,
                3.2887494574518405e-06,
                1.3709567165530083e-06,
                1.670141786295194e-05,
                4.222833947960866e-06
            ],
            [
                1.0677028700363782e-06,
                1.0677029973192638e-06,
                9.422450431989127e-07,
                7.338209805133949e-07,
                8.315277302788957e-07,
                3.726639284125553e-06,
                1.5534983101393749e-06,
                7.338209805170655e-07,
                5.04347528440776e-07,
                1.370956716529941e-06
            ],
            [
                1.0677033791437343e-06,
                2.2603245673279107e-06,
                4.222833444590791e-06,
                6.962255419868303e-06,
                1.855391681906175e-07,
                2.561281294760143e-06,
                1.994729721518893e-06,
                5.04347348075149e-07,
                2.7535697667202906e-05,
                2.260323758987159e-06
            ],
            [
                6.1441746020359e-06,
                1.3709575337078829e-06,
                1.3709570434178922e-06,
                4.2228334445370225e-06,
                2.9023109472244114e-06,
                6.962256249885085e-06,
                1.9947299592933255e-06,
                2.2603234895053587e-06,
                8.315284241597959e-07,
                1.3007126914612648e-05
            ],
            [
                1.2098662604247682e-06,
                2.3823690999160957e-07,
                7.338209805224048e-07,
                1.7603425837855082e-06,
                1.0677031245990084e-06,
                7.338212429537553e-07,
                1.2098662604291696e-06,
                2.5612825160562587e-06,
                5.715003107755449e-07,
                1.7603438428740716e-06
            ],
            [
                1.067703124601679e-06,
                3.4663266243111764e-07,
                NaN,
                NaN,
                3.927862002641863e-07,
                NaN,
                2.3823688159291947e-07,
                2.5612828213934817e-06,
                4.450852641737424e-07,
                6.144173137170873e-06
            ],
            [
                1.5534983101644536e-06,
                1.9947297214544894e-06,
                3.2887490653872164e-06,
                NaN,
                3.7266383956509585e-06,
                4.222833444590791e-06,
                1.7603436330179102e-06,
                9.422442569334097e-07,
                1.7603440527334603e-06,
                1.0677027427624903e-06
            ],
            [
                4.785093353940187e-06,
                2.2603234895289998e-06,
                1.4449795205429202e-07,
                1.3709568799919866e-06,
                2.6995784182140636e-07,
                3.46632497145457e-07,
                7.338210680021253e-07,
                7.338210680021253e-07,
                1.855391239544352e-07,
                2.6995771309523475e-07
            ],
            [
                NaN,
                1.370956716529941e-06,
                6.962255419931625e-06,
                1.5534983101644536e-06,
                2.90231094723893e-06,
                9.422449308789479e-07,
                2.2603251062270446e-06,
                3.288750241561788e-06,
                1.2098652508347793e-06,
                NaN
            ],
            [
                2.9023119851266288e-06,
                2.26032402841657e-06,
                6.475947209985977e-07,
                1.3709567165579959e-06,
                4.785096206013061e-06,
                6.475947982022763e-07,
                1.7603434231777837e-06,
                1.209865683518615e-06,
                2.430023783734196e-05,
                2.2603237589676295e-06
            ],
            [
                5.422221555380179e-06,
                5.422219616265831e-06,
                NaN,
                NaN,
                3.7266406168624155e-06,
                NaN,
                1.9947304348703948e-06,
                NaN,
                NaN,
                3.7266406168827523e-06
            ],
            [
                3.4663274507713016e-07,
                3.05902190458764e-07,
                2.5612834320563895e-06,
                9.422450432030903e-07,
                NaN,
                1.3709570434219446e-06,
                1.760343213335281e-06,
                NaN,
                2.6995790618350237e-07,
                2.4300234941880266e-05
            ],
            [
                7.338209805224048e-07,
                1.3709572068272963e-06,
                5.715004470295662e-07,
                4.450849458200093e-07,
                8.315278294072958e-07,
                5.715003788993679e-07,
                1.2098659719757836e-06,
                5.715006514167015e-07,
                3.4663278639738526e-07,
                4.785093924330255e-06
            ],
            [
                1.2098662604247682e-06,
                7.338211554783522e-07,
                3.927862939075802e-07,
                1.5534975693869924e-06,
                1.2098662604247682e-06,
                2.260324836776948e-06,
                1.5534975693707442e-06,
                1.0129987357287368e-05,
                1.0129990980100021e-05,
                4.450848927637999e-07
            ],
            [
                1.9947304348703948e-06,
                2.561281600049467e-06,
                4.222834451254188e-06,
                3.7266397283231055e-06,
                1.994730672668496e-06,
                1.0129992187658463e-05,
                4.785095635592258e-06,
                2.9023112931873767e-06,
                2.9023126771227976e-06,
                1.3709573702778664e-06
            ],
            [
                9.422448185478557e-07,
                8.315277302857965e-07,
                9.422442569097361e-07,
                2.3823685319244518e-07,
                1.5534971990169383e-06,
                1.3709572068522336e-06,
                7.338208930391909e-07,
                2.382368531929327e-07,
                7.338207180864763e-07,
                6.475947210031623e-07
            ],
            [
                2.3823690999290963e-07,
                5.715005832895975e-07,
                1.760342793638743e-06,
                9.422445939054222e-07,
                5.71500515159253e-07,
                NaN,
                NaN,
                3.726639284144195e-06,
                NaN,
                1.6373772528704005e-07
            ],
            [
                7.889260704531226e-06,
                3.726639728370556e-06,
                NaN,
                1.7603427935967163e-06,
                3.726639728370556e-06,
                4.2228339479858295e-06,
                1.553498124964492e-06,
                2.5612816000331606e-06,
                2.5612819054133693e-06,
                1.670142980893658e-05
            ],
            [
                7.338208055680009e-07,
                5.043476486915964e-07,
                1.4449798650551755e-07,
                1.8553907971879076e-07,
                1.8553905760062447e-07,
                8.315284241650899e-07,
                2.2603242978871282e-06,
                1.4449807263312446e-07,
                4.450849988811838e-07,
                6.825602910433871e-08
            ],
            [
                1.7603436330259153e-06,
                NaN,
                8.315281267861397e-07,
                6.475951069985296e-07,
                1.9947299593014888e-06,
                2.902311639183378e-06,
                1.300713156582635e-05,
                6.475947210031623e-07,
                4.222832941193893e-06,
                9.422447062202052e-07
            ],
            [
                2.9023130231176453e-06,
                0.00023050663315114637,
                4.222834954778007e-06,
                1.2098661161927025e-06,
                3.2887502415438413e-06,
                1.0129989772532511e-05,
                1.012999460278499e-05,
                5.4222209089700225e-06,
                0.00026119024761339036,
                6.962257909722651e-06
            ],
            [
                8.939698435657833e-06,
                6.605212895289091e-05,
                1.7603440527222532e-06,
                3.726639284144195e-06,
                1.2098653950656417e-06,
                5.422219616265831e-06,
                4.785096205778054e-06,
                6.9622587397397306e-06,
                2.902312331170226e-06,
                1.3709570434178922e-06
            ],
            [
                1.4449802095666915e-07,
                9.931187406410953e-08,
                3.4663278639892215e-07,
                6.475945666063607e-07,
                2.260325375677174e-06,
                NaN,
                5.043476486924565e-07,
                3.466325384661554e-07,
                2.3823682479292225e-07,
                9.422445939054222e-07
            ],
            [
                2.5612834320563895e-06,
                6.96225873967641e-06,
                NaN,
                1.7603432133136672e-06,
                1.147877359957198e-05,
                4.450851049991497e-07,
                3.7266401725935817e-06,
                NaN,
                1.994729008151319e-06,
                3.5356238073889594e-05
            ],
            [
                NaN,
                3.2887498495150166e-06,
                3.288747889284851e-06,
                2.6995784182140636e-07,
                1.9947299592933255e-06,
                2.9023119851899796e-06,
                2.1024334103505245e-07,
                1.3709572068522336e-06,
                5.715003789046955e-07,
                2.6995774527718623e-07
            ],
            [
                1.6701425826525565e-05,
                4.222831934352267e-06,
                5.422219616228845e-06,
                8.93969950132721e-06,
                3.288749849498565e-06,
                1.1478772231086046e-05,
                1.3007130015488633e-05,
                6.605216831371112e-05,
                4.785095065204162e-06,
                1.1478764020883773e-05
            ],
            [
                5.043472879540142e-07,
                3.927861066170637e-07,
                1.5534971990169383e-06,
                1.0677026154806063e-06,
                7.33821330437595e-07,
                7.338210679909462e-07,
                1.760342793583908e-06,
                NaN,
                9.422449308716635e-07,
                2.69957906184239e-07
            ],
            [
                2.902312677137316e-06,
                NaN,
                4.785093353940187e-06,
                7.338210680021253e-07,
                2.753568453712307e-05,
                2.5612819054133693e-06,
                6.47595107001401e-07,
                5.043472879540142e-07,
                5.715007195447234e-07,
                1.3709575337016483e-06
            ],
            [
                3.05902336324494e-07,
                1.275190580890061e-07,
                1.2098659719788098e-06,
                6.475945666063607e-07,
                2.1024336609843824e-07,
                3.9278620026686556e-07,
                3.927862470905692e-07,
                3.9278629391427843e-07,
                5.043474081993875e-07,
                7.33821330437595e-07
            ],
            [
                2.561282210740037e-06,
                2.2603248367949354e-06,
                2.260323758987159e-06,
                NaN,
                3.1201922535494165e-05,
                3.2887498495150166e-06,
                4.450848927650143e-07,
                9.422444815814404e-07,
                1.994729483723626e-06,
                1.1478770862882149e-05
            ],
            [
                3.7266392839425286e-06,
                3.7266401725681614e-06,
                1.2098659719757836e-06,
                8.939698435560267e-06,
                3.288750241561788e-06,
                7.338211554783522e-07,
                2.9023133690425823e-06,
                2.902312677137316e-06,
                2.902311293147782e-06,
                2.5612822107167428e-06
            ],
            [
                5.715003107738556e-07,
                3.7266406168827523e-06,
                3.726641061085547e-06,
                2.561281905390075e-06,
                0.0001233945896995423,
                6.144176799334096e-06,
                8.315277302841894e-07,
                4.5397884884891014e-05,
                6.144173137170873e-06,
                NaN
            ],
            [
                7.338213304283347e-07,
                4.785093924362895e-06,
                1.0677032518748838e-06,
                1.0677031245905116e-06,
                9.422444815765128e-07,
                1.5534975693792215e-06,
                5.043472278280699e-07,
                1.2098661161927025e-06,
                8.31528126775552e-07,
                1.9947292459265734e-06
            ],
            [
                NaN,
                2.90231094723893e-06,
                9.422444815814404e-07,
                1.0677029973219343e-06,
                1.2098659719788098e-06,
                NaN,
                1.9947299592570416e-06,
                6.9622595696935874e-06,
                2.2603253756956754e-06,
                5.043472879525233e-07
            ],
            [
                3.05902117523595e-07,
                3.466325797888292e-07,
                4.4508505193932864e-07,
                2.6995784182140636e-07,
                2.10243290909724e-07,
                2.260325106237323e-06,
                1.275191036933194e-07,
                1.1253508156363576e-07,
                2.1024334103581732e-07,
                1.2751899728286965e-07
            ],
            [
                2.2603251062450327e-06,
                3.0590215399183813e-07,
                2.5612834320563895e-06,
                3.7266383956509585e-06,
                1.7603438428848787e-06,
                9.422443692574719e-07,
                5.043475284430694e-07,
                5.043472278322555e-07,
                6.475946438055299e-07,
                9.422449308716635e-07
            ],
            [
                8.315277302841894e-07,
                5.715007195431641e-07,
                7.338209805224048e-07,
                5.043473480766399e-07,
                3.2887478892683997e-06,
                1.5534971990126997e-06,
                1.994730197090463e-06,
                6.962259569484628e-06,
                4.785093924362895e-06,
                9.422449308716635e-07
            ],
            [
                4.785096206047877e-06,
                2.1444948415296896e-05,
                3.288749849498565e-06,
                7.338211554783522e-07,
                6.962257909785973e-06,
                NaN,
                1.2098661161927025e-06,
                NaN,
                3.7266410611296085e-06,
                NaN
            ],
            [
                2.5612812947508257e-06,
                2.144495608327478e-05,
                1.6701419854156377e-05,
                1.4738981972323349e-05,
                1.0129995810343862e-05,
                2.144494841482881e-05,
                3.726641061109272e-06,
                7.88926070489716e-06,
                2.5612822107167428e-06,
                1.3007133116542802e-05
            ],
            [
                7.73442776303243e-08,
                2.382370235933104e-07,
                3.059021175261338e-07,
                2.260324567337161e-06,
                9.422447062270609e-07,
                1.9947299593078385e-06,
                1.855391239544352e-07,
                2.699577452775239e-07,
                3.05902263391829e-07,
                8.315282259089153e-07
            ],
            [
                2.1444943301674863e-05,
                NaN,
                3.288747889284851e-06,
                2.902313369111213e-06,
                4.450849988811838e-07,
                9.422443692446175e-07,
                1.300712846477255e-05,
                1.3709570434219446e-06,
                1.6701419854156377e-05,
                4.0063706519072155e-05
            ],
            [
                4.450851580540182e-07,
                7.338212429582604e-07,
                9.422442569290178e-07,
                NaN,
                6.475947982037486e-07,
                2.9023116392097746e-06,
                4.450851580540182e-07,
                6.475947209985977e-07,
                8.315279285351409e-07,
                9.422443692489024e-07
            ],
            [
                1.8553903548231313e-07,
                3.0590215399183813e-07,
                1.2098652508391807e-06,
                1.994729008105057e-06,
                2.69957906184239e-07,
                3.9278634073732336e-07,
                5.04347348075149e-07,
                1.2098662604247682e-06,
                4.222832941193893e-06,
                4.450852641717689e-07
            ],
            [
                NaN,
                1.2098656835224664e-06,
                NaN,
                NaN,
                NaN,
                7.338213304283347e-07,
                4.4508515805735777e-07,
                1.5534975693979422e-06,
                5.04347528446051e-07,
                NaN
            ],
            [
                1.5534983101549167e-06,
                2.75356878194421e-05,
                1.8925148241872038e-05,
                3.288748673360027e-06,
                NaN,
                2.430024652792821e-05,
                2.5612834320470717e-06,
                4.78509278348926e-06,
                1.2098659719757836e-06,
                9.422450431989127e-07
            ],
            [
                2.561281905376098e-06,
                4.222833947960866e-06,
                8.939695238536645e-06,
                1.3709575337078829e-06,
                3.2887506335906595e-06,
                2.9023126771227976e-06,
                3.2887478892683997e-06,
                4.222831934379152e-06,
                1.5534973841895917e-06,
                8.315280276580819e-07
            ],
            [
                4.450849988758202e-07,
                1.3709572068522336e-06,
                9.422443692527585e-07,
                5.715002426460124e-07,
                2.2603251062013478e-06,
                6.962255419868303e-06,
                2.3823696679230424e-07,
                6.475946438022905e-07,
                8.315277302747361e-07,
                3.4663253846718004e-07
            ],
            [
                2.260324836787226e-06,
                NaN,
                7.338212429582604e-07,
                3.059022998576899e-07,
                4.450852111148132e-07,
                4.4508494582405734e-07,
                5.715005832853093e-07,
                9.422447062294175e-07,
                5.04347528446051e-07,
                1.7603427936335396e-06
            ],
            [
                8.939693106987645e-06,
                1.0129989772274546e-05,
                1.0677032518785256e-06,
                4.785093353874907e-06,
                1.147876949310201e-05,
                1.5534979397500702e-06,
                2.144495608378187e-05,
                2.1444940745839484e-05,
                3.7266401725935817e-06,
                2.902312677137316e-06
            ],
            [
                2.102434162245973e-07,
                1.209865539295696e-06,
                8.315281267834927e-07,
                6.475947210046347e-07,
                4.450852111155216e-07,
                3.059021175261338e-07,
                1.0677028700422047e-06,
                2.5612834320563895e-06,
                1.2098661162056318e-06,
                2.2603253756956754e-06
            ],
            [
                3.4663262110945863e-07,
                3.7266410611296085e-06,
                2.2603234895289998e-06,
                4.785096206013061e-06,
                2.9023123311055552e-06,
                5.422220909009474e-06,
                2.5612831267202583e-06,
                4.222832941193893e-06,
                2.2603242978665707e-06,
                1.9947292459347367e-06
            ],
            [
                2.1444940745839484e-05,
                NaN,
                5.043476486915964e-07,
                1.0677027427600627e-06,
                2.902311639183378e-06,
                1.4738983729294318e-05,
                NaN,
                1.760343633031919e-06,
                2.7535694384882703e-05,
                8.939696304311336e-06
            ],
            [
                5.715002426475718e-07,
                3.059022998576899e-07,
                9.422444815765128e-07,
                1.3709573702778664e-06,
                9.422445939002803e-07,
                2.5612834320470717e-06,
                9.422448185510695e-07,
                4.450852111135988e-07,
                5.715003107738556e-07,
                9.422445939032799e-07
            ],
            [
                3.466327450765785e-07,
                1.7603425837903113e-06,
                NaN,
                6.144172404738491e-06,
                3.466327037539638e-07,
                8.315280276546789e-07,
                3.288747889284851e-06,
                5.422217677152175e-06,
                4.450852111148132e-07,
                1.2098662604247682e-06
            ],
            [
                9.422442569315887e-07,
                6.475947210046347e-07,
                5.043473480777865e-07,
                3.0590237279085045e-07,
                7.338208055664991e-07,
                7.338212429582604e-07,
                3.927862002663297e-07,
                1.444980209564556e-07,
                5.043473480777865e-07,
                2.6995784182140636e-07
            ],
            [
                1.2098652508287273e-06,
                1.209866260432471e-06,
                1.3709568799592562e-06,
                1.55349775456958e-06,
                1.3709568799879344e-06,
                1.7603430034743913e-06,
                5.422220262636381e-06,
                3.2887506336086064e-06,
                1.7603425837494853e-06,
                2.2603248367358324e-06
            ],
            [
                5.043472879540142e-07,
                8.939699501416646e-06,
                1.994730197090463e-06,
                5.715003107655392e-07,
                2.9023119851781017e-06,
                1.2098659719757836e-06,
                8.939693107288474e-06,
                5.422218323487975e-06,
                1.994730434879465e-06,
                1.0677027427600627e-06
            ],
            [
                2.699576809143613e-07,
                1.4449805540740185e-07,
                NaN,
                NaN,
                1.2751901248454963e-07,
                NaN,
                NaN,
                3.059022269254856e-07,
                9.422442569334097e-07,
                1.5534973842076057e-06
            ],
            [
                NaN,
                NaN,
                2.5612816000646084e-06,
                1.5534979397829198e-06,
                1.0677027427624903e-06,
                8.315280276626197e-07,
                8.315279285370317e-07,
                6.47594952603035e-07,
                5.71500719545698e-07,
                2.5612828213934817e-06
            ]
        ]
    },
    {
        "q_id": "9955_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            120,
            121,
            122,
            123,
            124,
            126,
            127
        ],
        "rewards": [
            [
                3.059022998581767e-07,
                1.1253526937697666e-07,
                3.927863407379485e-07,
                1.4449802095666915e-07,
                3.059022269250683e-07,
                3.9278629391427843e-07,
                2.6995790618469934e-07,
                2.699576809143613e-07,
                1.0677028700422047e-06,
                3.0590237279085045e-07
            ],
            [
                1.3007126914435202e-05,
                2.6995784182183607e-07,
                2.3823685319320354e-07,
                5.715002426486762e-07,
                1.6373764721091427e-07,
                1.7603425837791042e-06,
                8.764242227418718e-08,
                1.4449796928021588e-07,
                NaN,
                1.7603427936335396e-06
            ],
            [
                0.9999989322972584,
                3.0590237279032884e-07,
                1.8553916819032217e-07,
                1.0677027427525368e-06,
                4.450851580540182e-07,
                1.2098655392921197e-06,
                6.475945666051092e-07,
                3.466327037548308e-07,
                1.855391239544352e-07,
                5.422221555380179e-06
            ],
            [
                1.6373772528704005e-07,
                8.315284241650899e-07,
                2.699578740032504e-07,
                1.5534979397790343e-06,
                1.1253517547010071e-07,
                5.04347468323289e-07,
                3.059022998576899e-07,
                4.4508510499849186e-07,
                NaN,
                7.338207180898968e-07
            ],
            [
                0.9999974387180973,
                0.9999993106387085,
                0.9999984465024333,
                0.999968798077756,
                0.9999996533674205,
                0.99999967436882,
                0.999999607213847,
                4.691159887151251e-08,
                0.9999996940977368,
                0.9999938558276137
            ],
            [
                NaN,
                1.275190124846946e-07,
                7.734428685047173e-08,
                1.6373770576776313e-07,
                1.275189972832538e-07,
                8.764242227418718e-08,
                NaN,
                1.275190124846946e-07,
                2.382368815932174e-07,
                3.466327037553825e-07
            ],
            [
                NaN,
                1.0677028700422047e-06,
                2.3823682479292225e-07,
                1.444979692800516e-07,
                4.4508494582314646e-07,
                NaN,
                4.450850519403407e-07,
                2.699578740032504e-07,
                NaN,
                NaN
            ],
            [
                3.466326211113502e-07,
                2.561282516066741e-06,
                3.0590237279085045e-07,
                1.4449795205472734e-07,
                1.6373772528704005e-07,
                1.0677026154806063e-06,
                9.422445939054222e-07,
                1.4449805540763184e-07,
                2.3823696679327928e-07,
                2.699576809143613e-07
            ],
            [
                6.475945666063607e-07,
                3.6534838223576766e-08,
                8.7642526752214e-08,
                7.734425919002834e-08,
                3.059021175261338e-07,
                5.315788140303327e-08,
                2.699578740032504e-07,
                1.0677032518748838e-06,
                NaN,
                6.47595107001401e-07
            ],
            [
                5.04347468323289e-07,
                5.715003107767143e-07,
                1.7603425837855082e-06,
                5.8291251656508296e-05,
                4.450851580555361e-07,
                6.475945666051092e-07,
                1.7603436330259153e-06,
                5.715003107767143e-07,
                4.222834954778007e-06,
                8.315279285370317e-07
            ],
            [
                2.699578740032504e-07,
                3.288747889284851e-06,
                9.422445939032799e-07,
                6.475949526020042e-07,
                NaN,
                1.209866260432471e-06,
                2.2603234895372223e-06,
                5.715005151606823e-07,
                1.5534971990169383e-06,
                5.715006514167015e-07
            ],
            [
                2.699578096403948e-07,
                1.0677029973219343e-06,
                9.422443692574719e-07,
                2.3823690999323465e-07,
                1.4449795205472734e-07,
                1.0677029973219343e-06,
                1.637376862489725e-07,
                NaN,
                2.10243290909963e-07,
                9.422443692574719e-07
            ],
            [
                0.9999989969859123,
                0.999999825702163,
                4.139935079796334e-08,
                0.9999994631250604,
                8.315280276607289e-07,
                0.999998863436019,
                0.9999983463110065,
                0.9999996940977732,
                7.734416698849138e-08,
                1.4449805540651476e-07
            ],
            [
                0.9999998024947038,
                0.9999998724810027,
                0.999999825702059,
                0.9999997463981938,
                1.1253518888531272e-07,
                0.9999989322967493,
                0.9999998942830737,
                0.9999988634358838,
                0.9999994284996895,
                0.9999985406239552
            ],
            [
                1.0677033791291683e-06,
                9.422443692574719e-07,
                2.561282210740037e-06,
                2.2603234895372223e-06,
                NaN,
                6.475945666063607e-07,
                1.3709568799919866e-06,
                3.927860597945825e-07,
                1.3709572068522336e-06,
                3.288747889284851e-06
            ],
            [
                5.043476486924565e-07,
                2.902312677150514e-06,
                6.475947210046347e-07,
                3.9278610661902853e-07,
                1.5534971990126997e-06,
                7.338208930460318e-07,
                2.5612819054028872e-06,
                8.315282259138311e-07,
                2.561281600076256e-06,
                1.760343003481596e-06
            ],
            [
                2.1024334103581732e-07,
                1.7603434231833873e-06,
                NaN,
                5.043472278322555e-07,
                2.2603242978871282e-06,
                6.962258739530771e-06,
                2.382370235933104e-07,
                3.466326211113502e-07,
                1.300713466685723e-05,
                1.8553919030826963e-07
            ],
            [
                4.222834954801051e-06,
                1.0677033791612137e-06,
                1.1253513522447425e-07,
                1.5534973842076057e-06,
                7.734415776836702e-08,
                3.059022998581767e-07,
                2.9023116392097746e-06,
                3.466325797900508e-07,
                1.855391239547094e-07,
                1.7603430034867993e-06
            ],
            [
                NaN,
                NaN,
                2.2603234895372223e-06,
                1.0129993395336818e-05,
                3.4663249714612693e-07,
                5.422220262636381e-06,
                NaN,
                7.33821330437595e-07,
                1.637376862489725e-07,
                8.315281267882195e-07
            ],
            [
                1.4449807263312446e-07,
                2.902312677150514e-06,
                7.338213304343413e-07,
                1.2098658277264215e-06,
                1.209865539295696e-06,
                2.3823690999323465e-07,
                1.8553907971855875e-07,
                1.8553919030858602e-07,
                1.0677026154806063e-06,
                8.315277302841894e-07
            ],
            [
                8.315284241650899e-07,
                4.450852641737424e-07,
                3.120192625482384e-05,
                2.5612819054028872e-06,
                0.9999623635530994,
                5.043476486924565e-07,
                0.9999992661786712,
                0.9999994284993492,
                7.338208930460318e-07,
                0.00013982210758122318
            ],
            [
                5.71500719545698e-07,
                0.9999986290427944,
                0.9999993524053564,
                0.9999992188519493,
                0.9999987121043248,
                0.9999984465022465,
                1.4449800373118268e-07,
                2.3823702359290413e-07,
                0.9999981261250649,
                0.9999974387180973
            ],
            [
                0.9999993524052794,
                2.260324567337161e-06,
                8.7642558095602e-08,
                1.0677027427624903e-06,
                0.9999990577555191,
                6.825597214718257e-08,
                2.382368815932174e-07,
                0.9999999123574419,
                6.825608606172863e-08,
                6.023568448589658e-08
            ],
            [
                0.9999994631249963,
                0.9999991148430702,
                6.475947210046347e-07,
                1.1253525596174225e-07,
                0.999999114843281,
                0.9999994284995531,
                NaN,
                0.9999949062937892,
                0.9999993916408186,
                0.9999989969862713
            ],
            [
                3.535625914621054e-05,
                1.9947297215043796e-06,
                1.5534984953298217e-06,
                4.785095065204162e-06,
                0.00017952790215813958,
                3.2887506336086064e-06,
                6.1441724046434924e-06,
                6.144176066850984e-06,
                8.315283250371857e-07,
                4.2228324377740105e-06
            ],
            [
                0.9999998802069159,
                0.9999994956525922,
                0.9999980052705221,
                0.9999974387168775,
                0.9999991148429651,
                0.9999998144608762,
                NaN,
                0.9999991684719731,
                0.9999989322968762,
                0.9999995262093863
            ],
            [
                9.422448185534261e-07,
                1.0677027427600627e-06,
                1.3709567165579959e-06,
                6.475945666033422e-07,
                6.962253760024999e-06,
                1.2098659719757836e-06,
                7.338210679949506e-07,
                7.338210679979539e-07,
                1.994729008145876e-06,
                NaN
            ],
            [
                0.9999974387184044,
                0.9999994284992809,
                4.139935079796334e-08,
                1.275190428875671e-07,
                0.9999998942829225,
                9.931200429212718e-08,
                9.931189774187203e-08,
                9.931202796993203e-08,
                8.764241182641775e-08,
                9.931194509740267e-08
            ],
            [
                0.9999993916410362,
                0.9999994284996897,
                0.9999996940976638,
                0.9999994284996897,
                0.9999994631248048,
                8.315281267882195e-07,
                0.9999998144609205,
                8.315282259138311e-07,
                0.9999984465016926,
                0.9999994956526527
            ],
            [
                2.144495863958007e-05,
                0.9999964991464234,
                NaN,
                1.0677029973219343e-06,
                0.999999114843176,
                0.9999623635622126,
                0.999997273529407,
                0.9999991684716755,
                0.9999985406241279,
                0.9999974387174864
            ],
            [
                0.9999982396559496,
                1.6373766672973748e-07,
                0.9999991148426483,
                0.9999983463104154,
                0.9999983463106124,
                0.9999985406243025,
                0.9999990577550696,
                1.444979692800516e-07,
                0.9999981261246186,
                0.9999995262092165
            ],
            [
                3.466326624336003e-07,
                1.3007123813382511e-05,
                4.222833444590791e-06,
                1.370957860576702e-06,
                2.3823702359290413e-07,
                3.726639284144195e-06,
                2.3823690999323465e-07,
                NaN,
                1.0677026154806063e-06,
                3.9278605979534166e-07
            ],
            [
                3.7266397283908927e-06,
                2.6995790618469934e-07,
                8.7642558095602e-08,
                2.2603240284371276e-06,
                5.043476486924565e-07,
                1.855391681906175e-07,
                3.05902336324494e-07,
                1.6373774480605869e-07,
                1.209865827752005e-06,
                9.422450432014836e-07
            ],
            [
                2.902313369111213e-06,
                5.043472879540142e-07,
                1.209866260432471e-06,
                5.71500719545698e-07,
                NaN,
                1.5534973842076057e-06,
                8.939693107190907e-06,
                4.785092783519724e-06,
                1.067703124601679e-06,
                1.0677024882009222e-06
            ],
            [
                2.561281600076256e-06,
                2.9023123311583482e-06,
                5.715002426486762e-07,
                1.994729721518893e-06,
                1.0677032518785256e-06,
                NaN,
                3.466326211113502e-07,
                5.715007195447234e-07,
                1.855391681891831e-07,
                2.3823693839325527e-07
            ],
            [
                3.4663249714612693e-07,
                5.04347287955046e-07,
                4.222835458148261e-06,
                4.450852111148132e-07,
                3.927860597945825e-07,
                1.0677032518814388e-06,
                3.466325797896173e-07,
                5.715003788993679e-07,
                4.4508515805735777e-07,
                2.561283432035425e-06
            ],
            [
                6.475945666063607e-07,
                1.855391239547094e-07,
                5.71500651413193e-07,
                NaN,
                1.7603440527286572e-06,
                3.059023727894942e-07,
                2.3823696679327928e-07,
                2.3823693839325527e-07,
                1.3709570434178922e-06,
                1.5534981249697903e-06
            ],
            [
                1.7603438428800754e-06,
                7.338210679979539e-07,
                2.2603253756956754e-06,
                5.043474081993875e-07,
                8.315279285351409e-07,
                3.059023727894942e-07,
                7.338207180864763e-07,
                2.260325106237323e-06,
                1.994729008145876e-06,
                1.7603440527222532e-06
            ],
            [
                NaN,
                7.734414854823498e-08,
                8.7642526752214e-08,
                1.8553907971879076e-07,
                NaN,
                1.855390576008354e-07,
                8.764253720001207e-08,
                NaN,
                4.4508515805735777e-07,
                1.2751902768612997e-07
            ],
            [
                NaN,
                NaN,
                0.9999980052707571,
                1.275189972832538e-07,
                0.9999997463981637,
                9.422443692574719e-07,
                1.1253517547010071e-07,
                0.9999974387171836,
                3.927863875616689e-07,
                3.9278620026686556e-07
            ],
            [
                7.889261645090304e-06,
                1.7603427936335396e-06,
                NaN,
                3.2887506336086064e-06,
                1.2098652508347793e-06,
                7.338208930460318e-07,
                1.0129993395088066e-05,
                1.1478765388898939e-05,
                NaN,
                1.994730672668496e-06
            ],
            [
                0.9999957771660656,
                0.9999151889945479,
                0.9999969105066723,
                0.9999985406234333,
                0.9999975938976654,
                0.99997246431974,
                0.9999985406241291,
                9.422450431912e-07,
                0.9999967112513364,
                0.999994577781699
            ],
            [
                0.9999989322971311,
                0.9999978766212865,
                0.9999994956525321,
                0.9999996072138936,
                0.9999993916408912,
                0.9999994284995535,
                0.9999998362622358,
                0.9999995549147891,
                0.9999993524053569,
                0.9999993916411813
            ],
            [
                6.144177531767002e-06,
                1.3709572068522336e-06,
                2.561282210729555e-06,
                7.889264466725156e-06,
                NaN,
                8.939698435657833e-06,
                6.9622537599680095e-06,
                3.726639728370556e-06,
                7.889262585814522e-06,
                6.962258739796719e-06
            ],
            [
                4.4508494582405734e-07,
                1.0677024882009222e-06,
                7.338209805240734e-07,
                1.0677029973219343e-06,
                3.927863875616689e-07,
                8.315280276626197e-07,
                1.855391239547094e-07,
                2.1024334103581732e-07,
                2.6995771309523475e-07,
                4.450852111148132e-07
            ],
            [
                1.6701417863559525e-05,
                1.9947304348862686e-06,
                7.734426841017797e-08,
                1.1253509497883659e-07,
                2.6995784182140636e-07,
                NaN,
                2.9023119851899796e-06,
                0.9999938558224772,
                1.2751904288710323e-07,
                3.059022269250683e-07
            ],
            [
                4.450852641737424e-07,
                1.6373766672973748e-07,
                3.05902263391829e-07,
                4.539786865090791e-05,
                3.927862002663297e-07,
                1.8553905760062447e-07,
                1.8553910183674878e-07,
                1.2098659719788098e-06,
                8.315277302857965e-07,
                2.6995784182183607e-07
            ],
            [
                1.1253526937697666e-07,
                1.4449800373118268e-07,
                7.734425919002834e-08,
                6.023578501513224e-08,
                8.315278294114555e-07,
                1.27519088491875e-07,
                5.422217677152175e-06,
                6.825608606172863e-08,
                2.5612834320563895e-06,
                4.450852111155216e-07
            ],
            [
                8.764254764780641e-08,
                6.023569884718319e-08,
                7.338213304363436e-07,
                9.422444815814404e-07,
                2.5612819054133693e-06,
                1.275189972832538e-07,
                7.734415776836702e-08,
                1.209865827752005e-06,
                1.99472900813862e-06,
                1.2098656835224664e-06
            ],
            [
                0.9999991148428592,
                0.9999980052709949,
                5.043476486924565e-07,
                0.9999985406230842,
                0.9999987121052462,
                0.9999995262093296,
                0.9999910603038451,
                0.999999631011416,
                0.9999980052695676,
                0.9999989322966221
            ],
            [
                6.144173137170873e-06,
                8.939694172957213e-06,
                2.9023116391978967e-06,
                1.7603436330259153e-06,
                1.3709568799879344e-06,
                6.962254589978262e-06,
                1.5534971990126997e-06,
                1.2098656835224664e-06,
                5.71500651413193e-07,
                8.315282259117513e-07
            ],
            [
                8.315282259089153e-07,
                0.9999997463981032,
                0.9999996310114602,
                0.9999991148431762,
                0.9999989322972583,
                7.338208930460318e-07,
                0.9999992661788452,
                3.4663249714612693e-07,
                0.9999997617631187,
                0.9999999006880312
            ],
            [
                6.825598028392069e-08,
                3.466327037553825e-07,
                1.0677032518785256e-06,
                9.422449308335287e-07,
                NaN,
                1.444980726324838e-07,
                1.637376862489725e-07,
                7.73442776300517e-08,
                1.553498124964492e-06,
                8.315280276626197e-07
            ],
            [
                8.315282259138311e-07,
                5.71500719545698e-07,
                1.8553910183674878e-07,
                9.931187406410953e-08,
                NaN,
                5.043475885696228e-07,
                8.764245361752286e-08,
                3.9278629391427843e-07,
                1.125351083940518e-07,
                5.315780536011123e-08
            ],
            [
                1.5534975693979422e-06,
                1.0677027427624903e-06,
                3.05902263391829e-07,
                5.422217677152175e-06,
                2.2603248367949354e-06,
                NaN,
                NaN,
                1.994729483723626e-06,
                2.561281600086738e-06,
                5.04347287955046e-07
            ],
            [
                0.99999921885167,
                1.275190276859705e-07,
                0.9999993916411812,
                0.9999987121049403,
                0.9999996533673791,
                0.999999168471973,
                0.9999975938979521,
                0.9999988634361552,
                0.9999996940976273,
                0.9999988634365615
            ],
            [
                1.994729483723626e-06,
                0.9999994631248047,
                0.9999984465022468,
                0.9999989969859128,
                0.9999974387177928,
                2.5612828213934817e-06,
                0.9999990577551824,
                0.999999526209386,
                0.9999861539987773,
                0.9999977396759753
            ],
            [
                1.0677027427624903e-06,
                1.637377057680051e-07,
                2.1024339116168358e-07,
                1.5534975693979422e-06,
                1.209866260432471e-06,
                3.4663274507713016e-07,
                3.059022269254856e-07,
                2.1024334103581732e-07,
                3.05902263391829e-07,
                2.382369951932796e-07
            ],
            [
                4.450850519403407e-07,
                1.7603438428800754e-06,
                2.90231094723893e-06,
                5.715003789046955e-07,
                3.466325797896173e-07,
                3.72663883989755e-06,
                5.715006514167015e-07,
                1.1478765389222573e-05,
                1.7603427936335396e-06,
                1.7603440527286572e-06
            ],
            [
                0.9999999123575464,
                8.764254764780641e-08,
                0.9999995549150015,
                0.9999988634361547,
                7.734428685047173e-08,
                1.3709576971425944e-06,
                1.855391681906175e-07,
                0.999999114843387,
                0.9999949062950051,
                0.9999930377421204
            ],
            [
                2.699576809143613e-07,
                5.04347468323289e-07,
                5.715005151606823e-07,
                3.4663274507713016e-07,
                3.05902190458764e-07,
                3.059021175261338e-07,
                3.0590215399183813e-07,
                1.6373770576776313e-07,
                2.1024331597288867e-07,
                3.9278610661902853e-07
            ],
            [
                1.2098655392871682e-06,
                1.5534983101644536e-06,
                4.4508510499849186e-07,
                1.994729008151319e-06,
                NaN,
                8.315277302841894e-07,
                0.9999991148426481,
                0.9999993106392013,
                0.9999989969859128,
                0.9999964991439194
            ],
            [
                3.927862002663297e-07,
                0.9999984465022493,
                0.999997876622303,
                0.9999987121044802,
                0.9999985406234354,
                0.9999960330126876,
                0.9999982396569993,
                0.9999989969857945,
                0.9999599362893784,
                0.9999980052693308
            ],
            [
                1.4449805540763184e-07,
                0.9999991148427537,
                0.9999990577550697,
                0.9999993106389549,
                0.9999993916409639,
                0.999998863436697,
                0.999999168472072,
                0.9999970976890582,
                0.9999994631248684,
                0.9999997617630617
            ],
            [
                2.382370235933104e-07,
                2.1024341622368903e-07,
                3.9278634073732336e-07,
                1.275190580890061e-07,
                3.9278605979534166e-07,
                1.8553914607267268e-07,
                3.4663278639892215e-07,
                2.69957906184239e-07,
                7.338208930460318e-07,
                1.2751899728286965e-07
            ],
            [
                NaN,
                9.422444815814404e-07,
                NaN,
                0.9999952149066647,
                6.475950298011458e-07,
                0.9999978766220459,
                2.10243290909963e-07,
                1.3709572068522336e-06,
                5.715006514176113e-07,
                0.9999987121050925
            ],
            [
                1.760342793638743e-06,
                1.4738985486506781e-05,
                7.338209805240734e-07,
                3.927862002663297e-07,
                2.6995790618469934e-07,
                5.71500515161527e-07,
                1.3709578605729614e-06,
                6.962255419931625e-06,
                9.422447062294175e-07,
                2.9023119851899796e-06
            ],
            [
                0.9999997617630334,
                0.999995777168069,
                0.9999987121046322,
                0.9999904837517504,
                0.9999985406232587,
                0.9999832985762356,
                2.2603251062450327e-06,
                1.5534971990126997e-06,
                4.450851580555361e-07,
                0.999998863435749
            ],
            [
                6.9622595696935874e-06,
                6.962256249758443e-06,
                1.1478772231086046e-05,
                6.1441746020359e-06,
                2.561283432035425e-06,
                7.338213304283347e-07,
                NaN,
                1.6701429808632785e-05,
                3.059021175261338e-07,
                2.4300249425247723e-05
            ],
            [
                2.6995790618469934e-07,
                0.9999898700126556,
                3.466326211105621e-07,
                5.043472278322555e-07,
                1.7603427936335396e-06,
                0.9999706884723292,
                7.338210680021253e-07,
                6.475949526020042e-07,
                0.9999892166878068,
                6.475948754012522e-07
            ],
            [
                1.1253525596174225e-07,
                1.2751902768612997e-07,
                9.931200429212718e-08,
                1.1253518888531272e-07,
                3.4663278639892215e-07,
                NaN,
                3.05902263391829e-07,
                1.1253524254650944e-07,
                6.475949526020042e-07,
                1.6373766672994222e-07
            ],
            [
                1.27519088491875e-07,
                NaN,
                1.275190732904469e-07,
                1.1253508156363576e-07,
                NaN,
                7.734428685019034e-08,
                1.2098659719788098e-06,
                1.444979692800516e-07,
                1.7603440527286572e-06,
                7.338212429582604e-07
            ],
            [
                2.3823688159237777e-07,
                2.6995784182140636e-07,
                3.466326624336003e-07,
                NaN,
                5.715006514176113e-07,
                1.4738981972323349e-05,
                6.47595107001401e-07,
                1.6373774480479287e-07,
                1.275190732904469e-07,
                6.47595107001401e-07
            ],
            [
                0.9999892166903832,
                7.33821330437595e-07,
                2.1024334103581732e-07,
                0.9999706884721432,
                NaN,
                0.9999038975638261,
                2.10243290909963e-07,
                0.9999991684722703,
                0.9999991148428589,
                0.9999970976880188
            ],
            [
                1.8553905760062447e-07,
                0.0002034269248525461,
                2.6995774527718623e-07,
                4.450849988811838e-07,
                2.5612812947508257e-06,
                5.043476486924565e-07,
                1.3709573702822306e-06,
                3.9278605979534166e-07,
                1.2098652508424818e-06,
                8.315284241650899e-07
            ],
            [
                1.3709572068522336e-06,
                4.0063711294555596e-05,
                1.553497754583709e-06,
                1.553497199007048e-06,
                NaN,
                0.0001398221242266438,
                5.043473480777865e-07,
                2.102434162245973e-07,
                1.3709576971463352e-06,
                1.0677029973192638e-06
            ],
            [
                3.927862002663297e-07,
                3.466326211113502e-07,
                2.6995771309523475e-07,
                1.6373776432509826e-07,
                9.422443692574719e-07,
                2.5612828213934817e-06,
                1.444980209564556e-07,
                1.637377057680051e-07,
                1.6373770576776313e-07,
                1.1253506814842375e-07
            ],
            [
                7.889264466545779e-06,
                3.288749457469787e-06,
                3.2887478892683997e-06,
                7.338209805170655e-07,
                2.5612819054028872e-06,
                7.889265407255982e-06,
                3.726638395634011e-06,
                1.7603438428740716e-06,
                2.9023119851781017e-06,
                8.31527928532683e-07
            ],
            [
                0.9999987901347508,
                0.999998863436156,
                0.9999987901347508,
                0.9999985406236068,
                7.338209805240734e-07,
                0.9999994631249962,
                0.9999997126314468,
                1.5534971990169383e-06,
                7.338211554801876e-07,
                0.9999998642566381
            ],
            [
                NaN,
                2.6995784182183607e-07,
                7.734414854823498e-08,
                3.4663274507713016e-07,
                2.1024331597288867e-07,
                9.93120161310289e-08,
                1.1253509497883659e-07,
                1.8553907971879076e-07,
                1.012999098021058e-05,
                1.1253514863909295e-07
            ],
            [
                9.422450432030903e-07,
                1.6373764721072816e-07,
                5.04347287955046e-07,
                2.3823702359138736e-07,
                3.05902263391829e-07,
                3.4663274507713016e-07,
                5.715005832895975e-07,
                8.315282259138311e-07,
                1.6373766672973748e-07,
                1.444979692800516e-07
            ],
            [
                7.338209805200689e-07,
                2.1444958637941764e-05,
                3.0590237279032884e-07,
                2.5612825160562587e-06,
                3.466325797896173e-07,
                2.902311985146426e-06,
                5.04347468323289e-07,
                9.422450431989127e-07,
                5.1442195268327955e-05,
                3.288749065423109e-06
            ],
            [
                1.637376862489725e-07,
                1.0677027427600627e-06,
                1.0677026154806063e-06,
                1.8553919030858602e-07,
                5.043474082005342e-07,
                9.422445939054222e-07,
                9.422449308748773e-07,
                8.315281267861397e-07,
                9.422450431989127e-07,
                2.2603240284371276e-06
            ],
            [
                4.4508515805735777e-07,
                1.3709573702822306e-06,
                6.475950298021765e-07,
                1.0677027427600627e-06,
                3.5356238069902345e-05,
                6.47595107001401e-07,
                1.9947297215125433e-06,
                NaN,
                6.144176799334096e-06,
                NaN
            ],
            [
                1.5534977545886537e-06,
                1.0677029973219343e-06,
                9.422443692574719e-07,
                NaN,
                1.3709568799919866e-06,
                7.338212429582604e-07,
                7.338210680002898e-07,
                1.5534979397790343e-06,
                4.785096776499213e-06,
                1.209865827752005e-06
            ],
            [
                2.9023119851899796e-06,
                4.539785782605375e-05,
                0.9999992661787583,
                1.994729721518893e-06,
                2.2603253756956754e-06,
                0.9999997126315154,
                1.7603425837903113e-06,
                1.5534981249697903e-06,
                1.4449798650551755e-07,
                0.9999991684719732
            ],
            [
                1.2751902768612997e-07,
                NaN,
                8.764249540862797e-08,
                6.023577065381482e-08,
                1.4449796928021588e-07,
                8.7642558095602e-08,
                NaN,
                1.8553914607267268e-07,
                2.3823693839325527e-07,
                1.6373764721091427e-07
            ],
            [
                2.9023133690980155e-06,
                2.902312677137316e-06,
                2.4300234940642642e-05,
                9.422442569290178e-07,
                4.4508510499849186e-07,
                8.315280276607289e-07,
                4.450848927658745e-07,
                3.726639728370556e-06,
                3.4663266242969896e-07,
                9.422442569290178e-07
            ],
            [
                0.9999983463104153,
                0.9999986290427946,
                0.999998790133741,
                1.5534971990169383e-06,
                0.999995777167568,
                0.9999998362623334,
                0.9999991684717747,
                0.9999986290427946,
                0.9999995818814267,
                0.9999996072139407
            ],
            [
                0.9999852610110347,
                9.931190958076104e-08,
                1.8553919030858602e-07,
                3.53562422882756e-05,
                0.9999978766205273,
                3.059023363231725e-07,
                3.059021175255426e-07,
                1.7603434231833873e-06,
                3.927861066170637e-07,
                2.9023112932296107e-06
            ],
            [
                1.0677026154806063e-06,
                3.059022998576899e-07,
                3.059021175261338e-07,
                3.4663262111182307e-07,
                1.6373764721091427e-07,
                3.927860597935108e-07,
                3.466327450765785e-07,
                NaN,
                6.475947982037486e-07,
                3.05902190458764e-07
            ],
            [
                7.338208930460318e-07,
                1.8553919030858602e-07,
                0.9999988634357483,
                1.855391681906175e-07,
                NaN,
                0.9999981261246208,
                2.2603234895372223e-06,
                7.734428685047173e-08,
                1.5534973842076057e-06,
                1.5534973842076057e-06
            ],
            [
                7.338212429582604e-07,
                7.889263526345123e-06,
                2.3823696679327928e-07,
                1.2751910369310194e-07,
                5.043472278322555e-07,
                NaN,
                3.05902336324494e-07,
                1.4449803818215767e-07,
                3.0590237279032884e-07,
                3.927860597945825e-07
            ],
            [
                7.338207180898968e-07,
                1.0677029973219343e-06,
                NaN,
                NaN,
                5.71500719545698e-07,
                8.31528325040778e-07,
                4.450852111155216e-07,
                1.7603440527334603e-06,
                3.059021175261338e-07,
                1.4449803818215767e-07
            ],
            [
                3.0590237279085045e-07,
                1.637376862489725e-07,
                NaN,
                1.6373764721072816e-07,
                NaN,
                1.275190580890061e-07,
                4.785096205882502e-06,
                4.4508515805735777e-07,
                2.1024334103581732e-07,
                NaN
            ],
            [
                NaN,
                NaN,
                1.855391239547094e-07,
                1.4449800373118268e-07,
                1.8553910183674878e-07,
                8.764254764780641e-08,
                1.637376862489725e-07,
                2.1024326584639497e-07,
                3.059022269254856e-07,
                2.3823696679327928e-07
            ],
            [
                0.9999980052693297,
                2.9023119851899796e-06,
                2.382369951932796e-07,
                0.9999982396567877,
                0.999994577781682,
                0.9999952149072202,
                0.9999974387177918,
                0.9999987121043246,
                1.3709572068522336e-06,
                0.9999981261241712
            ],
            [
                3.9278610661902853e-07,
                2.2603251062450327e-06,
                2.69957906184239e-07,
                1.670142980920999e-05,
                6.47595107001401e-07,
                5.715002426486762e-07,
                1.637377448057981e-07,
                3.466327037553825e-07,
                9.422444815814404e-07,
                3.05902263391829e-07
            ],
            [
                9.422445939032799e-07,
                5.04347287955046e-07,
                2.5612831267202583e-06,
                2.5612831267202583e-06,
                2.5612819054028872e-06,
                7.338213304363436e-07,
                7.338208930460318e-07,
                1.2098658277489788e-06,
                6.475949526020042e-07,
                1.5534979397790343e-06
            ],
            [
                7.734425919002834e-08,
                8.764254764780641e-08,
                4.450852641737424e-07,
                1.994729721518893e-06,
                NaN,
                1.0677028700422047e-06,
                1.275190580890061e-07,
                3.9278610661902853e-07,
                3.9278605979534166e-07,
                1.0677032518785256e-06
            ],
            [
                2.260323758987159e-06,
                2.902313369111213e-06,
                6.475949525981759e-07,
                2.2603240284371276e-06,
                2.902312677150514e-06,
                1.0677028700320085e-06,
                1.5534981249697903e-06,
                7.338208055664991e-07,
                1.3709567165617364e-06,
                9.422450431989127e-07
            ],
            [
                6.962254589914941e-06,
                3.1201922531407855e-05,
                NaN,
                2.5612812947508257e-06,
                4.450851580555361e-07,
                NaN,
                7.338211554783522e-07,
                3.288748673360027e-06,
                5.715004470295662e-07,
                3.0590215399183813e-07
            ],
            [
                0.9999982396561615,
                0.9999989322971314,
                0.9999989969855543,
                0.9999989322967493,
                0.999999266179108,
                0.9999996072136128,
                1.2098661162056318e-06,
                0.9999998461827139,
                0.9999904837472308,
                0.9999998362623529
            ],
            [
                3.05902263391829e-07,
                1.275190124842887e-07,
                1.275190428875671e-07,
                7.734415776836702e-08,
                3.4663249714612693e-07,
                1.275190732904469e-07,
                1.5534981249697903e-06,
                1.370957860576702e-06,
                1.760343633031919e-06,
                4.450852111148132e-07
            ],
            [
                1.0677026154806063e-06,
                2.1024334103581732e-07,
                NaN,
                1.855391681906175e-07,
                8.764242227418718e-08,
                NaN,
                0.9999998461826223,
                7.338208055680009e-07,
                0.9999832985822427,
                0.9999991148433868
            ],
            [
                0.9999038975629633,
                3.0590219045914655e-07,
                1.2751904288739315e-07,
                8.7642558095602e-08,
                1.6373776432509826e-07,
                4.1399400149893274e-08,
                1.209865827752005e-06,
                3.4663249714612693e-07,
                8.764253720001207e-08,
                NaN
            ],
            [
                4.785095065204162e-06,
                9.422448185478557e-07,
                6.475950298011458e-07,
                9.422444815765128e-07,
                7.889261645427538e-06,
                1.0129995810463632e-05,
                5.715005832886879e-07,
                8.939700567004841e-06,
                2.3823685319244518e-07,
                2.260324028427877e-06
            ],
            [
                0.9999996533672963,
                0.9999997761970516,
                1.855391460719133e-07,
                1.8553910183649565e-07,
                1.4449803818215767e-07,
                0.9999987901338846,
                0.9999962733620529,
                8.764244316973974e-08,
                0.9999996072138466,
                6.023572038912295e-08
            ],
            [
                3.05902263391829e-07,
                7.734416698849138e-08,
                1.6701421844753466e-05,
                5.043474683240344e-07,
                3.927861534431675e-07,
                8.7642558095602e-08,
                3.4663274507713016e-07,
                1.8553910183674878e-07,
                4.139941002027314e-08,
                1.4449802095666915e-07
            ],
            [
                1.0677033791583005e-06,
                5.043473480777865e-07,
                1.0677026154774503e-06,
                1.6373764721072816e-07,
                1.0677027427624903e-06,
                1.1253525596174225e-07,
                1.275189972832538e-07,
                1.7603425837855082e-06,
                3.466327037553825e-07,
                8.315283250394546e-07
            ],
            [
                0.9999982396572078,
                0.9999910603015933,
                9.931192141912081e-08,
                6.023578501513224e-08,
                9.931196877517082e-08,
                0.9999997463981637,
                0.9999998144609424,
                0.9999993916408185,
                1.8553914607237736e-07,
                7.734423152941018e-08
            ],
            [
                0.9999991148427539,
                1.1253513522447425e-07,
                0.9999980052705197,
                0.9999995262096121,
                0.9999981261246191,
                1.6373764721039308e-07,
                0.9999970976866349,
                0.9999989969854346,
                0.9999996310116361,
                3.927862470899887e-07
            ],
            [
                8.31528325040778e-07,
                1.3709576971463352e-06,
                5.715004470334646e-07,
                6.475946438055299e-07,
                5.715006514176113e-07,
                1.5534975693979422e-06,
                4.4508515805735777e-07,
                6.475947210031623e-07,
                3.466326624336003e-07,
                6.475945666063607e-07
            ],
            [
                5.315789407685159e-08,
                1.1253522913127183e-07,
                2.699578740032504e-07,
                6.475947210046347e-07,
                3.653479467066246e-08,
                5.715006514176113e-07,
                0.9999822214545473,
                NaN,
                7.338211554783522e-07,
                7.3382080556433e-07
            ],
            [
                1.760342793638743e-06,
                1.275190732904469e-07,
                4.4508510499849186e-07,
                1.4449798650551755e-07,
                2.1024331597262577e-07,
                7.484624513510494e-05,
                3.4663266242969896e-07,
                1.27519088491875e-07,
                3.927860597945825e-07,
                2.3823682479181176e-07
            ],
            [
                2.699576809143613e-07,
                2.1024339116168358e-07,
                2.699578740032504e-07,
                6.47595107001401e-07,
                2.102434162245973e-07,
                3.9278605979534166e-07,
                3.466325797888292e-07,
                3.9278629391427843e-07,
                1.8553907971855875e-07,
                5.043475885696228e-07
            ],
            [
                0.9999974387180981,
                6.47595107001401e-07,
                0.9999942280806693,
                0.9999984465022476,
                0.9999977396759758,
                0.9999985406237808,
                0.9999861540004465,
                2.3823693839325527e-07,
                0.9999996310115481,
                2.902313369111213e-06
            ],
            [
                3.653485564473625e-08,
                5.043473480777865e-07,
                3.4663266243308805e-07,
                6.962257079832313e-06,
                3.466325797900508e-07,
                4.4508494582314646e-07,
                1.0677029973114952e-06,
                1.994730672668496e-06,
                8.31528424162821e-07,
                1.7603436330091044e-06
            ]
        ]
    },
    {
        "q_id": "10087_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            16,
            17,
            18,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            31,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            41,
            43,
            44,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            64,
            65,
            67,
            68,
            69,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            119,
            120,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.1253518888531272e-07,
                3.2887478892504536e-06,
                3.288749065423109e-06,
                1.7603436329978976e-06,
                3.927862002663297e-07,
                1.4738976700366126e-05,
                1.4449798650551755e-07,
                4.222833444590791e-06,
                NaN,
                4.222831934352267e-06
            ],
            [
                5.715003789033962e-07,
                1.2098653950606901e-06,
                NaN,
                9.931186222523604e-08,
                4.450852111148132e-07,
                2.3823696679327928e-07,
                8.315283250394546e-07,
                1.5534984953453635e-06,
                2.561282210740037e-06,
                1.7603425837791042e-06
            ],
            [
                3.927863407379485e-07,
                4.450852111148132e-07,
                2.699576809143613e-07,
                9.422448185534261e-07,
                7.734423152941018e-08,
                NaN,
                1.0677026154806063e-06,
                3.059022269250683e-07,
                9.422448185534261e-07,
                3.4663266243308805e-07
            ],
            [
                2.5612816000646084e-06,
                1.0677032518785256e-06,
                1.3709575337078829e-06,
                3.466325384661554e-07,
                NaN,
                2.260325106237323e-06,
                1.0677027427525368e-06,
                NaN,
                4.785096206013061e-06,
                1.7603440527286572e-06
            ],
            [
                2.2603248367949354e-06,
                1.5534984953552536e-06,
                0.9999983463108104,
                0.9999955048162871,
                0.9999925887201361,
                1.760343213335281e-06,
                0.9999975938979511,
                3.4663278639892215e-07,
                8.315282259138311e-07,
                3.466327037553825e-07
            ],
            [
                2.102434412875379e-07,
                1.7603438428800754e-06,
                NaN,
                1.994729483723626e-06,
                NaN,
                1.5534977545497995e-06,
                5.715005832886879e-07,
                3.9278615344178325e-07,
                1.0677032518785256e-06,
                3.288748673360027e-06
            ],
            [
                1.1478770862735993e-05,
                4.222832437443716e-06,
                2.9023133690425823e-06,
                2.260324836787226e-06,
                1.2098658277335738e-06,
                1.6701421843720577e-05,
                NaN,
                6.1441731370702875e-06,
                2.5612819054028872e-06,
                5.422219616140078e-06
            ],
            [
                0.9999994284992809,
                0.9999989969857931,
                0.999998790134462,
                0.9999898700102415,
                0.9999987121047852,
                0.9999991684722705,
                0.999997739675976,
                0.9999934595627926,
                0.9999516743680804,
                0.9999990577552951
            ],
            [
                1.0677029973158649e-06,
                8.315284241560147e-07,
                5.715006514151423e-07,
                2.9023112932177327e-06,
                2.5612819054028872e-06,
                1.7603427936335396e-06,
                4.785092783519724e-06,
                1.7603436330259153e-06,
                NaN,
                NaN
            ],
            [
                2.561282516066741e-06,
                2.102434162245973e-07,
                NaN,
                2.75356878194421e-05,
                0.9999945777784575,
                3.46632497145457e-07,
                0.999937949505269,
                8.315279285370317e-07,
                1.637376862489725e-07,
                1.5534983101644536e-06
            ],
            [
                1.4449798650551755e-07,
                9.931193325852072e-08,
                7.338210680021253e-07,
                1.275190428875671e-07,
                6.825597214718257e-08,
                2.561282516066741e-06,
                8.764245361752286e-08,
                6.825600469412533e-08,
                1.2751908849167202e-07,
                2.1024334103581732e-07
            ],
            [
                2.5612819054028872e-06,
                3.466326211113502e-07,
                1.2098662604291696e-06,
                6.475948754012522e-07,
                1.3709576971425944e-06,
                NaN,
                2.5612819054028872e-06,
                6.1441746020359e-06,
                NaN,
                1.0677032518785256e-06
            ],
            [
                9.931190958076104e-08,
                NaN,
                1.9947304348862686e-06,
                6.023574911170301e-08,
                3.9278605979534166e-07,
                1.1253509497883659e-07,
                1.5534973842076057e-06,
                1.5534971990169383e-06,
                4.450852111155216e-07,
                4.139934586278605e-08
            ],
            [
                NaN,
                NaN,
                3.927863407379485e-07,
                5.71500719545698e-07,
                NaN,
                1.4738983729535602e-05,
                8.315279285370317e-07,
                1.5534983101602148e-06,
                1.2098661162056318e-06,
                NaN
            ],
            [
                1.2098659719757836e-06,
                2.382369951932796e-07,
                2.260325106237323e-06,
                1.5534975693979422e-06,
                1.637377057680051e-07,
                1.209865827752005e-06,
                1.5534983101602148e-06,
                9.422450432014836e-07,
                2.382370235933104e-07,
                1.6701417859944398e-05
            ],
            [
                8.764242227418718e-08,
                1.3709568799919866e-06,
                2.2603251062450327e-06,
                2.1024336609843824e-07,
                1.5534983101602148e-06,
                8.315280276626197e-07,
                2.69957906184239e-07,
                3.059021904571643e-07,
                1.6373774480605869e-07,
                5.715003107767143e-07
            ],
            [
                6.825598028392069e-08,
                NaN,
                1.2751899728311609e-07,
                3.059022998581767e-07,
                1.855391239547094e-07,
                1.1253526937697666e-07,
                1.209865539274514e-06,
                8.315278294072958e-07,
                2.382370235933104e-07,
                9.93120161306789e-08
            ],
            [
                3.9278610661902853e-07,
                1.760343213322473e-06,
                2.1444950970626095e-05,
                2.699578740011634e-07,
                2.5612828213690224e-06,
                3.05902190458764e-07,
                3.2887502415438413e-06,
                2.1024334103505245e-07,
                7.338213304363436e-07,
                5.829126555256903e-05
            ],
            [
                7.338208055664991e-07,
                2.6995784182140636e-07,
                9.422448185510695e-07,
                7.338209805200689e-07,
                1.7603438428800754e-06,
                5.04347528446051e-07,
                9.422447062294175e-07,
                0.00023050679815207037,
                8.315281267861397e-07,
                3.466327863983311e-07
            ],
            [
                4.139934586278605e-08,
                6.825609419848033e-08,
                4.450848927650143e-07,
                9.422442569315887e-07,
                1.855391681906175e-07,
                8.315280276626197e-07,
                2.6995784182140636e-07,
                4.4508515805735777e-07,
                6.475947982037486e-07,
                NaN
            ],
            [
                2.699576809143613e-07,
                3.059022998581767e-07,
                7.338210680021253e-07,
                3.927863407379485e-07,
                6.475947982037486e-07,
                8.764247451307293e-08,
                4.450851580540182e-07,
                5.04347468323289e-07,
                3.05902263391829e-07,
                1.4449803818215767e-07
            ],
            [
                6.144172404693786e-06,
                1.5534975693707442e-06,
                1.0677033791437343e-06,
                1.300713156582635e-05,
                5.422218323399208e-06,
                NaN,
                4.222832437677995e-06,
                1.3709575336947905e-06,
                1.7603438428740716e-06,
                1.0677027427525368e-06
            ],
            [
                7.734416698849138e-08,
                6.825598842065202e-08,
                2.561282516042282e-06,
                1.6373766672973748e-07,
                9.931200429212718e-08,
                1.8925145985895816e-05,
                1.1253509497883659e-07,
                2.382369951932796e-07,
                0.0007096705569099884,
                9.931187406410953e-08
            ],
            [
                9.931200429181105e-08,
                6.825605351455307e-08,
                1.6373762769138607e-07,
                1.444980726324838e-07,
                6.825602910433871e-08,
                9.931185038635267e-08,
                1.4449802095609418e-07,
                5.04347287955046e-07,
                2.3823693839325527e-07,
                1.2751899728286965e-07
            ],
            [
                5.715005151606823e-07,
                NaN,
                1.5534975693933505e-06,
                3.7266406168624155e-06,
                1.300713156582635e-05,
                1.0677032518785256e-06,
                1.760343213335281e-06,
                5.043472879540142e-07,
                9.422447062270609e-07,
                NaN
            ],
            [
                NaN,
                2.561283432035425e-06,
                2.382368247924618e-07,
                1.3709567165579959e-06,
                2.5612834320470717e-06,
                3.726639284144195e-06,
                1.0129988564974359e-05,
                3.53562422882756e-05,
                1.5534981249697903e-06,
                1.0129995810343862e-05
            ],
            [
                0.999998790134461,
                NaN,
                0.99990389756239,
                1.1253509497883659e-07,
                0.007577240735603619,
                0.004070137215684434,
                0.998073265769188,
                1.637377057680051e-07,
                7.338209805200689e-07,
                3.05902190458764e-07
            ],
            [
                NaN,
                2.902312677150514e-06,
                NaN,
                4.78509563546605e-06,
                5.422217030747413e-06,
                2.902312331125353e-06,
                NaN,
                6.144173137126169e-06,
                6.144176799166453e-06,
                1.8925152752999112e-05
            ],
            [
                3.059023727894942e-07,
                1.7603425837855082e-06,
                2.1024334103505245e-07,
                3.466326211113502e-07,
                5.04347287955046e-07,
                8.315277302857965e-07,
                2.1024326584639497e-07,
                1.7603430034867993e-06,
                4.450850519403407e-07,
                1.275190580884987e-07
            ],
            [
                0.99999649914434,
                6.475947210031623e-07,
                2.6995790618350237e-07,
                3.927860597935108e-07,
                3.2887478892055875e-06,
                2.5612825160562587e-06,
                3.0590237279085045e-07,
                2.382369383923073e-07,
                3.0590226338838606e-07,
                2.10243290909724e-07
            ],
            [
                2.260324567337161e-06,
                2.699578740032504e-07,
                1.4449802095666915e-07,
                7.734414854823498e-08,
                3.4663253846718004e-07,
                NaN,
                8.315280276626197e-07,
                NaN,
                1.275190580890061e-07,
                3.059021175247079e-07
            ],
            [
                1.3709570434178922e-06,
                NaN,
                NaN,
                1.2098662604247682e-06,
                1.5534984953552536e-06,
                1.553497754583709e-06,
                6.475947982037486e-07,
                2.260324836787226e-06,
                1.7603432133296774e-06,
                6.144173137126169e-06
            ],
            [
                1.994730434879465e-06,
                2.3823688159291947e-07,
                1.2751899728311609e-07,
                1.0677032518785256e-06,
                6.962255419868303e-06,
                7.338208055664991e-07,
                3.726638839878908e-06,
                7.338212429537553e-07,
                4.450849988811838e-07,
                5.715003107755449e-07
            ],
            [
                0.9999964991464254,
                0.9999945777823344,
                0.9999038975997816,
                0.9999984465015056,
                0.9999925887192589,
                0.9999993106390371,
                1.0,
                0.9999996310114599,
                NaN,
                0.999999266178845
            ],
            [
                1.6373766672973748e-07,
                2.1024334103505245e-07,
                0.9999667857933388,
                7.734418542875216e-08,
                2.382369383923073e-07,
                2.9023109472244114e-06,
                2.6995771309523475e-07,
                7.338210680021253e-07,
                3.059021904571643e-07,
                3.12019150949065e-05
            ],
            [
                0.9999960330140935,
                0.999999554914842,
                0.9999852610215855,
                0.9999996310115918,
                0.9999998461826589,
                1.7603425837791042e-06,
                0.9999997897565839,
                0.9999994284994168,
                0.9999993916408184,
                0.9999969105062937
            ],
            [
                5.715005832886879e-07,
                3.288748673376478e-06,
                7.734428685047173e-08,
                4.450852641737424e-07,
                1.994729483723626e-06,
                3.927863407379485e-07,
                7.734422230927814e-08,
                6.825601283086733e-08,
                2.6995790618469934e-07,
                1.275190276859705e-07
            ],
            [
                8.315279285351409e-07,
                2.1024331597262577e-07,
                2.2603234895289998e-06,
                1.7603438428800754e-06,
                4.222831934352267e-06,
                NaN,
                2.4300234941261454e-05,
                1.5534983101549167e-06,
                1.2098659719716573e-06,
                3.726638839878908e-06
            ],
            [
                7.889262585728421e-06,
                3.7266401726173067e-06,
                1.2098658277451275e-06,
                7.338212429537553e-07,
                NaN,
                1.7603427936335396e-06,
                3.7266401725681614e-06,
                2.2603248367656408e-06,
                1.0677028700363782e-06,
                1.2098658277489788e-06
            ],
            [
                2.6995790618469934e-07,
                5.71500719545698e-07,
                3.927862470905692e-07,
                1.2098659719788098e-06,
                3.4663274507713016e-07,
                1.5534981249697903e-06,
                7.338209805240734e-07,
                3.4663266243308805e-07,
                1.8553905760062447e-07,
                9.422442569315887e-07
            ],
            [
                1.1478772230762415e-05,
                6.475950298011458e-07,
                4.785096776499213e-06,
                8.939695238536645e-06,
                1.0677029973219343e-06,
                1.209865539295696e-06,
                1.1478773599425825e-05,
                3.2887498495150166e-06,
                1.9947297215125433e-06,
                2.699578096403948e-07
            ],
            [
                5.043472879540142e-07,
                3.288749065423109e-06,
                1.2098662604291696e-06,
                6.475947982037486e-07,
                7.338209805224048e-07,
                4.450848927650143e-07,
                8.315280276626197e-07,
                9.422450431989127e-07,
                3.9278610661902853e-07,
                5.715005151550947e-07
            ],
            [
                2.1444950971601277e-05,
                1.5534977545886537e-06,
                2.9023116392097746e-06,
                2.6995774527718623e-07,
                NaN,
                6.475950298011458e-07,
                2.2603242978778778e-06,
                1.4449796927932878e-07,
                2.699578096403948e-07,
                2.902312677150514e-06
            ],
            [
                0.9999990577557439,
                0.9999967112509429,
                3.927863407379485e-07,
                7.338210680002898e-07,
                NaN,
                2.3823690999290963e-07,
                NaN,
                0.9999995549150545,
                0.9999987121049388,
                6.023571320847322e-08
            ],
            [
                1.1478766757404937e-05,
                6.475945666051092e-07,
                2.5612819054028872e-06,
                7.889259764359722e-06,
                1.5534981249697903e-06,
                NaN,
                NaN,
                4.222835458175145e-06,
                2.5612825160562587e-06,
                6.475948753991907e-07
            ],
            [
                NaN,
                1.3709568799879344e-06,
                8.315283250371857e-07,
                NaN,
                2.5612819053586272e-06,
                1.7603440527286572e-06,
                2.7535681254804434e-05,
                4.785095065171522e-06,
                8.939700567004841e-06,
                1.5534971990126997e-06
            ],
            [
                7.338209805240734e-07,
                NaN,
                NaN,
                NaN,
                3.059022269250683e-07,
                1.0677032518814388e-06,
                6.475945666051092e-07,
                3.059021175261338e-07,
                5.043476486915964e-07,
                2.9023119851781017e-06
            ],
            [
                5.71500651413193e-07,
                2.1024326584582131e-07,
                1.2098652508424818e-06,
                5.715003789046955e-07,
                1.275190580884987e-07,
                1.8553919030776337e-07,
                1.637377448057981e-07,
                2.5612828213934817e-06,
                1.2098656835136636e-06,
                9.422449308748773e-07
            ],
            [
                0.9999993916411086,
                0.999991601930979,
                0.9999962733593876,
                0.9999934595612195,
                0.9999974387171823,
                5.715005151606823e-07,
                0.9999646437451921,
                3.9278615344178325e-07,
                0.99999577716656,
                1.1253518888531272e-07
            ],
            [
                0.9999869928746823,
                4.450848927658745e-07,
                1.0677029973219343e-06,
                2.69957906184239e-07,
                0.9999832985821541,
                3.466325797896173e-07,
                2.5612819053166966e-06,
                1.855391681906175e-07,
                2.9023123311583482e-06,
                2.260324567337161e-06
            ],
            [
                1.5534983101478522e-06,
                2.561281600076256e-06,
                2.561281600076256e-06,
                3.466325797896173e-07,
                8.315283250371857e-07,
                2.561283432035425e-06,
                3.9278634073732336e-07,
                1.1478764020883773e-05,
                8.315281267834927e-07,
                6.475949526020042e-07
            ],
            [
                1.994729008145876e-06,
                NaN,
                NaN,
                NaN,
                NaN,
                9.422450431989127e-07,
                0.012431650418695919,
                1.994729483723626e-06,
                2.902313369111213e-06,
                NaN
            ],
            [
                1.2098655392871682e-06,
                5.043472278280699e-07,
                NaN,
                1.7603430034439723e-06,
                5.715002426439334e-07,
                6.475948754012522e-07,
                1.7603432133136672e-06,
                6.144174601879434e-06,
                0.009708476177040046,
                1.760344052714248e-06
            ],
            [
                NaN,
                3.0590237279032884e-07,
                3.927863875616689e-07,
                NaN,
                1.855391239544352e-07,
                2.69957906184239e-07,
                1.444979692800516e-07,
                2.382368531929327e-07,
                1.8553905759969634e-07,
                1.0677026154806063e-06
            ],
            [
                1.9947306726594253e-06,
                3.4663257978780455e-07,
                3.726639728370556e-06,
                8.939700567004841e-06,
                2.5612828213934817e-06,
                NaN,
                4.785092783519724e-06,
                3.726641061109272e-06,
                3.120191509274984e-05,
                1.6373774480605869e-07
            ],
            [
                6.475947210012481e-07,
                8.315279285370317e-07,
                1.3709570434219446e-06,
                9.422448185435711e-07,
                3.927862470899887e-07,
                NaN,
                3.2887478892683997e-06,
                NaN,
                1.209865539295696e-06,
                1.994729008145876e-06
            ],
            [
                7.338213304363436e-07,
                8.315282259117513e-07,
                2.9023116391978967e-06,
                1.760343213335281e-06,
                0.9999599363080034,
                8.315277302841894e-07,
                1.0677027427600627e-06,
                1.209865539295696e-06,
                1.3709573702822306e-06,
                0.999978555044086
            ],
            [
                6.475947982037486e-07,
                5.715004470313855e-07,
                5.422220262599396e-06,
                9.422448185478557e-07,
                NaN,
                3.2887498495150166e-06,
                9.422442569315887e-07,
                5.4222183235249605e-06,
                4.2228324377740105e-06,
                1.3709575337159875e-06
            ],
            [
                1.0677027427340866e-06,
                1.2098662604247682e-06,
                1.7603425837366772e-06,
                3.7266379512518984e-06,
                3.2887498494551953e-06,
                4.222831934321543e-06,
                1.5534971989809095e-06,
                1.7603432133136672e-06,
                3.535625071473396e-05,
                2.2603251061849014e-06
            ],
            [
                2.9023112932177327e-06,
                1.0129995810076682e-05,
                6.475947210046347e-07,
                0.9999955048168181,
                NaN,
                NaN,
                NaN,
                8.939694172867777e-06,
                5.715006514167015e-07,
                2.3823688159237777e-07
            ],
            [
                NaN,
                4.222831934352267e-06,
                6.475949526020042e-07,
                2.2603242978665707e-06,
                8.315284241560147e-07,
                3.4663253846718004e-07,
                3.535624207425073e-05,
                6.9622595696935874e-06,
                1.0677031245905116e-06,
                2.699578096393206e-07
            ],
            [
                1.637377448057981e-07,
                3.726638839806038e-06,
                9.422442569315887e-07,
                1.3709573702722555e-06,
                1.2098653950656417e-06,
                1.7603427936335396e-06,
                4.78509278348926e-06,
                1.1478765389368729e-05,
                3.726641061109272e-06,
                4.785093353940187e-06
            ],
            [
                0.9999995549147891,
                0.9999986290421409,
                0.9999990577557438,
                0.99999926617867,
                0.9999978766220454,
                0.9999975938973774,
                0.9999994956523516,
                0.9999980052707568,
                0.9999984465026175,
                0.9999990577551818
            ],
            [
                8.315277302857965e-07,
                2.382370235922541e-07,
                8.315278294097538e-07,
                8.315279285351409e-07,
                3.4663262110945863e-07,
                2.382370235922541e-07,
                3.9278634073625165e-07,
                5.715003789033962e-07,
                2.699577774560111e-07,
                5.043475885674441e-07
            ],
            [
                1.6373774480535133e-07,
                1.3709576971425944e-06,
                1.9947301970451086e-06,
                2.9023126770343703e-06,
                2.2603242978871282e-06,
                1.3709567165530083e-06,
                3.7266383950934104e-06,
                2.3823690999236795e-07,
                3.288749849477628e-06,
                1.7603434231777837e-06
            ],
            [
                1.994730197090463e-06,
                3.0590226339061185e-07,
                NaN,
                7.338213304283347e-07,
                1.7603436330179102e-06,
                2.2603234895289998e-06,
                9.422448185510695e-07,
                6.144173869446876e-06,
                NaN,
                1.0677032518748838e-06
            ],
            [
                4.450848927650143e-07,
                1.275190124846946e-07,
                9.931187406410953e-08,
                2.2603242978871282e-06,
                1.0677032518748838e-06,
                1.5534983101602148e-06,
                6.825600469412533e-08,
                9.931193325852072e-08,
                2.699578418198104e-07,
                6.023574911170301e-08
            ],
            [
                1.3709570434219446e-06,
                2.3823693839325527e-07,
                9.931202796993203e-08,
                0.9999417087280368,
                1.5534984953510149e-06,
                0.9999822214418247,
                1.1253509497883659e-07,
                NaN,
                1.994729483705484e-06,
                1.8553916819032217e-07
            ],
            [
                1.3709576971425944e-06,
                1.994729483729522e-06,
                8.315278294097538e-07,
                2.90231094723893e-06,
                NaN,
                7.338208055664991e-07,
                3.4663249714612693e-07,
                1.3007133115667397e-05,
                1.8553910183607374e-07,
                4.450851580555361e-07
            ],
            [
                1.275190580890061e-07,
                2.6995790618469934e-07,
                3.120190021657421e-05,
                3.4663249714612693e-07,
                2.2603234895053587e-06,
                0.9999949062962228,
                9.422450432014836e-07,
                2.902311639183378e-06,
                3.9278629391427843e-07,
                1.27519088491875e-07
            ],
            [
                1.553497754577351e-06,
                5.715005151606823e-07,
                7.338211554783522e-07,
                1.8553910183674878e-07,
                0.0010322312193409501,
                NaN,
                7.889266347786918e-06,
                7.338210680002898e-07,
                1.0677028700266676e-06,
                5.043475284430694e-07
            ],
            [
                6.475947210031623e-07,
                NaN,
                5.043475885696228e-07,
                1.5534983101602148e-06,
                1.275190428875671e-07,
                1.8553905760062447e-07,
                1.0677032518814388e-06,
                6.475945666063607e-07,
                6.475949526020042e-07,
                1.2098661161982042e-06
            ],
            [
                0.9999986290421407,
                0.9999993106389548,
                8.315277302841894e-07,
                6.962257909785973e-06,
                0.9999992188516698,
                1.3709567165617364e-06,
                0.9999997761970247,
                2.561281905390075e-06,
                2.1444945858953813e-05,
                0.9999925887174875
            ],
            [
                1.2098659719441482e-06,
                1.0677031245905116e-06,
                3.059022998576899e-07,
                3.0590215399183813e-07,
                1.0677031245905116e-06,
                7.338212429582604e-07,
                1.6373768624837685e-07,
                1.8553916819032217e-07,
                9.422448185478557e-07,
                3.059023727894942e-07
            ],
            [
                3.927863875616689e-07,
                1.8553916819032217e-07,
                2.10243290909724e-07,
                4.4508494582405734e-07,
                1.8553914607267268e-07,
                3.466326624336003e-07,
                5.715003789046955e-07,
                1.855391239544352e-07,
                6.475945666063607e-07,
                1.6373774480605869e-07
            ],
            [
                8.764247451307293e-08,
                2.382368531929327e-07,
                2.5110008886993497e-08,
                NaN,
                4.4508510499849186e-07,
                3.4663278639892215e-07,
                2.5612819054028872e-06,
                6.023576347299818e-08,
                1.275190732904469e-07,
                3.4663249714612693e-07
            ],
            [
                6.825598842065202e-08,
                1.3007125363908762e-05,
                NaN,
                0.9999983463098238,
                NaN,
                0.999989870012674,
                0.9999995262095551,
                0.9999997897565838,
                NaN,
                0.9999945777791021
            ],
            [
                2.699576809143613e-07,
                3.059022269250683e-07,
                NaN,
                5.715005151606823e-07,
                3.0590237279032884e-07,
                6.475945666051092e-07,
                2.10243290909724e-07,
                2.382370235933104e-07,
                2.1024331597262577e-07,
                5.715007195447234e-07
            ],
            [
                1.275190124846946e-07,
                6.023577783447482e-08,
                NaN,
                1.4449805540763184e-07,
                2.10243290909724e-07,
                1.4449795205472734e-07,
                1.275190732904469e-07,
                4.139934586278605e-08,
                1.4449805540763184e-07,
                1.275190428875671e-07
            ],
            [
                8.939694172867777e-06,
                2.5612816000646084e-06,
                6.475950298011458e-07,
                1.5534979397790343e-06,
                2.561282210740037e-06,
                3.2887478892683997e-06,
                1.5534983101602148e-06,
                1.7603425837791042e-06,
                4.450848927658745e-07,
                4.2228334445658276e-06
            ],
            [
                1.2751901248454963e-07,
                1.4449798650551755e-07,
                5.715005151606823e-07,
                1.8553910183674878e-07,
                2.699577774589574e-07,
                5.043475885696228e-07,
                3.466327037553825e-07,
                1.444979692800516e-07,
                2.699578740032504e-07,
                5.715005832886879e-07
            ],
            [
                NaN,
                8.315281267649641e-07,
                5.04347348075149e-07,
                7.338213304363436e-07,
                3.466325797896173e-07,
                7.338207180801359e-07,
                2.382368531929327e-07,
                1.855391681898159e-07,
                1.0677032518785256e-06,
                5.715003107767143e-07
            ],
            [
                1.7603427936263351e-06,
                1.5534975693933505e-06,
                2.5612812947508257e-06,
                1.4449798650569826e-07,
                2.6995784182183607e-07,
                7.338213304363436e-07,
                NaN,
                3.288749457469787e-06,
                6.962254589914941e-06,
                4.785093353787868e-06
            ],
            [
                9.93120161306789e-08,
                4.785096776433933e-06,
                9.422443692446175e-07,
                1.994729008145876e-06,
                1.4449800373065699e-07,
                1.6373774480535133e-07,
                3.927862002641863e-07,
                3.059022998558814e-07,
                4.4508515805199415e-07,
                2.382368815916736e-07
            ],
            [
                1.5534975693933505e-06,
                2.5612831267202583e-06,
                2.2603234895053587e-06,
                1.5534979397740895e-06,
                2.1024329090867228e-07,
                6.144172404218801e-06,
                2.5612812947380135e-06,
                1.9947292459347367e-06,
                2.9023112932177327e-06,
                1.0129993395217047e-05
            ],
            [
                1.1253506814842375e-07,
                1.855391239547094e-07,
                NaN,
                1.6373762769138607e-07,
                NaN,
                2.699578740032504e-07,
                9.931193325852072e-08,
                1.125352291309328e-07,
                2.1444950971601277e-05,
                1.1253520229983549e-07
            ],
            [
                1.5534984953298217e-06,
                9.422443692446175e-07,
                8.93969950132721e-06,
                1.9947297215043796e-06,
                NaN,
                2.5612825160562587e-06,
                2.561282210729555e-06,
                NaN,
                3.726638395634011e-06,
                9.422449308774482e-07
            ],
            [
                NaN,
                1.9947304348703948e-06,
                NaN,
                3.726640616748873e-06,
                1.6701421845361053e-05,
                1.2098662604291696e-06,
                4.222831934202483e-06,
                4.785094494628999e-06,
                NaN,
                5.422220909009474e-06
            ],
            [
                6.475946437996402e-07,
                5.715004470313855e-07,
                9.422442569315887e-07,
                2.69957906184239e-07,
                1.0677029973192638e-06,
                3.927862939126708e-07,
                8.31528126775552e-07,
                2.699578096403948e-07,
                1.7603434231833873e-06,
                2.9023112932177327e-06
            ],
            [
                1.2098652508424818e-06,
                7.338213304363436e-07,
                6.475945666063607e-07,
                7.338208055664991e-07,
                1.5534975693933505e-06,
                1.2098659719757836e-06,
                1.3709573702822306e-06,
                6.475946438055299e-07,
                NaN,
                2.5612812947508257e-06
            ],
            [
                2.699578740032504e-07,
                0.9999990577552943,
                0.9999945777797498,
                0.9999771720110779,
                0.9999967112505466,
                NaN,
                0.9999930377429369,
                0.9999981261243954,
                0.9999962733607244,
                0.9999977396754351
            ],
            [
                7.338209805224048e-07,
                NaN,
                3.927862470899887e-07,
                3.9278634073732336e-07,
                NaN,
                5.4222176771176554e-06,
                8.315281267861397e-07,
                2.2603234895372223e-06,
                1.3709573702822306e-06,
                6.962257079775324e-06
            ],
            [
                2.9023112931873767e-06,
                1.9947299593014888e-06,
                0.9999599363032001,
                1.3709576971425944e-06,
                9.422442569315887e-07,
                3.288749457469787e-06,
                1.5534971990126997e-06,
                1.5534971990126997e-06,
                1.2098652508287273e-06,
                6.144173869558639e-06
            ],
            [
                3.05902336324494e-07,
                3.059021175261338e-07,
                5.04347287955046e-07,
                NaN,
                3.726641061109272e-06,
                3.9278605979534166e-07,
                9.422443692555439e-07,
                8.764242227418718e-08,
                2.3823696679327928e-07,
                7.338211554783522e-07
            ],
            [
                NaN,
                2.2603253756956754e-06,
                2.3823693839325527e-07,
                1.275190124846946e-07,
                9.93120161310289e-08,
                3.05902336324494e-07,
                1.637376862489725e-07,
                1.4449800373118268e-07,
                NaN,
                6.475945666051092e-07
            ],
            [
                3.059022269250683e-07,
                5.043474683204221e-07,
                3.927860597935108e-07,
                1.3709573702778664e-06,
                4.222834451355964e-06,
                6.475949525981759e-07,
                5.043472879540142e-07,
                5.043474683204221e-07,
                3.927863875584984e-07,
                2.26032402841657e-06
            ],
            [
                0.9999986290421415,
                1.1478770862735993e-05,
                0.9999983463096276,
                0.999876605412595,
                0.9999964991439195,
                3.9278615344178325e-07,
                0.9999983463098245,
                0.9999945777791,
                0.999998346310613,
                0.9999964991460121
            ],
            [
                1.209865539295696e-06,
                3.466326211113502e-07,
                4.450848927650143e-07,
                4.450852111148132e-07,
                3.927863875584984e-07,
                3.4663249714612693e-07,
                6.475947210046347e-07,
                5.04347348070562e-07,
                7.338208055664991e-07,
                9.422448185534261e-07
            ],
            [
                1.4449807263312446e-07,
                1.1253512180925583e-07,
                3.120191137659974e-05,
                1.855391239544352e-07,
                4.450852111155216e-07,
                4.785094494811783e-06,
                6.475946438055299e-07,
                6.023579219579052e-08,
                1.6373764721039308e-07,
                9.931186222523604e-08
            ],
            [
                5.043473480777865e-07,
                1.0677027427600627e-06,
                6.475948754012522e-07,
                5.043474081993875e-07,
                0.000123394604405714,
                6.144176066795103e-06,
                2.902310947208574e-06,
                NaN,
                1.0129994602656007e-05,
                2.4300237837960777e-05
            ],
            [
                2.10243290909724e-07,
                NaN,
                1.6373772528704005e-07,
                1.9947299593014888e-06,
                1.8553919030858602e-07,
                1.9947292459347367e-06,
                1.6373776432509826e-07,
                6.475945666051092e-07,
                NaN,
                3.05902190458764e-07
            ],
            [
                2.2603234895372223e-06,
                5.715006514167015e-07,
                1.6373764721072816e-07,
                1.7603425837855082e-06,
                NaN,
                1.27519088491875e-07,
                1.3709567165617364e-06,
                8.315278294097538e-07,
                6.475947210031623e-07,
                7.338210680021253e-07
            ],
            [
                2.3823688159291947e-07,
                6.475946438055299e-07,
                6.475947210031623e-07,
                7.338209805240734e-07,
                2.382369951932796e-07,
                3.0590237279032884e-07,
                5.04347468323289e-07,
                1.1253508156363576e-07,
                6.475945666051092e-07,
                1.6373768624837685e-07
            ],
            [
                5.715005832886879e-07,
                7.338211554783522e-07,
                NaN,
                5.715005151574337e-07,
                5.04347528440776e-07,
                2.2603234895372223e-06,
                6.475946438055299e-07,
                6.475945666051092e-07,
                NaN,
                8.315280276626197e-07
            ],
            [
                3.726637951367137e-06,
                3.059021175247079e-07,
                2.90231233114251e-06,
                6.1441724046434924e-06,
                5.043472278255469e-07,
                2.382368531929327e-07,
                4.785096776468749e-06,
                6.475948754012522e-07,
                3.0590226339061185e-07,
                3.0590237279032884e-07
            ],
            [
                2.1024329090929374e-07,
                2.3823685319244518e-07,
                1.3709578605729614e-06,
                2.382370235933104e-07,
                5.043472879525233e-07,
                3.46632497145457e-07,
                NaN,
                1.3007133116732079e-05,
                NaN,
                4.785095065232451e-06
            ],
            [
                4.4508494582405734e-07,
                3.466327863983311e-07,
                NaN,
                3.9278605979534166e-07,
                1.2098653949842147e-06,
                1.9947304348862686e-06,
                2.2603242978778778e-06,
                2.5612812947508257e-06,
                1.553498495338299e-06,
                5.715003107767143e-07
            ],
            [
                0.9999997126313098,
                1.3709575337078829e-06,
                8.764242227418718e-08,
                0.9999987121043247,
                0.000123394633832426,
                0.9999771720029469,
                5.043472278312808e-07,
                0.9999993106387903,
                NaN,
                0.9999991148428592
            ],
            [
                8.76424013786396e-08,
                9.422444815765128e-07,
                1.7603427936335396e-06,
                1.2751905808881762e-07,
                6.023573475041126e-08,
                1.3709567165386693e-06,
                2.1024331597262577e-07,
                7.338208055613267e-07,
                0.9999892166839442,
                0.99999862904214
            ],
            [
                1.3709573702778664e-06,
                8.939697369671496e-06,
                4.4508494582314646e-07,
                2.260325106237323e-06,
                5.043475885674441e-07,
                8.315278294114555e-07,
                1.0677026154806063e-06,
                7.338212429582604e-07,
                3.466325797896173e-07,
                4.450851580555361e-07
            ],
            [
                1.7603434231777837e-06,
                5.043472879525233e-07,
                6.144176066850984e-06,
                NaN,
                8.939693106873817e-06,
                7.889261645269683e-06,
                2.260325375664839e-06,
                3.726641061085547e-06,
                4.785092783415276e-06,
                NaN
            ],
            [
                1.067703251864202e-06,
                2.5612825160562587e-06,
                NaN,
                1.7603425837855082e-06,
                2.90231094723893e-06,
                3.726637951387472e-06,
                2.9023116391978967e-06,
                NaN,
                1.9947299593014888e-06,
                4.2228339479858295e-06
            ],
            [
                NaN,
                3.466326211113502e-07,
                2.1024336609843824e-07,
                0.9998911030399258,
                8.315279285370317e-07,
                5.715005832886879e-07,
                4.785093924362895e-06,
                7.338212429582604e-07,
                5.043476486915964e-07,
                6.1441746018123775e-06
            ],
            [
                1.8553907971855875e-07,
                3.288750241561788e-06,
                6.825608606148807e-08,
                8.764249540862797e-08,
                1.8553907971855875e-07,
                1.1253521571574156e-07,
                9.931186222523604e-08,
                3.0590215399183813e-07,
                1.27519088491875e-07,
                4.139934092743992e-08
            ],
            [
                0.9999983463096267,
                0.9999980052700422,
                0.9999962733593873,
                1.067702870039777e-06,
                0.9999969105048216,
                0.9999975938965162,
                1.9947299593014888e-06,
                2.902311639183378e-06,
                0.9999955048168182,
                0.9999997463981334
            ],
            [
                9.422449308774482e-07,
                1.855391460719133e-07,
                5.71500515159253e-07,
                3.726639284144195e-06,
                5.715003107767143e-07,
                NaN,
                1.370957860576702e-06,
                1.209865539295696e-06,
                2.2603245673279107e-06,
                1.5534981249697903e-06
            ]
        ]
    },
    {
        "q_id": "9393_mmlu_physics",
        "cot_ids": [
            0,
            1,
            5,
            7,
            8,
            10,
            11,
            12,
            14,
            15,
            16,
            18,
            19,
            20,
            21,
            22,
            24,
            27,
            28,
            29,
            30,
            32,
            33,
            35,
            36,
            37,
            40,
            41,
            42,
            43,
            44,
            48,
            49,
            50,
            51,
            52,
            54,
            55,
            57,
            58,
            59,
            60,
            63,
            64,
            67,
            69,
            70,
            71,
            74,
            75,
            76,
            77,
            78,
            79,
            82,
            83,
            84,
            85,
            86,
            87,
            89,
            90,
            91,
            92,
            93,
            95,
            96,
            97,
            101,
            102,
            103,
            105,
            107,
            108,
            109,
            111,
            112,
            114,
            115,
            116,
            117,
            118,
            121,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                1.27519088491875e-07,
                7.734418542875216e-08,
                1.4449805540740185e-07,
                1.8553916819032217e-07,
                4.450848927637999e-07,
                5.315784971839039e-08,
                1.4449798650476187e-07,
                1.2751901248454963e-07,
                7.734424996967756e-08,
                6.825606165129312e-08
            ],
            [
                1.3709567165617364e-06,
                7.338208930460318e-07,
                2.9023112932177327e-06,
                1.4738978458382043e-05,
                1.1478765389368729e-05,
                3.288748673376478e-06,
                1.9947294837154625e-06,
                1.2098658277489788e-06,
                1.2098659719757836e-06,
                1.4738978458140753e-05
            ],
            [
                1.5534971990169383e-06,
                2.1024334103581732e-07,
                3.927863875616689e-07,
                1.6373766672973748e-07,
                6.475945666063607e-07,
                1.275190124846946e-07,
                8.764245361752286e-08,
                2.2603248367949354e-06,
                1.209865827752005e-06,
                2.2603242978943238e-06
            ],
            [
                1.3709572068522336e-06,
                3.059023727894942e-07,
                6.023576347315567e-08,
                1.5534975693933505e-06,
                0.0,
                NaN,
                NaN,
                9.931199245322124e-08,
                1.0677033791583005e-06,
                1.4449795205472734e-07
            ],
            [
                2.9023112932296107e-06,
                5.715004470334646e-07,
                NaN,
                8.315277302857965e-07,
                1.2098661162056318e-06,
                9.422449308789479e-07,
                2.1024326584702836e-07,
                8.315283250394546e-07,
                6.47594952603035e-07,
                5.043474082012222e-07
            ],
            [
                8.315277302788957e-07,
                8.315280276546789e-07,
                4.222834451382849e-06,
                1.7603430034743913e-06,
                1.2098661162023305e-06,
                1.3709573702822306e-06,
                7.338207180864763e-07,
                1.5534984953298217e-06,
                6.475951069985296e-07,
                9.422448185510695e-07
            ],
            [
                3.288747889229516e-06,
                1.7603440527286572e-06,
                1.7603438428800754e-06,
                NaN,
                4.222834451382849e-06,
                4.222834954778007e-06,
                5.422219616140078e-06,
                5.715003789046955e-07,
                1.209865539295696e-06,
                2.5612819054028872e-06
            ],
            [
                3.9278610661822475e-07,
                6.475948753930064e-07,
                5.043473480766399e-07,
                5.043475284430694e-07,
                1.5534973842030142e-06,
                3.46632497145457e-07,
                3.9278634073625165e-07,
                3.466325797888292e-07,
                1.8553910183607374e-07,
                4.450850519403407e-07
            ],
            [
                NaN,
                8.764241182641775e-08,
                5.315787506598473e-08,
                7.734418542875216e-08,
                4.139934586278605e-08,
                6.023571320847322e-08,
                2.1024334103581732e-07,
                4.139939521459479e-08,
                5.315784971839039e-08,
                1.4449805540763184e-07
            ],
            [
                5.715007195447234e-07,
                6.475947210031623e-07,
                4.450848927658745e-07,
                9.422442569315887e-07,
                1.0677032518748838e-06,
                3.927862470899887e-07,
                1.5534981249697903e-06,
                1.5534979397677313e-06,
                NaN,
                5.715003107767143e-07
            ],
            [
                2.6995784182140636e-07,
                5.715002426475718e-07,
                6.475947210031623e-07,
                2.3823702359290413e-07,
                4.450852111148132e-07,
                1.5534971990126997e-06,
                2.1024336609843824e-07,
                1.0677027427624903e-06,
                3.9278605979534166e-07,
                2.6995771309523475e-07
            ],
            [
                4.691161005609407e-08,
                6.825609419848033e-08,
                2.8453367631661124e-08,
                3.22418970812682e-08,
                2.5110011880337063e-08,
                3.6534807736504303e-08,
                7.734428685047173e-08,
                2.5109981946866052e-08,
                1.1253508156363576e-07,
                8.76424013786396e-08
            ],
            [
                2.2603234895289998e-06,
                3.2887482813149375e-06,
                1.3709567165579959e-06,
                6.475951069985296e-07,
                9.422447062202052e-07,
                9.422448185478557e-07,
                7.889266347715168e-06,
                3.4663278639738526e-07,
                1.0677032518748838e-06,
                6.475949525981759e-07
            ],
            [
                3.059022998576899e-07,
                7.338207180864763e-07,
                2.561281294760143e-06,
                3.466327037548308e-07,
                7.338210680021253e-07,
                4.450850519403407e-07,
                6.475950297942253e-07,
                NaN,
                2.2603234895372223e-06,
                1.209865539295696e-06
            ],
            [
                6.023572038912295e-08,
                9.93120161310289e-08,
                8.764247451307293e-08,
                2.1024334103581732e-07,
                NaN,
                3.653481209178873e-08,
                8.764247451307293e-08,
                2.8453364239757298e-08,
                8.7642516304188e-08,
                1.4449805540740185e-07
            ],
            [
                7.734414854823498e-08,
                NaN,
                6.47594875403829e-07,
                3.9278629391427843e-07,
                9.422443692574719e-07,
                9.422450432030903e-07,
                5.043474683240344e-07,
                3.466326624336003e-07,
                4.785093353940187e-06,
                8.315284241665078e-07
            ],
            [
                3.927860597945825e-07,
                3.05902263391829e-07,
                9.422442569334097e-07,
                1.8553910183607374e-07,
                6.475947982037486e-07,
                8.764247451307293e-08,
                2.561282210740037e-06,
                1.855391239544352e-07,
                1.6373774480605869e-07,
                3.4663253846718004e-07
            ],
            [
                6.023569166654288e-08,
                5.315784971839039e-08,
                4.139936066832438e-08,
                6.825602910433871e-08,
                9.931186222523604e-08,
                8.7642516304188e-08,
                6.023572038912295e-08,
                6.023568448589658e-08,
                1.1253516205489029e-07,
                5.315786239218605e-08
            ],
            [
                NaN,
                NaN,
                1.209865827752005e-06,
                5.043472278322555e-07,
                5.715006514176113e-07,
                1.8553916819032217e-07,
                5.043474081993875e-07,
                2.382370235933104e-07,
                1.6373776432509826e-07,
                1.6373776432509826e-07
            ],
            [
                7.338208930391909e-07,
                1.5534981249496567e-06,
                2.69957906184239e-07,
                1.2098661161927025e-06,
                1.99472900813862e-06,
                1.012999581021488e-05,
                1.2098662604291696e-06,
                1.0677026154730804e-06,
                3.288748281295496e-06,
                1.3007123813382511e-05
            ],
            [
                9.422443692555439e-07,
                1.2098655392811161e-06,
                2.260323489490968e-06,
                2.2603245673279107e-06,
                2.9023130230846496e-06,
                1.0677032518700286e-06,
                2.2603242978871282e-06,
                1.0677031245905116e-06,
                9.422442569290178e-07,
                1.2098661161927025e-06
            ],
            [
                6.023576347299818e-08,
                1.8553910183674878e-07,
                8.7642516304188e-08,
                2.3823693839290317e-07,
                5.715003107767143e-07,
                1.1253525596134564e-07,
                1.275190732904469e-07,
                7.734414854823498e-08,
                1.2751899728286965e-07,
                7.734421308914719e-08
            ],
            [
                8.31527928532683e-07,
                3.466327037539638e-07,
                7.338209805240734e-07,
                4.450849988811838e-07,
                6.475945666051092e-07,
                7.338213304283347e-07,
                5.715003789033962e-07,
                8.315277302841894e-07,
                9.422443692446175e-07,
                8.315277302788957e-07
            ],
            [
                1.994729483729522e-06,
                1.8925148242250705e-05,
                6.962257909842961e-06,
                2.75356812556058e-05,
                5.422220262636381e-06,
                9.422449308774482e-07,
                1.9947301970972664e-06,
                4.785092783519724e-06,
                8.939694172957213e-06,
                3.2887482813149375e-06
            ],
            [
                1.3709568799919866e-06,
                1.7603427936335396e-06,
                1.4449798650476187e-07,
                1.444980209564556e-07,
                4.450852641737424e-07,
                1.4449800373065699e-07,
                2.3823693839290317e-07,
                5.043472879540142e-07,
                8.315282259138311e-07,
                4.450851580555361e-07
            ],
            [
                5.043472278227948e-07,
                5.715006514105942e-07,
                5.043472879540142e-07,
                5.04347528446051e-07,
                7.338209805170655e-07,
                7.338208055664991e-07,
                4.450849988798682e-07,
                6.475946438022905e-07,
                3.9278624708775595e-07,
                1.3709572068522336e-06
            ],
            [
                1.2098656835224664e-06,
                5.715003789046955e-07,
                2.102434162245973e-07,
                2.6995774527718623e-07,
                2.3823690999323465e-07,
                5.715005832886879e-07,
                4.450852641737424e-07,
                1.4449805540700758e-07,
                1.4449807263312446e-07,
                2.102434162245973e-07
            ],
            [
                1.0677024881980089e-06,
                1.9947299592933255e-06,
                2.2603240283888175e-06,
                3.288749849477628e-06,
                1.2098652508347793e-06,
                8.315284241560147e-07,
                7.338212429537553e-07,
                7.338207180864763e-07,
                2.2603237589676295e-06,
                7.338209805170655e-07
            ],
            [
                1.1253509497883659e-07,
                3.05902226923399e-07,
                1.89251527534122e-05,
                1.0677026154774503e-06,
                3.4663278639892215e-07,
                6.475946438022905e-07,
                7.73441946488886e-08,
                2.699576809143613e-07,
                7.338207180864763e-07,
                3.0590226339061185e-07
            ],
            [
                9.931193325852072e-08,
                1.1253513522447425e-07,
                1.275190428875671e-07,
                1.6373768624837685e-07,
                1.2751901248454963e-07,
                9.93120161310289e-08,
                2.102434412875379e-07,
                2.699577452775239e-07,
                1.4449796928021588e-07,
                1.6373770576776313e-07
            ],
            [
                2.902312677137316e-06,
                9.422445939002803e-07,
                1.89251527534122e-05,
                4.539789029616496e-05,
                4.222835458117536e-06,
                6.144173137126169e-06,
                2.561281600049467e-06,
                4.539787406217992e-05,
                3.726641061085547e-06,
                2.9023119851635836e-06
            ],
            [
                9.931192141912081e-08,
                5.715005151606823e-07,
                2.6995774527718623e-07,
                1.855391239547094e-07,
                7.734424996967756e-08,
                6.023571320847322e-08,
                1.8553919030858602e-07,
                1.2751902768612997e-07,
                1.4449805540740185e-07,
                3.9278610661902853e-07
            ],
            [
                5.043475885674441e-07,
                3.927862002641863e-07,
                4.450852111148132e-07,
                5.04347528446051e-07,
                6.475948754012522e-07,
                3.466327037548308e-07,
                3.9278634073625165e-07,
                6.475948754012522e-07,
                5.71500651413193e-07,
                6.475948754012522e-07
            ],
            [
                NaN,
                8.31528325040778e-07,
                3.4663278639892215e-07,
                2.3823690999323465e-07,
                9.93120161310289e-08,
                1.855391239547094e-07,
                NaN,
                3.059021175261338e-07,
                1.855391239544352e-07,
                6.825609419848033e-08
            ],
            [
                1.8553905760062447e-07,
                6.475946438055299e-07,
                1.8553905760062447e-07,
                1.275191036933194e-07,
                5.715003107767143e-07,
                3.059022998581767e-07,
                5.715003107767143e-07,
                3.4663278639892215e-07,
                1.444980209564556e-07,
                1.275190276859705e-07
            ],
            [
                5.715005832886879e-07,
                3.927862002663297e-07,
                2.1024339116134898e-07,
                1.3709576971463352e-06,
                1.209865539295696e-06,
                3.288749457469787e-06,
                3.2887506336235617e-06,
                9.422444815814404e-07,
                9.422443692555439e-07,
                9.422449308774482e-07
            ],
            [
                1.1253508156363576e-07,
                1.1253514863909295e-07,
                1.1253512180925583e-07,
                1.6373766672973748e-07,
                9.931200429212718e-08,
                1.8553919030776337e-07,
                6.825604537781398e-08,
                3.466327037553825e-07,
                6.825602910433871e-08,
                1.2751902768478173e-07
            ],
            [
                3.059021904571643e-07,
                2.561281600076256e-06,
                2.1024334103352274e-07,
                1.0677024881980089e-06,
                3.059023727894942e-07,
                5.043475885674441e-07,
                3.466327863945479e-07,
                3.4663270375278157e-07,
                3.466326624322211e-07,
                5.71500515159253e-07
            ],
            [
                3.9278629391427843e-07,
                7.338207180898968e-07,
                NaN,
                1.4449798650569826e-07,
                2.3823693839325527e-07,
                NaN,
                NaN,
                1.637376862489725e-07,
                2.102434162245973e-07,
                3.466326624336003e-07
            ],
            [
                4.222833444590791e-06,
                9.422443692555439e-07,
                5.715003107755449e-07,
                1.553498124964492e-06,
                2.6995784182140636e-07,
                7.338207180864763e-07,
                4.450849988811838e-07,
                4.222831934352267e-06,
                1.0677033791583005e-06,
                6.475947210031623e-07
            ],
            [
                1.1253525596174225e-07,
                7.734415776836702e-08,
                1.4449807263312446e-07,
                8.764242227418718e-08,
                1.4449798650551755e-07,
                7.734428685047173e-08,
                6.023577783447482e-08,
                2.1024334103581732e-07,
                6.023579219579052e-08,
                6.023568448589658e-08
            ],
            [
                8.764245361752286e-08,
                7.734423152941018e-08,
                3.22418970812682e-08,
                6.023571320847322e-08,
                6.82560779249779e-08,
                9.931186222523604e-08,
                1.8553903548231313e-07,
                5.315786239218605e-08,
                9.93120161310289e-08,
                4.139935079796334e-08
            ],
            [
                NaN,
                1.0677031245990084e-06,
                7.338213304363436e-07,
                1.7603436330259153e-06,
                1.9947299592933255e-06,
                7.338213304363436e-07,
                2.2603245673155757e-06,
                3.535626336072768e-05,
                4.785093924362895e-06,
                4.222831934352267e-06
            ],
            [
                1.6373772528704005e-07,
                2.699578740032504e-07,
                2.382369383923073e-07,
                8.315280276626197e-07,
                NaN,
                1.0677027427624903e-06,
                8.315282259138311e-07,
                4.450848927650143e-07,
                2.382370235933104e-07,
                2.2603234895372223e-06
            ],
            [
                2.3823685319244518e-07,
                2.1024336609843824e-07,
                2.69957906184239e-07,
                2.6995784182140636e-07,
                7.338208930460318e-07,
                9.422444815814404e-07,
                3.0590237279085045e-07,
                8.764247451307293e-08,
                2.69957906184239e-07,
                3.4663253846718004e-07
            ],
            [
                6.475947209985977e-07,
                4.450852641656969e-07,
                5.043476486915964e-07,
                8.315278294001114e-07,
                5.715002426460124e-07,
                1.7603436329978976e-06,
                5.71500651413193e-07,
                5.043474081993875e-07,
                2.382369667929001e-07,
                5.715004470295662e-07
            ],
            [
                4.222834451403972e-06,
                1.7603425837903113e-06,
                3.2887506336235617e-06,
                2.1444940746307572e-05,
                8.939694172957213e-06,
                2.902313023130843e-06,
                3.927863875616689e-07,
                1.994729721518893e-06,
                3.288749849529972e-06,
                3.4663262110945863e-07
            ],
            [
                5.715003789017068e-07,
                8.315280275900177e-07,
                5.715006514105942e-07,
                9.422445938861406e-07,
                5.04347348075149e-07,
                8.315278293899016e-07,
                2.2603237589542675e-06,
                8.31527928532683e-07,
                4.222833947960866e-06,
                9.422450431860582e-07
            ],
            [
                4.450852111135988e-07,
                1.0677028700422047e-06,
                1.670142781709299e-05,
                9.422443692555439e-07,
                1.3709570434219446e-06,
                2.1024334103505245e-07,
                4.450852111148132e-07,
                8.315277302841894e-07,
                6.475947210046347e-07,
                8.315281267861397e-07
            ],
            [
                2.3823693839325527e-07,
                8.764254764780641e-08,
                8.764245361752286e-08,
                1.444980209564556e-07,
                1.1253517547010071e-07,
                1.1253526937697666e-07,
                8.764242227418718e-08,
                7.734416698815724e-08,
                5.315780536011123e-08,
                7.734424996967756e-08
            ],
            [
                8.7642516304188e-08,
                1.5534977545886537e-06,
                1.4449798650551755e-07,
                1.855391239544352e-07,
                9.422447062270609e-07,
                1.275190428875671e-07,
                NaN,
                3.466326624336003e-07,
                3.4663249714451116e-07,
                9.931186222523604e-08
            ],
            [
                4.450849458218309e-07,
                7.338213304316717e-07,
                4.450849988758202e-07,
                1.0677032518700286e-06,
                6.475948753930064e-07,
                9.422448185435711e-07,
                4.450849458218309e-07,
                NaN,
                5.043475284430694e-07,
                7.338209805200689e-07
            ],
            [
                0.9999964991451783,
                0.9999969105066602,
                7.338207180898968e-07,
                0.9999970976866339,
                0.9999942280786074,
                0.9999741325633377,
                0.9999934595612334,
                1.9947304348862686e-06,
                2.6995771309523475e-07,
                0.9999964991455909
            ],
            [
                1.2098653950656417e-06,
                8.315279285351409e-07,
                1.0677029973056687e-06,
                1.2098661162056318e-06,
                3.7266383956509585e-06,
                1.2098659719788098e-06,
                2.3823702359290413e-07,
                NaN,
                1.0677027427624903e-06,
                2.561282210729555e-06
            ],
            [
                8.764244316933122e-08,
                8.764244316973974e-08,
                7.734418542875216e-08,
                1.6373762769138607e-07,
                1.855391681898159e-07,
                2.382368531929327e-07,
                1.1253516205489029e-07,
                3.288750241473551e-06,
                1.855391681906175e-07,
                7.338208055664991e-07
            ],
            [
                1.0677027427600627e-06,
                4.450852111148132e-07,
                3.4663249714325014e-07,
                9.931195693628605e-08,
                1.067702870039777e-06,
                9.422442569290178e-07,
                1.3709576971425944e-06,
                1.855391239544352e-07,
                3.0590226339061185e-07,
                8.315277302788957e-07
            ],
            [
                0.9999972735307097,
                2.4300237837960777e-05,
                3.288750241561788e-06,
                3.726637951367137e-06,
                4.785096776468749e-06,
                2.5612831267202583e-06,
                1.9947304348703948e-06,
                2.9023119851781017e-06,
                1.5534984953453635e-06,
                7.338211554783522e-07
            ],
            [
                2.1024334103505245e-07,
                1.4449805540740185e-07,
                6.825598028364134e-08,
                2.1024341622426268e-07,
                1.637377448057981e-07,
                4.4508515805199415e-07,
                1.6373766672888118e-07,
                3.927862002625787e-07,
                2.3823690999160957e-07,
                1.6373768624837685e-07
            ],
            [
                5.71500515161527e-07,
                3.46632497145457e-07,
                2.3823688159291947e-07,
                2.5612819054133693e-06,
                1.8553907971758842e-07,
                7.338212429582604e-07,
                2.699576809143613e-07,
                2.3823693839290317e-07,
                3.059022998581767e-07,
                1.5534973842076057e-06
            ],
            [
                3.059022998569248e-07,
                8.315282259117513e-07,
                2.6995774527657245e-07,
                5.422220262636381e-06,
                1.9947292459347367e-06,
                8.31527928532683e-07,
                5.043476486915964e-07,
                1.7603438428740716e-06,
                8.315283250371857e-07,
                1.9947297215125433e-06
            ],
            [
                4.222835458175145e-06,
                1.7603427936335396e-06,
                2.9023109472244114e-06,
                7.338213304316717e-07,
                1.3007130015488633e-05,
                3.7266406168624155e-06,
                2.1444943301674863e-05,
                5.71500719545698e-07,
                7.889259763469998e-06,
                2.902312677150514e-06
            ],
            [
                4.450849458200093e-07,
                1.1253525596174225e-07,
                1.7603440527286572e-06,
                1.0677031245990084e-06,
                1.4449805540740185e-07,
                7.338210680002898e-07,
                5.715003107655392e-07,
                9.422447062270609e-07,
                4.450850519403407e-07,
                6.475947982022763e-07
            ],
            [
                2.2603245673443566e-06,
                1.0677026154827912e-06,
                8.315278294114555e-07,
                3.7266379514061143e-06,
                7.33821330437595e-07,
                1.4449807263312446e-07,
                3.466326624336003e-07,
                2.3823682479292225e-07,
                NaN,
                2.1024331597262577e-07
            ],
            [
                1.0677028700422047e-06,
                3.2887506336235617e-06,
                2.2603253756956754e-06,
                1.6701423836262173e-05,
                2.144495608424996e-05,
                2.2603242978871282e-06,
                0.9999964991447541,
                5.422218969769604e-06,
                NaN,
                8.315283250371857e-07
            ],
            [
                4.2228319344021954e-06,
                5.715005832886879e-07,
                3.0590226339061185e-07,
                1.0677032518748838e-06,
                1.9947292459347367e-06,
                1.9947299593078385e-06,
                6.475947982037486e-07,
                1.994730197090463e-06,
                2.6995771309523475e-07,
                1.209865539295696e-06
            ],
            [
                5.715003789033962e-07,
                3.7266410611296085e-06,
                1.5534983101549167e-06,
                5.043474082005342e-07,
                2.5612819054028872e-06,
                2.430024652854702e-05,
                5.71500378896509e-07,
                3.0590237279032884e-07,
                4.222834954801051e-06,
                8.315281267861397e-07
            ],
            [
                1.4449802095666915e-07,
                5.043472278322555e-07,
                2.6995784182140636e-07,
                1.9947294837154625e-06,
                4.450852641737424e-07,
                6.023571320847322e-08,
                8.764245361752286e-08,
                1.1253516205489029e-07,
                1.6373766672994222e-07,
                1.855391681906175e-07
            ],
            [
                1.9947299593014888e-06,
                7.889261645427538e-06,
                4.222831934379152e-06,
                7.338209805200689e-07,
                1.5534975693869924e-06,
                4.4508515805199415e-07,
                4.4508505193791187e-07,
                4.222832941142044e-06,
                NaN,
                6.475947982037486e-07
            ],
            [
                1.3709572068522336e-06,
                7.338208055664991e-07,
                1.3709567165617364e-06,
                3.288748281329893e-06,
                1.2098659719788098e-06,
                1.3709573702822306e-06,
                1.0677032518814388e-06,
                1.5534981249697903e-06,
                8.315281267861397e-07,
                1.209866260432471e-06
            ],
            [
                3.059022998576899e-07,
                8.315283250394546e-07,
                9.422445939054222e-07,
                2.102434412875379e-07,
                3.9278634073732336e-07,
                1.7603430034867993e-06,
                3.059021175261338e-07,
                2.699578740032504e-07,
                3.4663249714451116e-07,
                3.4663249714451116e-07
            ],
            [
                3.927861066170637e-07,
                2.6995771309523475e-07,
                1.0129995810463632e-05,
                3.9278605979534166e-07,
                3.4663274507713016e-07,
                3.7266406168827523e-06,
                5.422217030781934e-06,
                9.422448185534261e-07,
                1.5534975693979422e-06,
                7.338212429582604e-07
            ],
            [
                6.47594952603035e-07,
                2.699578096403948e-07,
                8.764245361752286e-08,
                9.931193325852072e-08,
                1.27519088491875e-07,
                1.8553905760062447e-07,
                1.275190732904469e-07,
                1.6373766672973748e-07,
                1.5534975693979422e-06,
                1.2751901248454963e-07
            ],
            [
                1.1253521571574156e-07,
                1.1253513522447425e-07,
                1.2751902768612997e-07,
                NaN,
                8.76424013786396e-08,
                3.2241847115356483e-08,
                9.931186222523604e-08,
                5.315784971839039e-08,
                6.825602910433871e-08,
                6.023573475041126e-08
            ],
            [
                2.1024341622426268e-07,
                1.8553910183607374e-07,
                1.2751899728311609e-07,
                8.7642516304188e-08,
                2.3823696679327928e-07,
                3.4663278639892215e-07,
                1.444979692800516e-07,
                NaN,
                2.699576809143613e-07,
                1.6373766672973748e-07
            ],
            [
                3.0590215399183813e-07,
                5.043476486915964e-07,
                2.382370235922541e-07,
                3.466324971415162e-07,
                5.715004470313855e-07,
                1.8553905759969634e-07,
                3.059022998581767e-07,
                4.450848927650143e-07,
                1.855391681906175e-07,
                4.450852111155216e-07
            ],
            [
                6.475947210031623e-07,
                5.715005832886879e-07,
                1.125352291309328e-07,
                5.043473480777865e-07,
                1.444979692800516e-07,
                2.3823690999290963e-07,
                1.3709572068522336e-06,
                1.6373770576776313e-07,
                2.6995774527718623e-07,
                1.2751904288710323e-07
            ],
            [
                6.475948754012522e-07,
                NaN,
                2.3823699519035448e-07,
                2.6995780963428734e-07,
                6.475946438022905e-07,
                3.466327863961242e-07,
                NaN,
                4.450849988811838e-07,
                2.1024331597152624e-07,
                5.715003789017068e-07
            ],
            [
                1.4449805540651476e-07,
                3.0590226339061185e-07,
                NaN,
                1.1253508156363576e-07,
                1.7603438428848787e-06,
                7.734421308914719e-08,
                9.931200429212718e-08,
                1.4449807263312446e-07,
                1.1253512180925583e-07,
                1.444979692797559e-07
            ],
            [
                3.927862002663297e-07,
                9.422450431989127e-07,
                3.466326211113502e-07,
                2.26032402841657e-06,
                1.9947306726594253e-06,
                7.338208930460318e-07,
                NaN,
                8.315278294114555e-07,
                3.059022998581767e-07,
                4.785093924251918e-06
            ],
            [
                1.3709578605617394e-06,
                6.144172404693786e-06,
                7.338212429504183e-07,
                1.3709567165579959e-06,
                2.9023116391477434e-06,
                1.2098661161927025e-06,
                5.043475284350422e-07,
                1.9947294837154625e-06,
                6.962257909785973e-06,
                1.3007133116542802e-05
            ],
            [
                7.889266347786918e-06,
                1.012999581057419e-05,
                6.475947982022763e-07,
                1.3709572068522336e-06,
                3.2887498495150166e-06,
                1.7603434231833873e-06,
                3.288749849529972e-06,
                3.0590226339061185e-07,
                1.7603425837855082e-06,
                1.994729483723626e-06
            ],
            [
                3.535623807260338e-05,
                5.422217030747413e-06,
                4.785092783519724e-06,
                3.2887506335906595e-06,
                2.561283432035425e-06,
                2.2603234895289998e-06,
                3.927862470899887e-07,
                7.889261645427538e-06,
                1.6701427818034747e-05,
                4.222831934379152e-06
            ],
            [
                NaN,
                3.0590219045914655e-07,
                2.3823682479317953e-07,
                1.5534984953453635e-06,
                4.450851049991497e-07,
                5.715004470334646e-07,
                5.715004470334646e-07,
                2.1024334103581732e-07,
                5.715004470334646e-07,
                2.699577452775239e-07
            ],
            [
                1.8925145985895816e-05,
                1.5534983101393749e-06,
                0.18242552380635635,
                3.7266383956509585e-06,
                5.422217677152175e-06,
                3.726638395634011e-06,
                5.043473480777865e-07,
                0.9999949062950009,
                9.422449308716635e-07,
                8.31528325040778e-07
            ],
            [
                8.315281267861397e-07,
                9.610243790717279e-05,
                2.561282516066741e-06,
                4.785096776468749e-06,
                2.2603234895176927e-06,
                NaN,
                NaN,
                6.475947982022763e-07,
                5.715007195431641e-07,
                9.422444815765128e-07
            ],
            [
                NaN,
                1.209865827752005e-06,
                2.9023116392097746e-06,
                2.561282210740037e-06,
                1.3007128465151102e-05,
                7.338207180898968e-07,
                1.3007123813559956e-05,
                3.72663883989755e-06,
                2.2603248367949354e-06,
                4.222834954801051e-06
            ],
            [
                7.889264466868659e-06,
                6.023571320847322e-08,
                5.043474683240344e-07,
                1.6373762769187936e-07,
                9.931187406410953e-08,
                1.3709575337159875e-06,
                1.27519088491875e-07,
                3.466325797900508e-07,
                2.699578096403948e-07,
                2.102434162245973e-07
            ],
            [
                7.33821330437595e-07,
                6.47595107001401e-07,
                1.0677024882029858e-06,
                9.422443692574719e-07,
                5.715005832895975e-07,
                1.994729008151319e-06,
                7.338207180898968e-07,
                4.4508515805735777e-07,
                4.450850519409479e-07,
                7.338212429594283e-07
            ]
        ]
    },
    {
        "q_id": "10289_mmlu_physics",
        "cot_ids": [
            0,
            1,
            2,
            3,
            4,
            5,
            6,
            7,
            8,
            9,
            10,
            11,
            12,
            13,
            14,
            15,
            17,
            19,
            20,
            21,
            22,
            23,
            24,
            25,
            26,
            27,
            28,
            29,
            30,
            32,
            33,
            34,
            35,
            36,
            37,
            38,
            39,
            40,
            41,
            42,
            43,
            44,
            45,
            46,
            47,
            48,
            49,
            50,
            51,
            52,
            53,
            54,
            55,
            56,
            57,
            58,
            59,
            60,
            61,
            62,
            63,
            64,
            65,
            66,
            67,
            68,
            69,
            70,
            71,
            72,
            73,
            74,
            75,
            76,
            77,
            78,
            79,
            80,
            81,
            82,
            83,
            84,
            85,
            86,
            87,
            88,
            89,
            90,
            91,
            92,
            93,
            94,
            95,
            96,
            97,
            98,
            99,
            100,
            101,
            102,
            103,
            104,
            105,
            106,
            107,
            108,
            109,
            110,
            111,
            112,
            113,
            114,
            115,
            116,
            117,
            118,
            119,
            121,
            122,
            123,
            124,
            125,
            126,
            127
        ],
        "rewards": [
            [
                NaN,
                0.9999921107346011,
                0.9999934595627804,
                0.9998415638460051,
                0.9999945777790966,
                0.9999978766215392,
                0.9999980052702804,
                6.825597214718257e-08,
                0.999990483743781,
                0.9999810748540496
            ],
            [
                7.338212429582604e-07,
                6.475945666051092e-07,
                9.422447062294175e-07,
                3.0590215399183813e-07,
                2.382369951932796e-07,
                3.9278605979534166e-07,
                8.315277302857965e-07,
                1.0129993395336818e-05,
                1.209866260432471e-06,
                7.338213304363436e-07
            ],
            [
                3.927863875616689e-07,
                3.466327037553825e-07,
                5.715002426486762e-07,
                6.475947982037486e-07,
                4.450852641737424e-07,
                9.422443692574719e-07,
                NaN,
                1.370957860576702e-06,
                6.475947982037486e-07,
                2.382370235933104e-07
            ],
            [
                0.9999724643024115,
                6.144173137126169e-06,
                1.994730197090463e-06,
                1.7603427936263351e-06,
                4.450850519403407e-07,
                1.7603434231833873e-06,
                2.430025232128576e-05,
                1.994729483723626e-06,
                2.9023112932177327e-06,
                0.9999925887227926
            ],
            [
                2.382370235933104e-07,
                8.315283250343497e-07,
                6.475949526020042e-07,
                6.962255419804982e-06,
                2.5612834317908303e-06,
                5.422219616140078e-06,
                7.88926446679691e-06,
                1.855391239544352e-07,
                1.9947299592570416e-06,
                1.275190428875671e-07
            ],
            [
                0.9999898700078323,
                0.9999934595612212,
                2.2603237589676295e-06,
                2.9023133690980155e-06,
                1.3709576971425944e-06,
                0.9999861539987764,
                0.9999987901347498,
                1.2098656835224664e-06,
                1.0677029973219343e-06,
                0.9999962733589413
            ],
            [
                2.1024334103505245e-07,
                2.3823690999290963e-07,
                3.0590237279032884e-07,
                3.466327037548308e-07,
                2.3823682479181176e-07,
                1.1253516205489029e-07,
                3.927862002641863e-07,
                4.450852641737424e-07,
                1.8553919030858602e-07,
                1.6373774480605869e-07
            ],
            [
                6.962253760024999e-06,
                4.2228329411708495e-06,
                8.315281267882195e-07,
                2.5612831267202583e-06,
                8.315279285370317e-07,
                7.889263526345123e-06,
                1.7603434231833873e-06,
                4.22283545819819e-06,
                1.0677032518814388e-06,
                3.466326211113502e-07
            ],
            [
                3.059022998576899e-07,
                3.927860597945825e-07,
                8.481103129578775e-05,
                5.715003107767143e-07,
                3.466326624336003e-07,
                3.927860597945825e-07,
                NaN,
                0.9999417087069233,
                0.9999904837471952,
                4.22283545819819e-06
            ],
            [
                1.067702870039777e-06,
                1.30071315662049e-05,
                9.422443692527585e-07,
                8.939694172957213e-06,
                4.222834451382849e-06,
                3.120191881321371e-05,
                1.3709576971463352e-06,
                NaN,
                2.561281600086738e-06,
                1.2098659719757836e-06
            ],
            [
                3.288747889284851e-06,
                NaN,
                7.338210680021253e-07,
                2.9023119851781017e-06,
                NaN,
                7.338208930460318e-07,
                0.0,
                3.7266401726359486e-06,
                1.0129992187658463e-05,
                1.012999218776902e-05
            ],
            [
                0.9999898700078186,
                0.9999832985721976,
                0.9999485578049455,
                0.9999916019249692,
                NaN,
                0.999977172000163,
                0.9999852610162828,
                0.999860177910232,
                0.9999646437620147,
                0.00020342697374003694
            ],
            [
                2.561283432035425e-06,
                3.2887506335906595e-06,
                2.2603234895053587e-06,
                1.0677031245990084e-06,
                1.5534971990126997e-06,
                1.0677024881980089e-06,
                6.475947209985977e-07,
                1.7603436330259153e-06,
                1.0677029973192638e-06,
                3.927862002663297e-07
            ],
            [
                6.475949526020042e-07,
                6.475947210031623e-07,
                2.2603253756956754e-06,
                8.764241182641775e-08,
                1.0677032518814388e-06,
                6.475947982037486e-07,
                5.04347528446051e-07,
                9.422444815792981e-07,
                9.422445939032799e-07,
                2.6995784182140636e-07
            ],
            [
                2.753568453712307e-05,
                8.481105151274973e-05,
                1.4738983729294318e-05,
                1.0677032518814388e-06,
                NaN,
                8.939694172957213e-06,
                3.2887478892683997e-06,
                2.144494841482881e-05,
                5.1442201405453086e-05,
                2.5612831267202583e-06
            ],
            [
                1.8925150497435443e-05,
                3.726639284144195e-06,
                7.889261645427538e-06,
                3.2887482813149375e-06,
                2.9023133690637e-06,
                2.7535694384882703e-05,
                1.8925143729575624e-05,
                3.726638395611981e-06,
                1.670141786295194e-05,
                6.962256249885085e-06
            ],
            [
                1.9947292459347367e-06,
                1.3709567165579959e-06,
                2.1444943302181958e-05,
                3.466325797896173e-07,
                1.0677027427600627e-06,
                5.715007195431641e-07,
                1.0677029973219343e-06,
                3.120191881525687e-05,
                5.043476486924565e-07,
                2.561282210740037e-06
            ],
            [
                7.338209805240734e-07,
                1.0677032518814388e-06,
                2.5612819054133693e-06,
                2.5612819054133693e-06,
                2.699578740032504e-07,
                1.1253526937697666e-07,
                1.855391239547094e-07,
                9.422445938964242e-07,
                1.3007123813382511e-05,
                3.2887478892683997e-06
            ],
            [
                8.315282259089153e-07,
                3.288749065423109e-06,
                7.889263526266196e-06,
                7.338209805200689e-07,
                1.6701421845057263e-05,
                3.927862939126708e-07,
                1.7603438428740716e-06,
                7.484623620850474e-05,
                1.7603434231777837e-06,
                0.9999898700126605
            ],
            [
                1.067703124601679e-06,
                4.22283545819819e-06,
                1.067703124601679e-06,
                5.422220262636381e-06,
                1.9947304348862686e-06,
                7.338209805240734e-07,
                3.4663274507713016e-07,
                5.043473480777865e-07,
                2.2603253756956754e-06,
                2.3823688159291947e-07
            ],
            [
                1.0677033791583005e-06,
                0.9999785550413824,
                0.999998996985912,
                2.5612816000646084e-06,
                0.9998204719720346,
                9.422448185534261e-07,
                3.12019039369228e-05,
                9.422449308716635e-07,
                0.9999904837494537,
                0.9999910603005085
            ],
            [
                5.715003107755449e-07,
                1.7603434231777837e-06,
                9.422443692527585e-07,
                8.315279285370317e-07,
                NaN,
                7.338208055664991e-07,
                6.144174601991196e-06,
                1.9947301970972664e-06,
                1.209865539295696e-06,
                2.902311639183378e-06
            ],
            [
                0.999994577779096,
                0.9999981261237243,
                0.9999832985741941,
                0.999993855823938,
                0.999997438718097,
                0.9999938558246705,
                0.9999994284994169,
                0.9999921107393004,
                0.9999952149072213,
                0.9999942280820395
            ],
            [
                NaN,
                3.726638395634011e-06,
                NaN,
                5.043472278322555e-07,
                6.47595107001401e-07,
                2.699577774589574e-07,
                5.043475885696228e-07,
                1.5534981249697903e-06,
                1.9947299593078385e-06,
                1.275189972832538e-07
            ],
            [
                0.9999983463098236,
                2.90231094723893e-06,
                0.999994577782976,
                1.637377448057981e-07,
                0.9999994631249325,
                0.9999945777829737,
                0.9999972735290812,
                0.9999949062925748,
                0.9999987901340286,
                0.9999974387180968
            ],
            [
                0.9999599363127746,
                0.9999785550439443,
                1.3007128464346676e-05,
                0.9999974387174854,
                0.9999251537820766,
                0.9997388097259094,
                0.9999687980849824,
                0.9999785550465158,
                0.9999852610127782,
                0.9999251537550522
            ],
            [
                2.5612831267202583e-06,
                7.338210680021253e-07,
                3.927862939126708e-07,
                4.785094494783494e-06,
                6.962257909842961e-06,
                9.422450432014836e-07,
                4.006368264282944e-05,
                1.994730434879465e-06,
                6.475951069985296e-07,
                NaN
            ],
            [
                5.71500719545698e-07,
                6.475950298011458e-07,
                7.338207180898968e-07,
                5.04347468323289e-07,
                3.726639728370556e-06,
                1.994729008145876e-06,
                1.1478772231232203e-05,
                6.475945666063607e-07,
                9.422450432014836e-07,
                NaN
            ],
            [
                2.2603242978871282e-06,
                4.785093924389007e-06,
                2.260323758923431e-06,
                9.422444815814404e-07,
                NaN,
                1.0129987354108855e-05,
                7.338208930460318e-07,
                1.6701423836262173e-05,
                9.422444815814404e-07,
                1.9947292459265734e-06
            ],
            [
                1.7603434231777837e-06,
                2.260324567337161e-06,
                5.422220262636381e-06,
                1.3007130015677909e-05,
                5.715004470313855e-07,
                3.288749065423109e-06,
                1.2098653950656417e-06,
                5.715003107755449e-07,
                2.260323758987159e-06,
                2.5612834320470717e-06
            ],
            [
                7.734415776836702e-08,
                2.6995777745711594e-07,
                2.1024336609843824e-07,
                1.4449805540651476e-07,
                8.764247451307293e-08,
                1.4449805540740185e-07,
                3.466327863961242e-07,
                5.3157830707696514e-08,
                1.1253521571574156e-07,
                1.8553905760062447e-07
            ],
            [
                NaN,
                1.5534971990169383e-06,
                1.7603430034867993e-06,
                1.3709568799919866e-06,
                NaN,
                1.7603425837903113e-06,
                0.999997739676512,
                NaN,
                2.561281600086738e-06,
                0.9999869928746572
            ],
            [
                3.72663883989755e-06,
                3.7266406168827523e-06,
                6.1441746020359e-06,
                8.939693107288474e-06,
                0.0007096703034572937,
                7.889261645427538e-06,
                1.6701423836262173e-05,
                1.994729721518893e-06,
                0.9999417087486955,
                0.9998601778772219
            ],
            [
                3.05902336324494e-07,
                3.2887506336235617e-06,
                9.931195693628605e-08,
                2.260324567337161e-06,
                5.04347468323289e-07,
                3.059022998581767e-07,
                1.4449800373118268e-07,
                2.102434162245973e-07,
                7.338212429582604e-07,
                1.855391681906175e-07
            ],
            [
                6.475949526020042e-07,
                7.338210680021253e-07,
                NaN,
                5.422220909009474e-06,
                4.4508494582405734e-07,
                1.9947301970972664e-06,
                2.90231094723893e-06,
                1.0677032518785256e-06,
                NaN,
                6.144173869603344e-06
            ],
            [
                6.1441767993788005e-06,
                1.209865539295696e-06,
                3.9278605979534166e-07,
                3.2887482813149375e-06,
                3.059022269250683e-07,
                1.209865539295696e-06,
                7.338209805224048e-07,
                1.5534973842030142e-06,
                6.475947982037486e-07,
                5.04347528446051e-07
            ],
            [
                2.902313023130843e-06,
                1.0677027427624903e-06,
                3.726637951387472e-06,
                0.9999921107374231,
                0.9999810748540323,
                1.3709572068522336e-06,
                0.9999724643023973,
                0.9999910602994464,
                1.209865539295696e-06,
                0.9998601779447372
            ],
            [
                4.450849988811838e-07,
                4.222834451382849e-06,
                2.5612825160271407e-06,
                3.288747889284851e-06,
                9.422448185478557e-07,
                9.4224425692559e-07,
                1.2098653950656417e-06,
                1.1478768126057254e-05,
                5.043474081993875e-07,
                1.3709567165579959e-06
            ],
            [
                3.7266397283908927e-06,
                1.5534975693979422e-06,
                2.5612819054133693e-06,
                9.422450432014836e-07,
                1.9947301970972664e-06,
                2.430024073523505e-05,
                0.00012339463384858465,
                9.422445939054222e-07,
                6.962253760024999e-06,
                1.0129994602895546e-05
            ],
            [
                4.006369219393695e-05,
                4.222834954778007e-06,
                7.88926446679691e-06,
                1.1478773599425825e-05,
                1.3007130015488633e-05,
                6.962255419804982e-06,
                6.144177531767002e-06,
                1.3709575337078829e-06,
                3.7266406168827523e-06,
                1.209865827752005e-06
            ],
            [
                2.3823688159291947e-07,
                4.2228324377740105e-06,
                1.7603434231705793e-06,
                1.2098662604247682e-06,
                1.2098658277451275e-06,
                1.760344052714248e-06,
                5.043476486915964e-07,
                3.466326624322211e-07,
                3.0590215399183813e-07,
                6.475951069985296e-07
            ],
            [
                1.0677027427624903e-06,
                3.7266410611296085e-06,
                0.9999516743565472,
                9.422447062294175e-07,
                3.7266406168827523e-06,
                2.9023112932296107e-06,
                1.6701415872385704e-05,
                4.450850519403407e-07,
                2.9023119851899796e-06,
                NaN
            ],
            [
                NaN,
                5.04347287955046e-07,
                NaN,
                6.475947210046347e-07,
                2.3823696679327928e-07,
                7.73442776303243e-08,
                1.4449802095666915e-07,
                5.715005151606823e-07,
                4.4508515805735777e-07,
                6.82560779249779e-08
            ],
            [
                0.9997388096939909,
                0.9999978766205269,
                0.9999990577554067,
                0.9999785550567393,
                0.9999987121049388,
                0.9999985406243017,
                0.9999972735294089,
                0.9999981261239472,
                0.9999957771650498,
                0.9999977396748952
            ],
            [
                1.9947292459347367e-06,
                3.9278629391427843e-07,
                1.7603440527286572e-06,
                2.144495608378187e-05,
                1.0129993395217047e-05,
                2.561281600086738e-06,
                0.9999417087555027,
                0.9999687980886776,
                1.760342793638743e-06,
                6.825604537781398e-08
            ],
            [
                0.9999646437578606,
                0.9998766054108732,
                0.9999988634357476,
                8.315284241650899e-07,
                0.9999898700090297,
                0.9999972735307052,
                0.9999741325752961,
                0.9999987901346055,
                0.9999938558268656,
                0.9999987121044777
            ],
            [
                0.9999892166877965,
                0.9999832985722059,
                0.9999877809225437,
                0.9999962733589417,
                0.9999978766223,
                0.9999921107374274,
                0.9999869928746751,
                0.9999980052698048,
                0.9999949062950023,
                0.9999892166839456
            ],
            [
                5.715002426486762e-07,
                6.825606978822427e-08,
                4.4508510499849186e-07,
                1.6373772528704005e-07,
                1.4449803818215767e-07,
                2.102434162245973e-07,
                1.855390576008354e-07,
                4.450848927658745e-07,
                1.760343213335281e-06,
                2.1024339116168358e-07
            ],
            [
                0.9999921107393035,
                0.9999706884687605,
                0.9999969105062947,
                0.9999991148428595,
                0.9999972735303838,
                0.9999970976887099,
                0.9999925887219138,
                2.699576809143613e-07,
                0.9999957771650547,
                0.9999934595627898
            ],
            [
                0.9999898700090374,
                0.9999942280806655,
                0.9999955048194985,
                0.999996033014563,
                0.9999962733611633,
                0.9999955048194992,
                0.999996273361611,
                0.9999861539971175,
                0.9999885212264122,
                0.9999921107402484
            ],
            [
                5.71500719545698e-07,
                2.1024336609843824e-07,
                1.6373770576776313e-07,
                1.0677029973219343e-06,
                1.2098652508424818e-06,
                3.927862470899887e-07,
                3.4663274507713016e-07,
                3.2887506336235617e-06,
                8.315284241650899e-07,
                1.6373766672973748e-07
            ],
            [
                0.9999910603047755,
                0.9999982396561581,
                0.9999892166826646,
                0.9999989969857925,
                0.9999892166852283,
                0.9999977396759737,
                0.9999952149066509,
                0.9999952149043706,
                0.9999983463110064,
                0.9999986290426305
            ],
            [
                4.6911677163762064e-08,
                1.2098661162056318e-06,
                1.5534984953510149e-06,
                7.338209805224048e-07,
                1.2751901248454963e-07,
                7.338208055680009e-07,
                NaN,
                4.6911677163762064e-08,
                8.7642526752214e-08,
                3.4663278639892215e-07
            ],
            [
                0.9999822214524148,
                0.9999995549148951,
                0.9999989322972581,
                0.9999904837460467,
                0.9999988634357482,
                0.9999869928684538,
                0.9999970976883633,
                0.9999945777810346,
                0.9999972735287567,
                0.9999970976866334
            ],
            [
                4.785095065232451e-06,
                1.1253508156363576e-07,
                4.785094494783494e-06,
                8.315277302841894e-07,
                2.1024331597262577e-07,
                5.04347528446051e-07,
                5.715003107755449e-07,
                2.5612828213934817e-06,
                3.059022998576899e-07,
                1.444979692800516e-07
            ],
            [
                3.4663249714612693e-07,
                1.8553910183674878e-07,
                1.4738978457604563e-05,
                7.338207180898968e-07,
                6.475947210046347e-07,
                NaN,
                6.47595107001401e-07,
                5.715005832895975e-07,
                9.422444815814404e-07,
                5.71500719545698e-07
            ],
            [
                1.5534984953552536e-06,
                4.4508494582405734e-07,
                1.7603434231833873e-06,
                1.0677028700422047e-06,
                8.315284241650899e-07,
                5.715003107767143e-07,
                7.338208055664991e-07,
                5.043473480777865e-07,
                NaN,
                1.0677026154806063e-06
            ],
            [
                0.9999925887192527,
                6.962256249885085e-06,
                0.999954602126141,
                0.9999852610180496,
                0.9999952149037996,
                0.9999967112521136,
                0.0004878571215050234,
                0.9999962733589406,
                1.0677028700422047e-06,
                0.9999852610162889
            ],
            [
                0.9999038975981455,
                0.9999975938976611,
                0.9999885212332488,
                0.9999995262095551,
                0.9999785550491128,
                0.9999955048168163,
                0.9999991148432809,
                0.9999646437620555,
                9.422442569315887e-07,
                NaN
            ],
            [
                1.3709576971463352e-06,
                1.3709572068422585e-06,
                1.7603438428740716e-06,
                1.7603430034867993e-06,
                2.2603242978943238e-06,
                9.422447062294175e-07,
                NaN,
                5.715005832886879e-07,
                4.450852111155216e-07,
                2.5612819054133693e-06
            ],
            [
                8.315281267861397e-07,
                6.475947210031623e-07,
                3.0590226339061185e-07,
                3.927862002641863e-07,
                1.855391239544352e-07,
                3.2887506335906595e-06,
                1.0677031245990084e-06,
                6.144176799099397e-06,
                3.726641061085547e-06,
                7.338211554783522e-07
            ],
            [
                2.902311639183378e-06,
                1.30071315662049e-05,
                5.422219616265831e-06,
                1.1478770862735993e-05,
                2.561282210740037e-06,
                5.71500378896509e-07,
                1.5534979397790343e-06,
                1.670142383595838e-05,
                4.785095635592258e-06,
                1.1478766757561534e-05
            ],
            [
                1.9947292459347367e-06,
                0.9999957771645472,
                0.999997273530707,
                0.9999942280772222,
                0.999994577782974,
                7.88926446679691e-06,
                0.999994906294394,
                0.9999942280813499,
                1.3709568799823232e-06,
                1.7603440527286572e-06
            ],
            [
                NaN,
                2.382368531929327e-07,
                2.699578096403948e-07,
                2.5612834320563895e-06,
                4.450852111148132e-07,
                1.9947301970972664e-06,
                1.855391239547094e-07,
                1.1253509497883659e-07,
                1.7603425837903113e-06,
                9.931202796993203e-08
            ],
            [
                0.9999832985821797,
                0.9999977396759732,
                0.9999934595627796,
                0.9999810748518038,
                0.9999869928668987,
                0.9999925887201382,
                0.9999980052707552,
                1.3709576971425944e-06,
                0.9999970976873253,
                0.9999992661790198
            ],
            [
                4.450852111148132e-07,
                1.4449795205429202e-07,
                1.27519088491875e-07,
                4.691164920214251e-08,
                4.4508515805735777e-07,
                8.764245361752286e-08,
                1.8553910183607374e-07,
                1.444980209564556e-07,
                8.7642516304188e-08,
                1.2751904288739315e-07
            ],
            [
                0.9999942280786006,
                0.999994577779743,
                0.9999957771645459,
                0.999987780922541,
                1.7603434231833873e-06,
                0.9999916019309775,
                0.9999934595596622,
                0.9999877809210922,
                0.999997739675974,
                0.9999687980998521
            ],
            [
                7.338208930460318e-07,
                3.9278610661902853e-07,
                1.067703124601679e-06,
                1.1253521571574156e-07,
                4.785093353940187e-06,
                1.553497754577351e-06,
                3.059022998581767e-07,
                1.27519088491875e-07,
                2.5612812947508257e-06,
                1.0677027427525368e-06
            ],
            [
                NaN,
                2.3823690999323465e-07,
                1.275190428875671e-07,
                5.043472879525233e-07,
                9.931193325852072e-08,
                3.466325797888292e-07,
                2.6995790618469934e-07,
                NaN,
                6.023573475041126e-08,
                7.734425919002834e-08
            ],
            [
                0.9999724643089779,
                2.382369667929001e-07,
                1.2098658277451275e-06,
                4.450852641737424e-07,
                7.338208055664991e-07,
                2.5612819054133693e-06,
                9.931190958076104e-08,
                1.2751904288710323e-07,
                5.043472879540142e-07,
                5.715007195447234e-07
            ],
            [
                NaN,
                5.715005151606823e-07,
                2.5612812947508257e-06,
                3.4663266243308805e-07,
                7.338207180864763e-07,
                NaN,
                4.785095065204162e-06,
                7.338213304363436e-07,
                9.422443692555439e-07,
                1.1478770862735993e-05
            ],
            [
                0.9999995549149482,
                0.9999962733589459,
                0.9999885212305373,
                0.9999930377412727,
                0.9999916019289794,
                0.999992588721032,
                0.9999869928700376,
                0.9999832985762027,
                0.9999942280785982,
                0.9999930377412731
            ],
            [
                1.0129990979842057e-05,
                5.043473480777865e-07,
                8.315281267834927e-07,
                1.7603427936263351e-06,
                5.422221555380179e-06,
                5.715005832886879e-07,
                5.715002426475718e-07,
                1.147877359957198e-05,
                7.338209805224048e-07,
                2.5612812947508257e-06
            ],
            [
                5.422218969895357e-06,
                1.7603434231833873e-06,
                4.2228319344021954e-06,
                NaN,
                1.8553910183674878e-07,
                7.338207180898968e-07,
                3.535625071730638e-05,
                1.7603438428800754e-06,
                4.450851580555361e-07,
                1.9947292459347367e-06
            ],
            [
                1.1253521571574156e-07,
                1.6373764720990908e-07,
                1.2751910369275402e-07,
                1.8553905759969634e-07,
                1.4449795205429202e-07,
                3.9278615344178325e-07,
                9.931186222482958e-08,
                1.6373768624837685e-07,
                1.855391239547094e-07,
                4.450850519403407e-07
            ],
            [
                1.3709576971425944e-06,
                7.484626297142789e-05,
                1.0677029973192638e-06,
                3.726637951387472e-06,
                1.5534979397740895e-06,
                1.209865539295696e-06,
                2.5612812947508257e-06,
                8.315280276607289e-07,
                2.260324567337161e-06,
                3.726637951387472e-06
            ],
            [
                6.475949526020042e-07,
                2.3823693839290317e-07,
                8.315282259138311e-07,
                NaN,
                1.5534977545886537e-06,
                5.04347348075149e-07,
                5.715003107755449e-07,
                8.315284241650899e-07,
                1.2098659719757836e-06,
                4.2228339479858295e-06
            ],
            [
                1.9947299593014888e-06,
                1.7603425837903113e-06,
                1.5534971990169383e-06,
                1.9947301970972664e-06,
                4.4508494582405734e-07,
                1.209866260432471e-06,
                1.8925155009767892e-05,
                5.715003789046955e-07,
                4.2228339479858295e-06,
                1.370957860576702e-06
            ],
            [
                2.6995784182140636e-07,
                2.260324028427877e-06,
                0.999975699759319,
                2.1444948415296896e-05,
                1.3007134667070165e-05,
                2.1444945858953813e-05,
                5.1442207537151994e-05,
                4.222834451403972e-06,
                4.785096776499213e-06,
                1.0129994602895546e-05
            ],
            [
                6.1441767993788005e-06,
                6.475946438055299e-07,
                5.043476486924565e-07,
                1.6373774480605869e-07,
                7.889264466868659e-06,
                1.1253516205489029e-07,
                2.382370235933104e-07,
                2.102434162245973e-07,
                1.7603438428740716e-06,
                1.7603440527334603e-06
            ],
            [
                3.1201907657271834e-05,
                5.04347468318358e-07,
                7.338212429537553e-07,
                7.338209805200689e-07,
                5.043472278280699e-07,
                1.4738978458140753e-05,
                1.994729245878497e-06,
                3.059022998576899e-07,
                5.4222183234485234e-06,
                1.5534981249574276e-06
            ],
            [
                2.260324567337161e-06,
                2.260325106237323e-06,
                1.8925155009767892e-05,
                1.7603440527286572e-06,
                2.5612819054028872e-06,
                NaN,
                5.043472879525233e-07,
                5.715005832886879e-07,
                3.466327863961242e-07,
                5.043475885674441e-07
            ],
            [
                2.2603251062450327e-06,
                1.9947301970972664e-06,
                2.430025232128576e-05,
                1.0129993395336818e-05,
                NaN,
                5.829127250399344e-05,
                1.6701425827133152e-05,
                3.7266397283908927e-06,
                3.927863875616689e-07,
                0.9999452402182624
            ],
            [
                0.9999938558261412,
                0.9999877809182037,
                0.9999934595620008,
                0.9999952149055155,
                0.9999945777790995,
                1.3007133116542802e-05,
                0.9999798543046551,
                2.5612819054133693e-06,
                5.043475885696228e-07,
                0.9999934595612229
            ],
            [
                NaN,
                3.0590215399281185e-07,
                NaN,
                3.927863407379485e-07,
                1.637377448057981e-07,
                1.6373762769138607e-07,
                1.1253525596174225e-07,
                6.475946438055299e-07,
                1.637376862489725e-07,
                1.275190580890061e-07
            ],
            [
                1.1253508156363576e-07,
                0.9999822214418286,
                0.9999984465018761,
                0.9999994631247403,
                0.9999877809181846,
                0.9999942280820397,
                0.9999988634360188,
                2.1024334103581732e-07,
                1.6373764721072816e-07,
                6.144175334367959e-06
            ],
            [
                6.962256249885085e-06,
                NaN,
                4.2228319344021954e-06,
                7.889259764445822e-06,
                1.7603430034867993e-06,
                3.05902263391829e-07,
                1.855391239544352e-07,
                5.715003107767143e-07,
                1.0677028700422047e-06,
                5.043472278322555e-07
            ],
            [
                3.288748673360027e-06,
                7.889265407177056e-06,
                3.1201911375578156e-05,
                3.7266406168624155e-06,
                5.8291272497207844e-05,
                1.2098656835136636e-06,
                2.144495097113319e-05,
                1.0129987357158383e-05,
                4.785094494750855e-06,
                1.5534975693869924e-06
            ],
            [
                2.561282210740037e-06,
                4.785096205973894e-06,
                1.5534981249574276e-06,
                3.7266397283231055e-06,
                1.9947292459347367e-06,
                4.222833444590791e-06,
                1.9947304348595095e-06,
                4.2228319344021954e-06,
                9.42244593835151e-07,
                1.1478772230198667e-05
            ],
            [
                1.8553905760062447e-07,
                8.764242227418718e-08,
                5.043473480777865e-07,
                4.539786865090791e-05,
                7.338212429582604e-07,
                2.902312677137316e-06,
                5.315780536011123e-08,
                8.764244316973974e-08,
                0.9997965731010088,
                5.3157811697009444e-08
            ],
            [
                NaN,
                5.422221555380179e-06,
                3.927862470899887e-07,
                1.994729008145876e-06,
                2.260325106237323e-06,
                2.5612831267202583e-06,
                6.144172404738491e-06,
                3.288748673360027e-06,
                2.260325106237323e-06,
                3.726638395611981e-06
            ],
            [
                1.0677032518814388e-06,
                1.2098656835224664e-06,
                8.315284241665078e-07,
                6.475949525981759e-07,
                1.2098662604291696e-06,
                1.0677032518748838e-06,
                1.3709572068522336e-06,
                6.475945666063607e-07,
                6.962256249885085e-06,
                2.260325106237323e-06
            ],
            [
                0.9999724643122758,
                2.260324567337161e-06,
                0.9999417087138649,
                0.9999869928700044,
                0.9999910603058411,
                3.5356238073889594e-05,
                8.315284241650899e-07,
                0.999988521233266,
                3.288747889284851e-06,
                1.2098653950656417e-06
            ],
            [
                0.9999938558254012,
                0.9999984465026166,
                0.9999969105048175,
                0.9999724642991131,
                0.9999949062925729,
                0.9999916019279761,
                0.9999994631247404,
                0.999997273528431,
                0.9998911030804728,
                0.9999945777816849
            ],
            [
                0.9999996310113719,
                0.999986992865347,
                0.9999994631250603,
                0.9999646437367731,
                0.9999981261250639,
                0.9999981261237237,
                0.9999843104428316,
                0.9999861539954699,
                0.9999977396746261,
                0.9999988634365607
            ],
            [
                2.8453326928809566e-08,
                1.2751901248454963e-07,
                1.147877359957198e-05,
                2.9023119851899796e-06,
                2.6995790618350237e-07,
                1.370957860576702e-06,
                1.1253518888531272e-07,
                1.1253506814842375e-07,
                6.144173869558639e-06,
                4.691160446380562e-08
            ],
            [
                3.059022998581767e-07,
                1.5534984953453635e-06,
                1.6373762769138607e-07,
                1.1253512180925583e-07,
                6.47595107001401e-07,
                1.994729483729522e-06,
                1.7603434231833873e-06,
                3.927863875616689e-07,
                1.4449798650551755e-07,
                2.699578096403948e-07
            ],
            [
                2.5612828213934817e-06,
                1.300712536408621e-05,
                7.338211554801876e-07,
                1.0677026154806063e-06,
                8.315283250394546e-07,
                1.2098658277451275e-06,
                9.422442569290178e-07,
                2.6995784182183607e-07,
                0.9999339478322495,
                1.4449802095666915e-07
            ],
            [
                1.7603440527286572e-06,
                NaN,
                5.043476486915964e-07,
                3.05902190458764e-07,
                NaN,
                1.3007123813193233e-05,
                1.067702870039777e-06,
                7.338209805224048e-07,
                9.422442569315887e-07,
                8.939693107190907e-06
            ],
            [
                6.023578501513224e-08,
                1.637376862489725e-07,
                4.691160446380562e-08,
                1.1253524254650944e-07,
                7.338208055664991e-07,
                5.3157887739943563e-08,
                3.05902336324494e-07,
                3.927863407379485e-07,
                2.511001487368099e-08,
                1.275190580890061e-07
            ],
            [
                3.288748281329893e-06,
                NaN,
                8.315280276626197e-07,
                1.3709575337159875e-06,
                1.5534975693979422e-06,
                7.889261645427538e-06,
                NaN,
                1.5534977545886537e-06,
                5.71500719545698e-07,
                3.288748281329893e-06
            ],
            [
                6.605213682591808e-05,
                3.288749457469787e-06,
                0.00010889688337946374,
                2.144495097113319e-05,
                1.99472924590571e-06,
                1.7603438428740716e-06,
                6.144176066795103e-06,
                1.6701425827133152e-05,
                1.3007130015677909e-05,
                2.902312677104321e-06
            ],
            [
                2.5612828213934817e-06,
                4.785095065232451e-06,
                4.222832437798974e-06,
                1.3709576971463352e-06,
                1.067703124601679e-06,
                3.7266410611296085e-06,
                8.939700567004841e-06,
                1.8553905760062447e-07,
                4.4508494582405734e-07,
                4.4508515805735777e-07
            ],
            [
                0.9999832985742085,
                0.9999969105066591,
                0.999991601925974,
                0.9999957771660563,
                0.999992588718372,
                0.9999921107355408,
                0.9999930377454223,
                1.994730434879465e-06,
                0.9999949062956093,
                0.9999962733607186
            ],
            [
                1.637376862489725e-07,
                3.466326624336003e-07,
                2.382369951932796e-07,
                2.382368815932174e-07,
                1.855391239544352e-07,
                3.466327037553825e-07,
                1.6373776432509826e-07,
                1.1478764021029928e-05,
                9.931202796993203e-08,
                3.05902190458764e-07
            ],
            [
                NaN,
                8.764244316973974e-08,
                3.05902263389638e-07,
                3.05902336324494e-07,
                2.5612819054133693e-06,
                2.699576809143613e-07,
                1.209865827752005e-06,
                8.76424013786396e-08,
                1.8553903548231313e-07,
                4.450852641737424e-07
            ],
            [
                1.9947297215043796e-06,
                6.962257079889302e-06,
                1.7603438428660665e-06,
                5.043472879540142e-07,
                1.0677032518578904e-06,
                NaN,
                1.855391239547094e-07,
                1.855391681906175e-07,
                3.466327037553825e-07,
                3.05902190458764e-07
            ],
            [
                1.6373770576776313e-07,
                2.6995790618469934e-07,
                3.05902190458764e-07,
                2.5612812947508257e-06,
                2.5612831267202583e-06,
                1.444979692800516e-07,
                NaN,
                4.450852111155216e-07,
                7.338209805240734e-07,
                8.764245361752286e-08
            ],
            [
                0.999999554914736,
                0.9999942280786026,
                0.9999724643122855,
                0.999993037745423,
                0.9999810748472637,
                0.999986992874655,
                0.9999975938982347,
                0.9999960330131434,
                0.9999975938982352,
                0.9999957771655532
            ],
            [
                1.6373774480605869e-07,
                3.7266401726359486e-06,
                2.9023116392097746e-06,
                1.9947299593078385e-06,
                7.889259764517575e-06,
                6.475950298021765e-07,
                5.71500719545698e-07,
                2.561282210740037e-06,
                4.450850519409479e-07,
                2.2603253756956754e-06
            ],
            [
                3.726639728370556e-06,
                2.260325106237323e-06,
                9.422447062270609e-07,
                8.939696304311336e-06,
                1.7603425837791042e-06,
                1.209866260432471e-06,
                2.9023116391978967e-06,
                1.2098659719757836e-06,
                2.90231094723893e-06,
                1.553498124964492e-06
            ],
            [
                1.209866260432471e-06,
                1.637377057680051e-07,
                1.9947304348862686e-06,
                1.2098652508424818e-06,
                NaN,
                1.5534971990126997e-06,
                6.144176799334096e-06,
                3.7266397283908927e-06,
                9.93120161310289e-08,
                1.3709572068522336e-06
            ],
            [
                5.04347468323289e-07,
                8.315280276626197e-07,
                6.47595107001401e-07,
                3.05902336324494e-07,
                1.4449803818215767e-07,
                7.734428685047173e-08,
                1.067702870039777e-06,
                4.450849988811838e-07,
                8.7642558095602e-08,
                8.764245361752286e-08
            ],
            [
                6.023579219579052e-08,
                9.931199245322124e-08,
                1.1253509497883659e-07,
                4.6911677163762064e-08,
                1.2751902768612997e-07,
                7.734426841017797e-08,
                7.734415776836702e-08,
                1.4449807263325588e-07,
                1.1253525596174225e-07,
                0.9999910603037031
            ],
            [
                1.6373774480535133e-07,
                1.553498495338299e-06,
                3.0590237279085045e-07,
                1.6373770576776313e-07,
                1.5534984953510149e-06,
                2.902312677007974e-06,
                5.715005151606823e-07,
                9.422450431989127e-07,
                3.0590237279085045e-07,
                2.6995774527718623e-07
            ],
            [
                3.2887506336235617e-06,
                0.999989870009041,
                3.05902336324494e-07,
                0.9999885212332607,
                0.9999974387187065,
                0.999993855827603,
                0.999996273359386,
                0.9999934595651213,
                0.9999962733593856,
                0.9999952149038015
            ],
            [
                0.999990483744912,
                0.9999921107355442,
                0.9999822214439463,
                0.9999981261250643,
                0.9999756997593483,
                0.9999957771680682,
                2.382368531929327e-07,
                0.9999417087277357,
                0.9999995549148951,
                0.9999967112493682
            ],
            [
                NaN,
                3.6534807736504303e-08,
                NaN,
                6.475946438055299e-07,
                6.475946438055299e-07,
                1.2098659719757836e-06,
                2.102434412875379e-07,
                1.8553910183674878e-07,
                5.3157887739943563e-08,
                6.023569166654288e-08
            ],
            [
                8.31528325040778e-07,
                3.9278629391427843e-07,
                0.9996646499033405,
                1.0677026154827912e-06,
                5.04347468323289e-07,
                3.72663883989755e-06,
                1.5534984953552536e-06,
                7.338208930460318e-07,
                7.734415776836702e-08,
                NaN
            ],
            [
                5.715004470295662e-07,
                2.3823690999160957e-07,
                5.043476486915964e-07,
                5.043472879540142e-07,
                5.043472278280699e-07,
                2.102433159721477e-07,
                4.450852111148132e-07,
                3.1201926253802263e-05,
                2.3823688159291947e-07,
                2.260325106237323e-06
            ],
            [
                2.902312331170226e-06,
                1.4449798650569826e-07,
                6.962259569750576e-06,
                8.764254764780641e-08,
                NaN,
                3.9278634073732336e-07,
                0.9992903296976985,
                3.9278629391427843e-07,
                1.5534975693979422e-06,
                1.5534984953552536e-06
            ],
            [
                9.422445939054222e-07,
                3.4663278639892215e-07,
                1.0677024882009222e-06,
                5.043473480777865e-07,
                9.422442569315887e-07,
                7.338213304363436e-07,
                5.422220262555012e-06,
                3.059022998576899e-07,
                1.855391681906175e-07,
                2.561282516066741e-06
            ],
            [
                1.275190428875671e-07,
                1.6373764721072816e-07,
                1.8553905760062447e-07,
                1.1253525596174225e-07,
                6.475945666033422e-07,
                7.338213304363436e-07,
                1.8553919030858602e-07,
                1.1253526937697666e-07,
                1.8553905760062447e-07,
                3.4663253846718004e-07
            ],
            [
                NaN,
                1.1478772231232203e-05,
                9.422445939054222e-07,
                6.475945666063607e-07,
                1.3709573702822306e-06,
                4.4508515805735777e-07,
                1.9947299593078385e-06,
                5.715003107767143e-07,
                3.4663249714612693e-07,
                2.699577774589574e-07
            ]
        ]
    }
]